  We examine the anyon representation of the Laughlin quasi-holes, in
particular the one-dimensional, algebraic aspects of the representation. For
the cases of one and two quasi-holes an explicit mapping to anyon systems is
given, and the connection between the hole-states and coherent states of the
fundamental algebras of observables is examined. The quasi-electron case is
discussed more briefly, and some remaining questions are pointed out.


  Purpose: 3D Time-of-flight (TOF) MR Angiography (MRA) can accurately
visualize the intracranial vasculature, but is limited by long acquisition
times. Compressed sensing (CS) reconstruction can be used to substantially
accelerate acquisitions. The quality of those reconstructions depends on the
undersampling patterns used in the acquisitions. In this work, optimized sets
of undersampling parameters using various acceleration factors for Cartesian 3D
TOF-MRA are established.
  Methods: Fully-sampled datasets acquired at 7T were retrospectively
undersampled using variable-density Poisson-disk sampling with various
autocalibration region sizes, polynomial orders, and acceleration factors. The
accuracy of reconstructions from the different undersampled datasets was
assessed using the vessel-masked structural similarity index. Results were
compared for four imaging volumes, acquired from two different subjects.
Optimized undersampling parameters were validated using additional
prospectively undersampled datasets.
  Results: For all acceleration factors, using a fully-sampled calibration area
of 12x12 k-space lines and a polynomial order of around 2-2.4 resulted in the
highest image quality. The importance of sampling parameter optimization was
found to increase for higher acceleration factors. The results were consistent
across resolutions and regions of interest with vessels of varying sizes and
tortuosity. In prospectively undersampled acquisitions, using optimized
undersampling parameters resulted in a 7.2% increase in the number of visible
small vessels at R = 7.2.
  Conclusion: The image quality of CS TOF-MRA can be improved by appropriate
choice of undersampling parameters. The optimized sets of parameters are
independent of the acceleration factor.


  We show that the dual of every infinite-dimensional Lipschitz-free Banach
space contains an isometric copy of $\ell_\infty$ and that it is often the case
that a Lipschitz-free Banach space contains a $1$-complemented subspace
isometric to $\ell_1$. Even though we do not know whether the latter is true
for every infinite-dimensional Lipschitz-free Banach space, we show that the
space is never rotund.
  Further, in the last section we survey the relations between "isometric
embedding of~$\ell_\infty$ into the dual" and "containing as good copy
of~$\ell_1$ as possible" in a general Banach space.


  In this paper, the authors investigate the case of discrete multiple
orthogonal polynomials with two weights on the step line, which satisfy Pearson
equations. The discrete multiple orthogonal polynomials in question are
expressed in terms of tau functions, which are double Wronskians of generalized
hypergeometric series. The shifts in the spectral parameter for type II and
type I multiple orthogonal polynomials are described using banded matrices. It
is demonstrated that these polynomials offer solutions to multicomponent
integrable extensions of the nonlinear Toda equations. Additionally, the paper
characterizes extensions of the Nijhoff-Capel totally discrete Toda equations.
The hypergeometric $\tau$-functions are shown to provide solutions to these
integrable nonlinear equations. Furthermore, the authors explore Laguerre-Freud
equations, nonlinear equations for the recursion coefficients, with a
particular focus on the multiple Charlier, generalized multiple Charlier,
multiple Meixner II, and generalized multiple Meixner II cases.


  Finding community structures in social networks is considered to be a
challenging task as many of the proposed algorithms are computationally
expensive and does not scale well for large graphs. Most of the community
detection algorithms proposed till date are unsuitable for applications that
would require detection of communities in real-time, especially for massive
networks. The Louvain method, which uses modularity maximization to detect
clusters, is usually considered to be one of the fastest community detection
algorithms even without any provable bound on its running time. We propose a
novel graph traversal-based community detection framework, which not only runs
faster than the Louvain method but also generates clusters of better quality
for most of the benchmark datasets. We show that our algorithms run in O(|V | +
|E|) time to create an initial cover before using modularity maximization to
get the final cover.
  Keywords - community detection; Influenced Neighbor Score; brokers; community
nodes; communities


  Nano-machines circulating inside the human body, collecting data on tissue
conditions, represent a vital part of next-generation medical diagnostic
systems. However, for these devices to operate effectively, they need to relay
not only their medical measurements but also their positions. This paper
introduces a novel localization method for in-body nano-machines based on the
magnetic field, leveraging the advantageous magnetic permeability of all human
tissues. The entire proposed localization system is described, starting from
10x10 ${\mu}m^2$ magnetometers to be integrated into the nano-machines, to a
set of external wires generating the magnetic field. Mathematical equations for
the localization algorithm are also provided, assuming the nano-machines do not
execute the computations themselves, but transmit their magnetic field
measurements together with medical data outside of the body. The whole system
is validated with computer simulations that capture the measurement error of
the magnetometers, the error induced by the Earth magnetic field, and a human
body model assuming different possible positions of nano-machines. The results
show a very high system accuracy with localization errors even below 1 cm.


  Using a theorem of J. Groves we give a ping-pong proof of Osin's uniform
exponential growth for solvable groups. We discuss slow exponential growth and
show that this phenomenon disappears as one passes to a finite index subgroup.


  In this paper, we investigate the problem of multi-domain translation: given
an element $a$ of domain $A$, we would like to generate a corresponding $b$
sample in another domain $B$, and vice versa. Acquiring supervision in multiple
domains can be a tedious task, also we propose to learn this translation from
one domain to another when supervision is available as a pair $(a,b)\sim
A\times B$ and leveraging possible unpaired data when only $a\sim A$ or only
$b\sim B$ is available. We introduce a new unified framework called Latent
Space Mapping (\model) that exploits the manifold assumption in order to learn,
from each domain, a latent space. Unlike existing approaches, we propose to
further regularize each latent space using available domains by learning each
dependency between pairs of domains. We evaluate our approach in three tasks
performing i) synthetic dataset with image translation, ii) real-world task of
semantic segmentation for medical images, and iii) real-world task of facial
landmark detection.


  We present an account of different problems that arise in relation with
cyclicity problems in Dirichlet-type spaces, in particular with polynomials $p$
that minimize the norm $\|pf-1\|$.


  We investigate the dependence of the conductivity and the entanglement
entropy on the space-time dimensionality $d$ in two holographic
superconductors: one dual to a quantum critical point with spontaneous symmetry
breaking, and the other modeled by a charged scalar that condenses at a
sufficiently low temperature in the presence of a Maxwell field. In both cases
the gravity background is asymptotically Anti de Sitter (AdS). In the large $d$
limit we obtain explicit analytical results for the conductivity at zero
temperature and the entanglement entropy by a $1/d$ expansion. We show that the
entanglement entropy is always smaller in the broken phase. As dimensionality
increases, the entanglement entropy decreases, the coherence peak in the
conductivity becomes narrower and the ratio between the energy gap and the
critical temperature decreases. These results suggest that the condensate
interactions become weaker in high spatial dimensions.


  It is proved the existence and uniqueness of graphs with prescribed mean
curvature in Riemannian submersions fibered by flow lines of a vertical Killing
vector field.


  Chiral symmetry restoration at nonzero temperature is studied in the
framework of the O(4) linear sigma model and the U(N_f)_r x U(N_f)_l linear
sigma model with N_f=2,3, and 4 quark flavors. We investigate the temperature
dependence of the masses of the scalar and pseudoscalar mesons, and the
non-strange, strange, and charm condensates within the Hartree approximation as
derived from the Cornwall-Jackiw-Tomboulis formalism. We find that the masses
of the non-strange and strange mesons at nonzero temperature depend sensitively
on the particular symmetry of the model and the number of light quark flavors
N_f. On the other hand, due to the large charm quark mass, neither do charmed
mesons significantly affect the properties of the other mesons, nor do their
masses change appreciably in the temperature range around the chiral symmetry
restoration temperature. In the chiral limit, the transition temperatures for
chiral symmetry restoration are surprisingly close to those found in lattice
QCD.


  Large language models (LLMs) have achieved unprecedented performance in
various applications, yet their evaluation remains a critical issue. Existing
hallucination benchmarks are either static or lack adjustable complexity for
thorough analysis. We contend that utilizing existing relational databases is a
promising approach for constructing benchmarks due to their accurate knowledge
description via functional dependencies. We propose ERBench to automatically
convert any relational database into a benchmark based on the
entity-relationship (ER) model. Our key idea is to construct questions using
the database schema, records, and functional dependencies such that they can be
automatically verified. In addition, we use foreign key constraints to join
relations and construct multihop questions, which can be arbitrarily complex
and used to debug the intermediate answers of LLMs. Finally, ERBench supports
continuous evaluation, multimodal questions, and various prompt engineering
techniques. In our experiments, we construct an LLM benchmark using databases
of multiple domains and make an extensive comparison of contemporary LLMs. We
observe that better LLMs like GPT-4 can handle a larger variety of question
types, but are by no means perfect. Also, correct answers do not necessarily
imply correct rationales, which is an important evaluation that ERBench does
better than other benchmarks for various question types. Code is available at
https: //github.com/DILAB-KAIST/ERBench.


  This article introduces the package MatchingFields for Macaulay2 and
highlights some open problems. A matching field is a combinatorial object whose
data encodes a candidate toric degeneration of a Grassmannian or partial flag
variety of type A. Each coherent matching field is associated to a certain
maximal cone of the respective tropical variety. The MatchingFields package
provides methods to construct matching fields along with their rings, ideals,
polyhedra and matroids. The package also supplies methods to test whether a
matching field is coherent, linkage and gives rise to a toric degeneration.


  We contribute the largest publicly available dataset of naturally occurring
factual claims for the purpose of automatic claim verification. It is collected
from 26 fact checking websites in English, paired with textual sources and rich
metadata, and labelled for veracity by human expert journalists. We present an
in-depth analysis of the dataset, highlighting characteristics and challenges.
Further, we present results for automatic veracity prediction, both with
established baselines and with a novel method for joint ranking of evidence
pages and predicting veracity that outperforms all baselines. Significant
performance increases are achieved by encoding evidence, and by modelling
metadata. Our best-performing model achieves a Macro F1 of 49.2%, showing that
this is a challenging testbed for claim veracity prediction.


