  The first direct detection of gravitational waves has opened a new window to
study the Universe and would probably start a new era: the gravitational wave
Astronomy. Gravitational waves emitted by compact objects like neutron stars
could provide significant information about their structure, composition and
evolution.
  In this paper we calculate, using the relativistic Cowling approximation, the
oscillations of compact stars focusing on hybrid stars, with and without a
mixed phase in their cores. We study the existence of a possible hadron-quark
phase transition in the central regions of neutron stars and the changes it
produces on the gravitational modes frequencies emitted by these stars. We pay
particular attention to the $g$-modes, which are extremely important as they
could signal the existence of pure quark matter inside neutron stars. Our
results show a relationship between the frequency of the $g$-modes and the
constant speed of sound parametrization for the quark matter phase. We also
show that the inclusion of color superconductivity produces an increase on the
oscillation frequencies.
  We propose that observations of $g$-modes with frequencies $f_{\rm g}$
between $1$ kHz and $1.5$ kHz should be interpreted as an evidence of a sharp
hadron-quark phase transition in the core of a compact object.


  Based on the discussions about the Aharonov-Casher effect in the Lorentz
symmetry violation background, we show that the analogue of the relativistic
Landau quantization in the Aharonov-Casher setup can be achieved in the
Lorentz-symmetry violation background.


  Particles transported in fluid flows, such as cells, polymers, or nanorods,
are rarely spherical. In this study, we numerically and theoretically
investigate the dispersion of an initially localized patch of passive elongated
Brownian particles constrained to one degree of rotational freedom in a
two-dimensional Poiseuille flow, demonstrating that elongated particles exhibit
an enhanced longitudinal dispersion. In a shear flow, the rods translate due to
advection and diffusion and rotate due to rotational diffusion and their
classical Jeffery's orbit. The magnitude of the enhanced dispersion depends on
the particle's aspect ratio and the relative importance of its shear-induced
rotational advection and rotational diffusivity. When rotational diffusion
dominates, we recover the classical Taylor dispersion result for the
longitudinal spreading rate using an orientationally averaged translational
diffusivity for the rods. However, in the high-shear limit, the rods tend to
align with the flow and ultimately disperse more due to their anisotropic
diffusivities. Results from our Monte Carlo simulations of the particle
dispersion are captured remarkably well by a simple theory inspired by Taylor's
original work. For long times and large Peclet numbers, an effective
one-dimensional transport equation is derived with integral expressions for the
particles' longitudinal transport speed and dispersion coefficient. The
enhanced dispersion coefficient can be collapsed along a single curve for
particles of high aspect ratio, representing a simple correction factor that
extends Taylor's original prediction to elongated particles.


  We study localization phenomena in two dimensional systems of charged
particles in the presence of a metallic ground plane with a particular focus on
the superconductor-insulator transition. The ground plane introduces a
screening of the long-range Coulomb interaction, and provides a source of
dissipation due to the gapless diffusive electrons. The interplay of these two
effects leads to interesting physical phenomena which are analysed in detail in
this paper. We argue that the generic superconductor-insulator transition of
charged particles in the presence of the ground plane may be controlled by a
{\it fixed line} with variable critical exponents. This is illustrated by an
explicit calculation in an appropriate $\epsilon$ expansion. In contrast, the
universal properties of the superconductor-Mott insulator transition in the
clean limit at commensurate densities are shown to be unmodified by either the
metal or the long-range Coulomb interaction. A similar fixed line can arise in
the presence of a metallic ground plane for quantum Hall plateau transitions.
Implications for experiments on Josephson-junction arrays and quantum Hall
systems are described.


  Standardized large-scale testing can be a debatable topic, in which test
fairness sits at its very core. This study found that two out of five recent
multi-group DIF detection methods are capable of capturing both the uniform and
nonuniform DIF that affects test fairness. Still, no prior research has
demonstrated the relative performance of these two methods when they are
compared with each other. These two methods are the improved Wald test and the
generalized logistic regression procedure. This study assessed the
commonalities and differences between two sets of empirical results from these
two methods with the latest TIMSS math score data. The primary conclusion was
that the improved Wald test is relatively more established than the generalized
logistic regression procedure for multi-group DIF analysis. Empirical results
from this study may inform the selection of a multi-group DIF method in the
ILSA score analysis.


  Human mobility significantly impacts various aspects of society, including
transportation, urban planning, and public health. The increasing availability
of diverse mobility data and advancements in deep learning have revolutionized
mobility modeling. Existing deep learning models, however, mainly study
spatio-temporal patterns using trajectories and often fall short in capturing
the underlying semantic interdependency among activities. Moreover, they are
also constrained by the data source. These two factors thereby limit their
realism and adaptability, respectively. Meanwhile, traditional activity-based
models (ABMs) in transportation modeling rely on rigid assumptions and are
costly and time-consuming to calibrate, making them difficult to adapt and
scale to new regions, especially those regions with limited amount of required
conventional travel data. To address these limitations, we develop a novel
generative deep learning approach for human mobility modeling and synthesis,
using ubiquitous and open-source data. Additionally, the model can be
fine-tuned with local data, enabling adaptable and accurate representations of
mobility patterns across different regions. The model is evaluated on a
nationwide dataset of the United States, where it demonstrates superior
performance in generating activity chains that closely follow ground truth
distributions. Further tests using state- or city-specific datasets from
California, Washington, and Mexico City confirm its transferability. This
innovative approach offers substantial potential to advance mobility modeling
research, especially in generating human activity chains as input for
downstream activity-based mobility simulation models and providing enhanced
tools for urban planners and policymakers.


  We evaluate $N$ dependences of correlation functions in the bosonic part of
the IIB matrix model by the Monte Carlo method. We also evaluate those in two
sorts of regularized Schild models and find that the $N$ dependences are
different from those in the matrix model. In particular, the distribution of
the eigenvalues are logarithmically divergent in the regularized Schild model
when $g^2N$ is fixed.


  A current-carrying superconducting strip partly penetrated by magnetic flux
and surrounded by a bulk magnet of high permeability is considered. Two types
of samples are studied: those with critical current controlled by an edge
barrier dominating over the pinning, and those with high pinning-mediated
critical current masking the edge barrier.It is shown for both cases that the
current distribution in a central flux-free part of the strip is strongly
affected by the actual shape of the magnetic surroundings. Explicit analytical
solutions for the sheet current and self-field distributions are obtained which
show that, depending on the geometry, the effect may suppress the total
loss-free transport current of the strip or enhance it by orders of magnitude.
The effect depends strongly on the shape of the magnet and its distance to the
superconductor but only weakly on the magnetic permeability.


  Superconductivity at the interface of a heterostructure confined to
nanometer-sized scale offers unique opportunities to study the exotic physics
of two-dimensional superconductivity. The realization of superconductivity at
the interface between a topological insulator and an iron-chalcogenide compound
is highly attractive for exploring several recent theoretical predictions
involving these two new classes of materials. Here, we report transport
measurements on a Bi2Te3/FeTe heterostructure fabricated via van der Waals
epitaxy, which demonstrate superconductivity at the interface induced by the
Bi2Te3 epilayer with thickness even down to one quintuple layer. The
two-dimensional nature of the observed superconductivity with the highest
transition temperature around 12 K was verified by the existence of a
Berezinsky-Kosterlitz-Thouless transition and the diverging ratio of in-plane
to out-plane upper critical field on approaching the superconducting transition
temperature. With the combination of interface superconductivity and Dirac
surface states of Bi2Te3, the heterostructure studied in this work provides a
novel platform for realizing Majorana fermions.


  We present results from lattice calculations on the thermodynamics of QCD at
non-zero temperature and baryon chemical potential and discuss the role of
resonances for the occurrence of the transition to the quark-gluon plasma in
hot and dense matter. Properties of a hadronic resonance gas are compared to
lattice results on the equation of state at zero as well as non-zero baryon
chemical potential. Furthermore, it is shown that the quark mass dependence of
the transition temperature can be understood in terms of lines of constant
energy density in a resonance gas.


  As strength of disorder enhances beyond a threshold value in many-body
systems, a fundamental transformation happens through which the entire spectrum
localizes, a phenomenon known as many-body localization. This has profound
implications as it breaks down fundamental principles of statistical mechanics,
such as thermalization and ergodicity. Due to the complexity of the problem,
the investigation of the many-body localization transition has remained a big
challenge. The experimental exploration of the transition point is even more
challenging as most of the proposed quantities for studying such effect are
practically infeasible. Here, we experimentally implement a scalable protocol
for detecting the many-body localization transition point, using the dynamics
of a $N=12$ superconducting qubit array. We show that the sensitivity of the
dynamics to random samples becomes maximum at the transition point which leaves
its fingerprints in all spatial scales. By exploiting three quantities, each
with different spatial resolution, we identify the transition point with
excellent match between simulation and experiment. In addition, one can detect
the evidence of mobility edge through slight variation of the transition point
as the initial state varies. The protocol is easily scalable and can be
performed across various physical platforms.


  Quantum parallelism implies a spread of information over the space in
contradistinction to the classical mechanical situation where the information
is "centered" on a fixed trajectory of a classical particle. This means that a
quantum state becomes specified by more indefinite data. The above spread
resembles, without being an exact analogy, a transfer of energy to smaller and
smaller scales observed in the hydrodynamical turbulence. There, in spite of
the presence of dissipation (in a form of kinematic viscosity), energy is still
conserved. The analogy with the information spread in classical to quantum
transition means that in this process the information is also conserved. To
illustrate that, we show (using as an example a specific case of a coherent
quantum oscillator) how the Shannon information density continuously changes in
the above transition . In a more general scheme of things, such an analogy
allows us to introduce a "dissipative" term (connected with the information
spread) in the Hamilton-Jacobi equation and arrive in an elementary fashion at
the equations of classical quantum mechanics (ranging from the Schr\"{o}dinger
to Klein-Gordon equations). We also show that the principle of least action in
quantum mechanics is actually the requirement for the energy to be bounded from
below.


