  In this study by considering Balakrishnan mechanism a new form of alpha skew
distribution is proposed and properties are investigated. The suitability of
the proposed distribution has tested at the end with appropriate data fitting
experiment and then comparing the values of Akaike Information Criterion (AIC),
and Bayesian Information Criterion (BIC) with the values of some other related
distributions. Likelihood ratio test is carried out for nested models, that is,
for Laplace and the proposed distributions.
  Keywords: Skew Distribution, Alpha-Skew Distribution, Bimodal Distribution,
Alpha-Skew-Normal Distribution, Alpha-Skew-Laplace Distribution,
Balakrishnan-Alpha-Skew-Normal Distribution


  Determining the necessity of resecting malignant polyps during colonoscopy
screen is crucial for patient outcomes, yet challenging due to the
time-consuming and costly nature of histopathology examination. While deep
learning-based classification models have shown promise in achieving optical
biopsy with endoscopic images, they often suffer from a lack of explainability.
To overcome this limitation, we introduce EndoFinder, a content-based image
retrieval framework to find the 'digital twin' polyp in the reference database
given a newly detected polyp. The clinical semantics of the new polyp can be
inferred referring to the matched ones. EndoFinder pioneers a polyp-aware image
encoder that is pre-trained on a large polyp dataset in a self-supervised way,
merging masked image modeling with contrastive learning. This results in a
generic embedding space ready for different downstream clinical tasks based on
image retrieval. We validate the framework on polyp re-identification and
optical biopsy tasks, with extensive experiments demonstrating that EndoFinder
not only achieves explainable diagnostics but also matches the performance of
supervised classification models. EndoFinder's reliance on image retrieval has
the potential to support diverse downstream decision-making tasks during
real-time colonoscopy procedures.


  Entanglement lies at the heart of quantum mechanics, and has been identified
an essential resource for diverse applications in quantum information. If
entanglement could be verified without any trust in the devices of observers,
i.e., in a device-independent (DI) way, then unconditional security can be
guaranteed for various quantum information tasks. In this work, we propose an
experimental-friendly DI protocol to certify the presence of entanglement,
based on Einstein-Podolsky-Rosen (EPR) steering. We first establish the DI
verification framework, relying on the measurement-device-independent technique
and self-testing, and show it is able to verify all EPR-steerable states. In
the context of three-measurement settings as per party, it is found to be noise
robustness towards inefficient measurements and imperfect self-testing.
Finally, a four-photon experiment is implemented to device-independently verify
EPR-steering even for Bell local states. Our work paves the way for realistic
implementations of secure quantum information tasks.


  We have carried out the largest search for stable particles with fractional
electric charge, based on an oil drop method that incorporates a horizontal
electric field and upward air flow. No evidence for such particles was found,
giving a 95% C.L. upper limit of $1.15\times 10^{-22}$ particles per nucleon on
the abundance of fractional charge particles in silicone oil for $0.18 e \le
|Q_{residual}| \le 0.82 e$.


  The lifetime of trapped ion ensembles corresponds to a crucial parameter
determining the potential scalability of their prospective applications and is
often limited by the achievable vacuum level in the apparatus. We report on the
realization of a room-temperature $^{40}{\rm Ca}^{+}$ ion trapping vacuum
apparatus with unprecedentedly low reaction rates of ions with a dominant
vacuum contaminant: hydrogen. We present our trap assembly procedures and
hydrogen pressure characterization by analysis of the CaH$^+$ molecule
formation rate.


  Inelastic phonon scattering in graphene field-effect transistors (FETs) is
studied by numerically solving the Boltzmann transport equation in three
dimensional real and phase spaces (x, kx, ky). A kink behavior due to ambipolar
transport agreeing with experiments is observed. While low field behavior has
previously been mostly attributed to elastic impurity scattering in earlier
studies, it is found in the study that even low field mobility is affected by
inelastic phonon scattering in recent graphene FET experiments reporting high
mobilities . As the FET is biased in the saturation regime, the average carrier
injection velocity at the source end of the device is found to remain almost
constant with regard to the applied gate voltage over a wide voltage range,
which results in significantly improved transistor linearity compared to what a
simpler model would predict. Physical mechanisms for good linearity are
explained, showing the potential of graphene FETs for analogue electronics
applications.


  This paper studies a variant of multi-player reach-avoid game played between
intruders and defenders. The intruder team tries to score by sending as many
intruders as possible to the target area, while the defender team tries to
minimize this score by intercepting them. Specifically, we consider the case
where the defenders are constrained to move on the perimeter of the target
area. Since it is challenging to directly solve the multi-player game due to
the high dimensionality of the joint state space, we leverage the solutions to
smaller scale problems. First, we solve the one vs. one game, for which
existing works either rely on numerical approaches or make simplifying
assumptions (e.g., circular perimeter, or equal speed). This paper accommodates
target areas with any arbitrary convex shapes and provides analytical solution
which lends itself to a useful geometric interpretation. We also provide a
detailed discussion on the optimality of the derived strategies. Secondly, we
solve the two vs. one game to introduce a cooperative pincer maneuver, where a
pair of defenders team up to capture an intruder that cannot be captured by
either one of the defender individually. Finally, we introduce how the
aforementioned building blocks are used in three different assignment-based
defense strategies.


  In this paper we briefly review some of the most recent developments
concerning the formation of the first luminous objects in the universe, to
which we refer to as Pop III objects, and their observable effects. In
particular, we try to critically discuss the possible connection between them
and dwarf spheroidal galaxies. We come to the conclusion that, if the
properties of Pop IIIs are correctly predicted by hierarchical cosmological
models, their identification with present day dwarf galaxies presents several
difficulties.


  Multi-numerology waveform based 5G New Radio (NR) systems offer great
flexibility for different requirements of users and services. Providing
fairness between users is not an easy task due to inter-numerology interference
(INI) between multiple numerologies. This paper proposes two novel scheduling
algorithms to provide fairness for all users, especially at the edges of
numerologies. Signal-to-noise ratio (SIR) results for multi-numerology systems
are obtained through computer simulations.


  A method for introducing the higher order terms in the potential expansion to
study the continuous limits of the Toda hierarchy is proposed in this paper.
The method ensures that the higher order terms are differential polynomials of
the lower ones and can be continued to be performed indefinitly. By introducing
the higher order terms, the fewer equations in the Toda hierarchy are needed in
the so-called recombination method to recover the KdV hierarchy. It is shown
that the Lax pairs, the Poisson tensors, and the Hamiltonians of the Toda
hierarchy tend towards the corresponding ones of the KdV hierarchy in
continuous limit.


  For many protocols, quantum strategies have advantages compared with their
classical counter-partners, and these advantages have attracted many interests
and applications. One of the famous examples is the Clauser-Horne-Shimony-Holt
(CHSH) game, which recasts Bell's theorem~\cite{2} into the framework of a
game. In the CHSH game, two space-like separated players, Alice and Bob are
each assigned a classical bit $a$ and $b$ respectively. Then they return bits
$x$ and $y$ according to some pre-agreed strategies. They will win the game
when $x\oplus y= a\cdot b$. In the game, if the players use the classical
strategies, the optimal success probability $w(\text{CHSH})=0.75$.However, if
they add some quantum resources, the success probability will increase and up
to maximal value $cos^2(\pi/8)$, which is know as the Tsirelson's bound.
Moreover, Popescu and Rohrlich noted that the perfect success probability $1$
can also be achieved in a more general theory without violating the
no-signaling assumption


  Smoothing splines have been used pervasively in nonparametric regressions.
However, the computational burden of smoothing splines is significant when the
sample size $n$ is large. When the number of predictors $d\geq2$, the
computational cost for smoothing splines is at the order of $O(n^3)$ using the
standard approach. Many methods have been developed to approximate smoothing
spline estimators by using $q$ basis functions instead of $n$ ones, resulting
in a computational cost of the order $O(nq^2)$. These methods are called the
basis selection methods. Despite algorithmic benefits, most of the basis
selection methods require the assumption that the sample is
uniformly-distributed on a hyper-cube. These methods may have deteriorating
performance when such an assumption is not met. To overcome the obstacle, we
develop an efficient algorithm that is adaptive to the unknown probability
density function of the predictors. Theoretically, we show the proposed
estimator has the same convergence rate as the full-basis estimator when $q$ is
roughly at the order of $O[n^{2d/\{(pr+1)(d+2)\}}\quad]$, where $p\in[1,2]$ and
$r\approx 4$ are some constants depend on the type of the spline. Numerical
studies on various synthetic datasets demonstrate the superior performance of
the proposed estimator in comparison with mainstream competitors.


  We study the problem of estimating multivariate log-concave probability
density functions. We prove the first sample complexity upper bound for
learning log-concave densities on $\mathbb{R}^d$, for all $d \geq 1$. Prior to
our work, no upper bound on the sample complexity of this learning problem was
known for the case of $d>3$. In more detail, we give an estimator that, for any
$d \ge 1$ and $\epsilon>0$, draws $\tilde{O}_d \left( (1/\epsilon)^{(d+5)/2}
\right)$ samples from an unknown target log-concave density on $\mathbb{R}^d$,
and outputs a hypothesis that (with high probability) is $\epsilon$-close to
the target, in total variation distance. Our upper bound on the sample
complexity comes close to the known lower bound of $\Omega_d \left(
(1/\epsilon)^{(d+1)/2} \right)$ for this problem.


  We study the periodic Hartree-Fock model used for the description of
electrons in a crystal. The existence of a minimizer was previously shown by
Catto, Le Bris and Lions (Ann. Inst. H. Poincare Anal. Non Lineaire} 18 (2001),
no.6, 687--760). We prove in this paper that any minimizer is necessarily a
projector and that it solves a certain nonlinear equation, similarly to the
atomic case. In particular we show that the Fermi level is either empty or
totally filled.


  We consider the general Landau-Lifshitz-Gilbert theory underlying the
magnetization dynamics of a macrospin magnet subject to spin-torque effects and
thermal fluctuations. Thermally activated dynamical properties are analyzed by
averaging the full magnetization equations over constant- energy orbits. After
averaging, all the relevant dynamical scenarios are a function of the ratio
between hard and easy axis anisotropies. We derive analytically the range of
currents for which limit cycles exist and discuss the regimes in which the
constant energy orbit averaging technique is applicable.