  We estimate asymptotically the fourth moment of the Riemann zeta-function
twisted by a Dirichlet polynomial of length $T^{\frac14 - \varepsilon}$. Our
work relies crucially on Watt's theorem on averages of Kloosterman fractions.
In the context of the twisted fourth moment, Watt's result is an optimal
replacement for Selberg's eigenvalue conjecture.
  Our work extends the previous result of Hughes and Young, where Dirichlet
polynomials of length $T^{\frac{1}{11}-\varepsilon}$ were considered. Our
result has several applications, among others to the proportion of critical
zeros of the Riemann zeta-function, zero spacing and lower bounds for moments.
  Along the way we obtain an asymptotic formula for a quadratic divisor
problem, where the condition $a m_1 m_2 - b n_1 n_2 = h$ is summed with smooth
averaging on the variables $m_1, m_2, n_1, n_2, h$ and arbitrary weights in the
average on $a,b$. Using Watt's work allows us to exploit all averages
simultaneously. It turns out that averaging over $m_1, m_2, n_1, n_2, h$ right
away in the quadratic divisor problem simplifies considerably the combinatorics
of the main terms in the twisted fourth moment.


  We show that the Lorentz covariant formulation of N=2 string in a curved
space reveals an explicit hyper--K\"ahler structure. Apart from the metric, the
superconformal currents couple to a background two--form. By superconformal
symmetry the latter is constrained to be holomorphic and covariantly constant
and allows one to construct three complex structures obeying a
(pseudo)quaternion algebra.


  In this paper, we have studied the bit partitioning schemes for the multicell
multiple-input and single-output (MISO) infrastructure. Zero forcing
beamforming is used to null out the interference signals and the random vector
quantization, quantizes the channel vectors. For minimal feedback period (MFP),
the upper bound of rate loss is calculated and optimal bit partitioning among
the channels is shown. For adaptive feedback period scheme (AFP), joint
optimization schemes of feedback period and bit partitioning are proposed.
Finally, we compare the sum rate efficiency of each scheme and conclude that
minimal feedback period outperforms other schemes.


  We give two examples of polyhedral Banach spaces failing all the diameter two
properties, showing that there is not any connection between polyhedrality and
the diameter two properties.


  In this paper, we give an expository account of the geometric properties of
the moduli stack of $G$-bundles. For $G$ an algebraic group over a base field
and $X \to S$ a flat, finitely presented, projective morphism of schemes, we
give a complete proof that the moduli stack $Bun_G$ is an algebraic stack
locally of finite presentation over $S$ with schematic, affine diagonal. In the
process, we prove some properties of $BG$ and Hom stacks. We then define a
level structure on $Bun_G$ to provide alternative presentations of
quasi-compact open substacks. Finally, we prove that $Bun_G$ is smooth over $S$
if $G$ is smooth and $X \to S$ is a relative curve.


  Hamiltonian formulation of N=3 systems is considered in general. The Jacobi
equation is solved in three classes. Compatible Poisson structures in these
classes are determined and explicitly given. The corresponding bi-Hamiltonian
systems are constructed and some explicit examples are given.


  It is shown that the canonical quantum field theory of radiation based on the
field theoretical generalization of a recently proposed [1] commutation
relation between position and momentum operators of massless particles leads to
zero vacuum energy. This may be considered as a step toward the solution of the
cosmological constant problem at least for the electromagnetic (EM) field's
contribution.


  The universe's current acceleration is a pretty recent phenomenon in
cosmological time scales. This means that the modes that have left our horizon
since the beginning of the contemporary acceleration phase, have not really
reached the exact IR limit. Noting this observation, we reconsider the
possibility of having a ghost condensate as dark energy with a sixth-order
dispersion relation. Looking at the three-point function of such a theory, we
obtain the constraints on the coefficient of the sixth-order dispersion
relation to avoid strong coupling. Such a ghost condensate if coupled to the
standard model fields, induces a constant Lorentz-violating spin-dependent
force, which can gravitate or anti-gravitate.


  Recent years have witness remarkable performance improvements in maximum
satisfiability (MaxSAT) solvers. In practice, MaxSAT algorithms often target
the most generic MaxSAT formulation, whereas dedicated solvers, which address
specific subclasses of MaxSAT, have not been investigated. This paper shows
that a wide range of optimization and decision problems are either naturally
formulated as MaxSAT over Horn formulas, or permit simple encodings using Horn
MaxSAT. Furthermore, the paper also shows how linear time decision procedures
for Horn formulas can be used for developing novel algorithms for the Horn
MaxSAT problem.


  We consider a class of linear time dependent Schr\"odinger equations and
quasi-periodically forced nonlinear Hamiltonian wave/Klein Gordon and
Schr\"odinger equations on arbitrary flat tori. For the linear Schr\"odinger
equation, we prove a $t^\epsilon$ $(\forall \epsilon >0)$ upper bound for the
growth of the Sobolev norms as the time goes to infinity. For the nonlinear
Hamiltonian PDEs we construct families of time quasi-periodic solutions. Both
results are based on "clusterization properties" of the eigenvalues of the
Laplacian on a flat torus and on suitable "separation properties" of the
singular sites of Schr\"odinger and wave operators, which are integers, in
space-time Fourier lattice, close to a cone or a paraboloid. Thanks to these
properties we are able to apply Delort abstract theorem [Del10] to control the
speed of growth of the Sobolev norms, and Berti-Corsi-Procesi abstract
Nash-Moser theorem [BCP15] to construct quasi-periodic solutions.


  In the Token Jumping problem we are given a graph $G = (V,E)$ and two
independent sets $S$ and $T$ of $G$, each of size $k \geq 1$. The goal is to
determine whether there exists a sequence of $k$-sized independent sets in $G$,
$\langle S_0, S_1, \ldots, S_\ell \rangle$, such that for every $i$, $|S_i| =
k$, $S_i$ is an independent set, $S = S_0$, $S_\ell = T$, and $|S_i \Delta
S_{i+1}| = 2$. In other words, if we view each independent set as a collection
of tokens placed on a subset of the vertices of $G$, then the problem asks for
a sequence of independent sets which transforms $S$ to $T$ by individual token
jumps which maintain the independence of the sets. This problem is known to be
PSPACE-complete on very restricted graph classes, e.g., planar bounded degree
graphs and graphs of bounded bandwidth. A closely related problem is the Token
Sliding problem, where instead of allowing a token to jump to any vertex of the
graph we instead require that a token slides along an edge of the graph. Token
Sliding is also known to be PSPACE-complete on the aforementioned graph
classes. We investigate the parameterized complexity of both problems on
several graph classes, focusing on the effect of excluding certain cycles from
the input graph. In particular, we show that both Token Sliding and Token
Jumping are fixed-parameter tractable on $C_4$-free bipartite graphs when
parameterized by $k$. For Token Jumping, we in fact show that the problem
admits a polynomial kernel on $\{C_3,C_4\}$-free graphs. In the case of Token
Sliding, we also show that the problem admits a polynomial kernel on bipartite
graphs of bounded degree. We believe both of these results to be of independent
interest. We complement these positive results by showing that, for any
constant $p \geq 4$, both problems are W[1]-hard on $\{C_4, \dots, C_p\}$-free
graphs and Token Sliding remains W[1]-hard even on bipartite graphs.


  We introduce a multi-sorted stratified syllogistic, called 4LQSR, admitting
variables of four sorts and a restricted form of quantification over variables
of the first three sorts, and prove that it has a solvable satisfiability
problem by showing that it enjoys a small model property. Then, we consider the
fragments (4LQSR)^h of 4LQSR, consisting of 4LQSR-formulae whose quantifier
prefixes have length bounded by h > 1 and satisfying certain syntactic
constraints, and prove that each of them has an NP-complete satisfiability
problem. Finally we show that the modal logic K45 can be expressed in 4LQSR^3.


  (Strong) circular external difference families (which we denote as CEDFs and
SCEDFs) can be used to construct nonmalleable threshold schemes. They are a
variation of (strong) external difference families, which have been extensively
studied in recent years. We provide a variety of constructions for CEDFs based
on graceful labellings ($\alpha$-valuations) of lexicographic products $C_n
\boldsymbol{\cdot} K_{\ell}^c$, where $C_n$ denotes a cycle of length $n$.
SCEDFs having more than two subsets do not exist. However, we can construct
close approximations (more specifically, certain types of circular algebraic
manipulation detection (AMD) codes) using the theory of cyclotomic numbers in
finite fields.


  We have been developing optical resonant cavities for laser-Compton
scattering experiment at the Accelerator Test Facility in KEK. The main subject
of the R&D is to increase laser pulse energy by coherently accumulating the
pulses in an optical resonant cavity. We report previous results, current
status and future prospects, including a new idea of an optical resonant
cavity.


  We study a parametrically-driven nanomechanical resonator capacitively
coupled to a microwave cavity. If the nanoresonator can be cooled to near its
quantum ground state then quantum squeezing of a quadrature of the
nanoresonator motion becomes feasible. We consider the adiabatic limit in which
the cavity mode is slaved to the nanoresonator mode. By driving the cavity on
its red-detuned sideband, the squeezing can be coupled into the microwave field
at the cavity resonance. The red-detuned sideband drive is also compatible with
the goal of ground state cooling. Squeezing of the output microwave field may
be inferred using a technique similar to that used to infer squeezing of the
field produced by a Josephson parametric amplifier, and subsequently, squeezing
of the nanoresonator motion may be inferred. We have calculated the output
field microwave squeezing spectra and related this to squeezing of the
nanoresonator motion, both at zero and finite temperature. Driving the cavity
on the blue-detuned sideband, and on both the blue and red sidebands, have also
been considered within the same formalism.


  The phenomenon of anomalous localized resonance (ALR) is observed at the
interface between materials with positive and negative material parameters and
is characterized by the fact that, when a given source is placed near the
interface, the electric and magnetic fields start to have very fast and large
oscillations around the interface as the absorption in the materials becomes
very small while they remain smooth and regular away from the interface.
  In this paper, we discuss the phenomenon of anomalous localized resonance
(ALR) in the context of an infinite slab of homogeneous, nonmagnetic material
($\mu=1$) with permittivity $\epsilon_s=-1-\mathrm{i}\delta$ for some small
loss $\delta \ll 1$ surrounded by positive, nonmagnetic, homogeneous media. We
explicitly characterize the limit value of the product between frequency and
the width of slab beyond which the ALR phenomenon does not occur and analyze
the situation when the phenomenon is observed. In addition, we also construct
sources for which the ALR phenomenon never appears.


  We get obstructions to existence of semi-Riemannian submersions with totally
umbilic fibres.


