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For graphs $G$ and $H$, an $H$-coloring of $G$ is an edge-preserving mapping
from $V(G)$ to $V(H)$. Note that if $H$ is the triangle, then $H$-colorings are
equivalent to $3$-colorings. In this paper we are interested in the case that
$H$ is the five-vertex cycle $C_5$.
A minimal obstruction to $C_5$-coloring is a graph that does not have a
$C_5$-coloring, but every proper induced subgraph thereof has a $C_5$-coloring.
In this paper we are interested in minimal obstructions to $C_5$-coloring in
$F$-free graphs, i.e., graphs that exclude some fixed graph $F$ as an induced
subgraph. Let $P_t$ denote the path on $t$ vertices, and let $S_{a,b,c}$ denote
the graph obtained from paths $P_{a+1},P_{b+1},P_{c+1}$ by identifying one of
their endvertices.
We show that there is only a finite number of minimal obstructions to
$C_5$-coloring among $F$-free graphs, where $F \in \{ P_8, S_{2,2,1},
S_{3,1,1}\}$ and explicitly determine all such obstructions. This extends the
results of Kami\'nski and Pstrucha [Discr. Appl. Math. 261, 2019] who proved
that there is only a finite number of $P_7$-free minimal obstructions to
$C_5$-coloring, and of D\k{e}bski et al. [ISAAC 2022 Proc.] who showed that the
triangle is the unique $S_{2,1,1}$-free minimal obstruction to $C_5$-coloring.
We complement our results with a construction of an infinite family of
minimal obstructions to $C_5$-coloring, which are simultaneously $P_{13}$-free
and $S_{2,2,2}$-free. We also discuss infinite families of $F$-free minimal
obstructions to $H$-coloring for other graphs $H$.
|
2404.11704
|
A new analysis of high-resolution data from the Atacama Large
Millimeter/submillimeter Array (ALMA) for 5 luminous or ultra-luminous infrared
galaxies gives a slope for the Kennicutt-Schmidt (KS) relation equal to
$1.74^{+0.09}_{\rm -0.07}$ for gas surface densities $\Sigma_{\rm
mol}>10^3\;M_\odot$ pc$^{-2}$ and an assumed constant CO-to-H$_2$ conversion
factor. The velocity dispersion of the CO line, $\sigma_v$, scales
approximately as the inverse square root of $\Sigma_{\rm mol}$, making the
empirical gas scale height determined from $H\sim0.5\sigma^2/(\pi G\Sigma_{\rm
mol})$ nearly constant, 150-190 pc, over 1.5 orders of magnitude in
$\Sigma_{\rm mol}$. This constancy of $H$ implies that the average midplane
density, which is presumably dominated by CO-emitting gas for these extreme
star-forming galaxies, scales linearly with the gas surface density, which, in
turn, implies that the gas dynamical rate (the inverse of the free-fall time)
varies with $\Sigma_{\rm mol}^{1/2}$, thereby explaining most of the
super-linear slope in the KS relation. Consistent with these relations, we also
find that the mean efficiency of star formation per free-fall time is roughly
constant, 5%-7%, and the gas depletion time decreases at high $\Sigma_{\rm
mol}$, reaching only $\sim 16$ Myr at $\Sigma_{\rm mol}\sim10^4\;M_\odot$
pc$^{-2}$. The variation of $\sigma_v$ with $\Sigma_{\rm mol}$ and the
constancy of $H$ are in tension with some feedback-driven models, which predict
$\sigma_v$ to be more constant and $H$ to be more variable. However, these
results are consistent with simulations in which large-scale gravity drives
turbulence through a feedback process that maintains an approximately constant
Toomre $Q$ instability parameter.
|
1907.05432
|
The recent coronavirus pandemic follows in its early stages an almost
exponential growth, with the number of cases quite well fit in time by
$N(t)\propto e^{\alpha t}$, in many countries. We analyze the rate $\alpha$ for
each country, starting from a threshold of 30 total cases and using the next 12
days, capturing thus the early growth homogeneously. We look for a link between
$\alpha$ and the average temperature $T$ of each country, in the month of the
epidemic growth. We analyze a {\it base} set of 42 countries, which developed
the epidemic earlier, an {\it intermediate} set of 88 countries and an {\it
extended} set of 125 countries, which developed the epidemic more recently.
Applying a linear fit $\alpha(T)$, we find increasing evidence for a decreasing
$\alpha$ as a function of $T$, at $99.66\%$C.L., $99.86\%$C.L. and $99.99995
\%$ C.L. ($p$-value $5 \cdot 10^{-7}$, or 5$\sigma$ detection) in the {\it
base}, {\it intermediate} and {\it extended} dataset, respectively. The
doubling time is expected to increase by $40\%\sim 50\%$, going from $5^\circ$
C to $25^\circ$ C. In the {\it base} set, going beyond a linear model, a peak
at $(7.7\pm 3.6)^\circ C$ seems to be present, but its evidence disappears for
the larger datasets. We also analyzed a possible bias: poor countries, often
located in warm regions, might have less intense testing. By excluding
countries below a given GDP per capita, we find that our conclusions are only
slightly affected and only for the {\it extended} dataset. The significance
remains high, with a $p$-value of $10^{-3}-10^{-4}$ or less. Our findings give
hope that, for northern hemisphere countries, the growth rate should
significantly decrease as a result of both warmer weather and lockdown
policies. In general the propagation should be hopefully stopped by strong
lockdown, testing and tracking policies, before the arrival of the cold season.
|
2003.12417
|
In the present thesis we study absorption spectra of spin polarized isolated
systems. Thus we introduce the density functional theory (DFT) formalism and
its time dependent extension (TDDFT) together with the approximation used. In
particula the Casida formulation of TDDFT is described. The equations for the
description of open shell systems have been implemented in the abinit code.
Then we used the BeH molecule as a test case. Studying the results for this
molecule we underline the limits of the commonly used approximations. In
particular we discuss why the the spin symmetry of excited states is broken and
we propose a rule to find which excitation energies are affected by this
problem. Finally, in the last part, we discuss how a better approximation could
be obtained starting from the many body perturbation theory.
-----
Il lavoro della presente tesi \`e focalizzato sullo studio dello spettro di
eccitazione di sistemi isolati spin polarizzati. Quindi vengono esposte la
Density Functional Theory (DFT), la sua estensione al caso dipendente dal tempo
(TDDFT) e le approssimazioni utilizzate. In particolare vien esposta la
formulazione di Casida della TDDFT. Le equazioni per lo studio di sistemi
spin-polarizzati sono state implementate all'interno del software ABINIT. \`E
stata poi scelta la molecola di BeH per testare l'implementazione fatta. I
calcoli eseguiti ci hanno permesso di mettere in luce i limiti delle
approssimazioni comunemente utilizzate. In particolare abbiamo discusso
l'impossibilit\`a di mantenere la corretta simmetria di spin in sistemi spin
polarizzati. Viene quindi proposta una regola per individuare quali siano,
negli spettri calcolati, le energie di eccitazione affette da questo problema.
Nell'ultimo capitolo della tesi viene inoltre esposta una possibile soluzione
per superare l'approssimazione adiabatica.
|
1208.3152
|
The Dyck language, which consists of well-balanced sequences of parentheses,
is one of the most fundamental context-free languages. The Dyck edit distance
quantifies the number of edits (character insertions, deletions, and
substitutions) required to make a given parenthesis sequence well-balanced. RNA
Folding involves a similar problem, where a closing parenthesis can match an
opening parenthesis of the same type irrespective of their ordering. For
example, in RNA Folding, both $\tt{()}$ and $\tt{)(}$ are valid matches,
whereas the Dyck language only allows $\tt{()}$ as a match. Using fast matrix
multiplication, it is possible to compute their exact solutions of both
problems in time $O(n^{2.824})$. Whereas combinatorial algorithms would be more
desirable, the two problems are known to be at least as hard as Boolean matrix
multiplication. In terms of fast approximation algorithms that are
combinatorial in nature, both problems admit an $\epsilon n$-additive
approximation in $\tilde{O}(\frac{n^2}{\epsilon})$ time. Further, there is a
$O(\log n)$-factor approximation algorithm for Dyck edit distance in
near-linear time.
In this paper, we design a constant-factor approximation algorithm for Dyck
edit distance that runs in $O(n^{1.971})$ time. Moreover, we develop a
$(1+\epsilon)$-factor approximation algorithm running in
$\tilde{O}(\frac{n^2}{\epsilon})$ time, which improves upon the earlier
additive approximation. Finally, we design a $(3+\epsilon)$-approximation that
takes $\tilde{O}(\frac{nd}{\epsilon})$ time, where $d\ge 1$ is an upper bound
on the sought distance. As for RNA folding, for any $s\ge1$, we design a
factor-$s$ approximation algorithm that runs in $O(n+(\frac{n}{s})^3)$ time. To
the best of our knowledge, this is the first nontrivial approximation algorithm
for RNA Folding that can go below the $n^2$ barrier. All our algorithms are
combinatorial.
|
2112.05866
|
Let $d\ge1$ and $0<\alpha<2$. Consider the integro-differential operator \[
\mathcal{L}f(x)
=\int_{\mathbb{R}^{d}\backslash\{0\}}\left[f(x+h)-f(x)-\chi_{\alpha}(h)\nabla
f(x)\cdot
h\right]\frac{n(x,h)}{|h|^{d+\alpha}}\mathrm{d}h+\mathbf{1}_{\alpha>1}b(x)\cdot\nabla
f(x), \] where
$\chi_{\alpha}(h):=\mathbf{1}_{\alpha>1}+\mathbf{1}_{\alpha=1}\mathbf{1}_{\{|h|\le1\}}$,
$b:\mathbb{R}^{d}\to\mathbb{R}^{d}$ is bounded measurable, and
$n:\mathbb{R}^{d}\times\mathbb{R}^{d}\to\mathbb{R}$ is measurable and bounded
above and below respectively by two positive constants. Further, we assume that
$n(x,h)$ is H\"older continuous in $x$, uniformly with respect to
$h\in\mathbb{R}^{d}$. In the case $\alpha=1,$ we assume additionally
$\int_{\partial B_{r}}n(x,h)h\mathrm{d}S_{r}(h)=0$, $\forall r \in (0,\infty)$,
where $\mathrm{d}S_{r}$ is the surface measure on $\partial B_{r}$, the
boundary of the ball with radius $r$ and center $0$. In this paper, we
establish two-sided estimates for the heat kernel of the Markov process
associated with the operator $\mathcal{L}$. This extends a recent result of
Z.-Q. Chen and X. Zhang.
|
1709.02836
|
Nitrogen hydrides such as NH$_3$ and N$_2$H$^+$ are widely used by Galactic
observers to trace the cold dense regions of the interstellar medium. In
external galaxies, because of limited sensitivity, HCN has become the most
common tracer of dense gas over large parts of galaxies. We provide the first
systematic measurements of N$_2$H$^+$(1-0) across different environments of an
external spiral galaxy, NGC6946. We find a strong correlation ($r>0.98,p<0.01$)
between the HCN(1-0) and N$_2$H$^+$(1-0) intensities across the inner
$\sim8\mathrm{kpc}$ of the galaxy, at kiloparsec scales. This correlation is
equally strong between the ratios N$_2$H$^+$(1-0)/CO(1-0) and HCN(1-0)/CO(1-0),
tracers of dense gas fractions ($f_\mathrm{dense}$). We measure an average
intensity ratio of N$_2$H$^+$(1-0)/HCN(1-0)$=0.15\pm0.02$ over our set of five
IRAM-30m pointings. These trends are further supported by existing measurements
for Galactic and extragalactic sources. This narrow distribution in the average
ratio suggests that the observed systematic trends found in kiloparsec-scale
extragalactic studies of $f_\mathrm{dense}$ and the efficiency of dense gas
(SFE$_\mathrm{dense}$) would not change if we employed N$_2$H$^+$(1-0) as a
more direct tracer of dense gas. At kiloparsec scales our results indicate that
the HCN(1-0) emission can be used to predict the expected N$_2$H$^+$(1-0) over
those regions. Our results suggest that, even if HCN(1-0) and N$_2$H$^+$(1-0)
trace different density regimes within molecular clouds, subcloud differences
average out at kiloparsec scales, yielding the two tracers proportional to each
other.
|
2308.01342
|
We present evidence of non-excimer-based secondary scintillation in gaseous
xenon, obtained using both the NEXT-White TPC and a dedicated setup. Detailed
comparison with first-principle calculations allows us to assign this
scintillation mechanism to neutral bremsstrahlung (NBrS), a process that has
been postulated to exist in xenon that has been largely overlooked. For photon
emission below 1000 nm, the NBrS yield increases from about 10$^{-2}$
photon/e$^{-}$ cm$^{-1}$ bar$^{-1}$ at pressure-reduced electric field values
of 50 V cm$^{-1}$ bar$^{-1}$ to above 3$\times$10$^{-1}$ photon/e$^{-}$
cm$^{-1}$ bar$^{-1}$ at 500 V cm$^{-1}$ bar$^{-1}$. Above 1.5 kV cm$^{-1}$
bar$^{-1}$, values that are typically employed for electroluminescence, it is
estimated that NBrS is present with an intensity around 1 photon/e$^{-}$
cm$^{-1}$ bar$^{-1}$, which is about two orders of magnitude lower than
conventional, excimer-based electroluminescence. Despite being fainter than its
excimeric counterpart, our calculations reveal that NBrS causes luminous
backgrounds that can interfere, in either gas or liquid phase, with the ability
to distinguish and/or to precisely measure low primary-scintillation signals
(S1). In particular, we show this to be the case in the "buffer" and "veto"
regions, where keeping the electric field below the electroluminescence (EL)
threshold will not suffice to extinguish secondary scintillation. The electric
field in these regions should be chosen carefully to avoid intolerable levels
of NBrS emission. Furthermore, we show that this new source of light emission
opens up a viable path towards obtaining S2 signals for discrimination purposes
in future single-phase liquid TPCs for neutrino and dark matter physics, with
estimated yields up to 20-50 photons/e$^{-}$ cm$^{-1}$.
|
2202.02614
|
Recent results suggest that quantum computers possess the potential to speed
up nonconvex optimization problems. However, a crucial factor for the
implementation of quantum optimization algorithms is their robustness against
experimental and statistical noises. In this paper, we systematically study
quantum algorithms for finding an $\epsilon$-approximate second-order
stationary point ($\epsilon$-SOSP) of a $d$-dimensional nonconvex function, a
fundamental problem in nonconvex optimization, with noisy zeroth- or
first-order oracles as inputs. We first prove that, up to noise of
$O(\epsilon^{10}/d^5)$, accelerated perturbed gradient descent with quantum
gradient estimation takes $O(\log d/\epsilon^{1.75})$ quantum queries to find
an $\epsilon$-SOSP. We then prove that perturbed gradient descent is robust to
the noise of $O(\epsilon^6/d^4)$ and $O(\epsilon/d^{0.5+\zeta})$ for $\zeta>0$
on the zeroth- and first-order oracles, respectively, which provides a quantum
algorithm with poly-logarithmic query complexity. We then propose a stochastic
gradient descent algorithm using quantum mean estimation on the Gaussian
smoothing of noisy oracles, which is robust to $O(\epsilon^{1.5}/d)$ and
$O(\epsilon/\sqrt{d})$ noise on the zeroth- and first-order oracles,
respectively. The quantum algorithm takes $O(d^{2.5}/\epsilon^{3.5})$ and
$O(d^2/\epsilon^3)$ queries to the two oracles, giving a polynomial speedup
over the classical counterparts. Moreover, we characterize the domains where
quantum algorithms can find an $\epsilon$-SOSP with poly-logarithmic,
polynomial, or exponential number of queries in $d$, or the problem is
information-theoretically unsolvable even by an infinite number of queries. In
addition, we prove an $\Omega(\epsilon^{-12/7})$ lower bound in $\epsilon$ for
any randomized classical and quantum algorithm to find an $\epsilon$-SOSP using
either noisy zeroth- or first-order oracles.
|
2212.02548
|
Layered ferromagnetic-piezoelectric composites show mechanical strain
mediated electromagnetic coupling. Here we discuss dielectric and piezoelectric
properties of ferrite-lead zirconate titanate (PZT) and lanthanum manganite-PZT
samples. Results of our investigations on dielectric and pyroelectric
properties of multilayer ferromagnetic-piezoelectric are presented here. Lead
zircinate-titanate PbZrxTi1-xO3 (PZT) was used for the piezoelectric phase in
all the structures. The following materials were used for the ferromagnetic
component: nickel-zinc ferrites Ni0.9Zn 0.1Fe2O4 (NFO1) and Ni0.8Zn0.2Fe2O4
(NFO2), cobalt ferrite (CFO), lithium ferrite (LFO), lanthanum strontium
manganite La0.7Sr0.3MnO3 (LSM), and lanthanum-calcium manganite La0.7Ca0.3MnO3
(LCM). The pyroelectric effect was studied by measuring the current J flowing
through a closed loop containing the sample and an electrometer as the sample
temperature T was slowly varied at the rate 0.1 K/s. Polarized PZT layers
generate a pyroelectric current as the temperature changes. The main indicator
of pyroelectric nature of the current is the sign reversal when the thermal
cycle is switched from heating to cooling. Almost all of the multilayer
structures showed a pyroelectric current, but the pyroelectric coefficient
varied in a wide range. (i) For NFO1-PZT system the coefficient was in the
range 0.01 - 10 nC/(cm2 K), depending on the temperature. (ii) CFO-PZT and
LFO-PZT structures showed a large thermal current and a weak pyroelectric
effect. (iii) Thermal currents, however, were absent in LCM-PZT within the
temperature range from the room temperature to 400 K. (iv) In LSM-PZT, the
thermal current exceeded the pyroelectric current. A model is proposed for an
understanding of these results.
|
cond-mat/0401481
|
The stellar velocity distribution function (DF) in the solar vicinity is
re-examined using data from the SDSS APOGEE survey's DR16 and \emph{Gaia} DR2.
By exploiting APOGEE's ability to chemically discriminate with great
reliability the thin disk, thick disk and (accreted) halo populations, we can,
for the first time, derive the three-dimensional velocity DFs for these
chemically-separated populations. We employ this smaller, but more data-rich
APOGEE+{\it Gaia} sample to build a \emph{data-driven model} of the local
stellar population velocity DFs, and use these as basis vectors for assessing
the relative density proportions of these populations over 5 $<$ $R$ $<$ 12
kpc, and $-1.5$ $<$ $z$ $<$ 2.5 kpc range as derived from the larger, more
complete (i.e., all-sky, magnitude-limited) {\it Gaia} database. We find that
81.9 $\pm$ 3.1$\%$ of the objects in the selected \emph{Gaia} data-set are
thin-disk stars, 16.6 $\pm$ 3.2$\%$ are thick-disk stars, and 1.5 $\pm$ 0.1$\%$
belong to the Milky Way stellar halo. We also find the local thick-to-thin-disk
density normalization to be $\rho_{T}(R_{\odot})$/$\rho_{t}(R_{\odot})$ = 2.1
$\pm$ 0.2$\%$, a result consistent with, but determined in a completely
different way than, typical starcount/density analyses. Using the same
methodology, the local halo-to-disk density normalization is found to be
$\rho_{H}(R_{\odot})$/($\rho_{T}(R_{\odot})$ + $\rho_{t}(R_{\odot})$) = 1.2
$\pm$ 0.6$\%$, a value that may be inflated due to chemical overlap of halo and
metal-weak thick disk stars.
|
2005.14534
|
The decay amplitude analyses of $B^\pm\to \pi^+ \pi^-\pi^\pm$ decays in the
Dalitz plot performed by LHCb indicate that CP asymmetry for the dominant
quasi-two-body decay $B^\pm\to\rho(770)^0\pi^\pm$ was found to be consistent
with zero in all three approaches for the $S$-wave component and that
CP-violation effects related to the interference between the $\rho(770)^0$
resonance and the $S$-wave were clearly observed. We show that the nearly
vanishing CP violation in $B^\pm\to\rho^0\pi^\pm$ is understandable within the
framework of QCD factorization. There are two $1/m_b$ power corrections, one
from penguin annihilation and the other from hard spectator interactions. They
contribute destructively to $A_{CP}(B^\pm\to\rho^0\pi^\pm)$ to render it
compatible with zero, in contrast to the sizable negative CP asymmetry
predicted in most of the existing models. We next show that the measured
interference pattern between the $\rho$ and $S$-wave contributions in the low
$m_{\pi^+\pi^-}$ region separated by the sign of value of $\cos\theta$ with
$\theta$ being the angle between the two same charged pions measured in the
rest frame of the $\rho$ resonance can be explained in terms of the smallness
of $A_{CP}(B^+\to\rho^0\pi^+)$ and the interference between $\rho(770)$ and
$\sigma/f_0(500)$. If CP asymmetry in $B^\pm\to\rho^0\pi^\pm$ is not negligible
as predicted in many existing models, the observed interference pattern will be
destroyed. We conclude that the experimental observation of the interference
pattern between $P$- and $S$-waves in the low-$m_{\pi^+\pi^-}$ region between
0.5 and 1.0 GeV is consistent with a nearly vanishing CP violation in
$B^\pm\to\rho^0\pi^\pm$.
|
2211.03965
|
Let $S \subset \mathbb{R}^{n}$ be a nonempty set. Given $d \in [0,n)$ and a
cube $\overline{Q} \subset \mathbb{R}^{n}$ with $l=l(\overline{Q}) \in (0,1]$,
we show that if the $d$-Hausdorff content
$\mathcal{H}^{d}_{\infty}(\overline{Q} \cap S) < \overline{\lambda}l^{d}$ for
some $\overline{\lambda} \in (0,1)$, then the set $\overline{Q} \setminus S$
contains a specific cavity. More precisely, we prove existence of a
pseudometric $\rho=\rho_{S,d}$ such that for each sufficiently small $\delta >
0$ the $\delta$-neighborhood $U^{\rho}_{\delta l}(S)$ of $S$ in the
pseudometric $\rho$ does not contain the whole $\overline{Q}$. Moreover, we
establish the existence of constants
$\overline{\delta}=\overline{\delta}(n,d,\overline{\lambda})>0$ and
$\underline{\gamma}=\underline{\gamma}(n,d,\overline{\lambda})>0$ such that
$\mathcal{L}^{n}(\overline{Q} \setminus U^{\rho}_{\delta l}(S)) \geq
\underline{\gamma} l^{n}$ for all $\delta \in (0,\overline{\delta})$. If, in
addition, the set $S$ is $d$-lower content regular, we prove existence of a
constant $\underline{\tau}=\underline{\tau}(n,d,\overline{\lambda})>0$ such
that the cube $\overline{Q}$ is $\underline{\tau}$-porous. The sharpness of the
results is illustrated by several examples.
|
2101.03556
|
Let $X$ be a non-negative random variable and let the conditional
distribution of a random variable $Y$, given $X$, be ${Poisson}(\gamma \cdot
X)$, for a parameter $\gamma \geq 0$. We identify a natural loss function such
that: 1) The derivative of the mutual information between $X$ and $Y$ with
respect to $\gamma$ is equal to the \emph{minimum} mean loss in estimating $X$
based on $Y$, regardless of the distribution of $X$. 2) When $X \sim P$ is
estimated based on $Y$ by a mismatched estimator that would have minimized the
expected loss had $X \sim Q$, the integral over all values of $\gamma$ of the
excess mean loss is equal to the relative entropy between $P$ and $Q$.