  We demonstrate trapping in a surface-electrode ion trap fabricated in a 90-nm
CMOS (complementary metal-oxide-semiconductor) foundry process utilizing the
top metal layer of the process for the trap electrodes. The process includes
doped active regions and metal interconnect layers, allowing for co-fabrication
of standard CMOS circuitry as well as devices for optical control and
measurement. With one of the interconnect layers defining a ground plane
between the trap electrode layer and the p-type doped silicon substrate, ion
loading is robust and trapping is stable. We measure a motional heating rate
comparable to those seen in surface-electrode traps of similar size. This is
the first demonstration of scalable quantum computing hardware, in any
modality, utilizing a commercial CMOS process, and it opens the door to
integration and co-fabrication of electronics and photonics for large-scale
quantum processing in trapped-ion arrays.


  We revisit the concept of turnaround radius in cosmology, in the context of
modified gravity. While preliminary analyses were limited to
scalar-tensor/$F(R)$ gravity, we extend the definition and the study of this
quantity to a much broader class of theories including also quantum $R^2$
gravity. The turnaround radius is computed in terms of the parameters of the
theory and it is shown that a deviation not larger than 10\% of this quantity
from its value in Einstein's theory could constrain the model parameters and
even rule out some current theories.


  Noise subtraction methods are a set of techniques that aim to reduce the
variance of signals in LQCD which are often flooded with noise. The standard
approach is a pertubative subtraction. In this work, we demonstrate the
abilities of our new noise subtraction methods with methods which show
considerable improvement over pertubative subtraction in the reduction of the
variance for the set of LQCD operators that were studied. The methods were
tested at $\kappa_{crit}$ on quenched configurations, as well as on dynamical
quark configurations at $\kappa = 0.1453$. A significant improvement in the
reduction of operator variance was observed in both cases.


  Beam search is widely used for approximate decoding in structured prediction
problems. Models often use a beam at test time but ignore its existence at
train time, and therefore do not explicitly learn how to use the beam. We
develop an unifying meta-algorithm for learning beam search policies using
imitation learning. In our setting, the beam is part of the model, and not just
an artifact of approximate decoding. Our meta-algorithm captures existing
learning algorithms and suggests new ones. It also lets us show novel no-regret
guarantees for learning beam search policies.


  This paper develops some new analytical solutions to the
$f(\mathbb{R},\mathbb{T})$ field equations through extended gravitational
decoupling. For this purpose, we take spherical anisotropic configuration as a
seed source and extend it to an additional source. The modified field equations
comprise the impact of both sources which are then decoupled into two distinct
sets by applying the transformations on $g_{tt}$ and $g_{rr}$ metric
potentials. The original anisotropic source is adorned by the first sector, and
we make it solvable by considering two different well-behaved solutions. The
second sector is in terms of an additional source and we adopt some constraints
to find deformation functions. The first constraint is the isotropization
condition which transforms the total fluid distribution into an isotropic
system only for a specific value of the decoupling parameter. The other
constraint is taken as the complexity-free fluid distribution. The unknown
constants are calculated at the hypersurface through matching conditions. The
preliminary information (mass and radius) of a compact star $4U 1820-30$ is
employed to analyze physical attributes of the resulting models. We conclude
that certain values of both the coupling as well as decoupling parameter yield
viable and stable solutions in this theory.


  A novel formulation of fluid dynamics as a kinetic theory with tailored,
on-demand constructed particles removes any restrictions on Mach number and
temperature as compared to its predecessors, the lattice Boltzmann methods and
their modifications. In the new kinetic theory, discrete particles are
determined by a rigorous limit process which avoids ad hoc assumptions about
their velocities. Classical benchmarks for incompressible and compressible
flows demonstrate that the proposed discrete-particles kinetic theory opens up
an unprecedented wide domain of applications for computational fluid dynamics.


  The displacement field in highly non uniformly strained crystals is obtained
by addition of constraints to an iterative phase retrieval algorithm. These
constraints include direct space density uniformity and also constraints to the
sign and derivatives of the different components of the displacement field.
This algorithm is applied to an experimental reciprocal space map measured
using high resolution X-ray diffraction from an array of silicon lines and the
obtained component of the displacement field is in very good agreement with the
one calculated using a finite element model.


  In this paper, we study the space of stability conditions on a certain
$N$-Calabi-Yau ($\text{CY}_N$) category associated to an $A_n$-quiver.
Recently, Bridgeland and Smith constructed stability conditions on some
$\text{CY}_3$ categories from meromorphic quadratic differentials with simple
zeros. Generalizing their results to higher dimensional Calabi-Yau categories,
we describe the space of stability conditions as the universal cover of the
space of polynomials of degree $n+1$ with simple zeros. In particular, central
charges of stability conditions on $\text{CY}_N$ categories are constructed as
the periods of quadratic differentials with zeros of order $N-2$ which are
associated to polynomials.


  The existence of plasma oscillations at multiples of the magnetoplasmon
frequency in a strongly coupled two-dimensional magnetized Yukawa plasma is
reported, based on extensive molecular dynamics simulations. These modes are
the analogues of Bernstein modes which are renormalized by strong interparticle
correlations. Their properties are theoretically explained by a dielectric
function incorporating the combined effect of a magnetic field, strong
correlations and finite temperature.


  A new theory yields unconventional results for the angular distribution of
products like $b-\bar{b}$ jets in Higgs decays.


  We give an a geometric interpretation of the Hasse-Arf theorem for function
fields using the recently proved Oort conjecture.


  If a regular graph of degree $k$ and diameter $d$ has $v$ vertices then
$$v\le 1+k+k(k-1)+\dots+k(k-1)^{d-1}.$$ Graphs with
$v=1+k+k(k-1)+\dots+k(k-1)^{d-1}$ are called Moore graphs. Damerell proved that
a Moore graph of degree $k\ge 3$ has diameter $2$. If $\Gamma$ is a Moore graph
of diameter $2$, then $v=k^2+1$, $\Gamma$ is strongly regular with $\lambda=0$
and $\mu=1$, and one of the following statements holds{\rm:} $k=2$ and $\Gamma$
is the pentagon, $k=3$ and $\Gamma$ is the Petersen graph, $k=7$ and $\Gamma$
is the Hoffman-Singleton graph, or $k=57$. The existence of a Moore graph of
degree $57$ was unknown. Jurishich and Vidali have proved that the existence of
a Moore graph of degree $k>3$ is equivalent to the existence of a
distance-regular graph with intersection array $\{k-2,k-3,2;1,1,k-3\}$ (in the
case $k=57$ we have a distance-regular graph with intersection array
$\{55,54,2;1,1,54\}$). In this paper we prove that a distance-regular graph
with intersection array $\{55,54,2;1,1,54\}$ does not exist. As a corollary, we
prove that a Moore graph of degree $57$ does not exist.


  NEWS-G (New Experiments With Spheres-Gas) is an experiment aiming to shine a
light on the dark matter conundrum with a novel gaseous detector, the spherical
proportional counter. It uses light gases, such as hydrogen, helium, and neon,
as targets to expand dark matter searches to the sub-GeV/c$^{2}$ mass region.
NEWS-G produced its first results with a 60 cm in diameter detector installed
at LSM (France), excluding at 90% C.L. cross-sections above $4.4\cdot{10}^{37}$
cm$^{2}$ for dark matter candidates of 0.5 GeV/c$^{2}$ mass. Currently, a 140
cm in diameter detector is being built at LSM and a commissioning run is
underway, prior to its installation at SNOLAB (Canada) at the end of the year.
Presented here are developments incorporated in this new detector: a) sensor
technologies using resistive materials and multi-anode read-out that allow high
gain and high pressure operation; b) gas purification techniques to remove
contaminants (H$_{2}$O, O$_{2}$); c) reduction of ${}^{210}$Pb induced
background through copper electroforming methods; d) utilisation of UV-lasers
for detector calibration, detector response monitoring and estimation of gas
related fundamental properties. This next phase of NEWS-G will allow searches
for low mass dark matter with unprecedented sensitivity.


  Market-based instruments such as payments, auctions or tradable permits have
been proposed as flexible and cost-effective instruments for biodiversity
conservation on private lands. Trading the service of conservation requires one
to define a metric that determines the extent to which a conserved site adds to
the regional conservation objective. Yet, while markets for conservation are
widely discussed and increasingly applied, little research has been conducted
on explicitly accounting for spatial ecological processes in the trading. In
this paper, we use a coupled ecological economic simulation model to examine
how spatial connectivity may be considered in the financial incentives created
by a market-based conservation scheme. Land use decisions, driven by changing
conservation costs and the conservation market, are simulated by an agent-based
model of land users. On top of that, a metapopulation model evaluates the
conservational success of the market. We find that optimal spatial incentives
for agents correlate with species characteristics such as the dispersal
distance, but they also depend on the spatio-temporal distribution of
conservation costs. We conclude that a combined analysis of ecological and
socio-economic conditions should be applied when designing market instruments
to protect biodiversity.


  As an agent moves through the world, the apparent motion of scene elements is
(usually) inversely proportional to their depth. It is natural for a learning
agent to associate image patterns with the magnitude of their displacement over
time: as the agent moves, faraway mountains don't move much; nearby trees move
a lot. This natural relationship between the appearance of objects and their
motion is a rich source of information about the world. In this work, we start
by training a deep network, using fully automatic supervision, to predict
relative scene depth from single images. The relative depth training images are
automatically derived from simple videos of cars moving through a scene, using
recent motion segmentation techniques, and no human-provided labels. This proxy
task of predicting relative depth from a single image induces features in the
network that result in large improvements in a set of downstream tasks
including semantic segmentation, joint road segmentation and car detection, and
monocular (absolute) depth estimation, over a network trained from scratch. The
improvement on the semantic segmentation task is greater than those produced by
any other automatically supervised methods. Moreover, for monocular depth
estimation, our unsupervised pre-training method even outperforms supervised
pre-training with ImageNet. In addition, we demonstrate benefits from learning
to predict (unsupervised) relative depth in the specific videos associated with
various downstream tasks. We adapt to the specific scenes in those tasks in an
unsupervised manner to improve performance. In summary, for semantic
segmentation, we present state-of-the-art results among methods that do not use
supervised pre-training, and we even exceed the performance of supervised
ImageNet pre-trained models for monocular depth estimation, achieving results
that are comparable with state-of-the-art methods.