  This work addresses the challenge of comparing periocular images captured in
different spectra, which is known to produce significant drops in performance
in comparison to operating in the same spectrum. We propose the use of
Conditional Generative Adversarial Networks, trained to con-vert periocular
images between visible and near-infrared spectra, so that biometric
verification is carried out in the same spectrum. The proposed setup allows the
use of existing feature methods typically optimized to operate in a single
spectrum. Recognition experiments are done using a number of off-the-shelf
periocular comparators based both on hand-crafted features and CNN descriptors.
Using the Hong Kong Polytechnic University Cross-Spectral Iris Images Database
(PolyU) as benchmark dataset, our experiments show that cross-spectral
performance is substantially improved if both images are converted to the same
spectrum, in comparison to matching features extracted from images in different
spectra. In addition to this, we fine-tune a CNN based on the ResNet50
architecture, obtaining a cross-spectral periocular performance of EER=1%, and
GAR>99% @ FAR=1%, which is comparable to the state-of-the-art with the PolyU
database.


  Fractures occur in the shoulder area, which has a wider range of motion than
other joints in the body, for various reasons. To diagnose these fractures,
data gathered from Xradiation (X-ray), magnetic resonance imaging (MRI), or
computed tomography (CT) are used. This study aims to help physicians by
classifying shoulder images taken from X-ray devices as fracture / non-fracture
with artificial intelligence. For this purpose, the performances of 26 deep
learning-based pretrained models in the detection of shoulder fractures were
evaluated on the musculoskeletal radiographs (MURA) dataset, and two ensemble
learning models (EL1 and EL2) were developed. The pretrained models used are
ResNet, ResNeXt, DenseNet, VGG, Inception, MobileNet, and their spinal fully
connected (Spinal FC) versions. In the EL1 and EL2 models developed using
pretrained models with the best performance, test accuracy was 0.8455,0.8472,
Cohens kappa was 0.6907, 0.6942 and the area that was related with fracture
class under the receiver operating characteristic (ROC) curve (AUC) was
0.8862,0.8695. As a result of 28 different classifications in total, the
highest test accuracy and Cohens kappa values were obtained in the EL2 model,
and the highest AUC value was obtained in the EL1 model.


  We consider the astrophysical bounds on a new form of dark matter, the so
called Gravity-mediated Dark Matter. In this scenario, dark matter communicates
with us through a mediator sector composed of gravitational resonances, namely
a new scalar (radion) and a massive spin-two resonance (massive graviton). We
consider specific models motivated by natural electroweak symmetry breaking or
weak-scale dark matter in the context of models in warped extra-dimensions and
their composite duals. The main Dark Matter annihilation mechanism is due to
the interactions of KK gravitons to gauge bosons that propagate in bulk. We
impose the bounds on monochromatic or continuum photons from Fermi-LAT and
HESS. We also explore scenarios in which the Fermi gamma-ray line could be a
manifestation of Gravity-mediated Dark Matter.


  A central challenge in science is to understand how systems behaviors emerge
from complex networks. This often requires aggregating, reusing, and
integrating heterogeneous information. Supplementary spreadsheets to articles
are a key data source. Spreadsheets are popular because they are easy to read
and write. However, spreadsheets are often difficult to reanalyze because they
capture data ad hoc without schemas that define the objects, relationships, and
attributes that they represent. To help researchers reuse and compose
spreadsheets, we developed ObjTables, a toolkit that makes spreadsheets human-
and machine-readable by combining spreadsheets with schemas and an
object-relational mapping system. ObjTables includes a format for schemas;
markup for indicating the class and attribute represented by each spreadsheet
and column; numerous data types for scientific information; and high-level
software for using schemas to read, write, validate, compare, merge, revision,
and analyze spreadsheets. By making spreadsheets easier to reuse, ObjTables
could enable unprecedented secondary meta-analyses. By making it easy to build
new formats and associated software for new types of data, ObjTables can also
accelerate emerging scientific fields.


  Motivated by a recent interest in curved rigid supersymmetries, we construct
a new type of N=4, d=1 supersymmetric systems by employing superfields defined
on the cosets of the supergroup SU(2|1). The relevant worldline supersymmetry
is a deformation of the standard N=4, d=1 supersymmetry by a mass parameter m.
As instructive examples we consider, at the classical and quantum levels, the
models associated with the supermultiplets (1,4,3) and (2,4,2) and find out
interesting interrelations with some previous works on non-standard d=1
supersymmetry. In particular, the d=1 systems with "weak supersymmetry" are
naturally reproduced within our SU(2|1) superfield approach as a subclass of
the (1,4,3) models. A generalization to the N=8, d=1 case implies the
supergroup SU(2|2) as the candidate deformed worldline supersymmetry.


  Let ${\sf k}$ be a field, $S$ be a bigraded ${\sf k}$-algebra, and $S_\Delta$
denote the diagonal subalgebra of $S$ corresponding to $\Delta = \{ (cs,es) \;
| \; s \in \mathbb{Z} \}$. It is know that the $S_\Delta$ is Koszul for $c,e
\gg 0$. In this article, we find bounds for $c,e$ for $S_\Delta$ to be Koszul,
when $S$ is a geometric residual intersection. Furthermore, we also study the
Cohen-Macaulay property of these algebras. Finally, as an application, we look
at classes of linearly presented perfect ideals of height two in a polynomial
ring, show that all their powers have a linear resolution, and study the
Koszul, and Cohen-Macaulay property of the diagonal subalgebras of their Rees
algebras.


  We present a combination of local density approximation (LDA) with the
dynamical cluster approximation (LDA+DCA) in the framework of the
full-potential linear augmented plane-wave method, and compare our LDA+DCA
results for SrVO$_3$ to LDA with the dynamical mean field theory (LDA+DMFT)
calculations as well as experimental observations on SrVO$_3$. We find a
qualitative agreement of the momentum resolved spectral function with
angle-resolved photoemission spectra (ARPES) and former LDA+DMFT results. As a
correction to LDA+DMFT, we observe more pronounced coherent peaks below the
Fermi level, as indicated by ARPES experiments. In addition, we resolve the
spectral functions in the ${\bf K}_{0}=(0,0,0)$ and ${\bf K}_{1}=(\pi,\pi,\pi)$
sectors of DCA, where band insulating and metallic phases coexist. Our approach
can be applied to correlated compounds where not only local quantum
fluctuations but also spatial fluctuations are important.


  Observing the light emitted by the first accreting black holes (BHs) would
dramatically improve our understanding of the formation of quasars at z > 6,
possibly unveiling the nature of their supermassive black hole (SMBH) seeds. In
previous works we explored the relative role of the two main competing BH seed
formation channels, Population III remnants (low-mass seeds) and direct
collapse BHs (high-mass seeds), investigating the properties of their host
galaxies in a cosmological context. Building on this analysis, we predict here
the spectral energy distribution and observational features of low- and
high-mass BH seeds selected among the progenitors of a z~6 SMBH. We derive the
processed emission from both accreting BHs and stars by using the
photo-ionization code Cloudy, accounting for the evolution of metallicity and
dust-to-gas mass ratio in the interstellar medium of the host galaxies, as
predicted by the cosmological data- constrained model GAMETE/QSOdust. We show
how future missions like JWST and ATHENA will be able to detect the light
coming from SMBH progenitors already at z~16. We build upon previous
complementary studies and propose a method based on the combined analysis of
near infrared (NIR) colors, IR excess (IRX) and UV continuum slopes (i.e.
color-color and IRX-Beta diagrams) to distinguish growing seed BH host galaxies
from starburst-dominated systems in JWST surveys. Sources selected through this
criterion would be the best target for follow-up X-ray observations.


  I recent years, many mathematicians studied various degenerate version of
some spcial polynomials of which quite a few interesting results were
discovered. In this paper, we introduce the type 2 degenerate Bernoulli
polynomials of the second kind and their higher-order analogues, and study some
identities and expressions for these polynomials. Specially, we obtain a
relation between the type 2 degenerate Bernoulli polynomials of the second kind
and degenerate Bernoulli polynomials of the second kind, and identity involving
hihger-order analogues of those polynomials and the degenerate stirling number
of the second kin, and and expression of higher-order analogues of those
polynomials in terms of the higher-order type 2 degenerate Bernoulli
polynomials and the degenerate stirling number of the first kind.


  We introduce a new formulation of the Hidden Parameter Markov Decision
Process (HiP-MDP), a framework for modeling families of related tasks using
low-dimensional latent embeddings. Our new framework correctly models the joint
uncertainty in the latent parameters and the state space. We also replace the
original Gaussian Process-based model with a Bayesian Neural Network, enabling
more scalable inference. Thus, we expand the scope of the HiP-MDP to
applications with higher dimensions and more complex dynamics.


  Fault-tolerant (FT) computation by using quantum error correction (QEC) is
essential for realizing large-scale quantum algorithms. Devices are expected to
have enough qubits to demonstrate aspects of fault tolerance in the near
future. However, these near-term quantum processors will only contain a small
amount of noisy qubits and allow limited qubit connectivity. Fault-tolerant
schemes that not only have low qubit overhead but also comply with geometrical
interaction constraints are therefore necessary. In this work, we combine flag
fault tolerance with quantum circuit mapping, to enable an efficient
flag-bridge approach to implement FT QEC on near-term devices. We further show
an example of performing the Steane code error correction on two current
superconducting processors and numerically analyze their performance with
circuit level noise. The simulation results show that the QEC circuits that
measure more stabilisers in parallel have lower logical error rates. We also
observe that the Steane code can outperform the distance-3 surface code using
flag-bridge error correction. In addition, we foresee potential applications of
the flag-bridge approach such as FT computation using lattice surgery and code
deformation techniques.


  Both image-caption pairs and translation pairs provide the means to learn
deep representations of and connections between languages. We use both types of
pairs in MURAL (MUltimodal, MUltitask Representations Across Languages), a dual
encoder that solves two tasks: 1) image-text matching and 2) translation pair
matching. By incorporating billions of translation pairs, MURAL extends ALIGN
(Jia et al. PMLR'21)--a state-of-the-art dual encoder learned from 1.8 billion
noisy image-text pairs. When using the same encoders, MURAL's performance
matches or exceeds ALIGN's cross-modal retrieval performance on well-resourced
languages across several datasets. More importantly, it considerably improves
performance on under-resourced languages, showing that text-text learning can
overcome a paucity of image-caption examples for these languages. On the
Wikipedia Image-Text dataset, for example, MURAL-base improves zero-shot mean
recall by 8.1% on average for eight under-resourced languages and by 6.8% on
average when fine-tuning. We additionally show that MURAL's text
representations cluster not only with respect to genealogical connections but
also based on areal linguistics, such as the Balkan Sprachbund.


