  This paper classifies spherical objects in various geometric settings in
dimension two and three, including both minimal and partial crepant resolutions
of Kleinian singularities, as well as arbitrary flopping 3-fold contractions
with only Gorenstein terminal singularities. The main result is much more
general: in each such setting, we prove that all objects in the associated null
category with no negative Ext groups are the image, under the action of an
appropriate braid or pure braid group, of some object in the heart of a bounded
t-structure. The corollary is that all objects which admit no negative Exts,
and for which the self-Hom space is one dimensional, are the images of the
simples. A variation on this argument goes further, and classifies all bounded
t-structures. There are multiple geometric, topological and algebraic
consequences, primarily to autoequivalences and stability conditions. Our main
new technique also extends into representation theory, and we establish that in
the derived category of a finite dimensional algebra which is silting discrete,
every object with no negative Ext groups lies in the heart of a bounded
t-structure. As a consequence, every semibrick complex can be completed to a
simple minded collection.


  Finite-size (FS) effects are a major source of error in many-body (MB)
electronic structure calculations of extended systems. A method is presented to
correct for such errors. We show that MB FS effects can be effectively included
in a modified local density approximation calculation. A parametrization for
the FS exchange-correlation functional is obtained. The method is simple and
gives post-processing corrections that can be applied to any MB results.
Applications to a model insulator (P$_2$ in a supercell), to semiconducting Si,
and to metallic Na show that the method delivers greatly improved FS
corrections.


  Magnetically ordered materials tend to support bands of coherent propagating
spin wave, or magnon, excitations. Topologically protected surface states of
magnons offer a new path towards coherent spin transport for spintronics
applications. In this work we explore the variety of topological magnon band
structures and provide insight into how to efficiently identify topological
magnon bands in materials. We do this by adapting the topological quantum
chemistry approach that has used constraints imposed by time reversal and
crystalline symmetries to enumerate a large class of topological electronic
bands. We show how to identify physically relevant models of gapped magnon band
topology by using so-called decomposable elementary band representations, and
in turn discuss how to use symmetry data to infer the presence of exotic
symmetry enforced nodal topology.


  By the reduction theorems of Navarro--Tiep and Sp\"ath, a way to prove the
Alperin weight conjecture and its blockwise version is to verify the co-called
inductive Alperin weight condition and inductive blockwise Alperin weight
condition for all finie simple groups respectively. In this paper, we establish
the inductive blockwise Alperin weight condition for simple groups of type
$\mathsf B$ and odd primes, using a criterion given by Brough and Sp\"ath
recently.


  Face parsing aims to predict pixel-wise labels for facial components of a
target face in an image. Existing approaches usually crop the target face from
the input image with respect to a bounding box calculated during
pre-processing, and thus can only parse inner facial Regions of
Interest~(RoIs). Peripheral regions like hair are ignored and nearby faces that
are partially included in the bounding box can cause distractions. Moreover,
these methods are only trained and evaluated on near-frontal portrait images
and thus their performance for in-the-wild cases has been unexplored. To
address these issues, this paper makes three contributions. First, we introduce
iBugMask dataset for face parsing in the wild, which consists of 21,866
training images and 1,000 testing images. The training images are obtained by
augmenting an existing dataset with large face poses. The testing images are
manually annotated with $11$ facial regions and there are large variations in
sizes, poses, expressions and background. Second, we propose RoI Tanh-polar
transform that warps the whole image to a Tanh-polar representation with a
fixed ratio between the face area and the context, guided by the target
bounding box. The new representation contains all information in the original
image, and allows for rotation equivariance in the convolutional neural
networks~(CNNs). Third, we propose a hybrid residual representation learning
block, coined HybridBlock, that contains convolutional layers in both the
Tanh-polar space and the Tanh-Cartesian space, allowing for receptive fields of
different shapes in CNNs. Through extensive experiments, we show that the
proposed method improves the state-of-the-art for face parsing in the wild and
does not require facial landmarks for alignment.


  In this communication, we examine a nonlinear model with an impurity
emulating a bend. We justify the geometric interpretation of the model and
connect it with earlier work on models including geometric effects. We focus on
both the bifurcation and stability analysis of the modes that emerge as a
function of the strength of the bend angle, but we also examine dynamical
effects including the scattering of mobile localized modes (discrete breathers)
off of such a geometric structure. The potential outcomes of such numerical
experiments (including transmission, trapping within the bend as well as
reflection) are highlighted and qualitatively explained. Such models are of
interest both theoretically in understanding the interplay of breathers with
curvature, but also practically in simple models of photonic crystals or of
bent chains of DNA.


  Removing hazardous particulate and macromolecular contaminants as well as
viruses with sizes from a few nm up to the 100-nm-range from water and air is
crucial for ensuring sufficient sanitation and hygiene for a growing world
population. To this end, high-performance separation membranes are needed that
combine high permeance, high selectivity and sufficient mechanical stability
under operating conditions. However, design features of separation membranes
enhancing permeance reduce selectivity and vice versa. Membrane configurations
combining high permeance and high selectivity suffer in turn from a lack of
mechanical robustness. These problems may be tackled by using block copolymers
(BCPs) as a material platform for the design of separation membranes. BCPs are
macromolecules that consist of two or more chemically distinct block segments,
which undergo microphase separation yielding a wealth of ordered nanoscopic
domain structures. Various methods allow the transformation of these nanoscopic
domain structures into customized nanopore systems with pore sizes in the
sub-100-nm range and with narrow pore size distributions. This tutorial review
summarizes design strategies for nanoporous state-of-the-art BCP separation
membranes, their preparation, their device integration and their use for water
purification.


  We study the recombination process of three atoms scattering into an atom and
diatomic molecule in heteronuclear mixtures of ultracold atomic gases with
large and positive interspecies scattering length at finite temperature. We
calculate the temperature dependence of the three-body recombination rates by
extracting universal scaling functions that parametrize the energy dependence
of the scattering matrix. We compare our results to experimental data for the
40K-87Rb mixture and make a prediction for 6Li-87Rb. We find that contributions
from higher partial wave channels significantly impact the total rate and, in
systems with particularly large mass imbalance, can even obliterate the
recombination minima associated with the Efimov effect.


  Let $\mathfrak a$ be an ideal of a commutative Noetherian ring $R$ and $t$ be
a non-negative integer. Let $M$ and $N$ be two finitely generated $R$-modules.
In certain cases, we give some bounds under inclusion for the annihilators of
$\operatorname{Ext}^t_R(M, N)$ and $\operatorname{H}^t_{\mathfrak a}(M)$ in
terms of minimal primary decomposition of the zero submodule of $M$ which are
independent of the choice of minimal primary decomposition. Then, by using
those bounds, we compute the annihilators of local cohomology and Ext modules
in certain cases.


  We study nonlinear convection in a rapidly rotating sphere with internal
heating for values of the Prandtl number relevant for liquid metals
($Pr\in[10^{-2},10^{-1}]$). We use a numerical model based on the
quasi-geostrophic approximation, in which variations of the axial vorticity
along the rotation axis are neglected, whereas the temperature field is fully
three-dimensional. We identify two separate branches of convection close to
onset: (i) a well-known weak branch for Ekman numbers greater than $10^{-6}$,
which is continuous at the onset (supercritical bifurcation) and consists of
thermal Rossby waves, and (ii) a novel strong branch at lower Ekman numbers,
which is discontinuous at the onset. The strong branch becomes subcritical for
Ekman numbers of the order of $10^{-8}$. On the strong branch, the Reynolds
number of the flow is greater than $10^3$, and a strong zonal flow with
multiple jets develops, even close to the nonlinear onset of convection. We
find that the subcriticality is amplified by decreasing the Prandtl number. The
two branches can co-exist for intermediate Ekman numbers, leading to hysteresis
($Ek=10^{-6}$, $Pr=10^{-2}$). Nonlinear oscillations are observed near the
onset of convection for $Ek=10^{-7}$ and $Pr=10^{-1}$.


  This survey presents a necessarily incomplete (and biased) overview of
results at the intersection of arithmetic circuit complexity, structured
matrices and deep learning. Recently there has been some research activity in
replacing unstructured weight matrices in neural networks by structured ones
(with the aim of reducing the size of the corresponding deep learning models).
Most of this work has been experimental and in this survey, we formalize the
research question and show how a recent work that combines arithmetic circuit
complexity, structured matrices and deep learning essentially answers this
question.
  This survey is targeted at complexity theorists who might enjoy reading about
how tools developed in arithmetic circuit complexity helped design (to the best
of our knowledge) a new family of structured matrices, which in turn seem
well-suited for applications in deep learning. However, we hope that folks
primarily interested in deep learning would also appreciate the connections to
complexity theory.


  This paper introduces a control co-design (CCD) framework to simultaneously
explore the physical parameters and control spaces for a hydro-kinetic turbine
(HKT) rotor optimization. The optimization formulation incorporates a coupled
dynamic-hydrodynamic model to maximize the rotor power efficiency for various
time-variant flow profiles. The open-loop optimal control is applied for
maximum power tracking, and the blade element momentum theory (BEMT) is used to
model the hydrodynamics. Case studies with different control constraints are
investigated for CCD. Sensitivity analyses were conducted with respect to
different flow profiles and initial geometries. Comparisons are made between
CCD and the sequential process, with physical design followed by a control
design process under the same conditions. The results demonstrate the benefits
of CCD and reveal that, with control constraints, CCD leads to increased energy
production compared to the design obtained from the sequential design process.


  We investigate the birational geometry of Deligne-Mumford stacks and define
new birational invariants in this context.


  Using the formalism developed in [1,2] we carry out the first complete
calculation of kinematic power corrections to the helicity amplitudes of
deeply-virtual Compton scattering to the twist-four accuracy for a study case
of a (pseudo)scalar target. Our main result is that both finite-t, ~t/Q^2, and
target mass, ~m^2/Q^2, twist-four kinematic power corrections turn out to be
factorizable, at least to the leading order in the strong coupling. The
structure of these corrections is discussed and a short model study of their
numerical impact is presented.