  Unsupervised clustering of feature matrix data is an indispensible technique
for exploratory data analysis and quality control of experimental data.
However, clusters are difficult to assess for statistical significance in an
objective way. We prove a formula for the distribution of the size of the set
of samples, out of a population of fixed size, which display a given signature,
conditional on the marginals (frequencies) of each individual feature
comprising the signature. The resulting "exact test for coincidence" is widely
applicable to objective assessment of clusters in any binary data. We also
present a software package implementing the test, a suite of computational
verifications of the main theorems, and a supplemental tool for cluster
discovery using Formal Concept Analysis.


  Let R be the connected component of the identity of the variety of
representations of a finitely generated nilpotent group N into a connected
reductive complex affine algebraic group G. We determine the mixed Hodge
structure on the representation variety R and on the character variety R//G. We
obtain explicit formulae (both closed and recursive) for the mixed Hodge
polynomial of these representation and character varieties.


  We investigate cosmological models with a free scalar field and a viscous
fluid. We find exact solutions for a linear and nonlinear viscosity pressure.
Both yield singular and bouncing solutions. In the first regime, a de Sitter
stage is asymptotically stable, while in the second case we find power-law
evolutions for vanishing cosmological constant.


  Privacy is an increasing concern in cyber-physical systems that operates over
a shared network. In this paper, we propose a method for privacy verification
of cyber- physical systems modeled by Markov decision processes (MDPs) and
partially-observable Markov decision processes (POMDPs) based on barrier
certificates. To this end, we consider an opacity-based notion of privacy,
which is characterized by the beliefs in system states. We show that the belief
update equations can be represented as discrete-time switched systems, for
which we propose a set of conditions for privacy verification in terms of
barrier certificates. We further demonstrate that, for MDPs and for POMDPs,
privacy verification can be computationally implemented by solving a set of
semi-definite programs and sum-of-squares programs, respectively. The method is
illustrated by an application to privacy verification of an inventory
management system.


  We revisit the stability analysis of cylindrical thin shell wormholes which
have been studied in literature so far. Our approach is more systematic and in
parallel to the method which is used in spherically symmetric thin shell
wormholes. The stability condition is summarized as the positivity of the
second derivative of an effective potential at the equilibrium radius, i.e.
$V^{\prime \prime}\left(a_{0}\right) >0$. This may serve as the master equation
in all stability problems for the cylindrical thin-shell wormholes.


  Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie
algebras (with space isotropy) have recently been classified in all dimensions.
In this paper, we continue the study of these "maximally symmetric" spacetimes
by investigating their local geometry. For each such spacetime and relative to
exponential coordinates, we calculate the (infinitesimal) action of the
kinematical symmetries, paying particular attention to the action of the
boosts, showing in almost all cases that they act with generic non-compact
orbits. We also calculate the soldering form, the associated vielbein and any
invariant aristotelian, galilean or carrollian structures. The (conformal)
symmetries of the galilean and carrollian structures we determine are typically
infinite-dimensional and reminiscent of BMS Lie algebras. We also determine the
space of invariant affine connections on each homogeneous spacetime and work
out their torsion and curvature.


  Structural subtyping and parametric polymorphism provide similar flexibility
and reusability to programmers. For example, both features enable the
programmer to provide a wider record as an argument to a function that expects
a narrower one. However, the means by which they do so differs substantially,
and the precise details of the relationship between them exists, at best, as
folklore in literature.
  In this paper, we systematically study the relative expressive power of
structural subtyping and parametric polymorphism. We focus our investigation on
establishing the extent to which parametric polymorphism, in the form of row
and presence polymorphism, can encode structural subtyping for variant and
record types. We base our study on various Church-style $\lambda$-calculi
extended with records and variants, different forms of structural subtyping,
and row and presence polymorphism.
  We characterise expressiveness by exhibiting compositional translations
between calculi. For each translation we prove a type preservation and
operational correspondence result. We also prove a number of non-existence
results. By imposing restrictions on both source and target types, we reveal
further subtleties in the expressiveness landscape, the restrictions enabling
otherwise impossible translations to be defined. More specifically, we prove
that full subtyping cannot be encoded via polymorphism, but we show that
several restricted forms of subtyping can be encoded via particular forms of
polymorphism.


  Large language models (LLMs) have advanced the field of artificial
intelligence (AI) in medicine. However LLMs often generate outdated or
inaccurate information based on static training datasets. Retrieval augmented
generation (RAG) mitigates this by integrating outside data sources. While
previous RAG systems used pre-assembled, fixed databases with limited
flexibility, we have developed Radiology RAG (RadioRAG) as an end-to-end
framework that retrieves data from authoritative radiologic online sources in
real-time. RadioRAG is evaluated using a dedicated radiologic
question-and-answer dataset (RadioQA). We evaluate the diagnostic accuracy of
various LLMs when answering radiology-specific questions with and without
access to additional online information via RAG. Using 80 questions from RSNA
Case Collection across radiologic subspecialties and 24 additional
expert-curated questions, for which the correct gold-standard answers were
available, LLMs (GPT-3.5-turbo, GPT-4, Mistral-7B, Mixtral-8x7B, and Llama3 [8B
and 70B]) were prompted with and without RadioRAG. RadioRAG retrieved
context-specific information from www.radiopaedia.org in real-time and
incorporated them into its reply. RadioRAG consistently improved diagnostic
accuracy across all LLMs, with relative improvements ranging from 2% to 54%. It
matched or exceeded question answering without RAG across radiologic
subspecialties, particularly in breast imaging and emergency radiology.
However, degree of improvement varied among models; GPT-3.5-turbo and
Mixtral-8x7B-instruct-v0.1 saw notable gains, while Mistral-7B-instruct-v0.2
showed no improvement, highlighting variability in its effectiveness. LLMs
benefit when provided access to domain-specific data beyond their training
data. For radiology, RadioRAG establishes a robust framework that substantially
improves diagnostic accuracy and factuality in radiological question answering.


  We present a neural rendering framework that maps a voxelized scene into a
high quality image. Highly-textured objects and scene element interactions are
realistically rendered by our method, despite having a rough representation as
an input. Moreover, our approach allows controllable rendering: geometric and
appearance modifications in the input are accurately propagated to the output.
The user can move, rotate and scale an object, change its appearance and
texture or modify the position of the light and all these edits are represented
in the final rendering. We demonstrate the effectiveness of our approach by
rendering scenes with varying appearance, from single color per object to
complex, high-frequency textures. We show that our rerendering network can
generate very detailed images that represent precisely the appearance of the
input scene. Our experiments illustrate that our approach achieves more
accurate image synthesis results compared to alternatives and can also handle
low voxel grid resolutions. Finally, we show how our neural rendering framework
can capture and faithfully render objects from real images and from a diverse
set of classes.


  Starting from large cardinals we construct a model of $ZFC$ in which the
$GCH$ fails everywhere, but such that $GCH$ holds in its $HOD$. The result
answers a question of Sy Friedman. Also, relative to the existence of large
cardinals, we produce a model of $ZFC+GCH$ such that $GCH$ fails everywhere in
its $HOD$.


  Traffic dynamics on single or isolated complex networks has been extensively
studied in the past decade. Recently, several coupled network models have been
developed to describe the interactions between real-world networked systems. In
a system of interconnected networks, the coupling links refer to the physical
links between networks and provide paths for traffic transmission. Thus, the
coupling pattern, i.e., the way coupling links are added, has a profound
influence on the overall traffic performance. In this paper, we employ a
simulated annealing (SA) algorithm to find a near-optimal configuration of the
coupling links, which effectively improves the overall traffic capacity
compared with random, assortative and disassortative couplings. Furthermore, we
investigate the optimal configuration of coupling links given by the SA
algorithm and develop a faster method to select the coupling links.


  MOLLER is a future experiment designed to measure parity violation in Moller
scattering to extremely high precision. MOLLER will measure the right-left
scattering differential cross-section parity-violating asymmetry APV , in the
elastic scattering of polarized electrons off an unpolarized LH2 target to
extreme ppb precision. To make this measurement, the polarized electron source,
generated with a circularly polarized laser beam, must have the ability to
switch quickly between right and left helicity polarization states. The
polarized source must also maintain minimal right-left helicity correlated beam
asymmetries, including energy changes, position changes, intensity changes, or
spot-size changes. These requirements can be met with appropriate choice and
design of the Pockels cell used to generate the circularly polarized light.
Rubidium Titanyl Phosphate (RTP) has been used in recent years for ultra-fast
Pockels cell switches due to its lack of piezo-electric resonances at
frequencies up to several hundred MHz. However, crystal non-uniformity in this
material leads to poorer extinction ratios than in commonly used KD*P Pockels
cells when used in hald-wave configuration. It leads to voltage dependent beam
steering when used in quarter-wave configuration. Here we present an innovative
RTP Pockels cell design which uses electric field gradients to counteract
crystal non-uniformities and control beam steering down to the nm-level. We
demonstrate this RTP Pockels cell design is capable of producing precisely
controlled polarized electron beam at Jefferson Laboratory, a national
accelerator facility, for current experiments, including the recent PREX II
measurement, as well as the future MOLLER experiment.


  Given a countable metric space, we can consider its end. Then a basis of a
Hilbert space indexed by the metric space defines an end of the Hilbert space,
which is a new notion and different from an end as a metric space.
  Such an indexed basis also defines unitary operators of finite propagation,
and these operators preserve an end of a Hilbert space. Then, we can define a
Hilbert bundle with end, which lightens up new structures of Hilbert bundles.
In a special case, we can define characteristic classes of Hilbert bundles with
ends, which are new invariants of Hilbert bundles. We show Hilbert bundles with
ends appear in natural contexts. First, we generalize the pushforward of a
vector bundle along a finite covering to an infinite covering, which is a
Hilbert bundle with end under a mild condition. Then we compute characteristic
classes of some pushforwards along infinite coverings. Next, we will show the
spectral decompositions of nice differential operators give rise to Hilbert
bundles with ends, which elucidate new features of spectral decompositions. The
spectral decompositions we will consider are the Fourier transform and the
harmonic oscillators.


