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1904.04935

A multiscale model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities

We develop a novel multiscale model of interface motion for the Rayleigh-Taylor instability (RTI) and Richtmyer-Meshkov instability (RMI) for two-dimensional, inviscid, compressible flows with vorticity, which yields a fast-running numerical algorithm that produces both qualitatively and quantitatively similar results to a resolved gas dynamics code, while running approximately two orders of magnitude (in time) faster. Our multiscale model is founded upon a new compressible-incompressible decomposition of the velocity field $u=v+w$. The incompressible component $w$ of the velocity is also irrotational and is solved using a new asymptotic model of the Birkhoff-Rott singular integral formulation of the incompressible Euler equations, which reduces the problem to one spatial dimension. This asymptotic model, called the higher-order $z$-model, is derived using small nonlocality as the asymptotic parameter, allows for interface turn-over and roll-up, and yields a significant simplification for the equation describing the evolution of the amplitude of vorticity. This incompressible component $w$ of the velocity controls the small scale structures of the interface and can be solved efficiently on fine grids. Meanwhile, the compressible component of the velocity $v$ remains continuous near contact discontinuities and can be computed on relatively coarse grids, while receiving subgrid scale information from $w$. We first validate the incompressible higher-order $z$-model by comparison with classical RTI experiments as well as full point vortex simulations. We then consider both the RTI and the RMI problems for our multiscale model of compressible flow with vorticity, and show excellent agreement with our high-resolution gas dynamics solutions.

1905.09568

Fire Now, Fire Later: Alarm-Based Systems for Prescriptive Process Monitoring

Predictive process monitoring is a family of techniques to analyze events produced during the execution of a business process in order to predict the future state or the final outcome of running process instances. Existing techniques in this field are able to predict, at each step of a process instance, the likelihood that it will lead to an undesired outcome.These techniques, however, focus on generating predictions and do not prescribe when and how process workers should intervene to decrease the cost of undesired outcomes. This paper proposes a framework for prescriptive process monitoring, which extends predictive monitoring with the ability to generate alarms that trigger interventions to prevent an undesired outcome or mitigate its effect. The framework incorporates a parameterized cost model to assess the cost-benefit trade-off of generating alarms. We show how to optimize the generation of alarms given an event log of past process executions and a set of cost model parameters. The proposed approaches are empirically evaluated using a range of real-life event logs. The experimental results show that the net cost of undesired outcomes can be minimized by changing the threshold for generating alarms, as the process instance progresses. Moreover, introducing delays for triggering alarms, instead of triggering them as soon as the probability of an undesired outcome exceeds a threshold, leads to lower net costs.

2004.12793

EventWarden: A Decentralized Event-driven Proxy Service for Outsourcing Arbitrary Transactions in Ethereum-like Blockchains

Transactions represent a fundamental component in blockchains as they are the primary means for users to change the blockchain state. Current blockchain systems such as Bitcoin and Ethereum require users to constantly observe the state changes of interest or the events taking place in a blockchain and requires the user to explicitly release the required transactions to respond to the observed events in the blockchain. This paper proposes EventWarden, a decentralized event-driven proxy service for users to outsource transactions in Ethereum-like blockchains. EventWarden employs a novel combination of smart contracts and blockchain logs. EventWarden allows a user to create a proxy smart contract that specifies an interested event and also reserves an arbitrary transaction to release. Upon observing the occurrence of the prescribed event, anyone in the Blockchain network can call the proxy contract to earn the service fee reserved in the contract by proving to the contract that the event has been recorded into blockchain logs, which then automatically triggers the proxy contract to release the reserved transaction. We show that the reserved transaction can only get released from the proxy contract when the prescribed event has taken place. We also demonstrate that as long as a single member in the Blockchain network is incentivized by the service fee to call the proxy contract after the prescribed event has taken place, the reserved transaction is guaranteed to get released. We implement EventWarden over the Ethereum official test network. The results demonstrate that EventWarden is effective and is ready-to-use in practice.

0709.3491

Family Unification with SO(10)

Unification based on the group SO(10)^3 \times S_3 is studied. Each family has its own SO(10) group, and the S_3 permutes the three families and SO(10) factors. This is the maximal local symmetry for the known fermions. Family unification is achieved in the sense that all known fermions are in a single irreducible multiplet of the symmetry. The symmetry suppresses SUSY flavor changing effects by making all squarks and sleptons degenerate in the symmetry limit. Doublet-triplet splitting can arise simply, and non-trivial structure of the quark and lepton masses emerges from the gauge symmetry, including the "doubly lopsided" form.

1802.08551

On the Chow groups of some hyperkaehler fourfolds with a non-symplectic involution II

This article is about hyperk\"ahler fourfolds $X$ admitting a non-symplectic involution $\iota$. The Bloch-Beilinson conjectures predict the way $\iota$ should act on certain pieces of the Chow groups of $X$. The main result is a verification of this prediction for Fano varieties of lines on certain cubic fourfolds. This has some interesting consequences for the Chow ring of the quotient $X/\iota$.

1411.5985

Tight polyhedral embeddings and relative chromatic number of surfaces with boundary

The relative chromatic number $c\_0(S)$ of a compact surface $S$ with boundary is defined as the supremum of the chromatic numbers of graphs embedded in $S$ with all vertices on $\partial S$. This topological invariant was introduced for the study of the multiplicity of the first Steklov eigenvalue of $S$. In this article, we show that $c\_0(S)$ is also relevant for the study of tight polyhedral embeddings of $S$ byproving two results. The first one is that if there is a tight polyhedral embedding of $S$ in $\R^n$ which is not contained in a hyperplane, then $n\leq c\_0(S)-1$. The second result is that this inequality is sharp for surfaces of small genus.

1407.6631

Non-Unitary Neutrino Propagation From Neutrino Decay

Neutrino propagation in space-time is not constrained to be unitary if very light states - lighter than the active neutrinos - exist into which neutrinos may decay. If this is the case, neutrino flavor-change is governed by a handful of extra mixing and "oscillation" parameters, including new sources of CP-invariance violation. We compute the transition probabilities in the two- and three-flavor scenarios and discuss the different phenomenological consequences of the new physics. These are qualitatively different from other sources of unitarity violation discussed in the literature.

1410.2546

Static quark-antiquark potential in the quark-gluon plasma from lattice QCD

We present a state-of-the-art determination of the complex valued static quark-antiquark potential at phenomenologically relevant temperatures around the deconfinement phase transition. Its values are obtained from non-perturbative lattice QCD simulations using spectral functions extracted via a novel Bayesian inference prescription. We find that the real part, both in a gluonic medium as well as in realistic QCD with light $u$, $d$ and $s$ quarks, lies close to the color singlet free energies in Coulomb gauge and shows Debye screening above the (pseudo) critical temperature $T_c$. The imaginary part is estimated in the gluonic medium, where we find that it is of the same order of magnitude as in hard-thermal loop resummed perturbation theory in the deconfined phase.