  Warm absorbers are present in many Active Galactic Nuclei (AGN), seen as
mildly ionised gas outflowing with velocities of a few hundred to a few
thousand kilometres per second. These slow velocities imply a large launch
radius, pointing to the broad line region and/or torus as the origin of this
material. Thermal driving was originally suggested as a plausible mechanism for
launching this material but recent work has focused instead on magnetic winds,
unifying these slow, mildly ionised winds with the more highly ionised
ultra-fast outflows. Here we use the recently developed quantitative models for
thermal winds in black hole binary systems to predict the column density,
velocity and ionisation state from AGN. Thermal winds are sensitive to the
spectral energy distribution (SED), so we use realistic models for SEDs which
change as a function of mass and mass accretion rate, becoming X-ray weaker
(and hence more disc dominated) at higher Eddington ratio. These models allow
us to predict the launch radius, velocity, column density and ionisation state
of thermal winds as well as the mass loss rate and energetics. While these
match well to some of the observed properties of warm absorbers, the data point
to the presence of additional wind material, most likely from dust driving.


  In the model the entire high-energy part of the amplitude (Regge power
dependence from the total energy) comes as consequence of Gribov's diffusion of
the constituent quarks in the space of rapidities and impact parameters. Charge
exchange of the quarks, which goes at small quark anti-quark invariant masses,
is described by low-energy Nambu - Jona-Lasinio model. It is shown that spin
structure of the amplitudes and dominating spin-orbit (spin-flip) amplitudes
are well described by this model without free parameters.


  Based on entropy considerations and the arrow of time Penrose argued that the
universe must have started in a special initial singularity with vanishing Weyl
curvature. This is often interpreted to be at odds with inflation. Here we
argue just the opposite, that Penrose's persuasions are in fact consistent with
inflation. Using the example of power law inflation, we show that inflation
begins with a past null singularity, where Weyl tensor vanishes when the metric
is initially exactly conformally flat. This initial state precisely obeys
Penrose's conditions. The initial null singularity breaks $T$-reversal
spontaneously and picks the arrow of time. It can be regulated and interpreted
as a creation of a universe from nothing, initially fitting in a bubble of
Planckian size when it materializes. Penrose's initial conditions are favored
by the initial $O(4)$ symmetry of the bubble, selected by extremality of the
regulated Euclidean action. The predicted observables are marginally in tension
with the data, but they can fit if small corrections to power law inflation
kick in during the last 60 efolds.


  Two-ordinary-meson scattering in large-$N_c$ QCD implies consistency criteria
for intermediate-tetraquark contributions. Their fulfilment at $N_c$-leading
order constrains the nature of the spectrum of genuinely exotic tetraquark
states.


  We consider the quantum dynamics of a free nonrelativistic particle moving in
a cavity and we analyze the effect of a rapid switching between two different
boundary conditions. We show that this procedure induces, in the limit of
infinitely frequent switchings, a new effective dynamics in the cavity related
to a novel boundary condition. We obtain a dynamical composition law for
boundary conditions which gives the emerging boundary condition in terms of the
two initial ones.


  The pinning of vortex lines by an array of nanoparticles embedded inside
superconductors has become the most efficient practical way to achieve high
critical currents. In this situation pinning occurs via trapping of the
vortex-line segments and the critical current is determined by the typical
length of the trapped segments. To verify analytical estimates and develop a
quantitative description of strong pinning, we numerically simulated isolated
vortex lines driven through an array of nanoparticles. We found that the
critical force grows roughly as the square root of the pin density and it is
strongly suppressed by thermal noise. The configurations of pinned lines are
strongly anisotropic, displacements in the drive directions are much larger
than in the transverse direction. Moreover, we found that the roughening index
for the longitudinal displacements exceeds one. This indicates that the local
stresses in the critical region increase with the total line length and the
elastic description breaks down in the thermodynamic limit. Thermal noise
reduces the anisotropy of displacements in the critical regions and straightens
the lines.


  The words of a language are randomly replaced in time by new ones, but it has
long been known that words corresponding to some items (meanings) are less
frequently replaced than others. Usually, the rate of replacement for a given
item is not directly observable, but it is inferred by the estimated stability
which, on the contrary, is observable. This idea goes back a long way in the
lexicostatistical literature, nevertheless nothing ensures that it gives the
correct answer. The family of Romance languages allows for a direct test of the
estimated stabilities against the replacement rates since the proto-language
(Latin) is known and the replacement rates can be explicitly computed. The
output of the test is threefold:first, we prove that the standard approach
which tries to infer the replacement rates trough the estimated stabilities is
sound; second, we are able to rewrite the fundamental formula of
Glottochronology for a non universal replacement rate (a rate which depends on
the item); third, we give indisputable evidence that the stability ranking is
far from being the same for different families of languages. This last result
is also supported by comparison with the Malagasy family of dialects. As a side
result we also provide some evidence that Vulgar Latin and not Late Classical
Latin is at the root of modern Romance languages.


  In this follow-up to [M.G.~Cornet, P.~Torres, arXiv:2308.15603], where the
$k$-tuple domination number and the 2-packing number in Kneser graphs $K(n,r)$
were studied, we are concerned with two variations, the $k$-domination number,
${\gamma_{k}}(K(n,r))$, and the $k$-tuple total domination number,
${\gamma_{t\times k}}(K(n,r))$, of $K(n,r)$. For both invariants we prove
monotonicity results by showing that ${\gamma_{k}}(K(n,r))\ge
{\gamma_{k}}(K(n+1,r))$ holds for any $n\ge 2(k+r)$, and ${\gamma_{t\times
k}}(K(n,r))\ge {\gamma_{t\times k}}(K(n+1,r))$ holds for any $n\ge 2r+1$. We
prove that ${\gamma_{k}}(K(n,r))={\gamma_{t\times k}}(K(n,r))=k+r$ when $n\geq
r(k+r)$, and that in this case every ${\gamma_{k}}$-set and ${\gamma_{t\times
k}}$-set is a clique, while ${\gamma_{k}}(r(k+r)-1,r)={\gamma_{t\times
k}}(r(k+r)-1,r)=k+r+1$, for any $k\ge 2$. Concerning the 2-packing number,
$\rho_2(K(n,r))$, of $K(n,r)$, we prove the exact values of $\rho_2(K(3r-3,r))$
when $r\ge 10$, and give sufficient conditions for $\rho_2(K(n,r))$ to be equal
to some small values by imposing bounds on $r$ with respect to $n$. We also
prove a version of monotonicity for the $2$-packing number of Kneser graphs.


  We develop an asymptotic theory for $L^2$ norms of sample mean vectors of
high-dimensional data. An invariance principle for the $L^2$ norms is derived
under conditions that involve a delicate interplay between the dimension $p$,
the sample size $n$ and the moment condition. Under proper normalization,
central and non-central limit theorems are obtained. To facilitate the related
statistical inference, we propose a plug-in calibration method and a
re-sampling procedure to approximate the distributions of the $L^2$ norms. Our
results are applied to multiple tests and inference of covariance matrix
structures.


  This paper introduces SpotV2Net, a multivariate intraday spot volatility
forecasting model based on a Graph Attention Network architecture. SpotV2Net
represents assets as nodes within a graph and includes non-parametric
high-frequency Fourier estimates of the spot volatility and co-volatility as
node features. Further, it incorporates Fourier estimates of the spot
volatility of volatility and co-volatility of volatility as features for node
edges, to capture spillover effects. We test the forecasting accuracy of
SpotV2Net in an extensive empirical exercise, conducted with the components of
the Dow Jones Industrial Average index. The results we obtain suggest that
SpotV2Net yields statistically significant gains in forecasting accuracy, for
both single-step and multi-step forecasts, compared to a panel heterogenous
auto-regressive model and alternative machine-learning models. To interpret the
forecasts produced by SpotV2Net, we employ GNNExplainer
\citep{ying2019gnnexplainer}, a model-agnostic interpretability tool, and
thereby uncover subgraphs that are critical to a node's predictions.


  We consider the simplest quartic number fields $\mathbb{K}_m$ defined by the
irreducible quartic polynomials $$x^4-mx^3-6x^2+mx+1,$$ where $m$ runs over the
positive rational integers such that the odd part of $m^2+16$ is squarefree. In
this paper, we study the common index divisor $I(\mathbb K_m)$ and determine
explicitly the prime ideal decomposition for any prime number in any simplest
quartic number fields $\mathbb{K}_m$. On the other hand, we establish an
asymptotic formula for the number of simplest quartic fields with discriminant
$\leq x$ and given index.


  We consider $\Gamma=(X,E)$ a dual polar graph and we give a tight frame on
each eigenspace of the Laplacian operator associated to $\Gamma$. We compute
the constants associated to each tight frame and as an application we give a
formula for the product in the Norton algebra attached to the eigenspace
corresponding to the second largest eigenvalue of the Laplacian.


  In $D$-dimensional gauge theory with a kinetic term based on the p-form
tensor gauge field, we introduce a gauge invariant operator associated with the
composite formed from a electric $(p-1)$-brane and a magnetic $(q-1)$-brane in
$D=p+q+1$ spacetime dimensions. By evaluating the partition function for this
operator, we show that the expectation value of this operator gives rise to the
topological contributions identical to those in gauge theory with a topological
Chern-Simons BF term.


  Investigating the rigidly rotating disc of dust with constant specific
charge, we find that it leads to an extreme Kerr-Newman black hole in the
ultra-relativistic limit. A necessary and sufficient condition for a black hole
limit is, that the electric potential in the co-rotating frame is constant on
the disc. In that case certain other relations follow. These relations are
reviewed with a highly accurate post-Newtonian expansion.
  Remarkably it is possible to survey the leading order behaviour close to the
black hole limit with the post-Newtonian expansion. We find that the disc
solution close to that limit can be approximated very well by a
"hyper\-extreme" Kerr-Newman solution with the same gravitational mass, angular
momentum and charge.


  Let $I\subset (0,\infty )$ be an interval that is closed with respect to the
multiplication. The operations $C_{f,g}\colon I^{2}\rightarrow I$ of the form
\begin{equation*} C_{f,g}\left( x,y\right) =\left( f\circ g\right) ^{-1}\left(
f\left( x\right) \cdot g\left( y\right) \right) \text{,} \end{equation*} where
$f,g$ are bijections of $I$ are considered. Their connections with generalized
weighted quasi-geometric means is presented. It is shown that invariance
question within the class of this operations leads to means of iterative type
and to a problem on a composite functional equation. An application of the
invariance identity to determine effectively the limit of the sequence of
iterates of some generalized quasi-geometric mean-type mapping, and the form of
all continuous functions which are invariant with respect to this mapping are
given. The equality of two considered operations is also discussed.