  Cooperative behavior lies at the very basis of human societies, yet its
evolutionary origin remains a key unsolved puzzle. Whereas reciprocity or
conditional cooperation is one of the most prominent mechanisms proposed to
explain the emergence of cooperation in social dilemmas, recent experimental
findings on networked Prisoner's Dilemma games suggest that conditional
cooperation also depends on the previous action of the player---namely on the
`mood' in which the player currently is. Roughly, a majority of people behaves
as conditional cooperators if they cooperated in the past, while they ignore
the context and free-ride with high probability if they did not. However, the
ultimate origin of this behavior represents a conundrum itself. Here we aim
specifically at providing an evolutionary explanation of moody conditional
cooperation. To this end, we perform an extensive analysis of different
evolutionary dynamics for players' behavioral traits---ranging from standard
processes used in game theory based on payoff comparison to others that include
non-economic or social factors. Our results show that only a dynamic built upon
reinforcement learning is able to give rise to evolutionarily stable moody
conditional cooperation, and at the end to reproduce the human behaviors
observed in the experiments.


  We construct a uniformly expanding map of the interval, preserving Lebesgue
measure, such that the corresponding transfer operator admits a spectral gap on
the space of Lipschitz functions, but does not act continuously on the space of
bounded variation functions.


  Enzyme-mediated reactions may proceed through multiple intermediate
conformational states before creating a final product molecule, and one often
wishes to identify such intermediate structures from observations of the
product creation. In this paper, we address this problem by solving the
chemical master equations for various enzymatic reactions. We devise a
perturbation theory analogous to that used in quantum mechanics that allows us
to determine the first (<n>) and the second (variance) cumulants of the
distribution of created product molecules as a function of the substrate
concentration and the kinetic rates of the intermediate processes. The mean
product flux V=d<n>/dt (or "dose-response" curve) and the Fano factor
F=variance/<n> are both realistically measurable quantities, and while the mean
flux can often appear the same for different reaction types, the Fano factor
can be quite different. This suggests both qualitative and quantitative ways to
discriminate between different reaction schemes, and we explore this
possibility in the context of four sample multistep enzymatic reactions. We
argue that measuring both the mean flux and the Fano factor can not only
discriminate between reaction types, but can also provide some detailed
information about the internal, unobserved kinetic rates, and this can be done
without measuring single-molecule transition events.


  The thermal stability of 200 nm thick plasma enhanced chemical vapor
deposited a-C:H and a-C:D layers ranging from soft to hard layers has been
studied and compared to that of deposits collected on the Tore Supra tokamak
plasma facing components by means of in-situ Raman spectroscopy. Linear ramp
heating and long term isotherms (from several minutes to 21 days) have been
performed and correlations between spectrometric parameters have been found.
The information obtained on the sp 2 clustering has been investigated by
comparing the G band shift and the 514 nm photon absorption evolution due to
the thermal treatment of the layer. The effects of isotopic substitution have
also been investigated.


  For various positive integers $n$, we show the existence of infinite families
of elliptic curves over $\mathbb{Q}$ with $n$-division fields,
$\mathbb{Q}(E[n])$, that are not monogenic, i.e., the ring of integers does not
admit a power integral basis. We parametrize some of these families explicitly.
Moreover, we show that every $E/\mathbb{Q}$ without CM has infinitely many
non-monogenic division fields. Our main technique combines a global description
of the Frobenius obtained by Duke and T\'oth with a simple algorithm based on
ideas of Dedekind.


  We study classical particles on the sites of an open chain which diffuse,
coagulate and decoagulate preferentially in one direction. The master equation
is expressed in terms of a spin one-half Hamiltonian $H$ and the model is shown
to be completely solvable if all processes have the same asymmetry. The
relaxational spectrum is obtained directly from $H$ and via the equations of
motion for strings of empty sites. The structure and the solvability of these
equations are investigated in the general case. Two phases are shown to exist
for small and large asymmetry, respectively, which differ in their stationary
properties.


  In this contribution we examine the transverse momentum distributions in
dijet production at large rapidity intervals at the Tevatron, using the BFKL
resummation.


  Given a positive function F on S n satisfying an appropriate con-vexity
assumption, we consider hypersurfaces for which a linear combination of some
higher order anisotropic curvatures is constant. We define the varia-tional
problem for which these hypersurfaces are critical points and we prove that, up
to translations and homotheties, the Wulff shape is the only stable closed
hypersurface of the Euclidean space for this problem.


  The Garvey-Kelson relations (GKRs) are algebraic expressions originally
developed to predict nuclear masses. In this letter we show that the GKRs
provide a fruitful framework for the prediction of other physical observables
that also display a slowly-varying dynamics. Based on this concept, we extend
the GKRs to the study of nuclear charge radii. The GKRs are tested on 455 out
of the approximately 800 nuclei whose charge radius is experimentally known. We
find a rms deviation between the GK predictions and the experimental values of
only 0.01 fm. This should be contrasted against some of the most successful
microscopic models that yield rms deviations almost three times as large.
Predictions - with reliable uncertainties - are provided for 116 nuclei whose
charge radius is presently unknown.


  In this comment to [S. Lenjer, O. F. Schirmer, H. Hesse, and Th. W. Kool,
Phys. Rev. B {\bf 66}, 165106 (2002)] we discuss the electronic structure of
oxygen vacancies in perovskites. First principles computations are in favour of
rather deep levels in these vacancies, and Lenjer et al suggest that the
electrons' interaction energy is negative, but data on electroconductivity are
against.


  We consider the problem of energy-efficient scheduling across multiple
processors with a power-down mechanism. In this setting a set of $n$ jobs with
individual release times, deadlines, and processing volumes must be scheduled
across $m$ parallel processors while minimizing the consumed energy. Idle
processors can be turned off to save energy, while turning them on requires a
fixed amount of energy. For the special case of a single processor, the greedy
Left-to-Right algorithm guarantees an approximation factor of $2$. We
generalize this simple greedy policy to the case of $m \geq 1$ processors
running in parallel and show that the energy costs are still bounded by $2
\text{OPT} + P$, where $\text{OPT}$ is the energy consumed by an optimal
solution and $P < \text{OPT}$ is the total processing volume. Our algorithm has
a running time of $\mathcal{O}(n f \log d)$, where $d$ is the difference
between the latest deadline and the earliest release time, and $f$ is the
running time of a maximum flow calculation in a network of $\mathcal{O}(n)$
nodes.


  We report on the status of our QCD thermodynamics project. It is performed on
the QCDOC machine at Brookhaven National Laboratory and the APEnext machine at
Bielefeld University. Using a 2+1 flavor formulation of QCD at almost realistic
quark masses we calculated several thermodynamical quantities. In this
proceeding we show the susceptibilites of the chiral condensate and the
Polyakov loop, the static quark potential and the spatial string tension.


  In this paper, we consider the multi-armed bandit problem with
high-dimensional features. First, we prove a minimax lower bound,
$\mathcal{O}\big((\log d)^{\frac{\alpha+1}{2}}T^{\frac{1-\alpha}{2}}+\log
T\big)$, for the cumulative regret, in terms of horizon $T$, dimension $d$ and
a margin parameter $\alpha\in[0,1]$, which controls the separation between the
optimal and the sub-optimal arms. This new lower bound unifies existing regret
bound results that have different dependencies on T due to the use of different
values of margin parameter $\alpha$ explicitly implied by their assumptions.
Second, we propose a simple and computationally efficient algorithm inspired by
the general Upper Confidence Bound (UCB) strategy that achieves a regret upper
bound matching the lower bound. The proposed algorithm uses a properly centered
$\ell_1$-ball as the confidence set in contrast to the commonly used ellipsoid
confidence set. In addition, the algorithm does not require any forced sampling
step and is thereby adaptive to the practically unknown margin parameter.
Simulations and a real data analysis are conducted to compare the proposed
method with existing ones in the literature.


  The measurement of the mixing angle \theta_{13}, sign of \Delta m^2_{13} and
the CP or T violating phase \delta is fraught with ambiguities in neutrino
oscillation. In this paper we give an analytic treatment of the paramater
degeneracies associated with measuring the \nu_\mu -> \nu_e probability and its
CP and/or T conjugates. For CP violation, we give explicit solutions to allow
us to obtain the regions where there exist two-fold and four-fold degeneracies.
We calculate the fractional differences, \Delta \theta / \bar{\theta}, between
the allowed solutions which may be used to compare with the expected
sensitivities of the experiments. For T violation we show that there is always
a complete degeneracy between solutions with positive and negative \Delta
m^2_{13} which arises due to a symmetry and cannot be removed by observing one
neutrino oscillation probability and its T conjugate. Thus, there is always a
four fold parameter degeneracy apart from exceptional points. Explicit
solutions are also given and the fractional differences are computed. The
bi-probability CP/T trajectory diagrams are extensively used to illuminate the
nature of the degeneracies.


  The application of the conventional saddle-point approximation to condensed
Bose gases is thwarted by the approach of the saddle-point to the ground-state
singularity of the grand canonical partition function. We develop and test a
variant of the saddle-point method which takes proper care of this
complication, and provides accurate, flexible, and computationally efficient
access to both canonical and microcanonical statistics. Remarkably, the error
committed when naively employing the conventional approximation in the
condensate regime turns out to be universal, that is, independent of the
system's single-particle spectrum. The new scheme is able to cover all
temperatures, including the critical temperature interval that marks the onset
of Bose--Einstein condensation, and reveals in analytical detail how this onset
leads to sharp features in gases with a fixed number of particles. In
particular, within the canonical ensemble the crossover from the
high-temperature asymptotics to the condensate regime occurs in an
error-function-like manner; this error function reduces to a step function when
the particle number becomes large. Our saddle-point formulas for occupation
numbers and their fluctuations, verified by numerical calculations, clearly
bring out the special role played by the ground state.