  We derive an exact expression for the Seiberg-Witten map of noncommutative
gauge theory. It is found by studying the coupling of the gauge field to the
Ramond-Ramond potentials in string theory. Our result also proves the earlier
conjecture by Liu.


  For a unitary local system of rank one on a complete hyperbolic threefold of
finite volume which has only one cusp, we will compare the order of the
Alexander invariant at t=1 and one of Ruelle-Selberg L-function at s=0. Our
result may be considered as a geometric analog of the Iwasawa main conjecture
in the algebraic number theory.


  We present a framework for symbolically executing and model checking
higher-order programs with external (open) methods. We focus on the
client-library paradigm and in particular we aim to check libraries with
respect to any definable client. We combine traditional symbolic execution
techniques with operational game semantics to build a symbolic execution
semantics that captures arbitrary external behaviour. We prove the symbolic
semantics to be sound and complete. This yields a bounded technique by imposing
bounds on the depth of recursion and callbacks. We provide an implementation of
our technique in the K framework and showcase its performance on a custom
benchmark based on higher-order coding errors such as reentrancy bugs.


  This is a brief review of the theoretical status of Higgs production at the
LHC in the Standard Model, with an emphasis on the recent developments and
computations. In particular, I focus on both inclusive and differential cross
sections for the dominant production mode in the Standard Model, where the
theoretical uncertainties induced by the different interplays between top- and
bottom-quark effects in the gluon-fusion scattering amplitude are discussed.


  The rigidity of elastic networks depends sensitively on their internal
connectivity and the nature of the interactions between constituents. Particles
interacting via central forces undergo a zero-temperature rigidity-percolation
transition near the isostatic threshold, where the constraints and internal
degrees of freedom are equal in number. Fibrous networks, such as those that
form the cellular cytoskeleton, become rigid at a lower threshold due to
additional bending constraints. However, the degree to which bending governs
network mechanics remains a subject of considerable debate. We study disordered
fibrous networks with variable coordination number, both above and below the
central-force isostatic point. This point controls a broad crossover from
stretching- to bending-dominated elasticity. Strikingly, this crossover
exhibits an anomalous power-law dependence of the shear modulus on both
stretching and bending rigidities. At the central-force isostatic point---well
above the rigidity threshold---we find divergent strain fluctuations together
with a divergent correlation length $\xi$, implying a breakdown of continuum
elasticity in this simple mechanical system on length scales less than $\xi$.


  In this paper we explore the connection between the ranks of the magnitude
homology groups of a graph and the structure of its subgraphs. To this end, we
introduce variants of magnitude homology called eulerian magnitude homology and
discriminant magnitude homology. Leveraging the combinatorics of the
differential in magnitude homology, we illustrate a close relationship between
the ranks of the eulerian magnitude homology groups on the first diagonal and
counts of subgraphs which fall in specific classes. We leverage these tools to
study limiting behavior of the eulerian magnitude homology groups for
Erdos-Renyi random graphs and random geometric graphs, producing for both
models a vanishing threshold for the eulerian magnitude homology groups on the
first diagonal. This in turn provides a characterization of the generators for
the corresponding magnitude homology groups. Finally, we develop an explicit
asymptotic estimate the expected rank of eulerian magnitude homology along the
first diagonal for these random graph models.


  In this study, we constitute an adaptive hedging method based on empirical
mode decomposition (EMD) method to extract the adaptive hedging horizon and
build a time series cross-validation method for robust hedging performance
estimation. Basing on the variance reduction criterion and the value-at-risk
(VaR) criterion, we find that the estimation of in-sample hedging performance
is inconsistent with that of the out-sample hedging performance. The EMD
hedging method family exhibits superior performance on the VaR criterion
compared with the minimum variance hedging method. The matching degree of the
spot and futures contracts at the specific time scale is the key determinant of
the hedging performance in the corresponding hedging horizon.


  We consider viscous free-boundary magnetohydrodynamics(MHD) under vacuum in
$\mathbb{R}^3$, especially when vacuum magnetic field is identically zero. It
is a central problem in mathematics to perform vanishing viscosity limit to get
a solution of hyperbolic inviscid system. However, boundary layer behavior
happens near the free-boundary, so existence time $T^{\varepsilon} \rightarrow
0$ as kinematic viscosity $\varepsilon\rightarrow 0$ in standard sobolev space.
Inspired by \cite{NMFR1}, we use sobolev conormal space to derive uniform
regularity in viscosity $\varepsilon$. Finally, we get a solution of inviscid
free-boundary magnetohydrodynamics when initial magnetic field is zero on the
free-boundary and in vacuum.


  In this paper, we study the $2$D cubic nonlinear Schr\"odinger equation (NLS)
with the partial harmonic potential. First, we prove the local well-posedness
in Bourgain spaces by establishing a key bilinear estimate associated with the
partial harmonic oscillator. Then, we give the polynomial bound of the Sobolev
norms for the solutions using the method of the Planchon, Tzvetkov, and
Visciglia.


  The weight distribution and weight hierarchy of linear codes are two
important research topics in coding theory. In this paper, by choosing proper
defining sets from inhomogeneous quadratic functions over $\mathbb{F}_{q}^{2},$
we construct a family of $3$-weight $p$-ary linear codes and determine their
weight distributions and weight hierarchies. Most of the codes can be used in
secret sharing schemes.


  In this paper we consider the heat semigroup $\{W_t\}_{t>0}$ defined by the
combinatorial Laplacian and two subordinated families of $\{W_t\}_{t>0}$ on
homogeneous trees $X$. We characterize the weights $u$ on $X$ for which the
pointwise convergence to initial data of the above families holds for every
$f\in L^{p}(X,\mu,u)$ with $1\le p<\infty$, where $\mu$ represents the counting
measure in $X$ . We prove that this convergence property in $X$ is equivalent
to the fact that the maximal operator on $t\in (0,R)$, for some $R>0$, defined
by the semigroup is bounded from $L^{p}(X,\mu,u)$ into $L^{p}(X,\mu,v)$ for
some weight $v$ on $X$.


  In this paper a new mining algorithm is defined based on frequent item set.
Apriori Algorithm scans the database every time when it finds the frequent item
set so it is very time consuming and at each step it generates candidate item
set. So for large databases it takes lots of space to store candidate item set
.In undirected item set graph, it is improvement on apriori but it takes time
and space for tree generation. The defined algorithm scans the database at the
start only once and then from that scanned data base it generates the Trade
List. It contains the information of whole database. By considering minimum
support it finds the frequent item set and by considering the minimum
confidence it generates the association rule. If database and minimum support
is changed, the new algorithm finds the new frequent items by scanning Trade
List. That is why it's executing efficiency is improved distinctly compared to
traditional algorithm.


  In this paper we explicitly compute finite bases of disjunctive identities
and finite bases of regular representations for a number of interesting finite
groups.


  We prove new structural results for the rational homotopy type of the
classifying space $B\operatorname{aut}(X)$ of fibrations with fiber a simply
connected finite CW-complex $X$. We first study nilpotent covers of
$B\operatorname{aut}(X)$ and show that their rational cohomology groups are
algebraic representations of the associated transformation groups. For the
universal cover, this yields an extension of the Sullivan-Wilkerson theorem to
higher homotopy and cohomology groups. For the cover corresponding to the
kernel of the homology representation, this proves algebraicity of the
cohomology of the homotopy Torelli space. For the cover that classifies what we
call normal unipotent fibrations, we then prove the stronger result that there
exists a nilpotent dg Lie algebra $\mathfrak{g}(X)$ in algebraic
representations that models its equivariant rational homotopy type. This leads
to an algebraic model for the space $B\operatorname{aut}(X)$ and to a
description of its rational cohomology ring as the cohomology of a certain
arithmetic group $\Gamma(X)$ with coefficients in the Chevalley-Eilenberg
cohomology of $\mathfrak{g}(X)$. This has strong structural consequences for
the cohomology ring and, in certain cases, allows it to be completely
determined using invariant theory and calculations with modular forms. We
illustrate these points with concrete examples. As another application, we
significantly improve on certain results of Berglund-Madsen on self-homotopy
equivalences of highly connected even-dimensional manifolds, and we prove
parallel new results in odd dimensions.


  A central object in any axionic theory is its periodic potential, which is
typically generated by instantons. The goal of this paper is to understand what
physically happens to the theory when we lose control of the potential's
instanton expansion. We argue, using the Yang-Lee theory of phase transitions,
that the theory breaks down in the classic sense: states become light. However,
these states are not necessarily light for all values of the axion and there
can be large regions where the effective description remains valid. We find
alternative expressions for the effective potential in terms of the properties
of these light states, which remain useful even when the instanton expansion
breaks down, and thus initiate a push beyond the lamppost of large instanton
actions. Most of these questions are motivated by the axionic Weak Gravity
Conjecture, which we reformulate without reference to instanton actions. We
also comment on its ability to constrain large-field axion inflation.


  Dynamical friction and stellar orbital motion in spiral galaxies with dark
matter composed of ultralight bosons in the state of {rotating} Bose-Einstein
condensate (BEC) are studied. It is found that the dynamical friction force is
significantly affected by the topological charge of the vortex structure of the
BEC core with the strongest effect at distances near the galactic center. It is
also shown that the ultralight dark matter self-interaction plays an important
role in studying the dynamical friction.


  In this paper, we investigate the tunneling of vector boson particles across
the event horizon of Kerr-de Sitter black hole by using Hamilton-Jacobi ansatz
to Proca equation and WKB approximation. The surface gravity of KdS black hole
has been recovered by using direct calculation and Proca equation. These two
different methods give the same Hawking temperature at the event horizon.


  Complex networks or graphs provide a powerful framework to understand
importance of individuals and their interactions in real-world complex systems.
Several graph theoretical measures have been introduced to access importance of
the individual in systems represented by networks. Particularly, eigenvector
centrality (EC) measure has been very popular due to its ability in measuring
importance of the nodes based on not only number of interactions they acquire
but also particular structural positions they have in the networks.
Furthermore, the presence of certain structural features, such as the existence
of high degree nodes in a network is recognized to induce localization
transition of the principal eigenvector (PEV) of the network's adjacency
matrix. Localization of PEV has been shown to cause difficulties in assigning
centrality weights to the nodes based on the EC. We revisit PEV localization
and its relation with failure of EC problem, and by using simple model networks
demonstrate that in addition to the localization of the PEV, the delocalization
of PEV may also create difficulties for using EC as a measure to rank the
nodes. Our investigation while providing fundamental insight to the relation
between PEV localization and centrality of nodes in networks, suggests that for
the networks having delocalized PEVs, it is better to use degree centrality
measure to rank the nodes.