  Given any category $\mathcal{C}$ with pullbacks and a terminal object, we
show that the data consisting of the objects of $\mathcal{C}$, the spans of
$\mathcal{C}$, and the isomorphism classes of spans of spans of $\mathcal{C}$,
forms a bicategory. We denote this bicategory Span$_2(\mathcal{C})$ and show
that this construction can be applied to give a bicategory of $n$-manifolds,
cobordisms of those manifolds, and cobordisms of cobordisms.


  We propose an adaptive environment (CABINET) to support caselaw analysis
(identifying key argument elements) based on a novel cognitive computing
framework that carefully matches various machine learning (ML) capabilities to
the proficiency of a user. CABINET supports law students in their learning as
well as professionals in their work. The results of our experiments focused on
the feasibility of the proposed framework are promising. We show that the
system is capable of identifying a potential error in the analysis with very
low false positives rate (2.0-3.5%), as well as of predicting the key argument
element type (e.g., an issue or a holding) with a reasonably high F1-score
(0.74).


  We study the interaction effects on the ground state of nanographite ribbons
with zigzag edges. Within the mean-field approximation, we found that there are
two possible phases: the superconducting (SC) phase and the excitonic insulator
(EI). The two phases are separated by a first-order transition point. After
taking into account the low-lying fluctuations around the mean-field solutions,
the SC phase becomes a spin liquid phase with one gapless charge mode.
  On the other hand, all excitations in the EI phase, especially the spin
excitations, are gapped.


  We undertake a thorough analysis of the thermodynamics of the trajectories
followed by a quantum harmonic oscillator coupled to $N$ dissipative baths by
using a new approach to large-deviation theory inspired by phase-space quantum
optics. As an illustrative example, we study the archetypal case of a harmonic
oscillator coupled to two thermal baths, allowing for a comparison with the
analogous classical result. In the low-temperature limit, we find a significant
quantum suppression in the rate of work exchanged between the system and each
bath. We further show how the presented method is capable of giving analytical
results even for the case of a driven harmonic oscillator. Based on that
result, we analyse the laser cooling of the motion of a trapped ion or
optomechanical system, illustrating how the emission statistics can be
controllably altered by the driving force.


  The gravitational wave detectors currently in operation perform the analysis
of their scientific data jointly. Concerning the search for bursting sources,
coherent data analysis methods have been shown to be more efficient. In the
coherent approach, the data collected by the detectors are time-shifted and
linearly combined so that the signatures received by each detector add up
constructively (thus improving the resulting signal-to-noise ratio). This
operation has to be performed over a sky grid (which determines the sky
locations to be searched). A limitation of those pipelines is their large
computing cost. One of the available degrees of freedom to reduce the cost is
the choice of the sky grid. Ideally, the sky sampling scheme should adapt the
angular resolution associated with the considered gravitational wave detector
network. As the geometry of detector network is not regular (the detectors are
not equally spaced and oriented), the angular resolution varies largely
depending on the sky location. We propose here a procedure which designs sky
grids that permit a complete sky coverage with a minimum number of vertices and
thus adapt the local resolution.


  Several lines of evidence point to a relationship between gamma-ray bursts
(GRBs) and the high mass stars that explode as supernovae. Arguments that GRB
sources accelerate cosmic rays (CRs) are summarized. High-energy neutrino
detection from individual GRBs would mean that they are hadronically dominated,
that is, that the amount of energy deposited in the form of nonthermal hadrons
in GRB blast waves greatly exceeds the radiated energy inferred from their
photon emission spectra. Such a detection would make GRBs the favored candidate
sources of ultra-high energy and super-GZK CRs. Cascade radiation induced by
high-energy hadrons could be detected from GRBs with gamma-ray telescopes.


  It has been recently suggested that when an Anderson impurity is immersed in
the bulk of a topological insulator, a Kondo resonant peak will appear
simultaneously with an in-gap bound-state when the band-dispersion has an
"inverted-Mexican-hat" form. The mid-gap bound-state generates another spin
state and the Kondo effect is thereby screened. In this paper we study this
problem within a weak-coupling RG scheme where we show that the system exhibits
complex crossover behavior between different symmetry configurations and may
evolve into a self-screened-Kondo or SO(3) low energy fix point. Experimental
consequences of this scenario are pointed out.


  The capacitance between any two arbitrary lattice sites in an infinite square
lattice is studied when one bond is removed (i.e. perturbed). A connection is
made between the capacitance and the Lattice Green's Function of the perturbed
network, where they are expressed in terms of those of the perfect network. The
asymptotic behavior of the perturbed capacitance is investigated as the
separation between the two sites goes to infinity. Finally, numerical results
are obtained along different directions and a comparison is carried out with
the perfect capacitances


  The wireless networks technologies are becoming more prevalent. As part of
our courses, we have to deal with the technical aspects of these technologies.
However, the experience of mobile telephony has shown fears that these products
can lead to the general public. The latter comes from the use of
electromagnetic waves at frequencies close to the frequencies of microwaves
oven(2.45 GHz). Studies are under way for years in order to identify the
possible effects on the body related to prolonged use of mobile phones.
Wireless networks like WiFi or ZigBee for example works with microwave
frequencies. On the other hand, problems relating to electromagnetic
compatibility waves with the electronic devices must also be studied. The
question of the safety of these technologies must be addressed with the
students. They will may need to install such equipment. We have integrated the
teaching of wireless networks in a chapter dealing with current standards of
exposure to electromagnetic waves for living beings and the electronic devices.
The aim of our approach is the obtention of knowledges by the student. so he
will be able to form an opinion and to provide a speech enlightened to future
users of these networks. To this end, we have developed a visualization tool
for the distribution of electromagnetic fields. This tool being used will help
you understand the electromagnetic environment in which we live and quantify
the values of electromagnetic fields (telephony, television, radio, WiFi,
Bluetooth, ZigBee, microwave oven, etc.).


  In this work, we give the sharp upper bound for the number of cliques in
graphs with bounded odd circumferences. This generalized Tur\'an-type result is
an extension of the celebrated Erd\H{o}s and Gallai theorem and a strengthening
of Luo's recent result. The same bound for graphs with bounded even
circumferences is a trivial application of the theorem of Li and Ning.


  The main idea of nested sampling is to substitute the high-dimensional
likelihood integral over the parameter space $\Omega$ by an integral over the
unit line $[0,1]$ by employing a push-forward with respect to a suitable
transformation. For this substitution, it is often implicitly or explicitly
assumed that samples from the prior are uniformly distributed along this unit
line after having been mapped by this transformation. We show that this
assumption is wrong, especially in the case of a likelihood function with
plateaus. Nevertheless, we show that the substitution enacted by nested
sampling works because of more interesting reasons which we lay out. Although
this means that analytically, nested sampling can deal with plateaus in the
likelihood function, the actual performance of the algorithm suffers under such
a setting and the method fails to approximate the evidence, mean and variance
appropriately. We suggest a robust implementation of nested sampling by a
simple decomposition idea which demonstrably overcomes this issue.


  Subtraction schemes provide a systematic way to compute fully-differential
cross sections beyond the leading order in the strong coupling constant. These
methods make singular real-emission corrections integrable in phase space by
the addition of suitable counterterms. Such counterterms may be defined using
momentum mappings, which are parametrisations of the phase space that factorise
the variables that describe the particles becoming unresolved in some infrared
or collinear limit from the variables that describe an on-shell phase space for
the resolved particles. In this work, we review existing momentum mappings in a
unified framework and introduce new ones for final-collinear and soft
counterterms. The new mappings work in the presence of massive particles and
with an arbitrary number of soft particles or of clusters of collinear
particles, making them fit for subtraction methods at any order in perturbation
theory. The new mapping for final-collinear counterterms is also used to
elucidate relations among existing final-collinear mappings.


  In nature, symmetry governs regularities, while symmetry breaking brings
texture. In artificial neural networks, symmetry has been a central design
principle to efficiently capture regularities in the world, but the role of
symmetry breaking is not well understood. Here, we develop a theoretical
framework to study the "geometry of learning dynamics" in neural networks, and
reveal a key mechanism of explicit symmetry breaking behind the efficiency and
stability of modern neural networks. To build this understanding, we model the
discrete learning dynamics of gradient descent using a continuous-time
Lagrangian formulation, in which the learning rule corresponds to the kinetic
energy and the loss function corresponds to the potential energy. Then, we
identify "kinetic symmetry breaking" (KSB), the condition when the kinetic
energy explicitly breaks the symmetry of the potential function. We generalize
Noether's theorem known in physics to take into account KSB and derive the
resulting motion of the Noether charge: "Noether's Learning Dynamics" (NLD).
Finally, we apply NLD to neural networks with normalization layers and reveal
how KSB introduces a mechanism of "implicit adaptive optimization",
establishing an analogy between learning dynamics induced by normalization
layers and RMSProp. Overall, through the lens of Lagrangian mechanics, we have
established a theoretical foundation to discover geometric design principles
for the learning dynamics of neural networks.


  We report on observation of the unusual kind of solar microflares, presumably
associated with the so-called "topological trigger" of magnetic reconnection,
which was theoretically suggested long time ago by Gorbachev et al. (Sov. Ast.
1988, v.32, p.308) but has not been clearly identified so far by observations.
As can be seen in pictures by Hinode SOT in CaII line, there may be a bright
loop connecting two sunspots, which looks at the first sight just as a magnetic
field line connecting the opposite poles. However, a closer inspection of SDO
HMI magnetograms shows that the respective arc is anchored in the regions of
the same polarity near the sunspot boundaries. Yet another peculiar feature is
that the arc flashes almost instantly as a thin strip and then begins to expand
and decay, while the typical chromospheric flares in CaII line are much wider
and propagate progressively in space. A qualitative explanation of the unusual
flare can be given by the above-mentioned model of topological trigger. Namely,
there are such configurations of the magnetic sources on the surface of
photosphere that their tiny displacements result in the formation and fast
motion of a 3D null point along the arc located well above the plane of the
sources. So, such a null point can quickly ignite a magnetic reconnection along
the entire its trajectory. Pictorially, this can be presented as flipping the
so-called two-dome magnetic-field structure (which is just the reason why such
mechanism was called topological). The most important prerequisite for the
development of topological instability in the two-dome structure is a cruciform
arrangement of the magnetic sources in its base, and this condition is really
satisfied in the case under consideration.


  Remote sensing research focusing on feature selection has long attracted the
attention of the remote sensing community because feature selection is a
prerequisite for image processing and various applications. Different feature
selection methods have been proposed to improve the classification accuracy.
They vary from basic search techniques to clonal selections, and various
optimal criteria have been investigated. Recently, methods using
dependence-based measures have attracted much attention due to their ability to
deal with very high dimensional datasets. However, these methods are based on
Cramers V test, which has performance issues with large datasets. In this
paper, we propose a parallel approach to improve their performance. We evaluate
our approach on hyper-spectral and high spatial resolution images and compare
it to the proposed methods with a centralized version as preliminary results.
The results are very promising.


