  With the massive increase in the popularity of smartphones and mobile data
applications demanding bandwidth requiring data rates of the order of Gigabits
per second, exploration of untapped frequency spectrum such as millimeter-wave
has begun. Along with providing seamless connectivity and catering to achieving
high Quality of Service and Quality of Experience, investigations are ongoing
to enhance our knowledge about biological safety at high frequencies. There is
a need to ensure safety and reliability for the exposed public and updating the
government policies regarding safety standards and regulations. This article is
consecrated to provide an insight into health effects pertaining to millimeter
frequencies, addressing aspects such as thermal heating in the body tissues
with temperature rise, specific absorption rate, power density. As a solution,
a proposal has been given for Electromagnetic radiation reduction for the
mobile communication system in the form of a proposed mode that is, Thermal
Radiation mode endorsing its safe use, promoting Green WCN along with increased
energy efficiency and reduced complexity for the future generations to come.
The proposal also validates reduced power density, Specific Absorption Rate,
and temperature elevation produced in the human tissue when compared to other
models in the form of simulation results obtained. It can increase the safety
and reliability of 5G and beyond i.e. 6G networks in the future.


  We present lower and upper bounds for the geometric-arithmetic index of
unicyclic graphs and provide extremal graphs for the corresponding bounds.


  We have measured the effect of dipole-dipole interactions on the frequency of
a collective mode of a Bose-Einstein condensate. At relatively large numbers of
atoms, the experimental measurements are in good agreement with zero
temperature theoretical predictions based on the Thomas Fermi approach.
Experimental results obtained for the dipolar shift of a collective mode show a
larger dependency to both the trap geometry and the atom number than the ones
obtained when measuring the modification of the condensate aspect ratio due to
dipolar forces. These findings are in good agreement with simulations based on
a gaussian ansatz.


  The gravitational modes of the Kerr geometry include both quasinormal modes
and total-transmission modes. Sequences of these modes are parameterized by the
angular momentum of the black hole. The quasinormal and total-transmission
modes are usually distinct, having mode frequencies that are different at any
given value of the angular momentum. But a discrete and countably infinite
subset of the left-total-transmission modes are simultaneously quasinormal
modes. Most of these special modes exist along previously unknown branches of
the gravitational total-transmission modes. In this paper, we give detailed
plots of the total-transmission modes for harmonic indices $\ell=[2,7]$, with
special emphasis given to the $m=0$ modes which all contain previously unknown
branches. All of these unknown branches have purely imaginary mode frequencies.
We find that as we approach the Schwarzschild limit along these new branches,
the mode frequencies approach $-i\infty$ in stark contrast to the finite mode
frequency obtained in the Schwarzschild limit along the previously known
branches. We explain when and why, at certain frequencies, the
left-total-transmission modes are simultaneously quasinormal modes. At these
same frequencies, the right-total-transmission modes are missing. We also
derive analytic expressions for the asymptotic behavior of the
total-transmission mode frequencies, and for the values of the angular momentum
at which the modes are simultaneously quasinormal modes.


  We present an improved model for the antenna phase center motion effect for
high-gain mechanically steerable ground-based and spacecraft-mounted antennas
that takes into account non-perfect antenna pointing. Using tracking data of
the RadioAstron spacecraft we show that our model can result in a correction of
the computed value of the effect of up to $2\times10^{-14}$ in terms of the
fractional frequency shift, which is significant for high-accuracy spacecraft
tracking experiments. The total fractional frequency shift due to the phase
center motion effect can exceed $1\times10^{-11}$ both for the ground and space
antennas depending on the spacecraft orbit and antenna parameters. We also
analyze the error in the computed value of the effect and find that it can be
as large as $4\times10^{-14}$ due to uncertainties in the spacecraft antenna
axis position, ground antenna axis offset and misalignment, and others.
Finally, we present a way to reduce both the ground and space antenna phase
center motion effects by several orders of magnitude, e.g. for RadioAstron to
below $1\times10^{-16}$, by tracking the spacecraft simultaneously in the
one-way downlink and two-way phase-locked loop modes, i.e. using the Gravity
Probe A configuration of the communications links.


  In seven dimensions any spin manifold admits an SU(2) structure and therefore
very general M-theory compactifications have the potential to allow for a
reduction to N=4 gauged supergravity. We perform this general SU(2) reduction
and give the relation of SU(2) torsion classes and fluxes to gaugings in the
N=4 theory. We furthermore show explicitly that this reduction is a consistent
truncation of the eleven-dimensional theory, in other words classical solutions
of the reduced theory also solve the eleven-dimensional equations of motion.
This reduction generalizes previous M-theory reductions on Tri-Sasakian
manifolds and type IIA reductions on Calabi-Yau manifolds of vanishing Euler
number. Moreover, it can also be applied to compactifications on certain G2
holonomy manifolds and to more general flux backgrounds.


  The paper studies the exact solution of two kinds of generalized
Fokker-Planck equations in which the integral kernels are given either by the
distributed order function $k_{1}(t) = \int_{0}^{1} t^{-\mu}/\Gamma(1- \mu)
d\mu$ or the distributed order Prabhakar function $k_{2}(\alpha, \gamma;
\lambda; t) = \int_{0}^{1} e^{-\gamma}_{\alpha, 1 - \mu}(\lambda; t) d\mu$,
where the Prabhakar function is denoted as $e^{-\gamma}_{\alpha, 1 -
\mu}(\lambda; t)$. Both of these integral kernels can be called the fading
memory functions and are the Stieltjes functions. It is also shown that their
Stieltjes character is enough to ensure the non-negativity of the mean square
values and higher even moments. The odd moments vanish. Thus, the solution of
generalized Fokker-Planck equations can be called the probability density
functions. We introduce also the Volterra-Prabhakar function and its
generalization which are involved in the definition of $k_{2}(\alpha, \gamma;
\lambda; t)$ and generated by it the probability density function $p_2(x, t)$.


  Current medical artificial intelligence systems are often limited to narrow
applications, hindering their widespread adoption in clinical practice. To
address this limitation, we propose MedVersa, a generalist learner that enables
flexible learning and tasking for medical image interpretation. By leveraging a
large language model as a learnable orchestrator, MedVersa can learn from both
visual and linguistic supervision, support multimodal inputs, and perform
real-time task specification. This versatility allows MedVersa to adapt to
various clinical scenarios and perform multifaceted medical image analysis. We
introduce MedInterp, the largest multimodal dataset to date for medical image
interpretation, consisting of over 13 million annotated instances spanning 11
tasks across 3 modalities, to support the development of MedVersa. Our
experiments demonstrate that MedVersa achieves state-of-the-art performance in
9 tasks, sometimes outperforming specialist counterparts by over 10%. MedVersa
is the first to showcase the viability of multimodal generative medical AI in
implementing multimodal outputs, inputs, and dynamic task specification,
highlighting its potential as a multifunctional system for comprehensive
medical image analysis. This generalist approach to medical image
interpretation paves the way for more adaptable and efficient AI-assisted
clinical decision-making.


  This paper addresses the complexity reduction of stochastic homogenisation of
a class of random materials for a stationary diffusion equation. A
cost-efficient approximation of the correctors is built using a method designed
to exploit quasi-periodicity. Accuracy and cost reduction are investigated for
local perturbations or small transformations of periodic materials as well as
for materials with no periodicity but a mesoscopic structure, for which the
limitations of the method are shown. Finally, for materials outside the scope
of this method, we propose to use the approximation of homogenised quantities
as control variates for variance reduction of a more accurate and costly Monte
Carlo estimator (using a multi-fidelity Monte Carlo method). The resulting cost
reduction is illustrated in a numerical experiment with a control variate from
weakly stochastic homogenisation for comparison, and the limits of this
variance reduction technique are tested on materials without periodicity or
mesoscopic structure.