  There exist two major subclasses in the class of superquadratic functions,
one comprises concave and decreasing functions, while the other consists of
convex and monotone increasing functions. Leveraging this distinction, we
introduce eigenvalue inequalities for each case. The characteristics of these
functions allow us to advance our findings in two ways: firstly, by refining
existing results related to eigenvalues for convex functions, and secondly, by
deriving complementary inequalities for other function types. To bolster our
claims, we will provide illustrative examples.


  The shifted Tietz-Wei (sTW) oscillator is as good as traditional Morse
potential in simulating the atomic interaction in diatomic molecules. By using
the Pekeris-type approximation to deal with the centrifugal term, we obtain the
bound-state solutions of the radial Schr\"odinger equation with this typical
molecular model via the exact quantization rule (EQR). The energy spectrum for
a set of diatomic molecules ($NO \left(a^4\Pi_i\right)$, $NO
\left(B^2\Pi_r\right)$, $NO \left(L'^2\phi\right)$, $NO
\left(b^4\Sigma^{-}\right)$, $ICl\left(X^1\Sigma_g^{+}\right)$,
$ICl\left(A^3\Pi_1\right)$ and $ICl\left(A'^3\Pi_2\right)$ for arbitrary values
of $n$ and $\ell$ quantum numbers are obtained. For the sake of completeness,
we study the corresponding wavefunctions using the formula method.


  Deep Linear and Nonlinear learning methods have already been vital machine
learning methods for investigating the hierarchical features such as functional
connectivity in the human brain via functional Magnetic Resonance signals;
however, there are three major shortcomings: 1). For deep linear learning
methods, although the identified hierarchy of functional connectivity is easily
explainable, it is challenging to reveal more hierarchical functional
connectivity; 2). For deep nonlinear learning methods, although non-fully
connected architecture reduces the complexity of neural network structures that
are easy to optimize and not vulnerable to overfitting, the functional
connectivity hierarchy is difficult to explain; 3). Importantly, it is
challenging for Deep Linear/Nonlinear methods to detect meta and sub-functional
connectivity even in the shallow layers; 4). Like most conventional Deep
Nonlinear Methods, such as Deep Neural Networks, the hyperparameters must be
tuned manually, which is time-consuming. Thus, in this work, we propose a novel
deep hybrid learning method named SEmi-Nonlinear Deep Efficient Reconstruction
(SENDER), to overcome the aforementioned shortcomings: 1). SENDER utilizes a
multiple-layer stacked structure for the linear learning methods to detect the
canonical functional connectivity; 2). SENDER implements a non-fully connected
architecture conducted for the nonlinear learning methods to reveal the
meta-functional connectivity through shallow and deeper layers; 3). SENDER
incorporates the proposed background components to extract the sub-functional
connectivity; 4). SENDER adopts a novel rank reduction operator to implement
the hyperparameters tuning automatically. To further validate the
effectiveness, we compared SENDER with four peer methodologies using real
functional Magnetic Resonance Imaging data for the human brain.


  In recent years, several hacking attacks have broken the security of quantum
cryptography implementations by exploiting the presence of losses and the
ability of the eavesdropper to tune detection efficiencies. We present a simple
attack of this form that applies to any protocol in which the key is
constructed from the results of untrusted measurements performed on particles
coming from an insecure source or channel. Because of its generality, the
attack applies to a large class of protocols, from standard prepare-and-measure
to device-independent schemes. Our attack gives bounds on the critical
detection efficiencies necessary for secure quantum distribution, which show
that the implementation of most partly device independent solutions is, from
the point of view of detection efficiency, almost as demanding as fully
device-independent ones. We also show how our attack implies the existence of a
form of bound randomness, namely non-local correlations in which a
non-signalling eavesdropper can find out a posteriori the result of any
implemented measurement.


  Learning robust audio representations currently demands extensive datasets of
real-world sound recordings. By applying artificial transformations to these
recordings, models can learn to recognize similarities despite subtle
variations through techniques like contrastive learning. However, these
transformations are only approximations of the true diversity found in
real-world sounds, which are generated by complex interactions of physical
processes, from vocal cord vibrations to the resonance of musical instruments.
We propose a solution to both the data scale and transformation limitations,
leveraging synthetic audio. By randomly perturbing the parameters of a sound
synthesizer, we generate audio doppelg\"angers-synthetic positive pairs with
causally manipulated variations in timbre, pitch, and temporal envelopes. These
variations, difficult to achieve through transformations of existing audio,
provide a rich source of contrastive information. Despite the shift to randomly
generated synthetic data, our method produces strong representations,
competitive with real data on standard audio classification benchmarks.
Notably, our approach is lightweight, requires no data storage, and has only a
single hyperparameter, which we extensively analyze. We offer this method as a
complement to existing strategies for contrastive learning in audio, using
synthesized sounds to reduce the data burden on practitioners.


  We study the stochastic gravitational waves from string gas cosmology. With
the help of the Lambert W function, we derive the exact energy density spectrum
of the stochastic gravitational waves in term of tensor-to-scalar. New feathers
with the spectrum are found. First, the non-Hagedorn phase can be ruled out by
the current B-mode polarization in the cosmic microwave background. Second, the
exact spectrum from the Hagedorn phase with a logarithmic term is shown to be
unique in the measurable frequency range. Third, which is the most important,
we find the string length can be constrained to be lower than 7 $\sim$ orders
of that Planck scale.


  We investigated the reliability and applicability of so-called magnetic force
linear response method to calculate spin-spin interaction strengths from
first-principles. We examined the dependence on the numerical parameters
including the number of basis orbitals and their cutoff radii within
non-orthogonal LCPAO (linear combination of pseudo-atomic orbitals) formalism.
It is shown that the parameter dependence and the ambiguity caused by these
choices are small enough in comparison to the other computation approach and
experiments. Further, we tried to pursue the possible extension of this
technique to a wider range of applications. We showed that magnetic force
theorem can provide the reasonable estimation especially for the case of
strongly localized moments even when the ground state configuration is unknown
or the total energy value is not accessible. The formalism is extended to carry
the orbital resolution from which the matrix form of the magnetic coupling
constant is calculated. From the applications to Fe-based superconductors
including LaFeAsO, NaFeAs, BaFe$_2$As$_2$ and FeTe, the distinctive
characteristics of orbital-resolved interactions are clearly noticed in between
single-stripe pnictides and double-stripe chalcogenides.


  Modern deep learning models are over-parameterized, where different optima
can result in widely varying generalization performance. The Sharpness-Aware
Minimization (SAM) technique modifies the fundamental loss function that steers
gradient descent methods toward flatter minima, which are believed to exhibit
enhanced generalization prowess. Our study delves into a specific variant of
SAM known as micro-batch SAM (mSAM). This variation involves aggregating
updates derived from adversarial perturbations across multiple shards
(micro-batches) of a mini-batch during training. We extend a recently developed
and well-studied general framework for flatness analysis to theoretically show
that SAM achieves flatter minima than SGD, and mSAM achieves even flatter
minima than SAM. We provide a thorough empirical evaluation of various image
classification and natural language processing tasks to substantiate this
theoretical advancement. We also show that contrary to previous work, mSAM can
be implemented in a flexible and parallelizable manner without significantly
increasing computational costs. Our implementation of mSAM yields superior
generalization performance across a wide range of tasks compared to SAM,
further supporting our theoretical framework.


  The impact of nonrenormalizable gluon operators upon inclusive jet cross
sections is studied. Such operators could arise in an effective strong
interaction Lagrangian from gluon substructure and would induce observable
cross section deviations from pure QCD at high transverse jet energies.
Comparison of the theoretical predictions with recent CDF data yields a lower
limit on the gluon compositeness scale $\Lambda$. We find $\Lambda > 2.03 \TeV$
at $95\%$~CL.


  We discuss the Bloch-Messiah decomposition for the broadband squeezed light
generated by type-I parametric down-conversion with monochromatic pump. Using
an exact solution for this process, we evaluate the squeezing parameters and
the corresponding squeezing eigenmodes. Next, we consider the Magnus expansion
of the quantum-mechanical evolution operator for this process and obtain its
first three approximation orders. Using these approximated solutions, we
evaluate the corresponding approximations for the Bloch-Messiah decomposition.
Our results allow us to conclude that the first-order approximation of the
Magnus expansion is sufficient for description of the broadband squeezed light
for squeezing values below 12.5 dB. For higher degrees of squeezing we show
fast convergence of the Magnus series providing a good approximation for the
exact solution already in the third order. We propose a quantitative criterion
for this ultra-high-gain regime of parametric down-conversion when the
higher-orders terms of the Magnus expansion, known in the literature as the
operator-ordering effects, become necessary.


  Solving Quadratic equation is one of the intrinsic interests as it is the
simplest nonlinear equations. A novel approach for solving Quadratic Equation
based on Genetic Algorithms (GAs) is presented. Genetic Algorithms (GAs) are a
technique to solve problems which need optimization. Generation of trial
solutions have been formed by this method. Many examples have been worked out,
and in most cases we find out the exact solution. We have discussed the effect
of different parameters on the performance of the developed algorithm. The
results are concluded after rigorous testing on different equations.


  In the paper it is discussed the relations of the Riemann $\zeta-$function to
classes of generating functions of multiply positive sequences according to
Schoenberg (also called P\'olya frequency sequences).
  Key words: multiply positive sequences, totally positive sequences, P\'olya
frequency sequences, Laguerre-P\'olya class, Riemann $\zeta-$function.


  Using a new technique to improve the sensitivity to weak Quasi-Periodic
Oscillations (QPO) we discovered a new QPO peak at about 1100 Hz in the March
1996 outburst observations of 4U 1608-52, simultaneous with the ~ 600-900 Hz
peak previously reported from these data. The frequency separation between the
upper and the lower QPO peak varied significantly from $232.7 \pm 11.5$ Hz on
March 3, to $293.1 \pm 6.6$ Hz on March 6. This is the first case of a variable
kHz peak separation in an atoll source. We discuss to what extent this result
could be accommodated in beat-frequency models such as proposed for the kHz
QPOs. We measured the rms fractional amplitude of both QPOs as a function of
energy, and we found that the relation is steeper for the lower than for the
upper frequency peak. This is the first source where such difference between
the energy spectrum of the two kHz QPOs could be measured.