  If $V$ is an equidimensional codimension $c$ subscheme of an $n$-dimensional
projective space, and $V$ is linked to $V'$ by a complete intersection $X$,
then we say that $V$ is {\em minimally linked} to $V'$ if $X$ is a codimension
$c$ complete intersection of smallest degree containing $V$. Gaeta showed that
if $V$ is any arithmetically Cohen-Macaulay (ACM) subscheme of codimension two
then there is a finite sequence of minimal links beginning with $V$ and
arriving at a complete intersection. We extend this work in the following ways:
1) In the codimension 2 non-ACM case, we show that for any $n \geq 3$ there are
examples of subschemes that are not minimal in their even liaison class, and
cannot be minimally linked in any number of steps to a minimal subscheme. 2)
Nevertheless, there are examples of non-ACM liaison classes of curves in
projective 3-space where all elements are minimally linked in a finite number
of steps to a minimal curve. 3) Extending previous work of the authors with
Huneke and Ulrich (about the licci case), we show that also in the non-ACM case
in any higher codimension there are non-minimal subschemes that are not
minimally linked to a minimal subscheme in the even liaison class. 4) J.
Watanabe had shown many years ago that codimension 3 graded Gorenstein ideals
of any dimension are licci. Here we show that any such ideal is minimally
linked in a finite number of steps to a complete intersection, and that it
admits a sequence of strictly decreasing CI-biliaisons down to a complete
intersection, extending work of Hartshorne, Sabadini and Schlesinger.


  We have examined a sample of 13 sub-Eddington supermassive black holes hosted
by galaxies spanning a variety of morphological classifications to further
understand the empirical fundamental plane of black hole activity. This plane
describes black holes from stellar-mass to supermassive and relates the mass of
an accreting black hole and its radio and X-ray luminosities. A key factor in
studying the fundamental plane is the turnover frequency, the frequency at
which the radio continuum emission becomes optically thin. We measured this
turnover frequency using new VLA observations combined, when necessary, with
archival Chandra observations. Radio observations are in the range of 5--40 GHz
across four frequency bands in B-configuration, giving high spatial resolution
to focus on the core emission. We use Markov Chain Monte Carlo methods to fit
the continuum emission in order to find the turnover frequency. After testing
for correlations, the turnover frequency does not display a significant
dependence on either mass or mass accretion rate, indicating that more
complicated physics than simple scaling and optical depth effects are at play,
as has been suggested by recent theoretical work.


  We have discovered a new AM Her system as the optical counterpart of the
ROSAT All-Sky-Survey source RX J1016.9-4103 (= 1RXS J101659.4-410332). The
X-ray spectrum is very soft and the X-ray intensity is strongly modulated with
the orbital period. Optical photometric and spectroscopic follow-up
observations reveal a synchronously rotating binary with an orbital period of
134 min, placing RX J1016.9-4103 in the period gap. The strength of the TiO
bands suggests a secondary spectral type later than M3 V and a distance of
615+/-150 pc. Based on two clearly visible broad humps in the optical spectrum
(interpreted as cyclotron features) a magnetic field strength of 52 MG is
deduced thus proving the polar classification.


  Deep Learning is having a remarkable impact on the design of Reduced Order
Models (ROMs) for Partial Differential Equations (PDEs), where it is exploited
as a powerful tool for tackling complex problems for which classical methods
might fail. In this respect, deep autoencoders play a fundamental role, as they
provide an extremely flexible tool for reducing the dimensionality of a given
problem by leveraging on the nonlinear capabilities of neural networks. Indeed,
starting from this paradigm, several successful approaches have already been
developed, which are here referred to as Deep Learning-based ROMs (DL-ROMs).
Nevertheless, when it comes to stochastic problems parameterized by random
fields, the current understanding of DL-ROMs is mostly based on empirical
evidence: in fact, their theoretical analysis is currently limited to the case
of PDEs depending on a finite number of (deterministic) parameters. The purpose
of this work is to extend the existing literature by providing some theoretical
insights about the use of DL-ROMs in the presence of stochasticity generated by
random fields. In particular, we derive explicit error bounds that can guide
domain practitioners when choosing the latent dimension of deep autoencoders.
We evaluate the practical usefulness of our theory by means of numerical
experiments, showing how our analysis can significantly impact the performance
of DL-ROMs.


  A topological index is a real number which is derived from a network or a
graph by mathematically that characterizes the whole of its structural
properties. Recently, there are various topological indices that have been
introduced in mathematical chemistry to predict the properties of molecular
topology. Among, the degree based topological indices such as Zagreb indices,
forgotten topological index, redefined Zagreb index, Randic index, general
first Zagreb index, symmetric division deg index and hence so forth are most
important, because of their chemical significance. In this work, we study the
general Zagreb index of hexagonal and triangular lattice networks.


  A mechanism of the parity effect in the thermally assisted resonant tunneling
is proposed in the view point of nonadiabatic transitions of thermally excited
states. In this mechanism, alternating enhancement of the relaxation is
naturally understood as a general property of quantum relaxation of uniaxial
magnets at finite temperatures where appreciable populations are pumped up to
excited states. It is also found that the enhanced sequence depends on the
sweeping rate of the field.


  We derive quantum constraints on the minimal amount of noise added in linear
amplification involving input or output signals whose component operators do
not necessarily have c-number commutators, as is the case for fermion currents.
This is a generalization of constraints derived for the amplification of
bosonic fields whose components posses c-number commutators.


  Let $G$ be a complex simply-connected semisimple Lie group and let $\g=
\hbox{\rm Lie}\,G$. Let $\g = \n_- +\hh + \n$ be a triangular decomposition of
$\g$. The authors in [LW] introduce a very nice representation theory idea for
the construction of certain elements in $\hbox{\rm cent}\,U(n)$. A key lemma in
[LW] is incorrect but the idea is in fact valid. In our paper here we modify
the construction so as to yield the desired elements in $\hbox{\rm
cent}\,U(\n)$.


  The mechanism of confinement in Yang-Mills theories remains a challenge to
our understanding of nonperturbative gauge dynamics. While it is widely
perceived that confinement may arise from chromo-magnetically charged gauge
configurations with nontrivial topology, it is not clear what types of
configurations could do that and how, in pure Yang-Mills and QCD-like
(non-supersymmetric) theories. Recently a promising approach has emerged, based
on statistical ensembles of dyons/anti-dyons that are constituents of
instanton/anti-instanton solutions with nontrivial holonomy where the holonomy
plays a vital role as an effective "Higgsing" mechanism. We report a thorough
numerical investigation of the confinement dynamics in SU(2) Yang-Mills theory
by constructing such a statistical ensemble of correlated instanton-dyons.


  For $1<p\le \infty$, we show the existence of a Banach space which is both
injectively and surjectively universal for the class of all separable Banach
spaces with an equivalent $p$-asymptotically uniformly smooth norm. We prove
that this class is analytic complete in the class of separable Banach spaces.
These results extend previous works by Kalton, Werner and Kurka in the case
$p=\infty$.


  In this work we consider the influence of mass media in the dynamics of the
two-dimensional Sznajd model. This influence acts as an external field, and it
is introduced in the model by means of a probability $p$ of the agents to
follow the media opinion. We performed Monte Carlo simulations on square
lattices with different sizes, and our numerical results suggest a change on
the critical behavior of the model, with the absence of the usual phase
transition for $p>\sim 0.18$. Another effect of the probability $p$ is to
decrease the average relaxation times $\tau$, that are log-normally
distributed, as in the standard model. In addition, the $\tau$ values depend on
the lattice size $L$ in a power-law form, $\tau\sim L^{\alpha}$, where the
power-law exponent depends on the probability $p$.


  Superclusters form from the largest enhancements in the primordial density
perturbation field and extend for tens of Mpc, tracing the large-scale
structure of the Universe. We characterise XLSSsCN01, a rich supercluster at
z~0.3 detected in the XXL Survey, composed of X-ray clusters of different
virial masses and luminosities. As one of the first studies on this topic, we
investigate the stellar populations of galaxies in different environments in
the supercluster region. We study a magnitude-limited (r<=20) and a
mass-limited sample (log(M*/M_sun)>10.8) of galaxies in the virialised region
and in the outskirts of 11 XLSSsCN01 clusters, in high- and low-density field.
We compute the stellar population properties of galaxies using spectral energy
distribution and spectral fitting techniques, and study the dependence of star
formation rates (SFR), colours, and stellar ages on environment. For r<20, the
fraction of SFing/blue galaxies, computed either from the specific-SFR (sSFR)
or rest-frame(rf) colour, shows depletion within the cluster virial radii,
where the number of galaxies with log(sSFR/yr^-1)>-12 and with (g-r)_rf<0.6 is
lower than in the field. For log(M*/M_sun)>10.8, no trends with environment
emerge, as massive galaxies are mostly already passive in all environments. No
differences among low- and high-density field members and cluster members
emerge in the sSFR-mass relation. The luminosity-weighted age-mass relation of
the passive populations within cluster virial radii show signatures of recent
environmental quenching. The study of luminous and massive galaxies in this
supercluster shows that while environment has a prominent role in determining
the fractions of SFing/blue galaxies, its effects on the star formation
activity in SFing galaxies are negligible.


  Radio continuum observations have proven to be a workhorse in our
understanding of the star formation process (i.e., stellar birth and death)
from galaxies both in the nearby universe and out to the highest redshifts. In
this article we focus on how the ngVLA will transform our understanding of star
formation by enabling one to map and decompose the radio continuum emission
from large, heterogeneous samples of nearby galaxies on $\gtrsim 10$\,pc scales
to conduct a proper accounting of the energetic processes powering it. At the
discussed sensitivity and angular resolution, the ngVLA will simultaneously be
able to create maps of current star formation activity at $\sim$100\,pc scales,
as well as detect and characterize (e.g., size, spectral shape, density, etc.)
discrete H{\sc ii} regions and supernova remnants on 10\,pc scales in galaxies
out to the distance of the Virgo cluster. Their properties can then be used to
see how they relate to the local and global ISM and star formation conditions.
Such investigations are essential for understanding the astrophysics of
high-$z$ measurements of galaxies, allowing for proper modeling of galaxy
formation and evolution.


  We present an exact many body solution for the dynamics of the population
difference $N_2-N_1$ induced by an rf-field in the two-component atomic cloud
characterized by equal scattering lengths. This situation is very close to the
actual JILA experiments with the two-component $^{87}$Rb vapor. We show that no
intrinsic decoherence exists for $N_2-N_1$, provided the exact SU(2) symmetry
holds. This contrasts with finite dissipation of the normal modes even in the
presence of the SU(2) symmetry. The intrinsic decoherence for \$N_2-N_1$ may
occur as long as deviations from the exact SU(2) symmetry are taken into
account. Such decoherence, however, should be characterized by very long times
governed by the smallness of the deviations from the symmetry. We suggest
testing the evolution of $N_2-N_1$ by conducting echo-type experiments.