  In this study, an early fire detection algorithm has been proposed based on
low cost array sensing system, utilizing gas sensors, dust particles and
ambient sensors such as temperature and humidity sensor. The odor or
smell-print emanated from various fire sources and building construction
materials at early stage are measured. For this purpose, odor profile data from
five common fire sources and three common building construction materials were
used to develop the classification model. Normalized feature extractions of the
smell print data were performed before subjected to prediction classifier.
These features represent the odor signals in the time domain. The obtained
features undergo the proposed multi-stage feature selection technique and
lastly, further reduced by Principal Component Analysis (PCA), a dimension
reduction technique. The hybrid PCA-PNN based approach has been applied on
different datasets from in-house developed system and the portable electronic
nose unit. Experimental classification results show that the dimension
reduction process performed by PCA has improved the classification accuracy and
provided high reliability, regardless of ambient temperature and humidity
variation, baseline sensor drift, the different gas concentration level and
exposure towards different heating temperature range.


  In the present paper our aim is to introduce some models for the
generalization of the kinetic theory of electrons and phonons (KTEP), as well
as to study equilibrium solutions and their stability for the generalized KTEP
(GKTEP) equations. We consider a couple of models, relevant to non standard
quantum statistics, which give rise to inverse power law decays of the
distribution function with respect to energy. In the case of electrons in a
phonon background, equilibrium and stability are investigated by means of
Lyapounov theory. Connections with thermodynamics are pointed out.


  This paper is concerned with the existence of multiple points of Gaussian
random fields. Under the framework of Dalang et al. (2017), we prove that, for
a wide class of Gaussian random fields, multiple points do not exist in
critical dimensions. The result is applicable to fractional Brownian sheets and
the solutions of systems of stochastic heat and wave equations.


  Imaging of flux vortices in high quality MgB$_2$ single crystals has been
successfully performed in a commercial Field Emission Gun-based Transmission
Electron Microscope. In Cryo-Lorentz Microscopy, the sample quality and the
vortex lattice can be monitored simultaneously, allowing one to relate
microscopically the surface quality and the vortex dynamics. Such a vortex
motion ultimately determines the flow resistivity, $\rho_{f}$, the knowledge of
which is indispensable for practical applications such as superconducting
magnets or wires for Magnetic Resonance Imaging. The observed patterns have
been analyzed and compared with other studies by Cryo-Lorentz Microscopy or
Bitter decoration. We find that the vortex lattice arrangement depends strongly
on the surface quality obtained during the specimen preparation, and tends to
form an hexagonal Abrikosov lattice at a relatively low magnetic field. Stripes
or gossamer-like patterns, recently suggested as potential signatures of an
unconventional behavior of MgB$_2$, were not observed.


  Model-agnostic meta-learning (MAML) is one of the most successful
meta-learning algorithms. It has a bi-level optimization structure where the
outer-loop process learns a shared initialization and the inner-loop process
optimizes task-specific weights. Although MAML relies on the standard gradient
descent in the inner-loop, recent studies have shown that controlling the
inner-loop's gradient descent with a meta-learned preconditioner can be
beneficial. Existing preconditioners, however, cannot simultaneously adapt in a
task-specific and path-dependent way. Additionally, they do not satisfy the
Riemannian metric condition, which can enable the steepest descent learning
with preconditioned gradient. In this study, we propose Geometry-Adaptive
Preconditioned gradient descent (GAP) that can overcome the limitations in
MAML; GAP can efficiently meta-learn a preconditioner that is dependent on
task-specific parameters, and its preconditioner can be shown to be a
Riemannian metric. Thanks to the two properties, the geometry-adaptive
preconditioner is effective for improving the inner-loop optimization.
Experiment results show that GAP outperforms the state-of-the-art MAML family
and preconditioned gradient descent-MAML (PGD-MAML) family in a variety of
few-shot learning tasks. Code is available at:
https://github.com/Suhyun777/CVPR23-GAP.


  We investigate the effect of including the HERA run I + II combined cross
section data on the MMHT2014 PDFs. We present the fit quality within the
context of the global fit and when only the HERA data are included. We examine
the changes in both the central values and uncertainties in the PDFs. We find
that the prediction for the data is good, and only relatively small
improvements in $\chi^2$ and changes in the PDFs are obtained with a refit at
both NLO and NNLO. PDF uncertainties are slightly reduced. There is a small
dependence of the fit quality on the value of $Q^2_{\min}$. This can be
improved by phenomenologically motived corrections to $F_L(x,Q^2)$ which
parametrically are largely in the form of higher-twist type contributions.


  The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a
mean-field theory of out-of-time-ordered commutators in locally interacting
quantum chaotic systems at high energy density; in the systems with power-law
interactions, the corresponding fractional-derivative FKPP equation provides an
analogous mean-field theory. However, the fractional FKPP description is
potentially subject to strong quantum fluctuation effects, so it is not clear a
priori if it provides a suitable effective description for generic chaotic
systems with power-law interactions. Here we study this problem using a model
of coupled quantum dots with interactions decaying as $\frac{1}{r^{\alpha}}$,
where each dot hosts $N$ degrees of freedom. The large $N$ limit corresponds to
the mean-field description, while quantum fluctuations contributing to the OTOC
can be modeled by $\frac{1}{N}$ corrections consisting of a cutoff function and
noise. Within this framework, we show that the parameters of the effective
theory can be chosen to reproduce the butterfly light cone scalings that we
previously found for $N=1$ and generic finite $N$. In order to reproduce these
scalings, the fractional index $\mu$ in the FKPP equation needs to be shifted
from the na\"ive value of $\mu = 2\alpha - 1$ to a renormalized value $\mu =
2\alpha - 2$. We provide supporting analytic evidence for the cutoff model and
numerical confirmation for the full fractional FKPP equation with cutoff and
noise.


  Coarse-graining techniques play a central role in reducing the complexity of
stochastic models, and are typically characterised by a mapping which projects
the full state of the system onto a smaller set of variables which captures the
essential features of the system. Starting with a continuous-time Markov chain,
in this work we propose and analyse an effective dynamics, which approximates
the dynamical information in the coarse-grained chain. Without assuming
explicit scale-separation, we provide sufficient conditions under which this
effective dynamics stays close to the original system and provide quantitative
bounds on the approximation error. We also compare the effective dynamics and
corresponding error bounds to the averaging literature on Markov chains which
involve explicit scale-separation. We demonstrate our findings on an
illustrative test example.


  We present a proposal to realize the quantum Zeno effect (QZE) and quantum
Zeno-like effect (QZLE) in a proximal $\mathrm{^{13}C}$ nuclear spin by
controlling a proximal electron spin of a nitrogen vacancy (NV) center. The
measurement is performed by applying a microwave pulse to induce the transition
between different electronic spin states. Under the practical experimental
conditions, our calculations show that there exist both QZE and QZLE in a
$^{13}$C nuclear spin in the vicinity of an NV center.


  We investigate the evolution of Ca 2p and Sr 3d core level spectra in
Ca(1-x)SrxRuO3 using photoemission spectroscopy. Core level spectra in this
system exhibit multiple features and unusual evolution with the composition and
temperatures. Analysis of the core level spectra in conjunction with the band
structure results reveal novel final state effects due to different core hole
screening channels. Changes in the core level spectra suggest significant
modification in Ca-O covalency in Ca dominated samples, which gradually reduces
with the increase in Sr content and becomes minimum in SrRuO3. This study thus,
provides a direct evidence of the role of cation-oxygen covalency in the ground
state properties of these novel materials.