1607.04832

Phases of kinky holographic nuclear matter

Holographic QCD at finite baryon number density and zero temperature is studied within the five-dimensional Sakai-Sugimoto model. We introduce a new approximation that models a smeared crystal of solitonic baryons by assuming spatial homogeneity to obtain an effective kink theory in the holographic direction. The kink theory correctly reproduces a first order phase transition to lightly bound nuclear matter. As the density is further increased the kink splits into a pair of half-kink constituents, providing a concrete realization of the previously suggested dyonic salt phase, where the bulk soliton splits into constituents at high density. The kink model also captures the phenomenon of baryonic popcorn, in which a first order phase transition generates an additional soliton layer in the holographic direction. We find that this popcorn transition takes place at a density below the dyonic salt phase, making the latter energetically unfavourable. However, the kink model predicts only one pop, rather than the sequence of pops suggested by previous approximations. In the kink model the two layers produced by the single pop form the surface of a soliton bag that increases in size as the baryon chemical potential is increased. The interior of the bag is filled with abelian electric potential and the instanton charge density is localized on the surface of the bag. The soliton bag may provide a holographic description of a quarkyonic phase.

2204.09799

Uniform regularity in the low Mach number and inviscid limits for the full Navier-Stokes system in domains with boundaries

In the present work, motivated by the studies on the low Mach number limit problem, we establish uniform regularity estimates with respect to the Mach number for the non-isentropic compressible Navier-Stokes system in smooth domains with Navier-slip boundary conditions, in the general case of ill-prepared initial data. The thermal conduction is taken into account and the large variation of temperature is allowed. Moreover, the obtained regularity estimates are also uniform in the Reynolds number $\text{Re}\in[1,+\infty),$ P\'eclet number $\text{Pe}\in [1,+\infty),$ provided $$\big|\frac{1}{\text{Re}}-\frac{\iota_0}{\text{Pe}}\big|\lesssim \frac{1}{\text{Pe}^{\frac{1}{2}}}\frac{1}{\text{Re}},$$ where $\iota_0$ is a fixed constant independent of the Mach number, Reynolds number, and P\'eclet number. The large temperature variation as well as the interactions of two kinds of boundary layers are the main obstacles to the proof.

2302.03436

What can one learn about Fe-Cr alloys using M\"ossbauer spectroscopy?

Applications of the M\"ossbauer spectroscopy (MS) in the investigation of Fe-Cr alloys are reviewed. A high sensitivity of the hyperfine magnetic field to the presence of Cr atoms in the vicinity of the probe Fe atoms permits quantitative investigation of various aspects related both to the crystallographic as well as to the magnetic phase diagram of this alloy system. Concerning the former, presented is the relevance of MS for determining borders of the miscibility gap and kinetics of the phase decomposition, distinguishing between nucleation and growth and spinodal decomposition, identifying the sigma-phase and studying kinetics of its precipitation. Regarding the magnetic phase diagram, MS is useful for determining the Curie, the N\'eel and the spin-freezing temperature, hence studying paramagnetic-ferromagnetic, paramagnetic-antiferromagnetic and paramagnetic-spin-glass transitions. An effect of different heat treatments, strain and irradiation with various particles on a distribution of Cr atoms in the Fe matrix is demonstrated, too. For bcc-FeCr alloys relevance of MS for determining changes in spin and charge densities at Fe-sites induced by neighboring Cr atoms is illustrated, as well as its usefulness in studying changes caused by a high-temperature sulphidation and oxidation. Concerning properties of sigma-FeCr alloys the application of MS for determining the Curie and Debye temperature is reviewed. Application of MS to study an effect of magnetism on the lattice dynamics of Fe atoms in sigma-FeCr is also exemplified. Last but not least, determining a magnetic texture and mechanical alloying is addressed.

0705.1383

The effect of randomness on the quantum spin system Tl$_{1-x}$K$_x$CuCl$_3$ with ${\boldmath $x$}$ = 0.44 studied by the Zero-field Muon-Spin-Relaxation (ZF-$\mu$SR) method

Zero-field muon-spin-relaxation (ZF-{\boldmath $\mu$}SR) measurements were carried out down to 80 mK on the randomness bond system Tl$_{1-x}$K$_x$CuCl$_3$ with $x$ = 0.44. Time spectra are well fitted by the stretched exponential function $\exp (-\lambda t)^{\beta}$. The muon spin relaxation rate $\lambda$ increases rapidly with decreasing temperature, and $\beta$ tends to 0.5 at 80 mK. The divergent increase of $\lambda$ suggests the critical slowing down of the frequency of the Cu-3{\it d} spin fluctuations toward a spin frozen state below 80 mK, and the root-exponential-like behavior of the time spectrum indicates that the origin of the relaxation is possibly the spatially-fixed fluctuating dilute moments.

math/0009104

The top Chern class of the Hodge bundle on the moduli space of abelian varieties

We give upper and lower bounds for the order of the top Chern class of the Hodge bundle on the moduli space of principally polarized abelian varieties. We also give a generalization to higher genera of the famous formula $12 \lambda_1=\delta$ for genus 1.

1710.06464

New Variable Compliance Method for Estimating In-Situ Stress and Leak-Off from DFIT Data

It is shown that using Carter leak-off is an oversimplification that leads to significant errors in the interpretation of DFIT data. Most importantly, this article reveals that previous methods of estimating minimum in-situ stress often lead to significant over or underestimates. Based on our modeling and simulation results, we propose a much more accurate and reliable method to estimate the minimum in-situ stress and fracture pressure dependent leak-off rate.

1410.8174

On the dynamics of lattice systems with unbounded on-site terms in the Hamiltonian

We supply the mathematical arguments required to complete the proofs of two previously published results: Lieb-Robinson bounds for the dynamics of quantum lattice systems with unbounded on-site terms in the Hamiltonian and the existence of the thermodynamic limit of the dynamics of such systems.

2212.11253

Inference for Non-Stationary Heavy Tailed Time Series

We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with heavy-tails. This enable us to introduce a local approximation-based estimator which estimates consistently time-varying parameters of the model at hand. To develop a robust method, we also suggest a self-weighing scheme which is shown to recover the asymptotic normality of the estimator regardless of whether the finite variance of the underlying process exists. Empirical evidence favoring this approach is provided.

2004.01578

Hot-Carrier Separation in Heterostructure Nanowires observed by Electron-Beam Induced Current

The separation of hot carriers in semiconductors is of interest for applications such as thermovoltaic photodetection and third-generation photovoltaics. Semiconductor nanowires offer several potential advantages for effective hot-carrier separation such as: a high degree of control and flexibility in heterostructure-based band engineering, increased hot-carrier temperatures compared to bulk, and a geometry well suited for local control of light absorption. Indeed, InAs nanowires with a short InP energy barrier have been observed to produce electric power under global illumination, with an open-circuit voltage exceeding the Shockley-Queisser limit. To understand this behaviour in more detail, it is necessary to maintain control over the precise location of electron-hole pair-generation in the nanowire. In this work we perform electron-beam induced current measurements with high spatial resolution, and demonstrate the role of the InP barrier in extracting energetic electrons. We interprete the results in terms of hot-carrier separation, and extract estimates of the hot carrier mean free path.

