  Large-language models and large-vision models are increasingly capable of
solving compositional reasoning tasks, as measured by breakthroughs in
visual-question answering benchmarks. However, state-of-the-art solutions often
involve careful construction of large pre-training and fine-tuning datasets,
which can be expensive. The use of external tools, whether other ML models,
search engines, or APIs, can significantly improve performance by breaking down
high-level reasoning questions into sub-questions that are answerable by
individual tools, but this approach has similar dataset construction costs to
teach fine-tuned models how to use the available tools. We propose a technique
in which existing training sets can be directly used for constructing
computational environments with task metrics as rewards. This enables a model
to autonomously teach itself to use itself or another model as a tool. By doing
so, we augment training sets by integrating external signals. The proposed
method starts with zero-shot prompts and iteratively refines them by selecting
few-shot examples that maximize the task metric on the training set. Our
experiments showcase how Gemini learns how to use itself, or another smaller
and specialized model such as ScreenAI, to iteratively improve performance on
training sets. Our approach successfully generalizes and improves upon zeroshot
performance on charts, infographics, and document visual question-answering
datasets


  In an exclusive measurement of the reaction $\gamma d \to K^+ K^- p n$, a
narrow peak that can be attributed to an exotic baryon with strangeness $S=+1$
is seen in the $K^+n$ invariant mass spectrum. The peak is at $1.542\pm 0.005$
GeV/c$^2$ with a measured width of 0.021 GeV/c$^2$ FWHM, which is largely
determined by experimental mass resolution. The statistical significance of the
peak is $5.2 \pm 0.6 \sigma$. The mass and width of the observed peak are
consistent with recent reports of a narrow $S=+1$ baryon by other experimental
groups.


  Modern mainstream financial theory is underpinned by the efficient market
hypothesis, which posits the rapid incorporation of relevant information into
asset pricing. Limited prior studies in the operational research literature
have investigated tests designed for random number generators to check for
these informational efficiencies. Treating binary daily returns as a hardware
random number generator analogue, tests of overlapping permutations have
indicated that these time series feature idiosyncratic recurrent patterns.
Contrary to prior studies, we split our analysis into two streams at the annual
and company level, and investigate longer-term efficiency over a larger time
frame for Nasdaq-listed public companies to diminish the effects of trading
noise and allow the market to realistically digest new information. Our results
demonstrate that information efficiency varies across years and reflects
large-scale market impacts such as financial crises. We also show the proximity
to results of a well-tested pseudo-random number generator, discuss the
distinction between theoretical and practical market efficiency, and find that
the statistical qualification of stock-separated returns in support of the
efficient market hypothesis is dependent on the driving factor of small
inefficient subsets that skew market assessments.


  We present photometry and analysis of the microlensing alert MACHO 96-LMC-2.
The ~3% photometry provided by the Global Microlensing Alert Network follow--up
effort reveals a periodic modulation in the lightcurve. We attribute this to
binarity of the lensed source. Microlensing fits to a rotating binary source
magnified by a single lens converge on two minima, separated by delta chi^2 ~
1. The most significant fit X1 predicts a primary which contributes ~100% of
the light, a dark secondary, and an orbital period (T) of 9.2 days. The second
fit X2 yields a binary source with two stars of roughly equal mass and
luminosity, and T = 21.2 days.
  The lensed object appears to lie on the upper LMC main sequence. We estimate
the mass of the primary component of the binary system, M ~2 M_sun. For the
preferred model X1, we explore the range of dark companions by assuming 0.1
M_sun and 1.4 M_sun objects in models X1a and X1b, respectively. We find lens
velocities projected to the LMC in these models of v^hat_X1a = 18.3 +/- 3.1
km/s and v^hat_X1b = 188 +/- 32 k/ms. In both these cases, a likelihood
analysis suggests an LMC lens is preferred over a Galactic halo lens, although
only marginally so in model X1b. We also find v^hat_X2 = 39.6 +/- 6.1 k/ms,
where the likelihood for the lens location is strongly dominated by the LMC
disk. In all cases, the lens mass is consistent with that of an M-dwarf. The
LMC self-lensing rate contributed by 96-LMC-2 is consistent with model
self-lensing rates. (Abridged)


  This paper investigates the energy efficiency (EE) optimization in downlink
multi-cell massive multiple-input multiple-output (MIMO). In our research, the
statistical channel state information (CSI) is exploited to reduce the
signaling overhead. To maximize the minimum EE among the neighbouring cells, we
design the transmit covariance matrices for each base station (BS).
Specifically, optimization schemes for this max-min EE problem are developed,
in the centralized and distributed ways, respectively. To obtain the transmit
covariance matrices, we first find out the closed-form optimal transmit
eigenmatrices for the BS in each cell, and convert the original transmit
covariance matrices designing problem into a power allocation one. Then, to
lower the computational complexity, we utilize an asymptotic approximation
expression for the problem objective. Moreover, for the power allocation
design, we adopt the minorization maximization method to address the
non-convexity of the ergodic rate, and use Dinkelbach's transform to convert
the max-min fractional problem into a series of convex optimization
subproblems. To tackle the transformed subproblems, we propose a centralized
iterative water-filling scheme. For reducing the backhaul burden, we further
develop a distributed algorithm for the power allocation problem, which
requires limited inter-cell information sharing. Finally, the performance of
the proposed algorithms are demonstrated by extensive numerical results.


  Based on the two flavor NJL model with a proper time regularization, we used
stationary wave condition (SWC) for the first time to study the influence of
the finite volume effects on the chiral phase transition of quark matter at
finite temperature. It is found that when the cubic volume size L is large than
LSWC = 500 fm, the chiral quark condensate is indistinguishable from that max
at L = $\infinity$,Here it should be noted that 500 fm is far greater than the
size of QGP produced at laboratory and the lattice QCD simulation space size.
It is also much larger than the previous limit size LAPBC = 5 fm estimated by
the commonly used anti-periodic boundary condition (APBC). max We also found
that when the space size L is less than LSWC = 0.25 fm, the spontaneous
symmetry min breaking concept is no longer valid. In addition, we first
introduce the spatial susceptibility, and through the study of the spatial
susceptibility, it was revealed for the first time that the chiral phase
transition caused by the finite volume effects in the nonchiral limit is a
crossover.


  Interactions between an internal flow and wall deformation occur in many
biological systems. Such interactions can involve a complex and rich dynamical
behavior and a number of peculiarities which depend on the flow parameter
range. The aim of this paper is to present a variant (obtained via a weighted
residual approach) of the averaged one-dimensional model derived by Stewart et
al. "Local and global instabilities of flow in a flexible-walled channel," Eur.
J. Mech. B/Fluids 28, 541-557 (2009)]. The asymptotic expansions for small
Reynolds numbers of these two models, compared to the exact solution obtained
from the lubrication approach, reveal some quantitative difference, even at
higher Reynolds numbers. Qualitatively, the two models give similar results at
least at a linear level. It is shown that for relatively low membrane tension
(T), there are distinct regions in the (T,R) parameter space where steady
bifurcating flows may occur. These flows can also be observed at vanishingly
small Reynolds numbers combined with relatively high membrane tension. At
sufficiently high T and R, the bifurcating flow is rather time periodic. A
weakly nonlinear analysis is then performed in both cases leading to the
derivation of evolution equations for the amplitudes of the bifurcating flows.
The amplitude equations show that the saddle node bifurcation has a
transcritical character while the Hopf bifurcation is either subcritical or
supercritical, depending both on the mode number and membrane tension.


  The ability to repeat the experiments from a research study and obtain
similar results is a corner stone in experiment-based scientific discovery.
This essential feature has been often ignored by the distributed computing and
networking community. There are many reasons for that, such as the complexity
of provisioning, configuring, and orchestrating the resources used by
experiments, their multiple external dependencies, and the difficulty to
seamlessly record these dependencies. This paper describes a methodology based
on well-established principles to plan, prepare and execute experiments. We
propose and describe a family of tools, the LabWiki workspace, to support an
experimenter's workflow based on that methodology. This proposed workspace
provides services and mechanisms for each step of an experiment-based study,
while automatically capturing the necessary information to allow others to
repeat, inspect, validate and modify prior experiments. Our LabWiki workspace
builds on existing contributions, and de-facto protocol and model standards,
which emerged from recent experimental facility initiatives. We use a real
experiment as a thread to guide and illustrate the discussion throughout this
paper.


  We study the adaptation dynamics of an initially maladapted asexual
population with genotypes represented by binary sequences of length $L$. The
population evolves in a maximally rugged fitness landscape with a large number
of local optima. We find that whether the evolutionary trajectory is
deterministic or stochastic depends on the effective mutational distance
$d_{\mathrm{eff}}$ upto which the population can spread in genotype space. For
$d_{\mathrm{eff}}=L$, the deterministic quasispecies theory operates while for
$d_{\mathrm{eff}} < 1$, the evolution is completely stochastic. Between these
two limiting cases, the dynamics are described by a local quasispecies theory
below a crossover time $T_{\times}$ while above $T_{\times}$, the population
gets trapped at a local fitness peak and manages to find a better peak either
via stochastic tunneling or double mutations. In the stochastic regime
$d_\mathrm{eff} < 1$, we identify two subregimes associated with clonal
interference and uphill adaptive walks, respectively. We argue that our
findings are relevant to the interepretation of evolution experiments with
microbial populations.


  We measured the relative positions between two pairs of compact extragalactic
sources (CESs), J1925-2219 \& J1923-2104 (C1--C2) and J1925-2219 \& J1928-2035
(C1--C3) on 2020 October 23--25 and 2021 February 5 (totaling four epochs),
respectively, using the Very Long Baseline Array (VLBA) at 15 GHz. Accounting
for the deflection angle dominated by Jupiter, as well as the contributions
from the Sun, planets other than Earth, the Moon and Ganymede (the most massive
of the solar system's moons), our theoretical calculations predict that the
dynamical ranges of the relative positions across four epochs in R.A. of the
C1--C2 pair and C1--C3 pair are 841.2 and 1127.9 $\mu$as, respectively. The
formal accuracy in R.A. is about 20 $\mu$as, but the error in Decl. is poor.
The measured standard deviations of the relative positions across the four
epochs are 51.0 and 29.7 $\mu$as in R.A. for C1--C2 and C1--C3, respectively.
These values indicate that the accuracy of the post-Newtonian relativistic
parameter, $\gamma$, is $\sim 0.061$ for C1--C2 and $\sim 0.026$ for C1--C3.
Combining the two CES pairs, the measured value of $\gamma$ is $0.984 \pm
0.037$, which is comparable to the latest published results for Jupiter as a
gravitational lens reported by Fomalont \& Kopeikin, i.e., $1.01 \pm 0.03$.