  There has been significant recent interest in developing AI agents capable of
effectively interacting and teaming with humans. While each of these works try
to tackle a problem quite central to the problem of human-AI interaction, they
tend to rely on myopic formulations that obscure the possible inter-relatedness
and complementarity of many of these works. The human-aware AI framework was a
recent effort to provide a unified account for human-AI interaction by casting
them in terms of their relationship to various mental models. Unfortunately,
the current accounts of human-aware AI are insufficient to explain the
landscape of the work doing in the space of human-AI interaction due to their
focus on limited settings. In this paper, we aim to correct this shortcoming by
introducing a significantly general version of human-aware AI interaction
scheme, called generalized human-aware interaction (GHAI), that talks about
(mental) models of six types. Through this paper, we will see how this new
framework allows us to capture the various works done in the space of human-AI
interaction and identify the fundamental behavioral patterns supported by these
works. We will also use this framework to identify potential gaps in the
current literature and suggest future research directions to address these
shortcomings.


  The kinematic properties of young stars that have not yet reached the stage
of the main sequence are studied. The selection of these stars was recently
carried out by Marton et al. (2019) and Vioque et al. (2020) according to the
Gaia DR2 catalog using a number of photometric infrared surveys. We have
determined the rotation parameters of the Galaxy and the parameters of the
ellipsoids of the residual velocities. The linear velocity of the circular
rotation of a solar region around the center of the Galaxy, found using 4431
stars, is equal to V_0=229.1+-4.4 km/s. The following ellipsoid parameters of
their residual velocities are found from low-mass stars (of type T Tau):
$\sigma_{1,2,3}=(9.45,6.99,6.61)\pm(0.94,0.43,0.32)$ km/s. For stars of
intermediate masses (Herbig Ae/Be stars), their values turned out to be
somewhat larger $\sigma_{1,2,3}=(13.67,9.25,7.26)\pm(2.40,2.44,0.88)$ km/s.
Distant stars from both Catalogs trace the local spiral arm well. For 1212
stars, a new estimate of the pitch angle of the Local spiral arm is equal to
i=-8.9+-0.1 deg.


  We theoretically investigate the Fano effect in dc Josephson current at the
absolute zero of temperature. The system under consideration is a double-path
Josephson junction in which one path is through an insulating barrier and the
other one is through a quantum dot (QD). Here the Kondo temperature is assumed
to be much smaller than the superconducting gap, and the Coulomb interaction
inside the QD is treated by the Hartree-Fock approximation. It is shown that
the Josephson critical current exhibits an asymmetric resonance against the QD
energy level. This behavior is caused by the interference between the two
tunneling processes between the superconductors; the direct tunneling across
the insulating barrier and the resonant one through the QD. Moreover, we find
that the Josephson critical current changes its sign around the resonance when
the Coulomb interaction is sufficiently strong. Our results suggest that
0-$\pi$ transition is induced by the cooperation of the Fano effect and the
Coulomb interaction inside the QD.


  The rest-frame instant form of the positive-energy part of the open Nambu
string is developed. The string is described as a decoupled non-local canonical
non-covariant Newton-Wigner center of mass plus a canonical basis of
Wigner-covariant relative variables living in the Wigner 3-spaces. The center
of mass carries a realization of the Poincare' algebra depending upon the
invariant mass and the rest-spin of the string, functions of the relative
variables. A canonical basis of gauge invariant Dirac observables is built with
Frenet-Serret geometrical methods. Some comments on canonical quantization are
made.


  Materials that exhibit ferroaxial order hold potential for novel multiferroic
applications. However, in pure ferroaxials, domains are not directly coupled to
stress or static electric field due to their symmetry, limiting the ability to
pole and switch between domains -- features required for real-world
applications. Here we propose a general approach to selectively condense and
switch between ferroaxial domains with light. We show that circularly polarized
light pulses on resonance with infrared-active phonons manifest
helicity-dependent control over ferroaxial domains. Nonlinear contributions to
the lattice polarizability play an essential role in this phenomenon. We
illustrate the feasibility of our approach using first-principle calculations
and dynamical simulations for the archetypal ferroaxial material
RbFe(MoO$_4$)$_2$. Our results are discussed in the context of future
pump-probe optical experiments, where polarization, carrier frequency, and
fluence threshold are explored.


  Interval graphs are intersection graphs of closed intervals of the real-line.
The well-known computational problem, called recognition, asks whether an input
graph $G$ can be represented by closed intervals, i.e., whether $G$ is an
interval graph. There are several linear-time algorithms known for recognizing
interval graphs, the oldest one is by Booth and Lueker [J. Comput. System Sci.,
13 (1976)] based on PQ-trees.
  In this paper, we study a generalization of recognition, called partial
representation extension. The input of this problem consists of a graph $G$
with a partial representation $\cal R'$ fixing the positions of some intervals.
The problem asks whether it is possible to place the remaining interval and
create an interval representation $\cal R$ of the entire graph $G$ extending
$\cal R'$. We generalize the characterization of interval graphs by Fulkerson
and Gross [Pac. J. Math., 15 (1965)] to extendible partial representations.
Using it, we give a linear-time algorithm for partial representation extension
based on a reordering problem of PQ-trees.


  We study the local persistence probability during non-stationary time
evolutions in disordered contact processes with long-range interactions by a
combination of the strong-disorder renormalization group (SDRG) method, a
phenomenological theory of rare regions, and numerical simulations. We find
that, for interactions decaying as an inverse power of the distance, the
persistence probability tends to a non-zero limit not only in the inactive
phase but also in the critical point. Thus, unlike in the contact process with
short-range interactions, the persistence in the limit $t\to\infty$ is a
discontinuous function of the control parameter. For stretched exponentially
decaying interactions, the limiting value of the persistence is found to remain
continuous, similar to the model with short-range interactions.


  The effect of Mg-substitution on the crystal structure of wurtzite ZnO is
presented based on synchrotron X-ray diffraction studies of polycrystalline
Zn1-xMgxO (0 <= x <= 0.15). Increase in Mg concentration results in pronounced
c-axis compression of the hexagonal lattice, and in diminution of the
off-center cation displacement within each tetrahedral ZnO4 unit. Going from
ZnO to Zn0.85Mg0.15O, significant changes in the ionic polarization are
observed (-5.6 to -4.8 uC/cm2), despite only subtle increments in the cell
volume (~0.03 %) and the ab-area dimension (~0.1 %). The optical properties of
the samples have also been characterized and the band gap changes from 3.24 eV
(ZnO) to 3.35 eV (Zn0.85Mg0.15O).


  Through an exact method we numerically solve the time evolution of the
density profile for an initially localized state in the one-dimensional bosons
with repulsive short-range interactions. We show that a localized state with a
density notch is constructed by superposing one-hole excitations. The initial
density profile overlaps the plot of the squared amplitude of a dark soliton in
the weak coupling regime. We observe the localized state collapsing into a flat
profile in equilibrium for a large number of particles such as N=1000. The
relaxation time increases as the coupling constant decreases, which suggests
the existence of off-diagonal long-range order. We show a recurrence phenomenon
for a small number of particles such as N=20.