  Many massive star forming disc galaxies in the redshift range 3 to 0.5 are
observed to have a clumpy morphology showing giant clumps of size $\sim$1 kpc
and masses of about $10^7M_{\odot}$ to $10^{10} M_{\odot}$. The nature and fate
of these giant clumps is still under debate. In this work we use 19
high-resolution simulations of disc galaxies from the NIHAO sample to study the
formation and the evolution of clumps in the discs of high redshift galaxies.
We use mock HST - CANDELS observations created with the radiative transfer code
GRASIL-3D to carry out, for the first time, a quantitative comparison of the
observed fraction of clumpy galaxies and its evolution with redshift with
simulations. We find a good agreement between the observed clumpy fraction and
the one of the NIHAO galaxies. We find that dust attenuation can suppress
intrinsically bright clumps and enhance less luminous ones. In our galaxy
sample we only find clumps in light (u-band) from young stars but not in
stellar mass surface density maps. This means that the NIHAO sample does not
show clumpy stellar discs but rather a clumpy light distribution originating
from clumpy star formation events. The clumps found in the NIHAO sample match
observed age/color gradients as a function of distance from the galaxy center
but they show no sign of inward migration. Clumps in our simulations disperse
on timescales of a about a hundred Myr and their contribution to bulge growth
is negligible.


  Let L be a positive definite even lattice and V_L^+ be the fixed points of
the lattice VOA V_L associated to L under an automorphism of V_L lifting the -1
isometry of L. For any positive rank, the full automotphism group of V_L^+ is
determined if L does not have vectors of norm 2 or 4. For any L of rank 2, a
set of generators and the full automorphism group of V_L^+ are determined.


  We conducted a spectropolarimetic survey of 58 high proper-motion white
dwarfs which achieved uncertainties of >2 kG in the Halpha line and >5 kG in
the upper Balmer line series. The survey aimed at detecting low magnetic fields
(< 100 kG) and helped identify the new magnetic white dwarfs NLTT 2219, with a
longitudinal field B_l = -97 kG, and NLTT 10480 (B_l=-212 kG). Also, we report
the possible identification of a very low-field white dwarf with B_l = -4.6 kG.
The observations show that ~5% of white dwarfs harbour low fields (~10 to ~10^2
kG) and that increased survey sensitivity may help uncover several new magnetic
white dwarfs with fields below ~1 kG. A series of observations of the high
field white dwarf NLTT 12758 revealed changes in polarity occurring within an
hour possibly associated to an inclined, fast rotating dipole. Also, the
relative strength of the pi and sigma components in NLTT 12758 possibly
revealed the effect of a field concentration ("spot"), or, most likely, the
presence of a non-magnetic white dwarf companion. Similar observations of NLTT
13015 also showed possible polarity variations, but without a clear indication
of the timescale. The survey data also proved useful in constraining the
chemical composition, age and kinematics of a sample of cool white dwarfs as
well as in constraining the incidence of double degenerates.


  For several different boundary conditions (Dirichlet, Neumann, Robin), we
prove norm-resolvent convergence for the operator $-\Delta$ in the perforated
domain $\Omega\setminus \bigcup_{ i\in 2\varepsilon\mathbb Z^d
}B_{a_\varepsilon}(i),$ $a_\varepsilon\ll\varepsilon,$ to the limit operator
$-\Delta+\mu_{\iota}$ on $L^2(\Omega)$, where $\mu_\iota\in\mathbb C$ is a
constant depending on the choice of boundary conditions.
  This is an improvement of previous results [Cioranescu & Murat. A Strange
Term Coming From Nowhere, Progress in Nonlinear Differential Equations and
Their Applications, 31, (1997)], [S. Kaizu. The Robin Problems on Domains with
Many Tiny Holes. Pro c. Japan Acad., 61, Ser. A (1985)], which show strong
resolvent convergence. In particular, our result implies Hausdorff convergence
of the spectrum of the resolvent for the perforated domain problem.


  In the present work, we consider the existence and spectral stability of
multi-pulse solitary wave solutions to a nonlinear Schr\"odinger equation with
both fourth and second order dispersion terms. We first give a criterion for
the existence of a single solitary wave solution in terms of the coefficients
of the dispersion terms, and then show that a discrete family of multi-pulse
solutions exists which is characterized by the distances between the individual
pulses. We then reduce the spectral stability problem for these multi-pulses to
computing the determinant of a matrix which is, to leading order, block
diagonal. Under an additional assumption, which can be verified numerically, we
show that all multi-pulses are spectrally unstable. For double pulses,
numerical computations are presented which are in good agreement with our
analytical results.


  In this paper, we will determine the factorization of global period attached
to the spherical variety $X:=\mathrm{SO}(n-1)\backslash \mathrm{SO}(n)$, which
is a special case of the Sakellaridis-Venkatesh conjecture. The main idea is to
build a connection between the periods of $X$ and the periods of the Whittaker
case $N,\psi\backslash \mathrm{SL}_2$ (n even) or $N,\psi\backslash
\mathrm{Mp}_2$ (n odd) using the tool of theta correspondence. In the local
setting, we determine the Plancherel formula of $L^2(X)$, the relative
character identities and give an explicite integral formula of transfer between
$X$-side and Whittaker-side which coincides with the theory of transfer
developed by Sakellaridis.


  It is widely perceived that the correlation effect may play an important role
in several unconventional superconducting families, such as cuprate, iron-based
and heavy-fermion superconductors. The application of high pressure can tune
the ground state properties and balance the localization and itineracy of
electrons in correlated systems, which may trigger unconventional
superconductivity. Moreover, non-centrosymmetric structure may induce the spin
triplet pairing which is very rare in nature. Here, we report a new compound
ScZrCo1-${\delta}$ crystallizing in the Ti2Ni structure with the space group of
FD3-MS without a spatial inversion center. The resistivity of the material at
ambient pressure shows a bad metal and weak semiconducting behavior.
Furthermore, specific heat and magnetic susceptibility measurements yield a
rather large value of Wilson ratio ~4.47. Both suggest a ground state with
correlation effect. By applying pressure, the up-going behavior of resistivity
in lowering temperature at ambient pressure is suppressed and gradually it
becomes metallic. At a pressure of about 19.5 GPa superconductivity emerges. Up
to 36.05 GPa, a superconducting transition at about 3.6 K with a quite high
upper critical field is observed. Our discovery here provides a new platform
for investigating the relationship between correlation effect and
superconductivity.


  The urban environment is amongst the most difficult domains for autonomous
vehicles. The vehicle must be able to plan a safe route on challenging road
layouts, in the presence of various dynamic traffic participants such as
vehicles, cyclists and pedestrians and in various environmental conditions. The
challenge remains to have motion planners that are computationally fast and
that account for future movements of other road users proactively. This paper
describes an computationally efficient sampling-based trajectory planner for
safe and comfortable driving in urban environments. The planner improves the
Stable-Sparse-RRT algorithm by adding initial exploration branches to the
search tree based on road layout information and reiterating the previous
solution. Furthermore, the trajectory planner accounts for the predicted motion
of other traffic participants to allow for safe driving in urban traffic.
Simulation studies show that the planner is capable of planning collision-free,
comfortable trajectories in several urban traffic scenarios. Adding the
domain-knowledge-based exploration branches increases the efficiency of
exploration of highly interesting areas, thereby increasing the overall
planning performance.


  Federated learning (FL) has attracted increasing attention in recent years.
As a privacy-preserving collaborative learning paradigm, it enables a broader
range of applications, especially for computer vision and natural language
processing tasks. However, to date, there is limited research of federated
learning on relational data, namely Knowledge Graph (KG). In this work, we
present a modified version of the graph neural network algorithm that performs
federated modeling over KGs across different participants. Specifically, to
tackle the inherent data heterogeneity issue and inefficiency in algorithm
convergence, we propose a novel optimization algorithm, named FedAlign, with 1)
optimal transportation (OT) for on-client personalization and 2) weight
constraint to speed up the convergence. Extensive experiments have been
conducted on several widely used datasets. Empirical results show that our
proposed method outperforms the state-of-the-art FL methods, such as FedAVG and
FedProx, with better convergence.


  Electrophysiological recordings of neural activity in a mouse's brain are
very popular among neuroscientists for understanding brain function. One
particular area of interest is acquiring recordings from the Purkinje cells in
the cerebellum in order to understand brain injuries and the loss of motor
functions. However, current setups for such experiments do not allow the mouse
to move freely and, thus, do not capture its natural behaviour since they have
a wired connection between the animal's head stage and an acquisition device.
In this work, we propose a lightweight neuronal-spike detection and
classification architecture that leverages on the unique characteristics of the
Purkinje cells to discard unneeded information from the sparse neural data in
real time. This allows the (condensed) data to be easily stored on a removable
storage device on the head stage, alleviating the need for wires. Synthesis
results reveal a >95% overall classification accuracy while still resulting in
a small-form-factor design, which allows for the free movement of mice during
experiments. Moreover, the power-efficient nature of the design and the usage
of STT-RAM (Spin Transfer Torque Magnetic Random Access Memory) as the
removable storage allows the head stage to easily operate on a tiny battery for
up to approximately 4 days.


  Observed transmission line outage data is grouped into successive generations
of events. The empirical distribution of the number of generations in the
cascades follows a Zipf distribution that implies the increasing propagation as
cascades progress. The slope of the Zipf distribution gives a System Event
Propagation Slope Index (SEPSI). This new metric quantifies the cascade
propagation, varies as expected, and determines the probabilities of small,
medium, and large cascades.


  We present a scheme to construct grand unified models based on the
superconformal algebra and the inclusion of matter fields in the adjoint
representation of supersymmetry. As an illustration, we implemented the
Georgi-Glashow $SU(5)$ model. The model predics the existence of a hidden
$(\mathbf{1},\mathbf{24},0) + (\mathbf{5},\mathbf{5}^\ast,-y') +
(\mathbf{5}^\ast,\mathbf{5},y')$ sector and an anomalous $U(1)_Z$.