  Massive disk galaxies like our Milky Way should host an ancient, metal-poor,
and centrally concentrated stellar population. This population reflects the
star formation and enrichment in the few most massive progenitor components
that coalesced at high redshift to form the proto-Galaxy. While metal-poor
stars are known to reside in the inner few kiloparsecs of our Galaxy, current
data do not yet provide a comprehensive picture of such a metal-poor "heart" of
the Milky Way. We use information from Gaia DR3, especially the XP spectra, to
construct a sample of 2 million bright (BP $<15.5$ mag) giant stars within
$30^\circ$ of the Galactic Center with robust [M/H] estimates, $\delta$ [M/H]
$\lesssim 0.1$. For most sample members we can calculate orbits based on Gaia
RVS velocities and astrometry. This sample reveals an extensive, ancient, and
metal-poor population that includes $\sim 18,000$ stars with $-2.7<$ [M/H]
$<-1.5$, representing a stellar mass of $\gtrsim 5\times 10^7$ M$_\odot$. The
spatial distribution of these [M/H] $<-1.5$ stars has a Gaussian extent of only
$\sigma_{\mathrm{R_{GC}}} \sim 2.7$ kpc around the Galactic center, with most
of these orbits being confined to the inner Galaxy. At high orbital
eccentricities, there is clear evidence for accreted halo stars in their
pericentral orbit phase. Stars with [M/H] $< -2$ show no net rotation, whereas
those with [M/H] $\sim -1$ are rotation dominated. Most of the tightly bound
stars show $[\alpha/\text{Fe}]$-enhancement and [Al/Fe]-[Mn/Fe] abundance
patterns expected for an origin in the more massive portions of the
proto-Galaxy. These central, metal-poor stars most likely predate the oldest
part of the disk ($\tau_{\text{age}}\approx 12.5$ Gyrs), which implies that
they formed at $z\gtrsim 5$, forging the proto-Milky Way.


  Recent work has shown that Variational Autoencoders (VAEs) can be used to
upper-bound the information rate-distortion (R-D) function of images, i.e., the
fundamental limit of lossy image compression. In this paper, we report an
improved upper bound on the R-D function of images implemented by (1)
introducing a new VAE model architecture, (2) applying variable-rate
compression techniques, and (3) proposing a novel \ourfunction{} to stabilize
training. We demonstrate that at least 30\% BD-rate reduction w.r.t. the intra
prediction mode in VVC codec is achievable, suggesting that there is still
great potential for improving lossy image compression. Code is made publicly
available at https://github.com/duanzhiihao/lossy-vae.


  Quantum mechanics predicts that measurements of incompatible observables
carry a minimum uncertainty which is independent of technical deficiencies of
the measurement apparatus or incomplete knowledge of the state of the system.
Nothing yet seems to prevent a single physical quantity, such as one spin
component, from being measured with arbitrary precision. Here we show that an
intrinsic quantum uncertainty on a single observable is ineludible in a number
of physical situations. When revealed on local observables of a bipartite
system, such uncertainty defines an entire class of bona fide measures of
nonclassical correlations. For the case of 2 x d systems, we find that a unique
measure is defined, which we evaluate in closed form. We then discuss the role
that these correlations, which are of the 'discord' type, can play in the
context of quantum metrology. We show in particular that the amount of discord
present in a bipartite mixed probe state guarantees a minimum precision, as
quantified by the quantum Fisher information, in the optimal phase estimation
protocol.


  A combinatorial optimization problem (COP) has a finite groundset
$E(\left|E\right|=N$), a weight vector $c=\left(c^e:e\in E\right)$ and a family
$T\in E$ of feasible subsets with objective to find $t\in T$ with maximal
weight: ${max}\{\sum_{e\in t}c^e$: $t\in T\}$. Polyhedral combinatorics
reformulates combinatorial optimization as linear program: $T$ is mapped into
the set $X\in R^N$ of 0/1 incidence vectors and $c\in R^N$ is maximized over
the convex hull of $X$: ${max}\{cx: x\in conv(X)\}$. In theory, complementary
slackness conditions for the induced linear program provide optimality
conditions for the COP. However, in general case, optimality conditions for
combinatorial optimization have not been formulated analytically as for many
problems complete description of the induced polytopes is available only as a
convex hull of extreme points rather than a system of linear inequalities.
Here, we formulate optimality conditions for a COP in general case: $x_k\in X\
\ $is optimal if and only if $c\in cone\left(H_k\right)\ $ where $H_k$ $=\{h\in
V:\ {hx}_k\ \ge hx$ for all $x\in X\}$ and $V$ is the set of all -1/0/1 valued
vectors in $R^N$. This provides basis to get, in theory, a complete description
of a combinatorial polytope induced by any COP: all facet inducing inequalities
for $conv(X)$ can be written as $hx\le l$ where $h\in V$ and $l$ is integer. A
vector $h\in V$ induces a nonredundent facet if and only if $h\in H_k^o$ $\in
H_k$ for at least one $x_k\in X\ $(where $H_k^o$$=\{h\in H_k:h\notin
cone(H_k\setminus \{h\})\}$ ) and $l=\ $ $x_kh$.


  The quadric $\operatorname{Q}_{2n}$ is the ${\mathbb Z}$-scheme defined by
the equation $\sum_{i=1}^n x_i y_i = z(1-z)$. We show that
$\operatorname{Q}_{2n}$ is a homogeneous space for the split reductive group
scheme $\operatorname{SO}_{2n+1}$ over ${\mathbb Z}$. The quadric
$\operatorname{Q}_{2n}$ is known to have the ${\mathbb A}^1$-homotopy type of a
motivic sphere and the identification as a homogeneous space allows us to give
a characteristic independent affine representability statement for motivic
spheres. This last observation allows us to give characteristic independent
comparison results between Chow--Witt groups, motivic stable cohomotopy groups
and Euler class groups.


  We consider the problem of ESPRIT-oriented precoder design for beamspace
angle-of-departure (AoD) estimation in downlink mmWave multiple-input
single-output communications. Standard precoders (i.e., directional/sum beams)
yield poor performance in AoD estimation, while Cramer-Rao bound-optimized
precoders undermine the so-called shift invariance property (SIP) of ESPRIT. To
tackle this issue, the problem of designing ESPRIT-oriented precoders is
formulated to jointly optimize over the precoding matrix and the SIP-restoring
matrix of ESPRIT. We develop an alternating optimization approach that updates
these two matrices under unit-modulus constraints for analog beamforming
architectures. Simulation results demonstrate the validity of the proposed
approach while providing valuable insights on the beampatterns of the
ESPRIT-oriented precoders.


  Quasar J152645.61+193006.7 ($z_{\rm e}=2.5771$) was observed by the Sloan
Digital Sky Survey (SDSS) on 2006 May 31, and again on 2011 April 9. The time
interval of the SDSS two observations is 497.4 days at the quasar rest frame.
From the spectra of this quasar, we detect a phenomenon of disappearance of a
narrow $\rm Mg II \lambda\lambda2796,2803$ absorption system with a velocity up
to $\rm 166,129 km s^{-1}$ with respect to the quasar. This disappearance event
can be caused by changes in the ionization state of absorbing gas or by the
bulk motion of the absorbing gas across the quasar sightline. The coverage
fraction analysis shows that this absorber partially covers the background
emission sources with an effective coverage fraction of $C_{\rm
f}=0.40\pm0.06$. The time variation analysis and the coverage fraction analysis
imply that this absorber might be intrinsic to the quasar. However, the
scenario of a cosmologically separated foreground object located at $z=0.9170$
accounting for the phenomenon cannot be ruled out according to current
available data.


  In this paper, we study the dynamics of a Bianchi Type I potential in the
presence of a concave potential of the form $V(\phi) = V_0 \left[1- \left(
\frac{\phi}{\mu}\right)^n\right]$, where $V_0$ is a constant, and $\mu$ is a
mass scale. We show that there are two classes of equilibrium points. The first
class corresponds to $\phi \neq 0$, $\mu \neq 0$, $n = 0$, and $\dot{\phi} =
0$, which describe expanding and contracting de Sitter universes, for which the
shear anisotropy is zero. We show that the expanding de Sitter universe is a
local sink of the system, and therefore has associated to it a stable manifold.
Thus, orbits will approach this point at late times. In other words, such a
model is found to inflate and isotropize at late times as long as $n = 0$. The
second class of equilibrium points corresponds to an expanding and contracting
anisotropic universe. However, these points are found to emerge only when $n >
1$, $\phi = \dot{\phi} = 0$, which importantly implies that $V = V_0 < 0$ at
this point in order to ensure that the square of the shear scalar, $\sigma^2$
is real. Therefore, such equilibrium points correspond to the ekpyrotic
cosmological models. Further, we show that for $n = 2$, by Lyapunov's stability
theorem, the expanding equilibrium point is asymptotically stable, while for $n
> 2$, a two-dimensional stable manifold exists corresponding to the fact that
for $n > 2$, such an equilibrium point represents a local sink of the system.
Finally, we give a general condition for inflation to occur in this model in
terms of the deceleration parameter, and show that the expanding ekpyrotic
equilibrium point undergoes the phenomenon of anisotropic inflation if
$-3\Lambda/5 < V_0 < 0$, where $\Lambda > 0$ is the cosmological constant.


  We present a general framework for incorporating astrophysical information
into Bayesian parameter estimation techniques used by gravitational wave data
analysis to facilitate multi-messenger astronomy. Since the progenitors of
transient gravitational wave events, such as compact binary coalescences, are
likely to be associated with a host galaxy, improvements to the source sky
location estimates through the use of host galaxy information are explored. To
demonstrate how host galaxy properties can be included, we simulate a
population of compact binary coalescences and show that for ~8.5% of
simulations with in 200Mpc, the top ten most likely galaxies account for a ~50%
of the total probability of hosting a gravitational wave source. The true
gravitational wave source host galaxy is in the top ten galaxy candidates ~10%
of the time. Furthermore, we show that by including host galaxy information, a
better estimate of the inclination angle of a compact binary gravitational wave
source can be obtained. We also demonstrate the flexibility of our method by
incorporating the use of either B or K band into our analysis.


  Vacuum polarization in QED in a background gravitational field induces
interactions which {\it effectively} modify the classical picture of light rays
as the null geodesics of spacetime. After a short introduction on the main
aspects of the quantum gravitational optics, as a nontrivial example, we study
this effect in the background of NUT space characterizing the spacetime of a
spherical mass endowed with a gravitomagnetic monopole charge, the so called
NUT factor.