  We investigate age and metallicity distributions of bright globular clusters
(GCs) in the candidate intermediate-age early-type galaxies NGC 3610, NGC 584
and NGC 3377 using a combination of new Gemini/NIRI K'-band imaging and
existing optical V,I photometry from HST data. The V-I vs I-K' colour-colour
diagram is found to break the age-metallicity degeneracy present in optical
colours, as I-K' primarily measures a populations' metallicity and is
relatively insensitive, unlike optical spectroscopy, to the effect of hot
horizontal branch (HB) stars, known to be present in massive old GCs. We derive
GCs' photometric age, Z and masses. In general, metal-poor ([Z/H]<-0.7dex) GCs
are older than more metal-rich GCs. For the most massive GCs (M>6x10^5 M_sol)
in NGC 3610 with available spectroscopic data, photometric ages are older by ~2
Gyr, and this difference is more pronounced for the metal-poor GCs. However,
photometric and spectroscopic metallicities are in good agreement. We suggest
that this indicates the presence of a hot HB in these massive clusters, which
renders spectroscopic ages from Balmer line strengths to be underestimated. To
support this suggestion we show that all Galactic GCs with M>6x10^5 M_sol
feature hot HBs, except 47 Tuc. Using the relation between the most massive GC
mass and the galaxy's SFR, we find that the galaxies' peak SFR was attained at
the epoch of the formation of the oldest (metal-poor) GCs. Age and [Z/H]
distributions of the metal-rich GCs are broad, indicating prolonged galaxy star
formation histories. The peak value of the age and [Z/H] distributions of the
GCs correlates with host galaxy integrated age and [Z/H], showing that GCs can
indeed be used as relevant proxies of the star formation histories of
galaxies.(Abridged)


  We show how to solve initial-boundary value problems for integrable nonlinear
differential-difference equations on a finite set of integers. The method we
employ is the discrete analogue of the unified transform (Fokas method). The
implementation of this method to the Ablowitz-Ladik system yields the solution
in terms of the unique solution of a matrix Riemann-Hilbert problem, which has
a jump matrix with explicit $(n,t)$-dependence involving certain functions
referred to as spectral functions. Some of these functions are defined in terms
of the initial value, while the remaining spectral functions are defined in
terms of two sets of boundary values. These spectral functions are not
independent but satisfy an algebraic relation called global relation. We
analyze the global relation to characterize the unknown boundary values in
terms of the given initial and boundary values. We also discuss the
linearizable boundary conditions.


  The healthcare industry is growing rapidly in the United States because of
the increased number of the aging population, shared consciousness of personal
health problems, and medical technology improvements. As a result of the
growing industry of healthcare, new emerging issues occur in the collection and
storage of patient data, and new ways to process, analyze and distribute these
data. This has exposed various security threats to personal health data (Lee,
2022). In this case study, we will discuss the issues Vanderbilt University
Medical Center (VUMC) challenges while implementing EHR systems which are used
to analyze and monitor health records by the users such as doctors,
organizations staff, and pharmaceutical agencies(Kaul et al., 2020), and we
will analyze these issues and provide solutions and recommendations to solve
them.


  Decentralized learning is widely employed for collaboratively training models
using distributed data over wireless networks. Existing decentralized learning
methods primarily focus on training single-modal networks. For the
decentralized multi-modal learning (DMML), the modality heterogeneity and the
non-independent and non-identically distributed (non-IID) data across devices
make it difficult for the training model to capture the correlated features
across different modalities. Moreover, modality competition can result in
training imbalance among different modalities, which can significantly impact
the performance of DMML. To improve the training performance in the presence of
non-IID data and modality heterogeneity, we propose a novel DMML with knowledge
distillation (DMML-KD) framework, which decomposes the extracted feature into
the modality-common and the modality-specific components. In the proposed
DMML-KD, a generator is applied to learn the global conditional distribution of
the modality-common features, thereby guiding the modality-common features of
different devices towards the same distribution. Meanwhile, we propose to
decrease the number of local iterations for the modalities with fast training
speed in DMML-KD to address the imbalanced training. We design a balance metric
based on the parameter variation to evaluate the training speed of different
modalities in DMML-KD. Using this metric, we optimize the number of local
iterations for different modalities on each device under the constraint of
remaining energy on devices. Experimental results demonstrate that the proposed
DMML-KD with training balance can effectively improve the training performance
of DMML.


  It is of general agreement that a quantum gravity theory will most probably
mean a breakdown of the standard structure of space-time at the Planck scale.
This has motivated the study of Planck-scale Lorentz Invariance Violating (LIV)
theories and the search for its observational signals. Yet, it has been
recently shown that, in a simple scalar-spinor Yukawa theory, radiative
corrections to tree-level Planck-scale LIV theories can induce large Lorentz
violations at low energies, in strong contradiction with experiment, unless an
unnatural fine-tuning mechanism is present. In this letter, we show the
calculation of the electron self-energy in the framework given by the
Myers-Pospelov model for a Lorentz Invariance Violating QED. We find a
contribution that depends on the prefered's frame four-velocity which is not
Planck-scale suppressed, showing that this model suffers from the same disease.
Comparison with Hughes-Drever experiments requires a fine-tuning of 21 orders
of magnitude for this model not to disagree with experiment.


  Designing systems that can reason across cultures requires that they are
grounded in the norms of the contexts in which they operate. However, current
research on developing computational models of social norms has primarily
focused on American society. Here, we propose a novel approach to discover and
compare descriptive social norms across Chinese and American cultures. We
demonstrate our approach by leveraging discussions on a Chinese Q&A platform
(Zhihu) and the existing SocialChemistry dataset as proxies for contrasting
cultural axes, align social situations cross-culturally, and extract social
norms from texts using in-context learning. Embedding Chain-of-Thought
prompting in a human-AI collaborative framework, we build a high-quality
dataset of 3,069 social norms aligned with social situations across Chinese and
American cultures alongside corresponding free-text explanations. To test the
ability of models to reason about social norms across cultures, we introduce
the task of explainable social norm entailment, showing that existing models
under 3B parameters have significant room for improvement in both automatic and
human evaluation. Further analysis of cross-cultural norm differences based on
our dataset shows empirical alignment with the social orientations framework,
revealing several situational and descriptive nuances in norms across these
cultures.


  We discuss the four-dimensional cosmological constant problem in a
five-dimensional setting. A scalar field coupled to the SM forms dynamically a
smooth brane with four-dimensional Poincare invariance, independently of SM
physics. In this respect, our solution may be regarded as a self-tuning
solution, free of any singularities and fine-tuning problems.


  We compute the class of a divisor on M_{g,n} given as the closure of the
locus of smooth pointed curves [C; x_1,..., x_n] for which \sum d_j x_j has an
effective representative, where d_j are integers summing up to g-1, not all
positive. The techniques used are a vector bundle computation, a pushdown
argument reducing the number of marked points, and the method of test curves.


  In this paper, we consider a wireless-powered cooperative communication
network, which consists of one hybrid access point (AP), one source and one
relay to assist information transmission. Unlike conventional cooperative
networks, the source and relay are assumed to have no embedded energy supplies
in the considered system. Hence, they need to first harvest energy from the
radio-frequency (RF) signals radiated by the AP in the downlink (DL) before
information transmission in the uplink (UL). Inspired by the recently proposed
harvest-then-transmit (HTT) and harvest-then-cooperate (HTC) protocols, we
develop a new adaptive transmission (AT) protocol. In the proposed protocol, at
the beginning of each transmission block, the AP charges the source. AP and
source then perform channel estimation to acquire the channel state information
(CSI) between them. Based on the CSI estimate, the AP adaptively chooses the
source to perform UL information transmission either directly or cooperatively
with the relay. We derive an approximate closed-form expression for the average
throughput of the proposed AT protocol over Nakagami-m fading channels. The
analysis is then verified by Monte Carlo simulations. Results show that the
proposed AT protocol considerably outperforms both the HTT and HTC protocols.


  The theory of the dislocation motion in the periodic potential relief of the
crystal lattice (the Peierls-Nabarro barriers) is reviewed. On the basis of the
kink mechanism the temperature dependence of the flow stress is described for a
wide class of materials. The theory of quantum mechanical dislocation
tunnelling through the Peierls-Nabarro barriers is extended and compared with
experimental data on the plasticity of alkali halides, BCC and HCP metals at
low temperatures. The behavior of the flow stress at the range of athermic
anomalies is modeled by changing the mechanism of the dislocation motion from
the thermally activated hopping over the barriers to the quantum tunnelling
through them. Some results of previous calculations are represented in a more
explicit convenient for applications form. The pronounced effect of the
switching between the normal and the superconducting states on the flow stress
of metals is explained on the basis of the change in the dissipative properties
of the electron subsystem affecting the dislocation motion.