  The Quantum Inverse Scattering Method is a scheme for solving integrable
models in $1+1$ dimensions, building on an $R$-matrix that satisfies the
Yang--Baxter equation and in terms of which one constructs a commuting family
of transfer matrices. In the standard formulation, this $R$-matrix acts on a
tensor product of vector spaces. Here, we relax this tensorial property and
develop a framework for describing and analysing integrable models based on
planar algebras, allowing non-separable \textit{$R$-operators} satisfying
\textit{generalised} Yang--Baxter equations. We also re-evaluate the notion of
integrals of motion and characterise when an (algebraic) \textit{transfer
operator} is polynomial in a single integral of motion. We refer to such models
as {\em polynomially integrable}. In an eight-vertex model, we demonstrate that
the corresponding transfer operator is polynomial in the natural hamiltonian.
In the Temperley--Lieb loop model with loop fugacity $\beta\in\mathbb{C}$, we
likewise find that, for all but finitely many $\beta$-values, the transfer
operator is polynomial in the usual hamiltonian element of the Temperley--Lieb
algebra $\mathrm{TL}_n(\beta)$, at least for $n\leq17$. Moreover, we find that
this model admits a second canonical hamiltonian, and that this hamiltonian
also acts as a polynomial integrability generator for small $n$ and all but
finitely many $\beta$-values.


  We test the usual hypothesis that the Cosmic Microwave Background (CMB)
dipole, its largest anisotropy, is due to our peculiar velocity with respect to
the Hubble flow by measuring independently the Doppler and aberration effects
on the CMB using Planck 2018 data. We remove the spurious contributions from
the conversion of intensity into temperature and arrive at measurements which
are independent from the CMB dipole itself for both temperature and
polarization maps and both SMICA and NILC component-separation methods.
Combining these new measurements with the dipole one we get the first
constraints on the intrinsic CMB dipole. Assuming a standard dipolar lensing
contribution we can put an upper limit on the intrinsic amplitude: 3.7 mK (95%
CI). We estimate the peculiar velocity of the solar system without assuming a
negligible intrinsic dipole contribution: $v = (300^{+111}_{-93})$ km/s with
$(l,b) = (276 \pm 33, 51 \pm 19)^\circ$ [SMICA], and $v = (296^{+111}_{-88})$
km/s with $(l,b) = (280 \pm 33, 50 \pm 20)^\circ$ [NILC] with negligible
systematic contributions. These values are consistent with the peculiar
velocity hypothesis of the dipole.


  Only four globular cluster planetary nebulae (GCPN) are known so far in the
Milky Way. About 50 new globular clusters have been recently discovered towards
the Galactic bulge. We present a search for planetary nebulae within 3 arcmin
of the new globular clusters, revealing the identification of new candidate
GCPN. These possible associations are PN SB 2 with the GC Minni 06, PN
G354.9-02.8 with the GC Minni 11, PN G356.8-03.6 with the GC Minni 28, and PN
Pe 2-11 with the GC Minni 31. We discard PN H 2-14 located well within the
projected tidal radius of the new globular cluster FSR1758 because they have
different measured radial velocities. These are interesting objects that need
follow-up observations (especially radial velocities) in order to confirm
membership, and to measure their physical properties in detail. If confirmed,
this would double the total number of Galactic GCPN.


  We introduce a new mechanism for producing locally stable de-Sitter or
Minkowski vacua, with spontaneously broken N=1 supersymmetry and no massless
scalars, applicable to superstring and M-theory compactifications with fluxes.
We illustrate the mechanism with a simple N=1 supergravity model that provides
parametric control on the sign and the size of the vacuum energy. The crucial
ingredient is a gauged U(1) that involves both an axionic shift and an
R-symmetry, and severely constrains the F- and D-term contributions to the
potential.


  Quantum mechanics and relativistic causality together imply nonlocality:
nonlocal correlations (that violate the CHSH inequality) and nonlocal equations
of motion (the Aharonov-Bohm effect). Can we invert the logical order? We
consider a conjecture that nonlocality and relativistic causality together
imply quantum mechanics. We show that correlations preserving relativistic
causality can violate the CHSH inequality more strongly than quantum
correlations. Also, we describe nonlocal equations of motion, preserving
relativistic causality, that do not arise in quantum mechanics. In these
nonlocal equations of motion, an experimenter ``jams" nonlocal correlations
between quantum systems.


  By using the Hamilton-Jacobi [HJ] framework the topological theories
associated with Euler and Pontryagin classes are analyzed. We report the
construction of a fundamental $HJ$ differential where the characteristic
equations and the symmetries of the theory are identified. Moreover, we work in
both theories with the same phase space variables and we show that in spite of
Pontryagin and Euler classes share the same equations of motion their
symmetries are different. In addition, we report all HJ Hamiltonians and we
compare our results with other formulations reported in the literature.


  Using the face as a biometric identity trait is motivated by the contactless
nature of the capture process and the high accuracy of the recognition
algorithms. After the current COVID-19 pandemic, wearing a face mask has been
imposed in public places to keep the pandemic under control. However, face
occlusion due to wearing a mask presents an emerging challenge for face
recognition systems. In this paper, we present a solution to improve masked
face recognition performance. Specifically, we propose the Embedding Unmasking
Model (EUM) operated on top of existing face recognition models. We also
propose a novel loss function, the Self-restrained Triplet (SRT), which enabled
the EUM to produce embeddings similar to these of unmasked faces of the same
identities. The achieved evaluation results on three face recognition models,
two real masked datasets, and two synthetically generated masked face datasets
proved that our proposed approach significantly improves the performance in
most experimental settings.


  An asymptotic limit of a class of Cahn-Hilliard systems is investigated to
obtain a general nonlinear diffusion equation. The target diffusion equation
may reproduce a number of well-known model equations: Stefan problem, porous
media equation, Hele-Shaw profile, nonlinear diffusion of singular logarithmic
type, nonlinear diffusion of Penrose-Fife type, fast diffusion equation and so
on. Namely, by setting the suitable potential of the Cahn-Hilliard systems, all
of these problems can be obtained as limits of the Cahn-Hilliard related
problems. Convergence results and error estimates are proved.


  Zuk's criterion give us a condition for a finitely generated group to have
Property(T): the smallest non - zero eigenvalue of Laplace operator
corresponding to the simple random walk on the associated graph have to be
greater than 1/2. We present here two examples that prove that this condition
cannot be improved.


  Background: An increased QT/RR slope is hypothesized to be predictive of
sudden cardiac death after myocardial infarction. Previous studies have shown
that beta-adrenergic stimulation increases QT/RR slope, but the effects of
beta-adrenergic stimulation on QT/RR slope in heart failure are unknown.
Methods: New Zealand White rabbits underwent coronary ligation (n=15) or sham
surgery (n=11), and implantation of a pediatric pacemaker lead in the right
ventricle for chronic ECG recording. Eight weeks after surgery, unsedated
rabbits were given intravenous administrations of 0.25 to 2.0 ml of 1
micromol/l isoprenaline, while peak QRS to QRS (RR) and Q to T peak (QT)
intervals were measured. Results: Ligated rabbits (n=6) had lower LVEF than
sham rabbits (n=7, p<.0001), but similar baseline RR (269 +/- 15 vs 292 +/- 23
ms, p=.07), QT (104 +/- 17 vs 91 +/- 9 ms, p=.1) and minimum RR (204 +/- 11 vs
208 +/- 6 ms, p=.4) intervals induced by isoprenaline (0.79 +/- 0.18 vs 0.73
+/- 0.14 ml, p=.6). Hysteresis in QT vs TQ interval plots displayed biphasic
restitution and regions of negative slope. The slope of the positive slope
region was >1 in ligated rabbits (1.27 +/- 0.66) and <1 in sham rabbits (0.35
+/- 0.14, p=.004). Absolute value of the negative slope was greater in ligated
rabbits (-0.81 +/- 0.52 vs -0.35 +/- 0.14, p=.04). Conclusion: Ischaemic heart
failure produces steeper restitution slopes during beta-adrenergically induced
QT/TQ hysteresis. This could underlie the propensity of failing hearts to
arrhythmias.


  In this paper, we study the existence and qualitative properties of positive
solutions to a Choquard-type equation with Hardy potential. We develop a
nonlocal version of concentration-compactness principle involving the Hardy
potential to study the existence and the asymptotic behavior of positive
solutions by transforming the original problem into a new nonlocal problem in
the weighted Sobolev space. Moreover, we obtain the symmetry of solutions by
using the moving plane method.


  Frozen natural orbitals (FNOs) are used to augment IP/EA-EOM-CCSD
calculations targeting the band gap of trans-polyacetylene and polyacene. We
show the resulting electron affinities (EAs), ionization potentials (IPs), and
extrapolated band gaps incur errors that are largely tunable to a desired
accuracy, yet require many orders of magnitude fewer core-hours as compared to
the corresponding full calculation. The relationship between various FNO
truncation schemes and (cc-pV$n$Z) basis set is also examined.


  This paper proposes strategies to detect time reversibility in stationary
stochastic processes by using the properties of mixed causal and noncausal
models. It shows that they can also be used for non-stationary processes when
the trend component is computed with the Hodrick-Prescott filter rendering a
time-reversible closed-form solution. This paper also links the concept of an
environmental tipping point to the statistical property of time irreversibility
and assesses fourteen climate indicators. We find evidence of time
irreversibility in $GHG$ emissions, global temperature, global sea levels, sea
ice area, and some natural oscillation indices. While not conclusive, our
findings urge the implementation of correction policies to avoid the worst
consequences of climate change and not miss the opportunity window, which might
still be available, despite closing quickly.


  In relativistic quantum constraint mechanics the state of a physical system
is constrained to a 3-dimensional subspace of Minkowski 4-space. Fourier
transformation can be used to relate this state between constraint spaces in
4-position and 4-momentum space. It is shown that integral transforms of this
nature can be carried out using Lorentz-invariant 3-dimensional constraint
space coordinates such that a complete equivalence class of 4-space
representations can be constructed from the transform. This method is further
applied to develop a relativistic generalization of the Segal-Bargmann
transformation that leads to the representation of quantum systems in a
three-dimensional subspace of Bargmann 4-space.


  Deep neural networks (DNNs) are sensitive to adversarial data in a variety of
scenarios, including the black-box scenario, where the attacker is only allowed
to query the trained model and receive an output. Existing black-box methods
for creating adversarial instances are costly, often using gradient estimation
or training a replacement network. This paper introduces
\textbf{Qu}ery-Efficient \textbf{E}volutiona\textbf{ry} \textbf{Attack},
\textit{QuEry Attack}, an untargeted, score-based, black-box attack. QuEry
Attack is based on a novel objective function that can be used in gradient-free
optimization problems. The attack only requires access to the output logits of
the classifier and is thus not affected by gradient masking. No additional
information is needed, rendering our method more suitable to real-life
situations. We test its performance with three different state-of-the-art
models -- Inception-v3, ResNet-50, and VGG-16-BN -- against three benchmark
datasets: MNIST, CIFAR10 and ImageNet. Furthermore, we evaluate QuEry Attack's
performance on non-differential transformation defenses and state-of-the-art
robust models. Our results demonstrate the superior performance of QuEry
Attack, both in terms of accuracy score and query efficiency.