  At present the three major unknowns in neutrino oscillation parameters are
the mass hierarchy, the octant of $\theta_{23}$ and the CP phase $\delta_{CP}$.
It is well known that the presence of hierarchy$-\delta_{CP}$ and octant
degeneracies affects the unambiguous determination of these parameters. In this
paper we show that a comprehensive way to study the remaining parameter
degeneracies is in the form of a generalized hierarchy-$\theta_{23}$ -
$\delta_{CP}$ degeneracy. We show that the wrong-hierarchy and/or wrong-octant
solutions can be further classified into eight different solutions depending on
whether they occur with the wrong or right value of $\delta_{CP}$. These eight
solutions are different from the original eightfold degenerate solutions and
can exist, in principle, even if $\theta_{13}$ is known. These multiple
solutions, apart from affecting the determination of the true hierarchy and
octant, also affect the accurate estimation of $\delta_{CP}$. We identify which
of these eight different degenerate solutions can occur in the test
($\theta_{23} - \delta_{CP}$) parameter space, taking the long-baseline
experiment NO$\nu$A running in the neutrino mode as an example. The inclusion
of the NO$\nu$A antineutrino run removes the wrong-octant solutions appearing
with both right and wrong hierarchy. Adding T2K data to this resolves the wrong
hierarchy -- right octant solutions to a large extent. The remaining wrong
hierarchy solutions can be removed by combining NO$\nu$A + T2K with atmospheric
neutrino data. We demonstrate this using ICAL@INO as the prototype atmospheric
neutrino detector. We find that the degeneracies can be resolved at the
$2\sigma$ level by the combined data set, for the true parameter space
considered in the study.


  In this article, we study a notion of the extraction rate of Turing
functionals that translate between notions of randomness with respect to
different underlying probability measures. We analyze several classes of
extraction procedures: a first class that generalizes von Neumann's trick for
extracting unbiased randomness from the tosses of a biased coin, a second class
based on work of generating biased randomness from unbiased randomness by Knuth
and Yao, and a third class independently developed by Levin and Kautz that
generalizes the data compression technique of arithmetic coding. For the first
two classes of extraction procedures, we identify a level of algorithmic
randomness for an input that guarantees that we attain the extraction rate
along that input, while for the third class, we calculate the rate attained
along sufficiently random input sequences.


  We propose a simple and general framework for nonparametric estimation of
heterogeneous treatment effects under fairness constraints. Under standard
regularity conditions, we show that the resulting estimators possess the double
robustness property. We use this framework to characterize the trade-off
between fairness and the maximum welfare achievable by the optimal policy. We
evaluate the methods in a simulation study and illustrate them in a real-world
case study.


  This article investigates parameter estimation of affine term structure
models by means of the generalized method of moments. Exact moments of the
affine latent process as well as of the yields are obtained by using results
derived for p-polynomial processes. Then the generalized method of moments,
combined with Quasi-Bayesian methods, is used to get reliable parameter
estimates and to perform inference. After a simulation study, the estimation
procedure is applied to empirical interest rate data.


  The recent TRIUMF experiment for $\mu^- p \to n \nu_{\mu} \gamma$ gave a
surprising result that the induced pseudoscalar coupling constant $g_P$ was
larger than the value obtained from $\mu^- p \to n \nu_{\mu}$ experiment as
much as 44 %. Reexamining axial vector current on the gauge theory, we found an
additional term to the matrix element of Beder and Fearing which was used to
extract the $g_P$ value from the measured photon energy spectrum. This
additional term, which is self gauge invariant, plays a key role in restoring
the reliability of $g_P (- 0.88 m_{\mu}^2) = 6.77 g_A (0)$. Comparison with
conventional approaches is also presented.


  Gazeau-Klauder coherent states of the extended trigonometric Scarf potential,
underlying the quadratic energy spectrum and associated with Jacobi-type Xm
exceptional orthogonal polynomials P(a,b,m) n (x), are constructed. The
temporal evolution of wave-packet coherent states are performed by means of an
autocorrelation function and the full revival properties are investigated in
the usual time-domain analysis. This latter seems to be less useful for
describing the fractional revivals due to the complicated nature of coherent
wave-packet. Fortunately the autocorrelation function revels a little signature
of fractional revivals at the vicinity of quarters of the revival time Trev due
to the quadratic energy spectrum and the use of the wavelet-based
time-frequency analysis of the autocorrelation function provides an analytical
and numerical observation of the fractional revivals at different orders of the
system.


  The Lema\^{\i}tre -- Tolman model with $\Lambda = 0$ and constant bang time
that imitates the luminosity distance -- redshift relation of the $\Lambda$CDM
model using the energy function $E$ alone contains shell crossings. In this
paper, the location in spacetime and the consequences of existence of the
shell-crossing set (SCS) are investigated. The SCS would come into view of the
central observer only at $t \approx 1064 T$ to the future from now, where $T$
is the present age of the Universe, but would not leave any recognizable trace
in her observations. Light rays emitted near to the SCS are blueshifted at the
initial points, but the blueshift is finite, and is overcompensated by
later-induced redshifts if the observer is sufficiently far. The local
blueshifts cause that $z$ along a light ray is not a monotonic function of the
comoving radial coordinate $r$. As a consequence, the angular diameter distance
$D_A$ and the luminosity distance $D_L$ from the central observer fail to be
functions of $z$; the relations $D_A(z)$ and $D_L(z)$ are multiple-valued in a
vicinity of the SCS. The following quantities are calculated and displayed: (1)
The distribution of mass density on a few characteristic hypersurfaces of
constant time; some of them intersect the SCS. (2) The distribution of density
along the past light cone of the present central observer. (3) A few light
cones intersecting the SCS at characteristic instants. (4) The redshift
profiles along several light cones. (5) The extremum-redshift hypersurface. (6)
The $D_A(z)$ and $D_L(z)$ relations. (7) The last scattering time and its
comparison with the $\Lambda$CDM last scattering epoch.


  We present 3.5cm and 6.2cm radio continuum maps in total and polarized
intensity of the barred galaxies NGC 1097 and NGC 1365. Both galaxies exhibit
radio ridges roughly overlapping with the massive dust lanes in the bar region.
The contrast in total intensity across the radio ridges is compatible with
compression and shear of an isotropic random magnetic field. The contrast in
polarized intensity is significantly smaller than that expected from
compression and shearing of the regular magnetic field; this could be the
result of decoupling of the regular field from the dense molecular clouds. The
regular field in the ridge is probably strong enough to reduce significantly
shear in the diffuse gas (to which it is coupled) and hence to reduce magnetic
field amplification by shearing. This contributes to the misalignment of the
observed field orientation with respect to the velocity vectors of the dense
gas. Our observations, for the first time, indicate that magnetic forces can
control the flow of the diffuse interstellar gas at kiloparsec scales. The
total radio intensity reaches its maximum in the circumnuclear starburst
regions, where the equipartition field strength is about 60\mu G, amongst the
strongest fields detected in spiral galaxies so far. The regular field in the
inner region has a spiral shape with large pitch angle, indicating the action
of a dynamo. Magnetic stress leads to mass inflow towards the centre,
sufficient to feed the active nucleus in NGC 1097. We detected diffuse X-ray
emission, possibly forming a halo of hot gas around NGC 1097.


  In this work, we attempt to address unsupervised domain adaptation by
devising simple and compact conditional domain adversarial training methods. We
first revisit the simple concatenation conditioning strategy where features are
concatenated with output predictions as the input of the discriminator. We find
the concatenation strategy suffers from the weak conditioning strength. We
further demonstrate that enlarging the norm of concatenated predictions can
effectively energize the conditional domain alignment. Thus we improve
concatenation conditioning by normalizing the output predictions to have the
same norm of features, and term the derived method as Normalized OutpUt
coNditioner~(NOUN). However, conditioning on raw output predictions for domain
alignment, NOUN suffers from inaccurate predictions of the target domain. To
this end, we propose to condition the cross-domain feature alignment in the
prototype space rather than in the output space. Combining the novel
prototype-based conditioning with NOUN, we term the enhanced method as
PROtotype-based Normalized OutpUt coNditioner~(PRONOUN). Experiments on both
object recognition and semantic segmentation show that NOUN can effectively
align the multi-modal structures across domains and even outperform
state-of-the-art domain adversarial training methods. Together with
prototype-based conditioning, PRONOUN further improves the adaptation
performance over NOUN on multiple object recognition benchmarks for UDA.


  We studied the transient neutron-star low-mass X-ray binary GRS 1747-312,
located in the globular cluster Terzan 6, in its quiescent state after its
outburst in August 2004, using an archival XMM-Newton observation. A source was
detected in this cluster and its X-ray spectrum can be fitted with the
combination of a soft, neutron-star atmosphere model and a hard, power-law
model. Both contributed roughly equally to the observed 0.5-10 keV luminosity
(~4.8X10^33 erg/s). This type of X-ray spectrum is typically observed for
quiescent neutron-star X-ray transients that are perhaps accreting in
quiescence at very low rates. Therefore, if this X-ray source is the quiescent
counterpart of GRS 1747-312, then this source is also accreting at low levels
in-between outbursts. Since source confusion a likely problem in globular
clusters, it is quite possible that part, if not all, of the emission we
observed is not related to GRS 1747-312, and is instead associated with another
source or conglomeration of sources in the cluster. Currently, it is not
possible to determine exactly which part of the emission truly originates from
GRS 1747-312, and a Chandra observation (when no source is in outburst in
Terzan 6) is needed to be conclusive. Assuming that the detected emission is
due to GRS 1747-312, we discuss the observed results in the context of what is
known about other quiescent systems. We also investigated the thermal evolution
of the neutron star in GRS 1747-312, and inferred that GRS 1747-312 can be
considered a typical quiescent system under our assumptions.


  It has been known since Julia that polynomials commuting under composition
have the same Julia set. More recently in the works of Baker and Eremenko,
Fern\'andez, and Beardon, results were given on the converse question: When do
two polynomials have the same Julia set? We give a complete answer to this
question and show the exact relation between the two problems of polynomials
with the same Julia set and commuting pairs.