For a continuous time setting where $X^T = \{X_t, 0 \leq t \leq T \}$ is a
non-negative stochastic process and the conditional law of $Y^T=\{Y_t, 0\le
t\le T\}$, given $X^T$, is that of a non-homogeneous Poisson process with
intensity function $\gamma \cdot X^T$, under the same loss function: 1) The
minimum mean loss in \emph{causal} filtering when $\gamma = \gamma_0$ is equal
to the expected value of the minimum mean loss in \emph{non-causal} filtering
(smoothing) achieved with a channel whose parameter $\gamma$ is uniformly
distributed between 0 and $\gamma_0$. Bridging the two quantities is the mutual
information between $X^T$ and $Y^T$. 2) This relationship between the mean
losses in causal and non-causal filtering holds also in the case where the
filters employed are mismatched, i.e., optimized assuming a law on $X^T$ which
is not the true one. Bridging the two quantities in this case is the sum of the
mutual information and the relative entropy between the true and the mismatched
distribution of $Y^T$. Thus, relative entropy quantifies the excess estimation
loss due to mismatch in this setting.
These results parallel those recently found for the Gaussian channel.
|
1101.0302
|
We present novel tests of pre$-$main-sequence models based on individual
dynamical masses for the M7 binary LSPM J1314+1320AB. Joint analysis of our
Keck adaptive optics astrometric monitoring along with Very Long Baseline Array
radio data from a companion paper yield component masses of $0.0885\pm0.0006$
$M_{\odot}$ and $0.0875\pm0.0010$ $M_{\odot}$ and a parallactic distance of
$17.249\pm0.013$ pc. We also derive component luminosities that are consistent
with the system being coeval at an age of $80.8\pm2.5$ Myr, according to BHAC15
evolutionary models. The presence of lithium is consistent with model
predictions, marking the first time the theoretical lithium depletion boundary
has been tested with ultracool dwarfs of known mass. However, we find that the
average evolutionary model-derived effective temperature ($2950\pm5$ K) is 180
K hotter than we derive from a spectral type$-$$T_{\rm eff}$ relation based on
BT-Settl models ($2770\pm100$ K). We suggest that the dominant source of this
discrepancy is model radii being too small by $\approx$13%. In a test that
mimics the typical application of evolutionary models by observers, we derive
masses on the H-R diagram using the luminosity and BT-Settl temperature. The
estimated masses are $46^{+16}_{-19}$% (2.0$\sigma$) lower than we measure
dynamically and would imply that this is a system of $\approx$50 $M_{\rm Jup}$
brown dwarfs, highlighting the large systematic errors possible when inferring
masses from the H-R diagram. This is first time masses have been measured for
ultracool ($\geq$M6) dwarfs displaying spectral signatures of low gravity.
Based on features in the infrared, LSPM J1314+1320AB appears higher gravity
than typical Pleiades and AB Dor members, opposite the expectation given its
younger age. The components of LSPM J1314+1320AB are now the nearest, lowest
mass pre$-$main-sequence stars with direct mass measurements.
|
1605.07182
|
Observations of recurrent explosive events (EEs) with time scale of 3-5
minutes are reported. These EEs have been observed with the Interface Region
Imaging Spectrograph (IRIS) and have a spatial dimension of $\sim1.5"$ along
the slit. The spectral line profiles of \ion{C}{2}~$1335/1336$ \AA\ and
\ion{Si}{4}~$1394/1403$ \AA\ become highly broadened both in red as well as
blue wings. Several absorption lines on top of the broadened profiles were
identified. In addition, emission lines corresponding to neutral lines such as
\ion{Cl}{1}~1351.66~{\AA}, \ion{C}{1}~1354.29~{\AA}, and
\ion{C}{1}~1355.84~{\AA} were identified. The \ion{C}{1}~1354.29~{\AA}, and
\ion{C}{1}~1355.84 {\AA} lines were found only during the EEs whereas
\ion{Cl}{1}~1351.66~{\AA} broadens during the EEs. The estimated lower limit on
electron number density obtained using the line ratios of \ion{Si}{4} and
\ion{O}{4} is about $10^{13.5}$ cm$^{-3}$, suggesting that the observed events
are most likely occurring at heights corresponding to lower chromosphere. To
the best of our knowledge, for the first time we have detected short-period
variability (30 s and 60--90 s) within the EE bursts. Observations of
photospheric magnetic field underneath EEs indicate that negative polarity
field emerges in the neighbourhood of oppositely directed positive fields which
undergo repetitive reconnection (magnetic flux cancellation) events. The
dynamic changes observed in AIA 1700 \AA, 1600 \AA, \ion{C}{2} 1330 \AA\ and
\ion{Si}{4} 1400 \AA\ intensity images corresponded very well with the
emergence and cancellation of photospheric magnetic field (negative polarity)
on the time scale of 3--5 min. The observations reported here suggests that
these EEs are formed due to magnetic reconnection and are occurring in the
lower chromosphere.
|
1506.05327
|
We present and compare in this paper new photometric redshift catalogs of the
galaxies in three public fields: the NTT Deep Field, the HDF-N and the HDF-S.
Photometric redshifts have been obtained for thewhole sample, by adopting a
$\chi^2$ minimization technique on a spectral library drawn from the Bruzual
and Charlot synthesis models, with the addition of dust and intergalactic
absorption. The accuracy, determined from 125 galaxies with known spectroscopic
redshifts, is $\sigma_z\sim 0.08 (0.3)$ in the redshift intervals $z=0-1.5
(1.5-3.5)$. The global redshift distribution of I-selected galaxies shows a
distinct peak at intermediate redshifts, z~0.6 at I_{AB}<26 and z~0.8 at
I_{AB}<27.5 followed by a tail extending to z~6. We also present for the first
time the redshift distribution of the total IR-selected sample to faint limits
($Ks \leq 21$ and $J\leq22$). It is found that the number density of galaxies
at 1.25<z<1.5 is ~ 0.1 /arcmin^22 at J<=21 and ~1./arcmin^2} at J<22, and drops
to 0.3/arcmin^2 (at J<22) at 1.5<z<2. The HDFs data sets are used to compare
the different results from color selection criteria and photometric redshifts
in detecting galaxies in the redshift range 3.5<z<4.5 Photometric redshifts
predict a number of high z candidates in both the HDF-N and HDF-S that is
nearly 2 times larger than color selection criteria, and it is shown that this
is primarily due to the inclusion of dusty models that were discarded in the
original color selection criteria by Madau et al 1998. In several cases, the
selection of these objects is made possible by the constraints from the IR
bands. Finally, it is shown that galactic M stars may mimic z>5 candidates in
the HDF filter set and that the 4 brightest candidates at $z>5$ in the HDF-S
are indeed most likely M stars. (ABRIDGED)
|
astro-ph/0009158
|
Hydrogen-like light muonic ions, in which one negative muon replaces all the
electrons, are extremely sensitive probes of nuclear structure, because the
large muon mass increases tremendously the wave function overlap with the
nucleus. Using pulsed laser spectroscopy we have measured three 2S-2P
transitions in the muonic helium-3 ion ($\mu^3$He$^+$), an ion formed by a
negative muon and bare helium-3 nucleus. This allowed us to extract the Lamb
shift $E(2P_{1/2}-2S_{1/2})= 1258.598(48)^{\rm exp}(3)^{\rm theo}$ meV, the 2P
fine structure splitting $E_{\rm FS}^{\rm exp} = 144.958(114)$ meV, and the
2S-hyperfine splitting (HFS) $E_{\rm HFS}^{\rm exp} = -166.495(104)^{\rm
exp}(3)^{\rm theo}$ meV in $\mu^3$He$^+$. Comparing these measurements to
theory we determine the rms charge radius of the helion ($^3$He nucleus) to be
$r_h$ = 1.97007(94) fm. This radius represents a benchmark for few nucleon
theories and opens the way for precision tests in $^3$He atoms and $^3$He-ions.
This radius is in good agreement with the value from elastic electron
scattering, but a factor 15 more accurate. Combining our Lamb shift measurement
with our earlier one in $\mu^4$He$^+$ we obtain $r_h^2-r_\alpha^2 =
1.0636(6)^{\rm exp}(30)^{\rm theo}$ fm$^2$ to be compared to results from the
isotope shift measurements in regular He atoms, which are however affected by
long-standing tensions. By comparing $E_{\rm HFS}^{\rm exp}$ with theory we
also obtain the two-photon-exchange contribution (including higher orders)
which is another important benchmark for ab-initio few-nucleon theories aiming
at understanding the magnetic and current structure of light nuclei.
|
2305.11679
|
The impact of cosmic reionization on the Ly$\alpha$ forest power spectrum has
recently been shown to be significant even at low redshifts ($z \sim 2$). This
memory of reionization survives cosmological time scales because high-entropy
mean-density gas is heated to $\sim 3\times10^4$ K by reionization, which is
inhomogeneous, and subsequent shocks from denser regions. In the near future,
the first measurements of the Ly$\alpha$ forest 3D power spectrum will be very
likely achieved by upcoming observational efforts such as the Dark Energy
Spectroscopic Instrument (DESI). In addition to abundant cosmological
information, these observations have the potential to extract the astrophysics
of reionization from the Ly$\alpha$ forest. We forecast, for the first time,
the accuracy with which the measurements of Ly$\alpha$ forest 3D power spectrum
can place constraints on the reionization parameters with DESI. Specifically,
we demonstrate that the constraints on the ionization efficiency, $\zeta$, and
the threshold mass for haloes that host ionizing sources, $m_{\rm turn}$, will
have the $1\sigma$ error at the level of $\zeta = 25.0 \pm 11.6$ and $\log_{10}
(m_{\rm turn}/{\rm M}_\odot) = 8.7^{+0.36}_{-0.70}$, respectively. The
Ly$\alpha$ forest 3D power spectrum will thus provide an independent probe of
reionization, probably even earlier in detection with DESI, with a sensitivity
only slightly worse than the upcoming 21 cm power spectrum measurement with the
Hydrogen Epoch of Reionization Array (HERA), i.e.\ $\sigma_{\rm DESI} /
\sigma_{\rm HERA} \approx 1.5$ for $\zeta$ and $\sigma_{\rm DESI}/\sigma_{\rm
HERA} \approx 2.0$ for $\log_{10}(m_{\rm turn} / $M$_\odot)$. Nevertheless, the
Ly$\alpha$ forest constraint will be improved about three times tighter than
the current constraint from reionization observations with high-z galaxy
priors.
|
2106.14492
|
In the prevailing model of galaxy formation and evolution, the process of gas
accretion onto central galaxies undergoes a transition from cold-dominated to
hot-dominated modes. This shift occurs when the mass of the parent dark matter
halos exceeds a critical threshold known as $M_{shock}$. Moreover, cold gas
usually flows onto central galaxies through filamentary structures, currently
referred to as cold streams. However, the evolution of cold streams in halos
with masses around $M_{shock}$, particularly how they are disrupted, remains
unclear. To address this issue, we conduct a set of idealised hydrodynamic
simulations. Our simulations show that (1) for a gas metallicity
$Z=0.001-0.1Z_{\odot}$, cold stream with an inflow rate $\sim 3\,
\rm{M_{\odot}}/yr$ per each can persist and effectively transport cold and cool
gas to the central region ($< 0.2$ virial radius) in halos with mass $10^{12}\,
\rm{M_{\odot}}$, but is disrupted at a radius around $0.2$ virial radius due to
compression heating for halos with mass $3 \times 10^{12}\, \rm{M_{\odot}}$.
(2) At $z\sim 2$, the maximum halo mass that capable of hosting and sustaining
cold streams $M_{stream}$ is between $1\times 10^{12} \rm{M_{\odot}}$ and
$1.5\times 10^{12}\rm{M_{\odot}}$ for gas metallicity $Z=0.001Z_{\odot}$, while
for a higher gas metallicity $Z=0.1Z_{\odot}$, this value increases to $\sim
1.5\times 10^{12}\rm{M_{\odot}}$. (3) The evolution and ultimate fate of cold
streams are determined primarily by the rivalry between radiative cooling and
compression. Stronger heating due to compression in halos more massive than
$M_{stream}$ can surpass cooling and heat the gas in cold streams to the hot
($\geq 10^6\,$ K) phase.
|
2403.08631
|
Our goal was to characterize the distant gaseous and dust activity of comet
C\2012 S1 (ISON), inbound, from observations of H2O, CO and the dust coma in
the far-infrared and submillimeter domains. In this paper, we report
observations undertaken with the Herschel Space Observatory on 8 & 13 March
2013 (rh = 4.54 - 4.47AU) and with the 30m telescope of Institut de
Radioastronomie Millim\'etrique (IRAM) in March and April 2013 (rh = 4.45 -
4.18 AU). The HIFI instrument aboard Herschel was used to observe the H$_{2}$O
$1_{10}-1_{01}$ line at 557 GHz, whereas images of the dust coma at 70 and 160
{\mu}m were acquired with the PACS instrument. Spectra acquired at the IRAM 30m
telescope cover the CO J(2-1) line at 230.5 GHz. The spectral observations were
analysed with excitation and radiative transfer models. A model of dust thermal
emission taking into account a range of dust sizes is used to analyse the PACS
maps. While H$_{2}$O was not detected in our 8 March 2013 observation, we
derive a sensitive 3 $\sigma$ upper limit of QH$_{2}$O < 3.5 x 10$^{26}$
molecules/s for this date. A marginal 3.2 $\sigma$ detection of CO is found,
corresponding to a CO production rate of QCO = 3.5 x 10$^{27}$ molecules/s. The
Herschel PACS measurements show a clear detection of the coma and tail in both
the 70 {\mu}m and 160 {\mu}m maps. Under the assumption of a 2 km radius
nucleus, we infer dust production rates in the range 10 - 13 kg/s or 40 - 70
kg/s depending on whether a low or high gaseous activity from the nucleus
surface is assumed. We constrain the size distribution of the emitted dust by
comparing PACS 70 and 160 {\mu}m data, and considering optical data. Size
indices between -4 and -3.6 are suggested. The morphology of the tail observed
on 70 {\mu}m images can be explained by the presence of grains with ages older
than 60 days.
|
1311.6452
|
We revisit, in an elementary way, the classical statement of various ``Main
Conjectures'' for $p$-class groups $\mathcal{H}_K$ and $p$-ramified torsion
groups $\mathcal{T}_K$ of abelian fields $K$, in the non semi-simple case $p
\mid [K : \mathbb{Q}]$. The classical ``algebraic'' definition of the $p$-adic
isotopic components, $\mathcal{H}^{\rm alg}{K,\varphi}$, used in the
literature, is inappropriate with respect to analytical formulas. For that
reason we have introduced, in the 1970's, an ``arithmetic'' definition,
$\mathcal{H}^{\rm ar}{K,\varphi}$, in perfect correspondence with all
analytical formulas and giving a natural ``Main Conjecture'', still unproved
for real fields in the non semi-simple case. The two notions coincide for
relative class groups $\mathcal{H}_K^-$ and groups $\mathcal{T}_K$ since, in
$p$-extensions, transfer maps are injective for these groups but not
necessarily for real class groups. Numerical evidence of the gap between the
two notions is given (Examples A.2.2, A.2.3) and PARI calculations corroborate
that the true Real Main Conjecture for $K$ writes on the form $\#
\mathcal{H}^{\rm ar}_{K,\varphi} = \# (\mathcal{E}_K / \hat{\mathcal{E}}_K \,
\mathcal{F}_{\!K})_{\varphi}$, in terms of units $\mathcal{E}_K$,
$\hat{\mathcal{E}}_K$ (units of the strict subfields) and $\mathcal{F}_K$
(Leopoldt's cyclotomic units). A recent approach, conjecturing the capitulation
of $\mathcal{H}_K$ in some auxiliary cyclotomic extensions $K(\mu_\ell^{})$,
proves the difficult real case.
|
2112.02865
|
Terbium doped silicon oxynitride host matrix is suitable for various
applications such as light emitters compatible with CMOS technology or
frequency converter systems for photovoltaic cells. In this study, amorphous
Tb3+ ion doped nitrogen-rich silicon oxynitride (NRSON) thin films were
fabricated using a reactive magnetron co-sputtering method, with various N2
flows and annealing conditions, in order to study their structural and emission
properties. Rutherford backscattering (RBS) measurements and refractive index
values confirmed the silicon oxynitride nature of the films. An electron
microscopy analysis conducted for different annealing temperatures (T A) was
also performed up to 1200 {\textdegree}C. Transmission electron microscopy
(TEM) images revealed two different sublayers. The top layer showed porosities
coming from a degassing of oxygen during deposition and annealing, while in the
region close to the substrate, a multilayer-like structure of SiO2 and Si3N4
phases appeared, involving a spinodal decomposition. Upon a 1200 {\textdegree}C
annealing treatment, a significant density of Tb clusters was detected,
indicating a higher thermal threshold of rare earth (RE) clusterization in
comparison to the silicon oxide matrix. With an opposite variation of the N2
flow during the deposition, the nitrogen excess parameter (Nex) estimated by
RBS measurements was introduced to investigate the Fourier transform infrared
(FTIR) spectrum behavior and emission properties. Different vibration modes of
the Si--N and Si--O bonds have been carefully identified from the FTIR spectra
characterizing such host matrices, especially the 'out-of-phase' stretching
vibration mode of the Si--O bond. The highest Tb3+ photoluminescence (PL)
intensity was obtained by optimizing the N incorporation and the annealing
conditions. In addition, according to these conditions, the integrated PL
intensity variation confirmed that the silicon nitride-based host matrix had a
higher thermal threshold of rare earth clusterization than its silicon oxide
counterpart. Analysis of time-resolved PL intensity versus T A showed the
impact of Tb clustering on decay times, in agreement with the TEM observations.
Finally, PL and PL excitation (PLE) experiments and comparison of the related
spectra between undoped and Tb-doped samples were carried out to investigate
the impact of the band tails on the excitation mechanism of Tb3+ ions.
|
1703.02096
|
During recent years, the renaissance of neural networks as the major machine
learning paradigm and more specifically, the confirmation that deep learning
techniques provide state-of-the-art results for most of computer vision tasks
has been shaking up traditional research in image processing. The same can be
said for research in communities working on applied harmonic analysis,
information geometry, variational methods, etc. For many researchers, this is
viewed as an existential threat. On the one hand, research funding agencies
privilege mainstream approaches especially when these are unquestionably
suitable for solving real problems and for making progress on artificial
intelligence. On the other hand, successful publishing of research in our
communities is becoming almost exclusively based on a quantitative improvement
of the accuracy of any benchmark task. As most of my colleagues sharing this
research field, I am confronted with the dilemma of continuing to invest my
time and intellectual effort on mathematical morphology as my driving force for
research, or simply focussing on how to use deep learning and contributing to
it. The solution is not obvious to any of us since our research is not
fundamental, it is just oriented to solve challenging problems, which can be
more or less theoretical. Certainly, it would be foolish for anyone to claim
that deep learning is insignificant or to think that one's favourite image
processing domain is productive enough to ignore the state-of-the-art. I fully
understand that the labs and leading people in image processing communities
have been shifting their research to almost exclusively focus on deep learning
techniques. My own position is different: I do think there is room for progress
on mathematically grounded image processing branches, under the condition that
these are rethought in a broader sense from the deep learning paradigm. Indeed,
I firmly believe that the convergence between mathematical morphology and the
computation methods which gravitate around deep learning (fully connected
networks, convolutional neural networks, residual neural networks, recurrent
neural networks, etc.) is worthwhile. The goal of this talk is to discuss my
personal vision regarding these potential interactions. Without any pretension
of being exhaustive, I want to address it with a series of open questions,
covering a wide range of specificities of morphological operators and
representations, which could be tackled and revisited under the paradigm of
deep learning. An expected benefit of such convergence between morphology and
deep learning is a cross-fertilization of concepts and techniques between both
fields. In addition, I think the future answer to some of these questions can
provide some insight on understanding, interpreting and simplifying deep
learning networks.
|
2105.01339
|
With the grand desert hypothesis, we have proposed to probe the
supersymmetric Grand Unified Theories (GUTs) at the future proton-proton (pp)
colliders and Hyper-Kamiokande experiment previously. In this paper, we study
the supersymmetric GUTs with gravity mediated supersymmetry breaking in
details. First, considering the dimension-six proton decay via heavy gauge
boson exchange, we point out that we can probe the supersymmetric GUTs with GUT
scale $M_{GUT}$ up to $1.778\times 10^{16}$ GeV at the Hyper-Kamiokande
experiment. Second, for the supersymmetric GUTs with $M_{GUT} \ge 1.0\times
10^{16}$ GeV and $M_{GUT} \ge 1.2\times 10^{16}$ GeV, we show that the upper
bounds on the universal gaugino mass are $7.2$ TeV and 3.5 TeV, respectively,
and thus the corresponding upper bounds on gluino mass are 15 TeV and 8 TeV,
respectively. Also, we shall study the masses for charginos, neutralinos,
squarks, sleptons, and Higgs particles in details. In particular, the
supersymmetric GUTs with $M_{GUT} \leq 1.2\times 10^{16}$ GeV can be probed at
the Hyper-Kamiokande experiment, and the supersymmetric GUTs with $M_{GUT}\ge
1.2\times 10^{16}$ GeV can be probed at the future 100 TeV pp collider
experiments such as the ${\rm FCC}_{\rm hh}$ and SppC via gluino searches.