  The complexity of strongly correlated electron physics in vanadium dioxide is
exemplified as its rich phase diagrams of all kinds, which in turn shed light
on the mechanisms behind its various phase transitions. In this work, we map
out the hydrostatic pressure - temperature phase diagram of vanadium dioxide
nanobeams by independently varying pressure and temperature with a diamond
anvil cell. In addition to the well-known insulating M1 (monoclinic) and
metallic R (tetragonal) phases, the diagram identifies the existence at high
pressures of the insulating M1' (monoclinic, more conductive than M1) phase,
and two metallic phases of X (monoclinic) and O (orthorhombic, at high
temperature only). Systematic optical and electrical measurements combined with
density functional calculations allow us to delineate their phase boundaries as
well as reveal some basic features of the transitions.


  This note introduces a new Bayesian control chart to compare two processes by
monitoring the ratio of their percentiles under Weibull assumption. Both
in-control and out-of-control parameters are supposed unknown. The chart
analyses the sampling data directly, instead of transforming them in order to
comply with the usual normality assumption, as most charts do. The chart uses
the whole accumulated knowledge, resulting from the current and all the past
samples, to monitor the current value of the ratio. Two real applications in
the wood industry and in the concrete industry give a first picture of the
features of the chart.


  We give refined estimates for the discrete time and continuous time versions
of some basic random walks on the symmetric and alternating groups $S_n$ and
$A_n$. We consider the following models: random transposition, transpose top
with random, random insertion, and walks generated by the uniform measure on a
conjugacy class. In the case of random walks on $S_n$ and $A_n$ generated by
the uniform measure on a conjugacy class, we show that in continuous time the
$\ell^2$-cuttoff has a lower bound of $(n/2)\log n$. This result, along with
the results of M\"uller, Schlage-Puchta and Roichman, demonstrates that the
continuous time version of these walks may take much longer to reach
stationarity than its discrete time counterpart.


  Hyper-order cumulants $C_5/C_1$ and $C_6/C_2$ of net-baryon distributions are
anticipated to offer crucial insights into the phase transition from
quark-gluon plasma to hadronic matter in heavy-ion collisions. However, the
accuracy of $C_5$ and $C_6$ is highly contingent on the fine shape of the
distribution's tail, the detectable range of which could be essentially
truncated by low statistics. In this paper, we use the fast Skellam-based
simulations, as well as the Ultrarelativistic Quantum Molecular Dynamics model,
to assess the impact of limited statistics on the measurements of $C_5/C_1$ and
$C_6/C_2$ of net-proton distributions at lower RHIC energies. Both ratios
decrease from the unity baseline as we reduce statistics, and could even turn
negative without a pertinent physics mechanism. By incorporating statistics
akin to experimental data, we can replicate the net-proton $C_5/C_1$ and
$C_6/C_2$ values comparable to the corresponding measurements for Au+Au
collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5 and 14.5 GeV. Our findings underscore
a caveat to the interpretation of the observed beam energy dependence of
hyper-order cumulants.


  Divergences often play important roles for study in information science so
that it is indispensable to investigate their fundamental properties. There is
also a mathematical significance of such results. In this paper, we introduce
some parametric extended divergences combining Jeffreys divergence and Tsallis
entropy defined by generalized logarithmic functions, which lead to new
inequalities. In addition, we give lower bounds for one-parameter extended
Fermi-Dirac and Bose-Einstein divergences. Finally, we establish some
inequalities for the Tsallis entropy, the Tsallis relative entropy and some
divergences by the use of the Young's inequality.


  The ability to uniquely identify a quantum state is integral to quantum
science, but for non-orthogonal states, quantum mechanics precludes
deterministic, error-free discrimination. However, using the non-deterministic
protocol of unambiguous state discrimination (USD) enables error-free
differentiation of states, at the cost of a lower frequency of success. We
discriminate experimentally between non-orthogonal, high-dimensional states
encoded in single photons; our results range from dimension $d=2$ to $d=14$. We
quantify the performance of our method by comparing the total measured error
rate to the theoretical rate predicted by minimum-error state discrimination.
For the chosen states, we find a lower error rate by more than one standard
deviation for dimensions up to $d=12$. This method will find immediate
application in high-dimensional implementations of quantum information
protocols, such as quantum cryptography.


  In this paper we consider completely regular codes, obtained from perfect
(Hamming) codes by lifting the ground field. More exactly, for a given perfect
code C of length n=(q^m-1)/(q-1) over F_q with a parity check matrix H_m, we
define a new code C_{(m,r)} of length n over F_{q^r}, r > 1, with this parity
check matrix H_m. The resulting code C_{(m,r)} is completely regular with
covering radius R = min{r,m}. We compute the intersection numbers of such codes
and, finally, we prove that Hamming codes are the only codes that, after
lifting the ground field, result in completely regular codes.


  Using a generalization of the non-crossing approximation which incorporates
Andreev reflection, we study the properties of an infinite-U Anderson impurity
coupled to two superconducting leads. In the regime where $\Delta$ and $T_K$
are comparable, we find that the position of the sub-gap resonance in the
impurity spectral function develops a strong anomalous phase dependence-- its
energy is a minimum when the phase difference between the superconductors is
equal to $\pi$. Calculating the Josephson current through the impurity, we find
that $\pi$-junction behaviour is lost as the position of the bound-state moves
above the Fermi energy.


  We study a single risky financial asset model subject to price impact and
transaction cost over an finite time horizon. An investor needs to execute a
long position in the asset affecting the price of the asset and possibly
incurring in fixed transaction cost. The objective is to maximize the
discounted revenue obtained by this transaction. This problem is formulated as
an impulse control problem and we characterize the value function using the
viscosity solutions framework. We establish an associated optimal stopping
problem that provides bounds and in some cases the solution of the value
function.


  Let $B^H$ be a fractional Brownian motion on $\mathbb{R}$ with Hurst
parameter $H\in(0,1)$, $F$ be its pathwise antiderivative with $F(0)=0$, and
let $B$ be a standard Brownian motion, independent of $B^H$. We show that the
zero energy part $A_t=F(B_t)-\int_0^t F'(B_s)dB_s$ of $F(B)$ has positive and
finite $p$-variation in a special sense for $p_0=\frac{2}{1+H}$. We also
present some simulation results about the zero energy part of a certain median
process which suggest that its $4/3$-variation is positive and finite.


  In currently most popular explicitly correlated electronic structure theories
the dependence of the wave function on the interelectronic distance rij is
built via the correlation factor f(rij). While the short-distance behavior of
this factor is well understood, little is known about the form of f(rij) at
large rij. In this work we investigate the optimal form of f(r12) on the
example of the helium atom and helium-like ions and several well-motivated
models of the wave function. Using the Rayleigh-Ritz variational principle we
derive a differential equation for f(r12) and solve it using numerical
propagation or analytic asymptotic expansion techniques. We found that for
every model under consideration, f(r12) behaves at large r12 as r12^{\rho}
exp(B r12) and obtained simple analytic expressions for the system dependent
values of {\rho} and B. For the ground state of the helium-like ions the value
of B is positive, so that f(r12) diverges as r12 tends to infinity. The
numerical propagation confirms this result. When the Hartree-Fock orbitals,
multiplied by the correlation factor, are expanded in terms of Slater functions
r^n exp(-{\beta}r), the numerical propagation reveals a minimum in f(r12) with
depth increasing with N. For the lowest triplet state B is negative. Employing
our analytical findings, we propose a new 'range-separated' form of the
correlation factor with the short- and long-range r12 regimes approximated by
appropriate asymptotic formulas connected by a switching function. Exemplary
calculations show that this new form of f(r12) performs somewhat better than
the correlation factors used thus far in the standard R12 or F12 theories.