  We use deep observations obtained with the Photodetector Array Camera and
Spectrometer (PACS) onboard the Herschel space observatory to study the
far-infrared (FIR) properties of submm and optically faint radio galaxies (SMGs
and OFRGs). From literature we compiled a sample of 35 securely identified SMGs
and nine OFRGs located in the GOODS-N and the A2218 fields. This sample is
cross-matched with our PACS 100 um and 160 um multi-wavelength catalogs. About
half of the galaxies in our sample are detected with PACS. The dust
temperatures and the infrared luminosities of our galaxies are derived by
fitting their PACS and SCUBA 850 um (only the upper limits for the OFRGs) flux
densities with a single modified (beta=1.5) black body function. The median
dust temperature of our SMG sample is T=36+/-8K while for our OFRG sample it is
T=47+/-3K. For both samples, median dust temperatures derived from Herschel
data agree well with previous estimates. In particular, Chapman et al. (2005)
found a dust temperature of T=36+/-7K for a large sample of SMGs assuming the
validity of the FIR/radio correlation. The agreement between our studies
confirms that the local FIR/radio correlation effectively holds at high
redshift even though we find <q>=2.17+/-0.19, a slightly lower value than that
observed in local systems. The median IR luminosities of SMGs and OFRGs are
4.6*10^12 Lsun and 2.6*10^12 Lsun, respectively. We note that for both samples
the IR luminosity estimates from the radio part of the spectral energy
distribution are accurate, while estimates from the mid-IR are considerably
(x3) more uncertain. Our observations confirm the remarkably high luminosities
of SMGs and thus imply median star-formation rates of 960Msun yr^-1 for SMGs
with S(850um)>5mJy and 460Msun yr^-1 for SMGs with S(850um)>2mJy, assuming a
Chabrier IMF and no dominant AGN contribution to the far-infrared luminosity.


  A major challenge in scaling object detection is the difficulty of obtaining
labeled images for large numbers of categories. Recently, deep convolutional
neural networks (CNNs) have emerged as clear winners on object classification
benchmarks, in part due to training with 1.2M+ labeled classification images.
Unfortunately, only a small fraction of those labels are available for the
detection task. It is much cheaper and easier to collect large quantities of
image-level labels from search engines than it is to collect detection data and
label it with precise bounding boxes. In this paper, we propose Large Scale
Detection through Adaptation (LSDA), an algorithm which learns the difference
between the two tasks and transfers this knowledge to classifiers for
categories without bounding box annotated data, turning them into detectors.
Our method has the potential to enable detection for the tens of thousands of
categories that lack bounding box annotations, yet have plenty of
classification data. Evaluation on the ImageNet LSVRC-2013 detection challenge
demonstrates the efficacy of our approach. This algorithm enables us to produce
a >7.6K detector by using available classification data from leaf nodes in the
ImageNet tree. We additionally demonstrate how to modify our architecture to
produce a fast detector (running at 2fps for the 7.6K detector). Models and
software are available at


  In this paper, we analyze different decay observables of semileptonic $ B_c$
decays into $(D_(s,d)^((*))){\mu}^+ {\mu}^-$ such as branching ratio,
forward-backward asymmetry, polarization fraction and lepton polarization
asymmetry in the non-universal Z' model. We have also studied the dependence of
branching fraction to the new model parameters. Here, we have found that the
values of different decay parameters increase in the Z' model, which provides a
possible way out for the search of new physics as well as the unknown phenomena
of charm B meson.


  We have performed a first principles study of structural, mechanical,
electronic, and optical properties of orthorhombic Sb2S3 and Sb2Se3 compounds.
The calculations have been carried out within the local density approximation
using norm conserving pseudopotentials. The lattice parameters, bulk modulus,
and its pressure derivatives of the these compounds have been obtained. The
second-order elastic constants have been calculated, and the other related
quantities such as the Young's modulus, shear modulus, Poisson's ratio,
anisotropy factor, sound velocities and Debye temperature have also been
estimated in the present work. The linear photon-energy dependent dielectric
functions and some optical properties such as the energy-loss function, the
effective number of valance electrons and the effective optical dielectric
constant are calculated. Our structural estimation and some other results are
in agreement with the available experimental and theoretical data.


  We propose an iterative algorithm to interpolate graph signals from only a
partial set of samples. Our method is derived from the well known
Papoulis-Gerchberg algorithm by considering the optimal value of a constant
involved in the iteration step. Compared with existing graph signal
reconstruction algorithms, the proposed method achieves similar or better
performance both in terms of convergence rate and computational efficiency.


  We study the effect of a static electric field on lithium donor spins in
silicon. The anisotropy of the effective mass leads to the anisotropy of the
quadratic Stark susceptibility, which we determined using the Dalgarno-Lewis
exact summation method. The theory is asymptotically exact in the field domain
below Li-donor ionization threshold, relevant to the Stark-tuning electron spin
resonance experiments. To obtain the generalized Stark susceptibilities at
arbitrary fields, we propose a new variational wave function which reproduces
the exact results in the low-field limit. With the calculated susceptibilities
at hand, we are able to predict and analyze several important physical effects.
First, we observe that the energy level shifts due to the quadratic Stark
effect for Li donors in Si are equivalent to, and can be mapped onto, those
produced by an external stress.
  Second, we demonstrate that the Stark effect anisotropy, combined with the
unique valley-orbit splitting of a Li donor in Si, spin-orbit interaction and
specially tuned external stress, may lead to a very strong modulation of the
donor spin $g$-factor by the electric field. Third, we investigate the
influence of random strains on the $g$-factor shifts and quantify the random
strain limits and requirements to Si material purity necessary to observe the
$g$-factor Stark shifts experimentally. Finally, we discuss possible
implications of our results for quantum information processing with Li spin
qubits in Si.


  Let $(X_t,t\geq 0)$ be a random walk on $\mathbb{Z}^d$. Let $ l_T(x)=
\int_0^T \delta_x(X_s)ds$ the local time at the state $x$ and $ I_T=
\sum\limits_{x\in\mathbb{Z}^d} l_T(x)^q $ the q-fold self-intersection local
time (SILT). In \cite{Castell} Castell proves a large deviations principle for
the SILT of the simple random walk in the critical case $q(d-2)=d$. In the
supercritical case $q(d-2)>d$, Chen and M\"orters obtain in \cite{ChenMorters}
a large deviations principle for the intersection of $q$ independent random
walks, and Asselah obtains in \cite{Asselah5} a large deviations principle for
the SILT with $q=2$. We extend these results to an $\alpha$-stable process
(i.e. $\alpha\in]0,2]$) in the case where $q(d-\alpha)\geq d$.


  Using the "Updated Nearby Galaxy Catalog", we consider different properties
of companion galaxies around luminous hosts in the Local Volume. The data on
stellar masses, linear diameters,surface brightnesses, HI-richness, specific
star formation rate (sSFR), and morphological types are discussed for members
of the nearest groups, including the Milky Way and M 31 groups, as a function
of their separation from the hosts. Companion galaxies in groups tend to have
lower stellar masses, smaller linear diameters and fainter mean surface
brightnesses as the distance to their host decreases. The hydrogen-to-stellar
mass ratio of the companions increases with their linear projected separation
from the dominant luminous galaxy. This tendency is more expressed around the
bulge-dominated hosts. While linear separation of the companions decreases,
their mean sSFR becomes lower, accompanied with the increasing sSFR scatter.
Typical linear projected separation of dSphs around the bulge-dominated hosts,
350 kpc, is substantially larger than that around the disk-dominated ones, 130
kpc. This difference probably indicates the presence of larger hot/warm gas
haloes around the early-type host galaxies. The mean fraction of dSph
(quenched) companions in 11 the nearest groups as a function of their projected
separation R_p can be expressed as f(E) = 0.55 - 0.69 x R_p. The fraction of
dSphs around the Milky Way and M 31 looks much higher than in other nearby
groups because the quenching efficiency dramatically increases towards the
ultra-low mass companions. We emphasize that the observed properties of the
Local Group are not typical for other groups in the Local Volume due to the
role of selection effects caused by our location inside the Local Group.


  We consider the distributed optimization problem where $n$ agents each
possessing a local cost function, collaboratively minimize the average of the
$n$ cost functions over a connected network. Assuming stochastic gradient
information is available, we study a distributed stochastic gradient algorithm,
called exact diffusion with adaptive stepsizes (EDAS) adapted from the Exact
Diffusion method and NIDS and perform a non-asymptotic convergence analysis. We
not only show that EDAS asymptotically achieves the same network independent
convergence rate as centralized stochastic gradient descent (SGD) for
minimizing strongly convex and smooth objective functions, but also
characterize the transient time needed for the algorithm to approach the
asymptotic convergence rate, which behaves as
$K_T=\mathcal{O}\left(\frac{n}{1-\lambda_2}\right)$, where $1-\lambda_2$ stands
for the spectral gap of the mixing matrix. To the best of our knowledge, EDAS
achieves the shortest transient time when the average of the $n$ cost functions
is strongly convex and each cost function is smooth. Numerical simulations
further corroborate and strengthen the obtained theoretical results.


  The calculation of common factor means in structured means analysis (SMM) is
considered. The SMM equations imply that the unique factors are defined as
having zero means. It was shown within the one factor solution that this
definition implies larger absolute common factor loadings to co-occur with
larger absolute expectations of the observed variables in the single group
case. This result was illustrated by means of a small simulation study. It is
argued that the proportionality of factor loadings and observed means should be
critically examined in the context of SMM. It is recommended that researchers
should freely estimate the observed expectations, whenever, the proportionality
of loadings and observed means does not make sense. It was also shown that for
a given size of observed expectations, smaller common factor loadings result in
larger common factor mean estimates. It should therefore be checked whether
variables with very small factor loadings occur when SMM results in very large
absolute common factor means.


  In the framework of analytic approach to QCD the nonperturbative
contributions in running coupling of strong interaction up to 4-loop order are
obtained in an explicit form. For all $Q>\Lambda$ they are shown to be
represented in the form of an expansion in inverse powers of Euclidean momentum
squared. The expansion coefficients are calculated for different numbers of
active quark flavors $n_f$ and for different number of loops taken into
account. On basis of the stated expansion the effective method for precise
calculation of the analytic running coupling can be developed.


  We present results for lattice QCD with staggered fermions in the limit of
infinite gauge coupling, obtained from a worm-type Monte Carlo algorithm on a
discrete spatial lattice but with continuous Euclidean time. This is obtained
by sending both the anisotropy parameter $\xi=a_\sigma/a_\tau$ and the number
of time-slices $N_\tau$ to infinity, keeping the ratio $aT=\xi/N\tau$ fixed.
The obvious gain is that no continuum extrapolation $N_\tau \rightarrow \infty$
has to be carried out. Moreover, the algorithm is faster and the sign problem
disappears. We derive the continuous time partition function and the
corresponding Hamiltonian formulation. We compare our computations with those
on discrete lattices and study both zero and finite temperature properties of
lattice QCD in this regime.