  The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically
samples the exact $N$-body density matrix for interacting electrons at finite
temperature. We introduce a simple modification to the interaction picture
DMQMC method (IP-DMQMC) which overcomes the limitation of only sampling one
inverse temperature point at a time, instead allowing for the sampling of a
temperature range within a single calculation thereby reducing the
computational cost. At the target inverse temperature, instead of ending the
simulation, we incorporate a change of picture away from the interaction
picture. The resulting equations of motion have piecewise functions and use the
interaction picture in the first phase of a simulation, followed by the
application of the Bloch equation once the target inverse temperature is
reached. We find that the performance of this method is similar to or better
than the DMQMC and IP-DMQMC algorithms in a variety of molecular test systems.


  We discuss how the concept of equality is used by mathematicians (including
Grothendieck), and what effect this has when trying to formalise mathematics.
We challenge various reasonable-sounding slogans about equality.


  The pygmy dipole resonance and photon strength functions (PSF) in stable and
unstable Ni and Sn isotopes are calculated within the microscopic
self-consistent version of the extended theory of finite fermi systems in the
quasiparticle time blocking approximation. The approach includes phonon
coupling (PC) effects in addition to the standard QRPA approach. The Skyrme
force SLy4 is used. A pygmy dipole resonance in 72Ni is predicted at the mean
energy of 12.4 MeV exhausting 25.7% of the total energy-weighted sum rule. With
our microscopic E1 PSFs in the EMPIRE 3.1 code, the following radiative nuclear
reaction characteristics have been calculated for several stable and unstable
even-even Sn and Ni isotopes: 1) neutron capture cross sections, 2)
corresponding neutron capture gamma-spectra, 3) average radiative widths of
neutron resonances. Here, three variants of the microscopic nuclear level
density models have been used and a comparison with the phenomenological
generalized superfluid model (GSM) has been performed. In all the considered
properties, including the recent experimental data for PSF in Sn isotopes, the
PC contributions turned out to be significant, as compared with the QRPA one,
and necessary to explain the available experimental data. The phenomenological
GSM NLD model used in EMPIRE3.1 gives, on the whole, the worse results than the
microscopic HFB plus combinatorial NLD model.


  When trapped atoms are illuminated by weak lasers, off-resonant transitions
cause shifts in the frequencies of the vibrational-sideband resonances. These
frequency shifts may be understood in terms of Stark-shifts of the individual
levels or, as proposed here, as a vibrational Bloch-Siegert shift, an effect
closely related to the usual (radio-frequency or optical) Bloch-Siegert shift
and associated with rapidly oscillating terms when the Rotating Wave
Approximation is not made. Explicit analytic expressions are derived and
compared to numerical results, and the similarities and differences between the
usual and the vibrational Bloch-Siegert shifts are also spelled out.


  The goal of future quantum networks is to enable new internet applications
that are impossible to achieve using solely classical communication. Up to now,
demonstrations of quantum network applications and functionalities on quantum
processors have been performed in ad-hoc software that was specific to the
experimental setup, programmed to perform one single task (the application
experiment) directly into low-level control devices using expertise in
experimental physics. Here, we report on the design and implementation of the
first architecture capable of executing quantum network applications on quantum
processors in platform-independent high-level software. We demonstrate the
architecture's capability to execute applications in high-level software, by
implementing it as a quantum network operating system -- QNodeOS -- and
executing test programs including a delegated computation from a client to a
server on two quantum network nodes based on nitrogen-vacancy (NV) centers in
diamond. We show how our architecture allows us to maximize the use of quantum
network hardware, by multitasking different applications on a quantum network
for the first time. Our architecture can be used to execute programs on any
quantum processor platform corresponding to our system model, which we
illustrate by demonstrating an additional driver for QNodeOS for a trapped-ion
quantum network node based on a single $^{40}\text{Ca}^+$ atom. Our
architecture lays the groundwork for computer science research in the domain of
quantum network programming, and paves the way for the development of software
that can bring quantum network technology to society.


  In this paper, we investigate the robust resource allocation design for
secure communication in an integrated sensing and communication (ISAC) system.
A multi-antenna dual-functional radar-communication (DFRC) base station (BS)
serves multiple single-antenna legitimate users and senses for targets
simultaneously, where already identified targets are treated as potential
single-antenna eavesdroppers. The DFRC BS scans a sector with a sequence of
dedicated beams, and the ISAC system takes a snapshot of the environment during
the transmission of each beam. Based on the sensing information, the DFRC BS
can acquire the channel state information (CSI) of the potential eavesdroppers.
Different from existing works that focused on the resource allocation design
for a single snapshot, in this paper, we propose a novel optimization framework
that jointly optimizes the communication and sensing resources over a sequence
of snapshots with adjustable durations. To this end, we jointly optimize the
duration of each snapshot, the beamforming vector, and the covariance matrix of
the AN for maximization of the system sum secrecy rate over a sequence of
snapshots while guaranteeing a minimum required average achievable rate and a
maximum information leakage constraint for each legitimate user. The resource
allocation algorithm design is formulated as a non-convex optimization problem,
where we account for the imperfect CSI of both the legitimate users and the
potential eavesdroppers. To make the problem tractable, we derive a bound for
the uncertainty region of the potential eavesdroppers' small-scale fading based
on a safe approximation, which facilitates the development of a block
coordinate descent-based iterative algorithm for obtaining an efficient
suboptimal solution.


  We derive information bounds for the regression parameters in Cox models when
data are missing at random. These calculations are of interest for
understanding the behavior of efficient estimation in case-cohort designs, a
type of two-phase design often used in cohort studies. The derivations make use
of key lemmas appearing in Robins, Rotnitzky and Zhao [J. Amer. Statist. Assoc.
89 (1994) 846-866] and Robins, Hsieh and Newey [J. Roy. Statist. Soc. Ser. B 57
(1995) 409-424], but in a form suited for our purposes here. We begin by
summarizing the results of Robins, Rotnitzky and Zhao in a form that leads
directly to the projection method which will be of use for our model of
interest. We then proceed to derive new information bounds for the regression
parameters of the Cox model with data Missing At Random (MAR). In the final
section we exemplify our calculations with several models of interest in cohort
studies, including an i.i.d. version of the classical case-cohort design of
Prentice [Biometrika 73 (1986) 1-11]


  If $M$ is a set of nonsingular $k\times k$ matrices then for many pairs of
matrices, $A,B\in M,$ the sum is nonsingular, $\det(A+B)\neq 0.$ We prove a
more general statement on nonsingular sums with an application.


  Graviton propagator diverges in certain gauges in de Sitter spacetime. We
address this problem in this work by generalizing the infinitesimal BRST
transformations in de Sitter spacetime to finite field-dependent BRST (FFBRST)
transformations. These FFBRST transformations are symmetry of the classical
action, but do not leave path integral measure invariant for the graviton
theory in de Sitter spacetime. Due to the non-trivial Jacobian of such finite
transformation the path integral measure changes and hence FFBRST
transformation is capable of relating theories in two different gauges. We
explicitly construct FFBRST transformation which relates theory with diverging
graviton two-point function to theory with infrared (IR) finite graviton. The
FFBRST transformation thus establishes that divergence in graviton two-point
function may be only a gauge artifact.


  Stochastic Structural Stability Theory (S3T) provides analytical methods for
understanding the emergence and equilibration of jets from the turbulence in
planetary atmospheres based on the dynamics of the statistical mean state of
the turbulence closed at second order. Predictions for formation and
equilibration of turbulent jets made using S3T are critically compared with
results of simulations made using the associated quasi-linear and nonlinear
models. S3T predicts the observed bifurcation behavior associated with the
emergence of jets, their equilibration and their breakdown as a function of
parameters. Quantitative differences in bifurcation parameter values between
predictions of S3T and results of nonlinear simulations are traced to
modification of the eddy spectrum which results from two processes: nonlinear
eddy-eddy interactions and formation of discrete non-zonal structures.
Remarkably, these non-zonal structures, which substantially modify the
turbulence spectrum, are found to arise from S3T instability. Formation as
linear instabilities and equilibration at finite amplitude of multiple
equilibria for identical parameter values in the form of jets with distinct
meridional wavenumbers is verified as is the existence at equilibrium of finite
amplitude non-zonal structures in the form of nonlinearly modified Rossby
waves. When zonal jets and nonlinearly modified Rossby waves coexist at finite
amplitude the jet structure is generally found to dominate even if it is
linearly less unstable. The physical reality of the manifold of S3T jets and
non-zonal structures is underscored by the existence in nonlinear simulations
of jet structure at subcritical S3T parameter values which are identified with
stable S3T jet modes excited by turbulent fluctuations.


  A disentangled representation of a data set should be capable of recovering
the underlying factors that generated it. One question that arises is whether
using Euclidean space for latent variable models can produce a disentangled
representation when the underlying generating factors have a certain
geometrical structure. Take for example the images of a car seen from different
angles. The angle has a periodic structure but a 1-dimensional representation
would fail to capture this topology. How can we address this problem? The
submissions presented for the first stage of the NeurIPS2019 Disentanglement
Challenge consist of a Diffusion Variational Autoencoder ($\Delta$VAE) with a
hyperspherical latent space which can, for example, recover periodic true
factors. The training of the $\Delta$VAE is enhanced by incorporating a
modified version of the Evidence Lower Bound (ELBO) for tailoring the encoding
capacity of the posterior approximate.


  The cube graph Q_n is the skeleton of the n-dimensional cube. It is an
n-regular graph on 2^n vertices. The Ramsey number r(Q_n, K_s) is the minimum N
such that every graph of order N contains the cube graph Q_n or an independent
set of order s. Burr and Erdos in 1983 asked whether the simple lower bound
r(Q_n, K_s) >= (s-1)(2^n - 1)+1 is tight for s fixed and n sufficiently large.
We make progress on this problem, obtaining the first upper bound which is
within a constant factor of the lower bound.