  The abelian Higgs model is the textbook example for the superconducting
transition and the Anderson-Higgs mechanism, and has become pivotal in the
description of deconfined quantum criticality. We study the abelian Higgs model
with $n$ complex scalar fields at unprecedented four-loop order in the
$4-\epsilon$ expansion and find that the annihilation of the critical and
bicritical points occurs at a critical number of $n_c \approx 182.95\left(1 -
1.752\epsilon + 0.798 \epsilon^2 + 0.362\epsilon^3\right) +
\mathcal{O}\left(\epsilon^4\right)\nonumber$. Consequently, below $n_c$, the
transition turns from second to first order. Resummation of the series to
extract the result in three-dimensions provides strong evidence for a critical
$n_c(d=3)$ which is significantly below the leading-order value, but the
estimates for $n_c$ are widely spread. Conjecturing the topology of the
renormalization group flow between two and four dimensions, we obtain a smooth
interpolation function for $n_c(d)$ and find $n_c(3)\approx 12.2\pm 3.9$ as our
best estimate in three dimensions. Finally, we discuss Miransky scaling
occurring below $n_c$ and comment on implications for weakly first-order
behavior of deconfined quantum transitions. We predict an emergent hierarchy of
length scales between deconfined quantum transitions corresponding to different
$n$.


  Let $E$ be the Whitney sum of complex line bundles over a topological space
$X$. Then, the projectivization $P(E)$ of $E$ is called a \emph{projective
bundle} over $X$. If $X$ is a non-singular complete toric variety, so is
$P(E)$. In this paper, we show that the cohomology ring of a non-singular
projective toric variety $M$ determines whether it admits a projective bundle
structure over a non-singular complete toric surface. In addition, we show that
two 6-dimensional projective bundles over 4-dimensional quasitoric manifolds
are diffeomorphic if their cohomology rings are isomorphic as graded rings.
Furthermore, we study the smooth classification of higher dimensional
projective bundles over 4-dimensional quasitoric manifolds.


  This paper considers the massive connectivity problem in an asynchronous
grant-free random access system, where a huge number of devices sporadically
transmit data to a base station (BS) with imperfect synchronization. The goal
is to design algorithms for joint user activity detection, delay detection, and
channel estimation. By exploiting the sparsity on both user activity and
delays, we formulate a hierarchical sparse signal recovery problem in both the
single-antenna and the multiple-antenna scenarios. While traditional compressed
sensing algorithms can be applied to these problems, they suffer high
computational complexity and often require the perfect statistical information
of channel and devices. This paper solves these problems by designing the
Learned Approximate Message Passing (LAMP) network, which belongs to
model-driven deep learning approaches and ensures efficient performance without
tremendous training data. Particularly, in the multiple-antenna scenario, we
design three different LAMP structures, namely, distributed, centralized and
hybrid ones, to balance the performance and complexity. Simulation results
demonstrate that the proposed LAMP networks can significantly outperform the
conventional AMP method thanks to their ability of parameter learning. It is
also shown that LAMP has robust performance to the maximal delay spread of the
asynchronous users.


  Context. The discovery and tracking of 2018 LA marks only the third instance
in history that the parent body of a fireball has been identified before its
eventual disintegration in our atmosphere. The subsequent recovery of
meteorites from 2018 LA was only the second time materials from outer space
that reached the ground could be linked with certitude to a particular minor
body. However, meteoroids like 2018 LA and its forerunners, 2008 TC3 and 2014
AA, are perhaps fragments of larger members of the near-Earth object (NEO)
population. As the processes leading to the production of such fragments are
unlikely to spawn just one meteoroid per event, it is important to identify
putative siblings and plausible candidates from which the observed meteoroids
might have originated.
  Aims. Here, we study the pre-impact orbital evolution of 2018 LA to place
this meteoroid within the dynamical context of other NEOs that follow similar
trajectories.
  Methods. Our statistical analyses are based on the results of direct N-body
calculations that use the latest orbit determinations and include perturbations
by the eight major planets, the Moon, the barycentre of the Pluto-Charon
system, and the three largest asteroids. A state-of-the-art NEO orbit model was
used to interpret our findings and a randomization test was applied to estimate
their statistical significance.
  Results. We find a statistically significant excess of NEOs in 2018 LA-like
orbits; among these objects, we find one impactor, 2018 LA, and the fourth
closest known passer-by, 2018 UA. A possible connection with the Chi-Scorpiids
meteor shower is also discussed. The largest known NEO with an orbit similar to
that of 2018 LA is the potentially hazardous asteroid (454100) 2013 BO73 and we
speculate that they both originate from a common precursor via a collisional
cascade.


  Using the fermion-spin transformation to implement spin-charge separation of
constrained electrons, a model of two $t-J$ chains with interchain
single-electron hopping is studied by abelian bosonization. After spin-charge
decoupling the charge dynamics can be trivially solved, while the spin dynamics
is determined by a strong-coupling fixed point where the correlation functions
can be calculated explicitly. This is a generalization of the Luther-Emery line
for two-coupled $t-J$ chains. The interchain single-electron hopping changes
the asymptotic behavior of the interchain spin-spin correlation functions and
the electron Green function, but their exponents are independent of the
coupling strength.


  We study the (trace) norm of a linearly invariant family in the ball in $\C$.
By adapting an approach that in one variable yields optimal results, we are
able to derive an upper bound for the norm of the family in terms of the
Schwarzian norm and the dimension $n$.


  To describe a massive particle with fixed, but arbitrary, spin on $d=4$
anti-de Sitter space $M^4$, we propose the point-particle model with
configuration space ${\cal M}^6 = M^{4}\times S^{2}$, where the sphere $S^2$
corresponds to the spin degrees of freedom. The model possesses two gauge
symmetries expressing strong conservation of the phase-space counterparts of
the second- and fourth-order Casimir operators for $so(3,2)$. We prove that the
requirement of energy to have a global positive minimum $E_o$ over the
configuration space is equivalent to the relation $E_o > s$, $s$ being the
particle's spin, what presents the classical counterpart of the quantum massive
condition. States with the minimal energy are studied in detail. The model is
shown to be exactly solvable. It can be straightforwardly generalized to
describe a spinning particle on $d$-dimensional anti-de Sitter space $M^d$,
with ${\cal M}^{2(d-1)} = M^d \times S^{(d-2)}$ the corresponding configuration
space.


  This paper develops asymptotic approximations of $P(\int_Te^{f(t)}\,dt>b)$ as
$b\rightarrow\infty$ for a homogeneous smooth Gaussian random field, $f$,
living on a compact $d$-dimensional Jordan measurable set $T$. The integral of
an exponent of a Gaussian random field is an important random variable for many
generic models in spatial point processes, portfolio risk analysis, asset
pricing and so forth. The analysis technique consists of two steps: 1. evaluate
the tail probability $P(\int_{\Xi}e^{f(t)}\,dt>b)$ over a small domain $\Xi$
depending on $b$, where $\operatorname {mes}(\Xi)\rightarrow0$ as $b\rightarrow
\infty$ and $\operatorname {mes}(\cdot)$ is the Lebesgue measure; 2. with $\Xi$
appropriately chosen, we show that
$P(\int_Te^{f(t)}\,dt>b)=(1+o(1))\operatorname{mes}(T)\times
\operatorname{mes}^{-1}(\Xi)P(\int_{\Xi}e^{f(t)}\,dt>b)$.


  Motivated by a synchronization problem in distributed computing we studied a
simple growth model on regular and small-world networks, embedded in one and
two-dimensions. We find that the synchronization landscape (corresponding to
the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like
kinetic roughening on regular networks with short-range communication links.
Although the processors, on average, progress at a nonzero rate, their spread
(the width of the synchronization landscape) diverges with the number of nodes
(desynchronized state) hindering efficient data management. When random
communication links are added on top of the one and two-dimensional regular
networks (resulting in a small-world network), large fluctuations in the
synchronization landscape are suppressed and the width approaches a finite
value in the large system-size limit (synchronized state). In the resulting
synchronization scheme, the processors make close-to-uniform progress with a
nonzero rate without global intervention. We obtain our results by ``simulating
the simulations", based on the exact algorithmic rules, supported by
coarse-grained arguments.


  We discuss the correlation between the evolution of the TeV emission and
X-ray radiation observed in high-energy peaked BL Lac objects. We describe such
a correlation by a simple power law. In the first part of this work we present
correlations obtained for the activity of Mrk~501 observed in 1997 April and
for the activity of Mrk~421 observed in 2000 February. We also discuss results
of similar correlation obtained for this source by other authors. They report
an almost quadratic correlations observed between the evolution of the TeV and
X-ray emission. In the second part of this paper we present a phenomenological
model which describes the evolution of the synchrotron and inverse Compton
emission of a simple spherical homogeneous source. Neglecting the radiative
cooling of the particles we derive analytical expressions that describe the
evolution. Then we use a numerical code to investigate the impact of radiative
cooling on the evolution. The quadratic correlation observed during the decay
phase of the flare observed in Mrk~421 on 2001 March 19 appears problematic for
this basic modeling. The quadratic correlation can be explained only for
specific choices of the spectral bands used for the calculation. Therefore,
looking for more robust solutions, we investigate the evolution of the emission
generated by a cylindrical source. However this model does not provide robust
solutions for the problem of a quadratic correlation. factor. Finally we
briefly discuss the possible influence of the light travel time effect on our
results.


  The interplay between various many body effects in a quantum dot attached to
two normal and one superconducting lead is considered in the limit of large
superconducting gap. By the proximity effect the superconducting lead induces
pairing correlations on the quantum dot. In the subgap region one observes the
anomalous tunneling via direct and crossed Andreev scattering, whereas the
usual single particle electronic transfer is suppressed. The interactions of
electrons on the dot leading to such phenomena as the Coulomb blockade and the
Kondo effect severely modify the currents flowing in the system. In particular:
(i) they prevent the existence of the negative differential conductance
observed for non-interacting quantum dot over the whole range of voltages, (ii)
affect the distribution of the currents as function of the applied voltage and
(iii) lead to the appearance of additional low bias feature due to the
formation of the Abrikosov-Suhl resonance. The non-local correlations in the
Coulomb blockade regime are most pronounced for the particle-hole symmetric dot
and thus can be easily tuned by means of gate voltage. They are observed even
in the Kondo regime and dominate the behavior close to the Abrikosov-Suhl
resonance showing convincingly that Kondo correlations do not destroy subtle
entanglement between electrons.