  In this paper we explain how we deal with the problems related to the
constitution of the Aliento database, the complexity of which has to do with
the type of phrases we work with, the differences between languages, the type
of information we want to see emerge. The correct tagging of the specific
polysemy of brief sapiential units is an important step in the preparation of
the text within the corpus which will be submitted to compute similarities and
posterity of the units.


  We analyze density profiles for atomic quantum Hall states, which are
expected to form in systems of rotating cold atoms in the high-rotation limit.
For a two-dimensional (single-layer) system we predict a density landscape
showing plateaus at quantized densities, signaling the formation of
incompressible groundstates. For a set-up with parallel, coupled layers, we
predict (i) at intermediate values of the inter-layer tunneling: a continuously
varying density profile $\rho(z)$ across the layers, showing cusps at specific
positions, (ii) at small values for the tunneling, quantum Hall-Mott phases,
with individual layers at sharply quantized particle number, and plateaus in
the density profile $\rho(z)$.


  We construct a Hamiltonian for a quantum-mechanical model of nonrelativistic
particles in three dimensions interacting via the creation and annihilation of
a second type of nonrelativistic particles, which are bosons. The interaction
between the two types of particles is a point interaction concentrated on the
points in configuration space where the positions of two different particles
coincide. We define the operator, and its domain of self-adjointness, in terms
of co-dimension-three boundary conditions on the set of collision
configurations relating sectors with different numbers of particles.


  Massive gravity previously constructed as the spin-2 quantum gauge theory is
studied in the classical limit. The vector-graviton field v which does not
decouple in the limit of vanishing graviton mass gives rise to a modification
of general relativity. The modified Schwarzschild solution contains a
contribution which can be interpreted as the dark mass density. We calculate
the density profile in the simplest spherically symmetric geometry.


  A zero-magnetic-field Josephson diode effect (JDE) is observed in an
asymmetric superconducting quantum interference device (SQUID) mediated by
Dirac semimetal Cd3As2. Herein it is shown that phase coupling between the
surface and bulk superconducting channels, a unique phenomenon recently
identified in the observations of fractional Josephson effect and Leggett modes
in Cd3As2, can break time reversal symmetry (TRS) and, therefore, give rise to
the zero-field JDE. It is identified that the efficiency of the JDE can be
readily controlled by varying the geometry of the Josephson junction (JJ) arms
in the SQUIDs, thus providing an explanation of different JDE behaviors in two
SQUIDs examined in this work. Our results are anticipated to have important
implications in superconducting electronic circuit applications.


  We show how NOON states may be generated entangling two cavities by passing
atoms through them. The atoms interact with each cavity via two-photon resonant
transitions. We take advantage of the fact that depending on the state the atom
enter (excite or ground), it leaves or takes two photons per interaction and
leaves the cavities in a pure state.


  We are concerned with the following semi-linear polyharmonic equation with
integral constraint \begin{align} \left\{\begin{array}{rl}
&(-\Delta)^pu=u^\gamma_+ ~~ \mbox{ in }{\mathbb{R}^n},\\ \nonumber
&\int_{\mathbb{R}^n}u_+^{\gamma}dx<+\infty, \end{array}\right. \end{align}
where $n>2p$, $p\geq2$ and $p\in\mathbb{Z}$. We obtain for
$\gamma\in(1,\frac{n}{n-2p})$ that any nonconstant solution satisfying certain
growth at infinity is radial symmetric about some point in $\mathbb{R}^{n}$ and
monotone decreasing in the radial direction. In the case $p=2$, the same
results are established for more general exponent
$\gamma\in(1,\frac{n+4}{n-4})$. For the following fractional equation with
integral constraint \begin{equation*} \left\{\begin{array}{rl}
&(-\Delta)^sv=v^\gamma_+ ~~ \mbox{ in }{\mathbb{R}^n},~~~~\\
&\int_{\mathbb{R}^n}v_+^{\frac{n(\gamma-1)}{2s}}dx<+\infty,~~~~~
\end{array}\right. \end{equation*} where $s\in(0,1)$, $\gamma \in (1,
\frac{n+2s}{n-2s})$ and $n\geq 2$, we also complete the classification of
solutions with certain growth at infinity. In addition, observe that the
assumptions of the maximum principle named decay at infinity in \cite{chen} can
be weakened slightly. Based on this observation, we classify all positive
solutions of two semi-linear fractional equations without integral constraint.


  It is believed that soon after the Planck era, space time should have a
semi-classical nature. According to this, the escape from General Relativity
theory is unavoidable. Two geometric counter-terms are needed to regularize the
divergences which come from the expected value. These counter-terms are
responsible for a higher derivative metric gravitation. Starobinsky idea was
that these higher derivatives could mimic a cosmological constant. In this work
it is considered numerical solutions for general Bianchi I anisotropic
space-times in this higher derivative theory. The approach is ``experimental''
in the sense that there is no attempt to an analytical investigation of the
results. It is shown that for zero cosmological constant $\Lambda=0$, there are
sets of initial conditions which form basins of attraction that asymptote
Minkowski space. The complement of this set of initial conditions form basins
which are attracted to some singular solutions. It is also shown, for a
cosmological constant $\Lambda> 0$ that there are basins of attraction to a
specific de Sitter solution. This result is consistent with Starobinsky's
initial idea. The complement of this set also forms basins that are attracted
to some type of singular solution. Because the singularity is characterized by
curvature scalars, it must be stressed that the basin structure obtained is a
topological invariant, i.e., coordinate independent.


  We develop a theory of local asymptotic normality in the quantum domain based
on a noncommutative extension of the Lebesgue decomposition. This formulation
gives a substantial generalization of the previous paper [Yamagata, Fujiwara,
and Gill (2013). Ann. Statist., 41, 2197-2217.], extending the scope of the
quantum local asymptotic normality to a wider class of quantum statistical
models that comprise density operators of mixed ranks.


  Evolutionary game theory is a framework to formalize the evolution of
collectives ("populations") of competing agents that are playing a game and,
after every round, update their strategies to maximize individual payoffs.
There are two complementary approaches to modeling evolution of player
populations. The first addresses essentially finite populations by implementing
the apparatus of Markov chains. The second assumes that the populations are
infinite and operates with a system of mean-field deterministic differential
equations. By using a model of two antagonistic populations, which are playing
a game with stationary or periodically varying payoffs, we demonstrate that it
exhibits metastable dynamics that is reducible neither to an immediate
transition to a fixation (extinction of all but one strategy in a finite-size
population) nor to the mean-field picture. In the case of stationary payoffs,
this dynamics can be captured with a system of stochastic differential
equations and interpreted as a stochastic Hopf bifurcation. In the case of
varying payoffs, the metastable dynamics is much more complex than the dynamics
of the means.


  Many plants, such as Mimosa pudica (the sensitive plant), employ
electrochemical signals known as action potentials (APs) for rapid
intercellular communication. In this paper, we consider a reaction diffusion
model of individual AP signals to analyze APs from a communication and
information theoretic perspective. We use concepts from molecular communication
to explain the underlying process of information transfer in a plant for a
single AP pulse that is shared with one or more receiver cells. We also use the
chemical Langevin equation to accommodate the deterministic as well as
stochastic component of the system. Finally we present an information theoretic
analysis of single action potentials, obtaining achievable information rates
for these signals. We show that, in general, the presence of an AP signal can
increase the mutual information and information propagation speed among
neighboring cells with receivers in different settings.


  The next generation ultra-reliable and low-latency communications (xURLLC)
need novel design to provide satisfactory services to the emerging
mission-critical applications. To improve the spectrum efficiency and enhance
the robustness of xURLLC, this paper proposes a robust beamforming and
rate-splitting design in the finite blocklength (FBL) regime for downlink
multi-user multi-antenna xURLLC systems. In the design, adaptive rate-splitting
is introduced to flexibly handle the complex inter-user interference and thus
improve the spectrum efficiency. Taking the imperfection of the channel state
information at the transmitter (CSIT) into consideration, a max-min user rate
problem is formulated to optimize the common and private beamforming vectors
and the rate-splitting vector under the premise of ensuring the requirements of
transmission latency and reliability of all the users. The optimization problem
is intractable due to the non-convexity of the constraint set and the infinite
constraints caused by CSIT uncertainties. To solve it, we convert the infinite
constraints into finite ones by the S-Procedure method and transform the
original problem into a difference of convex (DC) programming. A constrained
concave convex procedure (CCCP) and the Gaussian randomization based iterative
algorithm is proposed to obtain a local minimum. Simulation results confirm the
convergence, robustness and effectiveness of the proposed robust beamforming
and rate-splitting design in the FBL regime. It is also shown that the proposed
robust design achieves considerable performance gain in the worst user rate
compared with existing transmission schemes under various blocklength and block
error rate requirements.


  The separation of the Milky Way disk into a thin and thick component is
supported by differences in the spatial, kinematic and metallicity
distributions of their stars. These differences have led to the view that the
thick disk formed early via a cataclysmic event and constitutes fossil evidence
of the hierarchical growth of the Milky Way. We show here, using N-body
simulations, how a double-exponential vertical structure, with stellar
populations displaying similar dichotomies can arise purely through internal
evolution. In this picture, stars migrate radially, while retaining nearly
circular orbits, as described by Sellwood & Binney (2002). As stars move
outwards they populate a thickened component. Such stars found at the present
time in the solar neighborhood formed early in the disk's history at smaller
radii where stars are more metal-poor and alpha-enhanced, leading to the
properties observed for thick disk stars. Classifying stars as members of the
thin or thick disk by either velocity or metallicity leads to an apparent
separation in the other property as observed. This scenario is supported by the
SDSS observation that stars in the transition region do not show any
correlation between rotational velocity and metallicity. The good qualitative
agreement between our simulation and observations in the Milky Way hint that
the thick disk may be a ubiquitous galaxy feature generated by stellar
migration. Nonetheless, we cannot exclude that some fraction of the thick disk
is a fossil of a past more violent history, nor can this scenario explain thick
disks in all galaxies.


  This article develops a duality principle for non-linear elasticity. The
results are obtained through standard tools of convex analysis and the Legendre
transform concept. We emphasize the dual variational formulation is concave.
Moreover, sufficient optimality conditions are also established.