  In this paper, we examine the use case of general adversarial networks (GANs)
in the field of marketing. In particular, we analyze how GAN models can
replicate text patterns from successful product listings on Airbnb, a
peer-to-peer online market for short-term apartment rentals. To do so, we
define the Diehl-Martinez-Kamalu (DMK) loss function as a new class of
functions that forces the model's generated output to include a set of
user-defined keywords. This allows the general adversarial network to recommend
a way of rewording the phrasing of a listing description to increase the
likelihood that it is booked. Although we tailor our analysis to Airbnb data,
we believe this framework establishes a more general model for how generative
algorithms can be used to produce text samples for the purposes of marketing.


  Gravitational lensing by large-scale structure induces weak coherent
alignments in the shapes of background galaxies. Here we present evidence for
the detection of this `cosmic shear' at the 3.4 sigma significance level with
the William Herschel Telescope. Analysis and removal of notable systematic
effects, such as shear induced by telescope optics and smearing by tracking and
seeing, are conducted in order to recover the physical weak shear signal.
Positive results for shear recovery on realistic simulated data are presented,
enhancing confidence in the measurement method. The detection of cosmic shear
is statistically characterised, and its cosmological significance is discussed.


  The Internet of Things (IoT) applications have grown in exorbitant numbers,
generating a large amount of data required for intelligent data processing.
However, the varying IoT infrastructures (i.e., cloud, edge, fog) and the
limitations of the IoT application layer protocols in transmitting/receiving
messages become the barriers in creating intelligent IoT applications. These
barriers prevent current intelligent IoT applications to adaptively learn from
other IoT applications. In this paper, we critically review how IoT-generated
data are processed for machine learning analysis and highlight the current
challenges in furthering intelligent solutions in the IoT environment.
Furthermore, we propose a framework to enable IoT applications to adaptively
learn from other IoT applications and present a case study in how the framework
can be applied to the real studies in the literature. Finally, we discuss the
key factors that have an impact on future intelligent applications for the IoT.


  Despite the major advances in NLP, significant disparities in NLP system
performance across languages still exist. Arguably, these are due to uneven
resource allocation and sub-optimal incentives to work on less resourced
languages. To track and further incentivize the global development of equitable
language technology, we introduce GlobalBench. Prior multilingual benchmarks
are static and have focused on a limited number of tasks and languages. In
contrast, GlobalBench is an ever-expanding collection that aims to dynamically
track progress on all NLP datasets in all languages. Rather than solely
measuring accuracy, GlobalBench also tracks the estimated per-speaker utility
and equity of technology across all languages, providing a multi-faceted view
of how language technology is serving people of the world. Furthermore,
GlobalBench is designed to identify the most under-served languages, and
rewards research efforts directed towards those languages. At present, the most
under-served languages are the ones with a relatively high population, but
nonetheless overlooked by composite multilingual benchmarks (like Punjabi,
Portuguese, and Wu Chinese). Currently, GlobalBench covers 966 datasets in 190
languages, and has 1,128 system submissions spanning 62 languages.


  Partial differential equations (p.d.e) equipped of spatial derivatives of
fractional order capture anomalous transport behaviors observed in diverse
fields of Science. A number of numerical methods approximate their solutions in
dimension one. Focusing our effort on such p.d.e. in higher dimension with
Dirichlet boundary conditions, we present an approximation based on Lattice
Boltzmann Method with Bhatnagar-Gross-Krook (BGK) or Multiple-Relaxation-Time
(MRT) collision operators. First, an equilibrium distribution function is
defined for simulating space-fractional diffusion equations in dimensions 2 and
3. Then, we check the accuracy of the solutions by comparing with i) random
walks derived from stable L\'evy motion, and ii) exact solutions. Because of
its additional freedom degrees, the MRT collision operator provides accurate
approximations to space-fractional advection-diffusion equations, even in the
cases which the BGK fails to represent because of anisotropic diffusion tensor
or of flow rate destabilizing the BGK LBM scheme.


  The celebrated geodesic congruence equation of Raychaudhuri, together with
the resulting singularity theorems of Penrose and Hawking that it enabled,
yield a highly general set of conditions under which a spacetime (or, more
generically, a pseudo-Riemannian manifold) is expected to become geodesically
incomplete. It is a non-trivial question to ask whether (and to what extent)
there exist equivalently general conditions under which one expects discrete
spacetimes to become geodesically incomplete, and how these conditions might
differ from those in the continuum. This article builds upon previous work, in
which the conformal and covariant Z4 (CCZ4) formulation of the Cauchy problem
for the Einstein field equations, with constraint-violation damping, was
defined in terms of Wolfram model evolution over discrete (spatial) hypergraphs
for the case of vacuum spacetimes, and proceeds to consider a minimal extension
to the non-vacuum case by introducing a massive scalar field distribution,
defined in either spherical or axial symmetry. Under appropriate assumptions,
this scalar field distribution admits a physical interpretation as a collapsing
(and, in the axially-symmetric case, uniformly rotating) dust, and we are able
to show, through a combination of rigorous mathematical analysis and explicit
numerical simulation, that the resulting discrete spacetimes converge
asymptotically to either non-rotating Schwarzschild black hole solutions or
maximally-rotating (extremal) Kerr black hole solutions, respectively. Although
the assumptions used in obtaining these preliminary results are very strong,
they nevertheless offer hope that a more general, perhaps ultimately
``Penrose-like'', singularity theorem may be provable in the discrete spacetime
case too.


  Finding a new class of materials supporting a long spin lifetime is essential
in development of energy-saving spintronics, which is achievable by using a
persistent spin helix (PSH) materials. However, for spintronic devices, the PSH
states with large spin splitting is required for operation at room temperature.
By employing first-principles calculations, we show that the PSH states with
large spin splitting are achieved in the SnSe monolayer (ML) functionalized by
a substitutional halogen impurity. We find the PSH states in the Fermi level
where k-space Fermi surface is characterized by the shifted two loops,
dominated by out-of-plane spin orientations. We clarify the PSH states in term
of an effective k.p Hamiltonian obtained from symmetry consideration. Finally,
large spin-orbit strength in the PSH states with a substantially small
wavelength are found, rendering that this system is promising for the
development of an efficient and high-density scalable spintronic devices
operating at room temperatures.


  Discord is a refinement of the concept of anomalous subsequence of a time
series. The task of discords discovery is applied in a wide range of subject
domains related to time series: medicine, economics, climate modeling, etc. In
this paper, we propose a novel parallel algorithm for discords discovery for
the Intel Xeon Phi Knights Landing (KNL) many-core systems for the case when
input data fit in main memory. The algorithm exploits the ability to
independently calculate Euclidean distances between the subsequences of the
time series. Computations are paralleled through OpenMP technology. The
algorithm consists of two stages, namely precomputations and discovery. At the
precomputations stage, we construct the auxiliary matrix data structures, which
ensure efficient vectorization of computations on Intel Xeon Phi KNL. At the
discovery stage, the algorithm finds discord based upon the structures above.
Experimental evaluation confirms the high scalability of the developed
algorithm.


  Polymer architecture plays critical roles in both bulk rheological properties
and microscale macromolecular dynamics in entangled polymer solutions and
composites. Ring polymers, in particular, have been the topic of much debate
due to the inability of the celebrated reptation model to capture their
observed dynamics. Macrorheology and differential dynamic microscopy (DDM) are
powerful methods to determine entangled polymer dynamics across scales, yet
they typically require different samples under different conditions, preventing
direct coupling of bulk rheological properties to the underlying macromolecular
dynamics. Here, we perform macrorheology on composites of highly-overlapping
DNA and dextran polymers, focusing on the role of DNA topology (rings versus
linear chains) as well as the relative volume fractions of DNA and dextran. On
the same samples under the same conditions, we perform DDM and single-molecule
tracking on embedded fluorescent-labeled DNA molecules immediately before and
after bulk measurements. We show DNA-dextran composites exhibit unexpected
non-monotonic dependences of bulk viscoelasticity and molecular-level transport
properties on the fraction of DNA comprising the composites, with
characteristics that are strongly dependent on the DNA topology. We rationalize
our results as arising from stretching and bundling of linear DNA versus
compaction, swelling, and threading of rings driven by dextran-mediated
depletion interactions.


  Scattering of electromagnetic fields by a defect layer embedded in a
slow-light periodically layered ambient medium exhibits phenomena markedly
different from typical scattering problems. In a slow-light periodic medium,
constructed by Figotin and Vitebskiy, the energy velocity of a propagating mode
in one direction slows to zero, creating a "frozen mode" at a single frequency
within a pass band, where the dispersion relation possesses a flat inflection
point. The slow-light regime is characterized by a $3\!\times\!3$ Jordan block
of the log of the $4\!\times\!4$ monodromy matrix for EM fields in a periodic
medium at special frequency and parallel wavevector. The scattering problem
breaks down as the 2D rightward and leftward mode spaces intersect in the
frozen mode and therefore span only a 3D subspace $\mathring{V}$ of the 4D
space of EM fields.
  Analysis of pathological scattering near the slow-light frequency and
wavevector is based on the interaction between the flux-unitary transfer matrix
$T$ across the defect layer and the projections to the rightward and leftward
spaces, which blow up as Laurent-Puiseux series. Two distinct cases emerge: the
generic, non-resonant case when $T$ does not map $\mathring{V}$ to itself and
the quadratically growing mode is excited; and the resonant case, when
$\mathring{V}$ is invariant under $T$ and a guided frozen mode is resonantly
excited.


  In the present letter, we introduce a new method to quantify the effect of
disorder on spatiotemporal chaos [Y. Braiman, etc. Nature, 378, p465 (1995)].
Base on the autocorrelation function, we define a parameter to measure the
effect of disorder. The results are intriguing and similar to the results
obtained by J. Lindner etc. [J. Lindner, etc. Physics Letters A, 231, p164
(1997)]. Using this order parameter, the effect of disorder on spatiotemporal
chaos in different conditions has also been discussed.