  We present a Satisfiability (SAT)-based approach for building Mixed Covering
Arrays with Constraints of minimum length, referred to as the Covering Array
Number problem. This problem is central in Combinatorial Testing for the
detection of system failures. In particular, we show how to apply Maximum
Satisfiability (MaxSAT) technology by describing efficient encodings for
different classes of complete and incomplete MaxSAT solvers to compute optimal
and suboptimal solutions, respectively. Similarly, we show how to solve through
MaxSAT technology a closely related problem, the Tuple Number problem, which we
extend to incorporate constraints. For this problem, we additionally provide a
new MaxSAT-based incomplete algorithm. The extensive experimental evaluation we
carry out on the available Mixed Covering Arrays with Constraints benchmarks
and the comparison with state-of-the-art tools confirm the good performance of
our approaches.


  We consider the problem of approximating an unknown function in a nonlinear
model class from point evaluations. When obtaining these point evaluations is
costly, minimising the required sample size becomes crucial. Recently, an
increasing focus has been on employing adaptive sampling strategies to achieve
this. These strategies are based on linear spaces related to the nonlinear
model class, for which the optimal sampling measures are known. However, the
resulting optimal sampling measures depend on an orthonormal basis of the
linear space, which is known rarely. Consequently, sampling from these measures
is challenging in practice. This manuscript presents a sampling strategy that
iteratively refines an estimate of the optimal sampling measure by updating it
based on previously drawn samples. This strategy can be performed offline and
does not require evaluations of the sought function. We establish convergence
and illustrate the practical performance through numerical experiments.
Comparing the presented approach with standard Monte Carlo sampling
demonstrates a significant reduction in the number of samples required to
achieve a good estimation of an orthonormal basis.


  In this letter we show for the first time that the usual CPT-even gauge term
of the standard model extension (SME) can be radiatively generated, in a gauge
invariant level, in the context of a modified QED endowed with a dimension-five
nonminimal coupling term recently proposed in the literature. As a consequence,
the existing upper bounds on the coefficients of the tensor $(K_{F}) $ can be
used improve the bounds on the magnitude of the nonminimal coupling,
$\lambda(K_{F}),$ by the factors $10^{5}$ or $10^{25}.$ The nonminimal coupling
also generates higher-order derivative contributions to the gauge field
effective action quadratic terms.


  Bell inequalities are one of the cornerstones of quantum foundations, and
fundamental tools for quantum technologies. Recently, the scientific community
worldwide has put a lot of effort towards them, which culminated with
loophole-free experiments. Nonetheless, none of the experimental tests so far
was able to extract information on the full inequality from each entangled
pair, since the wave function collapse forbids performing, on the same quantum
state, all the measurements needed for evaluating the entire Bell parameter. We
present here the first single-pair Bell inequality test, able to obtain a Bell
parameter value for every entangled pair detected. This is made possible by
exploiting sequential weak measurements, allowing to measure non-commuting
observables in sequence on the same state, on each entangled particle. Such an
approach not only grants unprecedented measurement capability, but also removes
the need to choose between different measurement bases, intrinsically
eliminating the freedom-of-choice loophole and stretching the concept of
counterfactual-definiteness (since it allows measuring in the otherwise
not-chosen bases). We also demonstrate how, after the Bell parameter
measurement, the pair under test still presents a noteworthy amount of
entanglement, providing evidence of the absence of (complete) wave function
collapse and allowing to exploit this quantum resource for further protocols.


  We perform a key step towards the proof of Zvonkine's conjectural $r$-ELSV
formula that relates Hurwitz numbers with completed $(r+1)$-cycles to the
geometry of the moduli spaces of the $r$-spin structures on curves: we prove
the quasi-polynomiality property prescribed by Zvonkine's conjecture. Moreover,
we propose an orbifold generalization of Zvonkine's conjecture and prove the
quasi-polynomiality property in this case as well. In addition to that, we
study the $(0,1)$- and $(0,2)$-functions in this generalized case and we show
that these unstable cases are correctly reproduced by the spectral curve
initial data.


  This paper presents the verified methodology for wireless authentication
system using infrared barcode based scanner. An alternate approach of scanning
a barcode using an infrared communication is implemented here, comprises of a
card on which a barcode is printed is illuminated with an infrared beam. The
reflections from the card are received by an infrared receiver and transmit
them to a remote machine over wireless channel where the retrieve information
is further processed and converted into the corresponding barcode digits which
are further matched against the database stored in the server and the
authenticity of the user is established. The system developed is
cost-effective, efficient, provide double security and robust.


  We study the lensing magnification effect on background galaxies.
Differential magnification due to different magnifications of different source
regions of a galaxy will change the lensed composite spectra. The derived
properties of the background galaxies are therefore biased. For simplicity, we
model galaxies as a superposition of an axis-symmetric bulge and a face-on disk
in order to study the differential magnification effect on the composite
spectra. We find that some properties derived from the spectra (e.g., velocity
dispersion, star formation rate and metallicity) are modified. Depending on the
relative positions of the source and the lens, the inferred results can be
either over- or under-estimates of the true values. In general, for an extended
source at strong lensing regions with high magnifications, the inferred
physical parameters (e.g. metallicity) can be strongly biased. Therefore
detailed lens modelling is necessary to obtain the true properties of the
lensed galaxies.


  Recent relativistic coupled-cluster (RCC) calculations of electric dipole
moments (EDMs) of diamagnetic atoms due to parity and time-reversal violating
(P,T-odd) interactions, that are essential ingredients for probing new physics
beyond the standard model of particle interactions, differ substantially from
the previous theoretical results. It is therefore necessary to perform an
independent test of the validity of these results. In view of this, the normal
coupled-cluster (NCC) method has been extended to the relativistic regime to
calculate the EDMs of atoms by simultaneously incorporating the electrostatic
and P,T-odd interactions in order to overcome the shortcomings of the ordinary
RCC method. This new relativistic method has been applied to $^{199}$Hg, which
currently has a lower EDM limit than that of any other system. The results of
our relativistic NCC and self-consistent RCC calculations of the EDM of this
atom are found to be close. The discrepancies between these two results on the
one hand and those of previous calculations on the other are elucidated.
Furthermore, the electric dipole polarizability of this atom, which has
computational similarities with the EDM, is evaluated and it is in very good
agreement with its measured value.


  We show a surprising link between experimental setups to realize
high-dimensional multipartite quantum states and Graph Theory. In these setups,
the paths of photons are identified such that the photon-source information is
never created. We find that each of these setups corresponds to an undirected
graph, and every undirected graph corresponds to an experimental setup. Every
term in the emerging quantum superposition corresponds to a perfect matching in
the graph. Calculating the final quantum state is in the complexity class
#P-complete, thus cannot be done efficiently. To strengthen the link further,
theorems from Graph Theory -- such as Hall's marriage problem -- are rephrased
in the language of pair creation in quantum experiments. We show explicitly how
this link allows to answer questions about quantum experiments (such as which
classes of entangled states can be created) with graph theoretical methods, and
potentially simulate properties of Graphs and Networks with quantum experiments
(such as critical exponents and phase transitions).


  Truly polymorphic circuits, whose functionality/circuit behavior can be
altered using a control variable, can provide tremendous benefits in
multi-functional system design and resource sharing. For secure and fault
tolerant hardware designs these can be crucial as well. Polymorphic circuits
work in literature so far either rely on environmental parameters such as
temperature, variation etc. or on special devices such as ambipolar FET,
configurable magnetic devices, etc., that often result in inefficiencies in
performance and/or realization. In this paper, we introduce a novel polymorphic
circuit design approach where deterministic interference between nano-metal
lines is leveraged for logic computing and configuration. For computing, the
proposed approach relies on nano-metal lines, their interference and commonly
used FETs, and for polymorphism, it requires only an extra metal line that
carries the control signal. In this paper, we show a wide range of crosstalk
polymorphic (CT-P) logic gates and their evaluation results. We also show an
example of a large circuit that performs both the functionalities of multiplier
and sorter depending on the configuration signal. Our benchmarking results are
presented in this paper. For CT-P, the transistor count was found to be
significantly less compared to other existing approaches, ranging from 25% to
83%. For example, CT-P AOI21-OA21 cell show 83%, 85% and 50% transistor count
reduction, and MultiplierSorter circuit show 40%, 36% and 28% transistor count
reduction with respect to CMOS, genetically evolved, and ambipolar transistor
based polymorphic circuits respectively.


  Consistency models possess high capabilities for image generation, advancing
sampling steps to a single step through their advanced techniques. Current
advancements move one step forward consistency training techniques and
eliminates the limitation of distillation training. Even though the proposed
curriculum and noise scheduling in improved training techniques yield better
results than basic consistency models, it lacks well balanced noise
distribution and its consistency between curriculum. In this study, it is
investigated the balance between high and low noise levels in noise
distribution and offered polynomial noise distribution to maintain the
stability. This proposed polynomial noise distribution is also supported with a
predefined Karras noises to prevent unique noise levels arises with Karras
noise generation algorithm. Furthermore, by elimination of learned noisy steps
with a curriculum based on sinusoidal function increase the performance of the
model in denoising. To make a fair comparison with the latest released
consistency model training techniques, experiments are conducted with same
hyper-parameters except curriculum and noise distribution. The models utilized
during experiments are determined with low depth to prove the robustness of our
proposed technique. The results show that the polynomial noise distribution
outperforms the model trained with log-normal noise distribution, yielding a
33.54 FID score after 100,000 training steps with constant discretization
steps. Additionally, the implementation of a sinusoidal-based curriculum
enhances denoising performance, resulting in a FID score of 30.48.