  The final $p_{T}$-spectra measured at RHIC at $\sqrt{s_{NN}}=130$ and 200 GeV
are fitted within the Cracow single-freeze-out model. Then the global variables
like the transverse energy at midrapidity, the charged particle multiplicity at
midrapidity and the total multiplicity of charged particles are evaluated. The
predictions agree fairly well with the experimental data. The centrality
independence of the total number of charged particles per participant pair has
been also reproduced.


  The attainable transformer ratio in plasma accelerators is limited by
instabilities. Using three-dimensional particle-in-cell simulations, we
demonstrate that these can be controlled using a hollow plasma channel with a
co-axial plasma filament. The driver scatters electrons from the filament, and
the slow pinch of the ions leads to a strong chirp of the effective betatron
frequency, preventing beam breakup. We demonstrate the monoenergetic
acceleration of an electron bunch to 20 GeV over 4.4 m, achieving a transformer
ratio of 10, an energy efficiency of 40% and an emittance of 1.8 um.


  We report systematic $^{75}$As NMR studies on LaFeAs(O$_{1-x}$F$_{x}$) ($0\le
x\le0.14$). At $x=0.04$ near the phase boundary, from resistivity, spin-lattice
relaxation rate $1/T_1$, and NMR spectrum measurements, we found weak magnetic
order at $T_N\simeq 30$ K. Antiferromagnetic (AFM) fluctuations proved through
$1/T_1$ are suppressed significantly with F-doping, and pseudogap behavior
without pronounced AFM fluctuations is observed at $x=0.11$ where $T_c$ is
maximum. This significant suppression of $1/T_1T$ upon F-doping while $T_c$
remains nearly unchanged suggests that low-energy AFM fluctuations probed with
$^{75}$As NMR do not play a crucial role in the superconductivity.


  Context. We use Hubble Space Telescope photometry of six rich, compact star
clusters in the Large Magellanic Cloud (LMC), with ages ranging from 0.01 to
1.0 Gyr, to derive the clusters' stellar mass functions (MFs) at their
half-mass radii.
  Aims. The LMC is an ideal environment to study stellar MFs, because it
contains a large population of compact clusters at different evolutionary
stages. We aim to obtain constraints on the initial MFs (IMFs) of our sample
clusters on the basis of their present-day MFs, combined with our understanding
of their dynamical and photometric evolution.
  Methods. We derive the clusters' present-day MFs below 1.0 Msun using deep
observations with the Space Telescope Imaging Spectrograph and updated stellar
population synthesis models.
  Results. Since the relaxation timescales of low-mass stars are very long,
dynamical evolution will not have affected the MFs below 1.0 Msun
significantly, so that - within the uncertainties - the derived MFs are
consistent with the solar-neighbourhood IMF, at least for the younger clusters.
  Conclusions. The IMF in the low-density, low-metallicity environment of the
LMC disk is not significantly different from that in the solar neighbourhood.


  The BTC40 Survey for high-redshift quasars is a multicolor search using
images obtained with the Big Throughput Camera (BTC) on the CTIO 4-m telescope
in V, I, and z filters to search for quasars at redshifts of 4.8 < z < 6. The
survey covers 40 sq. deg. in B, V, & I and 36 sq. deg. in z. Limiting
magnitudes (3 sigma) reach to V = 24.6, I = 22.9 and z = 22.9. We used the
(V-I) vs. (I-z) two-color diagram to select high-redshift quasar candidates
from the objects classified as point sources in the imaging data. Follow-up
spectroscopy with the AAT and CTIO 4-m telescopes of candidates having I < 21.5
has yielded two quasars with redshifts of z = 4.6 and z = 4.8 as well as four
emission line galaxies with z = 0.6. Fainter candidates have been identified
down to I = 22 for future spectroscopy on 8-m class telescopes.


  An equilibrium picture of thermodynamics is discussed at the apparent horizon
of FRW universe in $f(T,T_G)$ gravity, where $T$ represents the torsion
invariant and $T_G$ is the teleparallel equivalent of the Gauss-Bonnet term. It
is found that one can translate the Friedmann equations to the standard form of
first law of thermodynamics. We discuss GSLT in the locality of assumption that
temperature of matter inside the horizon is similar to that of horizon.
Finally, we consider particular models in this theory and generate constraints
on the coupling parameter for the validity of GSLT in terms of recent cosmic
parameters and power law solutions.


  Let the reciprocal Newton 'constant' be an apparently non-dynamical
Brans-Dicke scalar field damped oscillating towards its General Relativistic
VEV. We show, without introducing additional matter fields or dust, that the
corresponding cosmological evolution averagely resembles, in the Jordan frame,
the familiar dark radiation -> dark matter -> dark energy domination sequence.
The fingerprints of our theory are fine ripples, hopefully testable, in the FRW
scale factor; they die away at the General Relativity limit. The possibility
that the Brans-Dicke scalar also serves as the inflaton is favorably examined.


  We analyze over 500 million Twitter messages from an eight month period and
find that tracking a small number of flu-related keywords allows us to forecast
future influenza rates with high accuracy, obtaining a 95% correlation with
national health statistics. We then analyze the robustness of this approach to
spurious keyword matches, and we propose a document classification component to
filter these misleading messages. We find that this document classifier can
reduce error rates by over half in simulated false alarm experiments, though
more research is needed to develop methods that are robust in cases of
extremely high noise.


  Thermal distortion of test masses, as well as thermal drift of their
vibrational mode frequencies, present a major challenge for operation of the
Advanced LIGO and Advanced VIRGO interferometers, reducing optical efficiency,
which limits sensitivity and potentially causing instabilities which reduce
duty-cycle. In this paper, we demonstrate that test-mass vibrational mode
frequency data can be used to overcome some of these difficulties. First, we
derive a general expression for the change in a mode frequency as a function of
temperature distribution inside the test mass. Then we show how the mode
frequency dependence on temperature distribution can be used to identify the
wavefunction of observed vibrational modes. We then show how monitoring the
frequencies of multiple vibrational modes allows the temperature distribution
inside the test mass to be strongly constrained. Finally, we demonstrate using
simulations, the potential to improve the thermal model of the test mass,
providing independent and improved estimates of important parameters such as
the coating absorption coefficient and the location of point absorbers.


  This paper presents the prospects of measuring $\sigma(e^{+}e^{-}\to
ZH)\times Br(H \to \gamma\gamma)$ in 3 $Z$ decay channels $Z \to q\bar{q} /
\mu^{+} \mu^{-} / \nu\bar{\nu}$ using the baseline detector with $\sqrt{s} =
240 GeV$ at the Circular Electron Positron Collider (CEPC) . The simulated
Monte Carlo events are generated and scaled to an integrated luminosity of 5.6
$ab^{-1}$ to mimic the data. Extrapolated results to 20 $ab^{-1}$ are also
shown. The expected statistical precision of this measurement after combining 3
channels of $Z$ boson decay is 7.7\%. With some preliminary estimation on the
systematical uncertainties, the total precision is 7.9\%. The performance of
CEPC electro-magnetic calorimeter (ECAL) is studied by smearing the photon
energy resolution in simulated events in $e^{+}e^{-} \to ZH \to
q\bar{q}\gamma\gamma$ channel. In present ECAL design, the stochastic term in
resolution plays the dominant role in the precision of Higgs measurements in $H
\to \gamma\gamma$ channel. The impact of the resolution on the measured
precision of $\sigma(ZH)\times Br(ZH \to q\bar{q}\gamma\gamma)$ as well as the
optimization of ECAL constant term and stochastic term are studied for the
further detector design.


  We bound the maximal number N of singular points of a plane algebraic curve C
that has precisely one place at infinity with one branch in terms of its first
Betti number $b_1(C)$. Asymptotically we prove that $N<\sim{17/11}b_1(C)$ for
large $b_1$. In particular, in the case of curves with one place at infinity,
we confirm the Zaidenberg and Lin conjecture stating that $N\le 2b_1+1$.


  In this paper, we propose a three-component Camassa-Holm (3CH) system with
cubic nonlinearity and peakons. The 3CH model is proven integrable in the sense
of Lax pair, Hamiltonian structure, and conservation laws. We show that this
system admits peaked soliton (peakon) and multi-peakon solutions. Additionally,
reductions of the 3CH system are investigated so that a new integrable
perturbed CH equation with cubic nonlinearity is generated to possess peakon
solutions.


  This paper investigates the entanglement entropy inequality and explores the
presentation of mutual information and conditional mutual information in
kinematic space. Specifically, we examine the regions within kinematic space
responsible for computing these physical quantities, enabling a more intuitive
understanding of the entanglement entropy inequality. Building upon this, we
employ the concept of double holography to analyze the properties of the
entanglement inequality in any given region. By utilizing kinematic space, we
calculate the contribution of the bulk to the holographic entanglement entropy
in double holography. In conclusion, we establish that kinematic space
substantiates a conjecture, namely that the entanglement entropy of an entire
region can be expressed as a linear combination of the entanglement entropy of
a single interval within the entangled region.


  We present theoretical model for the proximity effect in F-SFF-F structures
(F is ferromagnet, S is superconductor) with non-collinear magnetizations
vectors in the F-layers and with arbitrary magnitudes of exchange fields.
Electrical conductance of these structures is analyzed within the
Keldysh-Usadel formalism in the diffusive regime as a function of a
misorientation angle between magnetizations of the F-layers and transparencies
of SF and FF interfaces. We show that long-range triplet superconducting
correlations manifest themselves either as a zero-bias peak in the case of
perfect transparency of FF interface, or as a two-peak structure in the case of
finite transparency. The predicted features may serve as a diagnostic tool for
characterization of interfaces in superconducting hybrid structures


  Hierarchical coordination of controllers often uses symbolic state
representations that fully abstract their underlying low-level controllers,
treating them as "black boxes" to the symbolic action abstraction. This paper
proposes a framework to realize robust behavior, which we call
Feasibility-based Control Chain Coordination (FC$^3$). Our controllers expose
the geometric features and constraints they operate on. Based on this, FC$^3$
can reason over the controllers' feasibility and their sequence feasibility.
For a given task, FC$^3$ first automatically constructs a library of potential
controller chains using a symbolic action tree, which is then used to
coordinate controllers in a chain, evaluate task feasibility, as well as
switching between controller chains if necessary. In several real-world
experiments we demonstrate FC$^3$'s robustness and awareness of the task's
feasibility through its own actions and gradual responses to different
interferences.