Thus, the supersymmetric GUTs with gravity mediation can be probed by the ${\rm
FCC}_{\rm hh}$, SppC, and Hyper-Kamiokande experiments. In our previous study,
we have shown that the supersymmetric GUTs with anomaly and gauge mediated
supersymmetry breakings are well within the reaches of these experiments.
Therefore, our proposal provides the concrete scientific goal for the ${\rm
FCC}_{\rm hh}$, SppC, and Hyper-Kamiokande experiments: probing the
supersymmetric GUTs.
|
2208.05257
|
The main purpose of this paper is to study the generalized Hilbert operator
{equation*}
\mathcal{H}_g(f)(z)=\int_0^1f(t)g'(tz)\,dt
{equation*} acting on the weighted Bergman space $A^p_\om$, where the weight
function $\om$ belongs to the class $\R$ of regular radial weights and
satisfies the Muckenhoupt type condition
{equation}\label{Mpconditionaabstract}
\sup_{0\le
r<1}\bigg(\int_{r}^1(\int_t^1\om(s)ds)^{-\frac{p'}{p}}\,dt\bigg)^\frac{p}{p'}
\int_{0}^r(1-t)^{-p}(\int_t^1\om(s)ds)\,dt<\infty. \tag{\dag}
{equation} If $q=p$, the condition on $g$ that characterizes the boundedness
(or the compactness) of $\hg: A^p_\om\to A^q_\om$ depends on $p$ only, but the
situation is completely different in the case $q\ne p$ in which the inducing
weight $\om$ plays a crucial role. The results obtained also reveal a natural
connection to the Muckenhoupt type condition \eqref{Mpconditionaabstract}.
Indeed, it is shown that the classical Hilbert operator (the case
$g(z)=\log\frac{1}{1-z}$ of $\H_g$) is bounded from
$L^p_{\int_{t}^1\om(s)\,ds}([0,1))$ (the natural restriction of $A^p_\om$ to
functions defined on $[0,1)$) to $A^p_\om$ if and only if $\om$ satisfies the
condition \eqref{Mpconditionaabstract}. On the way to these results
decomposition norms for the weighted Bergman space $A^p_\om$ are established.
|
1210.3315
|
We proceed to study the $CP$ asymmetry in the angular distributions of
$\tau\to K_S\pi\nu_\tau$ decays within a general effective field theory
framework including four-fermion operators up to dimension-six. It is found
that, besides the commonly considered scalar-vector interference, the
tensor-scalar interference can also produce a non-zero $CP$ asymmetry in the
angular distributions. Bounds on the effective couplings of the non-standard
scalar and tensor interactions are obtained under the combined constraints from
the measured $CP$ asymmetries and the branching ratio of $\tau^-\to
K_S\pi^-\nu_\tau$ decay, with $\mathrm{Im}[\hat{\epsilon}_S]=-0.008\pm0.027$
and $\mathrm{Im}[\hat{\epsilon}_T]=0.03\pm0.12$, at the scale
$\mu_\tau=2~\mathrm{GeV}$ in the $\mathrm{\overline{MS}}$ scheme. Using the
best-fit values, we also find that the distributions of the $CP$ asymmetries
can deviate significantly from the SM expectation in almost the whole $K\pi$
invariant-mass region. Nevertheless, the current bounds are still plagued by
large experimental uncertainties, but will be improved with more precise
measurements from Belle II as well as the proposed Tera-Z and STCF facilities.
Assuming further that the non-standard scalar and tensor interactions originate
from a weakly-coupled heavy new physics well above the electroweak scale, the
$SU(2)_L$ invariance of the resulting SMEFT Lagrangian would indicate that very
strong limits on $\mathrm{Im}[\hat{\epsilon}_S]$ and
$\mathrm{Im}[\hat{\epsilon}_T]$ could also be obtained from the neutron
electric dipole moment and the $D^0-\bar{D}^0$ mixing. With the bounds from
these processes taken into account, it is then found that, unless there exist
extraordinary cancellations between the new physics contributions, neither the
scalar nor the tensor interaction can produce any significant effects on the
$CP$ asymmetries in the processes considered.
|
2107.12310
|
The near-Earth asteroid (NEA) 2015 TB145 had a very close encounter with
Earth at 1.3 lunar distances on October 31, 2015. We obtained 3-band
mid-infrared observations with the ESO VLT-VISIR instrument and visual
lightcurves during the close-encounter phase. The NEA has a (most likely)
rotation period of 2.939 +/- 0.005 hours and the visual lightcurve shows a
peak-to-peak amplitude of approximately 0.12+/-0.02 mag. We estimate a V-R
colour of 0.56+/-0.05 mag from MPC database entries. Applying different phase
relations to the available R-/V-band observations produced H_R = 18.6 mag
(standard H-G calculations) or H_R = 19.2 mag & H_V = 19.8 mag (via the H-G12
procedure), with large uncertainties of approximately 1 mag. We performed a
detailed thermophysical model analysis by using spherical and ellipsoidal shape
models. The thermal properties are best explained by an equator-on (+/- ~30
deg) viewing geometry during our measurements with a thermal inertia in the
range 250-700 Jm-2s-0.5K-1 (retrograde rotation) or above 500 Jm-2s-0.5K-1
(prograde rotation). We find that the NEA has a minimum size of 625 m, a
maximum size of just below 700 m, and a slightly elongated shape with a/b ~1.1.
The best match to all thermal measurements is found for: (i) Thermal inertia of
900 Jm-2s-0.5K-1; D_eff = 644 m, p_V = 5.5% (prograde rotation); regolith grain
sizes of ~50-100 mm; (ii) thermal inertia of 400 Jm-2s-0.5K-1; D_eff = 667 m,
p_V = 5.1% (retrograde rotation); regolith grain sizes of ~10-20 mm. A
near-Earth asteroid model (NEATM) confirms an object size well above 600 m,
significantly larger than early estimates based on radar measurements. We give
recommendations for improved observing strategies for similar events in the
future.
|
1610.08267
|
As in the case of soliton PDEs in 2+1 dimensions, the evolutionary form of
integrable dispersionless multidimensional PDEs is non-local, and the proper
choice of integration constants should be the one dictated by the associated
Inverse Scattering Transform (IST). Using the recently made rigorous IST for
vector fields associated with the so-called Pavlov equation
$v_{xt}+v_{yy}+v_xv_{xy}-v_yv_{xx}=0$, we have recently esatablished that, in
the nonlocal part of its evolutionary form $v_{t}=
v_{x}v_{y}-\partial^{-1}_{x}\,\partial_{y}\,[v_{y}+v^2_{x}]$, the formal
integral $\partial^{-1}_{x}$ corresponding to the solutions of the Cauchy
problem constructed by such an IST is the asymmetric integral
$-\int_x^{\infty}dx'$. In this paper we show that this results could be guessed
in a simple way using a, to the best of our knowledge, novel integral geometry
lemma. Such a lemma establishes that it is possible to express the integral of
a fairly general and smooth function $f(X,Y)$ over a parabola of the $(X,Y)$
plane in terms of the integrals of $f(X,Y)$ over all straight lines non
intersecting the parabola. A similar result, in which the parabola is replaced
by the circle, is already known in the literature and finds applications in
tomography. Indeed, in a two-dimensional linear tomographic problem with a
convex opaque obstacle, only the integrals along the straight lines
non-intersecting the obstacle are known, and in the class of potentials
$f(X,Y)$ with polynomial decay we do not have unique solvability of the inverse
problem anymore. Therefore, for the problem with an obstacle, it is natural not
to try to reconstruct the complete potential, but only some integral
characteristics like the integral over the boundary of the obstacle. Due to the
above two lemmas, this can be done, at the moment, for opaque bodies having as
boundary a parabola and a circle (an ellipse).
|
1511.04436
|
A long time ago, Brochard and de Gennes predicted the possibility of
significantly decreasing the critical magnetic field of the Fredericksz
transition (the magnetic Fredericksz threshold) in a mixture of nematic liquid
crystals and ferromagnetic particles, the so-called ferronematics. This
phenomenon has rarely been measured, usually due to soft homeotropic anchoring
induced at the nanoparticle surface. Here we present an optical study of the
magnetic Fredericksz transition combined with a light scattering study of the
classical nematic liquid crystal, 5CB, doped with 6 nm diameter magnetic and
non-magnetic nanoparticles. Surprisingly, for both nanoparticles, we observe at
room temperature a net decrease of the threshold field of the Fredericksz
transition at low nanoparticle concentrations, which appears associated with a
coating of the nanoparticles by a brush of polydimethylsiloxane copolymer
chains inducing planar anchoring of the director on the nanoparticle surface.
Moreover the magnetic Fredericksz threshold exhibits non-monotonic behaviour as
a function of the nanoparticle concentration for both types of nanoparticles,
first decreasing down to a value from 23\% to 31\% below that of pure 5CB, then
increasing with a further increase of nanoparticle concentration. This is
interpreted as an aggregation starting at around 0.02 weight fraction that
consumes more isolated nanoparticles than those introduced when the
concentration is increased above $c = 0.05$ weight fraction (volume fraction
$3.5 \times 10^{-2}$). This shows the larger effect of isolated nanoparticles
on the threshold with respect to aggregates. From dynamic light scattering
measurements we deduced that, if the decrease of the magnetic threshold when
the nanoparticle concentration increases is similar for both kinds of
nanoparticles, the origin of this decrease is different for magnetic and
non-magnetic nanoparticles. For non-magnetic nanoparticles, the behavior may be
associated with a decrease of the elastic constant due to weak planar
anchoring. For magnetic nanoparticles there are non-negligible local magnetic
interactions between liquid crystal molecules and magnetic nanoparticles,
leading to an increase of the average order parameter. This magnetic
interaction thus favors an easier liquid crystal director rotation in the
presence of external magnetic field, able to reorient the magnetic moments of
the nanoparticles along with the molecules.
|
1708.00286
|
The precise localization of the repeating fast radio burst (FRB 121102) has
provided the first unambiguous association (chance coincidence probability
$p\lesssim3\times10^{-4}$) of an FRB with an optical and persistent radio
counterpart. We report on optical imaging and spectroscopy of the counterpart
and find that it is an extended ($0.6^{\prime\prime}-0.8^{\prime\prime}$)
object displaying prominent Balmer and [OIII] emission lines. Based on the
spectrum and emission line ratios, we classify the counterpart as a
low-metallicity, star-forming, $m_{r^\prime} = 25.1$ AB mag dwarf galaxy at a
redshift of $z=0.19273(8)$, corresponding to a luminosity distance of 972 Mpc.
From the angular size, the redshift, and luminosity, we estimate the host
galaxy to have a diameter $\lesssim4$ kpc and a stellar mass of
$M_*\sim4-7\times 10^{7}\,M_\odot$, assuming a mass-to-light ratio between 2 to
3$\,M_\odot\,L_\odot^{-1}$. Based on the H$\alpha$ flux, we estimate the star
formation rate of the host to be $0.4\,M_\odot\,\mathrm{yr^{-1}}$ and a
substantial host dispersion measure depth $\lesssim 324\,\mathrm{pc\,cm^{-3}}$.
The net dispersion measure contribution of the host galaxy to FRB 121102 is
likely to be lower than this value depending on geometrical factors. We show
that the persistent radio source at FRB 121102's location reported by Marcote
et al (2017) is offset from the galaxy's center of light by $\sim$200 mas and
the host galaxy does not show optical signatures for AGN activity. If FRB
121102 is typical of the wider FRB population and if future interferometric
localizations preferentially find them in dwarf galaxies with low metallicities
and prominent emission lines, they would share such a preference with long
gamma ray bursts and superluminous supernovae.
|
1701.01100
|
A study on the intermediate polar EX Hya is presented, based on simultaneous
photometry and high dispersion spectroscopic observations, during four
consecutive nights. The strong photometric modulation related to with the
67-min spin period of the primary star is clearly present, as well as the
narrow eclipses associated to the orbital modulation. Since our eclipse timings
have been obtained almost 91,000 cycles since the last reported observations,
we present new linear ephemeris, although we cannot rule out a sinusoidal
variation suggested by previous authors. The system mainly shows double-peaked
H$\alpha$, H$\beta$ and HeI $\lambda$5876 \AA emission lines. From the profile
of the H$\alpha$ line, we find two components; one with a steep rise and
velocities not larger than $\sim$1000 km s$^{-1}$ and another broader component
extending up to $\sim$2000 km s$^{-1}$, which we interpret as coming mainly
from the inner disc. A strong and variable hotspot is found and a stream-like
structure is seen at times. We show that the best solution correspond to $K_1 =
58 \pm 5$ km s$^{-1}$ from H$\alpha$, from the two emission components, which
are both in phase with the orbital modulation. We remark on a peculiar effect
in the radial velocity curve around phase zero, which could be interpreted as a
Rositter-MacLaughlin-like effect, which has been taken into account before
deriving $K_1$. This value is compatible with the values found in
high-resolution both in the ultraviolet and X-ray. We find: $M_{1} = 0.78 \pm
0.03$ M$_{\odot}$, $ M_{2} = 0.10 \pm 0.02$ M$_{\odot}$ and $a = 0.67 \pm 0.01$
R$_{\odot}$. Doppler Tomography has been applied, to construct six Doppler
tomograms for single orbital cycles spanning the four days of observations to
support our conclusions. Our results indicate that EX Hya has a well formed
disc and that the magnetosphere should extend only to about
$3.75\,R_{\rm{WD}}$.
|
1606.03734
|
We report the detection of fulvenallene ($c$-C$_5$H$_4$CCH$_2$) in the
direction of TMC-1 with the QUIJOTE line survey. Thirty rotational transitions
with $K_a$=0,1,2,3 and $J$=9-15 were detected. The best rotational temperature
fitting of the data is 9\,K and a derived column density is
(2.7$\pm$0.3)$\times$10$^{12}$ cm$^{-2}$, which is only a factor of 4.4 below
that of its potential precursor cyclopentadiene ($c$-C$_5$H$_6$), and 1.4--1.9
times higher than that of the ethynyl derivatives of cyclopentadiene. We
searched for fulvene ($c$-C$_5$H$_4$CH$_2$), a CH$_2$ derivative of
cyclopentadiene, for which we derive a 3$\sigma$ upper limit to its column
density of (3.5$\pm$0.5)$\times$10$^{12}$ cm$^{-2}$. Upper limits were also
obtained for toluene (C$_6$H$_5$CH$_3$) and styrene (C$_6$H$_5$C$_2$H$_3$), the
methyl and vinyl derivatives of benzene. Fulvenallene and ethynyl
cyclopentadiene are likely formed in the reaction between cyclopentadiene
($c$-C$_5$H$_6$) and the ehtynyl radical (CCH). However, the bottom-up
gas-phase synthesis of cycles in TMC-1 underestimates the abundance of
cyclopentadiene by two orders of magnitude, which strengthens the need to study
all possible chemical pathways to cyclisation in cold dark cloud environments,
such as TMC-1. However, the inclusion of the reaction between C$_3$H$_3^+$ and
C$_2$H$_4$ produces a good agreement between model and observed abundances.
|
2207.09369
|
Since the main cooling lines of the gas phase are important tracers of the
interstellar medium in Galactic and extragalactic sources, proper and detailed
understanding of their emission, and the ambient conditions of the emitting
gas, is necessary for a robust interpretation of the observations. With high
resolution (7"-9") maps (~3x3 pc^2) of mid-J molecular lines we aim to probe
the physical conditions and spatial distribution of the warm (50 to few hundred
K) and dense gas (n(H_2)>10^5 cm^-3) across the interface region of M17 SW
nebula. We have used the dual color multiple pixel receiver CHAMP+ on APEX
telescope to obtain a 5'.3x4'.7 map of the J=6-5 and J=7-6 transitions of 12CO,
the 13CO J=6-5 line, and the {^3P_2}-{^3P_1} 370 um fine-structure transition
of [C I] in M17 SW. LTE and non-LTE radiative transfer models are used to
constrain the ambient conditions. The warm gas extends up to a distance of ~2.2
pc from the M17 SW ridge. The 13CO J=6-5 and [C I] 370 um lines have a narrower
spatial extent of about 1.3 pc along a strip line at P.A=63 deg. The structure
and distribution of the [C I] {^3P_2}-{^3P_1} 370 um map indicate that its
emission arises from the interclump medium with densities of the order of 10^3
cm^-3. The warmest gas is located along the ridge of the cloud, close to the
ionization front. An LTE approximation indicates that the excitation
temperature of the embedded clumps goes up to ~120 K. The non-LTE model
suggests that the kinetic temperature at four selected positions cannot exceed
230 K in clumps of density n(H_2)~5x10^5 cm^-3, and that the warm T_k>100 K and
dense (n(H_2)>10^4 cm^-3) gas traced by the mid-J 12CO lines represent just
about 2% of the bulk of the molecular gas. The clump volume filling factor
ranges between 0.04 and 0.11 at these positions.
|
0910.4937
|
Let $p$ be a homogeneous polynomial of degree $n$ in $n$ variables,
$p(z_1,...,z_n) = p(Z)$, $Z \in C^{n}$. We call such a polynomial $p$ {\bf
H-Stable} if $p(z_1,...,z_n) \neq 0$ provided the real parts $Re(z_i) > 0, 1
\leq i \leq n$. This notion from {\it Control Theory} is closely related to the
notion of {\it Hyperbolicity} used intensively in the {\it PDE} theory.
The main theorem in this paper states that if $p(x_1,...,x_n)$ is a
homogeneous {\bf H-Stable} polynomial of degree $n$ with nonnegative
coefficients; $deg_{p}(i)$ is the maximum degree of the variable $x_i$, $C_i =
\min(deg_{p}(i),i)$ and $$ Cap(p) = \inf_{x_i > 0, 1 \leq i \leq n}
\frac{p(x_1,...,x_n)}{x_1 ... x_n} $$ then the following inequality holds $$
\frac{\partial^n}{\partial x_1... \partial x_n} p(0,...,0) \geq Cap(p) \prod_{2
\leq i \leq n} (\frac{C_i -1}{C_i})^{C_{i}-1}. $$
This inequality is a vast (and unifying) generalization of the Van der
Waerden conjecture on the permanents of doubly stochastic matrices as well as
the Schrijver-Valiant conjecture on the number of perfect matchings in
$k$-regular bipartite graphs. These two famous results correspond to the {\bf
H-Stable} polynomials which are products of linear forms.
Our proof is relatively simple and ``noncomputational''; it uses just very
basic properties of complex numbers and the AM/GM inequality.
|
0711.3496
|
In this paper, we prove Dahmen and Beukers' conjecture that the number of
integral Lam\'{e} equations with index $n$ modulo scalar equivalence with the
monodromy group dihedral $D_{N}$ of order $2N$ is given by
\[L_{n}(N)=\frac{1}{2}\left( \frac{n(n+1)\Psi(N)}{24}-\left( a_{n}%
\phi(N)+b_{n}\phi(\tfrac{N}{2}) \right) \right) +\frac{2}%
{3}\varepsilon_{n}(N).\] Our main tool is the new pre-modular form
$Z_{r,s}^{(n)}(\tau)$ of weight $n(n+1)/2$ introduced by Lin and Wang
\cite{LW2} and the associated modular form
$M_{n,N}(\tau):=\prod_{(r,s)}Z_{r,s}^{(n)}(\tau)$ of weight
$\Psi(N)n(n+1)/{2}$, where the product runs over all $N$-torsion points $(r,s)$
of exact order $N$. We show that this conjecture is equivalent to the precise
formula of the vanishing order of $M_{n,N}(\tau)$ at infinity:
\[v_{\infty}(M_{n,N}(\tau))=a_{n}\phi(N)+b_{n}\phi( N/2).\] This formula is
extremely hard to prove because the explicit expression of
$Z_{r,s}^{(n)}(\tau)$ is not known for general $n$. Here we succeed to prove it
by using certain Painlev\'{e} VI equations. Our result also indicates that this
conjecture is intimately connected with the problem of counting pole numbers of
algebraic solutions of certain Painlev\'{e} VI equations. The main results of
this paper has been announced in \cite{Lin-CDM}.
|
2105.04734
|
We study the supersymmetric extension of $SO(10)$-inspired thermal
leptogenesis showing the constraints on neutrino parameters and on the reheat
temperature $T_{\rm RH}$ that derive from the condition of successful
leptogenesis from next-to-lightest right handed (RH) neutrinos ($N_2$) decays
and the more stringent ones when independence of the initial conditions (strong
thermal leptogenesis) is superimposed. In the latter case, the increase of the
lightest right-handed neutrino ($N_1$) decay parameters helps the wash-out of a
pre-existing asymmetry and constraints relax compared to the non-supersymmetric
case. We find significant changes especially in the case of large $\tan\beta$
values $(\gtrsim 15)$. In particular, for normal ordering, the atmospheric
mixing angle can now be also maximal. The lightest (ordinary) neutrino mass is
still constrained within the range $10 \lesssim m_1/{\rm meV} \lesssim 30$
(corresponding to $75\lesssim \sum_i m_i/{\rm meV} \lesssim 120$). Inverted
ordering is still disfavoured, but an allowed region satisfying strong thermal
leptogenesis opens up at large $\tan\beta$ values. We also study in detail the
lower bound on $T_{\rm RH}$ finding $T_{\rm RH}\gtrsim 1 \times 10^{10}\,{\rm
GeV}$ independently of the initial $N_2$ abundance. Finally, we propose a new
$N_2$-dominated scenario where the $N_1$ mass is lower than the sphaleron
freeze-out temperature. In this case there is no $N_1$ wash-out and we find
$T_{\rm RH} \gtrsim 1\times 10^{9}\,{\rm GeV}$. These results indicate that
$SO(10)$-inspired thermal leptogenesis can be made compatible with the upper
bound from the gravitino problem, an important result in light of the role
often played by supersymmetry in the quest of a realistic model of fermion
masses.
|
1512.06739
|
The (generalised) Mellin transforms of certain Chebyshev and Gegenbauer
functions based upon the Chebyshev and Gegenbauer polynomials, have polynomial
factors $p_n(s)$, whose zeros lie all on the `critical line' $\Re\,s=1/2$ or on
the real axis (called critical polynomials). The transforms are identified in
terms of combinatorial sums related to H. W. Gould's S:4/3, S:4/2 and S:3/1
binomial coefficient forms. Their `critical polynomial' factors are then
identified as variants of the S:4/1 form, and more compactly in terms of
certain $_3F_2(1)$ hypergeometric functions. Furthermore, we extend these
results to a $1$-parameter family of polynomials with zeros only on the
critical line. These polynomials possess the functional equation
$p_n(s;\beta)=\pm p_n(1-s;\beta)$, similar to that for the Riemann xi function.