2211.11272

Strongly Interacting Dark Matter from $Sp(4)$ Gauge Theory

The stable hadronic bound states in a hidden new non-Abelian gauge sector provide interesting candidates for strongly-interacting Dark Matter (DM). A particular example are theories in which DM is made up of dark pions which set the DM relic abundance through self-annihilation. One of the simplest realizations is $Sp(4)_c$ gauge theory with two Dirac fermions. We discuss its mesonic multiplets for degenerate and non-degenerate fermions, construct a low-energy effective theory and present lattice results for the pseudoscalar mesons and vector mesons.

gr-qc/9608023

Reissner-Nordstr\"om Type Black Holes in Dilaton-Axion Gravity

A $2p + 5$ parametric family of black holes is constructed in dilaton--axion gravity with $p$ vector fields using a holomorphic representation of U--duality in three dimensions. The metric of the non--extremal black holes has a Reissner--Nordstr\"om type structure and generically possesses an internal horizon. However in the extremal limit the generic solution exhibits a dilatonic type null singularity. Only in the case of the orthogonal electric and magnetic charges (if $p>1$) the extremal solution may have a non--singular event horizon.

1503.05132

Sur la capitulation des 2-classes d'id\'eaux du corps Q(\sqrt{2p_1p_2}, i)

Let $p_1$ and $p_2$ be two primes such that $p_1\equiv p_2\equiv1 \pmod4$ and at least two of the three elements $\{(\frac{2}{p_1}), (\frac{2}{p_2}), (\frac{p_1}{p_2})\}$ are equal to -1. Put $i=\sqrt{-1}$, $d=2p_1p_2$ and $k =Q(\sqrt{d}, i)$. Let $k_2^{(1)}$ be the Hilbert 2-class field of $k$ and $k^{(*)}=Q(\sqrt{p_1},\sqrt{p_2},\sqrt 2, i)$ be its genus field. Let $C_{k,2}$ denote the 2-part of the class group of $k$. The unramified abelian extensions of $k$ are $K_1=k(\sqrt{p_1})$, $K_2=k(\sqrt{p_2})$, $K_3=k(\sqrt{2})$ and $k^{(*)}$. Our goal is to study the capitulation problem of the 2-classes of $k$ in these four extensions.

1510.05287

$\epsilon$-Expansion in the Gross-Neveu CFT

We use the recently developed CFT techniques of Rychkov and Tan to compute anomalous dimensions in the $O(N)$ Gross-Neveu model in $d=2+\epsilon$ dimensions. To do this, we extend the "cowpie contraction" algorithm of arXiv:1506.06616 to theories with fermions. Our results match perfectly with Feynman diagram computations.

2111.13725

Giant Non-resonant Infrared Second Order Nonlinearity in $\gamma$-NaAsSe$_2$

Infrared laser systems are vital for applications in spectroscopy, communications, and biomedical devices, where infrared nonlinear optical (NLO) crystals are required for broadband frequency down-conversion. Such crystals need to have high non-resonant NLO coefficients, a large bandgap, low absorption coefficient, phase-matchability among other competing demands, e.g., a larger bandgap leads to smaller NLO coefficients. Here, we report the successful growth of single crystals of $\gamma$-NaAsSe$_2$ that exhibit a giant second harmonic generation (SHG) susceptibility of d$_{11}$=590 pm V$^{-1}$ at 2$\mu$m wavelength; this is ~ eighteen times larger than that of commercial AgGaSe$_2$ while retaining a similar bandgap of ~1.87eV, making it an outstanding candidate for quasi-phase-matched devices utilizing d$_{11}$. In addition, $\gamma$-NaAsSe$_2$ is both Type I and Type II phase-matchable, and has a transparency range up to 16$\mu$m wavelength. Thus $\gamma$-NaAsSe2 is a promising bulk NLO crystal for infrared laser applications.

2109.03564

NSP-BERT: A Prompt-based Few-Shot Learner Through an Original Pre-training Task--Next Sentence Prediction

Using prompts to utilize language models to perform various downstream tasks, also known as prompt-based learning or prompt-learning, has lately gained significant success in comparison to the pre-train and fine-tune paradigm. Nonetheless, virtually all prompt-based methods are token-level, meaning they all utilize GPT's left-to-right language model or BERT's masked language model to perform cloze-style tasks. In this paper, we attempt to accomplish several NLP tasks in the zero-shot scenario using a BERT original pre-training task abandoned by RoBERTa and other models--Next Sentence Prediction (NSP). Unlike token-level techniques, our sentence-level prompt-based method NSP-BERT does not need to fix the length of the prompt or the position to be predicted, allowing it to handle tasks such as entity linking with ease. Based on the characteristics of NSP-BERT, we offer several quick building templates for various downstream tasks. We suggest a two-stage prompt method for word sense disambiguation tasks in particular. Our strategies for mapping the labels significantly enhance the model's performance on sentence pair tasks. On the FewCLUE benchmark, our NSP-BERT outperforms other zero-shot methods on most of these tasks and comes close to the few-shot methods.

1610.10041

Competence building framework requirements for information technology for educational management

Progressive efforts have been evolving continuously for the betterment of the services of the Information Technology for Educational Management(ITEM). These services require data intensive and communication intensive applications. Due to the massive growth of information, situation becomes difficult to manage these services. Here the role of the Information and Communication Technology (ICT) infrastructure particularly data centre with communication components becomes important to facilitate these services. The present paper discusses the related issues such as competent staff, appropriate ICT infrastructure, ICT acceptance level etc. required for ITEM competence building framework considering the earlier approach for core competences for ITEM. It this connection, it is also necessary to consider the procurement of standard and appropriate ICT facilities. This will help in the integration of these facilities for the future expansion. This will also enable to create and foresee the impact of the pairing the management with information, technology, and education components individually and combined. These efforts will establish a strong coupling between the ITEM activities and resource management for effective implementation of the framework.

1511.07286

Polarized neutron channeling as a tool for the investigations of weakly magnetic thin films

We present and apply a new method to measure directly weak magnetization in thin films. The polarization of a neutron beam channeling through a thin film structure is measured after exiting the structure edge as a microbeam. We have applied the method to a tri-layer thin film structure acting as a planar waveguide for polarized neutrons. The middle guiding layer is a rare earth based ferrimagnetic material TbCo5 with a low magnetization of about 20 mT. We demonstrate that the channeling method is more sensitive than the specular neutron reflection method.

math/0305206

Character sheaves on disconnected groups, I

We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.