  Type Ia supernovae are understood to arise from the thermonuclear explosion
of a carbon-oxygen white dwarf, yet the evolutionary mechanisms leading to such
events remain unknown. Many proposed channels, including the classical
single-degenerate scenario, invoke a hot, luminous evolutionary phase for the
progenitor, in which it is a prodigious source of photoionizing emission. Here,
we examine the environment of SN 2014J for evidence of a photoionized nebula in
pre- and post-explosion [O III] $\lambda5007$ \AA\ and H$\beta$ images taken
with the Hubble Space Telescope. From the absence of any extended emission, we
exclude a stable nuclear-burning white dwarf at the location of SN 2014J in the
last ~100,000 years, assuming a typical warm interstellar medium (ISM) particle
density of 1 cm$^{-3}$. These limits greatly exceed existing X-ray constraints
at temperatures typical of known supersoft sources. Significant extreme-UV/soft
X-ray emission prior to explosion remains plausible for lower ISM densities
(e.g., $n_{\rm ISM}\sim 0.1~\rm{cm}^{-3}$). In this case, however, any putative
nebula would be even more extended, allowing deeper follow-up observations to
resolve this ambiguity in the near future.


  We characterize the irreducible representations of the general linear group
GL(V) that have multiplicity 1 in the direct sum of all Schur modules of a
given exterior power of V. These have come up in connection with the relations
of the lower order minors of a generic matrix. We show that the minimal
relations conjectured by Bruns, Conca and Varbaro are exactly those coming from
partitions of single exterior type.


  We give an example of a horocycle in the Teichm\"uller space of the
five-times-punctured sphere that does not converge in the Gardiner--Masur
compactification, or equivalently in the horofunction compactification of the
Teichm\"uller metric. As an intermediate step, we exhibit a simple closed curve
whose extremal length is periodic but not constant along the horocycle. The
example lifts to any Teichm\"uller space of complex dimension greater than one
via covering constructions.


  Residual stress and plastic strain in additive manufactured materials can
exhibit significant microscopic variation at the powder scale, profoundly
influencing the overall properties of printed components. This variation
depends on processing parameters and stems from multiple factors, including
differences in powder bed morphology, non-uniform thermo-structural profiles,
and inter-layer fusion. In this research, we propose a powder-resolved
multilayer multiphysics simulation scheme tailored for porous materials through
the process of selective laser sintering. This approach seamlessly integrates
finite element method (FEM)-based non-isothermal phase-field simulation with
thermo-elasto-plastic simulation, incorporating temperature- and
phase-dependent material properties. The outcome of this investigation includes
a detailed depiction of the mesoscopic evolution of stress and plastic strain
within a transient thermo-microstructure, evaluated across a spectrum of beam
power and scan speed parameters. Simulation results further reveal the
underlying mechanisms. For instance, stress concentration primarily occurs at
the necking region of partially melted particles and the junctions between
different layers, resulting in the accumulation of plastic strain and residual
stress, ultimately leading to structural distortion in the materials. Based on
the simulation data, phenomenological relation regarding porosity/densification
control by the beam energy input was examined along with the comparison to
experimental results. Regression models were also proposed to describe the
dependency of the residual stress and the plastic strain on the beam energy
input.


  Thompson sampling, a Bayesian method for balancing exploration and
exploitation in bandit problems, has theoretical guarantees and exhibits strong
empirical performance in many domains. Traditional Thompson sampling, however,
assumes perfect compliance, where an agent's chosen action is treated as the
implemented action. This article introduces a stochastic noncompliance model
that relaxes this assumption. We prove that any noncompliance in a 2-armed
Bernoulli bandit increases existing regret bounds. With our noncompliance
model, we derive Thompson sampling variants that explicitly handle both
observed and latent noncompliance. With extensive empirical analysis, we
demonstrate that our algorithms either match or outperform traditional Thompson
sampling in both compliant and noncompliant environments.


  We are using the 2dF spectrograph on the Anglo-Australian Telescope to obtain
spectra for a complete sample of all 14000 objects with 16.5<B<19.7 in a 12
square degree area centred on the Fornax cluster. The aims of this project
include the study of dwarf galaxies in the cluster (both known low surface
brightness objects and putative normal surface brightness dwarfs) and a
comparison sample of background field galaxies. We will also measure quasars,
any previously unrecognised compact galaxies and a large sample of Galactic
stars. Here we present initial results from the first 680 objects observed,
including the discovery of a number of dwarf galaxies in the cluster more
compact than any previously known.


  We present high statistics measurements of diboson production in ppbar
collisions at the D\O{} experiment in multiple channels, including $ZZ \to
llll$, $Z\gamma \to \nu\nu\gamma$, $WW \to l \nu l \nu$ and $WW/WZ \to l \nu
jj$. These measurements both test physics beyond the standard model and
demonstrate the sensitivity of hadron colliders to rare signals such as Higgs
boson production.


  Molecular dynamics simulations were carried out to test the thermodynamic
theory of weakly excited, two-dimensional granular systems [Hayakawa and Hong,
Phys. Rev. Lett. 78, 2764 (1997)], where granular materials are viewed as a
collection of spinless Fermions. We first determine the global temperature T by
fitting the steady state density profile to the Fermi distribution function,
and then measure the center of mass, <z(T)>, and its fluctuations, <(\Delta
z(T))^2> as a function of T. We find a fairly good agreement between theory and
simulations, in particular, in the estimation of the temperature and the
scaling behavior of <z(T)> and <(\Delta z(T))^2>.


  Oscillations of the giant magnetoresistance (GMR) and thermo-electric power
(TEP) vs. both the thickness of the non-magnetic spacer and also that of the
ferromagnetic slabs are studied in the current-perpendicular-to-plane (CPP)
geometry of magnetic trilayer systems, in terms of a single-band tight-binding
model without impurities. The spin-dependent conductance has been calculated
from the Kubo formula by means of a recursion Green's function method and the
semi-infinite ideal-lead wires trick. Additionally the TEP is obtained directly
from Mott's formula. In general, the thickness oscillations of the GMR and the
TEP may have just one or two (short and long) oscillations. The long period,
related to spectacular beats, is apparently of non-RKKY type. The TEP
oscillations are strongly enhanced with respect to those of the GMR, have the
same periods, but different phases and a negative bias.


  We study the relationship between the residuality of the set of norm
attaining functionals on a Banach space and the residuality and the denseness
of the set of norm attaining operators between Banach spaces. Our first main
result says that if $C$ is a bounded subset of a Banach space $X$ which admit
an LUR renorming satisfying that, for every Banach space $Y$, the operators $T$
from $X$ to $Y$ for which the supremum of $\|Tx\|$ with $x\in C$ is attained
are dense, then the $G_\delta$ set of those functionals which strongly exposes
$C$ is dense in $X^*$. This extends previous results by J.\ Bourgain and K.-S.\
Lau. The particular case in which $C$ is the unit ball of $X$, in which we get
that the norm of $X^*$ is Fr\'{e}chet differentiable at a dense subset,
improves a result by J.\ Lindenstrauss and we even present an example showing
that Lindenstrauss' result was not optimal. In the reverse direction, we obtain
results for the density of the $G_\delta$ set of absolutely strongly exposing
operators from $X$ to $Y$ by requiring that the set of strongly exposing
functionals on $X$ is dense and conditions on $Y$ or $Y^*$ involving RNP and
discreteness on the set of strongly exposed points of $Y$ or $Y^*$. These
results include examples in which even the denseness of norm attaining
operators was unknown. We also show that the residuality of the set of norm
attaining operators implies the denseness of the set of absolutely strongly
exposing operators provided the domain space and the dual of the range space
are separable, extending a recent result for functionals. Finally, our results
find important applications, among which we point out that we solve a proposed
open problem showing that the unique predual of the space of Lipschitz
functions from the Euclidean unit circle fails to have Lindenstrauss property
A.