It is shown that via manipulation of the binomial factors, these `critical
polynomials' can be simplified to an S:3/2 form, which after normalisation
yields the rational function $q_n(s).$ The denominator of the rational form has
singularities on the negative real axis, and so $q_n(s)$ has the same `critical
zeros' as the `critical polynomial' $p_n(s)$. Moreover as $s\rightarrow \infty$
along the positive real axis, $q_n(s)\rightarrow 1$ from below, mimicking
$1/\zeta(s)$ on the positive real line.
In the case of the Chebyshev parameters we deduce the simpler S:2/1 binomial
form, and with $\mathcal{C}_n$ the $n$th Catalan number, $s$ an integer, we
show that polynomials $4\mathcal{C}_{n-1}p_{2n}(s)$ and
$\mathcal{C}_{n}p_{2n+1}(s)$ yield integers with only odd prime factors. The
results touch on analytic number theory, special function theory, and
combinatorics.
|
1703.09251
|
We revisit the direct sum questions in communication complexity which asks
whether the resource needed to solve $n$ communication problems together is
(approximately) the sum of resources needed to solve these problems separately.
Our work starts with the observation that Dinur and Meir's fortification lemma
can be generalized to a general fortification lemma for a sub-additive measure
over set. By applying this lemma to the case of cover number, we obtain a dual
form of cover number, called "$\delta$-fooling set" which is a generalized
fooling set. Any rectangle which contains enough number of elements from a
$\delta$-fooling set can not be monochromatic.
With this fact, we are able to reprove the classic direct sum theorem of
cover number with a simple double counting argument. Formally, let $S \subseteq
(A\times B) \times O$ and $T \subseteq (P\times Q) \times Z$ be two
communication problems, $ \log \mathsf{Cov}\left(S\times T\right) \geq \log
\mathsf{Cov}\left(S\right) + \log\mathsf{Cov}(T) -\log\log|P||Q|-4.$ where
$\mathsf{Cov}$ denotes the cover number. One issue of current deterministic
direct sum theorems about communication complexity is that they provide no
information when $n$ is small, especially when $n=2$. In this work, we prove a
new direct sum theorem about protocol size which imply a better direct sum
theorem for two functions in terms of protocol size. Formally, let $\mathsf{L}$
denotes complexity of the protocol size of a communication problem, given a
communication problem $F:A \times B \rightarrow
\{0,1\}$, $
\log\mathsf{L}\left(F\times F\right)\geq
\log \mathsf{L}\left(F\right)
+\Omega\left(\sqrt{\log\mathsf{L}\left(F\right)}\right)-\log\log|A||B| -4$. All
our results are obtained in a similar way using the $\delta$-fooling set to
construct a hardcore for the direct sum problem.
|
2208.07730
|
It is well known that any graph admits a crossing-free straight-line drawing
in $\mathbb{R}^3$ and that any planar graph admits the same even in
$\mathbb{R}^2$. For a graph $G$ and $d \in \{2,3\}$, let $\rho^1_d(G)$ denote
the smallest number of lines in $\mathbb{R}^d$ whose union contains a
crossing-free straight-line drawing of $G$. For $d=2$, $G$ must be planar.
Similarly, let $\rho^2_3(G)$ denote the smallest number of planes in
$\mathbb{R}^3$ whose union contains a crossing-free straight-line drawing of
$G$.
We investigate the complexity of computing these three parameters and obtain
the following hardness and algorithmic results.
- For $d\in\{2,3\}$, we prove that deciding whether $\rho^1_d(G)\le k$ for a
given graph $G$ and integer $k$ is ${\exists\mathbb{R}}$-complete.
- Since $\mathrm{NP}\subseteq{\exists\mathbb{R}}$, deciding $\rho^1_d(G)\le
k$ is NP-hard for $d\in\{2,3\}$. On the positive side, we show that the problem
is fixed-parameter tractable with respect to $k$.
- Since ${\exists\mathbb{R}}\subseteq\mathrm{PSPACE}$, both $\rho^1_2(G)$ and
$\rho^1_3(G)$ are computable in polynomial space. On the negative side, we show
that drawings that are optimal with respect to $\rho^1_2$ or $\rho^1_3$
sometimes require irrational coordinates.
- We prove that deciding whether $\rho^2_3(G)\le k$ is NP-hard for any fixed
$k \ge 2$. Hence, the problem is not fixed-parameter tractable with respect to
$k$ unless $\mathrm{P}=\mathrm{NP}$.
|
1607.06444
|
We present a collection of $\mathrm{CP}$-odd observables for the process
$pp\to t\,\left(\rightarrow b {\ell}^+ \nu_{\ell}\right)
\bar{t}\,\left(\rightarrow \bar{b} {\ell}^-{\bar{\nu}}_{\ell}\right)\,H$ that
are linearly dependent on the scalar ($\kappa_t$) and pseudoscalar
($\tilde{\kappa}_t$) top-Higgs coupling and hence sensitive to the
corresponding relative sign. The proposed observables are based on triple
product (TP) correlations that we extract from the expression for the
differential cross section in terms of the spin vectors of the top and antitop
quarks. In order to explore other possibilities, we progressively modify these
TPs, first by combining them, and then by replacing the spin vectors by the
lepton momenta or the $t$ and $\bar{t}$ momenta by their visible parts. We
generate Monte Carlo data sets for several benchmark scenarios, including the
Standard Model ($\kappa_t=1$, $\tilde{\kappa}_t=0$) and two scenarios with
mixed $\mathrm{CP}$ properties ($\kappa_t=1$, $\tilde{\kappa}_t=\pm 1$).
Assuming an integrated luminosity that is consistent with that envisioned for
the High Luminosity Large Hadron Collider, using Monte Carlo-truth and taking
into account only statistical uncertainties, we find that the most promising
observable can disentangle the "$\mathrm{CP}$-mixed" scenarios with an
effective separation of $\sim 19\sigma$. In the case of observables that do not
require the reconstruction of the $t$ and $\bar{t}$ momenta, the power of
discrimination is up to $\sim 13\sigma$ for the same number of events. We also
show that the most promising observables can still disentangle the
$\mathrm{CP}$-mixed scenarios when the number of events is reduced to values
consistent with expectations for the Large Hadron Collider in the near term.
|
1603.03632
|
This paper presents a study of the chemical compositions in cool gas around a
sample of 27 intermediate-redshift galaxies. The sample comprises 13 massive
quiescent galaxies at z=0.40-0.73 probed by QSO sightlines at projected
distances d=3-400 kpc, and 14 star-forming galaxies at z=0.10-1.24 probed by
QSO sightlines at d=8-163 kpc. The main goal of this study is to examine the
radial profiles of the gas-phase Fe/{\alpha} ratio in galaxy halos based on the
observed Fe II to Mg II column density ratios. Because Mg+ and Fe+ share
similar ionization potentials, the relative ionization correction is small in
moderately ionized gas and the observed ionic abundance ratio N(Fe II)/N(Mg II)
places a lower limit to the underlying (Fe/Mg) elemental abundance ratio. For
quiescent galaxies, a median and dispersion of log <N(Fe II)/N(Mg II)>
=-0.06+/-0.15 is found at d<~60 kpc, which declines to log <N(Fe II)/N(Mg II)>
<-0.3 at d>~100 kpc. On the other hand, star-forming galaxies exhibit log <N(Fe
II)/N(Mg II)> =-0.25+/-0.21 at d<~60 kpc and log <N(Fe II)/N(Mg II)>
=-0.9+/-0.4 at larger distances. Including possible differential dust depletion
or ionization correction would only increase the inferred (Fe/Mg) ratio. The
observed N(FeII)/N(Mg II) implies super-solar Fe/{\alpha} ratios in the inner
halo of quiescent galaxies. An enhanced Fe abundance indicates a substantial
contribution by Type Ia supernovae in the chemical enrichment, which is at
least comparable to what is observed in the solar neighborhood or in
intracluster media but differs from young star-forming regions. In the outer
halos of quiescent galaxies and in halos around star-forming galaxies, however,
the observed N(Fe II)/N(Mg II) is consistent with an {\alpha}-element enhanced
enrichment pattern, suggesting a core-collapse supernovae dominated enrichment
history.
|
1611.09874
|
Let $f = P[F]$ denote the Poisson integral of $F$ in the unit disk
$\mathbb{D}$ with $F$ is an absolute continuous in the unit circle $\mathbb{T}$
and $\dot{F}\in L^p(\mathbb{T})$, where $\dot{F}(e^{it}) = \frac{d}{dt}
F(e^{it})$ and $p \in [1,\infty]$. Recently, Chen et al. (J. Geom. Anal., 2021)
extended Zhu's results (J. Geom. Anal., 2020) and proved that (i) if $f$ is a
harmonic mapping and $1 \leq p < \infty$, then $f_z$ and
$\overline{f_{\overline{z}}} \in B^p(\mathbb{D})$, the Bergman spaces of
$\mathbb{D}$. Moreover, (ii) under additional conditions as $f$ being harmonic
quasiregular mapping in \cite{Zhu} or $f$ being harmonic elliptic mapping in
\cite{CPW}, they proved that $f_z$ and $\overline{f_{\overline{z}}}\in
H^p(\mathbb{D})$, the Hardy space of $\mathbb{D}$, for $1 \leq p \leq \infty$.
The aim of this paper is to extend these results by showing that (ii) holds for
$p\in(1,\infty)$ without any extra conditions and for $p=1$ or $p=\infty$,
$f_z$ and $\overline{f_{\bar{z}}}\in H^p(\mathbb{D})$ if and only if
$H(\dot{F})\in L^p(\mathbb{T})$, the Hilbert transform of $\dot{F}$ and in that
case, it yields $zf_z=P[\frac{\dot{F}+iH(\dot{F})}{2i}]$.
|
2302.09623
|
In the article [GS96], Gillet and Soul\'e define a weight complex on the
category of Voevodsky motives over a field of characteristic 0. In [Bon07],
Bondarko generalizes this construction for any f-category with a bounded weight
structure, as is the case for Beilinson motives (following Cisinski-D\'eglise ;
[CD09]). The first purpose of this note is to generalize [GS96, thm. 2] in the
world of Beilinson motives. This done, we will naturally be led to define the
motivic Euler characteristic dual to that considered by Bondarko in [Bon10].
This fact will motivate the second line of this note : proving that the duality
operation exchanges the weight as is the case for t-structure ([BBD,
5.1.14.(iii)]). ----- Dans l'article [GS96], Gillet et Soul\'e d\'efinissent un
complexe de poids sur la cat\'egorie des motifs de Voevodsky d\'efinie sur un
corps de caract\'eristique 0. Dans [Bon07], Bondarko g\'en\'eralise cette
construction pour toute f-cat\'egorie munie d'une structure de poids born\'ee,
comme c'est le cas pour les motifs de Beilinson (suivant Cisinski-D\'eglise ;
[CD09]). Le premier but de cette note est de g\'en\'eraliser [GS96, thm. 2]
dans le monde des motifs de Beilinson. Ceci fait, on sera naturellement amen\'e
\`a d\'efinir la caract\'eristique d'Euler motivique duale \`a celle
consid\'er\'ee par Bondarko dans [Bon10]. Ce fait motivera le second axe de
cette note : prouver que l'op\'eration de dualit\'e \'echange les poids comme
c'est le cas pour les t-structures ([BBD, 5.1.14.(iii)]).
|
1010.5469
|
We present the discovery of a nuclear transient with the Caltech-NRAO Stripe
82 Survey (CNSS), a dedicated radio transient survey carried out with the Karl
G. Jansky Very Large Array (VLA). This transient, CNSS J001947.3+003527,
exhibited a turn-on over a timescale of $\lesssim$1 yr, increasing in flux
density at 3 GHz from $<0.14$ mJy in 2014 February to $4.4\pm0.1$ mJy in 2015
March, reaching a peak luminosity of $5\times10^{28} \text{erg s}^{-1}
\text{Hz}^{-1}$ around 2015 October. The association of CNSS J0019+00 with the
nucleus (Gaia and our VLBI positions are consistent to within 1 pc) of a nearby
S0 Seyfert galaxy at 77 Mpc, together with the radio spectral evolution,
implies that this transient is most likely a tidal disruption event (TDE). Our
equipartition analysis indicates the presence of a $\sim$15,000 km s$^{-1}$
outflow, having energy $\sim$10$^{49}$ erg. We derive the radial density
profile for the circumnuclear material in the host galaxy to be proportional to
$R^{-2.5}$. All of these properties suggest resemblance with radio-detected
thermal TDEs like ASASSN-14li and XMMSL1 J0740-85. No significant X-ray or
optical emission is detected from CNSS J0019+00, although this may simply be
due to the thermal emission being weak during our late-time follow-up
observations. From the CNSS survey we have obtained the first unbiased
measurement of the rate of radio TDEs, $R(>500 \mu{\rm Jy})$ of about
$2\times10^{-3}$ deg$^{-2}$, or equivalently a volumetric rate of about 10
Gpc$^{-3}$ yr$^{-1}$. This rate implies that all-sky radio surveys such as the
VLA Sky Survey and those planned with ASKAP, will find many tens of radio TDEs
over the next few years.
|
1910.11912
|
We present a framework to obtain photometric redshifts (photo-zs) for
gamma-ray burst afterglows. Using multi-band photometry from GROND and
Swift/UVOT, photo-zs are derived for five GRBs for which spectroscopic
redshifts are not available. We use UV/optical/NIR data and synthetic
photometry based on afterglow observations and theory to derive the photometric
redshifts of GRBs and their accuracy. Taking into account the afterglow
synchrotron emission properties, we investigate the application of photometry
to derive redshifts in a theoretical range between z~1 and z~12. The
measurement of photo-zs for GRB afterglows provides a quick, robust and
reliable determination of the distance scale to the burst, particularly in
those cases where spectroscopic observations in the optical/NIR range cannot be
obtained. Given a sufficiently bright and mildly reddened afterglow, the
relative photo-z accuracy is better than 10% between z=1.5 and z~7 and better
than 5% between z=2 and z=6. We detail the approach on 5 sources without
spectroscopic redshifts observed with UVOT on-board Swift and/or GROND. The
distance scale to those same afterglows is measured to be
$z=4.31^{+0.14}_{-0.15}$ for GRB 080825B, $z=2.13^{+0.14}_{-0.20}$ for GRB
080906, $z=3.44^{+0.15}_{-0.32}$ for GRB 081228, $z=2.03^{+0.16}_{-0.14}$ for
GRB 081230 and $z=1.28^{+0.16}_{-0.15}$ for GRB 090530. Combining the response
from UVOT with ground-based observatories and in particular GROND operating in
the optical/NIR wavelength regime, reliable photo-zs can be obtained from z ~
1.0 out to z ~ 10, and possibly even at higher redshifts in some favorable
cases, provided that these GRBs exist, are localized quickly, have sufficiently
bright afterglows and are not heavily obscured.
|
1011.1205
|
Let $g$ be locally homogeneous (LH) Riemannian metric on a differentiable
compact manifold $M$, and $K$ be a compact Lie group endowed with an $\mathrm
{ad}$-invariant inner product on its Lie algebra $\mathfrak{k}$. A connection
$A$ on a principal $K$-bundle $p:P\to M$ on $M$ is locally homogeneous if for
any two points $x_1$, $x_2\in M$ there exists an isometry $\varphi:U_1\to U_2$
between open neighborhoods $U_i\ni x_i$ which sends $x_1$ to $x_2$ and admits a
$\varphi$-covering bundle isomorphism preserving the connection $A$. This
condition is invariant under the action of the automorphism group (gauge group)
of the bundle, so the classification problem for LH connections leads to an
interesting moduli problem: for fixed objects $(M,g,K)$ as above describe
geometrically the moduli space of all LH connections on principal $K$-bundles
on $M$ (up to bundle isomorphisms). Note that if $A$ is LH, then the associated
connection metric $g_A$ on $P$ is locally homogenous, so it defines a geometric
structure (in the sense of Thurston) on the total space of the bundle.
Therefore this moduli problem is related to the classification of LH
(geometric) Riemannian manifolds which admit a Riemannian submersion onto the
given manifold $M$.
Omitting the details, our moduli problem concerns the classification of
geometric fibre bundles over a given geometric base. We develop a general
method for describing moduli spaces of LH connections on a given base. Using
our method we give explicit descriptions of these moduli spaces when the base
manifold is a hyperbolic Riemann surface $(M,g)$ and $K\in\{S^1,PU(2)\}$. The
case $K=S^1$ leads to a new construction of the moduli spaces of Yang-Mills
$S^1$-connections on hyperbolic Riemann surfaces, and the case $K=PU(2)$ leads
to a one-parameter family of compact, 5-dimensional geometric manifolds, which
we study in detail.
|
1811.07995
|
We present a detailed analysis from new multi-wavelength observations of the
exceptional galaxy cluster ACT-CL J0102-4915 "El Gordo," likely the most
massive, hottest, most X-ray luminous and brightest Sunyaev-Zeldovich (SZ)
effect cluster known at z>0.6. The Atacama Cosmology Telescope collaboration
discovered El Gordo as the most significant SZ decrement in a sky survey area
of 755 deg^2. Our VLT/FORS2 spectra of 89 member galaxies yield a cluster
redshift, z=0.870, and velocity dispersion, s=1321+/-106 km/s. Our Chandra
observations reveal a hot and X-ray luminous system with an integrated
temperature of Tx=14.5+/-1.0 keV and 0.5-2.0 keV band luminosity of
Lx=(2.19+/-0.11)x10^45 h70^-2 erg/s. We obtain several statistically consistent
cluster mass estimates; using mass scaling relations with velocity dispersion,
X-ray Yx, and integrated SZ, we estimate a cluster mass of
M200a=(2.16+/-0.32)x10^15 M_sun/h70. The Chandra and VLT/FORS2 optical data
also reveal that El Gordo is undergoing a major merger between components with
a mass ratio of approximately 2 to 1. The X-ray data show significant
temperature variations from a low of 6.6+/-0.7 keV at the merging low-entropy,
high-metallicity, cool core to a high of 22+/-6 keV. We also see a wake in the
X-ray surface brightness caused by the passage of one cluster through the
other. Archival radio data at 843 MHz reveal diffuse radio emission that, if
associated with the cluster, indicates the presence of an intense double radio
relic, hosted by the highest redshift cluster yet. El Gordo is possibly a
high-redshift analog of the famous Bullet Cluster. Such a massive cluster at
this redshift is rare, although consistent with the standard L-CDM cosmology in
the lower part of its allowed mass range. Massive, high-redshift mergers like
El Gordo are unlikely to be reproduced in the current generation of numerical
N-body cosmological simulations.
|
1109.0953
|
We present near-infrared (NIR) broadband (0.80--2.42 $\mu$m) spectroscopy of
two low mass X-ray binaries: V404 Cyg and Cen X-4. One important parameter
required in the determination of the mass of the compact objects in these
systems is the binary inclination. We can determine the inclination by modeling
the ellipsoidal modulations of the Roche-lobe filling donor star, but the
contamination of the donor star light from other components of the binary,
particularly the accretion disk, must be taken into account. To this end, we
determined the donor star contribution to the infrared flux by comparing the
spectra of V404 Cyg and Cen X-4 to those of various field K-stars of known
spectral type. For V404 Cyg, we determined that the donor star has a spectral
type of K3 III. We determined the fractional donor contribution to the NIR flux
in the H- and K-bands as $0.98 \pm .05$ and $0.97 \pm .09$, respectively. We
remodeled the H-band light curve from \citet{sanwal1996} after correcting for
the donor star contribution to obtain a new value for the binary inclination.
From this, we determined the mass of the black hole in V404 Cyg to be $M_{BH}=
9.0^{+.2}_{-.6}M_{\odot}$. We performed the same spectral analysis for Cen X-4
and found the spectral type of the donor star to be in the range K5 -- M1V. The
donor star contribution in Cen X-4 is $0.94\pm.14$ in the H-band while in the
K-band, the accretion disk can contribute up to 10% of the infrared flux. We
remodeled the H-band light curve from \citet{shahbaz1993}, again correcting for
the fractional contribution of the donor star to obtain the inclination. From
this, we determined the mass of the neutron star as $M_{NS}=
1.5^{+.1}_{-.4}M_{\odot}$. However, the masses obtained for both systems should
be viewed with some caution since contemporaneous light curve and spectral data
are required to obtain definitive masses.
|
1004.5358
|
We investigate the asymmetry of the scattering cross section of radiation
around Ly$\alpha$ by atomic hydrogen, which may be applied to analyses of
scattering media with high column neutral hydrogen densities including damped
Ly$\alpha$ absorption systems of quasars. The exact scattering cross section is
given by the Kramers-Heisenberg formula obtained from the fully quantum
mechanical second-order time dependent theory, where, in the case of hydrogen,
each matrix element is given in a closed analytical form. The asymmetric
deviation of the scattering cross section from the Lorentzian near the line
center is computed by expanding the Kramers-Heisenberg formula in terms of
$\Delta\omega /\omega_{Ly\alpha}$,where $\omega_{Ly\alpha}$ is the angular
frequency of the Ly$\alpha$ transition and $\Delta\omega$ is the deviation of
incident radiation from $\omega_{Ly\alpha}$. To the first order of
$\Delta\omega/\omega_{Ly\alpha}$, we obtain $\sigma(\omega) = \sigma_T (0.5
f_{12} \omega_{Ly\alpha}/\Delta\omega)^2 (1-1.79\Delta\omega /
\omega_{Ly\alpha})$, where $\sigma_T$ is the Thomson scattering cross section
and $f_{12}=0.4162$ is the oscillator strength for the Ly$\alpha$ transition.