1703.05037

Interferometric confirmation of "water fountain" candidates

Water fountain stars (WFs) are evolved objects with water masers tracing high-velocity jets (up to several hundreds of km s$^{-1}$). They could represent one of the first manifestations of collimated mass-loss in evolved objects and thus, be a key to understanding the shaping mechanisms of planetary nebulae. Only 13 objects had been confirmed so far as WFs with interferometer observations. We present new observations with the Australia Telescope Compact Array and archival observations with the Very Large Array of four objects that are considered to be WF candidates, mainly based on single-dish observations. We confirm IRAS 17291-2147 and IRAS 18596+0315 (OH 37.1-0.8) as bona fide members of the WF class, with high-velocity water maser emission consistent with tracing bipolar jets. We argue that IRAS 15544-5332 has been wrongly considered as a WF in previous works, since we see no evidence in our data nor in the literature that this object harbours high-velocity water maser emission. In the case of IRAS 19067+0811, we did not detect any water maser emission, so its confirmation as a WF is still pending. With the result of this work, there are 15 objects that can be considered confirmed WFs. We speculate that there is no significant physical difference between WFs and obscured post-AGB stars in general. The absence of high-velocity water maser emission in some obscured post-AGB stars could be attributed to a variability or orientation effect.

math/0202295

Counting Hexagonal Lattice Animals

We describe Maple packages for the automatic generation of generating functions(and series expansions) for counting lattice animals(fixed polyominoes), in the two-dimensional hexagonal lattice, of bounded but arbitrary width. Our Maple packages(complete with source code) are easy-to-use and available from my website.

astro-ph/9804266

Variability Associated with Alpha Accretion Disc Theory for Standard and Advection Dominated Discs

The $\alpha$ turbulent viscosity formalism for accretion discs must be interpreted as a mean field theory. The extent to which the disc scale exceeds that of the turbulence determines the precision of the predicted luminosity $L_\nu$. The assumption of turbulence and use of $\a$ implies: (1) Field line stretching generates a magnetic pressure $\gsim \a^2/6$ of the total pressure generally, and a 1 to 1 relation between $\a$ and the pressure ratio when shearing instabilities dominate the viscosity. (2) Large eddy sizes and speeds in typical advection dominated accretion flows (ADAFs) lead to a lower precision in $L_\nu$ than for thin discs of a given total observation duration and central mass. The allowed variability (relative precision) at a particular frequency increases (decreases) with the size of the contributing region. For X-ray binary type ADAFs, the allowed variability is $\sim 5$% at $R \le 1000$ Schwarzchild radii for averages over $\gsim 1000$sec. But for large galactic nuclei like NGC 4258 and M87, the relative precision error can approach $50-100%$ even at $R \le 100 R_S$ for currently available observation durations. More data are then required to compare with ADAF predictions.

2312.04285

Rational Doping Strategy of Porous Materials for Hydrogen Storage: CNTs study case

Identifying a nanostructure suitable for hydrogen storage presents a promising avenue for the secure and cost-effective utilization of hydrogen as a green energy source. This study introduces a systematic approach for selecting optimal doping on porous materials, emphasizing the intricate interplay between doping with the material's structure and the interaction between doping and hydrogen. Our proposed approach serves as a framework for evaluating and predicting the performance of doped materials. To validate the efficacy of our strategy, we conduct a comprehensive investigation in carbon nanotubes (CNTs). Applying our criteria, we systematically screen several dopants in CNTs. The results highlight Cu-doped CNTs as promising candidates for hydrogen storage applications. Focusing on Cu-doped CNTs, we analyze binding energy, charge transfer, partial density of states (PDOS), and desorption temperature to assess the performance of modified CNTs. Additionally, we explore the feasibility of doped CNTs featuring various sizes of copper clusters and the effect on the release temperature, i.e., complete regeneration. The findings indicate that incorporating 5 to 6% copper impurity onto CNT surfaces renders these nanostructures highly applicable for reversible hydrogen storage near ambient conditions.

2105.04322

RelationTrack: Relation-aware Multiple Object Tracking with Decoupled Representation

Existing online multiple object tracking (MOT) algorithms often consist of two subtasks, detection and re-identification (ReID). In order to enhance the inference speed and reduce the complexity, current methods commonly integrate these double subtasks into a unified framework. Nevertheless, detection and ReID demand diverse features. This issue would result in an optimization contradiction during the training procedure. With the target of alleviating this contradiction, we devise a module named Global Context Disentangling (GCD) that decouples the learned representation into detection-specific and ReID-specific embeddings. As such, this module provides an implicit manner to balance the different requirements of these two subtasks. Moreover, we observe that preceding MOT methods typically leverage local information to associate the detected targets and neglect to consider the global semantic relation. To resolve this restriction, we develop a module, referred to as Guided Transformer Encoder (GTE), by combining the powerful reasoning ability of Transformer encoder and deformable attention. Unlike previous works, GTE avoids analyzing all the pixels and only attends to capture the relation between query nodes and a few self-adaptively selected key samples. Therefore, it is computationally efficient. Extensive experiments have been conducted on the MOT16, MOT17 and MOT20 benchmarks to demonstrate the superiority of the proposed MOT framework, namely RelationTrack. The experimental results indicate that RelationTrack has surpassed preceding methods significantly and established a new state-of-the-art performance, e.g., IDF1 of 70.5% and MOTA of 67.2% on MOT20.

cond-mat/0602604

Controllable Coupling in Phase-Coupled Flux Qubits

We propose a scheme for tunable coupling of phase-coupled flux qubits. The phase-coupling scheme can provide a strong coupling strength of the order of Josephson coupling energy of Josephson junctions in the connecting loop, while the previously studied inductive coupling scheme cannot provide due to small mutual inductance and induced currents. We show that, in order to control the coupling, we need {\it two} dc-SQUID's in the connecting loop and the control fluxes threading the dc-SQUID's must be in {\it opposite} directions. The coupling strength is analytically calculated as a function of the control flux at the co-resonance point.

astro-ph/0009299

HI Imaging of the Large Magellanic Cloud

We present results from the combined Australia Telescope Compact Array (ATCA) aperture synthesis mosaic survey of HI emission in the Large Magellanic Cloud with 64m Parkes single dish telescope observations.

1904.01177

Cosmic strings in compactified gauge theory

A solution of the vortex type is given in a six-dimensional $SU(2)\times U(1)$ pure gauge theory coupled to Einstein gravity in a compactified background geometry. We construct the solution of an effective abelian Higgs model in terms of dimensional reduction. The solution, however, has a peculiarity in its physically relevant quantity, a deficit angle, which is given as a function of the ratio of the gauge couplings of $SU(2)$ and $U(1)$. The size of the extra space (sphere) is shown to vary with the distance from the axis of the "string".