  Reconfigurable intelligent surface (RIS) is a promising technology for future
wireless communication systems. Channel estimation (CE) of RIS device is a
critical but also challenging issue for its development. The mainstream of
existing CE methods is confined to the so-called cascaded channel (CscdChn)
estimation scheme, which treats the multiplicative two-hop RIS channels as an
effective one and measures it as a whole. This CscdChn training method suffers
from severe double-fading attenuation loss, which significantly degrades the CE
accuracy. In this paper, we propose a novel RIS-transmitting (RIS-TX) based CE
scheme, which has lower pilot overhead than CscdChn scheme and effectively
overcomes the double-fading curse via incorporating only one single transmit
radio frequency (RF)-chain into RIS. We develop highly efficient gradient
descent (GD) and penalty duality decomposition (PDD)-based solutions to resolve
the pilot design task for the RIS-TX CE scheme, which is a difficult quartic
optimization problem. Our designed pilot signal outperforms the discrete
Fourier transform (DFT) sequence, which is reported to be optimal for CscdChn
scheme. Besides, both theoretical analysis and numerical results demonstrate
that our proposed RIS-TX scheme exhibits distinct performance characteristics
as opposed to its CscdChn counterpart and yields superior accuracy when RIS
device is not extremely large.


  We study the cubic defocusing nonlinear Schr\"odinger equation on
$\mathbb{R}^4$ with supercritical initial data. For randomized initial data in
$H^s(\mathbb{R}^4)$, we prove almost sure local wellposedness for $\frac{1}{7}
< s < 1$ and almost sure scattering for $\frac{5}{7} < s < 1$. The
randomization is based on a unit-scale decomposition in frequency space, a
decomposition in the angular variable, and - for the almost sure scattering
result - an additional unit-scale decomposition in physical space. We employ
new probabilistic estimates for the linear Schr\"odinger flow with randomized
data, where we effectively combine the advantages of the different
decompositions.


  Many LiDAR place recognition systems have been developed and tested
specifically for urban driving scenarios. Their performance in natural
environments such as forests and woodlands have been studied less closely. In
this paper, we analyzed the capabilities of four different LiDAR place
recognition systems, both handcrafted and learning-based methods, using LiDAR
data collected with a handheld device and legged robot within dense forest
environments. In particular, we focused on evaluating localization where there
is significant translational and orientation difference between corresponding
LiDAR scan pairs. This is particularly important for forest survey systems
where the sensor or robot does not follow a defined road or path. Extending our
analysis we then incorporated the best performing approach, Logg3dNet, into a
full 6-DoF pose estimation system -- introducing several verification layers
for precise registration. We demonstrated the performance of our methods in
three operational modes: online SLAM, offline multi-mission SLAM map merging,
and relocalization into a prior map. We evaluated these modes using data
captured in forests from three different countries, achieving 80% of correct
loop closures candidates with baseline distances up to 5m, and 60% up to 10m.


  Using Monte Carlo simulations we analyze the potential of the upcoming
transit survey Pan-Planets. The analysis covers the simulation of realistic
light curves (including the effects of ingress/egress and limb-darkening) with
both correlated and uncorrelated noise as well as the application of a
box-fitting-least-squares detection algorithm. In this work we show how
simulations can be a powerful tool in defining and optimizing the survey
strategy of a transiting planet survey. We find the Pan-Planets project to be
competitive with all other existing and planned transit surveys with the main
power being the large 7 square degree field of view. In the first year we
expect to find up to 25 Jupiter-sized planets with periods below 5 days around
stars brighter than V = 16.5 mag. The survey will also be sensitive to planets
with longer periods and planets with smaller radii. After the second year of
the survey, we expect to find up to 9 Warm Jupiters with periods between 5 and
9 days and 7 Very Hot Saturns around stars brighter than V = 16.5 mag as well
as 9 Very Hot Neptunes with periods from 1 to 3 days around stars brighter than
i' = 18.0 mag.


  This work derives the linearized equations of motion, the Lagrangian density,
the Hamiltonian density, and the canonical angular momentum density for general
perturbations [$\propto \exp(im\phi)$ with $m=0,\pm 1,..$] of a geometrically
thin self-gravitating, homentropic fluid disk including the pressure. The
theory is applied to ``eccentric,'' $m=\pm 1$ perturbations of a geometrically
thin Keplerian disk. We find $m=1$ modes at low frequencies relative to the
Keplerian frequency. Further, it shown that these modes can have negative
energy and negative angular momentum. The radial propagation of these low
frequency $m=1$ modes can transport angular momentum away from the inner region
of a disk and thus increase the rate of mass accretion. Depending on the radial
boundary conditions there can be discrete low-frequency, negative-energy, $m=1$
modes.


  We show that all kinds of biasing of cosmological phase transitions produce
qualitatively new type of domain wall networks. The biased networks consist of
compact, finite size, bag-like wall structures and exhibit a generic
instability. The surface of biased networks disappears exponentially fast after
a limited period of scaling. We argue that fluctuations of the background make
the network unstable even in the case of the ``symmetric on the average''
initial distribution. We observe that the variation in parameters of the
potential, like its hight, can influence the lifetime of the wall network,
contrary to the standard beliefs.


  The nuclear spins in nanostructured semiconductors play a central role in
quantum applications. The nuclear spins represent a useful resource for
generating local magnetic fields but nuclear spin noise represents a major
source of dephasing for spin qubits. Controlling the nuclear spins enhances the
resource while suppressing the noise. NMR techniques are challenging: the group
III and V isotopes have large spins with widely different gyromagnetic ratios;
in strained material there are large atom-dependent quadrupole shifts; and
nanoscale NMR is hard to detect. We report NMR on 100,000 nuclear spins of a
quantum dot using chirped radiofrequency pulses. Following polarization, we
demonstrate a reversal of the nuclear spin. We can flip the nuclear spin back
and forth a hundred times.We demonstrate that chirped NMR is a powerful way of
determining the chemical composition, the initial nuclear spin temperatures and
quadrupole frequency distributions for all the main isotopes. The key
observation is a plateau in the NMR signal as a function of sweep rate: we
achieve inversion at the first quantum transition for all isotopes
simultaneously. These experiments represent a generic technique for
manipulating nanoscale inhomogeneous nuclear spin ensembles and open the way to
probe the coherence of such mesoscopic systems.


  We consider exciton- and light-induced current in molecular nanojunctions.
Using a model comprising a two two-level sites bridge connecting free electron
reservoirs we show that the exciton coupling between the sites of the molecular
bridge can markedly effect the source-drain current through a molecular
junction. In some cases when excited and unexcited states of the sites are
coupled differently to the leads, the contribution from electron-hole
excitations can exceed the Landauer elastic current and dominate the observed
conduction. We have proposed an optical control method using chirped pulses for
enhancing charge transfer in unbiased junctions where the bridging molecule is
characterized by a strong charge-transfer transition.


  The Fermi Large Area Telescope (LAT) data have confirmed the pulsed emission
from all six high-confidence gamma-ray pulsars previously known from the EGRET
observations. We report results obtained from the analysis of 13 months of LAT
data for three of these pulsars (PSR J1057-5226, PSR J1709-4429, and PSR
J1952+3252) each of which had some unique feature among the EGRET pulsars. The
excellent sensitivity of LAT allows more detailed analysis of the evolution of
the pulse profile with energy and also of the variation of the spectral shape
with phase. We measure the cutoff energy of the pulsed emission from these
pulsars for the first time and provide a more complete picture of the emission
mechanism. The results confirm some, but not all, of the features seen in the
EGRET data.


  We discuss the limits on the neutrino magnetic moment and hypothetical
interactions with a hidden unparticle sector, coming from the first neutrino
data release of the Borexino experiment. The observed spectrum in Borexino
depends weakly on the solar model used in the analysis, since most of the
signal comes from the mono-energetic 7Be neutrinos. This fact allows us to
calibrate the nu-e scattering cross section through the spectral shape. In this
way, we have derived a limit on the magnetic moment for the neutrinos coming
from the Sun (in which a nu_mu and nu_tau component is present): mu_nu<8.4E-11
mu_B (90%CL) which is comparable with those obtained from low energy reactor
experiments. Moreover, we improve the previous upper limit on magnetic moment
of the nu_tau by three orders of magnitude and the limit on the coupling
constant of the neutrino with a hidden unparticle sector.


  The key to optimizing spatial resolution in a state-of-the-art scanning
transmission electron microscope is the ability to precisely measure and
correct for electron optical aberrations of the probe-forming lenses. Several
diagnostic methods for aberration measurement and correction with maximum
precision and accuracy have been proposed, albeit often at the cost of
relatively long acquisition times. Here, we illustrate how artificial
intelligence can be used to provide near-real-time diagnosis of aberrations
from individual Ronchigrams. The demonstrated speed of aberration measurement
is important as microscope conditions can change rapidly, as well as for the
operation of MEMS-based hardware correction elements that have less intrinsic
stability than conventional electromagnetic lenses.


  The near infrared (NIR) upgrade to the Robert Stobie Spectrograph (RSS) on
the Southern African Large Telescope (SALT), RSS/NIR, extends the spectral
coverage of all modes of the visible arm. The RSS/NIR is a low to medium
resolution spectrograph with broadband imaging, spectropolarimetric, and
Fabry-Perot imaging capabilities. The visible and NIR arms can be used
simultaneously to extend spectral coverage from approximately 3200 A to 1.6 um.
Both arms utilize high efficiency volume phase holographic gratings via
articulating gratings and cameras. The NIR camera is designed around a
2048x2048 HAWAII-2RG detector housed in a cryogenic dewar. The Epps optical
design of the camera consists of 6 spherical elements, providing sub-pixel rms
image sizes of 7.5 +/- 1.0 um over all wavelengths and field angles. The exact
long wavelength cutoff is yet to be determined in a detailed thermal analysis
and will depend on the semi-warm instrument cooling scheme. Initial estimates
place instrument limiting magnitudes at J = 23.4 and H(1.4-1.6 um) = 21.6 for
S/N = 3 in a 1 hour exposure well below the sky noise.