With this deviation, the line center of the damped wing profile apparently
shifts blueward of the true Ly$\alpha$ line center. In the case of a
dampedLy$\alpha$ system with a H I column density $5\times 10^{21}{\rm
cm^{-2}}$, the apparent line center shift relative to the true center amounts
to $0.2{\rm \AA}$ resulting in an underestimation of redshift by $\Delta z\sim
10^{-4}$. A measurable underestimation by an amount of $\Delta z\sim 10^{-3}$
is expected for absorbing systems with $N_{HI}\ge 4\times 10^{22}{\rm
cm^{-2}}$.
|
astro-ph/0308083
|
Using 281 pb^-1 of data collected with the CLEO-c detector, we report on
first observations and new measurements of Cabibbo-suppressed decays of D
mesons to 2, 3, 4, and 5 pions. Branching fractions of previously unobserved
modes are measured to be: B(D^0\to
pi^+pi^-pi^0pi^0)=(9.9\pm0.6\pm0.7\pm0.2\pm0.1)x10^-3,
B(D^0\to\pi^+\pi^+\pi^-\pi^-\pi^0)=(4.1\pm0.5\pm0.2\pm0.1\pm0.0)x10^-3,
B(D^+\to\pi^+\pi^0\pi^0)=(4.8\pm0.3\pm0.3\pm0.2)x10^-3,
B(D^+\to\pi^+\pi^+\pi^-\pi^0)=(11.6\pm0.4\pm0.6\pm0.4)x10^-3,
B(D^0\to\eta\pi^0)=(0.62\pm0.14\pm0.05\pm0.01\pm0.01)x10^-3, and
B(D^0\to\omega\pi^+\pi^-)=(1.7\pm0.5\pm0.2\pm0.0\pm0.0)x10^-3. The
uncertainties are from statistics, experimental systematics, normalization and
CP correlations (for D^0 modes only). Improvements in other multi-pion decay
modes are also presented. The D-->pi pi rates allow us to extract the ratio of
isospin amplitudes A(Delta I=3/2)/A(\Delta
I=1/2)=0.420\pm0.014(stat)\pm0.016(syst) and the strong phase shift of
delta_I=(86.4+-2.8+-3.3) degrees, which is quite large and now more precisely
determined.
|
hep-ex/0512063
|
For a strongly elliptic pseudodifferential operator $L$ of order $2a$
($0<a<1$) with real kernel, we show an integration-by-parts formula for
solutions of the homogeneous Dirichlet problem, in the model case where the
operator is $x$-independent with homogeneous symbol, considered on the
halfspace $R^n_+$. The new aspect compared to $(-\Delta )^a$ is that $L$ is
nonsymmetric, having both an even and an odd part. Hence it satisfies a $\mu
$-transmission condition where generally $\mu \ne a$.
We present a complex method, relying on a factorization in factors
holomorphic in $\xi_n$ in the lower or upper complex halfplane, using
order-reducing operators combined with a decomposition principle originating
from Wiener and Hopf. This is in contrast to a real, computational method
presented very recently by Dipierro, Ros-Oton, Serra and Valdinoci. Our method
allows $\mu $ in a larger range than they consider.
Another new contribution is the (model) study of "large" solutions of
nonhomogeneous Dirichlet problems when $\mu >0$. Here we deduce a "halfways
Green's formula" for $L$: $$ \int_{R^n_+} Lu\,\bar
v\,dx-\int_{R^n_+}u\,\overline{ L^*v}\,dx=c\int_{R^{n-1}}\gamma_0(u/x_n^{\mu -1
})\,{\gamma_0(\bar v/x_n^{\mu ^*})}\, dx', $$ when $u$ solves a nonhomogeneous
Dirichlet problem for $L$, and $v$ solves a homogeneous Dirichlet problem for
$L^*$; $\mu ^*=2a-\mu $. Finally, we show a full Green's formula, when both $u$
and $v$ solve nonhomogeneous Dirichlet problems; here both Dirichlet and
Neumann traces of $u$ and $v$ enter, as well as a first-order
pseudodifferential operator over the boundary.
|
2012.13964
|
We analyze two classic variants of the Traveling Salesman Problem using the
toolkit of fine-grained complexity. Our first set of results is motivated by
the Bitonic TSP problem: given a set of $n$ points in the plane, compute a
shortest tour consisting of two monotone chains. It is a classic
dynamic-programming exercise to solve this problem in $O(n^2)$ time. While the
near-quadratic dependency of similar dynamic programs for Longest Common
Subsequence and Discrete Frechet Distance has recently been proven to be
essentially optimal under the Strong Exponential Time Hypothesis, we show that
bitonic tours can be found in subquadratic time. More precisely, we present an
algorithm that solves bitonic TSP in $O(n \log^2 n)$ time and its bottleneck
version in $O(n \log^3 n)$ time. Our second set of results concerns the popular
$k$-OPT heuristic for TSP in the graph setting. More precisely, we study the
$k$-OPT decision problem, which asks whether a given tour can be improved by a
$k$-OPT move that replaces $k$ edges in the tour by $k$ new edges. A simple
algorithm solves $k$-OPT in $O(n^k)$ time for fixed $k$. For 2-OPT, this is
easily seen to be optimal. For $k=3$ we prove that an algorithm with a runtime
of the form $\tilde{O}(n^{3-\epsilon})$ exists if and only if All-Pairs
Shortest Paths in weighted digraphs has such an algorithm. The results for
$k=2,3$ may suggest that the actual time complexity of $k$-OPT is
$\Theta(n^k)$. We show that this is not the case, by presenting an algorithm
that finds the best $k$-move in $O(n^{\lfloor 2k/3 \rfloor + 1})$ time for
fixed $k \geq 3$. This implies that 4-OPT can be solved in $O(n^3)$ time,
matching the best-known algorithm for 3-OPT. Finally, we show how to beat the
quadratic barrier for $k=2$ in two important settings, namely for points in the
plane and when we want to solve 2-OPT repeatedly.
|
1607.02725
|
Measurements of gas mass in protoplanetary gas disks form the basis for
estimating the conditions of planet formation. Among the most important
constraints derived from disk diagnostics are the abundances of gas-phase
species critical for understanding disk chemistry. Towards this end, we present
direct line-of-sight measurements of H$_{2}$ and CO, employing UV absorption
spectroscopy from $HST$-COS to characterize disk composition, molecular
excitation temperatures, and spatial distribution in the circumstellar material
around the Herbig Ae stars HK Ori and T Ori. We observe strong CO (N(CO) =
10$^{15.5}$ cm$^{-2}$; T$_{rot}$(CO) = 19 K) and H$_{2}$ (N(H$_{2}$) =
10$^{20.34}$ cm$^{-2}$; T$_{rot}$(H$_{2}$) = 141 K) absorption towards HK Ori
with a CO/H$_{2}$ ratio ($\equiv$ N(CO)/N(H$_{2}$)) =
1.3$^{+1.6}_{-0.7}$~$\times$~10$^{-5}$. These measurements place direct
empirical constraints on the CO-to-H$_{2}$ conversion factor in the disk around
a Herbig Ae star for the first time, although there is uncertainty concerning
the exact viewing geometry of the disk. The spectra of T Ori show CO (N(CO) =
10$^{14.9}$ cm$^{-2}$; T$_{rot}$(CO) = 124 K) absorption. Interestingly, we do
not detect any H$_{2}$ absorption towards this star (N(H$_{2}$) $<$ 10$^{15.9}$
cm$^{-2}$). We discuss a potential scenario for the detection of CO without
H$_{2}$, which deserves further investigation. The low abundance ratio measured
around HK Ori suggests significant depletion of CO in the circumstellar gas,
which conforms with the handful of other recent CO abundance measurements in
protoplanetary disks.
|
2102.12558
|
We study approximate-near-neighbor data structures for time series under the
continuous Fr\'echet distance. For an attainable approximation factor $c>1$ and
a query radius $r$, an approximate-near-neighbor data structure can be used to
preprocess $n$ curves in $\mathbb{R}$ (aka time series), each of complexity
$m$, to answer queries with a curve of complexity $k$ by either returning a
curve that lies within Fr\'echet distance $cr$, or answering that there exists
no curve in the input within distance $r$. In both cases, the answer is
correct. Our first data structure achieves a $(5+\epsilon)$ approximation
factor, uses space in $n\cdot \mathcal{O}\left({\epsilon^{-1}}\right)^{k} +
\mathcal{O}(nm)$ and has query time in $\mathcal{O}\left(k\right)$. Our second
data structure achieves a $(2+\epsilon)$ approximation factor, uses space in
$n\cdot \mathcal{O}\left(\frac{m}{k\epsilon}\right)^{k} + \mathcal{O}(nm)$ and
has query time in $\mathcal{O}\left(k\cdot 2^k\right)$. Our third positive
result is a probabilistic data structure based on locality-sensitive hashing,
which achieves space in $\mathcal{O}(n\log n+nm)$ and query time in
$\mathcal{O}(k\log n)$, and which answers queries with an approximation factor
in $\mathcal{O}(k)$. All of our data structures make use of the concept of
signatures, which were originally introduced for the problem of clustering time
series under the Fr\'echet distance. In addition, we show lower bounds for this
problem. Consider any data structure which achieves an approximation factor
less than $2$ and which supports curves of arclength up to $L$ and answers the
query using only a constant number of probes. We show that under reasonable
assumptions on the word size any such data structure needs space in
$L^{\Omega(k)}$.
|
2008.09406
|
Matrix scaling is a simple to state, yet widely applicable linear-algebraic
problem: the goal is to scale the rows and columns of a given non-negative
matrix such that the rescaled matrix has prescribed row and column sums.
Motivated by recent results on first-order quantum algorithms for matrix
scaling, we investigate the possibilities for quantum speedups for classical
second-order algorithms, which comprise the state-of-the-art in the classical
setting.
We first show that there can be essentially no quantum speedup in terms of
the input size in the high-precision regime: any quantum algorithm that solves
the matrix scaling problem for $n \times n$ matrices with at most $m$ non-zero
entries and with $\ell_2$-error $\varepsilon=\widetilde\Theta(1/m)$ must make
$\widetilde\Omega(m)$ queries to the matrix, even when the success probability
is exponentially small in $n$. Additionally, we show that for
$\varepsilon\in[1/n,1/2]$, any quantum algorithm capable of producing
$\frac{\varepsilon}{100}$-$\ell_1$-approximations of the row-sum vector of a
(dense) normalized matrix uses $\Omega(n/\varepsilon)$ queries, and that there
exists a constant $\varepsilon_0>0$ for which this problem takes
$\Omega(n^{1.5})$ queries.
To complement these results we give improved quantum algorithms in the
low-precision regime: with quantum graph sparsification and amplitude
estimation, a box-constrained Newton method can be sped up in the
large-$\varepsilon$ regime, and outperforms previous quantum algorithms. For
entrywise-positive matrices, we find an $\varepsilon$-$\ell_1$-scaling in time
$\widetilde O(n^{1.5}/\varepsilon^2)$, whereas the best previously known bounds
were $\widetilde O(n^2\mathrm{polylog}(1/\varepsilon))$ (classical) and
$\widetilde O(n^{1.5}/\varepsilon^3)$ (quantum).
|
2109.15282
|
We report novel cosmological constraints obtained from cosmic voids in the
final BOSS DR12 dataset. They arise from the joint analysis of geometric and
dynamic distortions of average void shapes (i.e., the stacked void-galaxy
cross-correlation function) in redshift space. Our model uses tomographic
deprojection to infer real-space void profiles and self-consistently accounts
for the Alcock-Paczynski (AP) effect and redshift-space distortions (RSD)
without any prior assumptions on cosmology or structure formation. It is
derived from first physical principles and provides an extremely good
description of the data at linear perturbation order. We validate this model
with the help of mock catalogs and apply it to the final BOSS data to constrain
the RSD and AP parameters $f/b$ and $D_AH/c$, where $f$ is the linear growth
rate, $b$ the linear galaxy bias, $D_A$ the comoving angular diameter distance,
$H$ the Hubble rate, and $c$ the speed of light. In addition, we include two
nuisance parameters in our analysis to marginalize over potential systematics.
We obtain $f/b=0.540\pm0.091$ and $D_AH/c=0.588\pm0.004$ from the full void
sample at a mean redshift of $z=0.51$. In a flat $\Lambda$CDM cosmology, this
implies $\Omega_\mathrm{m}=0.312\pm0.020$ for the present-day matter density
parameter. When we use additional information from the survey mocks to
calibrate our model, these constraints improve to $f/b=0.347\pm0.023$,
$D_AH/c=0.588\pm0.003$, and $\Omega_\mathrm{m}=0.310\pm0.017$. However, we
emphasize that the calibration depends on the specific model of cosmology and
structure formation assumed in the mocks, so the calibrated results should be
considered less robust. Nevertheless, our calibration-independent constraints
are among the tightest of their kind to date, demonstrating the immense
potential of using cosmic voids for cosmology in current and future data.
|
2007.07895
|
In this work, a flavour theory of a neutrino mass model based on $ A_{4} $
symmetry is considered to explain the phenomenology of neutrino mixing. The
spontaneous symmetry breaking of $ A_{4} $ symmetry in this model leads to
tribimaximal mixing in the neutrino sector at a leading order. We consider the
effect of $ Z_{2} \times Z_{2}$ invariant perturbations in neutrino sector and
find the allowed region of correction terms in the perturbation matrix that is
consistent with 3$ \sigma $ ranges of the experimental values of the mixing
angles. We study the entanglement of this formalism on the other
phenomenological observables, such as $ \delta_{CP} $ phase, the neutrino
oscillation probability $ P(\nu_{\mu}\rightarrow \nu_{e} )$, the effective
Majorana mass $ |m_{ee} |$ and $ |m^{eff}_{\nu e} |$. A $ Z_{2} \times Z_{2}$
invariant perturbations in this model is introduced in the neutrino sector
which leads to testable predictions of $ \theta_{13} $ and CP violation. By
changing the magnitudes of perturbations in neutrino sector, one can generate
viable values of $ \delta_{CP} $ and neutrino oscillation parameters. Next we
investigate the feasibility of charged lepton flavour violation in type-I
seesaw models with leptonic flavour symmetries at high energy that leads to
tribimaximal neutrino mixing. We consider an effective theory with an $A_{4}
\times Z_{2} \times Z_{2} $ symmetry, which after spontaneous symmetry breaking
at high scale which is much higher than the electroweak scale leads to charged
lepton flavour violation processes once the heavy Majorana neutrino mass
degeneracy is lifted either by renormalization group effects or by a soft
breaking of the $ A_{4} $ symmetry. In this context the implications for
charged lepton flavour violation processes like $ \mu \rightarrow e \gamma $, $
\tau \rightarrow e \gamma $, $ \tau \rightarrow \mu \gamma $ are discussed.
|
2106.12503
|
Two very closely related Rahman polynomials are constructed explicitly as the
left eigenvectors of certain multi-dimensional discrete time Markov chain
operators $K_n^{(i)}({\boldsymbol x},{\boldsymbol y};N)$, $i=1,2$. They are
convolutions of an $n+1$-nomial distribution $W_n({\boldsymbol x};N)$ and an
$n$-tuple of binomial distributions $\prod_{i}W_1(x_i;N)$. The one for the
original Rahman polynomials is $K_n^{(1)}({\boldsymbol x},{\boldsymbol y};N)
=\sum_{\boldsymbol z}W_n({\boldsymbol x}-{\boldsymbol z};N-\sum_{i}z_i)
\prod_{i}W_1(z_i;y_i)$. The closely related one is \ $K_n^{(2)}({\boldsymbol
x},{\boldsymbol y};N) =\sum_{\boldsymbol z}W_n({\boldsymbol x}-{\boldsymbol
z};N-\sum_{i}y_i) \prod_{i}W_1(z_i;y_i)$. The original Markov chain was
introduced and discussed by Hoare, Rahman and Gr\"{u}nbaum as a multivariable
version of the known soluble single variable one. The new one is a
generalisation of that of Odake and myself. The anticipated solubility of the
model gave Rahman polynomials the prospect of the first multivariate
hypergeometric function of Aomoto-Gelfand type connected with solvable
dynamics. The promise is now realised. The $n^2$ system parameters
$\{u_{i\,j}\}$ of the Rahman polynomials are completely determined. These
$u_{i\,j}$'s are irrational functions of the original system parameters, the
probabilities of the multinomial and binomial distributions.
|
2310.17853
|
The iterative proportional fitting procedure, introduced in 1937 by Kruithof,
aims to adjust the elements of an array to satisfy specified row and column
sums. Given a rectangular non-negative matrix $X_0$ and two positive marginals
$a$ and $b$, the algorithm generates a sequence of matrices $(X_n)$ starting at
$X_0$, supposed to converge to a biproportional fitting, that is, to a matrix
$Y$ whose marginals are $a$ and $b$ and of the form $Y=D_1X_0D_2$, for some
diagonal matrices $D_1$ and $D_2$ with positive diagonal entries.
When a biproportional fitting does exist, it is unique and the sequence
$(X_n)$ converges to it at an at least geometric rate. More generally, when
there exists some matrix with marginal $a$ and $b$ and with support included in
the support of $X_0$, the sequence $(X_n)$ converges to the unique matrix whose
marginals are $a$ and $b$ and which can be written as a limit of matrices of
the form $D_1X_0D_2$. In the opposite case, the sequence $(X_n)$ diverges but
both subsequences $(X_{2n})$ and $(X_{2n+1})$ converge.
In the present paper, we use a new method to prove again these results and
determine the two limit-points in the case of divergence. Our proof relies on a
new convergence theorem for backward infinite products $\cdots M_2M_1$ of
stochatic matrices $M_n$, with diagonal entries $M_n(i,i)$ bounded away from
$0$ and with bounded ratios $M_n(j,i)/M_n(i,j)$. This theorem generalizes
Lorenz' stabilization theorem.
We also provide an alternative proof of Touric and Nedi\'c's theorem on
backward infinite products of doubly-stochatic matrices, with diagonal entries
bounded away from $0$. In both situations, we improve slightly the conclusion,
since we establish not only the convergence of the sequence $(M_n \cdots M_1)$,
but also its finite variation.
|
1606.09126
|
We introduce a family of random measures $M_{H,T} (d t)$, namely log S-fBM,
such that, for $H>0$, $M_{H,T}(d t) = e^{\omega_{H,T}(t)} d t$ where
$\omega_{H,T}(t)$ is a Gaussian process that can be considered as a stationary
version of an $H$-fractional Brownian motion. Moreover, when $H \to 0$, one has
$M_{H,T}(d t) \rightarrow {\widetilde M}_{T}(d t)$ (in the weak sense) where
${\widetilde M}_{T}(d t)$ is the celebrated log-normal multifractal random
measure (MRM). Thus, this model allows us to consider, within the same
framework, the two popular classes of multifractal ($H = 0$) and rough
volatility ($0<H < 1/2$) models. The main properties of the log S-fBM are
discussed and their estimation issues are addressed. We notably show that the
direct estimation of $H$ from the scaling properties of $\ln(M_{H,T}([t,
t+\tau]))$, at fixed $\tau$, can lead to strongly over-estimating the value of
$H$. We propose a better GMM estimation method which is shown to be valid in
the high-frequency asymptotic regime. When applied to a large set of empirical
volatility data, we observe that stock indices have values around $H=0.1$ while
individual stocks are characterized by values of $H$ that can be very close to
$0$ and thus well described by a MRM. We also bring evidence that unlike the
log-volatility variance $\nu^2$ whose estimation appears to be poorly reliable
(though used widely in the rough volatility literature), the estimation of the
so-called "intermittency coefficient" $\lambda^2$, which is the product of
$\nu^2$ and the Hurst exponent $H$, appears to be far more reliable leading to
values that seem to be universal for respectively all individual stocks and all
stock indices.
|
2201.09516
|
We use a well-motivated galaxy formation framework to predict stellar masses,
star formation rates (SFR), and ultraviolet (UV) luminosities of galaxy
populations at redshifts $z\in 5-16$, taking into account stochasticity of SFR
in a controlled manner. We demonstrate that the model can match observational
estimates of UV luminosity functions (LFs) at $5<z<10$ with a modest level of
SFR stochasticity, resulting in the scatter of absolute UV luminosity at a
given halo mass of $\sigma_{M_{\rm UV}}\approx 0.75$. To match the observed UV
LFs at $z\approx 11-13$ and $z\approx 16$ the SFR stochasticity should increase
so that $\sigma_{M_{\rm UV}}\approx 1-1.3$ and $\approx 2$, respectively. Model
galaxies at $z\approx 11-13$ have stellar masses and SFRs in good agreement
with existing measurements. The median fraction of the baryon budget that was
converted into stars, $f_\star$, is only $f_\star\approx 0.005-0.05$, but a
small fraction of galaxies at $z=16$ have $f_\star>1$ indicating that SFR
stochasticity cannot be higher. We discuss several testable consequences of the
increased SFR stochasticity at $z>10$. The increase of SFR stochasticity with
increasing $z$, for example, prevents steepening of UV LF and even results in
some flattening of UV LF at $z\gtrsim 13$. The median stellar ages of model
galaxies at $z\approx 11-16$ are predicted to decrease from $\approx 20-30$ Myr
for $M_{\rm UV}\gtrsim -21$ galaxies to $\approx 5-10$ Myr for brighter ones.
Likewise, the scatter in median stellar age is predicted to decrease with
increasing luminosity. The scatter in the ratio of star formation rates
averaged over 10 and 100 Myr should increase with redshift. Fluctuations of
ionizing flux should increase at $z>10$ resulting in the increasing scatter in
the line fluxes and their ratios for the lines sensitive to ionization
parameter.
|
2405.04578
|
In this work, we obtain the following new results.
1. Given a sequence $D=((h_1,s_1), (h_2,s_2) ..., (h_n,s_n))$ of number
pairs, where $s_i>0$ for all $i$, and a number $L_h$, we propose an O(n)-time
algorithm for finding an index interval $[i,j]$ that maximizes
$\frac{\sum_{k=i}^{j} h_k}{\sum_{k=i}^{j} s_k}$ subject to $\sum_{k=i}^{j} h_k
\geq L_h$.