1703.06605

Near-optimal bounds for phase synchronization

The problem of phase synchronization is to estimate the phases (angles) of a complex unit-modulus vector $z$ from their noisy pairwise relative measurements $C = zz^* + \sigma W$, where $W$ is a complex-valued Gaussian random matrix. The maximum likelihood estimator (MLE) is a solution to a unit-modulus constrained quadratic programming problem, which is nonconvex. Existing works have proposed polynomial-time algorithms such as a semidefinite relaxation (SDP) approach or the generalized power method (GPM) to solve it. Numerical experiments suggest both of these methods succeed with high probability for $\sigma$ up to $\tilde{\mathcal{O}}(n^{1/2})$, yet, existing analyses only confirm this observation for $\sigma$ up to $\mathcal{O}(n^{1/4})$. In this paper, we bridge the gap, by proving SDP is tight for $\sigma = \mathcal{O}(\sqrt{n /\log n})$, and GPM converges to the global optimum under the same regime. Moreover, we establish a linear convergence rate for GPM, and derive a tighter $\ell_\infty$ bound for the MLE. A novel technique we develop in this paper is to track (theoretically) $n$ closely related sequences of iterates, in addition to the sequence of iterates GPM actually produces. As a by-product, we obtain an $\ell_\infty$ perturbation bound for leading eigenvectors. Our result also confirms intuitions that use techniques from statistical mechanics.

1901.02119

Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries

We propose a one-dimensional nonintegrable spin model with local interactions that covers Dyson's three symmetry classes (classes A, AI, and AII) depending on the values of parameters. We show that the nearest-neighbor spacing distribution in each of these classes agrees with that of random matrices with the corresponding symmetry. By investigating the ratios between the standard deviations of diagonal and off-diagonal matrix elements, we numerically find that they become universal, depending only on symmetries of the Hamiltonian and an observable, as predicted by random matrix theory. These universal ratios are evaluated from long-time dynamics of small isolated quantum systems.

math/0701558

Free Actions of Extraspecial $p$-Groups on $S^n \times S^n$

Let $p$ be an odd regular prime, and let $G_p$ denote the extraspecial $p$--group of order $p^{3}$ and exponent $p$. We show that $G_p$ acts freely and smoothly on $S^{2p-1} \times S^{2p-1}$. For $p=3$ we explicitly construct a free smooth action of a Lie group $\widetilde{G}_3$ containing $G_3$ on $S^{5} \times S^{5}$. In addition, we show that any finite odd order subgroup of the exceptional Lie group $\Gtwo $ admits a free smooth action on $S^{11}\times S^{11}$.

1511.08101

A note on APN permutations in even dimension

APN permutations in even dimension are vectorial Boolean functions that play a special role in the design of block ciphers. We study their properties, providing some general results and some applications to the low-dimension cases. In particular, we prove that none of their components can be quadratic. For an APN vectorial Boolean function (in even dimension) with all cubic components we prove the existence of a component having a large number of balanced derivatives. Using these restrictions, we obtain the first theoretical proof of the non-existence of APN permutations in dimension 4. Moreover, we derive some contraints on APN permutations in dimension 6.

2011.01597

Thermal transport properties and some hydrodynamic-like behavior in 3D topological semimetal ZrTe5

Hydrodynamic fluidity in condensed matter physics has been experimentally demonstrated only in a limited number of compounds due to the stringent conditions that must be met. Herein, we performed thermal and electrical transport experiments in three-dimensional topological semimetal ZrTe5. By measuring the thermal properties in a wide temperature range, two representative experimental evidences of the hydrodynamics are observed in temperature window between the ballistic and diffusive regimes: a faster evolution of the thermal conductivity than in the ballistic regime and the non-monotonic temperature-dependent effective quasiparticle mean-free-path. In addition, magneto-thermal conductivity results indicate that charged quasiparticles, as well as phonons, may also play an important role in this hydrodynamic-like flow in ZrTe5.

1909.01262

On symplectic fillings of virtually overtwisted torus bundles

We use Menke's JSJ-type decomposition theorem for symplectic fillings to reduce the classification of strong and exact symplectic fillings of virtually overtwisted torus bundles to the same problem for tight lens spaces. For virtually overtwisted structures on elliptic or parabolic torus bundles, this gives a complete classification. For virtually overtwisted structures on hyperbolic torus bundles, we show that every strong or exact filling arises from a filling of a tight lens space via round symplectic 1-handle attachment, and we give a condition under which distinct tight lens space fillings yield the same torus bundle filling.

hep-th/0210106

Calculation of Expectation Values of S$_{z}$ and S$^{2}$ operators for spin-1 and spin-3/2 particles

In the present article we calculate the expectation values of of S$_{z}$ and S$^{2}$ operators for spin-1 and spin-3/2 particles by expanding a general wave function which includes all spin values. The results are same as in the stantard quantum mechanics.

1608.00346

Walksat stalls well below the satisfiability threshold

Partly on the basis of heuristic arguments from physics it has been suggested that the performance of certain types of algorithms on random $k$-SAT formulas is linked to phase transitions that affect the geometry of the set of satisfying assignments. But beyond intuition there has been scant rigorous evidence that "practical" algorithms are affected by these phase transitions. In this paper we prove that \walksat, a popular randomised satisfiability algorithm, fails on random $k$-SAT formulas not very far above clause/variable density where the set of satisfying assignments shatters into tiny, well-separated clusters. Specifically, we prove \walksat\ is ineffective with high probability if $m/n>c2^k\ln^2k/k$, where $m$ is the number of clauses, $n$ is the number of variables and $c>0$ is an absolute constant. By comparison, \walksat\ is known to find satisfying assignments in linear time \whp\ if $m/n<c'2^k/k$ for another constant $c'>0$ [Coja-Oghlan and Frieze, SIAM J.\ Computing 2014].

1412.3000

Upper expectation parametric regression

Every observation may follow a distribution that is randomly selected in a class of distributions. It is called the distribution uncertainty. This is a fact acknowledged in some research fields such as financial risk measure. Thus, the classical expectation is not identifiable in general.In this paper, a distribution uncertainty is defined, and then an upper expectation regression is proposed, which can describe the relationship between extreme events and relevant covariates under the framework of distribution uncertainty. As there are no classical methods available to estimate the parameters in the upper expectation regression, a two-step penalized maximum least squares procedure is proposed to estimate the mean function and the upper expectation of the error. The resulting estimators are consistent and asymptotically normal in a certain sense.Simulation studies and a real data example are conducted to show that the classical least squares estimation does not work and the penalized maximum least squares performs well.

2112.13769

Search for long-lived particles decaying into muon pairs in proton-proton collisions at $\sqrt{s} =$ 13 TeV collected with a dedicated high-rate data stream

A search for long-lived particles decaying into muon pairs is performed using proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the CMS experiment at the LHC in 2017 and 2018, corresponding to an integrated luminosity of 101 fb$^{-1}$. The data sets used in this search were collected with a dedicated dimuon trigger stream with low transverse momentum thresholds, recorded at high rate by retaining a reduced amount of information, in order to explore otherwise inaccessible phase space at low dimuon mass and nonzero displacement from the primary interaction vertex. No significant excess of events beyond the standard model expectation is found. Upper limits on branching fractions at 95% confidence level are set on a wide range of mass and lifetime hypotheses in beyond the standard model frameworks with the Higgs boson decaying into a pair of long-lived dark photons, or with a long-lived scalar resonance arising from a decay of a b hadron. The limits are the most stringent to date for substantial regions of the parameter space. These results can be also used to constrain models of displaced dimuons that are not explicitly considered in this paper.