  Given a holomorphic self-map $\varphi$ of $\D$ (the open unit disc in
$\mathbb{C}$), the composition operator $C_{\varphi} f = f \circ \varphi$, $f
\in H^2(\mathbb{\D})$, defines a bounded linear operator on the Hardy space
$H^2(\mathbb{\D})$. The model spaces are the backward shift-invariant closed
subspaces of $H^2(\mathbb{\D})$, which are canonically associated with inner
functions. In this paper, we study model spaces that are invariant under
composition operators. Emphasis is put on finite-dimensional model spaces,
affine transformations, and linear fractional transformations.


  We propose a sliding surface for systems on the Lie group $SO(3)\times
\mathbb{R}^3$ . The sliding surface is shown to be a Lie subgroup. The
reduced-order dynamics along the sliding subgroup have an almost globally
asymptotically stable equilibrium. The sliding surface is used to design a
sliding-mode controller for the attitude control of rigid bodies. The
closed-loop system is robust against matched disturbances and does not exhibit
the undesired unwinding phenomenon.


  Randomized algorithms are often enjoyed for their simplicity, but the hash
functions used to yield the desired theoretical guarantees are often neither
simple nor practical. Here we show that the simplest possible tabulation
hashing provides unexpectedly strong guarantees.
  The scheme itself dates back to Carter and Wegman (STOC'77). Keys are viewed
as consisting of c characters. We initialize c tables T_1, ..., T_c mapping
characters to random hash codes. A key x=(x_1, ..., x_q) is hashed to T_1[x_1]
xor ... xor T_c[x_c].
  While this scheme is not even 4-independent, we show that it provides many of
the guarantees that are normally obtained via higher independence, e.g.,
Chernoff-type concentration, min-wise hashing for estimating set intersection,
and cuckoo hashing.


  Eulerian simulations of the Vlasov-Poisson equations have been employed to
analyze the excitation of slow electrostatic fluctuations (with phase speed
close to the electron thermal speed), due to a beam-plasma interaction, and
their propagation in linear and nonlinear regime. In 1968, O'Neil and Malmberg
[Phys. Fluids {\bf 11}, 1754 (1968)] dubbed these waves "beam modes". In the
present paper, it is shown that, in the presence of a cold and low density
electron beam, these beam modes can become unstable and then survive Landau
damping unlike the Langmuir waves. When an electron beam is launched in a
plasma of Maxwellian electrons and motionless protons and this initial
equilibrium is perturbed by a monochromatic density disturbance, the electric
field amplitude grows exponentially in time and then undergoes nonlinear
saturation, associated with the kinetic effects of particle trapping and phase
space vortex generation. Moreover, if the initial density perturbation is setup
in the form of a low amplitude random phase noise, once the most unstable mode
has reached its nonlinear saturation amplitude after the linear growth, the
whole Fourier spectrum of wavenumbers is excited. As a result, the electric
field profile appears as a train of isolated pulses, each of them being
associated with a phase space vortex in the electron distribution function. At
later times, these vortical structures tend to merge and, correspondingly, the
electric pulses collapse, showing the tendency towards a time asymptotic
configuration with a single phase space structure associated to an electric
soliton-like pulse. This dynamical evolution is driven by purely kinetic
processes, possibly at work in many space and laboratory plasma environments.


  We study the Schrodinger equation for one-electron atoms in space-times with
d >= 4 spatial dimensions where the Gauss law is assumed to be valid. It is
shown that there are no normalizable wave functions corresponding to bound
states. The consistency with the classical limit is discussed.


  Synthetic aperture radar (SAR) images are widely used in target recognition
tasks nowadays. In this letter, we propose an automatic approach for radar
shadow detection and extraction from SAR images utilizing geometric projections
along with the digital elevation model (DEM) which corresponds to the given
geo-referenced SAR image. First, the DEM is rotated into the radar geometry so
that each row would match that of a radar line of sight. Next, we extract the
shadow regions by processing row by row until the image is covered fully. We
test the proposed shadow detection approach on different DEMs and a simulated
1D signals and 2D hills and volleys modeled by various variance based Gaussian
functions. Experimental results indicate the proposed algorithm produces good
results in detecting shadows in SAR images with high resolution.


  We theoretically analyze atom interferometry based on trapped ultracold
atoms, and employ optimal control theory in order to optimize number squeezing
and condensate trapping. In our simulations, we consider a setup where the
confinement potential is transformed from a single to a double well, which
allows to split the condensate. To avoid in the ensuing phase-accumulation
stage of the interferometer dephasing due to the nonlinear atom-atom
interactions, the atom number fluctuations between the two wells should be
sufficiently low. We show that low number fluctuations (high number squeezing)
can be obtained by optimized splitting protocols. Two types of solutions are
found: in the Josephson regime we find an oscillatory tunnel control and a
parametric amplification of number squeezing, while in the Fock regime
squeezing is obtained solely due to the nonlinear coupling, which is
transformed to number squeezing by peaked tunnel pulses. We study splitting and
squeezing within the frameworks of a generic two-mode model, which allows us to
study the basic physical mechanisms, and the multi-configurational time
dependent Hartree for bosons method, which allows for a microscopic modeling of
the splitting dynamics in realistic experiments. Both models give similar
results, thus highlighting the general nature of these two solution schemes. We
finally analyze our results in the context of atom interferometry.


The paper deals with continuous solutions of a Schilling's problem.


  Discrete distributions, particularly in high-dimensional deep models, are
often highly multimodal due to inherent discontinuities. While gradient-based
discrete sampling has proven effective, it is susceptible to becoming trapped
in local modes due to the gradient information. To tackle this challenge, we
propose an automatic cyclical scheduling, designed for efficient and accurate
sampling in multimodal discrete distributions. Our method contains three key
components: (1) a cyclical step size schedule where large steps discover new
modes and small steps exploit each mode; (2) a cyclical balancing schedule,
ensuring ``balanced" proposals for given step sizes and high efficiency of the
Markov chain; and (3) an automatic tuning scheme for adjusting the
hyperparameters in the cyclical schedules, allowing adaptability across diverse
datasets with minimal tuning. We prove the non-asymptotic convergence and
inference guarantee for our method in general discrete distributions. Extensive
experiments demonstrate the superiority of our method in sampling complex
multimodal discrete distributions.


  In this article we demonstrate the relationship between finitely exchangeable
arrays and finitely exchangeable sequences. We then derive sharp bounds on the
total variation distance between distributions of finitely and infinitely
exchangeable arrays.


  An important characteristic of many logics for Artificial Intelligence is
their nonmonotonicity. This means that adding a formula to the premises can
invalidate some of the consequences. There may, however, exist formulae that
can always be safely added to the premises without destroying any of the
consequences: we say they respect monotonicity. Also, there may be formulae
that, when they are a consequence, can not be invalidated when adding any
formula to the premises: we call them conservative. We study these two classes
of formulae for preferential logics, and show that they are closely linked to
the formulae whose truth-value is preserved along the (preferential) ordering.
We will consider some preferential logics for illustration, and prove syntactic
characterization results for them. The results in this paper may improve the
efficiency of theorem provers for preferential logics.


  We consider two types of nilpotent invariants associated to smooth
representations, namely generalized Whittaker models, and associated characters
(in the case of a real reductive group). We survey some recent results on the
behavior of these nilpotent invariants under local theta correspondence, and
highlight the special role of a certain double fiberation of moment maps.


  We consider general mixed $p$-spin mean field spin glass models and provide a
method to prove that the spectral gap of the Dirichlet form associated with the
Gibbs measure is of order one at sufficiently high temperature. Our proof is
based on an iteration scheme relating the spectral gap of the $N$-spin system
to that of suitably conditioned subsystems.


  Pole Expansion and Selected Inversion (PEXSI) is an efficient scheme for
evaluating selected entries of functions of large sparse matrices as required
e.g. in electronic structure algorithms. We show that the triangular
factorizations computed by the PEXSI scheme exhibit a localization property
similar to that of matrix functions, and we present a modified PEXSI algorithm
which exploits this observation to achieve linear scaling. To the best of our
knowledge, the resulting incomplete PEXSI (iPEXSI) algorithm is the first
linear-scaling algorithm which scales provably better than cubically even in
the absence of localization, and we hope that this will help to further lower
the critical system size where linear-scaling algorithms begin to outperform
the diagonalization algorithm.


  We discuss the quantization of the 2d gravity theory of Callan, Giddings,
Harvey, and Strominger (CGHS), following the procedure of David, and of Distler
and Kawai. We find that the physics depends crucially on whether the number of
matter fields is greater than or less than 24. In the latter case the
singularity pointed out by several authors is absent but the physical
interpretation is unclear. In the former case (the one studied by CGHS) the
quantum theory which gives CGHS in the linear dilaton semi-classical limit, is
different from that which gives CGHS in the extreme Liouville regime.


  Let X be a finite CW-complex, denote its fundamental group by G. Let R be an
n-dimensional complex repesentation of G. Any element A of the first cohomology
group of X with complex coefficients gives rise to the exponential deformation
of the representation R, which can be considered as a curve in the space of
representations. We show that the cohomology of X with local coefficients
corresponding to the generic point of this curve is computable from a spectral
sequence starting from the cohomology of X with R-twisted coefficients. We
compute the differentials of the spectral sequence in terms of Massey products.
We show that the spectral sequence degenerates in case when X is a Kaehler
manifold, and the representation R is semi-simple.
  If A is a real cohomology class, one associates to the triple (X,R,A) the
twisted Novikov homology (a module over the Novikov ring). We show that the
twisted Novikov Betti numbers equal the Betti numbers of X with coefficients in
the above local system. We investigate the dependance of these numbers on A and
prove that they are constant in the complement to a finite number of integral
hyperplanes in the first cohomology group.


  We use the new gamma-ray bursts (GRBs) data, combined with the baryon
acoustic oscillation(BAO) observation from the spectroscopic Sloan Digital Sky
Survey (SDSS) data release, the newly obtained $A$ parameter at $z=0.6$ from
the WiggleZ Dark Energy Survey, the cosmic microwave background (CMB)
observations from the 7-Year Wilkinson Microwave Anisotropy Probe (WMAP7)
results, and the type Ia supernovae (SNeIa) from Union2 set, to constrain a
phenomenological model describing possible interactions between dark energy and
dark matter, which was proposed to alleviate the coincidence problem of the
standard $\Lambda$CDM model. By using the Markov Chain Monte Carlo (MCMC)
method, we obtain the marginalized $1\sigma$ constraints
$\Omega_{m}=0.2886\pm{0.0135}$, $r_m=-0.0047\pm{0.0046}$, and
$w_X=-1.0658\pm{0.0564}$. We also consider other combinations of these data for
comparison. These results show that: (1) the energy of dark matter is slightly
transferring to that of dark energy; (2) even though the GRBs+BAO+CMB data
present less stringent constraints than SNe+BAO+CMB data do, the GRBs can help
eliminate the degeneracies among parameters.