  In a companion paper, we introduced raising operator series called
Catalanimals. Among them are Schur Catalanimals, which represent Schur
functions inside copies $\Lambda (X^{m,n})\subset \mathcal{E} $ of the algebra
of symmetric functions embedded in the elliptic Hall algebra $\mathcal{E} $ of
Burban and Schiffmann.
  Here we obtain a combinatorial formula for symmetric functions given by a
class of Catalanimals that includes the Schur Catalanimals. Our formula is
expressed as a weighted sum of LLT polynomials, with terms indexed by
configurations of nested lattice paths called nests, having endpoints and
bounding constraints controlled by data called a den.
  Applied to Schur Catalanimals for the alphabets $X^{m,1}$ with $n=1$, our
`nests in a den' formula proves the combinatorial formula conjectured by Loehr
and Warrington for $\nabla^m s_{\mu }$ as a weighted sum of LLT polynomials
indexed by systems of nested Dyck paths. When $n$ is arbitrary, our formula
establishes an $(m,n)$ version of the Loehr-Warrington conjecture.
  In the case where each nest consists of a single lattice path, the nests in a
den formula reduces to our previous shuffle theorem for paths under any line.
Both this and the $(m,n)$ Loehr-Warrington formula generalize the $(km,kn)$
shuffle theorem proven by Carlsson and Mellit (for $n=1$) and Mellit. Our
formula here unifies these two generalizations.


  This paper initiates a study into the century-old issue of market
predictability from the perspective of computational complexity. We develop a
simple agent-based model for a stock market where the agents are traders
equipped with simple trading strategies, and their trades together determine
the stock prices. Computer simulations show that a basic case of this model is
already capable of generating price graphs which are visually similar to the
recent price movements of high tech stocks. In the general model, we prove that
if there are a large number of traders but they employ a relatively small
number of strategies, then there is a polynomial-time algorithm for predicting
future price movements with high accuracy. On the other hand, if the number of
strategies is large, market prediction becomes complete in two new
computational complexity classes CPP and BCPP, which are between P^NP[O(log n)]
and PP. These computational completeness results open up a novel possibility
that the price graph of an actual stock could be sufficiently deterministic for
various prediction goals but appear random to all polynomial-time prediction
algorithms.


  The Radon transform and its adjoint, the back-projection operator, can both
be expressed as convolutions in log-polar coordinates. Hence, fast algorithms
for the application of the operators can be constructed by using FFT, if data
is resampled at log-polar coordinates. Radon data is typically measured on an
equally spaced grid in polar coordinates, and reconstructions are represented
(as images) in Cartesian coordinates. Therefore, in addition to FFT, several
steps of interpolation have to be conducted in order to apply the Radon
transform and the back-projection operator by means of convolutions.
  Both the interpolation and the FFT operations can be efficiently implemented
on Graphical Processor Units (GPUs). For the interpolation, it is possible to
make use of the fact that linear interpolation is hard-wired on GPUs, meaning
that it has the same computational cost as direct memory access. Cubic order
interpolation schemes can be constructed by combining linear interpolation
steps which provides important computation speedup.
  We provide details about how the Radon transform and the back-projection can
be implemented efficiently as convolution operators on GPUs. For large data
sizes, speedups of about 10 times are obtained in relation to the computational
times of other software packages based on GPU implementations of the Radon
transform and the back-projection operator. Moreover, speedups of more than a
1000 times are obtained against the CPU-implementations provided in the MATLAB
image processing toolbox.


  In this paper, the selective predator harvesting is considered in a predator
prey system. The logistic growth of prey and ratio-dependent functional
response is assumed. The dynamically varying effort is employed for selective
harvesting of predator species using Michaelis-Menten type function The
boundedness, positivity and persistence of the nonlinear dynamical system is
established. The system being non-singular about origin, its dynamics is
explored by transforming it to a regular system. It is observed that the system
may collapse even with positive initial conditions attracted to one of the
boundary points under certain conditions. The local stability of various other
equilibrium states of the dynamic model is investigated. The region of
attraction of interior equilibrium state is obtained using Lyapunov stability.
The occurrence of hopf bifurcation about the coexistence equilibrium point with
respect to the parameter m (fraction of predators available for harvesting) is
established. The sustainable harvesting is possible in two ways firstly in the
form of stable interior equilibrium state and secondly in the form of limit
cycle. Considering the fraction m as a control variable, the optimal harvesting
policy is obtained using Pontraygin's maximum principle. The two-parameter
bifurcation diagram is obtained with respect to c and d (the cost of harvesting
and the death rate of predators respectively). The two bi-stability regions of
parameter space are identified. It is proved that for sustainable harvesting of
predators the ratio of p to c (price to cost) should be greater than a certain
threshold value dependent on predator density. The analytical results are
illustrated numerically with different parametric values.


  As deep reinforcement learning (DRL) has been recognized as an effective
approach in quantitative finance, getting hands-on experiences is attractive to
beginners. However, to train a practical DRL trading agent that decides where
to trade, at what price, and what quantity involves error-prone and arduous
development and debugging. In this paper, we introduce a DRL library FinRL that
facilitates beginners to expose themselves to quantitative finance and to
develop their own stock trading strategies. Along with easily-reproducible
tutorials, FinRL library allows users to streamline their own developments and
to compare with existing schemes easily. Within FinRL, virtual environments are
configured with stock market datasets, trading agents are trained with neural
networks, and extensive backtesting is analyzed via trading performance.
Moreover, it incorporates important trading constraints such as transaction
cost, market liquidity and the investor's degree of risk-aversion. FinRL is
featured with completeness, hands-on tutorial and reproducibility that favors
beginners: (i) at multiple levels of time granularity, FinRL simulates trading
environments across various stock markets, including NASDAQ-100, DJIA, S&P 500,
HSI, SSE 50, and CSI 300; (ii) organized in a layered architecture with modular
structure, FinRL provides fine-tuned state-of-the-art DRL algorithms (DQN,
DDPG, PPO, SAC, A2C, TD3, etc.), commonly-used reward functions and standard
evaluation baselines to alleviate the debugging workloads and promote the
reproducibility, and (iii) being highly extendable, FinRL reserves a complete
set of user-import interfaces. Furthermore, we incorporated three application
demonstrations, namely single stock trading, multiple stock trading, and
portfolio allocation. The FinRL library will be available on Github at link
https://github.com/AI4Finance-LLC/FinRL-Library.


  The differential capacitance comprises the most relevant thermodynamic
information about an electrochemical system. Classical approaches to describe
electrochemical capacitance have difficulties to combine the treatment of the
ionic contribution of the electrolyte with the electronic contribution of the
electrode. Moreover, different approaches are typically required for the
description of the double-layer capacitance, on the one hand, and the
pseudocapacitive contribution due to adsorption or intercalation of reactive
species, on the other. In the present work, a new approach to describe
electrochemical capacitance from first principles is developed. The treatment
of a general electrochemical system at the level of multicomponent
density-functional theory (MCDFT) yields an exact analytical expression for the
total capacitance of the system, which corresponds to a formal series-circuit
partitioning into "quantum" capacitance contributions of the density of states
of electrons and ions, the (mean-field) electrostatic capacitance, as well as
capacitance contributions of exchange and correlation among all active species.
It is shown that the classical expression of the double-layer capacitance
involving the interfacial Galvani potential is obtained in the limit of
extended electrode and electrolyte regions. Importantly, the present formalism
also describes systems with confined electrode and electrolyte phases, where
the definition of the (classical) inner potentials of the electrode and
electrolyte domains becomes problematic. Moreover, the new approach unifies the
treatment of double-layer capacitance and pseudocapacitance resulting from
reactive processes.


  This is the second of a series of two articles in which we provide detailed
and self-contained account of the construction of a system of Kuranishi
structures on the moduli spaces of pseudo holomorphic disks. Using the notion
of obstruction bundle data introduced in [FOOO8], we give a systematic way of
constructing a system of Kuranishi structures on the moduli spaces of pseudo
holomorphic disks which are compatible at the boundary and corners. More
specifically, it defines a tree like K-system in the sense of [FOOO6,
Definition 21.9]. The method given in this paper does not only simplify the
description of the constructions in the earlier literature, but also is
designed to provide a systematic utility tool for the construction of a system
of Kuranishi structures in the future research. We also establish its
uniqueness.


  We present a new solution framework to solve the generalized trust region
subproblem (GTRS) of minimizing a quadratic objective over a quadratic
constraint. More specifically, we derive a convex quadratic reformulation (CQR)
via minimizing a linear objective over two convex quadratic constraints for the
GTRS. We show that an optimal solution of the GTRS can be recovered from an
optimal solution of the CQR. We further prove that this CQR is equivalent to
minimizing the maximum of the two convex quadratic functions derived from the
CQR for the case under our investigation. Although the latter minimax problem
is nonsmooth, it is well-structured and convex. We thus develop two steepest
descent algorithms corresponding to two different line search rules. We prove
for both algorithms their global sublinear convergence rates. We also obtain a
local linear convergence rate of the first algorithm by estimating the Kurdyka-
Lojasiewicz exponent at any optimal solution under mild conditions. We finally
demonstrate the efficiency of our algorithms in our numerical experiments.


  Wireless Sensor Networks (WSNs) is a promising technology with enormous
applications in almost every walk of life. One of the crucial applications of
WSNs is intrusion detection and surveillance at the border areas and in the
defense establishments. The border areas are stretched in hundreds to thousands
of miles, hence, it is not possible to patrol the entire border region. As a
result, an enemy may enter from any point absence of surveillance and cause the
loss of lives or destroy the military establishments. WSNs can be a feasible
solution for the problem of intrusion detection and surveillance at the border
areas. Detection of an enemy at the border areas and nearby critical areas such
as military cantonments is a time-sensitive task as a delay of few seconds may
have disastrous consequences. Therefore, it becomes imperative to design
systems that are able to identify and detect the enemy as soon as it comes in
the range of the deployed system. In this paper, we have proposed a deep
learning architecture based on a fully connected feed-forward Artificial Neural
Network (ANN) for the accurate prediction of the number of k-barriers for fast
intrusion detection and prevention. We have trained and evaluated the
feed-forward ANN model using four potential features, namely area of the
circular region, sensing range of sensors, the transmission range of sensors,
and the number of sensor for Gaussian and uniform sensor distribution. These
features are extracted through Monte Carlo simulation. In doing so, we found
that the model accurately predicts the number of k-barriers for both Gaussian
and uniform sensor distribution with correlation coefficient (R = 0.78) and
Root Mean Square Error (RMSE = 41.15) for the former and R = 0.79 and RMSE =
48.36 for the latter. Further, the proposed approach outperforms the other
benchmark algorithms in terms of accuracy and computational time complexity.