  We prove that \[ \sum_{k,{\ell}=1}^N\frac{(n_k,n_{\ell})^{2\alpha}}{(n_k
n_{\ell})^{\alpha}} \ll N^{2-2\alpha} (\log N)^{b(\alpha)} \] holds for
arbitrary integers $1\le n_1<\cdots < n_N$ and $0<\alpha<1/2$ and show by an
example that this bound is optimal, up to the precise value of the exponent
$b(\alpha)$. This estimate complements recent results for $1/2\le \alpha \le 1$
and shows that there is no "trace" of the functional equation for the Riemann
zeta function in estimates for such GCD sums when $0<\alpha<1/2$.


  The gauge invariant formulation of Maxwell's equations and the
electromagnetic duality transformations are given in the light-front (LF)
variables. The novel formulation of the LF canonical quantization, which is
based on the kinematic translation generator $P^{+}$ rather then on the
Hamiltonian $P^{-}$, is proposed. This canonical quantization is applied for
the free electromagnetic fields and for the fields generated by electric and
magnetic external currents. The covariant form of photon propagators, which
agrees with Schwinger's source theory, is achieved when the direct interaction
of external currents is properly chosen. Applying the path integral formalism,
the equivalent LF Lagrangian density, which depends on two Abelian gauge
potentials, is proposed. Some remarks on the Dirac strings and LF non local
structures are presented in the Appendix.


  In this paper, several convergence results for fine $p$-(super)minimizers on
quasiopen sets in metric spaces are obtained. For this purpose, we deduce a
Caccioppoli-type inequality and local-to-global principles for fine
$p$-(super)minimizers on quasiopen sets. A substantial part of these
considerations is to show that the functions belong to a suitable local fine
Sobolev space. We prove our results for a complete metric space equipped with a
doubling measure supporting a $p$-Poincar\'e inequality with $1<p< \infty$.
However, most of the results are new also for unweighted $\mathbf{R}^n$.


  Let $H$ be a Hardy field (a field consisting of germs of real-valued
functions at infinity that is closed under differentiation) and let $f \in H$
be a subpolynomial function. Let $\mathcal{P} = \{2, 3, 5, 7, \dots \}$ be the
(naturally ordered) set of primes. We show that $(f(n))_{n \in \mathbb{N}}$ is
uniformly distributed mod 1 if and only if $(f(p))_{p \in \mathcal{P}}$ is
uniformly distributed mod 1. This result is then utilized to derive various
ergodic and combinatorial statements which significantly generalize the results
obtained in [BKMST].


  We consider integrable models of the Haldane-Shastry type with open boundary
conditions. We define monodromy matrices, obeying the reflection equation,
which generate the symmetries of these models. Using a map to the
Calogero-Sutherland Hamiltonian of BC type, we derive the spectrum and the
highest weight eigenstates.


  We compute numerically the dimensions and OPE coefficients of several
operators in the 3d Ising CFT, and then try to reverse-engineer the solution to
crossing symmetry analytically. Our key tool is a set of new techniques for
computing infinite sums of SL(2,R) conformal blocks. Using these techniques, we
solve the lightcone bootstrap to all orders in an asymptotic expansion in large
spin, and suggest a strategy for going beyond the large spin limit. We carry
out the first steps of this strategy for the 3d Ising CFT, deriving analytic
approximations for the dimensions and OPE coefficients of several infinite
families of operators in terms of the initial data
$\{\Delta_\sigma,\Delta_\epsilon,f_{\sigma\sigma\epsilon},f_{\epsilon\epsilon\epsilon},c_T\}$.
The analytic results agree with numerics to high precision for about 100
low-twist operators (correctly accounting for O(1) mixing effects between
large-spin families). Plugging these results back into the crossing equations,
we obtain approximate analytic constraints on the initial data.


  Motivated by constraint-based CAD software, we develop the foundation for the
rigidity theory of a very general model: the body-and-cad structure, composed
of rigid bodies in 3D constrained by pairwise coincidence, angular and distance
constraints. We identify 21 relevant geometric constraints and develop the
corresponding infinitesimal rigidity theory for these structures. The classical
body-and-bar rigidity model can be viewed as a body-and-cad structure that uses
only one constraint from this new class. As a consequence, we identify a new,
necessary, but not sufficient, counting condition for minimal rigidity of
body-and-cad structures: nested sparsity. This is a slight generalization of
the well-known sparsity condition of Maxwell.


  We study the orthogonal projections of a large class of self-affine carpets,
which contains the carpets of Bedford and McMullen as special cases. Our main
result is that if $\Lambda$ is such a carpet, and certain natural irrationality
conditions hold, then every orthogonal projection of $\Lambda$ in a
non-principal direction has Hausdorff dimension $\min(\gamma,1)$, where
$\gamma$ is the Hausdorff dimension of $\Lambda$. This generalizes a recent
result of Peres and Shmerkin on sums of Cantor sets.


  We find supersymmmetric configurations of a D5-brane probe in the
Maldacena-Nunez background which are extended along one or two of the spatial
directions of the gauge theory. These embeddings are worldvolume solitons which
behave as codimension two or one defects in the gauge theory and preserve two
of the four supersymmetries of the background.


  Holomorphy of the superpotential promotes any continuous symmetry group G to
a complexified symmetry group G_C of the superpotential. For U(1) symmetry this
means that the superpotential is not only invariant under U(1) phase rotation
but also under some scaling. We use complexified R-symmetry to study the
connection between choices of U(1) R-charges and existence of runaway
directions as well as supersymmetry breaking global minimum in generic and
calculable models.


  Crack propagation in viscoelastic solids like rubber is of great practical
importance. Shrimali and Lopez-Pamies have proposed a new interesting approach
for the crack propagation in viscoelastic solids. We give comments on the
validity of the theory and point out some effects not included in the theory.


  We report on our study of the infrared gluon propagator for SU(2) lattice
gauge theory using large lattice volumes. The observed massive behavior is
discussed from the point of view of analytic predictions for the
zero-temperature case. Such a behavior is still present as the temperature is
switched on, but manifests itself differently in the electric and magnetic
channels.


  The objectives of this research are analysing the performance of the
state-of-the-art machine learning techniques for classifying COVID-19 from
cough sound and identifying the model(s) that consistently perform well across
different cough datasets. Different performance evaluation metrics (such as
precision, sensitivity, specificity, AUC, accuracy, etc.) make it difficult to
select the best performance model. To address this issue, in this paper, we
propose an ensemble-based multi-criteria decision making (MCDM) method for
selecting top performance machine learning technique(s) for COVID-19 cough
classification. We use four cough datasets, namely Cambridge, Coswara, Virufy,
and NoCoCoDa to verify the proposed method. At first, our proposed method uses
the audio features of cough samples and then applies machine learning (ML)
techniques to classify them as COVID-19 or non-COVID-19. Then, we consider a
multi-criteria decision-making (MCDM) method that combines ensemble
technologies (i.e., soft and hard) to select the best model. In MCDM, we use
the technique for order preference by similarity to ideal solution (TOPSIS) for
ranking purposes, while entropy is applied to calculate evaluation criteria
weights. In addition, we apply the feature reduction process through recursive
feature elimination with cross-validation under different estimators. The
results of our empirical evaluations show that the proposed method outperforms
the state-of-the-art models.


  We consider $q$-analytic derivations of the $q$-Gauss summation formula for a
$\, _2\phi _1$ that respect the symmetry in its upper parameters.


  We make the first study the optical energy level structure and interactions
of pairs of single rare earth ions using a hybrid electro-optical detection
method applied to Er-implanted silicon. Two examples of Er3+ pairs were
identified in the optical spectrum by their characteristic energy level
splitting patterns, and linear Zeeman spectra were used to characterise the
sites. One pair is positively identified as two identical Er3+ ions in sites of
at least C2 symmetry coupled via a large, 200 GHz Ising-like spin interaction
and 1.5 GHz resonant optical interaction. Small non-Ising contributions to the
spin interaction are attributed to distortion of the site measurable because of
the high resolution of the single-ion measurement. The interactions are
compared to previous measurements made using rare earth ensemble systems, and
the application of this type of strongly coupled ion array to quantum computing
is discussed.


  We propose a single-photon frequency converter via a one-dimensional
waveguide coupled to a $V$-type atom. The on-demand classical field allows the
atom to absorb a photon with a given frequency, then emit a photon with a
carried frequency different from the absorbed one. The absorption and
re-emission process is formulated as a two-channel scattering process. We study
the single-photon frequency conversion mechanism in two kinds of realistic
physical system: coupled resonator waveguide with cosine dispersion relation
and an optical waveguide with linear dispersion relation respectively. We find
that the driving field prefers weak in coupled resonator waveguide but
arbitrarily strong in optical waveguide to achieve an optical transfer
efficiency.


  Very High Energy (VHE) gamma rays constitute one of the main pillars of high
energy astrophysics. Gamma rays are produced under extreme relativistic
conditions in the Universe. VHE gamma$ rays can be detected indirectly on the
ground. Detection of these energetic photons poses several technological
challenges. Firstly, even though gamma rays are highly penetrative, the Earth's
atmosphere is opaque to them. Secondly, these gamma rays are to be detected
against the overwhelming background of cosmic rays. When a VHE gamma ray
arrives at the top of the atmosphere it produces charged secondaries. These
charged particles produce Cherenkov flashes in the optical band. Even though
the first attempts to detect these Cherenkov flashes were made almost 70 years
ago, it took several decades of relentless efforts to streamline the technique.
Ground-based VHE gamma-ray astronomy has now established itself as one of the
crucial branches of conventional high energy astronomy to study the
relativistic Universe. In this article we look back and present a historical
perspective followed by a discussion on the current status and finally what
lies ahead.


  We develop a stochastic volatility framework for modeling multiple currencies
based on CBI-time-changed L\'evy processes. The proposed framework captures the
typical risk characteristics of FX markets and is coherent with the symmetries
of FX rates. Moreover, due to the self-exciting behavior of CBI processes, the
volatilities of FX rates exhibit self-exciting dynamics. By relying on the
theory of affine processes, we show that our approach is analytically tractable
and that the model structure is invariant under a suitable class of
risk-neutral measures. A semi-closed pricing formula for currency options is
obtained by Fourier methods. We propose two calibration methods, also by
relying on deep-learning techniques, and show that a simple specification of
the model can achieve a good fit to market data on a currency triangle.