2. Given a sequence $D=((h_1,s_1), (h_2,s_2) ..., (h_n,s_n))$ of number
pairs, where $s_i=1$ for all $i$, and an integer $L_s$ with $1\leq L_s\leq n$,
we propose an $O(n\frac{T(L_s^{1/2})}{L_s^{1/2}})$-time algorithm for finding
an index interval $[i,j]$ that maximizes $\frac{\sum_{k=i}^{j}
h_k}{\sqrt{\sum_{k=i}^{j} s_k}}$ subject to $\sum_{k=i}^{j} s_k \geq L_s$,
where $T(n')$ is the time required to solve the all-pairs shortest paths
problem on a graph of $n'$ nodes. By the latest result of Chan \cite{Chan},
$T(n')=O(n'^3 \frac{(\log\log n')^3}{(\log n')^2})$, so our algorithm runs in
subquadratic time $O(nL_s\frac{(\log\log L_s)^3}{(\log L_s)^2})$.
|
0809.2097
|
We study the quasi-two-body decays $B\to D^*h \to D\pi h$ with $h=(\pi, K)$
in the perturbative QCD approach and focus on the virtual contributions from
the off-shell $D^{\ast}(2007)^0$ and $D^{\ast}(2010)^{\pm}$ in the four
measured decays $\bar B^0 \to D^0\pi^+\pi^-$, $\bar B^0\to D^0\pi^+K^-$, $B^-
\to D^+\pi^-\pi^-$ and $B^- \to D^+\pi^-K^-$. For the $\bar B^0 \to
D^{*+}\pi^-\to D^0\pi^+\pi^-$ and $\bar B^0\to D^{*+}K^-\to D^0\pi^+K^-$
decays, their branching fractions concentrate in a very small region of
$m_{D^0\pi^+}$ near $D^{*+}$ pole mass, and the virtual contributions from
$D^{*+}$, in the region $m_{D^0\pi^+}>2.1$ GeV, are about $5\%$ of the
corresponding quasi-two-body results. We define two ratios $R_{D^{*+}}$ and
$R_{D^{*0}}$, from which we conclude that the flavor-$SU(3)$ symmetry will be
maintained for the $B\to D^* h\to D\pi h$ decays with very small breaking at
any physical value of the $m_{D\pi}$. The $B^-\to D^{*0}\pi^-\to D^0\pi^0\pi^-$
and $B^-\to D^{*0}K^-\to D^0\pi^0K^-$ decays can be employed as a constraint
for the $D^{*0}$ decay width, with preferred values consistent with previous
theoretical predictions for this quantity.
|
1812.08524
|
The $d$-wave pseudospin current order ($d$PSCO) with staggered circulating
pseudospin current has been proposed as the hidden electronic order to describe
the unexpected breaking of spatial symmetries in stoichiometric
Sr$_{2}$IrO$_{4}$ and the unconventional pseudogap phenomena in electron doped
Sr$_{2}$IrO$_{4}$. However, a microscopic model for the emergence of $d$PSCO is
still lacking. The nearest neighbor Coulomb repulsion $V$, which is expected to
be significant in Sr$_{2}$IrO$_{4}$ due to the large spatial extension of the
Ir $5d$ orbitals, is capable of driving $d$PSCO on the mean-field level, albeit
the latter is energetically degenerate to the staggered flux phase with
circulating charge current. We find the in-plane anisotropy $\Gamma_2$ in the
effective superexchange interaction between $J_\text{eff}={1\over 2}$
pseudospins, originating from the cooperative interplay between Hund's rule
coupling and spin-orbit coupling of Ir $5d$ electrons, is able to lift the
degeneracy and stabilize the pseudospin currents. The effective single-orbital
model of $J_\text{eff}={1\over 2}$ electrons, including onsite Coulomb
repulsion $U$, nearest neighbor Coulomb repulsion $V$, and the in-plane
anisotropy $\Gamma_2$, is then studied. We obtain the mean-field ground states,
analyze their properties, and determine the phase diagram of stoichiometric
Sr$_{2}$IrO$_{4}$ in the plane spanned by $U$ and $V$ at a fixed $\Gamma_2$. We
demonstrate the realization of $d$PSCO, and its competition and coexistence
with antiferromagnetism. Remarkably, we find the coexistence of $d$PSCO and
antiferromagnetism naturally leads to spin bond nematicity, with the spin
directions of these three orders forming nontrivial chirality. Furthermore, we
show that the emergence of the coexistent state and its chirality can be tuned
by carrier doping.
|
2310.02119
|
We study the dust depletion pattern in eight well separated components of the
z=1.973, logN(HI)=20.83, damped Lyman-alpha system toward Q0013-004, four of
which have detectable H2 absorption. The apparent correlation between the
abundance ratios [Fe/S] and [Si/S] in the components indicates that the
abundance pattern is indeed due to dust-depletion. In particular, we find
evidence for depletion similar to what is observed in cold gas of the Galactic
disk ([Fe/Zn]=-1.59, Fe/S=-1.74, Zn/S=-0.15, [Si/S]=-0.85) in one of the
weakest components in which molecular hydrogen is detected with logN(H2)=16.5.
This is the first time such a large depletion is seen in a DLA system. This
observation supports the possibility that current samples of DLA systems might
be biased against the presence of cold and dusty gas along the line of sight.
The overall metallicities of this peculiar DLA system in which OI and CII are
spread over 1050 km/s are [P/H]=-0.64, [Zn/H]=-0.74 and [S/H]=-0.82 relative to
solar. The sub-DLA system at z=1.96753 has [P/H]>0.06, [Zn/H]>-0.02 and
[S/H]>-0.18. The overall molecular fraction is in the range -2.7<logf<-0.6. CO
is not detected (logN(CO)/N(HI)<-8) and HD could be present at z=1.97380. We
show that the presence of H2 is closely related to the physical conditions of
the gas: high particle density together with low temperature. The observed
excitation of high J H2 levels and the molecular fraction show large variations
from one component to the other suggesting that the UV radiation field is
highly inhomogeneous throughout the system. Gas pressure, estimated from CI
absorptions, is larger than what is observed in the ISM of our Galaxy. All this
is probably a consequence of intense star-formation activity in the vicinity of
the absorbing gas. (Abridged)
|
astro-ph/0201477
|
We discuss, study, and compare experimentally three methods for solving the
system of algebraic equations $\mathbb{A}^\alpha \bf{u}=\bf{f}$, $0< \alpha
<1$, where $\mathbb{A}$ is a symmetric and positive definite matrix obtained
from finite difference or finite element approximations of second order
elliptic problems in $\mathbb{R}^d$, $d=1,2,3$. The first method, introduced by
Harizanov et.al, based on the best uniform rational approximation (BURA)
$r_\alpha(t)$ of $t^{1-\alpha}$ for $0 \le t \le 1$, is used to get the
rational approximation of $t^{-\alpha}$ in the form $t^{-1}r_\alpha(t)$. Here
we develop another method, denoted by R-BURA, that is based on the best
rational approximation $r_{1-\alpha}(t)$ of $t^\alpha$ on the interval $[0,1]$
and approximates $t^{-\alpha}$ via $r^{-1}_{1-\alpha}(t)$. The third method,
introduced and studied by Bonito and Pasciak, is based on an exponentially
convergent quadrature scheme for the Dundord-Taylor integral representation of
the fractional powers of elliptic operators. All three methods reduce the
solution of the system $\mathbb{A}^\alpha \bf{u}=\bf{f}$ to solving a number of
equations of the type $(\mathbb{A} +c\mathbb{I})\bf{u}= \bf{f}$, $c \ge 0$.
Comprehensive numerical experiments on model problems with $\mathbb A$ obtained
by approximation of elliptic equations in one and two spatial dimensions are
used to compare the efficiency of these three algorithms depending on the
fractional power $\alpha$. The presented results prove the concept of the new
R-BURA method, which performs well for $\alpha$ close to $1$ in contrast to
BURA, which performs well for $\alpha $ close to $0$. As a result, we show
theoretically and experimentally, that they have mutually complementary
advantages.
|
1805.00711
|
We present sensitive 1-3 GHz ATCA radio continuum observations of the
hitherto unresolved star forming region known as either IRAS14482-5857 or
PMN1452-5910. At radio continuum frequencies, this source is characterised by a
"filled-bubble" structure reminiscent of a classical HII region, dominated by
three point sources, and surrounded by low-surface-brightness emission out to
the $3'\times4'$ source extent observed at other frequencies in the literature.
The infrared emission corresponds well to the radio emission, with polycyclic
aromatic hydrocarbon emission surrounding regions of hot dust towards the radio
bubbles. A bright 4.5 $\mu$m point source is seen towards the centre of the
radio source, suggesting a young stellar object. There is also a linear,
outflow-like structure radiating brightly at 8 and 24 $\mu$m towards the
brightest peak of the radio continuum. In order to estimate the distance to
this source, we have used Mopra Southern Galactic Plane CO Survey
$^{12}$CO(1-0) and $^{13}$CO(1-0) molecular line emission data.
Integrated-intensity, velocity at peak intensity and line-fitting of the
spectra all point towards the peak centred at $v_{LSR}$=-1.1 km/s being
connected to this cloud. This infers a distance to this cloud of ~12.7 kpc.
Assuming this distance, we estimate a column density and mass towards
IRAS14482-5857 of ~$1.5\times10^{21}$ cm$^{-2}$ and $2\times10^4$ $M_\odot$,
implying that this source is a site of massive star formation. Reinforcing this
conclusion, our broadband spectral fitting infers dust temperatures of 19 and
110K, emission measures for the sub-pc radio point-source of emission measure
$EM\sim10^{6-7}$ pc cm$^{-6}$, electron densities of $n_e\sim10^3$ cm$^{-3}$
and photon ionisation rates of $N_{Ly}~10^{46-48}$ s$^{-1}$. The evidence
strongly suggests that IRAS14482-5857 is a distant, and hence intense site of
massive star-formation.
|
1411.7054
|
Let $(M, g)$ denote a cosmological spacetime describing the evolution of a
universe which is isotropic and homogeneous on large scales, but highly
inhomogeneous on smaller scales. We consider two past lightcones, the first,
$\mathcal{C}^-_L(p, g)$, is associated with the physical observer $p\in\,M$ who
describes the actual physical spacetime geometry of $(M, g)$ at the length
scale $L$, whereas the second, $\mathcal{C}^-_L(p, \hat{g})$, is associated
with an idealized version of the observer $p$ who, notwithstanding the presence
of local inhomogeneities at the given scale $L$, wish to model $(M, g)$ with a
member $(M, \hat{g})$ of the family of Friedmann-Lemaitre-Robertson-Walker
spacetimes. In such a framework, we discuss a number of mathematical results
that allows a rigorous comparison between the two lightcones
$\mathcal{C}^-_L(p, g)$ and $\mathcal{C}^-_L(p, \hat{g})$. In particular, we
introduce a scale dependent ($L$) lightcone-comparison functional, defined by a
harmonic type energy, associated with a natural map between the physical
$\mathcal{C}^-_L(p, g)$ and the FLRW reference lightcone $\mathcal{C}^-_L(p,
\hat{g})$. This functional has a number of remarkable properties, in particular
it vanishes iff, at the given length-scale, the corresponding lightcone surface
sections (the celestial spheres) are isometric. We discuss in detail its
variational analysis and prove the existence of a minimum that characterizes a
natural scale-dependent distance functional between the two lightcones. We also
indicate how it is possible to extend our results to the case when caustics
develop on the physical past lightcone $\mathcal{C}^-_L(p, g)$. Finally, we
show how the distance functional is related to spacetime scalar curvature in
the causal past of the two lightcones, and briefly illustrate a number of its
possible applications.
|
2101.12698
|
Magic wavelengthsfor the $7S_{1/2}-7P_{1/2,3/2}$ transitions in Fr were
reported by Dammalapati \textit{et al.} in [Phys. Rev. A 93, 043407 (2016)].
These $\lambda_{\rm{magic}}$ were determined by plotting dynamic
polarizabilities ($\alpha$) of the involved states with the above transitions
against a desired range of wavelength. Electric dipole (E1) matrix elements
listed in [J. Phys. Chem. Ref. Data 36, 497 (2007)], from the measured
lifetimes of the $7P_{1/2,3/2}$ states and from the calculations considering
core-polarization effects in the relativistic Hartree-Fock (HFR) method, were
used to determine $\alpha$. However, contributions from core correlation
effects and from the E1 matrix elements of the $7P-7S$, $7P-8S$ and $7P-6D$
transitions to $\alpha$ of the $7P$ states were ignored. In this work, we
demonstrate importance of these contributions and improve accuracies of
$\alpha$ further by replacing the E1 matrix elements taken from the HFR method
by the values obtained employing relativistic coupled-cluster theory. Our
static $\alpha$ are found to be in excellent agreement with the other available
theoretical results; whereas substituting the E1 matrix elements used by
Dammalapati \textit{et al.} give very small $\alpha$ values for the $7P$
states. Owing to this, we find disagreement in $\lambda_{\rm{magic}}$ reported
by Dammalapati \textit{et al.} for linearly polarized light; especially at
wavelengths close to the D-lines and in the infrared region. As a consequence,
a $\lambda_{\rm{magic}}$ reported at 797.75 nm which was seen supporting a blue
detuned trap in their work is now estimated at 771.03 nm and is supporting a
red detuned trap. Also, none of our results match with the earlier results for
circularly polarized light. Moreover, our static values of $\alpha$ will be
very useful for guiding experiments to carry out their measurements.
|
1608.02073
|
We discuss the dynamics of multiple scalar fields and the possibility of
realistic inflation in the maximal gauged supergravity. In this paper, we
address this problem in the framework of recently discovered 1-parameter
deformation of ${\rm SO}(4,4)$ and ${\rm SO}(5,3)$ dyonic gaugings, for which
the base point of the scalar manifold corresponds to an unstable de Sitter
critical point. In the gauge-field frame where the embedding tensor takes the
value in the sum of the {\bf 36} and {\bf 36'} representations of ${\rm
SL}(8)$, we present a scheme that allows us to derive an analytic expression
for the scalar potential. With the help of this formalism, we derive the full
potential and gauge coupling functions in analytic forms for the ${\rm
SO}(3)\times {\rm SO}(3)$-invariant subsectors of ${\rm SO}(4,4)$ and ${\rm
SO}(5,3)$ gaugings, and argue that there exist no new critical points in
addition to those discovered so far. For the ${\rm SO}(4,4)$ gauging, we also
study the behavior of 6-dimensional scalar fields in this sector near the
Dall'Agata-Inverso de Sitter critical point at which the negative eigenvalue of
the scalar mass square with the largest modulus goes to zero as the deformation
parameter approaches a critical value. We find that when the deformation
parameter is taken sufficiently close to the critical value, inflation lasts
more than 60 e-folds even if the initial point of the inflaton allows an
$O(0.1)$ deviation in Planck units from the Dall'Agata-Inverso critical point.
It turns out that the spectral index $n_s$ of the curvature perturbation at the
time of the 60 e-folding number is always about 0.96 and within the $1\sigma$
range $n_s=0.9639\pm0.0047$ obtained by Planck, irrespective of the value of
the $\eta$ parameter at the critical saddle point. The tensor-scalar ratio
predicted by this model is around $10^{-3}$ and is close to the value in the
Starobinsky model.
|
1502.01378
|
Dirac electrons with a zero-gap state (ZGS) in organic conductor
$\alpha$-(BEDT-TTF)$_2$I$_3$ result from a fine tuning of the seven nearest
neighbors transfer integrals ($a_1, a_2, a_3, b_1, b_2, b_3, b_4$) between the
four molecules of the unit cell. In this work we show that for given moduli
$|a_1|,...|b_4|$, the possibility of having Dirac electron with a ZGS at $3/4$
(or $1/4$) filling strongly depends on the specific configurations of signs of
the seven transfer integral. More precisely it is possible to classify the sign
configurations into essentially four classes determined by $\chi_{a}={\rm sign}
(a_2a_3)$ and $\chi_b={\rm sign} (b_1b_2b_3b_4)$. Using extended numerics, we
show that for both weak and large inhomogeneity in the moduli, the class
$(\chi_a,\chi_b)=(-,-)$ is the most favorable to find Dirac electrons with ZGS
at $3/4$ (or $1/4$) filling. For the class $(\chi_a,\chi_b)=(+,+)$ in the
opposite case, we never found any ZGS at either $1/4$ or $3/4$ filling. The
last two classes \suzum{given by} $(\chi_a,\chi_b)=(+,-)$ and
$(\chi_a,\chi_b)=(-,+)$ corresponding to an intermediate situation; they allow
for ZGS at $3/4$ (resp. $1/4$) filling but are much less favorable than class
$(\chi_a,\chi_b)=(-,-)$. As a matter of fact, all previous numerical studies of
Dirac electrons and ZGS in $\alpha$-(BEDT-TTF)$_2$I$_3$ correspond to class
$(\chi_a,\chi_b)=(-,+)$.
|
1502.01167
|
A detector has been constructed for measuring ion mobilities of gas mixtures
at atmospheric pressure and room temperature. The detector consists of a
standard triple GEM amplification region and a drift region where ions drift. A
method has been developed to measure the ions' arrival time at a cathode
wire-grid by differentiating the recorded signals on this electrode.
Simulations prove that this method is accurate and robust. The ion mobility in
different gas mixtures is measured while applying different drift field values
ranging from 200 V cm$^{-1}$ to 1100 V cm$^{-1}$. From an extrapolation of a
Blanc's law fit to measurements in Ar-CO$_2$ mixtures we find the reduced
mobility of the drifting (cluster) ion species in pure argon to be
$1.94\pm0.01$ cm$^{2}$ V$^{-1}$ s$^{-1}$ and in pure carbon-dioxide to be
$1.10\pm0.01$ cm$^{2}$ V$^{-1}$ s$^{-1}$. Applying the same procedure to our
measurements in Ne-CO$_2$ yields $4.06\pm0.07$ cm$^{2}$ V$^{-1}$ s$^{-1}$ and
$1.09\pm0.01$ cm$^{2}$ V$^{- 1}$ s$^{-1}$ for the reduced mobilities in pure
neon and carbon-dioxide, respectively. Admixtures of N$_2$ to Ne-CO$_2$ reduce
somewhat the mobility. For the baseline gas mixture of the future ALICE Time
Projection Chamber, Ne- CO$_2$-N$_{2}$ (90-10-5), the measured reduced mobility
of the drifting ions is $2.92\pm0.04$ cm$^{2}$ V$^{-1}$ s$^{-1}$. Ion
mobilities are examined for different water content ranging from 70 ppm to
about 2000 ppm in the gas using Ar-CO$_2$ (90-10) and Ne-CO$_2$ (90-10). A
slight decrease of ion mobility is observed for the addition of several hundred
ppm of water.
|
1804.10288
|
We present a study of the CO isotopologues and the high-density tracers
H$_{2}$CO, HCO$^{+}$, and CS in Class 0/I proto-brown dwarfs (proto-BDs). We
have used the IRAM 30m telescope to observe the $^{12}$CO (2-1), $^{13}$CO
(2-1), C$^{18}$O (2-1), C$^{17}$O (2-1), H$_{2}$CO (3-2), HCO$^{+}$ (3-2), and
CS (5-4) lines in 7 proto-BDs. The hydrogen column density for the proto-BDs
derived from the CO gas emission is $\sim$2-15 times lower than that derived
from the dust continuum emission, indicating CO depletion from the gas-phase.
The mean H$_{2}$CO ortho-to-para ratio is $\sim$3 for the proto-BDs and
indicates gas-phase formation for H$_{2}$CO. We have investigated the
correlations in the molecular abundances between the proto-BDs and protostars.
Proto-BDs on average show a factor of $\sim$2 higher ortho-to-para H$_{2}$CO
ratio than the protostars. Possible explanations include a difference in the
H$_{2}$CO formation mechanism, spin-selective photo-dissociation,
self-shielding effects, or different emitting regions for the ortho and para
species. There is a tentative trend of a decline in the HCO$^{+}$ and H$_{2}$CO
abundances with decreasing bolometric luminosity, while the CS and CO
abundances show no particular difference between the proto-BDs and protostars.