  In this paper, we focus on online representation learning in non-stationary
environments which may require continuous adaptation of model architecture. We
propose a novel online dictionary-learning (sparse-coding) framework which
incorporates the addition and deletion of hidden units (dictionary elements),
and is inspired by the adult neurogenesis phenomenon in the dentate gyrus of
the hippocampus, known to be associated with improved cognitive function and
adaptation to new environments. In the online learning setting, where new input
instances arrive sequentially in batches, the neuronal-birth is implemented by
adding new units with random initial weights (random dictionary elements); the
number of new units is determined by the current performance (representation
error) of the dictionary, higher error causing an increase in the birth rate.
Neuronal-death is implemented by imposing l1/l2-regularization (group sparsity)
on the dictionary within the block-coordinate descent optimization at each
iteration of our online alternating minimization scheme, which iterates between
the code and dictionary updates. Finally, hidden unit connectivity adaptation
is facilitated by introducing sparsity in dictionary elements. Our empirical
evaluation on several real-life datasets (images and language) as well as on
synthetic data demonstrates that the proposed approach can considerably
outperform the state-of-art fixed-size (nonadaptive) online sparse coding of
Mairal et al. (2009) in the presence of nonstationary data. Moreover, we
identify certain properties of the data (e.g., sparse inputs with nearly
non-overlapping supports) and of the model (e.g., dictionary sparsity)
associated with such improvements.


  We report on the energetics of the 2012 March 12 polar coronal mass ejection
(CME) originating from a southern latitude of ~60o. The polar CME is similar to
low-latitude CMEs in almost all respects: three-part morphology, post eruption
arcade (PEA), CME and filament kinematics, CME mass and kinetic energy, and the
relative thermal energy content of the PEA. From polarized brightness images,
we estimate the CME mass, which is close to the average mass of low-latitude
CMEs. The CME kinetic energy (3.3x1030 erg) is also typical of the general
population of CMEs. From photospheric magnetograms, we estimate the free energy
(1.8x1031 erg) in the polar crown source region, which we find is sufficient to
power the CME and the PEA. About 19% of the free energy went into the CME
kinetic energy. We compute the thermal energy content of the PEA (2.3x1029 erg)
and find it to be a small fraction (6.8%) of the CME kinetic energy. This
fraction is remarkably similar to that in active region CMEs associated with
major flares. We also show that the 2012 March 12 is one among scores of polar
CMEs observed during the maximum phase of cycle 24. The cycle 24 polar crown
prominence eruptions have the same rate of association with CMEs as those from
low-latitudes. This investigation supports the view that all CMEs are
magnetically propelled from closed field regions, irrespective of their
location on the Sun (polar crown filament regions, quiescent filament regions
or active regions).


  Galaxies and supermassive black holes (SMBHs) are believed to evolve through
a process of hierarchical merging and accretion. Through this paradigm,
multiple SMBH systems are expected to be relatively common in the Universe.
However, to date there are poor observational constraints on multiple SMBHs
systems with separations comparable to a SMBH gravitational sphere of influence
(<< 1 kpc). In this chapter, we discuss how deep continuum observations with
the SKA will make leading contributions towards understanding how multiple
black hole systems impact galaxy evolution. In addition, these observations
will provide constraints on and an understanding of stochastic gravitational
wave background detections in the pulsar timing array sensitivity band (nanoHz
-microHz). We also discuss how targets for pointed gravitational wave
experiments (that cannot be resolved by VLBI) could potentially be found using
the large-scale radio-jet morphology, which can be modulated by the presence of
a close-pair binary SMBH system. The combination of direct imaging at high
angular resolution; low-surface brightness radio-jet tracers; and pulsar timing
arrays will allow the SKA to trace black hole binary evolution from separations
of a galaxy virial radius down to the sub-parsec level. This large dynamic
range in binary SMBH separation will ensure that the SKA plays a leading role
in this observational frontier.


  Atmospheric regime transitions are highly impactful as drivers of extreme
weather events, but pose two formidable modeling challenges: predicting the
next event (weather forecasting), and characterizing the statistics of events
of a given severity (the risk climatology). Each event has a different duration
and spatial structure, making it hard to define an objective "average event."
We argue here that transition path theory (TPT), a stochastic process
framework, is an appropriate tool for the task. We demonstrate TPT's capacities
on a wave-mean flow model of sudden stratospheric warmings (SSWs) developed by
Holton and Mass (1976), which is idealized enough for transparent TPT analysis
but complex enough to demonstrate computational scalability. Whereas a recent
article (Finkel et al. 2021) studied near-term SSW predictability, the present
article uses TPT to link predictability to long-term SSW frequency. This
requires not only forecasting forward in time from an initial condition, but
also \emph{backward in time} to assess the probability of the initial
conditions themselves. TPT enables one to condition the dynamics on the regime
transition occurring, and thus visualize its physical drivers with a vector
field called the \emph{reactive current}. The reactive current shows that
before an SSW, dissipation and stochastic forcing drive a slow decay of vortex
strength at lower altitudes. The response of upper-level winds is late and
sudden, occurring only after the transition is almost complete from a
probabilistic point of view. This case study demonstrates that TPT quantities,
visualized in a space of physically meaningful variables, can help one
understand the dynamics of regime transitions.


  In ultraperipheral collisions (UPCs) of relativistic nuclei without overlap
of nuclear densities, the two nuclei are excited by the Lorentz-contracted
Coulomb fields of their collision partners. In these UPCs, the typical nuclear
excitation energy is below a few tens of MeV, and a small number of nucleons
are emitted in electromagnetic dissociation (EMD) of primary nuclei, in
contrast to complete nuclear fragmentation in hadronic interactions. The cross
sections of emission of given numbers of neutrons in UPCs of $^{208}$Pb nuclei
at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV were measured with the neutron zero degree
calorimeters (ZDCs) of the ALICE detector at the LHC, exploiting a similar
technique to that used in previous studies performed at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. In addition, the cross sections for the
exclusive emission of one, two, three, four, and five forward neutrons in the
EMD, not accompanied by the emission of forward protons, and thus mostly
corresponding to the production of $^{207,206,205,204,203}$Pb, respectively,
were measured for the first time. The predictions from the available models
describe the measured cross sections well. These cross sections can be used for
evaluating the impact of secondary nuclei on the LHC components, in particular,
on superconducting magnets, and also provide useful input for the design of the
Future Circular Collider (FCC-hh).


  With the twelve-year long observations by {\sl Fermi}-LAT, we discover two
pairs of spin-down state transitions of PSR J1124--5916, making it the second
young pulsar detected to have such behaviors. PSR J1124--5916 shows mainly two
states according to its spin-down rate evolution, the normal spin-down state
and the low spin-down state. In about 80\% of the observation time, the pulsar
is in the normal spin-down state, in which the spin-down rate decreases
linearly and gives a braking index of $1.98\pm0.04$. The two transitions to the
low spin-down state are in MJD 55183--55803 and MJD 56114--56398 respectively,
with fractional amplitudes both $\sim0.4\%$. No significant difference between
the $\gamma$-ray profiles of the two spin-down states is detected, which is
similar to PSR B0540-69, the other young pulsar with state transition detected.