  A cyber-attack is a malicious attempt by experienced hackers to breach the
target information system. Usually, the cyber-attacks are characterized as
hybrid TTPs (Tactics, Techniques, and Procedures) and long-term adversarial
behaviors, making the traditional intrusion detection methods ineffective. Most
existing cyber-attack detection systems are implemented based on manually
designed rules by referring to domain knowledge (e.g., threat models, threat
intelligences). However, this process is lack of intelligence and
generalization ability. Aiming at this limitation, this paper proposes an
intelligent cyber-attack detection method based on provenance data. To
effective and efficient detect cyber-attacks from a huge number of system
events in the provenance data, we firstly model the provenance data by a
heterogeneous graph to capture the rich context information of each system
entities (e.g., process, file, socket, etc.), and learns a semantic vector
representation for each system entity. Then, we perform online cyber-attack
detection by sampling a small and compact local graph from the heterogeneous
graph, and classifying the key system entities as malicious or benign. We
conducted a series of experiments on two provenance datasets with real
cyber-attacks. The experiment results show that the proposed method outperforms
other learning based detection models, and has competitive performance against
state-of-the-art rule based cyber-attack detection systems.


  We investigate complex boundary conditions of the miscible displacement
system in two and three space dimensions with the commonly-used
Bear-Scheidegger diffusion-dispersion tensor, which describes, e.g., the porous
medium flow processes in petroleum reservoir simulation or groundwater
contaminant transport. Specifically, we incorporate the no-flux boundary
condition for the Darcy velocity to prove that the general no-flux boundary
condition for the transport equation is equivalent to the normal derivative
boundary condition of the concentration, based on which we further prove
several complex boundary conditions by the Bear-Scheidegger tensor and its
derivative. The derived boundary conditions not only provide new insights and
distinct properties of the Bear-Scheidegger diffusion-dispersion tensor, but
accommodate the coupling and the nonlinearity of the miscible displacement
system and the Bear-Scheidegger tensor in deriving the first-order optimality
condition of the corresponding optimal control problem for practical
application.


  We present a model for neutrino flares in accreting black holes based on the
injection of a non-thermal population of relativistic particles in a magnetized
corona. The most important products of hadronic and photohadronic interactions
at high energies are pions. Charged pions decay into muons and neutrinos; muons
also decay yielding neutrinos. Taking into account these effects, coupled
transport equations are solved for all species of particles and the neutrino
production is estimated for the case of accreting galactic black holes.


  We present discovery observations of a quasar in the Canada-France High-z
Quasar Survey (CFHQS) at redshift z=6.44. We also use near-IR spectroscopy of
nine CFHQS quasars at z~6 to determine black hole masses. These are compared
with similar estimates for more luminous Sloan Digital Sky Survey (SDSS)
quasars to investigate the relationship between black hole mass and quasar
luminosity. We find a strong correlation between MgII FWHM and UV luminosity
and that most quasars at this early epoch are accreting close to the Eddington
limit. Thus these quasars appear to be in an early stage of their life cycle
where they are building up their black hole mass exponentially. Combining these
results with the quasar luminosity function, we derive the black hole mass
function at z=6. Our black hole mass function is ~10^4 times lower than at z=0
and substantially below estimates from previous studies. The main uncertainties
which could increase the black hole mass function are a larger population of
obscured quasars at high-redshift than is observed at low-redshift and/or a low
quasar duty cycle at z=6. In comparison, the global stellar mass function is
only ~10^2 times lower at z=6 than at z=0. The difference between the black
hole and stellar mass function evolution is due to either rapid early star
formation which is not limited by radiation pressure as is the case for black
hole growth or inefficient black hole seeding. Our work predicts that the black
hole mass - stellar mass relation for a volume-limited sample of galaxies
declines rapidly at very high redshift. This is in contrast to the observed
increase at 4<z<6 from the local relation if one just studies the most massive
black holes.


  Despite substantial progress in abstractive text summarization to generate
fluent and informative texts, the factual inconsistency in the generated
summaries remains an important yet challenging problem to be solved. In this
paper, we construct causal graphs for abstractive text summarization and
identify the intrinsic causes of the factual inconsistency, i.e., the language
bias and irrelevancy bias, and further propose a debiasing framework, named
CoFactSum, to alleviate the causal effects of these biases by counterfactual
estimation. Specifically, the proposed CoFactSum provides two counterfactual
estimation strategies, i.e., Explicit Counterfactual Masking with an explicit
dynamic masking strategy, and Implicit Counterfactual Training with an implicit
discriminative cross-attention mechanism. Meanwhile, we design a Debiasing
Degree Adjustment mechanism to dynamically adapt the debiasing degree at each
decoding step. Extensive experiments on two widely-used summarization datasets
demonstrate the effectiveness of CoFactSum in enhancing the factual consistency
of generated summaries compared with several baselines.


  In this paper, we study a certain cohomology attached to a smooth function,
which arose naturally in Poisson geometry. We explain how this cohomology
depends on the function, and we prove that it satisfies both the excision and
the Mayer-Vietoris axioms. For a regular function we show that the cohomology
is related to the de Rham cohomology. Finally, we use it to give a new proof of
a well-known result of A. Dimca in complex analytic geometry.


  We compute the sphere and disk partition functions in semiclassical Liouville
and analogous quantities in double-scaled matrix integrals. The quantity
sphere/disk^2 is unambiguous and we find a precise numerical match between the
Liouville answer and the matrix integral answer. An application is to show that
the sphere partition function in JT gravity is infinite.


  We present combinatorial upper bounds on dimensions of certain imaginary root
spaces for symmetric Kac-Moody algebras. These come from the realization of the
corresponding infinity-crystal using quiver varieties. The framework is
general, but we only work out specifics in rank two. In that case we give
explicit bounds. These turn out to be quite accurate, and in many cases exact,
even for some fairly large roots.


  Exciton-polaritons, hybrid light-matter elementary excitations arising from
the strong coupling regime between excitons in semiconductors and photons in
photonic nanostructures, offer a fruitful playground to explore the physics of
quantum fluids of light as well as to develop all-optical devices. However,
achieving room temperature propagation of polaritons with a large excitonic
fraction, which would be crucial, e.g., for nonlinear light transport in
prospective devices, remains a significant challenge. } Here we report on
experimental studies of exciton-polariton propagation at room temperature in
resonant metasurfaces made from a sub-wavelength lattice of perovskite pillars.
Thanks to the large Rabi splitting, an order of magnitude larger than the
optical phonon energy, the lower polariton band is completely decoupled from
the phonon bath of perovskite crystals. The long lifetime of these cooled
polaritons, in combination with the high group velocity achieved through the
metasurface design, enables long-range propagation regardless of the polariton
excitonic fraction. Remarkably, we observed propagation distances exceeding
hundreds of micrometers at room temperature, even when the polaritons possess a
very high excitonic component, approximately {80}$\%$. Furthermore, the design
of the metasurface introduces an original mechanism for directing
uni-directional propagation through polarization control. This discovery of a
ballistic propagation mode, leveraging high-speed cooled polaritons, heralds a
promising avenue for the development of advanced polaritonic devices.


  We report a strategy based on introduction of point defects for improving the
thermoelectric properties of FeSb2, a promising candidate for low temperature
applications. Introduction of Sb deficiency to the tune of 20% leads to
enhancement in the values of electrical conductivity ({\sigma}) and Seebeck
coefficient (S) accompanied with a concomitant suppression in lattice thermal
conductivity (\k{appa}lat) values in samples prepared using conventional solid
state reaction route. These observations in polycrystalline FeSb2-x provides
ample motivation for a dedicated exploration of thermoelectric behavior of the
corresponding single crystalline as well as hot-pressed polycrystalline
counterparts.


  The structure of effective potential surface of the Nambu$-$Jona-Lasinio
(NJL) model with right-left asymmetric Majorana mass terms (corresponds to the
single-flavor type-II seesaw situation of neutrino) is investigated. After the
dynamical generation of Dirac mass, two collective modes appear similar to the
case of ordinary NJL model, and the phase mode (phason), which corresponds to
majoron or pion at vanishing Majorana mass parameter(s), has an excitation
mass. The mechanism of generation of phason as a pseudo Nambu-Goldstone boson
is examined by a mathematical manner, summarized into a theorem
  (claims as the generalized Nambu-Goldstone theorem). The mass of phason is
also evaluated in a supersymmetric version of the NJL-type model, and phason
mass takes the order of that of axion commonly accepted today. An
$SU(2_{c})$-gauge model is constructed for the context of neutrino seesaw
mechanism, and the Schwinger-Dyson equation of dynamical mass functions is
examined. Several physical implications such as decay modes of phason, a
non-linear sigma model for phason are given. It is proposed that the
method/result of this paper can be applied to an understanding on the origin of
the Kobayashi-Maskawa matrix.


  We discuss time-optimal control problems for two setups involving globally
driven Rydberg atoms in the blockade limit by deriving the associated
Hamilton-Jacobi-Bellman equations. From these equations, we extract the
globally optimal trajectories and the corresponding controls for several target
processes of the atomic system, using a generalized method of characteristics.
We apply this method to retrieve known results for CZ and C-phase gates, and to
find new optimal pulses for all elementary processes involved in the universal
quantum computation scheme introduced in [Physical Review Letters 131, 170601
(2023)].


  The robustness of complex networks with dependencies has been studied in
recent years. However, previous studies focused on the robustness of networks
composed of dependency links without network topology. In this study, we will
analyze the percolation properties of a realistic network model where
dependency links follow certain network topology. We perform the theoretical
analysis and numerical simulations to show the critical effects of topology of
dependency links on robustness of complex networks. For Erd\"os-R\'enyi (ER)
connectivity network, we find that the system with dependency of RR topology is
more vulnerable than system with dependency of ER topology. And RR-RR (i.e.
random-regular (RR) network with dependency of RR topology) disintegrates in an
abrupt transition. In particular, we find that the system of RR-ER shows
different types of phase transitions. For system of different combinations, the
type of percolation depends on the interaction between connectivity topology
and dependency topology.