These trends reflect the scaled-down physical structures for the proto-BDs
compared to protostars and differences in the peak emitting regions for these
species. The C$^{17}$O isotopologue is detected in all of the proto-BDs as well
as the more evolved Class Flat/Class II BDs in our sample, and can probe the
quiescent gas at both early and late evolutionary stages.
|
1811.01722
|
We study the single electron spectra from $D-$ and $B-$meson semileptonic
decays in Au+Au collisions at $\sqrt{s_{\rm NN}}=$200, 62.4, and 19.2 GeV by
employing the parton-hadron-string dynamics (PHSD) transport approach that has
been shown to reasonably describe the charm dynamics at RHIC and LHC energies
on a microscopic level. In this approach the initial heavy quarks are produced
by using the PYTHIA which is tuned to reproduce the FONLL calculations. The
produced heavy quarks interact with off-shell massive partons in QGP with
scattering cross sections which are calculated in the dynamical quasi-particle
model (DQPM). At energy densities close to the critical energy density the
heavy quarks are hadronized into heavy mesons through either coalescence or
fragmentation. After hadronization the heavy mesons interact with the light
hadrons by employing the scattering cross sections from an effective
Lagrangian. The final heavy mesons then produce single electrons through
semileptonic decay. We find that the PHSD approach well describes the nuclear
modification factor $R_{\rm AA}$ and elliptic flow $v_2$ of single electrons in
d+Au and Au+Au collisions at $\sqrt{s_{\rm NN}}=$ 200 GeV and the elliptic flow
in Au+Au reactions at $\sqrt{s_{\rm NN}}=$ 62.4 GeV from the PHENIX
collaboration, however, the large $R_{\rm AA}$ at $\sqrt{s_{\rm NN}}=$ 62.4 GeV
is not described at all. Furthermore, we make predictions for the $R_{\rm AA}$
of $D-$mesons and of single electrons at the lower energy of $\sqrt{s_{\rm
NN}}=$ 19.2 GeV. Additionally, the medium modification of the azimuthal angle
$\phi$ between a heavy quark and a heavy antiquark is studied. We find that the
transverse flow enhances the azimuthal angular distributions close to $\phi=$ 0
because the heavy flavors strongly interact with nuclear medium in relativistic
heavy-ion collisions and almost flow with the bulk matter.
|
1605.07887
|
Given a graph $F$ and an integer $r \ge 2$, a partition $\widehat{F}$ of the
edge set of $F$ into at most $r$ classes, and a graph $G$, define $c_{r,
\widehat{F}}(G)$ as the number of $r$-colorings of the edges of $G$ that do not
contain a copy of $F$ such that the edge partition induced by the coloring is
isomorphic to the one of $F$. We think of $\widehat{F}$ as the pattern of
coloring that should be avoided. The main question is, for a large enough $n$,
to find the (extremal) graph $G$ on $n$ vertices which maximizes $c_{r,
\widehat{F}}(G)$. This problem generalizes a question of Erd{\H o}s and
Rothschild, who originally asked about the number of colorings not containing a
monochromatic clique (which is equivalent to the case where $F$ is a clique and
the partition $\widehat{F}$ contains a single class). We use H\"{o}lder's
Inequality together with Zykov's Symmetrization to prove that, for any $r \geq
2$, $k \geq 3$ and any pattern $\widehat{K_k}$ of the clique $K_k$, there
exists a complete multipartite graph that is extremal. Furthermore, if the
pattern $\widehat{K_k}$ has at least two classes, with the possible exception
of two very small patterns (on three or four vertices), every extremal graph
must be a complete multipartite graph. In the case that $r=3$ and $\widehat{F}$
is a rainbow triangle (that is, where $F=K_3$ and each part is a singleton), we
show that an extremal graph must be an almost complete graph. Still for $r=3$,
we extend a result about monochromatic patterns of Alon, Balogh, Keevash and
Sudakov to some patterns that use two of the three colors, finding the exact
extremal graph. For the later two results, we use the Regularity and Stability
Method.
|
1605.08013
|
We explore the behaviour of [CII]-157.74um forbidden fine-structure line
observed in a sample of 28 galaxies selected from ~50deg^2 of the H-ATLAS
survey. The sample is restricted to galaxies with flux densities higher than
S_160um>150mJy and optical spectra from the GAMA survey at 0.02<z<0.2. Far-IR
spectra centred on this redshifted line were taken with the PACS instrument
on-board the Herschel Space Observatory. The galaxies span 10<log(L_IR/Lo)<12
(where L_IR=L_IR[8-1000um]) and 7.3<log(L_[CII]/Lo)<9.3, covering a variety of
optical galaxy morphologies. The sample exhibits the so-called [CII] deficit at
high IR luminosities, i.e. L_[CII]/L_IR (hereafter [CII]/IR) decreases at high
L_IR. We find significant differences between those galaxies presenting
[CII]/IR>2.5x10^-3 with respect to those showing lower ratios. In particular,
those with high ratios tend to have: (1) L_IR<10^11Lo; (2) cold dust
temperatures, T_d<30K; (3) disk-like morphologies in r-band images; (4) a WISE
colour 0.5<S_12um/S_22um<1.0; (5) low surface brightness Sigma_IR~10^8-9 Lo
kpc^-2, (6) and specific star-formation rates of sSFR~0.05-3 Gyr^-1. We suggest
that the strength of the far-UV radiation fields (<G_O>) is main parameter
responsible for controlling the [CII]/IR ratio. It is possible that relatively
high <G_O> creates a positively charged dust grain distribution, impeding an
efficient photo-electric extraction of electrons from these grains to then
collisionally excite carbon atoms. Within the brighter IR population,
11<log(L_IR/Lo)<12, the low [CII]/IR ratio is unlikely to be modified by [CII]
self absorption or controlled by the presence of a moderately luminous AGN
(identified via the BPT diagram).
|
1503.01128
|
The surface-density profiles of dense filaments, in particular those traced
by dust emission, appear to be well fit with Plummer profiles, i.e.
Sigma(b)=Sigma_B+Sigma_O{1+[b/w_O]^2}^{[1-p]/2}. Here Sigma_B is the background
surface-density; Sigma_B+Sigma_O is the surface-density on the filament spine;
b is the impact parameter of the line-of-sight relative to the filament spine;
w_O is the Plummer scale-length (which for fixed p is exactly proportional to
the full-width at half-maximum, w_O=FWHM/2{2^{2/[p-1]}-1}^{1/2}); and p is the
Plummer exponent (which reflects the slope of the surface-density profile away
from the spine).} In order to improve signal-to-noise it is standard practice
to average the observed surface-densities along a section of the filament, or
even along its whole length, before fitting the profile. We show that, if
filaments do indeed have intrinsic Plummer profiles with exponent p_INTRINSIC,
but there is a range of w_O values along the length of the filament (and
secondarily a range of Sigma_B values), the value of the Plummer exponent,
p_FIT, estimated by fitting the averaged profile, may be significantly less
than p_INTRINSIC. The decrease, Delta p = p_INTRINSIC - p_FIT, increases
monotonically with increasing p_INTRINSIC; with increasing range of w_O values;
and -- if, but only if, there is a finite range of w_O values -- with
increasing range of Sigma_B values. For typical filament parameters the
decrease is insignificant if p_INTRINSIC = 2 (0.05 <~ Delta p <~ 0.10), but for
p_INTRINSIC =3 it is larger (0.18 <~ Delta p <~ 0.50), and for p_INTRINSIC =4
it is substantial (0.50 <~ Delta p <~ 1.15). On its own this effect is probably
insufficient to support a value of p_INTRINSIC much greater than p_FIT ~ 2, but
it could be important in combination with other effects.
|
2109.11924
|
Let $\Sigma$ be a compact oriented 2-manifold (possibly with boundary), and
let $\mathcal G_{\Sigma}$ be the linear span of free homotopy classes of closed
oriented curves on $\Sigma$ equipped with the Goldman Lie bracket $[\cdot,
\cdot]_\mathrm{Goldman}$ defined in terms of intersections of curves. A theorem
of Goldman gives rise to a Lie homomorphism $\Phi^\mathrm{even}$ from
$(\mathcal G_{\Sigma}, [\cdot, \cdot]_\text{Goldman})$ to functions on the
moduli space of flat connections $\mathcal{M}_{\Sigma}(G)$ for $G=U(N), GL(N)$,
equipped with the Atiyah-Bott Poisson bracket.
The space $\mathcal{G}_{\Sigma}$ also carries the Turaev Lie cobracket
$\delta_\mathrm{Turaev}$ defined in terms of self-intersections of curves. In
this paper, we address the following natural question: which geometric
structure on moduli spaces of flat connections corresponds to the Turaev
cobracket?
We give a constructive answer to this question in the following context: for
$G$ a Lie supergroup with an odd invariant scalar product on its Lie
superalgebra, and for nonempty $\partial\Sigma$, we show that the moduli space
of flat connections $\mathcal{M}_{\Sigma}(G)$ carries a natural
Batalin-Vilkovisky (BV) structure, given by an explicit combinatorial
Fock-Rosly formula. Furthermore, for the queer Lie supergroup $G=Q(N)$, we
define a BV-morphism $\Phi^\mathrm{odd}\colon \wedge \mathcal{G}_{\Sigma} \to
\mathrm{Fun}(\mathcal{M}_{\Sigma}(Q(N)))$ which replaces the Goldman map, and
which captures the information both on the Goldman bracket and on the Turaev
cobracket. The map $\Phi^\mathrm{odd}$ is constructed using the "odd trace"
function on $Q(N)$.
|
2210.08944
|
We develop and evaluate point and interval estimates for the random effects
$\theta_i$, having made observations $y_i|\theta_i\stackrel{\m
athit{ind}}{\sim}N[\theta_i,V_i],i=1,...,k$ that follow a two-level Normal
hierarchical model. Fitting this model requires assessing the Level-2 variance
$A\equiv\operatorname {Var}(\theta_i)$ to estimate shrinkages $B_i\equiv
V_i/(V_i+A)$ toward a (possibly estimated) subspace, with $B_i$ as the target
because the conditional means and variances of $\theta_i$ depend linearly on
$B_i$, not on $A$. Adjustment for density maximization, ADM, can do the fitting
for any smooth prior on $A$. Like the MLE, ADM bases inferences on two
derivatives, but ADM can approximate with any Pearson family, with Beta
distributions being appropriate because shrinkage factors satisfy $0\le
B_i\le1$. Our emphasis is on frequency properties, which leads to adopting a
uniform prior on $A\ge0$, which then puts Stein's harmonic prior (SHP) on the
$k$ random effects. It is known for the "equal variances case" $V_1=...=V_k$
that formal Bayes procedures for this prior produce admissible minimax
estimates of the random effects, and that the posterior variances are large
enough to provide confidence intervals that meet their nominal coverages.
Similar results are seen to hold for our approximating "ADM-SHP" procedure for
equal variances and also for the unequal variances situations checked here. For
shrinkage coefficient estimation, the ADM-SHP procedure allows an alternative
frequency interpretation. Writing $L(A)$ as the likelihood of $B_i$ with $i$
fixed, ADM-SHP estimates $B_i$ as $\hat{B_i}=V_i/(V_i+\hat{A})$ with
$\hat{A}\equiv \operatorname {argmax}(A*L(A))$. This justifies the term
"adjustment for likelihood maximization," ALM.
|
1108.3234
|
We consider the reduced quasi-classical self-dual Yang-Mills equation (rYME)
and two recently found (Jahnov\'{a} and Voj\v{c}\'{a}k, 2024) invertible
recursion operators $\mathcal{R}^q$ and $\mathcal{R}^m$ for its full-fledged
(in a given differential covering) nonlocal symmetries. We introduce a
$\mathbb{Z}$-grading on the Lie algebra $\mathrm{sym}_{\mathcal{L}}^{\tau^W}
(\mathcal E)$ of all nonlocal Laurent polynomial symmetries of the rYME and
prove that both the operators $\mathcal{R}^q$ and $\mathcal{R}^m$ are
$\mathbb{Z}$-graded automorphisms of the underlying vector space on the set
$\mathrm{sym}_{\mathcal{L}}^{\tau^W} (\mathcal E)$. This inter alia implies
that all its vector subspaces formed by all homogeneous elements of a given
fixed degree (i.e. a weight in the context below) are mutually isomorphic, and
thus each of them can be uniquely reconstructed from the vector space of all
homogeneous symmetries of the zero degree. To the best of our knowledge, such a
result is unparalleled in the current body of literature. The obtained results
are used for the construction of a Lie subalgebra $V$ of
$\mathrm{sym}_{\mathcal{L}}^{\tau^W} (\mathcal E)$ which contains all known to
us nonlocal Laurent polynomial symmetries of the rYME. The Lie algebra $V$ is
subsequently described as the linear span of the orbits of a set of selected
zero-weight symmetries - we refer to them as to the seed generators of $V$.
Further, we study the hierarchies of symmetries related to the seed generators
under the action of the group of recursion operators generated by
$\mathcal{R}^q$ and $\mathcal{R}^m$. Finally, the linear
dependence/independence of the (sub)set of generators of $V$ is discussed.
|
2407.00622
|
We use FIRE-2 simulations to examine 3-D variations of gas-phase elemental
abundances of [O/H], [Fe/H], and [N/H] in 11 Milky Way (MW) and M31-mass
galaxies across their formation histories at $z \leq 1.5$ ($t_{\rm lookback}
\leq 9.4$ Gyr), motivated by characterizing the initial conditions of stars for
chemical tagging. Gas within $1$ kpc of the disk midplane is vertically
homogeneous to $\lesssim 0.008$ dex at all $z \leq 1.5$. We find negative
radial gradients (metallicity decreases with galactocentric radius) at all
times, which steepen over time from $\approx -0.01$ dex kpc$^{-1}$ at $z = 1$
($t_{\rm lookback} = 7.8$ Gyr) to $\approx -0.03$ dex kpc$^{-1}$ at $z = 0$,
and which broadly agree with observations of the MW, M31, and nearby
MW/M31-mass galaxies. Azimuthal variations at fixed radius are typically $0.14$
dex at $z = 1$, reducing to $0.05$ dex at $z = 0$. Thus, over time radial
gradients become steeper while azimuthal variations become weaker (more
homogeneous). As a result, azimuthal variations were larger than radial
variations at $z \gtrsim 0.8$ ($t_{\rm lookback} \gtrsim 6.9$ Gyr).
Furthermore, elemental abundances are measurably homogeneous (to $\lesssim
0.05$ dex) across a radial range of $\Delta R \approx 3.5$ kpc at $z \gtrsim 1$
and $\Delta R \approx 1.7$ kpc at $z = 0$. We also measure full distributions
of elemental abundances, finding typically negatively skewed normal
distributions at $z \gtrsim 1$ that evolve to typically Gaussian distributions
by $z = 0$. Our results on gas abundances inform the initial conditions for
stars, including the spatial and temporal scales for applying chemical tagging
to understand stellar birth in the MW.
|
2102.06220
|
Let $G$ be a graph and $t$ a nonnegative integer. Suppose $f$ is a mapping
from the vertex set of $G$ to $\{1,2,\dots, k\}$. If, for any vertex $u$ of
$G$, the number of neighbors $v$ of $u$ with $f(v)=f(u)$ is less than or equal
to $t$, then $f$ is called a $t$-relaxed $k$-coloring of $G$. And $G$ is said
to be $(k,t)$-colorable. The $t$-relaxed chromatic number of $G$, denote by
$\chi_t(G)$, is defined as the minimum integer $k$ such that $G$ is
$(k,t)$-colorable. A set $S$ of vertices in $G$ is $t$-sparse if $S$ induces a
graph with a maximum degree of at most $t$. Thus $G$ is $(k,t)$-colorable if
and only if the vertex set of $G$ can be partitioned into $k$ $t$-sparse sets.
It was proved by Belmonte, Lampis and Mitsou (2017) that the problem of
deciding if a complete multi-partite graph is $(k,t)$-colorable is NP-complete.
In this paper, we first give tight lower and up bounds for the $t$-relaxed
chromatic number of complete multi-partite graphs. And then we design an
algorithm to compute maximum $t$-sparse sets of complete multi-partite graphs
running in $O((t+1)^2)$ time. Applying this algorithm, we show that the greedy
algorithm for $\chi_t(G)$ is $2$-approximate and runs in $O(tn)$ time steps
(where $n$ is the vertex number of $G$). In particular, we prove that for $t\in
\{1,2,3,4,5,6\}$, the greedy algorithm produces an optimal $t$-relaxed coloring
of a complete multi-partite graph. While, for $t\ge 7$, examples are given to
illustrate that the greedy strategy does not always construct an optimal
$t$-relaxed coloring.
|
2106.07398
|
We consider the Laplacian on a class of smooth domains $\Omega\subset
\mathbb{R}^{\nu}$, $\nu\ge 2$, with attractive Robin boundary conditions: \[
Q^\Omega_\alpha u=-\Delta u, \quad \dfrac{\partial u}{\partial n}=\alpha u
\text{ on } \partial\Omega, \ \alpha>0, \] where $n$ is the outer unit normal,
and study the asymptotics of its eigenvalues $E_{j}(Q^\Omega_\alpha)$ as well
as some other spectral properties for $\alpha\to+\infty$ We work with both
compact domains and non-compact ones with a suitable behavior at infinity. For
domains with compact $C^2$ boundaries and fixed $j$, we show that \[
E_{j}(Q^\Omega_\alpha)=-\alpha^2+\mu_j(\alpha)+{\mathcal O}(\log \alpha), \]
where $\mu_j(\alpha)$ is the $j^{\mbox{th}}$ eigenvalue, as soon as it exists,
of $-\Delta_{S}-(\nu-1)\alpha H$ with $(-\Delta_{S})$ and $H$ being
respectively the positive Laplace-Beltrami operator and the mean curvature on
$\partial\Omega$. Analogous results are obtained for a class of domains with
non-compact boundaries. In particular, we discuss the existence of eigenvalues
in non-compact domains and the existence of spectral gaps for periodic domains.
We also show that the remainder estimate can be improved under stronger
regularity assumptions.
The effective Hamiltonian $-\Delta_{S}-(\nu-1)\alpha H$ enters the framework
of semi-classical Schr\"odinger operators on manifolds, and we provide the
asymptotics of its eigenvalues in the limit $\alpha\to+\infty$ under various
geometrical assumptions. In particular, we describe several cases for which
our asymptotics provides gaps between the eigenvalues of $Q^\Omega_\alpha$ for
large $\alpha$.
|
1502.00877
|
We present measurements of the branching fractions of eight $\overline
B{}^0\to D^{(*)+} K^- K^{(*)0}_{(S)}$, $B^{-}\to D^{(*)0} K^- K^{(*)0}_{(S)}$
decay channels. The results are based on data from SuperKEKB electron-positron
collisions at the $\Upsilon(4S)$ resonance collected with the Belle II
detector, corresponding to an integrated luminosity of $362~\text{fb}^{-1}$.
The event yields are extracted from fits to the distributions of the difference
between expected and observed $B$ meson energy, and are efficiency-corrected as
a function of $m(K^-K^{(*)0}_{(S)})$ and $m(D^{(*)}K^{(*)0}_{(S)})$ in order to
avoid dependence on the decay model. These results include the first
observation of $\overline B{}^0\to D^+K^-K_S^0$, $B^-\to D^{*0}K^-K_S^0$, and
$\overline B{}^0\to D^{*+}K^-K_S^0$ decays and a significant improvement in the
precision of the other channels compared to previous measurements. The
helicity-angle distributions and the invariant mass distributions of the $K^-
K^{(*)0}_{(S)}$ systems are compatible with quasi-two-body decays via a
resonant transition with spin-parity $J^P=1^-$ for the $K^-K_S^0$ systems and
$J^P= 1^+$ for the $K^-K^{*0}$ systems. We also present measurements of the
branching fractions of four $\overline B{}^0\to D^{(*)+} D_s^-$, $B^{-}\to
D^{(*)0} D_s^- $ decay channels with a precision compatible to the current
world averages.
|
2406.06277
|
We perform SubHalo Abundance Matching (SHAM) studies on UNIT simulations with
\{$\sigma, V_{\rm ceil}, v_{\rm smear}$\}-SHAM and \{$\sigma, V_{\rm
ceil},f_{\rm sat}$\}-SHAM. They are designed to reproduce the clustering on
5--30$\,\hmpc$ of Luminous Red Galaxies (LRGs), Emission Line Galaxies (ELGs)
and Quasi-Stellar Objects (QSOs) at $0.4<z<3.5$ from DESI One Percent Survey.
$V_{\rm ceil}$ is the incompleteness of the massive host (sub)haloes and is the
key to the generalized SHAM. $v_{\rm smear}$ models the clustering effect of
redshift uncertainties, providing measurments consistent with those from repeat
observations. A free satellite fraction $f_{\rm sat}$ is necessary to reproduce
the clustering of ELGs. We find ELGs present a more complex galaxy--halo mass
relation than LRGs reflected in their weak constraints on $\sigma$. LRGs, QSOs
and ELGs show increasing $V_{\rm ceil}$ values, corresponding to the massive
galaxy incompleteness of LRGs, the quenched star formation of ELGs and the
quenched black hole accretion of QSOs. For LRGs, a Gaussian $v_{\rm smear}$
presents a better profile for sub-samples at redshift bins than a Lorentzian
profile used for other tracers. The impact of the statistical redshift
uncertainty on ELG clustering is negligible. The best-fitting satellite
fraction for DESI ELGs is around 4 per cent, lower than previous estimations
for ELGs. The mean halo mass log$_{10}(\langle M_{\rm vir}\rangle)$ in
$\Msun{}$ for LRGs, ELGs and QSOs are ${13.16\pm0.01}$, ${11.90\pm0.06}$ and
${12.66\pm0.45}$ respectively. Our generalized SHAM algorithms facilitate the
production of mult-tracer galaxy mocks for cosmological tests.
|
2306.06313
|
Alspach [ Bull. Inst. Combin. Appl., 52 (2008), pp. 7-20] defined the maximal
matching sequencibility of a graph $G$, denoted $ms(G)$, to be the largest
integer $s$ for which there is an ordering of the edges of $G$ such that every
$s$ consecutive edges form a matching. Alspach also proved that $ms(K_n) =
\bigl\lfloor\frac{n-1}{2}\bigr\rfloor$. Brualdi et al. [ Australas. J. Combin.,
53 (2012), pp. 245-256] extended the definition to cyclic matching
sequencibility of a graph $G$, denoted $cms(G)$, which allows cyclical
orderings and proved that $cms(K_n) = \bigl\lfloor\frac{n-2}{2}\bigr\rfloor$.
In this paper, we generalise these definitions to require that every $s$
consecutive edges form a subgraph where every vertex has degree at most $r\geq
1$, and we denote the maximum such number for a graph $G$ by $ms_r(G)$ and
$cms_r(G)$ for the non-cyclic and cyclic cases, respectively. We conjecture
that $ms_r(K_n) = \bigl\lfloor\frac{rn-1}{2}\bigr\rfloor$ and
${\bigl\lfloor\frac{rn-1}{2}\bigr\rfloor-1}~ \leq cms_r(K_n) \leq
\bigl\lfloor\frac{rn-1}{2}\bigr\rfloor$ and that both bounds are attained for
some $r$ and $n$. We prove these conjectured identities for the majority of
cases, by defining and characterising selected decompositions of $K_n$. We also
provide bounds on $ms_r(G)$ and $cms_r(G)$ as well as results on hypergraph
analogues of $ms_r(G)$ and $cms_r(G)$.
|
1711.05013
|
We investigate the physical origins of the Balmer decrement anomalies in
GS-NDG-9422 (Cameron et al. 2023) and RXCJ2248-ID (Topping et al. 2024)
galaxies at $z\sim 6$ whose $\mathrm{H}\alpha/\mathrm{H}\beta$ values are
significantly smaller than $2.7$, the latter of which also shows anomalous
$\mathrm{H}\gamma/\mathrm{H}\beta$ and $\mathrm{H}\delta/\mathrm{H}\beta$
values beyond the errors. Because the anomalous Balmer decrements are not
reproduced under the Case B recombination, we explore the nebulae with the
optical depths smaller and larger than the Case B recombination by physical
modeling. We find two cases quantitatively explaining the anomalies; 1)
density-bounded nebulae that are opaque only up to around Ly$\gamma$-Ly8
transitions and 2) ionization-bounded nebulae partly/fully surrounded by
optically-thick excited H{\sc i} clouds. The case of 1) produces more H$\beta$
photons via Ly$\gamma$ absorption in the nebulae, requiring fine tuning in
optical depth values, while this case helps ionizing photon escape for cosmic
reionization. The case of 2) needs the optically-thick excited H{\sc i} clouds
with $N_2\simeq 10^{12}-10^{13}$ $\mathrm{cm^{-2}}$, where $N_2$ is the column
density of the hydrogen atom with the principal quantum number of $n=2$.