  We consider the link average of the half-BPS Wilson loop operators in N = 6
superconformal Chern-Simons-matter theory, which is called ABJM theory. We show
that this loop average is reduced to a (super)matrix integral by the
localization method, in a similar way to the bosonic U(N) Chern-Simons theory.
Using this matrix integral, we compute the two- and three-link averages with an
operator formalism inspired by a three-dimensional topological field theory. We
obtain a factorization of the link average, and the Verlinde formula in a
sector of supergroup representations. We also propose a refined version of ABJM
theory, and compute some refined link averages.


  This paper investigates the problem of interactively learning behaviors
communicated by a human teacher using positive and negative feedback. Much
previous work on this problem has made the assumption that people provide
feedback for decisions that is dependent on the behavior they are teaching and
is independent from the learner's current policy. We present empirical results
that show this assumption to be false -- whether human trainers give a positive
or negative feedback for a decision is influenced by the learner's current
policy. Based on this insight, we introduce {\em Convergent Actor-Critic by
Humans} (COACH), an algorithm for learning from policy-dependent feedback that
converges to a local optimum. Finally, we demonstrate that COACH can
successfully learn multiple behaviors on a physical robot.


  We combine a tunable continuous-wave optical parametric oscillator and a
femtosecond Ti:Sapphire laser frequency comb to provide a phase-coherent bridge
between the visible and mid-infrared spectral ranges. As a first demonstration
of this new technique we perform a direct frequency comparison between an
iodine stabilized Nd:YAG laser at 1064 nm and an infrared methane optical
frequency standard at $3.39 \mu$m.


  The aim of the present paper is to introduce a generalized quantum cluster
character, which assigns to each object V of a finitary Abelian category C over
a finite field FF_q and any sequence ii of simple objects in C the element
X_{V,ii} of the corresponding algebra P_{C,ii} of q-polynomials. We prove that
if C was hereditary, then the assignments V-> X_{V,ii} define algebra
homomorphisms from the (dual) Hall-Ringel algebra of C to the P_{C,ii}, which
generalize the well-known Feigin homomorphisms from the upper half of a quantum
group to q-polynomial algebras.
  If C is the representation category of an acyclic valued quiver (Q,d) and
ii=(ii_0,ii_0), where ii_0 is a repetition-free source-adapted sequence, then
we prove that the ii-character X_{V,ii} equals the quantum cluster character
X_V introduced earlier by the second author in [29] and [30]. Using this
identification, we deduce a quantum cluster structure on the quantum unipotent
cell corresponding to the square of a Coxeter element. As a corollary, we prove
a conjecture from the joint paper [5] of the first author with A. Zelevinsky
for such quantum unipotent cells. As a byproduct, we construct the quantum
twist and prove that it preserves the triangular basis introduced by A.
Zelevinsky and the first author in [6].


  We investigate Hamiltonian aspects of the integro-differential kinetic
equation for dense soliton gas which results as a thermodynamic limit of the
Whitham equations. Under a delta-functional ansatz, the kinetic equation
reduces to a non-diagonalisable system of hydrodynamic type whose matrix
consists of several $2\times 2$ Jordan blocks. We demonstrate that the
resulting system possesses local Hamiltonian structures of
differential-geometric type, for all standard two-soliton interaction kernels
(KdV, sinh-Gordon, hard-rod, Lieb-Liniger, DNLS, and separable cases). In the
hard-rod case, we show that the continuum limit of these structures provides a
local multi-Hamiltonian formulation of the full kinetic equation.


  Contrast Enhanced Spectral Mammography (CESM) is a dual-energy mammographic
imaging technique that first needs intravenously administration of an iodinated
contrast medium; then, it collects both a low-energy image, comparable to
standard mammography, and a high-energy image. The two scans are then combined
to get a recombined image showing contrast enhancement. Despite CESM diagnostic
advantages for breast cancer diagnosis, the use of contrast medium can cause
side effects, and CESM also beams patients with a higher radiation dose
compared to standard mammography. To address these limitations this work
proposes to use deep generative models for virtual contrast enhancement on
CESM, aiming to make the CESM contrast-free as well as to reduce the radiation
dose. Our deep networks, consisting of an autoencoder and two Generative
Adversarial Networks, the Pix2Pix, and the CycleGAN, generate synthetic
recombined images solely from low-energy images. We perform an extensive
quantitative and qualitative analysis of the model's performance, also
exploiting radiologists' assessments, on a novel CESM dataset that includes
1138 images that, as a further contribution of this work, we make publicly
available. The results show that CycleGAN is the most promising deep network to
generate synthetic recombined images, highlighting the potential of artificial
intelligence techniques for virtual contrast enhancement in this field.


  A graph $G$ is primarily orientable if it is possible to orient its edges in
such a way that the resulting oriented graph is prime, i.e., indecomposable
under modular decomposition. We characterize primarily orientable graphs.


  Bluesky is a nascent ``Twitter-like'' and decentralized social media network
with novel features and unprecedented data access. This paper provides a
characterization of the network, studying the political leaning, polarization,
network structure, and algorithmic curation mechanisms of five million users.
The dataset spans from the website's first release in February of 2023. Users
of the new social media site are predominantly left-center leaning and share
little to no links associated with questionable sources. In contrast to the
homogeneous political stance, we find significant issues-based divergence by
studying opinions related to the Israel-Palestine conflict. Two clear
homophilic clusters emerge: Pro-Palestinian voices make up the plurality of
messages related to the conflict and the proportion has increased with a
lessening of interest. We investigate multiple layers of the multi-scale
Bluesky network based on replies, likes, reposts, and follows, highlighting
differences and similarities between the layers. We differentiate between
persistent and non-persistent interactions and measure metrics of network
topology over time. All networks are heavy-tailed, clustered, and connected by
short paths. We showcase all feeds - algorithmic content recommenders - created
for and by users. A large number of custom feeds have been created but their
uptake by users is limited. Multiple popular feeds aim to provide similar feeds
that are neither topical nor chronological. We conclude by claiming that
Bluesky - for all its novel features - is very similar in terms of its network
structure to existing and larger social media sites and provides unprecedented
research opportunities for social scientists, network scientists, and political
scientists alike.


  Unsupervised Domain Adaptation (UDA) aims to bridge the gap between a source
domain, where labelled data are available, and a target domain only represented
with unlabelled data. If domain invariant representations have dramatically
improved the adaptability of models, to guarantee their good transferability
remains a challenging problem. This paper addresses this problem by using
active learning to annotate a small budget of target data. Although this setup,
called Active Domain Adaptation (ADA), deviates from UDA's standard setup, a
wide range of practical applications are faced with this situation. To this
purpose, we introduce \textit{Stochastic Adversarial Gradient Embedding}
(SAGE), a framework that makes a triple contribution to ADA. First, we select
for annotation target samples that are likely to improve the representations'
transferability by measuring the variation, before and after annotation, of the
transferability loss gradient. Second, we increase sampling diversity by
promoting different gradient directions. Third, we introduce a novel training
procedure for actively incorporating target samples when learning invariant
representations. SAGE is based on solid theoretical ground and validated on
various UDA benchmarks against several baselines. Our empirical investigation
demonstrates that SAGE takes the best of uncertainty \textit{vs} diversity
samplings and improves representations transferability substantially.


  The traditional interpretation of radiative emission and absorption asserts
that photons are created and annihilated in such processes. A Gedanken
experiment is considered in which kinetic energy from observed photons is
systematically removed until a limit of zero is reached. With the help of the
relativistic Doppler effect it is shown that even for infinitesimally small
kinetic energies the photons continue to exist, since in other inertial systems
they will be observed to have a much higher energy/frequency falling in an
easily detectable range. It is possible to formulate an alternative explanation
for absorption and emission processes on this basis in terms of real photons
with exactly zero kinetic energy being present before or after radiative
interactions. Bolstering this hypothesis is the fact that the statistical
mechanical treatment of photons interacting with oscillators in blackbody
radiation theory predicts an infinite density of photons of this energy, both
in the original Planck formulation employing Maxwell-Boltzmann statistics and
in the subsequent Bose-Einstein description. These considerations demonstrate
that the E = 0 state is greatly preferred as the product of absorption because
of the requirement to have the interaction occur in a relatively narrow region
of space- time. There is thus strong evidence that photons are not created and
annihilated in radiative processes but simply have their kinetic energy changed
either to or from a zero value. Accordingly a very high density of zero-energy
photons is expected to exist uniformly throughout the universe. Finally, this
development suggests that one should subject the creation-annihilation
hypothesis to careful scrutiny in other areas of physics as well.


  A physical description of the formation and propagation of the working
surface inside the relativistic jet of the Blazar PKS 1510-089 are used to
model its gamma-ray variability light curve using FERMI-LAT data from 2008 to
2012. The physical model is based on conservation laws of mass and momentum at
the working surface as explained by Mendoza et al. (2009). The hydrodynamical
description of the working surface is parametrised by the initial velocity and
mass injection rate at the base of the jet. We show that periodic variations on
the injected velocity profiles are able to account for the observed luminosity.
With this, we are able to obtain mass ejection rates of the central engine
which are injected at the base of the jet, and oscillation frequencies of the
flow, amongst other physical parameters.


  Using two experimental techniques, we studied single crystals of the 122-FeAs
family with almost the same critical temperature, Tc. We investigated the
temperature dependence of the lower critical field of a single crystal under
static magnetic fields parallel to the axis. The temperature dependence of the
London penetration depth can be described equally well either by a single
anisotropic -wave-like gap or by a two-gap model, while a d-wave approach
cannot be used to fit the London penetration depth data. Intrinsic multiple
Andreev reflection effect spectroscopy was used to detect bulk gap values in
single crystals of the intimate compound, with the same Tc. We estimated the
range of the large gap value 6-8 meV (depending on small variation of and its a
space anisotropy of about 30%, and the small gap 1.7 meV. This clearly
indicates that the gap structure of our investigated systems more likely
corresponds to a nodeless s-wave two gaps.


  The open-source nature of the Android OS makes it possible for manufacturers
to ship custom versions of the OS along with a set of pre-installed apps, often
for product differentiation. Some device vendors have recently come under
scrutiny for potentially invasive private data collection practices and other
potentially harmful or unwanted behavior of the pre-installed apps on their
devices. Yet, the landscape of pre-installed software in Android has largely
remained unexplored, particularly in terms of the security and privacy
implications of such customizations. In this paper, we present the first
large-scale study of pre-installed software on Android devices from more than
200 vendors. Our work relies on a large dataset of real-world Android firmware
acquired worldwide using crowd-sourcing methods. This allows us to answer
questions related to the stakeholders involved in the supply chain, from device
manufacturers and mobile network operators to third-party organizations like
advertising and tracking services, and social network platforms. Our study
allows us to also uncover relationships between these actors, which seem to
revolve primarily around advertising and data-driven services. Overall, the
supply chain around Android's open source model lacks transparency and has
facilitated potentially harmful behaviors and backdoored access to sensitive
data and services without user consent or awareness. We conclude the paper with
recommendations to improve transparency, attribution, and accountability in the
Android ecosystem.