  This paper describes and analyzes our participation in the 2023 Eval4NLP
shared task, which focuses on assessing the effectiveness of prompt-based
techniques to empower Large Language Models to handle the task of quality
estimation, particularly in the context of evaluating machine translations and
summaries. We conducted systematic experiments with various prompting
techniques, including standard prompting, prompts informed by annotator
instructions, and innovative chain-of-thought prompting. In addition, we
integrated these approaches with zero-shot and one-shot learning methods to
maximize the efficacy of our evaluation procedures. Our work reveals that
combining these approaches using a "small", open source model (orca_mini_v3_7B)
yields competitive results.


  We consider online learning of ensembles of portfolio selection algorithms
and aim to regularize risk by encouraging diversification with respect to a
predefined risk-driven grouping of stocks. Our procedure uses online convex
optimization to control capital allocation to underlying investment algorithms
while encouraging non-sparsity over the given grouping. We prove a logarithmic
regret for this procedure with respect to the best-in-hindsight ensemble. We
applied the procedure with known mean-reversion portfolio selection algorithms
using the standard GICS industry sector grouping. Empirical Experimental
results showed an impressive percentage increase of risk-adjusted return
(Sharpe ratio).


  We report on a very accurate measurement of the static quark potential in
SU(2) Yang-Mills theory in (2+1) dimensions in order to study the corrections
to the linear behaviour. We perform numerical simulations at zero and finite
temperature comparing our results with the corrections given by the effective
string picture in these two regimes. We also check for universal features
discussing our results together with those recently published for the (2+1)-d
Z(2) and SU(3) pure gauge theories.


  A uniform, flexible and frictionless chain falling link by link from a heap
by the edge of a table falls with an acceleration $g/3$ if the motion is
nonconservative, but $g/2$ if the motion is conservative, $g$ being the
acceleration due to gravity. Unable to construct such a falling chain, we use
instead higher-dimensional versions of it. A home camcorder is used to measure
the fall of a three-dimensional version called an $xyz$-slider. After
frictional effects are corrected for, its vertical falling acceleration is
found to be $a_x/g = 0.328 \pm 0.004$. This result agrees with the theoretical
value of $a_x/g = 1/3$ for an ideal energy-conserving $xyz$-slider.


  The high-precision Juno gravitational measurements allow us to infer the
structure of Jupiter's deep atmospheric zonal flow. Since this inference is
nonunique, it is important to explore the space of possible solutions. In this
paper, we consider a model in which Jupiter's deep atmospheric zonal flow is
barotropic, or invariant along the direction of the rotation axis, until it is
truncated at depth by some dynamical process (e.g., Reynolds stress, Lorentz or
viscous force). We calculate the density perturbation produced by the
$z$-invariant part of the flow using the thermal wind equation and compare the
associated odd zonal gravitational harmonics ($J_{3}$, $J_{5}$, $J_{7}$,
$J_{9}$) to the Juno-derived values. Most of the antisymmetric gravitational
signal measured by Juno can be explained by extending observed winds between
$20.9^{\circ}\rm{S}-26.4^{\circ}\rm{N}$ to depths of $\sim 1000$ km. Because
the small-scale features of the mid/high latitude zonal flow may not persist to
depth, we allow the zonal flow in this region to differ from the observed
surface winds. We find that the Juno odd zonal gravitational harmonics can be
fully explained by $\sim 1000$ km deep barotropic zonal flows involving the
observed winds between $20.9^{\circ}\rm{S}-26.4^{\circ}$N and a few broad
mid/high latitude jets.


  We deform the heat kernel and the Brownian motion on $\mathbb{R}^{N}$ from
the perspective of "$(k,a)$-generalized Fourier analysis" with $k=0$. This is a
new type of harmonic analysis proposed by S.Ben
Sa\"id--T.Kobayashi--B.{\O}rsted from the representation theoretic viewpoint.
In this paper, we construct the $a$-deformed heat kernel and $a$-deformed
Brownian motion, and explore their some basic properties. We also prove that
the $(k,a)$-generalized Fourier integral kernels are polynomial growth when
$k=0$, for a justification of some discussions.


  We use the most recent data release (DR9) of the DESI legacy imaging survey
and SDSS galaxy groups to measure the conditional luminosity function (CLF) for
groups with halo mass $M_{\rm h}\ge 10^{12}M_{\odot}$ and redshift $0.01\le
z\le 0.08$, down to a limiting $r$-band magnitude of $M_{\rm r}=-10\sim-12$.
For a given halo mass we measure the CLF for the total satellite population, as
well as separately for the red and blue populations classified using the
$(g-z)$ color. We find a clear faint-end upturn in the CLF of red satellites,
with a slope $\alpha\approx-1.8$ which is almost independent of halo mass. This
faint-end upturn is not seen for blue satellites and for the total population.
Our stellar population synthesis modeling shows that the $(g-z)$ color provides
a clean red/blue division, and that group galaxies in the red population
defined by $(g-z)$ are all dominated by old stellar populations. The fraction
of old galaxies as a function of galaxy luminosity shows a minimum at a
luminosity $M_{\rm r}\sim-18$, corresponding to a stellar mass
$M_\ast\sim10^{9.5}M_\odot$. This mass scale is independent of halo mass and is
comparable to the characteristic luminosity at which galaxies show a dichotomy
in surface brightness and size, suggesting that the dichotomy in the old
fraction and in galaxy structure may have a common origin. The rising of the
old fraction at the faint end for Milky Way (MW)-sized halos found here is in
good agreement with the quenched fraction measured both for the MW/M31 system
and from the ELVES survey. We discuss the implications of our results for the
formation and evolution of low-mass galaxies, and for the stellar mass
functions of low-mass galaxies to be observed at high redshift.


  In the limit of infinite yield time for stresses, the hydrodynamic equations
for viscoelastic, Non-Newtonian liquids such as polymer melts must reduce to
that for solids. This piece of information suffices to uniquely determine the
nonlinear convective derivative, an ongoing point of contention in the rheology
literature.


  Knowledge transfer is shown to be a very successful technique for training
neural classifiers: together with the ground truth data, it uses the
"privileged information" (PI) obtained by a "teacher" network to train a
"student" network. It has been observed that classifiers learn much faster and
more reliably via knowledge transfer. However, there has been little or no
theoretical analysis of this phenomenon. To bridge this gap, we propose to
approach the problem of knowledge transfer by regularizing the fit between the
teacher and the student with PI provided by the teacher. Using tools from
dynamical systems theory, we show that when the student is an extremely wide
two layer network, we can analyze it in the kernel regime and show that it is
able to interpolate between PI and the given data. This characterization sheds
new light on the relation between the training error and capacity of the
student relative to the teacher. Another contribution of the paper is a
quantitative statement on the convergence of student network. We prove that the
teacher reduces the number of required iterations for a student to learn, and
consequently improves the generalization power of the student. We give
corresponding experimental analysis that validates the theoretical results and
yield additional insights.


  We study isogeny relations between K3 surfaces and Kummer surfaces.
Specifically, we prove a Torelli-type theorem for the existence of rational
maps from K3 surfaces to Kummer surfaces, and a Kummer sandwich theorem for K3
surfaces with Shioda-Inose structure.


  We use local mirror symmetry in type IIA string compactifications on
Calabi-Yau n+1 folds $X_{n+1}$ to construct vector bundles on (possibly
singular) elliptically fibered Calabi-Yau n-folds Z_n. The interpretation of
these data as valid classical solutions of the heterotic string compactified on
Z_n proves F-theory/heterotic duality at the classical level. Toric geometry is
used to establish a systematic dictionary that assigns to each given toric
n+1-fold $X_{n+1}$ a toric n fold Z_n together with a specific family of sheafs
on it. This allows for a systematic construction of phenomenologically
interesting d=4 N=1 heterotic vacua, e.g. on deformations of the tangent
bundle, with grand unified and SU(3)\times SU(2) gauge groups. As another
application we find non-perturbative gauge enhancements of the heterotic string
on singular Calabi-Yau manifolds and new non-perturbative dualities relating
heterotic compactifications on different manifolds.


  We construct a nonrelativistic wave equation for spinning particles in the
noncommutative space (in a sense, a $\theta$-modification of the Pauli
equation). To this end, we consider the nonrelativistic limit of the
$\theta$-modified Dirac equation. To complete the consideration, we present a
pseudoclassical model (\`a la Berezin-Marinov) for the corresponding
nonrelativistic particle in the noncommutative space. To justify the latter
model, we demonstrate that its quantization leads to the $\theta$-modified
Pauli equation. We extract $\theta$-modified interaction between a
nonrelativistic spin and a magnetic field from such a Pauli equation and
construct a $\theta$-modification of the Heisenberg model for two coupled spins
placed in an external magnetic field. In the framework of such a model, we
calculate the probability transition between two orthogonal EPR
(Einstein-Podolsky-Rosen) states for a pair of spins in an oscillatory magnetic
field and show that some of such transitions, which are forbidden in the
commutative space, are possible due to the space noncommutativity. This allows
us to estimate an upper bound on the noncommutativity parameter.


  We present a systematic analysis of the X-ray spectral properties of a sample
of 22 ``narrow-line'' Seyfert 1 galaxies for which data are available from the
ASCA public archive. Many of these sources, which were selected on the basis of
their relatively narrow H-beta line width (FWHM <= 2000 km/s), show significant
spectral complexity in the X-ray band. Their measured hard power-law continua
have photon indices spanning the range 1.6 - 2.5 with a mean of 2.1, which is
only slightly steeper than the norm for ``broad-line'' Seyfert 1s. All but four
of the sources exhibit a soft excess, which can be modelled as blackbody
emission (T_{bb} ~ 100 - 300 eV) superposed on the underlying power-law. This
soft component is often so strong that, even in the relatively hard bandpass of
ASCA, it contains a significant fraction, if not the bulk, of the X-ray
luminosity, apparently ruling out models in which the soft excess is produced
entirely through reprocessing of the hard continuum.
  Most notably, 6 of the 22 objects show evidence for a broad absorption
feature centred in the energy range 1.1 - 1.4 keV, which could be the signature
of resonance absorption in highly ionized material. A further 3 sources exhibit
``warm absorption'' edges in the 0.7 - 0.9 keV bandpass. Remarkably, all 9
``absorbed'' sources have H-beta line widths below 1000 km/s, which is less
than the median value for the sample taken as a whole. This tendency for very
narrow line widths to correlate with the presence of ionized absorption
features in the soft X-ray spectra of NLS1s, if confirmed in larger samples,
may provide a further clue in the puzzle of active galactic nuclei.