  We study nonparametric estimators of conditional Kendall's tau, a measure of
concordance between two random variables given some covariates. We prove
non-asymptotic bounds with explicit constants, that hold with high
probabilities. We provide "direct proofs" of the consistency and the asymptotic
law of conditional Kendall's tau. A simulation study evaluates the numerical
performance of such nonparametric estimators.


  Many tasks in our modern life, such as planning an efficient travel, image
processing and optimizing integrated circuit design, are modeled as complex
combinatorial optimization problems with binary variables. Such problems can be
mapped to finding a ground state of the Ising Hamiltonian, thus various
physical systems have been studied to emulate and solve this Ising problem.
Recently, networks of mutually injected optical oscillators, called coherent
Ising machines, have been developed as promising solvers for the problem,
benefiting from programmability, scalability and room temperature operation.
Here, we report a 16-bit coherent Ising machine based on a network of
time-division-multiplexed femtosecond degenerate optical parametric
oscillators. The system experimentally gives more than 99.6 % of success rates
for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard
instances. The experimental and numerical results indicate that gradual pumping
of the network combined with multiple spectral and temporal modes of the
femtosecond pulses can improve the computational performance of the Ising
machine, offering a new path for tackling larger and more complex instances.


  Recently, direct data-driven prediction has found important applications for
controlling unknown systems, particularly in predictive control. Such an
approach provides exact prediction using behavioral system theory when
noise-free data are available. For stochastic data, although approximate
predictors exist based on different statistical criteria, they fail to provide
statistical guarantees of prediction accuracy. In this paper, confidence
regions are provided for these stochastic predictors based on the prediction
error distribution. Leveraging this, an optimal predictor which achieves
minimum mean-squared prediction error is also proposed to enhance prediction
accuracy. These results depend on some true model parameters, but they can also
be replaced with an approximate data-driven formulation in practice. Numerical
results show that the derived confidence region is valid and smaller prediction
errors are observed for the proposed minimum mean-squared error estimate, even
with the approximate data-driven formulation.


  We use the recently modified Friedmann equations obtained from string
T-duality effects that encode the zero-point length (Phys. Lett. B 836 (2023),
137621) to study the phase space analyses of a bouncing early universe. An
important implication of such stringy effects is that they can alleviate the
initial singularity since the Raychaudhuri equation is modified. We investigate
if the Universe can undergo an accelerated expansion phase for a specific
domain of the equation of state parameter. The stringy effects are encoded in
the parameter $\Gamma$, which depends not only on the zero-point length but
also on the state parameter $\omega$. We construct two dynamical systems
depending on whether $-1 < \omega \leq -1/3$ and $\omega \geq -1/3$, and we
classify the equilibrium points of each system. Exact solutions and
cosmological implications are discussed.


  We study the higher derivative chiral models with four supercharges and BPS
states in these models. The off-shell Lagrangian generically includes higher
powers of the auxiliary fields F which causes distinct on-shell branches
associated with the solutions to the auxiliary fields equation. We point out
that the model admits a supersymmetric completion of arbitrary higher
derivative bosonic models of a single complex scalar field and an arbitrary
scalar potential can be introduced even without superpotentials. As an example,
we present a supersymmetric extension of the Faddeev-Skyrme model without four
time derivatives, in contrast to the previously proposed supersymmetric
Faddeev-Skyrme-like model containing four time derivatives. In general, higher
derivative terms together with a superpotential result in deformed scalar
potentials. We find that higher derivative corrections to 1/2 BPS domain walls
and 1/2 BPS lumps are exactly canceled out while the 1/4 BPS lumps (as compact
baby Skyrmions) depend on a characteristic feature of the higher derivative
models. We also find a new 1/4 BPS condition for domain wall junctions which
generically receives higher derivative corrections.


  We consider a chain of Josephson-junction rhombi (proposed originally by
Doucot and Vidal) in quantum regime. In a regular chain with no disorder in the
maximally frustrated case when magnetic flux through each rhombi \Phi_r is
equal to one half of superconductive flux quantum \Phi_0, Josephson current is
due to correlated transport of pairs of Cooper pairs, i.e. charge is quantized
in units of $4e$. Sufficiently strong deviation \delta\Phi =|\Phi_r-\Phi_0/2| >
\delta\Phi^c from the maximally frustrated point brings the system back to
usual $2e$-quantized supercurrent. For a regular chain \delta\Phi^c was
calculated by us previously. Here we present detailed analysis of the effect of
quenched disorder (random stray charges and random fluxes piercing rhombi) on
the pairing effect.


  The African School of Fundamental Physics and Applications, also known as the
African School of Physics (ASP), was initiated in 2010, as a three-week
biennial event, to offer additional training in fundamental and applied physics
to African students with a minimum of three-year university education. Since
its inception, ASP has grown to be much more than a school. ASP has become a
series of activities and events with directed ethos towards physics as an
engine for development in Africa. We report on the seven African School of
Physics, ASP2022, organized at Nelson Mandela University, on November~28 to
December~8, 2022. ASP2022 included programs for university students, high
school teachers and high school pupils.


  A lot of exotic hadrons were reported in the past twenty years, which bring
us the renaissance of the hadron spectroscopy. Most of them can be understood
as hadronic molecules, whose interactions are mainly due to the exchange of
light mesons, and specifically, light vector mesons through the coupled-channel
unitary approach within the local hidden-gauge formalism. It is still
controversial whether the interaction arising from the exchange of heavy mesons
is capable of forming hadronic molecules. We apply the coupled-channel unitary
approach to study the fully-heavy $b \bar b c \bar c$ system, where the
exchanged mesons can only be the fully-heavy vector mesons $J/\psi$, $B_c^*$,
and $\Upsilon$. Especially, the $J/\psi$ meson is much lighter than the
$B_c^{(*)}$ mesons, so the present study can be taken as a general
investigation on the question whether a lower-mass fully-heavy meson is able to
bind two higher-mass fully-heavy hadrons. Our results suggest the existence of
the fully-heavy hadronic molecules $|B_c^{+} B_c^{-}; J^{PC}=0^{++} \rangle$,
$|B_c^{*+} B_c^{-} - c.c.; J^{PC}=1^{+-} \rangle$, and $|B_c^{*+} B_c^{*-};
J^{PC}=2^{++} \rangle$ as well as the possible existence of $|B_c^{*+} B_c^{-}
+ c.c.; J^{PC}=1^{++} \rangle$. These states are potentially to be observed in
the $\mu^+ \mu^- J/\psi$ and $\mu^+ \mu^- \Upsilon$ channels in future ATLAS,
CMS, and LHCb experiments.


  In this work, an image translation model is implemented to produce synthetic
amyloid-beta PET images from structural MRI that are quantitatively accurate.
Image pairs of amyloid-beta PET and structural MRI were used to train the
model. We found that the synthetic PET images could be produced with a high
degree of similarity to truth in terms of shape, contrast and overall high SSIM
and PSNR. This work demonstrates that performing structural to quantitative
image translation is feasible to enable the access amyloid-beta information
from only MRI.


  Tropical oriented matroids were defined by Ardila and Develin in 2007. They
are a tropical analogue of classical oriented matroids in the sense that they
encode the properties of the types of points in an arrangement of tropical
hyperplanes -- in much the same way as the covectors of (classical) oriented
matroids describe the types in arrangements of linear hyperplanes.
  Ardila and Develin proved that tropical oriented matroids can be represented
as mixed subdivisions of dilated simplices. In this paper we show that this
correspondence is a bijection. Moreover, a tropical analogue for the
Topological Representation Theorem for (classical) oriented matroids by Folkman
and Lawrence is presented.


  The recent advances in deep learning indicate significant progress in the
field of single image super-resolution. With the advent of these techniques,
high-resolution image with high peak signal to noise ratio (PSNR) and excellent
perceptual quality can be reconstructed. The major challenges associated with
existing deep convolutional neural networks are their computational complexity
and time; the increasing depth of the networks, often result in high space
complexity. To alleviate these issues, we developed an innovative shallow
residual feature representative network (SRFRN) that uses a bicubic
interpolated low-resolution image as input and residual representative units
(RFR) which include serially stacked residual non-linear convolutions.
Furthermore, the reconstruction of the high-resolution image is done by
combining the output of the RFR units and the residual output from the bicubic
interpolated LR image. Finally, multiple experiments have been performed on the
benchmark datasets and the proposed model illustrates superior performance for
higher scales. Besides, this model also exhibits faster execution time compared
to all the existing approaches.


  Prosody -- the suprasegmental component of speech, including pitch, loudness,
and tempo -- carries critical aspects of meaning. However, the relationship
between the information conveyed by prosody vs. by the words themselves remains
poorly understood. We use large language models (LLMs) to estimate how much
information is redundant between prosody and the words themselves. Using a
large spoken corpus of English audiobooks, we extract prosodic features aligned
to individual words and test how well they can be predicted from LLM
embeddings, compared to non-contextual word embeddings. We find a high degree
of redundancy between the information carried by the words and prosodic
information across several prosodic features, including intensity, duration,
pauses, and pitch contours. Furthermore, a word's prosodic information is
redundant with both the word itself and the context preceding as well as
following it. Still, we observe that prosodic features can not be fully
predicted from text, suggesting that prosody carries information above and
beyond the words. Along with this paper, we release a general-purpose data
processing pipeline for quantifying the relationship between linguistic
information and extra-linguistic features.


  In this paper, we introduce a new approach, called Posthoc Interpretation via
Quantization (PIQ), for interpreting decisions made by trained classifiers. Our
method utilizes vector quantization to transform the representations of a
classifier into a discrete, class-specific latent space. The class-specific
codebooks act as a bottleneck that forces the interpreter to focus on the parts
of the input data deemed relevant by the classifier for making a prediction.
Our model formulation also enables learning concepts by incorporating the
supervision of pretrained annotation models such as state-of-the-art image
segmentation models. We evaluated our method through quantitative and
qualitative studies involving black-and-white images, color images, and audio.
As a result of these studies we found that PIQ generates interpretations that
are more easily understood by participants to our user studies when compared to
several other interpretation methods in the literature.