  We show that three-body loss of trapped atoms leads to sub-Poissonian atom
number fluctuations. We prepare hundreds of dense ultracold ensembles in an
array of magnetic microtraps which undergo rapid three-body decay. The
shot-to-shot fluctuations of the number of atoms per trap are sub-Poissonian,
for ensembles comprising 50--300 atoms. The measured relative variance or Fano
factor $F=0.53\pm 0.22$ agrees very well with the prediction by an analytic
theory ($F=3/5$) and numerical calculations. These results will facilitate
studies of quantum information science with mesoscopic ensembles.


  We calculate the longitudinal ($\sigma_{xx}$) and Hall ($\sigma_{xy}$)
optical conductivities for two-dimensional metals with thermally disordered
antiferromagnetism using a generalization of an approximation introduced by
Lee, Rice and Anderson for the self energy. The conductivities are calculated
from the Kubo formula, with current vertex function treated in a conserving
approximation satisfying the Ward identity. In order to obtain a finite DC
limit, we introduce phenomenologically impurity scattering, with relaxation
time $\tau$. $\sigma_{xx}(\Omega)$ satisfies the $f$-sum rule. For the
infinitely peaked spin correlation function, $\chi(\mathbf{q})\propto
\delta(\mathbf{q}-\mathbf{Q})$, we recover the expressions for the
conductivities in the mean-field theory of the ordered state. When the spin
correlation length $\xi$ is large but finite, both $\sigma_{xx}$ and
$\sigma_{xy}$ show behaviors characteristic of the state with long-range order.
The calculation runs into difficulty for $\Omega\lesssim 1/\tau$. The
difficulties are traced to an inaccurate treatment of the very low energy
density of states within the Lee-Rice-Anderson approximation. The results for
$\sigma_{xx}(\Omega)$ and $\sigma_{xy}(\Omega)$ are qualitatively consistent
with data on electron-doped cuprates when $\Omega>1/\tau$.


  Context: The rapid evolution of Large Language Models (LLMs) has sparked
significant interest in leveraging their capabilities for automating code
review processes. Prior studies often focus on developing LLMs for code review
automation, yet require expensive resources, which is infeasible for
organizations with limited budgets and resources. Thus, fine-tuning and prompt
engineering are the two common approaches to leveraging LLMs for code review
automation. Objective: We aim to investigate the performance of LLMs-based code
review automation based on two contexts, i.e., when LLMs are leveraged by
fine-tuning and prompting. Fine-tuning involves training the model on a
specific code review dataset, while prompting involves providing explicit
instructions to guide the model's generation process without requiring a
specific code review dataset. Method: We leverage model fine-tuning and
inference techniques (i.e., zero-shot learning, few-shot learning and persona)
on LLMs-based code review automation. In total, we investigate 12 variations of
two LLMs-based code review automation (i.e., GPT- 3.5 and Magicoder), and
compare them with the Guo et al.'s approach and three existing code review
automation approaches. Results: The fine-tuning of GPT 3.5 with zero-shot
learning helps GPT-3.5 to achieve 73.17% -74.23% higher EM than the Guo et
al.'s approach. In addition, when GPT-3.5 is not fine-tuned, GPT-3.5 with
few-shot learning achieves 46.38% - 659.09% higher EM than GPT-3.5 with
zero-shot learning. Conclusions: Based on our results, we recommend that (1)
LLMs for code review automation should be fine-tuned to achieve the highest
performance; and (2) when data is not sufficient for model fine-tuning (e.g., a
cold-start problem), few-shot learning without a persona should be used for
LLMs for code review automation.


  This paper studies two crucial problems in the context of coded distributed
storage systems directly related to their performance: 1) for a fixed alphabet
size, determine the minimum number of servers the system must have for its
service rate region to contain a prescribed set of points; 2) for a given
number of servers, determine the minimum alphabet size for which the service
rate region of the system contains a prescribed set of points. The paper
establishes rigorous upper and lower bounds, as well as code constructions
based on techniques from coding theory, optimization, and projective geometry.


  Today, according to the Cisco Annual Internet Report (2018-2023), the
fastest-growing category of Internet traffic is machine-to-machine
communication. In particular, machine-to-machine communication of images and
videos represents a new challenge and opens up new perspectives in the context
of data compression. One possible solution approach consists of adapting
current human-targeted image and video coding standards to the use case of
machine consumption. Another approach consists of developing completely new
compression paradigms and architectures for machine-to-machine communications.
In this paper, we focus on image compression and present an inference-time
content-adaptive finetuning scheme that optimizes the latent representation of
an end-to-end learned image codec, aimed at improving the compression
efficiency for machine-consumption. The conducted experiments show that our
online finetuning brings an average bitrate saving (BD-rate) of -3.66% with
respect to our pretrained image codec. In particular, at low bitrate points,
our proposed method results in a significant bitrate saving of -9.85%. Overall,
our pretrained-and-then-finetuned system achieves -30.54% BD-rate over the
state-of-the-art image/video codec Versatile Video Coding (VVC).


  Aligning large language models (LLMs) with human values and intents
critically involves the use of human or AI feedback. While dense feedback
annotations are expensive to acquire and integrate, sparse feedback presents a
structural design choice between ratings (e.g., score Response A on a scale of
1-7) and rankings (e.g., is Response A better than Response B?). In this work,
we analyze the effect of this design choice for the alignment and evaluation of
LLMs. We uncover an inconsistency problem wherein the preferences inferred from
ratings and rankings significantly disagree 60% for both human and AI
annotators. Our subsequent analysis identifies various facets of annotator
biases that explain this phenomena, such as human annotators would rate denser
responses higher while preferring accuracy during pairwise judgments. To our
surprise, we also observe that the choice of feedback protocol also has a
significant effect on the evaluation of aligned LLMs. In particular, we find
that LLMs that leverage rankings data for alignment (say model X) are preferred
over those that leverage ratings data (say model Y), with a rank-based
evaluation protocol (is X/Y's response better than reference response?) but not
with a rating-based evaluation protocol (score Rank X/Y's response on a scale
of 1-7). Our findings thus shed light on critical gaps in methods for
evaluating the real-world utility of language models and their strong
dependence on the feedback protocol used for alignment. Our code and data are
available at https://github.com/Hritikbansal/sparse_feedback.


  Context. Abundance anomalies have been observed in field sdB stars and in
nearly all Horizontal Branch (HB) stars of globular clusters with Teff > 11
000K whatever be the cluster metallicity. Aims. The aim is to determine the
abundance variations to be expected in sdB stars and in HB stars of
metallicities Z \geq 0.0001 and what observed abundances teach us about
hydrodynamical processes competing with atomic diffusion. Methods. Complete
stellar evolution models, including the effects of atomic diffusion and
radiative acceleration, have been computed from the zero age main-sequence for
metallicities of Z0 = 0.0001, 0.001, 0.004 and 0.02. On the HB the masses were
selected to cover the Teff interval from 7000 to 37000K. Some 60 evolutionary
HB models were calculated. The calculations of surface abundance anomalies
during the horizontal branch depend on one parameter, the surface mixed mass.
Results. For sdB stars with Teff < 37000K and for HB stars with Teff > 11 000K
in all observed clusters, independent of metallicity, it was found that most
observed abundance anomalies (even up to ~ x 200) were compatible, within error
bars, with expected abundances. A mixed mass of ~1.E-7 M\odot was determined by
comparison with observations. Conclusions. Observations of globular cluster HB
stars with Teff > 11 000K and of sdB stars with Teff < 37 000K suggest that
most observed abundance anomalies can be explained by element separation driven
by radiative acceleration occuring at a mass fraction of ~1.E-7 M\odot. Mass
loss or turbulence appear to limit the separation between 1.E-7 M\odot and the
surface.


  We review recent developments in understanding quantum/string corrections to
BPS black holes and strings in five-dimensional supergravity. These objects are
solutions to the effective action obtained from M-theory compactified on a
Calabi-Yau threefold, including the one-loop corrections determined by anomaly
cancellation and supersymmetry. We introduce the off-shell formulation of this
theory obtained through the conformal supergravity method and review the
methods for investigating supersymmetric solutions. This leads to
quantum/string corrected attractor geometries, as well as asymptotically flat
black strings and spinning black holes. With these solutions in hand, we
compare our results with analogous studies in four-dimensional string-corrected
supergravity, emphasizing the distinctions between the four and five
dimensional theories.


  In the context of event-by-event hydrodynamic description, we analyze the
implications of two models characterized by distinct initial conditions. The
initial energy density of the first model adopts a Gaussian-type distribution,
while those of the second one are features by high energy peripheral tubes. We
calibrate the initial conditions of both models so that their initial
probability distribution of eccentricity are mostly identical. Subsequently,
the resultant scaled probability distributions of collective flow and the
correlations between flow harmonic and eccentricity coefficients are
investigated. Besides, the calculations are carried out for particle
correlations regarding the symmetric cumulant, mixed harmonics, and nonlinear
response coefficients. Although the resultant two-particle correlations possess
similar shapes, numerical calculations indicate a subtle difference between the
two models. To be specific, the difference resides in more detailed observables
such as the probability distributions of elliptic flow as well as Pearson
correlation coefficient regarding higher-order harmonics. We discuss several
essential aspects concerning the linearity and nonlinearity between initial
eccentricities and final state anisotropies. Further implications are
addressed.


  Benchmarking and comparing performance of a scientific simulation across
hardware platforms is a complex task. When the simulation in question is
constructed with an asynchronous, many-task (AMT) runtime offloading work to
GPUs, the task becomes even more complex. In this paper, we discuss the use of
a uniquely suited performance measurement library, APEX, to capture the
performance behavior of a simulation built on HPX, a highly scalable,
distributed AMT runtime. We examine the performance of the astrophysics
simulation carried-out by Octo-Tiger on two different supercomputing
architectures. We analyze the results of scaling and measurement overheads. In
addition, we look in-depth at two similarly configured executions on the two
systems to study how architectural differences affect performance and identify
opportunities for optimization. As one such opportunity, we optimize the
communication for the hydro solver and investigated its performance impact.


  We prove that a crepant resolution of a Ricci-flat K\"ahler cone X admits a
complete Ricci-flat K\"ahler metric asymptotic to the cone metric in every
K\"ahler class in H^2_c(Y,R). This result contains as a subcase the existence
of ALE Ricci-flat K\"ahler metrics on crepant resolutions of X=C^n /G, where G
is a finite subgroup of SL(n,C).
  We consider the case in which X is toric. A result of A. Futaki, H. Ono, and
G. Wang guarantees the existence of a Ricci-flat K\"ahler cone metric if X is
Gorenstein. We use toric geometry to construct crepant resolutions.