0707.3334

Dark matter annihilation near a black hole: plateau vs. weak cusp

Dark matter annihilation in so-called ``spikes'' near black holes is believed to be an important method of indirect dark matter detection. In the case of circular particle orbits, the density profile of dark matter has a plateau at small radii, the maximal density being limited by the annihilation cross-section. However, in the general case of arbitrary velocity anisotropy the situation is different. Particulary, for isotropic velocity distribution the density profile cannot be shallower than r^{-1/2} in the very centre. Indeed, a detailed study reveals that in many cases the term ``annihilation plateau'' is misleading, as the density actually continues to rise towards small radii and forms a weak cusp, rho ~ r^{-(beta+1/2)}, where beta is the anisotropy coefficient. The annihilation flux, however, does not change much in the latter case, if averaged over an area larger than the annihilation radius.

2205.06775

Twisted Gan-Gross-Prasad conjecture for certain tempered L-packets

In this paper, we investigate the twisted GGP conjecture for certain tempered representations using the theta correspondence and establish some special cases, namely when the L-parameter of the unitary group is the sum of conjugate-dual characters of the appropriate sign.

2111.00911

Pressure-induced metal-insulator transition in oxygen-deficient LiNbO$_3$-type ferroelectrics

Hydrostatic pressure and oxygen vacancies usually have deleterious effects on ferroelectric materials because both tend to reduce their polarization. In this work we use first-principles calculations to study an important class of ferroelectric materials - LiNbO$_3$-type ferroelectrics (LiNbO$_3$ as the prototype), and find that in oxygen-deficient LiNbO$_{3-\delta}$, hydrostatic pressure induces an unexpected metal-insulator transition between 8 and 9 GPa. Our calculations also find that strong polar displacements persist in both metallic and insulating oxygen-deficient LiNbO$_{3-\delta}$ and the size of polar displacements is comparable to pristine LiNbO$_3$ under the same pressure. These properties are distinct from widely used perovskite ferroelectric oxide BaTiO$_3$, whose polarization is quickly suppressed by hydrostatic pressure and/or oxygen vacancies. The anomalous pressure-driven metal-insulator transition in oxygen-deficient LiNbO$_{3-\delta}$ arises from the change of an oxygen vacancy defect state. Hydrostatic pressure increases the polar displacements of oxygen-deficient LiNbO$_{3-\delta}$, which reduces the band width of the defect state and eventually turns it into an in-gap state. In the insulating phase, the in-gap state is further pushed away from the conduction band edge under hydrostatic pressure, which increases the fundamental gap. Our work shows that for LiNbO$_3$-type strong ferroelectrics, oxygen vacancies and hydrostatic pressure combined can lead to new phenomena and potential functions, in contrast to the harmful effects occurring to perovskite ferroelectric oxides such as BaTiO$_3$.

1012.3186

Some remarks on a paper by G.-S. Yang and H.-C.Kim: Mass splitting of SU(3) baryons within a chiral soliton model

In a recent paper Yang and Kim discuss the lowest baryon mass formulas using a chiral soliton model. However, contrary to their assertion, their result is not equivalent to a generalized Gell Mann-Okubo mass formula derived (G.Morpurgo 1992) using only general properties of QCD (The General parameterization method). The reason for the non equivalence is that the generalized mass formula include all the main terms that break flavor at second order, whereas the Authors above do not go beyond first order flavor breaking (and should therefore find the usual Gell Mann Okubo formula). That is is not so, due to some inconsistencies. Below we confine to the part of the Yang-Kim paper dealing with the mass formula. We will not consider the other items of their paper.

1512.04674

Global Well-posedness of the NLS System for infinitely many fermions

In this paper, we study the mean field quantum fluctuation dynamics for a system of infinitely many fermions with delta pair interactions in the vicinity of an equilibrium solution (the Fermi sea) at zero temperature, in dimensions $d=2,3$, and prove global well-posedness of the corresponding Cauchy problem. Our work extends some of the recent important results obtained by M. Lewin and J. Sabin, who addressed this problem for more regular pair interactions.

2001.04054

Large and Robust Charge-to-Spin Conversion in Sputtered Conductive WTex with Disorder

Topological materials with large spin-orbit coupling and immunity to disorder-induced symmetry breaking show great promise for efficiently converting charge to spin. Here, we report that long-range disordered sputtered WTex thin films exhibit local chemical and structural order as those of Weyl semimetal WTe2 and conduction behavior that is consistent with semi-metallic Weyl fermion. We find large charge-to-spin conversion properties and electrical conductivity in thermally annealed sputtered WTex films that are comparable with those in crystalline WTe2 flakes. Besides, the strength of unidirectional spin Hall magnetoresistance in annealed WTex/Mo/CoFeB heterostructure is 5 to 20 times larger than typical SOT layer/ferromagnet heterostructures reported at room temperature. We further demonstrate room temperature damping-like SOT-driven magnetization switching of in-plane magnetized CoFeB. These large charge-to-spin conversion properties that are robust in the presence of long-range disorder and thermal annealing pave the way for industrial application of a new class of sputtered semimetals.

1008.4505

Thermodynamics of AdS/QCD within the 5D dilaton-gravity model

We calculate the pressure, entropy density, trace anomaly and speed of sound of the gluon plasma using the dilaton potential of Ref. arXiv:0911.0627[hep-ph] in the dilaton-gravity theory of AdS/QCD. The finite temperature observables are calculated from the Black Hole solutions of the Einstein equations, and using the Bekenstein-Hawking equality of the entropy with the area of the horizon. Renormalization is well defined, because the T=0 theory has asymptotic freedom. Comparison with lattice simulations is made.

1507.02406

The phase diagrams of iron-based superconductors: theory and experiments

Phase diagrams play a primary role in the understanding of materials properties. For iron-based superconductors (Fe-SC), the correct definition of their phase diagrams is crucial because of the close interplay between their crystallo-chemical and magnetic properties, on one side, and the possible coexistence of magnetism and superconductivity, on the other. The two most difficult issues for understanding the Fe-SC phase diagrams are: 1) the origin of the structural transformation taking place during cooling and its relationship with magnetism; 2) the correct description of the region where a crossover between the magnetic and superconducting electronic ground states takes place. Hence a proper and accurate definition of the structural, magnetic and electronic phase boundaries provides an extremely powerful tool for material scientists. For this reason, an exact definition of the thermodynamic phase fields characterizing the different structural and physical properties involved is needed, although it is not easy to obtain in many cases. Moreover, physical properties can often be strongly dependent on the occurrence of micro-structural and other local-scale features (lattice micro-strain, chemical fluctuations, domain walls, grain boundaries, defects), which, as a rule, are not described in a structural phase diagram. In this review, we critically summarize the results for the most studied 11-, 122- and 1111-type compound systems, providing a correlation between experimental evidence and theory.