  We present detailed results from performing general relativistic (GR)
simulations of stellar core collapse to a proto-neutron star, using a
microphysical equation of state (EoS) as well as an approximate description of
deleptonization during the collapse phase. We show that for a wide variety of
rotation rates and profiles the gravitational wave (GW) burst signals from the
core bounce are of a generic type, already known as Type I in the literature.
In addition, for most models the characteristic frequency of the GW burst
signal lies in a narrow range around approximately 718 Hz. In our systematic
study, using both GR and Newtonian gravity, we identify, individually quantify,
and discuss in detail the micro- and macrophysical mechanisms leading to this
result, i.e. the effects of rotation, the EoS, and deleptonization. We also
discuss the detectability prospects of such GW burst signals by GW detectors,
and infer that such a generic type of signal templates will likely facilitate a
more efficient search in current and future detectors of both interferometric
and resonant type.


  Dark photons that are sufficiently light and/or weakly-interacting represent
a compelling vision of dark matter. Dark photon decay into three photons, which
we call the dark photon trident, can be the dominant channel when the dark
photon mass falls below the electron pair threshold and can produce a
significant flux of x-rays. We use 16 years of data from INTEGRAL/SPI to
constrain sub-MeV dark photon decay, producing new worlds-best constraints on
the kinetic mixing parameter for dark photon masses between 61 keV and 1022
keV, and comment on the potential for future x-ray observatories to discover
the trident decay process.


  We consider a model for flow in a porous medium with a fracture in which the
flow in the fracture is governed by the Darcy-Forchheimer law while that in the
surrounding matrix is governed by Darcy's law. We give an appropriate mixed,
variational formulation and show existence and uniqueness of the solution. To
show existence we give an analogous formulation for the model in which the
Darcy-Forchheimer law is the governing equation throughout the domain. We show
existence and uniqueness of the solution and show that the solution for the
model with Darcy's law in the matrix is the weak limit of solutions of the
model with the Darcy-Forchheimer law in the entire domain when the Forchheimer
coefficient in the matrix tends toward zero.


  Recently, it has been experimentally shown by several other researchers in
the physics community that a properly designed periodic corrugation of a
metallic opaque screen may significantly enhance the power transmission through
a sub-wavelength hole in the optical frequency band. Oliner, Jackson and their
co-workers explained and justified this phenomenon as the result of the
excitation of the leaky waves supported by the corrugated screen. Here we
suggest another setup, in which metamaterial layers with special parameters may
be utilized as covers over a single sub-wavelength aperture in a perfectly
electric conducting (PEC) flat screen in order to increase the wave
transmission through this aperture, and we provide a detailed analytical
explanation for this aperture setup that may lead to similar, more pronounced
effects when the metamaterial layers are used in the entrance and the exit face
of the hole in the flat PEC screen with no corrugation. Some physical insights
into the function of these covers and some numerical results confirming this
theory are presented and discussed. We also discuss the sensitivity of the
transmission enhancement to the geometrical and electromagnetic parameters of
this structure.


  We consider supervised learning problems within the positive-definite kernel
framework, such as kernel ridge regression, kernel logistic regression or the
support vector machine. With kernels leading to infinite-dimensional feature
spaces, a common practical limiting difficulty is the necessity of computing
the kernel matrix, which most frequently leads to algorithms with running time
at least quadratic in the number of observations n, i.e., O(n^2). Low-rank
approximations of the kernel matrix are often considered as they allow the
reduction of running time complexities to O(p^2 n), where p is the rank of the
approximation. The practicality of such methods thus depends on the required
rank p. In this paper, we show that in the context of kernel ridge regression,
for approximations based on a random subset of columns of the original kernel
matrix, the rank p may be chosen to be linear in the degrees of freedom
associated with the problem, a quantity which is classically used in the
statistical analysis of such methods, and is often seen as the implicit number
of parameters of non-parametric estimators. This result enables simple
algorithms that have sub-quadratic running time complexity, but provably
exhibit the same predictive performance than existing algorithms, for any given
problem instance, and not only for worst-case situations.


  In this paper we consider $m$ ($m \geq 1$)conjunctions of Max-atoms that is
atoms of the form $\max(z,y) + r \geq x$, where the offset $r$ is a real
constant and $x,y,z$ are variables. We show that the Max-atom problem (MAP)
belongs to $\textsf{P}$. Indeed, we provide an algorithm which solves the MAP
in $O(n^{6} m^{2} + n^{4} m^{3} + n^{2} m^{4})$ operations, where $n$ is the
number of variables which compose the max-atoms. As a by-product other problems
also known to be in $\textsf{NP} \cap \textsf{co-NP}$ are in $\textsf{P}$. P1:
the problem to know if a tropical cone is trivial or not. P2: problem of
tropical rank of a tropical matrix. P3: parity game problem. P4: scheduling
problem with AND/OR precedence constraints. P5: problem on hypergraph (shortest
path). P6: problem in model checking and $\mu$-calculus.


  The No-Cloning property in Quantum Computation is known not to depend on the
unitarity of the operators involved, but only on their linearity. Based on that
fact, here it is shown that the No-Cloning property remains valid when Quantum
Mechanics is re-formulated within far wider frameworks of {\it scalars},
namely, one or the other of the infinitely many {\it reduced power algebras}
which can replace the usual real numbers $\mathbb{R}$, or complex numbers
$\mathbb{C}$.


  Prompt emissions from TeV blazars pair produce off the extragalactic
background light and the highly energetic resulting pair beams then cascade
through inverse Compton scattering to give rise to secondary gamma-rays. Such
reprocessed cascade emission that can be associated with individual blazar
sources has not been detected thus far. The absence of pair halos around these
sources, along with the non-observation of isotropic gamma-ray background
excess, seems to suggest that collective plasma effects, such as beam-plasma
instabilities, can play a crucial role in alleviating this GeV-TeV tension by
transferring the energy from the pair beams into the background plasma of the
intergalactic medium (IGM). This has profound implications not only for TeV
astrophysics, but also the strength of the intergalactic magnetic field and
properties of dark matter (DM). A direct consequence of the instability losses
and IGM heating is the modification of thermal history at late times, which
suppresses structure formation particularly in baryonically underdense regions,
potentially holding a clue towards resolving the small-scale crisis in
cosmology. In a blazar-heated universe, the observation of dwarf galaxies and
Lyman-$\alpha$ measurements present a favoured mass range for DM candidates
such as light axion-like particles.


  We report the result of an XMM-Newton observation of the black-hole X-ray
transient XTE J1650-500 in quiescence. The source was not detected and we set
upper limits on the 0.5-10 keV luminosity of 0.9e31-1.0e31 erg/s (for a newly
derived distance of 2.6 kpc). These limits are in line with the quiescent
luminosities of black-hole X-ray binaries with similar orbital periods (~7-8
hr)


  Dealing with large numbers of symmetries is often problematic. One solution
is to focus on just symmetries that generate the symmetry group. Whilst there
are special cases where breaking just the symmetries in a generating set is
complete, there are also cases where no irredundant generating set eliminates
all symmetry. However, focusing on just generators improves tractability. We
prove that it is polynomial in the size of the generating set to eliminate all
symmetric solutions, but NP-hard to prune all symmetric values. Our proof
considers row and column symmetry, a common type of symmetry in matrix models
where breaking just generator symmetries is very effective. We show that
propagating a conjunction of lexicographical ordering constraints on the rows
and columns of a matrix of decision variables is NP-hard.


  Low-rank decomposition has emerged as a vital tool for enhancing parameter
efficiency in neural network architectures, gaining traction across diverse
applications in machine learning. These techniques significantly lower the
number of parameters, striking a balance between compactness and performance.
However, a common challenge has been the compromise between parameter
efficiency and the accuracy of the model, where reduced parameters often lead
to diminished accuracy compared to their full-rank counterparts. In this work,
we propose a novel theoretical framework that integrates a sinusoidal function
within the low-rank decomposition process. This approach not only preserves the
benefits of the parameter efficiency characteristic of low-rank methods but
also increases the decomposition's rank, thereby enhancing model accuracy. Our
method proves to be an adaptable enhancement for existing low-rank models, as
evidenced by its successful application in Vision Transformers (ViT), Large
Language Models (LLMs), Neural Radiance Fields (NeRF), and 3D shape modeling.
This demonstrates the wide-ranging potential and efficiency of our proposed
technique.


  In recent years, the performance of object detection has advanced
significantly with the evolving deep convolutional neural networks. However,
the state-of-the-art object detection methods still rely on accurate bounding
box annotations that require extensive human labelling. Object detection
without bounding box annotations, i.e, weakly supervised detection methods, are
still lagging far behind. As weakly supervised detection only uses image level
labels and does not require the ground truth of bounding box location and label
of each object in an image, it is generally very difficult to distill knowledge
of the actual appearances of objects. Inspired by curriculum learning, this
paper proposes an easy-to-hard knowledge transfer scheme that incorporates easy
web images to provide prior knowledge of object appearance as a good starting
point. While exploiting large-scale free web imagery, we introduce a
sophisticated labour free method to construct a web dataset with good diversity
in object appearance. After that, semantic relevance and distribution relevance
are introduced and utilized in the proposed curriculum training scheme. Our
end-to-end learning with the constructed web data achieves remarkable
improvement across most object classes especially for the classes that are
often considered hard in other works.


  In this paper we study saturated fractions of a two-factor design under the
simple effect model. In particular, we define a criterion to check whether a
given fraction is saturated or not, and we compute the number of saturated
fractions. All proofs are constructive and can be used as actual methods to
build saturated fractions. Moreover, we show how the theory of Markov bases for
contingency tables can be applied to two-factor designs for moving between the
designs with given margins.


  We present the results of the first lattice QCD study of the strong coupling
g_{D^* D pi}. From our simulations in the quenched approximation, we obtain
g_{D^* D pi} = 18.8 +/- 2.3^{+1.1}_{-2.0} and hat(g)_c = 0.67 +/-
0.08^{+0.04}_{-0.06}. Whereas previous theoretical studies gave different
predictions, our result favours a large value for hat(g)_c. It agrees very well
with the recent experimental value by CLEO. hat(g) varies very little with the
heavy mass and we find in the infinite mass limit hat(g)_infinity = 0.69(18).