  We consider a class of single-particle one-dimensional stochastic equations
which include external field, additive and multiplicative noises. We use a
parameter $\theta \in [0,1]$ which enables the unification of the traditional
It\^o and Stratonovich approaches, now recovered respectively as the $\theta=0$
and $\theta=1/2$ particular cases to derive the associated Fokker-Planck
equation (FPE). These FPE is a {\it linear} one, and its stationary state is
given by a $q$-Gaussian distribution with $q = \frac{\tau + 2M (2 -
\theta)}{\tau + 2M (1 - \theta)}<3$, where $\tau \ge 0$ characterizes the
strength of the confining external field, and $M \ge 0$ is the (normalized)
amplitude of the multiplicative noise. We also calculate the standard kurtosis
$\kappa_1$ and the $q$-generalized kurtosis $\kappa_q$ (i.e., the standard
kurtosis but using the escort distribution instead of the direct one). Through
these two quantities we numerically follow the time evolution of the
distributions. Finally, we exhibit how these quantities can be used as
convenient calibrations for determining the index $q$ from numerical data
obtained through experiments, observations or numerical computations.


  Academic reading is a key component of higher education, and serves as a
basis for critical thinking, knowledge acquisition and effective communication.
Research shows many students struggle with comprehension and analysis tasks
with academic texts, despite the central importance of academic reading to
success in higher education. Undergraduates and researchers need to internalize
dense literature to scaffold their own work upon it. This reading task is
time-consuming and difficult to do. Oftentimes, students struggle to actively
and critically engage and as a result attain merely a cursory understanding of
a paper's contents, or worse, incorrectly interpret the text. How, then, can we
provide a means to more easily digest a text whilst also facilitating
meaningful, critical engagement and understanding? This paper locates itself
within the broader field of Human-Computer Interaction (HCI) to implement an
augmented reading interface that leverages the power of ChatGPT to
intelligently generate and co-locate comprehension and analysis questions in an
academic paper, thereby making the paper more digestible with the end goal of
facilitating deeper understanding, and developing critical reading skills.


  We study photoionization of various noble gas atoms by attosecond pulses
produced in High Harmonic Generation (HHG). We use a pump-probe experiment to
measure the time delays of electrons photoionized from Neon, Argon, and Krypton
relative to those photoionized from Helium atoms. The Attosecond Pulse Train
(APT) is characterized and the relative delay in photoionization of various
noble gases is measured. The photoionization delay of Ne, Ar, and Kr is
determined using previously calculated values for the He atomic delay and the
delay associated with the probe process.


  We consider the full driven quantum dynamics of a qubit realized as spin of
electron in a one-dimensional double quantum dot with spin-orbit coupling. The
driving perturbation is taken in the form of a single half-period pulse of
electric field. Spin-orbit coupling leads to a nontrivial evolution in the spin
and charge densities making the dynamics in both quantities irregular. As a
result, the charge density distribution becomes strongly spin-dependent. The
transition from the field-induced tunneling to the strong coupling regime is
clearly seen in the charge and spin channels. These results can be important
for the understanding of the techniques for the spin manipulation in
nanostructures.


  Thermal fluctuations in the coatings used to make high-reflectors are
becoming significant noise sources in precision optical measurements and are
particularly relevant to advanced gravitational wave detectors. There are two
recognized sources of coating thermal noise, mechanical loss and thermal
dissipation. Thermal dissipation causes thermal fluctuations in the coating
which produce noise via the thermo-elastic and thermo-refractive mechanisms. We
treat these mechanisms coherently, give a correction for finite coating
thickness, and evaluate the implications for Advanced LIGO.


  We show that Kellendonk's tiling semigroup of an FLC substitution tiling is
self-similar, in the sense of Bartholdi, Grigorchuk and Nekrashevych. We extend
the notion of the limit space of a self-similar group to the setting of
self-similar semigroups, and show that it is homeomorphic to the
Anderson--Putnam complex for such substitution tilings, with natural self-map
induced by the substitution. Thus, the inverse limit of the limit space, given
by the limit solenoid of the self-similar semigroup, is homeomorphic to the
translational hull of the tiling.


  We exploit a connection between distances in the infinite percolation
cluster, when the parameter is close to one, and the discrete-time TASEP on
$\mathbb{Z}$. This shows that when the parameter goes to one, large balls in
the cluster are asymptotically shaped near the axes like arcs of parabola.


  Given a compact four-dimensional Riemannian manifold $(M, g)$ with boundary,
we study the problem of existence of Riemannian metrics on $M$ conformal to $g$
with prescribed $Q$-curvature in the interior $\mathring{M}$ of $M$, and zero
$T$-curvature and mean curvature on the boundary $\partial M$ of $M$. This
geometric problem is equivalent to solving a fourth-order elliptic boundary
value problem (BVP) involving the Paneitz operator with boundary conditions of
Chang-Qing and Neumann operators. The corresponding BVP has a variational
formulation but the corresponding variational problem, in the case under study,
is not compact. To overcome such a difficulty we perform a systematic study,
\`a la Bahri, of the so called {\it critical points at infinity}, compute their
Morse indices, determine their contribution to the difference of topology
between the sublevel sets of associated Euler-Lagrange functional and hence
extend the full Morse Theory to this noncompact variational problem. To
establish Morse inequalities we were led to investigate from the topological
viewpoint the space of boundary-weighted barycenters of the underlying
manifold, which arise in the description of the topology of very negative
sublevel sets of the related functional. As an application of our approach we
derive various existence results and provide a Poincar\'e-Hopf type criterium
for the prescribed $Q$-curvature problem on compact four dimensional Riemannian
manifolds with boundary.


  As humans, we understand events in the visual world contextually, performing
multimodal reasoning across time to make inferences about the past, present,
and future. We introduce MERLOT, a model that learns multimodal script
knowledge by watching millions of YouTube videos with transcribed speech -- in
an entirely label-free, self-supervised manner. By pretraining with a mix of
both frame-level (spatial) and video-level (temporal) objectives, our model not
only learns to match images to temporally corresponding words, but also to
contextualize what is happening globally over time. As a result, MERLOT
exhibits strong out-of-the-box representations of temporal commonsense, and
achieves state-of-the-art performance on 12 different video QA datasets when
finetuned. It also transfers well to the world of static images, allowing
models to reason about the dynamic context behind visual scenes. On Visual
Commonsense Reasoning, MERLOT answers questions correctly with 80.6% accuracy,
outperforming state-of-the-art models of similar size by over 3%, even those
that make heavy use of auxiliary supervised data (like object bounding boxes).
  Ablation analyses demonstrate the complementary importance of: 1) training on
videos versus static images; 2) scaling the magnitude and diversity of the
pretraining video corpus; and 3) using diverse objectives that encourage
full-stack multimodal reasoning, from the recognition to cognition level.


  We present a new method to solve the dynamical Bethe-Salpeter Equation
numerically. The method allows one to investigate the effects of dynamical
dielectric screening on the spectral position of excitons in transition-metal
dichalcogenide monolayers. The dynamics accounts for the response of optical
phonons in the materials below and on top the monolayer to the electric field
lines between the electron and hole of the exciton. The inclusion of this
effect unravels the origin of a counterintuitive energy blueshift of the
exciton resonance, observed recently in monolayer semiconductors that are
supported on ionic crystals with large dielectric constants. A surprising
result is that while energy renormalization of a free electron in the
conduction band or a free hole in the valence band is controlled by the
low-frequency dielectric constant, the bandgap energy introduces a phase
between the photoexcited electron and hole, rendering contributions from the
high-frequency dielectric constant also important when evaluating self-energies
of the exciton components. As a result, bandgap renormalization of the exciton
is not the sum of independent contributions from energy shifts of the
conduction and valence bands. The theory correctly predicts the energy shifts
of exciton resonances in various dielectric environments that embed
two-dimensional semiconductors.


  Large language model (LLM) applications, such as ChatGPT, are a powerful tool
for online information-seeking (IS) and problem-solving tasks. However, users
still face challenges initializing and refining prompts, and their cognitive
barriers and biased perceptions further impede task completion. These issues
reflect broader challenges identified within the fields of IS and interactive
information retrieval (IIR). To address these, our approach integrates task
context and user perceptions into human-ChatGPT interactions through prompt
engineering. We developed a ChatGPT-like platform integrated with supportive
functions, including perception articulation, prompt suggestion, and
conversation explanation. Our findings of a user study demonstrate that the
supportive functions help users manage expectations, reduce cognitive loads,
better refine prompts, and increase user engagement. This research enhances our
comprehension of designing proactive and user-centric systems with LLMs. It
offers insights into evaluating human-LLM interactions and emphasizes potential
challenges for under served users.


  The Fermi Large Area Telescope observed an excess in gamma ray emission
spectrum coming from the center of the Milky Way galaxy. This data reveals that
a light Dark Matter (DM) candidate of mass in the range 31-40 GeV, dominantly
decaying into $b\bar b$ final state, can explain the presence of the observed
bump in photon energy. We try to interpret this observed phenomena by sneutrino
DM annihilation into pair of fermions in the Supersymmetric Inverse Seesaw
Model (SISM). This model can also account for tiny non-zero neutrino masses
satisfying existing neutrino oscillation data. We show that a Higgs portal DM
in this model is in perfect agreement with this new interpretation besides
satisfying all other existing collider, cosmological and low energy
experimental constraints.


  In this paper, we consider a kind of area preserving non-local flow for
convex curves in the plane. We show that the flow exists globally, the length
of evolving curve is non-increasing, and the curve converges to a circle in
C^{\infty} sense as time goes into infinity.


  The problem of the choice of tensor product decomposition in a system of two
fermions with the help of Bogoliubov transformations of creation and
annihilation operators is discussed. The set of physical states of the
composite system is restricted by the superselection rule forbidding the
superposition of fermions and bosons. It is shown that the Wootters concurrence
is not proper entanglement measure in this case. The explicit formula for the
entanglement of formation is found and its dependence on tensor product
decompositions of the Hilbert space is discussed. It is shown that the set of
separable states is narrower than in two-qubit case. Moreover, there exist
states which are separable with respect to all tensor product decompositions of
the Hilbert space.