Interestingly, the high $N_2$ values qualitatively agree with the recent claims
for GS-NDG-9422 with the strong nebular continuum requiring a number of
$2s$-state electrons and for RXCJ2248-ID with the dense ionized regions likely
coexisting with the optically-thick clouds. While the physical origin of the
optically-thick excited H{\sc i} clouds is unclear, these results may suggest
gas clouds with excessive collisional excitation caused by an amount of
accretion and supernovae in the high-$z$ galaxies.
|
2403.20118
|
The Standard Model (SM) does not contain by definition any new physics (NP)
contributions to any observable but contains four CKM parameters which are not
predicted by this model. We point out that if these four parameters are
determined in a global fit that includes processes which are infected by NP,
the resulting SM contributions to rare decay branching ratios cannot be
considered as true SM contributions to the latter. On the other hand true SM
predictions, that are free from the CKM dependence, can be obtained for
suitable ratios of the $K$ and $B$ rare decay branching ratios to $\Delta M_s$,
$\Delta M_d$ and $|\varepsilon_K|$, all calculated within the SM. These three
observables contain by now only small hadronic uncertainties and are already
well measured so that rather precise true SM predictions for the ratios in
question can be obtained. In this context the rapid test of NP infection in the
$\Delta F=2$ sector is provided by a $|V_{cb}|-\gamma$ plot that involves
$\Delta M_s$, $\Delta M_d$, $|\varepsilon_K|$, and the mixing induced
CP-asymmetry $S_{\psi K_S}$. As with the present hadronic matrix elements this
test turns out to be negative, assuming negligible NP infection in the $\Delta
F=2$ sector and setting the values of these four observables to the
experimental ones, allows to obtain SM predictions for all $K$ and $B$ rare
decay branching ratios that are most accurate to date and as a byproduct to
obtain the full CKM matrix on the basis of $\Delta F=2$ transitions alone.
Using this strategy we obtain SM predictions for 26 branching ratios for rare
semileptonic and leptonic $K$ and $B$ decays with the $\mu^+\mu^-$ pair or the
$\nu\bar\nu$ pair in the final state. Most interesting turn out to be the
anomalies in the low $q^2$ bin in $B^+\to K^+\mu^+\mu^-$ ($4.4\sigma$) and
$B_s\to \phi\mu^+\mu^-$ ($4.8\sigma$).
|
2209.03968
|
Lyman-$\alpha$ forest data are known to be a good probe of the small scale
matter power. In this paper, we explore the redshift evolution of the
observable effective optical depth $\tau_{\rm eff} (z)$ from the Lyman-$\alpha$
data as a discriminator between dark matter models that differ from the
$\Lambda$CDM model on small scales. We consider the thermal warm dark matter
(WDM) and the ultra-light axion (ULA) models for the following set of
parameters: the mass of ULA, $m_a \simeq 10^{-24}\hbox{--}5 \times 10^{-22} \,
\rm eV$ and WDM mass, $m_{\rm wdm} = 0.1 \hbox{--} 4.6 \, \rm keV$. We simulate
the line-of-sight HI density and velocity fields using semi-analytic methods.
The simulated effective optical depth for the alternative dark matter models
diverges from the $\Lambda$CDM model for $z \gtrsim 3$, which provides a
meaningful probe of the matter power at small scales. Using likelihood
analysis, we compare the simulated data with the high-resolution Lyman-$\alpha$
forest data in the redshift range $2 < z < 4.2$. The analysis yields the
following 1$\sigma$ bounds on dark matter masses: $m_{\rm wdm} > 0.7\, {\rm
keV}$ and $m_{\rm a} > 2 \times 10^{-23} \, {\rm eV}$. To further test the
efficacy of our proposed method, we simulate synthetic data sets compatible
with the $\Lambda$CDM model in the redshift range $2 \leq z \leq 6.5$ and
compare with theory. The 1$\sigma$ bounds obtained are significantly tighter:
$m_{\rm wdm} > 1.5 \, {\rm keV}$ and $m_{\rm a} > 7 \times 10^{-23} \, {\rm
eV}$. Although our method provides an alternative way of constraining dark
matter models, we note that these bounds are weaker than those obtained by
high-resolution hydrodynamical simulations.
|
2101.09917
|
We determine the source of the diffuse [CII] emission by studying its spatial
(radial and vertical) distributions. We used the HIFI [CII] Galactic survey
(GOT C+), along with HI, 12CO, and 13CO data toward 354 lines of sight, and
several HIFI [CII] and [CI] position-velocity maps. We quantified the emission
in each spectral line profile by evaluating the intensities in 3 km/s wide
velocity bins, 'spaxels'. Using the detection of [CII] with CO or [CI], we
separated the dense and diffuse gas components. We derived 2-D Galactic disk
maps using the spaxel velocities for kinematic distances. We separated the warm
and cold H2 gases by comparing CO emissions with and without associated [CII].
We find evidence of widespread diffuse [CII] emission with a z-scale
distribution larger than that for the total [CII] or CO. and it consists of (i)
diffuse molecular (CO-faint) H2 clouds and (ii) diffuse HI clouds and/or WIM.
In the inner Galaxy we find a lack of [CII] detections in a majority (~62%) of
HI spaxels and show that the diffuse component primarily comes from the WIM
(~21%) and that the HI gas is not a major contributor to the diffuse component
(~6%). The warm-H2 radial profile shows an excess in the range 4 to 7 kpc,
consistent with enhanced star formation there. We derive, for the first time,
the 2-D [CII] spatial distribution in the plane and the z-distributions of the
individual [CII] gas component. We estimate the fractional [CII] emission
tracing (i) H2 gas in dense and diffuse molecular clouds as ~48% and ~ 14%,
respectively, (ii) in the HI gas ~18%, and (iii) in the WIM ~21%. Including
non-detections from HI increases the [CII] in HI to ~ 27%. The z-scale
distributions FWHM are [CII] sources with CO, ~130 pc, (CO-faint) diffuse H2
gas, ~200 pc, and the diffuse HI and WIM, ~330 pc. CO observations, when
combined with [CII], probe the warm-H2 gas, tracing star formation.
|
1409.4788
|
Supernova (SN) 1987A was a peculiar H-rich event with a long-rising (LR)
light curve (LC), stemming from a compact blue supergiant star (BSG). Only a
few similar events have been presented in the literature. We present new data
for a sample of 6 LR Type II SNe (SNe II), 3 of which were discovered and
observed by the Palomar Transient Factory (PTF) and 3 observed by the Caltech
Core-Collapse Project (CCCP). Our aim is to enlarge the family of LR SNe II,
characterizing their properties. Spectra, LCs, and host-galaxies (HG) of these
SNe are presented. Comparisons with known SN 1987A-like events are shown, with
emphasis on the absolute magnitudes, colors, expansion velocities, and HG
metallicities. Bolometric properties are derived from the multiband LC. By
modeling the early-time LCs with scaling relations derived from the SuperNova
Explosion Code (SNEC) models of MESA progenitor stars, we estimate the
progenitor radii of these SNe and other progenitor parameters. We present
PTF12kso, a LR SN II with the largest amount of 56Ni mass for this class.
PTF09gpn and PTF12kso are found at the lowest HG metallicities for this SN
group. The variety of early LC luminosities depends on the wide range of
progenitor radii, from a few tens of solar radii (SN 2005ci) up to thousands
(SN 2004ek) with intermediate cases between 100 (PTF09gpn) and 300 solar radii
(SN 2004em). We confirm that LR SNe II with LC shapes closely resembling that
of SN 1987A generally arise from BSGs. However, some of them likely have
progenitors with larger radii (~300 solar radii, typical of yellow supergiants)
and can thus be regarded as intermediate cases between normal SNe IIP and SN
1987A-like SNe. Some extended red supergiant (RSG) stars such as the progenitor
of SN 2004ek can also produce LR SNe II if they synthesized a large amount of
56Ni. Low HG metallicity is confirmed as a characteristic of BSG SNe.
|
1601.07368
|
Recent BaBar limits on $\br(\Upsilon(3S)\to \gam a\to \gam \tau^+\tau^-)$ and
$\br(\Upsilon(3S)\to \gam a\to \gam \mu^+\mu^-)$ provide increased constraints
on the $a b\anti b$ coupling of a CP-odd Higgs boson, $a$, with
$m_a<M_{\Upsilon(3S)}$. We extract these limits from the BaBar data and compare
to the limits previously obtained using other data sets, especially the
CLEO-III $\br(\Upsilon(1S)\to \gam\to\tau^+\tau^-)$ limits. Comparisons are
made to predictions in the context of "ideal"-Higgs NMSSM scenarios, in which
the lightest CP-even Higgs boson, $h_1$, can have mass below $105\gev$ (as
preferred by precision electroweak data) and yet can escape old LEP limits by
virtue of decays to a pair of the lightest CP-odd Higgs bosons, $h_1\to
a_1a_1$, with $m_{a_1}<2m_B$. Most such scenarios with $m_{a_1}<2m_\tau$ are
eliminated, but the bulk of the $m_{a_1}>7.5\gev$ scenarios, which are
theoretically the most favored, survive. We also outline the impact of the new
ALEPH LEP results in the $\epem\to Z+4\tau$ channel. For $\tan\beta\geq 3$,
only NMSSM ideal Higgs scenarios with $m_{h_1}\gsim 98\gev$ and $m_{a_1}$ close
to $2m_B $ satisfy the ALEPH limits. For $\tan\beta\lsim 2$, the ALEPH limits
are easily satisfied for the most theoretically preferred NMSSM scenarios,
which are those with $m_{a_1}$ close to $2m_B$ and $m_{h_1}\sim
90\gev-100\gev$.
|
1002.1971
|
We investigate the size complexity of proofs in $Res(s)$ -- an extension of
Resolution working on $s$-DNFs instead of clauses -- for families of
contradictions given in the {\em unusual binary} encoding. A motivation of our
work is size lower bounds of refutations in Resolution for families of
contradictions in the usual unary encoding. Our main interest is the $k$-Clique
Principle, whose Resolution complexity is still unknown.
Our main result is a $n^{\Omega(k)}$ lower bound for the size of refutations
of the binary $k$-Clique Principle in $Res(\lfloor \frac{1}{2}\log \log
n\rfloor)$. This improves the result of Lauria, Pudl\'ak et al. [24] who proved
the lower bound for Resolution, that is $Res(1)$.
Our second lower bound proves that in $RES(s)$ for $s\leq
\log^{\frac{1}{2-\epsilon}}(n)$, the shortest proofs of the $BinPHP^m_n$,
requires size $2^{n^{1-\delta}}$, for any $\delta>0$. Furthermore we prove that
$BinPHP^m_n$ can be refuted in size $2^{\Theta(n)}$ in treelike $Res(1)$,
contrasting with the unary case, where $PHP^m_n$ requires treelike $RES(1)$ \
refutations of size $2^{\Omega(n \log n)}$ [9,16].
Furthermore we study under what conditions the complexity of refutations in
Resolution will not increase significantly (more than a polynomial factor) when
shifting between the unary encoding and the binary encoding. We show that this
is true, from unary to binary, for propositional encodings of principles
expressible as a $\Pi_2$-formula and involving {\em total variable
comparisons}. We then show that this is true, from binary to unary, when one
considers the \emph{functional unary encoding}. Finally we prove that the
binary encoding of the general Ordering principle $OP$ -- with no total
ordering constraints -- is polynomially provable in Resolution.
|
1809.02843
|
We report the detection of spatially resolved CO(1-0) emission in the z~3.4
submillimeter galaxies (SMGs) SMM J09431+4700 and SMM J13120+4242, using the
Expanded Very Large Array (EVLA). SMM J09431+4700 is resolved into the two
previously reported millimeter sources H6 and H7, separated by ~30kpc in
projection. We derive CO(1-0) line luminosities of L'(CO 1-0) = (2.49+/-0.86)
and (5.82+/-1.22) x 10^10 K km/s pc^2 for H6 and H7, and L'(CO 1-0) =
(23.4+/-4.1) x 10^10 K km/s pc^2 for SMM J13120+4242. These are ~1.5-4.5x
higher than what is expected from simple excitation modeling of higher-J CO
lines, suggesting the presence of copious amounts of low-excitation gas. This
is supported by the finding that the CO(1-0) line in SMM J13120+4242, the
system with lowest CO excitation, appears to have a broader profile and more
extended spatial structure than seen in higher-J CO lines (which is less
prominently seen in SMM J09431+4700). Based on L'(CO 1-0) and excitation
modeling, we find M_gas = 2.0-4.3 and 4.7-12.7 x 10^10 Msun for H6 and H7, and
M_gas = 18.7-69.4 x 10^10 Msun for SMM J13120+4242. The observed CO(1-0)
properties are consistent with the picture that SMM J09431+4700 represents an
early-stage, gas-rich major merger, and that SMM J13120+4242 represents such a
system in an advanced stage. This study thus highlights the importance of
spatially and dynamically resolved CO(1-0) observations of SMGs to further
understand the gas physics that drive star formation in these distant galaxies,
which becomes possible only now that the EVLA rises to its full capabilities.
|
1105.4177
|
In this work, we investigate the surface thermophysical properties (thermal
emissivity, thermal inertia, roughness fraction and geometric albedo) of
asteroid (99942) Apophis, using the currently available thermal infrared
observations of CanariCam on Gran Telescopio CANARIAS and far-infrared data by
PACS of Herschel, on the basis of the Advanced thermophysical model. We show
that the thermal emissivity of Apophis should be wavelength dependent from
$8.70~\mu m$ to $160~\mu m$, and the maximum emissivity may arise around
$20~\mu m$ similar to that of Vesta. Moreover, we further derive the thermal
inertia, roughness fraction, geometric albedo and effective diameter of Apophis
within a possible 1$\sigma$ scale of
$\Gamma=100^{+100}_{-52}\rm~Jm^{-2}s^{-0.5}K^{-1}$, $f_{\rm r}=0.78\sim1.0$,
$p_{\rm v}=0.286^{+0.030}_{-0.026}$, $D_{\rm eff}=378^{+19}_{-25}\rm~m$, and
3$\sigma$ scale of $\Gamma=100^{+240}_{-100}\rm~Jm^{-2}s^{-0.5}K^{-1}$, $f_{\rm
r}=0.2\sim1.0$, $p_{\rm v}=0.286^{+0.039}_{-0.029}$, $D_{\rm
eff}=378^{+27}_{-29}\rm~m$. The derived low thermal inertia but high roughness
fraction may imply that Apophis could have regolith on its surface, and less
regolith migration process has happened in comparison with asteroid Itokawa.
Our results show that small-size asteroids could also have fine regolith on the
surface, and further infer that Apophis may be delivered from the Main Belt by
Yarkovsky effect.
|
1703.06689
|
The hidden-charmed pentaquark $P_c(4450)$ and the charmonium-like state
$Y(4274)$ are investigated as a $\bar{D}^*\Sigma_c$ and a
$D_s\bar{D}_{s0}(2317)$ molecular state, respectively. The spin parities of
these two states cannot be well understood if only S-wave $\bar{D}^*\Sigma_c$
and $D_s\bar{D}_{s0}(2317)$ interactions are considered. In this work, the
interactions are studied in a quasipotential Bethe-Salpeter equation approach
with a partial wave decomposition on spin parity $J^P$, and the contributions
of different partial waves are studied in a two-channel scattering model
including a generating channel and an observation channel. Two poles at
$4447\pm4i$ and $4392\pm46i$ MeV are produced from the $\bar{D}^*\Sigma_c$
interaction coupled with the $J/\psi p$ channel in $3/2^-$ wave and $5/2^+$
wave, respectively. The peak for the $5/2^+$ state has a comparable height as
that of the $3/2^-$ state in the $J/\psi p$ invariant mass spectrum. The
$D_s\bar{D}_{s0}(2317)$ interaction coupled with the $J/\psi\phi$ channel is
studied and a pole at $4275\pm11i$ MeV is produced in $J^{P}=1^{+}$ wave, which
corresponds to P-wave $D_s\bar{D}_{s0}(2317)$ interaction. The pole from S-wave
$D_s\bar{D}_{s0}(2317)$ interaction is far below that from P-wave interaction
even the $J/\psi\phi$ threshold, so cannot be observed in the $J/\psi\phi$
channel. The result suggests that in these cases a state carrying a spin parity
corresponding to P-wave interaction should be taken as seriously as these
carrying a spin parity corresponding to S-wave interaction in the hadronic
molecular state picture.
|
1607.03223
|
The Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) has been conducted
over a five-year period at the CFHT with the MegaCam instrument, totaling 450
nights of observations. The Wide Synoptic Survey is one component of the
CFHTLS, covering 155 square degrees in four patches of 23 to 65 square degrees
through the whole MegaCam filter set (u*, g', r', i', z') down to i'$_{AB}$ =
24.5. With the motivation of searching for high-redshift quasars at redshifts
above 6.5, we extend the multi-wavelength CFHTLS-Wide data in the Y-band down
to magnitudes of $\sim$ 22.5 for point sources (5$\sigma$). We observed the
four CFHTLS-Wide fields (except one quarter of the W3 field) in the Y-band with
the WIRCam instrument at the CFHT. Each field was visited twice, at least three
weeks apart. Each visit consisted of two dithered exposures. The images are
reduced with the Elixir software used for the CFHTLS and modified to account
for the properties of near-InfraRed (IR) data. Two series of image stacks are
subsequently produced: four-image stacks for each WIRCam pointing, and
one-square-degree tiles matched to the format of the CFHTLS data release.
Photometric calibration is performed on stars by fitting stellar spectra to
their CFHTLS photometric data and extrapolating their Y-band magnitudes. We
measure a limiting magnitude of Y$_{AB} \simeq 22.4$ for point sources
(5$\sigma$) in an aperture diameter of 0.93", over 130 square degrees. We
produce a multi-wavelength catalogue combining the CFHTLS-Wide optical data
with our CFHQSIR (Canada-France High-z quasar survey in the near-InfraRed)
Y-band data. We derive the Y-band number counts and compare them to the VIDEO
survey. We find that the addition of the CFHQSIR Y-band data to the CFHTLS
optical data increases the accuracy of photometric redshifts and reduces the
outlier rate from 13.8% to 8.8% in the redshift range 1.05 $\lesssim$ z
$\lesssim$ 1.2.
|
1709.04308
|
We examine the Standard Model under the electroweak symmetry group
$U_{EW}(2)$ subject to the Lie algebra condition $\mathfrak{u}_{EW}(2)\not\cong
\mathfrak{su}_{I}(2)\oplus \mathfrak{u}_{Y}(1)$. Physically, the condition
ensures that all electroweak gauge bosons interact with each other prior to
symmetry breaking. This represents a crucial shift in the identification of
physical gauge bosons: Unlike the Standard Model which posits a change of Lie
algebra basis induced by spontaneous symmetry breaking, here the basis is
unaltered and $A,\,Z^0,\,W^\pm$ represent the physical bosons both before and
after spontaneous symmetry breaking. Our choice of $\mathfrak{u}_{EW}(2)$
requires some modification of the matter field representation of the Standard
Model. For $U_{EW}(2)$, there are two pertinent representations ${\mathbf{2}}$
and its $U(2)$-conjugate ${\mathbf{2^c}}$ related by a global gauge
transformation that squares to minus the identity. The product group structure
calls for strong-electroweak degrees of freedom in the
$(\mathbf{3},\mathbf{2})$ and the $(\mathbf{3},{\mathbf{2^c}})$ of
$SU_C(3)\times U_{EW}(2)$ that possess integer electric charge just like
leptons. These degrees of freedom play the role of quarks, and they lead to a
modified Lagrangian that nevertheless reproduces transition rates and cross
sections equivalent to the Standard Model. The close resemblance between quark
and lepton electroweak doublets suggests a mechanism for a speculative phase
transition between quarks and leptons that stems from the product structure of
the symmetry group. Our hypothesis is that the strong and electroweak bosons
see each other as a source of decoherence. In effect, lepton representations
get identified with the $SU(3)$-trace-reduced quark representations. This
mechanism allows for possible extensions of the Standard Model that don't
require large inclusive multiplets of matter fields.
|
1709.04346
|
We introduce a new technique to constrain the line-of-sight integrated
electron density of our Galactic halo $\text{DM}_\text{MW,halo}$ through
analysis of the observed dispersion measure distributions of pulsars
$\text{DM}_\text{pulsar}$ and fast radio bursts $\text{DM}_\text{FRB}$. We
model these distributions, correcting for the Galactic interstellar medium,
with kernel density estimation---well-suited to the small data regime---to find
lower/upper bounds to the corrected
$\text{DM}_\text{pulsar}$/$\text{DM}_\text{FRB}$ distributions:
$\max[\text{DM}_\text{pulsar}] \approx 7\pm2 \text{ (stat)} \pm 9 \text{ (sys)
pc cm}^{-3}$ and $\min[\text{DM}_\text{FRB}] \approx 63^{+27}_{-21} \text{
(stat)} \pm 9 \text{ (sys) pc cm}^{-3}$. Using bootstrap resampling to estimate
uncertainties, we set conservative limits on the Galactic halo dispersion
measure $-2 < \text{DM}_\text{MW,halo} < 123 \text{pc cm}^{-3}$ (95\% c.l.).
The upper limit is especially conservative because it may include a
non-negligible contribution from the FRB host galaxies and a non-zero
contribution from the cosmic web. It strongly disfavors models where the Galaxy
has retained the majority of its baryons with a density profile tracking the
presumed dark matter density profile. Last, we perform Monte Carlo simulations
of larger FRB samples to validate our technique and assess the sensitivity of
ongoing and future surveys. We recover bounds of several tens $\text{pc
cm}^{-3}$ which may be sufficient to test whether the Galaxy has retained a
majority of its baryonic mass. We estimate that a sample of several thousand
FRBs will significantly tighten constraints on $\text{DM}_\text{MW,halo}$ and
offer a valuable complement to other analyses.
|
2005.06256
|
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