  We consider a superconducting persistent-current qubit consisting of a
three-junction superconducting loop in an applied magnetic field. We show that
by choosing the field, Josephson couplings, and offset charges suitably, we can
perfectly suppress the tunneling between two oppositely directed states of
circulating current, leading to a vanishing of the splitting between the two
qubit states. The suppression arises for interference between tunneling along
different paths, and is analogous to that predicted previously for magnetic
particles with half-integer spin.


  Associate a unique numerical sequence called the modular signature with each
positive integer, using modular residues of each integer under the prime
numbers, and distinguishing between the core seed primes and non-core seed
primes used to create the modular signatures. Group the modular signatures
within primorials. Use elementary sieve properties and combinatorial principles
to prove the twin primes and Goldbach conjectures.


  In an effort to invariantly characterize the conformal curvature structure of
analogue spacetimes built from a nonrelativistic fluid background, we determine
the Petrov type of a variety of laboratory geometries. Starting from the
simplest examples, we increase the complexity of the background, and thereby
determine how the laboratory fluid symmetry affects the corresponding Petrov
type in the analogue spacetime realm of the sound waves. We find that for more
complex flows isolated hypersurfaces develop, which are of a Petrov type
differing from that of the surrounding fluid. {Finally, we demonstrate that
within the incompressible background approximation, as well as for all
compressible quasi-one-dimensional flows, the only possible Petrov types are
the algebraically general type I and the algebraically special types O and D.


  In this paper, we prove that any solution of K\"ahler-Ricci flow on a Fano
compactification $M$ of semisimple complex Lie group, is of type II, if $M$
admits no K\"ahler-Einstein metrics. As an application, we found two Fano
compactifications of $\mathrm{SO}_4(\mathbb{C})$ and one Fano compactification
of $\mathrm{Sp}_4(\mathbb{C})$, on which the K\"ahler-Ricci flow will develop
singularities of type II. To the authors' knowledge, these are the first
examples of Ricci flow with singularities of type II on Fano manifolds in the
literature.


  The paper describes the construction of entropy-stable discontinuous Galerkin
difference (DGD) discretizations for hyperbolic conservation laws on
unstructured grids. The construction takes advantage of existing theory for
entropy-stable summation-by-parts (SBP) discretizations. In particular, the
paper shows how DGD discretizations -- both linear and nonlinear -- can be
constructed by defining the SBP trial and test functions in terms of
interpolated DGD degrees of freedom. In the case of entropy-stable
discretizations, the entropy variables rather than the conservative variables
must be interpolated to the SBP nodes. A fully-discrete entropy-stable scheme
is obtained by adopting the relaxation Runge-Kutta version of the midpoint
method. In addition, DGD matrix operators for the first derivative are shown to
be dense-norm SBP operators. Numerical results are presented to verify the
accuracy and entropy-stability of the DGD discretization in the context of the
Euler equations. The results suggest that DGD and SBP solution errors are
similar for the same number of degrees of freedom. Finally, an investigation of
the DGD spectra shows that spectral radius is relatively insensitive to
discretization order; however, the high-order methods do suffer from the linear
instability reported for other entropy-stable discretizations.


  The energy dependence of charged-hadron production in relativistic heavy-ion
collisions is investigated in a nonequilibrium-statistical relativistic
diffusion model (RDM) with three sources. Theoretical pseudorapidity
distributions are compared with Au + Au data at RHIC energies of sqrt(s_NN) =
0.13 and 0.2 TeV, and computed for Pb + Pb central collisions at LHC energies
of 2.76 and 5.52 TeV. The central, nearly equilibrated source arising from
gluon-gluon collisions becomes the major origin of particle production at LHC
energies. The midrapidity dip is determined by the interplay of the three
sources.


  We prove that a theory $T$ has stable forking if and only if $T^\mathrm{eq}$
has stable forking.


  We present the theory, design, and realization of a polarization-insensitive
metamaterial absorber for terahertz frequencies. We derive
geometrical-independent conditions for effective medium absorbers in general,
and for resonant metamaterials specically. Our fabricated design reaches and
absorptivity of 78% at 1.145 Thz


  Consider a sequence of real data points $X_1,\ldots, X_n$ with underlying
means $\theta^*_1,\dots,\theta^*_n$. This paper starts from studying the
setting that $\theta^*_i$ is both piecewise constant and monotone as a function
of the index $i$. For this, we establish the exact minimax rate of estimating
such monotone functions, and thus give a non-trivial answer to an open problem
in the shape-constrained analysis literature. The minimax rate involves an
interesting iterated logarithmic dependence on the dimension, a phenomenon that
is revealed through characterizing the interplay between the isotonic shape
constraint and model selection complexity. We then develop a penalized
least-squares procedure for estimating the vector
$\theta^*=(\theta^*_1,\dots,\theta^*_n)^T$. This estimator is shown to achieve
the derived minimax rate adaptively. For the proposed estimator, we further
allow the model to be misspecified and derive oracle inequalities with the
optimal rates, and show there exists a computationally efficient algorithm to
compute the exact solution.


  We consider recently introduced self-focusing fields that carry orbital
angular momentum (OAM) [Opt. Lett. $\textbf{46}$, 2384$-$2387 (2021)] and in
particular, their propagation properties through a turbulent ocean. We show
that this type of field is especially robust against turbulence induced
degradation, when compared to a completely coherent beam. In moderately strong
oceanic turbulence, the self-focusing OAM beam features over five orders of
magnitude higher peak intensities at the receiver plane, an $\sim$80 $\%$
detection probability for the signal mode, as well as an energy transmission
efficiency in excess of 70 $\%$ over a link of $\sim$100 m.
Counter-intuitively, the focusing properties of such fields may be enhanced
with increasing turbulence, causing the mean squared waist to become smaller
with greater turbulence strength. Our results demonstrate that certain types of
partial coherence may be highly desirable for optical telecommunication
employing OAM.


  We consider a one-parameter family of nonlinear coherent states by replacing
the factorial in coefficients of the canonical coherent states by a specific
generalized factorial depending on a parameter gamma. These states are
superposition of eigenstates of the Hamiltonian with a symmetric Poschl-Teller
potential depending on a parameter nu > 1. The associated Bargmann-type
transform is defined for equal parameters. Some results on the infinite square
well potential are also derived. For some different values of gamma, we discuss
two sets of orthogonal polynomials that are naturally attached to these
coherent states.


  The purpose of this paper is to study the canonical totally real foliations
of CR-submanifolds in a locally conformal K\"{a}hler manifold.


  The K-alpha resonance complexes in oxygen ions O I - O VI are theoretically
computed and resonance oscillator strengths and wavelengths are presented. The
highly resolved photoionization cross sections, with relativistic fine
structure, are computed in the coupled channel approximation using the
Breit-Pauli R-matrix method. A number of strong K-alpha resonances are found to
be appreciable, with resonance oscillator strengths f_r > 0.1. The K-alpha
resonance wavelengths of O I-O VI lie in a relatively narrow wavelength range
22 - 23.5 A, and the X-ray opacity in this region should therefore be
significantly affected by K --> L transitions in oxygen. The results should be
useful in the interpretation of soft X-ray spectra observed from Chandra and
XMM-Newton.


  Safe reinforcement learning has many variants and it is still an open
research problem. Here, we focus on how to use action guidance by means of a
non-expert demonstrator to avoid catastrophic events in a domain with sparse,
delayed, and deceptive rewards: the recently-proposed multi-agent benchmark of
Pommerman. This domain is very challenging for reinforcement learning (RL) ---
past work has shown that model-free RL algorithms fail to achieve significant
learning. In this paper, we shed light into the reasons behind this failure by
exemplifying and analyzing the high rate of catastrophic events (i.e.,
suicides) that happen under random exploration in this domain. While model-free
random exploration is typically futile, we propose a new framework where even a
non-expert simulated demonstrator, e.g., planning algorithms such as Monte
Carlo tree search with small number of rollouts, can be integrated to
asynchronous distributed deep reinforcement learning methods. Compared to
vanilla deep RL algorithms, our proposed methods both learn faster and converge
to better policies on a two-player mini version of the Pommerman game.


  We report on the results from the observations in very high energy band (VHE,
E_gamma > 100 GeV) of the black hole X-ray binary (BHXB) Cygnus X-1. The
observations were performed with the MAGIC telescope, for a total of 40 hours
during 26 nights, spanning the period between June and November 2006. Searches
for steady gamma-ray signals yielded no positive result and upper limits to the
integral flux ranging between 1 and 2% of the Crab nebula flux, depending on
the energy, have been established. We also analyzed each observation night
independently, obtaining evidence of gamma-ray signals at the 4.0 standard
deviations (sigma) significance level (3.2 sigma after trial correction) for
154 minutes effective on-time (EOT) on September 24 between 20h58 and 23h41
UTC, coinciding with an X-ray flare seen by RXTE, Swift and INTEGRAL. A search
for faster-varying signals within a night resulted in an excess with a
significance of 4.9 sigma (4.1 sigma after trial correction) for 79 minutes EOT
between 22h17 and 23h41 UTC. The measured excess is compatible with a
point-like source at the position of Cygnus X-1, and excludes the nearby radio
nebula powered by its relativistic jet. The differential energy spectrum is
well fitted by an unbroken power-law described by dN/(dA dt dE) = (2.3+- 0.6) x
10^{-12} (E/1 TeV)^{-3.2 +- 0.6}. This is the first experimental evidence of
VHE emission from a stellar-mass black hole, and therefore from a confirmed
accreting X-ray binary.


  This paper aims to interpret the mechanism of feedforward ReLU networks by
exploring their solutions for piecewise linear functions, through the deduction
from basic rules. The constructed solution should be universal enough to
explain some network architectures of engineering; in order for that, several
ways are provided to enhance the solution universality. Some of the
consequences of our theories include: Under affine-geometry background, the
solutions of both three-layer networks and deep-layer networks are given,
particularly for those architectures applied in practice, such as multilayer
feedforward neural networks and decoders; We give clear and intuitive
interpretations of each component of network architectures; The
parameter-sharing mechanism for multi-outputs is investigated; We provide an
explanation of overparameterization solutions in terms of affine transforms;
Under our framework, an advantage of deep layers compared to shallower ones is
natural to be obtained. Some intermediate results are the basic knowledge for
the modeling or understanding of neural networks, such as the classification of
data embedded in a higher-dimensional space, the generalization of affine
transforms, the probabilistic model of matrix ranks, and the concept of
distinguishable data sets.