2309.06752

Multiscaling in the 3D critical site-diluted Ising ferromagnet

We have studied numerically the appearance of multiscaling behavior in the three-dimensional ferromagnetic Ising site diluted model, in the form of a multifractal distribution of the decay exponents for the spatial correlation functions at the critical temperature. We have computed the exponents of the long-distance decay of higher moments of the correlation function, up to the 10th power, by studying three different quantities: global susceptibilities, local susceptibilities and correlation functions. We have found very clear evidences for multiscaling behavior.

1709.03931

Blow-up of solutions to semi-discrete parabolic-elliptic Keller-Segel models

The existence of weak solutions and upper bounds for the blow-up time for time-discrete parabolic-elliptic Keller-Segel models for chemotaxis in the two-dimensional whole space are proved. For various time discretizations, including the implicit Euler, BDF, and Runge-Kutta methods, the same bounds for the blow-up time as in the continuous case are derived by discrete versions of the virial argument. The theoretical results are illustrated by numerical simulations using an upwind finite-element method combined with second-order time discretizations.

2103.00736

Rapid Convergence of First-Order Numerical Algorithms via Adaptive Conditioning

This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving large-scale conic optimization problems on distributed platforms such as {graphics processing unit} with orders-of-magnitude time improvement. Proof of global convergence is provided for the proposed algorithm. We argue that on the contrary to common belief, the condition number of the data matrix is not a reliable predictor of convergence speed. In light of this observation, an adaptive conditioning heuristic is proposed which enables higher accuracy compared to other first-order numerical algorithms. Numerical experiments on a wide range of large-scale linear programming and second-order cone programming problems demonstrate the scalability and computational advantages of the proposed algorithm compared to commercial and open-source state-of-the-art solvers.

2009.11465

Model Identification and Control of a Low-Cost Wheeled Mobile Robot Using Differentiable Physics

We present the design of a low-cost wheeled mobile robot, and an analytical model for predicting its motion under the influence of motor torques and friction forces. Using our proposed model, we show how to analytically compute the gradient of an appropriate loss function, that measures the deviation between predicted motion trajectories and real-world trajectories, which are estimated using Apriltags and an overhead camera. These analytical gradients allow us to automatically infer the unknown friction coefficients, by minimizing the loss function using gradient descent. Motion trajectories that are predicted by the optimized model are in excellent agreement with their real-world counterparts. Experiments show that our proposed approach is computationally superior to existing black-box system identification methods and other data-driven techniques, and also requires very few real-world samples for accurate trajectory prediction. The proposed approach combines the data efficiency of analytical models based on first principles, with the flexibility of data-driven methods, which makes it appropriate for low-cost robots. Using the learned model and our gradient-based optimization approach, we show how to automatically compute motor control signals for driving the robot along pre-specified curves.

2112.14202

Tau-functions for the Ablowitz--Ladik hierarchy: the matrix-resolvent method

We extend the matrix-resolvent method for computing logarithmic derivatives of tau-functions to the Ablowitz--Ladik hierarchy. In particular, we derive a formula for the generating series of the logarithmic derivatives of an arbitrary tau-function in terms of matrix resolvents. As an application, we provide a way of computing certain integrals over the unitary group.

1906.10127

Probing Proton Structure at the Large Hadron electron Collider

For the foreseeable future, the exploration of the high-energy frontier will be the domain of the Large Hadron Collider (LHC). Of particular significance will be its high-luminosity upgrade (HL-LHC), which will operate until the mid-2030s. In this endeavour, for the full exploitation of the HL-LHC physics potential an improved understanding of the parton distribution functions (PDFs) of the proton is critical. The HL-LHC program would be uniquely complemented by the proposed Large Hadron electron Collider (LHeC), a high-energy lepton-proton and lepton-nucleus collider based at CERN. In this work, we build on our recent PDF projections for the HL-LHC to assess the constraining power of the LHeC measurements of inclusive and heavy quark structure functions. We find that the impact of the LHeC would be significant, reducing PDF uncertainties by up to an order of magnitude in comparison to state-of-the-art global fits. In comparison to the HL-LHC projections, the PDF constraints from the LHeC are in general more significant for small and intermediate values of the momentum fraction x. At higher values of x, the impact of the LHeC and HL-LHC data is expected to be of a comparable size, with the HL-LHC constraints being more competitive in some cases, and the LHeC ones in others. Our results illustrate the encouraging complementarity of the HL-LHC and the LHeC in terms of charting the quark and gluon structure of the proton.

2201.08069

Analysis of the distribution, rotation and scale characteristics of solar wind switchbacks: comparison between the first and second encounters of Parker Solar Probe

The S-shaped magnetic structure in the solar wind formed by the twisting of magnetic field lines is called a switchback, whose main characteristics are the reversal of the magnetic field and the significant increase in the solar wind radial velocity. We identify 242 switchbacks during the first two encounters of Parker Solar Probe (PSP). Statistics methods are applied to analyze the distribution and the rotation angle and direction of the magnetic field rotation of the switchbacks. The diameter of switchbacks is estimated with a minimum variance analysis (MVA) method based on the assumption of a cylindrical magnetic tube. We also make a comparison between switchbacks from inside and the boundary of coronal holes. The main conclusions are as follows: (1) the rotation angles of switchbacks observed during the first encounter seem larger than those of the switchbacks observed during the second encounter in general; (2) the tangential component of the velocity inside the switchbacks tends to be more positive (westward) than in the ambient solar wind; (3) switchbacks are more likely to rotate clockwise than anticlockwise, and the number of switchbacks with clockwise rotation is 1.48 and 2.65 times of those with anticlockwise rotation during the first and second encounters, respectively; (4) the diameter of switchbacks is about 10^5 km on average and across five orders of magnitude (10^3 -- 10^7 km).

0911.3361

Mass loss from inhomogeneous hot star winds I. Resonance line formation in 2D models

Small-scale clumping in the winds of hot, massive stars is conventionally included in spectral analyses by assuming optically thin clumps, a void inter-clump medium, and a smooth velocity field. To reconcile investigations of different diagnostics within such models, a highly clumped wind with very low mass-loss rates needs to be invoked. Particularly, unsaturated UV resonance lines seem to indicate rates an order of magnitude (or even more) lower than previously accepted values. We investigate resonance line formation in inhomogeneous hot star winds with non-monotonic velocity fields by means of 2D stochastic and pseudo-2D radiation-hydrodynamic wind models. A Monte-Carlo radiative transfer code is presented and used to produce synthetic line spectra. Results: The optically thin clumping limit is only valid for very weak lines. For intermediate strong lines, the velocity spans of the clumps are of central importance. Current hydrodynamical models predict spans that are too large to reproduce observed profiles unless a very low mass-loss rate is invoked. By simulating lower spans in 2D stochastic models, the profile strengths become drastically reduced, and are consistent with higher mass-loss rates. To simultaneously meet the constraints from strong lines, the inter-clump medium must be non-void. A first comparison to the observed PV doublet in the O6 supergiant lam Cep confirms that a stochastic 2D model reproduces observations with a mass-loss rate roughly ten times higher than that derived from the same lines but assuming optically thin clumping. Tentatively this may resolve discrepancies between theoretical predictions, evolutionary constraints, and recent derived mass-loss rates, and suggests a re-investigation of the structure predicted by current hydrodynamical models.