  We propose a method to reliably and efficiently extract the fidelity of
many-qubit quantum circuits composed of continuously parametrized two-qubit
gates called matchgates. This method, which we call matchgate benchmarking,
relies on advanced techniques from randomized benchmarking as well as insights
from the representation theory of matchgate circuits. We argue the formal
correctness and scalability of the protocol, and moreover deploy it to estimate
the performance of matchgate circuits generated by two-qubit XY spin
interactions on a quantum processor.


  Dispersive time-decay estimates are proved for a one-parameter family of
one-dimensional Dirac Hamiltonians with dislocations; these are operators which
interpolate between two phase-shifted massive Dirac Hamiltonians at $x=+\infty$
and $x=-\infty$. This family of Hamiltonians arises in the theory of
topologically protected states of one-dimensional quantum materials. For
certain values of the phase-shift parameter, $\tau$, the Dirac Hamiltonian has
a {\it threshold resonance} at the endpoint of its essential spectrum. Such
resonances are known to influence the time-decay rate. Our main result
explicitly displays the transition in time-decay rate as $\tau$ varies between
resonant and non-resonant values. Our results appear to be the first dispersive
time-decay estimates for Dirac Hamiltonians which are not a relatively compact
perturbation of a free Dirac operator.


  Recently, millimeter-wave (mmWave) 5G localization has been shown to be to
provide centimeter-level accuracy, lending itself to many location-aware
applications, e.g., connected autonomous vehicles (CAVs). One assumption
usually made in the investigation of localization methods is that the user
equipment (UE), i.e., a CAV, and the base station (BS) are {time} synchronized.
In this paper, we remove this assumption and investigate two two-way
localization protocols: (i) a round-trip localization protocol (RLP), whereby
the BS and UE exchange signals in two rounds of transmission and then
localization is achieved using the signal received in the second round; (ii) a
collaborative localization protocol (CLP), whereby localization is achieved
using the signals received in the two rounds. We derive the position and
orientation error bounds applying beamforming at both ends and compare them to
the traditional one-way localization. Our results show that mmWave localization
is mainly limited by the angular rather than the temporal estimation and that
CLP significantly outperforms RLP. Our simulations also show that it is more
beneficial to have more antennas at the BS than at the UE.


  We employ the string/gauge theory correspondence to study properties of
strongly coupled quark-gluon plasmas in thermal gauge theories with a large
number of colors and flavors. In particular, we analyze non-critical string
duals of conformal (S)QCD, as well as ten dimensional wrapped fivebrane duals
of SQCD-like theories. We study general properties of the dual plasmas,
including the drag force exerted on a probe quark and the jet quenching
parameter. We find that these plasma observables depend on the number of colors
and flavors in the ``QCD dual''; in particular, we find that the jet quenching
parameter increases linearly with N_f/N_c at leading order in the probe limit.
In the ten dimensional case we find a non trivial drag coefficient but a
vanishing jet quenching parameter. We comment on the relation of this result
with total screening and argue that the same features are shared by all known
plasmas dual to fivebranes in ten dimensions. We also construct new D5 black
hole solutions with spherical horizon and show that they exhibit the same
features.


  On the basis of integral representations of Poisson and binomial distribution
functions via complete and incomplete Euler \Gamma- and B-functions, we
introduce and discuss continuous counterparts of the Poisson and binomial
distributions. The former turns out to be closely related to classical Volterra
functions as well. Under usual conditions, we also prove that the sequence of
continuous binomial distributions converges weakly to the continuous Poisson
one. At the end, we discuss a relationship between the continuous Poisson
distribution and the \Gamma-process.


  The appearance of quark matter in the centers of compact stars has a number
of astrophysical implications. In this contribution I discuss the structure and
stability of compact stars, gravitational radiation from non-axisymmetric
deformations, and nucleation and dynamics of vortices (flux tubes) in the color
superconducting phases.


  We propose and study various realizations of a Hofstadter-Hubbard model on a
cylinder geometry with fermionic cold atoms in optical lattices. The
cylindrical optical lattice is created by copropagating Laguerre-Gauss beams,
i.e.~light beams carrying orbital angular momentum. By strong focusing of the
light beams we create a real space optical lattice in the form of rings, which
are offset in energy. A second set of Laguerre-Gauss beams then induces a
Raman-hopping between these rings, imprinting phases corresponding to a
synthetic magnetic field (artificial gauge field). In addition, by rotating the
lattice potential, we achieve a slowly varying flux through the hole of the
cylinder, which allows us to probe the Hall response of the system as a
realization of Laughlin's thought experiment. We study how in the presence of
interactions fractional quantum Hall physics could be observed in this setup.


  With the emergence of diverse mobile applications (such as augmented
reality), the quality of experience of mobile users is greatly limited by their
computation capacity and finite battery lifetime. Mobile edge computing (MEC)
and wireless power transfer are promising to address this issue. However, these
two techniques are susceptible to propagation delay and loss. Motivated by the
chance of short-distance line-of-sight achieved by leveraging unmanned aerial
vehicle (UAV) communications, an UAV-enabled wireless powered MEC system is
studied. A power minimization problem is formulated subject to the constraints
on the number of the computation bits and energy harvesting causality. The
problem is non-convex and challenging to tackle. An alternative optimization
algorithm is proposed based on sequential convex optimization. Simulation
results show that our proposed design is superior to other benchmark schemes
and the proposed algorithm is efficient in terms of the convergence.


  In this letter, we present a novel markerless 3D human motion capture (MoCap)
system for unstructured, outdoor environments that uses a team of autonomous
unmanned aerial vehicles (UAVs) with on-board RGB cameras and computation.
Existing methods are limited by calibrated cameras and off-line processing.
Thus, we present the first method (AirPose) to estimate human pose and shape
using images captured by multiple extrinsically uncalibrated flying cameras.
AirPose itself calibrates the cameras relative to the person instead of relying
on any pre-calibration. It uses distributed neural networks running on each UAV
that communicate viewpoint-independent information with each other about the
person (i.e., their 3D shape and articulated pose). The person's shape and pose
are parameterized using the SMPL-X body model, resulting in a compact
representation, that minimizes communication between the UAVs. The network is
trained using synthetic images of realistic virtual environments, and
fine-tuned on a small set of real images. We also introduce an
optimization-based post-processing method (AirPose$^{+}$) for offline
applications that require higher MoCap quality. We make our method's code and
data available for research at
https://github.com/robot-perception-group/AirPose. A video describing the
approach and results is available at https://youtu.be/xLYe1TNHsfs.


  Given $\sigma$ a triangulation of bordered surface with marked points and
punctures $(S, M)$, we associate an ice quiver with potential $(Q_{\sigma},
W_{\sigma}, F)$ and define the corresponding Jacobian algebra
$\Gamma_{\sigma}$. We show that the boundary algebra $B(\sigma)$ of
$\Gamma_{\sigma}$ depends only on the surface $(S, M)$.


  A new polynomial identity is found for Dickson polynomials in characteristic
2. The identity is used to prove that the two polynomials $x^{q+1}+x+1/a$ and
$C(x)+a$ have the same splitting field over $F$, where $F$ is a field of
characteristic 2, $a$ is a nonzero element of $F$, $q=2^n>2$, and $C(x) = x
(\sum_{i=0}^{n-1} x^{2^i-1})^{q+1}$ is a M\"uller--Cohen--Matthews polynomial
of degree $(q^2-q)/2$. In addition, a new proof is obtained for the known
result that $C(x)$ induces a permutation on $F_{2^m}$ if $2m$ and $n$ are
relatively prime.


  We show a break down of the conventional partition of optical states into its
radiative and non-radiative parts. Large divergence of experimental
observations from current theory in the case of emitters interacting with fully
absorbing plasmonic nanoparticles only a few nanometers in dimensions, are now
evident. A model of fluctuation-dissipation demands non-local behavior from
limiting small metal nanoparticles and proximal metal surfaces. We point that
widely used techniques to enhance optical sensing such as
surface-enhanced-Raman-spectroscopy (SERS), may not have been viable but for
this effect. Qualitatively, this quantum effect seems to present itself only
when the classical probability of scattering of an emitted photon by a near-by
absorbing nanostructure approaches zero. Hence, though different in origin and
scale, this has an interesting analogy with quantum effects resulting in
Hawking radiation near a black-hole.


  The huge amount of data acquired by high-throughput sequencing requires data
reduction for effective analysis. Here we give a clustering algorithm for
genome-wide open chromatin data using a new data reduction method. This method
regards the genome as a string of $1$s and $0$s based on a set of peaks and
calculates the Hamming distances between the strings. This algorithm with the
systematically optimized set of peaks enables us to quantitatively evaluate
differences between samples of hematopoietic cells and classify cell types,
potentially leading to a better understanding of leukemia pathogenesis.


  The illumination of the accretion disc in a neutron star X-ray binary by
X-rays emitted from (or close to) the neutron star surface is explored through
general relativistic ray tracing simulations. The applicability of the
canonical suite of relativistically broadened emission line models (developed
for black holes) to discs around neutron stars is evaluated. These models were
found to describe well emission lines from neutron star accretion discs unless
the neutron star radius is larger than the innermost stable orbit of the
accretion disc at 6rg or the disc is viewed at high inclination, above 60deg
where shadowing of the back side of the disc becomes important. Theoretical
emissivity profiles were computed for accretion discs illuminated by hotspots
on the neutron star surfaces, bands of emission and emission by the entirety of
the hot, spherical star surface and in all cases, the emissivity profile of the
accretion disc was found to be well represented by a single power law falling
off slightly steeper than r^-3. Steepening of the emissivity index was found
where the emission is close to the disc plane and the disc can appear truncated
when illuminated by a hotspot at high latitude. The emissivity profile of the
accretion disc in Serpens X-1 was measured and found to be consistent with a
single unbroken power law with index q=3.5 (-0.4,+0.3), suggestive of
illumination by the boundary layer between the disc and neutron star surface.


  In recent years, Deep Learning has become the go-to solution for a broad
range of applications, often outperforming state-of-the-art. However, it is
important, for both theoreticians and practitioners, to gain a deeper
understanding of the difficulties and limitations associated with common
approaches and algorithms. We describe four types of simple problems, for which
the gradient-based algorithms commonly used in deep learning either fail or
suffer from significant difficulties. We illustrate the failures through
practical experiments, and provide theoretical insights explaining their
source, and how they might be remedied.