  Candidates for renormalisable gauge theory models on Moyal spaces constructed
recently have non trivial vacua. We show that these models support vacuum
states that are invariant under both global rotations and symplectic
isomorphisms which form a global symmetry group for the action. We compute the
explicit expression in the position space for these vacuum configurations in
two and four dimensions.


  We analyze cosmic superstring models in light of NANOGrav 15-year pulsar
timing data. A good fit is found for a string tension $G \mu \sim 10^{-12} -
10^{-11}$ and a string intercommutation probability $p \sim 10^{-3} - 10^{-1}$.
Extrapolation to higher frequencies assuming standard Big Bang cosmology is
compatible at the 68\% CL with the current LIGO/Virgo/KAGRA upper limit on a
stochastic gravitational wave background in the 10 to 100 Hz range. The
superstring interpretation of the NANOGrav data would be robustly testable by
future experiments even in modified cosmological scenarios.


  We present the results of a Hubble Space Telescope WFPC2 F555W and F814W
survey of 69 dwarf elliptical galaxies (dEs) in the Virgo and Fornax Clusters
and Leo Group. The $V-I$ colors of the dE globular clusters, nuclei, and
underlying field star populations are used to trace the dE star-formation
histories. We find that the dE globular cluster candidates are as blue as the
metal-poor globular clusters of the Milky Way. The observed correlation of the
dE globular cluster systems' $V-I$ color with the luminosity of the host dE is
strong evidence that the globular clusters were formed within the the halos of
dEs and do not have a pre-galactic origin. Assuming the majority of dE clusters
are old, the mean globular cluster color- host galaxy luminosity correlation
implies a cluster metallicity $-$ galaxy luminosity relation of $Z_{GC} \propto
L_B^{0.22 \pm 0.05}$, which is significantly shallower than the field star
metallicity - host galaxy luminosity relationship observed in Local Group
dwarfs ($Z_{FS} \propto L^{0.4}$). The dE stellar envelopes are $0.1-0.2$
magnitudes redder in $V-I$ than their globular clusters and nuclei. This color
offset implies separate star-formation episodes within the dEs for the clusters
and field stars, while the very blue colors of two dE nuclei trace a third
star-formation event in those dEs less than a Gyr ago.


  We discuss the problem of the information transfer (exchange of states
configuration) between two interacting quantum systems along their evolution in
time. We consider the specific case of two modes of the electromagnetic field
with rotating wave coupling interaction (up-conversion in a nonlinear crystal).
We verify that for certain initial states of the fields the swapping of state
configuration occurs with conservation of the mean energy of each mode (without
energy transfer), characterising thus pure information flow.


  In this work, we present a camera configuration for acquiring "stereoscopic
dark flash" images: a simultaneous stereo pair in which one camera is a
conventional RGB sensor, but the other camera is sensitive to near-infrared and
near-ultraviolet instead of R and B. When paired with a "dark" flash (i.e., one
having near-infrared and near-ultraviolet light, but no visible light) this
camera allows us to capture the two images in a flash/no-flash image pair at
the same time, all while not disturbing any human subjects or onlookers with a
dazzling visible flash. We present a hardware prototype of this camera that
approximates an idealized camera, and we present an imaging procedure that let
us acquire dark flash stereo pairs that closely resemble those we would get
from that idealized camera. We then present a technique for fusing these stereo
pairs, first by performing registration and warping, and then by using recent
advances in hyperspectral image fusion and deep learning to produce a final
image. Because our camera configuration and our data acquisition process allow
us to capture true low-noise long exposure RGB images alongside our dark flash
stereo pairs, our learned model can be trained end-to-end to produce a fused
image that retains the color and tone of a real RGB image while having the
low-noise properties of a flash image.


  In some recent papers, the relations existing between the metric properties
of Randers spaces and the conformal geometry of stationary Lorentzian manifolds
were discovered and investigated. In this note, we focus on the equality
between the index of a geodesic in a Randers space and that of its lightlike
lift in the associated conformal stationary spacetime. Moreover we make some
remarks about regularity of the energy functional of a Finsler metric on the
infinite dimensional manifold of $H^1$ curves between two points, in connection
with infinite dimensional techniques in Morse Theory.


  I build a SU(2)left x U(1) electroweak gauge theory of J=0 mesons, which
transform like sets of fermion-antifermion composite fields. SU(2)left x U(1)
is embedded in a natural way, compatible with the Glashow-Salam-Weinberg model
for quarks, into the chiral group U(N)left x U(N)right, N being the (even)
number of ``flavours''. The Lagrangian exhibits a chiral SU(2)left x SU(2)right
symmetry at the limit when the hypercharge coupling g' goes to zero. It is
spontaneously broken down to its diagonal SU(2)v subgroup; as the latter
includes the U(1) group of electromagnetism, this provides an explanation for
the quantization of the electric charge. Comparison with recent works by Cho et
al. unraveling dyon-like solution is an electroweak model with the same
structure suggests that electric-magnetic duality may be realized here, with
the occurrence of a strongly interacting sector. Chiral are electroweak
spontaneous breaking are identical. Consequences for the nature of the
Goldstone bosons are examined. The mass spectrum is analysed. It bears no
special connection with the nature of the ``fermionic content'' of the mesons
and shares with the leptonic sector the same arbitrariness. No information on
the mass of the Higgs boson can be expected without additional input. New
results about CP violation are obtained: ``indirect'' CP violation appears to
results from P violation (unitarity compels the electroweak mass eigenstates to
be C eigenstates), and the role of the Kobayashi-Maskawa mixing matrix for
fermions fades away: mesonic mass eigenstates can still be CP eigenstates
despite the presence of a complex phase. I briefly show how the customary
results for the leptonic decays of pseudoscalar mesons are recovered. The
extension to leptons is discussed.


  We give a characterization of the line digraph of a regular digraph. We make
use of the characterization, to show that the underlying digraph of a coined
quantum random walk is a line digraph. We remark the connection between line
digraphs and in-split graphs in symbolic dynamics.


  We combine the Duke-Imamoglu-Ikeda lifting with the theta lifting to produce
new CAP representations of metaplectic, symplectic and orthogonal groups. These
constructions partially generalize the theories of Waldspurger on the Shimura
correspondence and of Piatetski-Shapiro on the Saito-Kurokawa lifting to higher
dimensions. Applications include a relation between Fourier coefficients of
Hilbert cusp forms of weight k+1/2 and a weighted sum of the representation
numbers of a quadratic form of rank 2k by a quadratic form of rank 4k.


  We use stratified Morse theory for a manifold with corners to give a new
bound for the sum of the Betti numbers of a hypersurface in R^n_> defined by a
polynomial with n+l+1 terms.


  Based on the Dyson-Schwinger Equations (DSEs) with zero- and finite
temperature, the two quark condensate, the four quark condensate and quark
gluon mixed condensate in non-perturbative QCD state are investigated by
solving the DSEs respectively at zero and finite temperature. These condensates
are important input parameters in QCD sum rule with zero and finite temperature
and properties of hadronic study. The calculated results manifest that the
three condensates are almost independent of the temperature below the critical
point temperature $T_{c}$. The results also show that the chiral symmetry
restoration is obtained above $T_{c}$. At the same time, we also calculate the
ratio of the quark gluon mixed condensate to the two quark condensate which
could be quark virtuality. The calculations show that the ratio $m^{2}_{0}(T)$
is almost flat in the region of temperature from $0$ to $T_{c}$, although there
are drastic changes of the quark condensate and the quark gluon mixed
condensate at this region of $T_{c}$.The predicted ratio comes out to be
$m^{2}_{0}(T)= 2.41GeV^{2}$ for vacuum state at the Chiral limit, which
suggests the significance that the quark gluon mixed condensate has played in
OPE.


  We develop a theory of arithmetic Newton polygons of higher order, that
provides the factorization of a separable polynomial over a $p$-adic field,
together with relevant arithmetic information about the fields generated by the
irreducible factors. This carries out a program suggested by \O{}. Ore. As an
application, we obtain fast algorithms to compute discriminants, prime ideal
decomposition and integral bases of number fields.


  In this article, we introduce the weak ideal-Armendariz ring which combines
Armendariz ring and weakly semicommutative properties of rings. In fact, it is
a generalisation of an ideal-Armendariz ring. We investigate some properties of
weak ideal Armendariz rings and prove that R is a weak ideal-Armendariz ring if
and only if R[x] is weak ideal-Armendariz ring. Also, we generalise weak
ideal-Armendariz as strongly nil-IFP and a number of properties are discussed
which distinguishes it from other existing structures. We prove that if I is a
semicommutative ideal of a ring R and R/I is a strongly nil-IFP, then R is
strongly nil-IFP. Moreover, if R is 2-primal, then R[x]/<x^{n}> is a strongly
nil-IFP.


  The advent of Industrial IoT (IIoT) along with Cloud computing has brought a
huge paradigm shift in manufacturing industries resulting in yet another
industrial revolution, Industry 4.0. Huge amounts of delay-sensitive data of
diverse nature are being generated which needs to be locally processed and
secured due to its sensitivity. But, the low-end IoT devices are unable to
handle huge computational overheads. Also, the semi-trusted nature of Cloud
introduces several security concerns. To address these issues, this work
proposes a secure Fog-based IIoT architecture by suitably plugging a number of
security features into it and by offloading some of the tasks judiciously to
fog nodes. These features secure the system alongside reducing the trust and
burden on the cloud and resource-constrained devices respectively. We validate
our proposed architecture through both theoretical overhead analysis and
practical experimentation including simulation study and testbed
implementation.


  We find upper and lower bounds of the multiplicities of irreducible
admissible representations $\pi$ of a semisimple Lie group $G$ occurring in the
induced representations $Ind_H^G\tau$ from irreducible representations $\tau$
of a closed subgroup $H$.
  As corollaries, we establish geometric criteria for finiteness of the
dimension of $Hom_G(\pi,Ind_H^G \tau)$ (induction) and of $Hom_H(\pi|_H,\tau)$
(restriction) by means of the real flag variety $G/P$, and discover that
uniform boundedness property of these multiplicities is independent of real
forms and characterized by means of the complex flag variety.