0911.5612

Massive protostars as gamma-ray sources

Massive protostars have associated bipolar outflows with velocities of hundreds of km s$^{-1}$. Such outflows can produce strong shocks when interact with the ambient medium leading to regions of non-thermal radio emission. We aim at exploring under which conditions relativistic particles are accelerated at the terminal shocks of the protostellar jets and can produce significant gamma-ray emission. We estimate the conditions necessary for particle acceleration up to very high energies and gamma-ray production in the non-thermal hot spots of jets associated with massive protostars embedded in dense molecular clouds. We show that relativistic Bremsstrahlung and proton-proton collisions can make molecular clouds with massive young stellar objects detectable by the {\it Fermi}{} satellite at MeV-GeV energies and by Cherenkov telescope arrays in the GeV-TeV range. Gamma-ray astronomy can be used to probe the physical conditions in star forming regions and particle acceleration processes in the complex environment of massive molecular clouds.

1106.5057

Using a Differential Emission Measure and Density Measurements in an Active Region Core to Test a Steady Heating Model

The frequency of heating events in the corona is an important constraint on the coronal heating mechanisms. Observations indicate that the intensities and velocities measured in active region cores are effectively steady, suggesting that heating events occur rapidly enough to keep high temperature active region loops close to equilibrium. In this paper, we couple observations of Active Region 10955 made with XRT and EIS on \textit{Hinode} to test a simple steady heating model. First we calculate the differential emission measure of the apex region of the loops in the active region core. We find the DEM to be broad and peaked around 3\,MK. We then determine the densities in the corresponding footpoint regions. Using potential field extrapolations to approximate the loop lengths and the density-sensitive line ratios to infer the magnitude of the heating, we build a steady heating model for the active region core and find that we can match the general properties of the observed DEM for the temperature range of 6.3 $<$ Log T $<$ 6.7. This model, for the first time, accounts for the base pressure, loop length, and distribution of apex temperatures of the core loops. We find that the density-sensitive spectral line intensities and the bulk of the hot emission in the active region core are consistent with steady heating. We also find, however, that the steady heating model cannot address the emission observed at lower temperatures. This emission may be due to foreground or background structures, or may indicate that the heating in the core is more complicated. Different heating scenarios must be tested to determine if they have the same level of agreement.

2111.12431

A Large-Scale Multi-Rider Matching Problem with Reneging Passengers

This paper studies a large-scale ride-matching problem in a transport center with a large number of passengers who are different in terms of destinations and travel preferences. Passengers with similar itineraries can match each other and share the same vehicle for their potentially different destinations; and reneging passengers, who become impatient and leave the service system after waiting long time for shared rides, are considered in our model. We aim to maximize the long-run average revenue of the ride service vendor, which is defined as the difference between the long-run average reward earned by providing ride services and the long-run average penalty incurred by reneging passengers. The problem is complicated by its scale, the heterogeneity of passengers, and the reneging behavior. To this end, we formate the ride-matching problem as a specific Markov decision process and propose a scalable ride-matching policy, referred to as Bivariate Index (BI) policy. We demonstrate that the ride-matching problem reduces to a conventional restless multi-armed bandit problem in a special case, for which the BI policy reduces to the well-known Whittle index policy that prioritizes passengers with the highest Whittle indices. For the general case, following the Whittle relaxation technique, BI prioritizes passengers according to their bivariate indices that are curves in a real-valued coordinate and are assigned to each passengers. We prove that the ranking of the bivariate indices can be derived by the ranking of corresponding Whittle indices in a surrogate system. Through extensive numerical simulations for systems with real-world travel demands, it is demonstrated that BI significantly outperforms baseline policies.

1805.11049

Induced Chern-Simons modified gravity at finite temperature

We calculate the linearized four-dimensional gravitational Chern-Simons term at the finite temperature, show its finiteness and explicitly demonstrate that its transversal part matches the known result for the chiral vortical conductivity.

1907.11966

Small Time Behavior and Summability for the Schr\"odinger Equation

We consider the Carleson's problem regarding small time almost everywhere convergence to initial data for the Schr\"odinger equation, both linear and nonlinear on $\mathbb{R}$. It is shown, via the smoothing effect of the Schr\"odinger flow, that the (sharp) result proved by Dahlberg and Kenig for initial data in Sobolev spaces still holds when one considers the full Schr\"odinger equation with a certain class of potentials. As for $s<\frac{1}{4}$, the failure of $L^p$-boundedness of the (localized) maximal operator is investigated.

1510.08071

GM2Calc: Precise MSSM prediction for $(g - 2)$ of the muon

We present GM2Calc, a public C++ program for the calculation of MSSM contributions to the anomalous magnetic moment of the muon, $(g-2)_\mu$. The code computes $(g-2)_\mu$ precisely, by taking into account the latest two-loop corrections and by performing the calculation in a physical on-shell renormalization scheme. In particular the program includes a $\tan\beta$ resummation so that it is valid for arbitrarily high values of $\tan\beta$, as well as fermion/sfermion-loop corrections which lead to non-decoupling effects from heavy squarks. GM2Calc can be run with a standard SLHA input file, internally converting the input into on-shell parameters. Alternatively, input parameters may be specified directly in this on-shell scheme. In both cases the input file allows one to switch on/off individual contributions to study their relative impact. This paper also provides typical usage examples not only in conjunction with spectrum generators and plotting programs but also as C++ subroutines linked to other programs.

1803.01475

The Fu-Yau equation on compact astheno-K\"ahler manifolds

In this paper, we study the Fu-Yau equation on compact Hermitian manifolds and prove the existence of solutions of equation on astheno-K\"ahler manifolds. We also prove the uniqueness of solutions of Fu-Yau equation when the slope parameter $\alpha$ is negative.

2107.01937

Gravitationally Induced Particle Production through a Nonminimal Torsion-Matter Coupling

We investigate the possibility of gravitationally generated particle production via the mechanism of nonminimal torsion--matter coupling. An intriguing feature of this theory is that the divergence of the matter energy--momentum tensor does not vanish identically. We explore the physical and cosmological implications of the nonconservation of the energy--momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard $\Lambda$CDM cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy--momentum tensor. We consider specific models, and we show that cosmology with a torsion--matter coupling can almost perfectly reproduce the $\Lambda$CDM scenario, while it additionally gives rise to particle creation rates, creation pressures, and entropy generation through gravitational matter production in both low and high redshift limits.