  A new method to derive an essential integral kernel from any given
reaction-diffusion network is proposed. Any network describing metabolites or
signals with arbitrary many factors can be reduced to a single or a simpler
system of integro-differential equations called "effective equation" including
the reduced integral kernel (called "effective kernel" ) in the convolution
type. As one typical example, the Mexican hat shaped kernel is theoretically
derived from two component activator-inhibitor systems. It is also shown that a
three component system with quite different appearance from activator-inhibitor
systems is reduced to an effective equation with the Mexican hat shaped kernel.
It means that the two different systems have essentially the same effective
equations and that they exhibit essentially the same spatial and temporal
patterns. Thus, we can identify two different systems with the understanding in
unified concept through the reduced effective kernels. Other two applications
of this method are also given: Applications to pigment patterns on skins (two
factors network with long range interaction) and waves of differentiation
(called proneural waves) in visual systems on brains (four factors network with
long range interaction). In the applications, we observe the reproduction of
the same spatial and temporal patterns as those appearing in pre-existing
models through the numerical simulations of the effective equations.


  Slow magnetoacoustic waves represent an important tool for probing the solar
coronal plasma. We quantitatively assess the applicability of the weak thermal
conduction theory to coronal seismology by slow waves. We numerically model the
linear standing slow wave in a 1D coronal loop, with field-aligned thermal
conduction $\kappa_\parallel$ as a free parameter and no restrictions on its
efficiency. The time variations of the perturbed plasma parameters, obtained
numerically with full conductivity, are treated as potential observables and
analysed with the standard data processing techniques. The slow wave
oscillation period is found to increase with $\kappa_\parallel$ by about 30%,
indicating the corresponding modification in the effective wave speed, which is
missing from the weak conduction theory. Phase shifts between plasma
temperature and density perturbations are found to be well consistent with the
approximate weakly conductive solution for all considered values of
$\kappa_\parallel$. In contrast, the comparison of the numerically obtained
ratio of temperature and density perturbation amplitudes with the weak theory
revealed relative errors up to 30-40%. We use these parameters to measure the
effective adiabatic index of the coronal plasma directly as the ratio of the
effective slow wave speed to the standard sound speed and in the polytropic
assumption, which is found to be justified in a weakly conductive regime only,
with relative errors up to 14% otherwise. The damping of the initial
perturbation is found to be of a non-exponential form during the first cycle of
oscillation, which could be considered as an indirect signature of entropy
waves in the corona, also not described by weak conduction theory. The
performed analysis and obtained results offer a more robust scheme of coronal
seismology by slow waves, with reasonable simplifications and without the loss
of accuracy.


  Simulation results for head-on collisions of equal-sized spherical polymer
nanodroplets using molecular dynamics are presented. Elastic behavior of an
initial compressed phase for the colliding droplets is analyzed. Deformations
and contact radii of the nanodroplets are compared with the Hertzian model of
elastic solid balls. It is found that at least the initial phase of collision
can be explained by this continuum model, except at the very moment of the
beginning of collision.


  You have a rocket in a high circular orbit around a massive central body (a
planet, or the Sun) and wish to escape with the fastest possible speed at
infinity for a given amount of fuel.


  The CMS muon system operates gas-based detectors. Upgrades of the detectors
and trigger components are needed to cope with increasingly challenging
conditions of the HL-LHC. New irradiation tests are performed to ensure that
the muon detectors will survive the harsher conditions and operate reliably.
The new CERN GIF++ (Gamma Irradiation Facility) allowed to perform aging tests.
We present results in terms of system performance under large backgrounds and
after accelerated aging tests. New detectors will be added to improve the
performance in the critical forward region: gas electron multiplier (GEM)
detectors will be installed in LS2 in the region 1.6 $<$ $|\eta|$ $<$ 2.4,
aiming at suppressing background triggers while maintaining high trigger
efficiency. Further enhancements are foreseen with a second GEM station and
with two stations of new generation RPCs, having low resistivity electrodes.
These detectors will combine tracking and triggering capabilities and can stand
particle rates up to few kHz/cm$^2$. In addition, to take advantage of the
pixel tracking coverage extension, a new GEM detector covering up to $|\eta|$ =
2.8. is foreseen behind the new forward calorimeter.


  We study the problem of learning fair prediction models for unseen test sets
distributed differently from the train set. Stability against changes in data
distribution is an important mandate for responsible deployment of models. The
domain adaptation literature addresses this concern, albeit with the notion of
stability limited to that of prediction accuracy. We identify sufficient
conditions under which stable models, both in terms of prediction accuracy and
fairness, can be learned. Using the causal graph describing the data and the
anticipated shifts, we specify an approach based on feature selection that
exploits conditional independencies in the data to estimate accuracy and
fairness metrics for the test set. We show that for specific fairness
definitions, the resulting model satisfies a form of worst-case optimality. In
context of a healthcare task, we illustrate the advantages of the approach in
making more equitable decisions.


  We provide an overview of the robotic Super-LOTIS (Livermore Optical
Transient Imaging System) telescope and present results from gamma-ray burst
(GRB) afterglow observations using Super-LOTIS and other Steward Observatory
telescopes. The 0.6-m Super-LOTIS telescope is a fully robotic system dedicated
to the measurement of prompt and early time optical emission from GRBs. The
system began routine operations from its Steward Observatory site atop Kitt
Peak in April 2000 and currently operates every clear night. The telescope is
instrumented with an optical CCD camera and a four position filter wheel. It is
capable of observing Swift Burst Alert Telescope (BAT) error boxes as early or
earlier than the Swift UV/Optical Telescope (UVOT). Super-LOTIS complements the
UVOT observations by providing early R- and I-band imaging. We also use the
suite of Steward Observatory telescopes including the 1.6-m Kuiper, the 2.3-m
Bok, the 6.5-m MMT, and the 8.4-m Large Binocular Telescope to perform
follow-up optical and near infrared observations of GRB afterglows. These
follow-up observations have traditionally required human intervention but we
are currently working to automate the 1.6-m Kuiper telescope to minimize its
response time.


  How do organisms recognize their environment by acquiring knowledge about the
world, and what actions do they take based on this knowledge? This article
examines hypotheses about organisms' adaptation to the environment from machine
learning, information-theoretic, and thermodynamic perspectives. We start with
constructing a hierarchical model of the world as an internal model in the
brain, and review standard machine learning methods to infer causes by
approximately learning the model under the maximum likelihood principle. This
in turn provides an overview of the free energy principle for an organism, a
hypothesis to explain perception and action from the principle of least
surprise. Treating this statistical learning as communication between the world
and brain, learning is interpreted as a process to maximize information about
the world. We investigate how the classical theories of perception such as the
infomax principle relates to learning the hierarchical model. We then present
an approach to the recognition and learning based on thermodynamics, showing
that adaptation by causal learning results in the second law of thermodynamics
whereas inference dynamics that fuses observation with prior knowledge forms a
thermodynamic process. These provide a unified view on the adaptation of
organisms to the environment.


  In this work we study the geodesic structure of the space $\Sigma (X)$ of
compact balls of a complete and locally compact metric length space endowed
with the Hausdorff distance $d_H$. In particular, we focus on a geometric
condition (referred to as the shooting property) that enables us to give an
explicit isometry between $(\Sigma (X),d_H)$ and the closed half-space $
X\times \mathbb{R}_{\ge 0}$ endowed with a taxicab metric.


  Ratio of the intensity of D- Raman peak and G- Raman peak (ID/IG) is often
used for characterization of diamond-like carbon films, for example to estimate
number and size of the sp2 clusters. In this paper we investigate how the
interference effects in the film influence this ratio. It is shown that for
films on silicon substrates the distortion of the real ratio can reach 10 % and
for films on metals even 40 %. This should be taken into account if some
conclusions are made from the measured ID/IG ratio.


  We consider the De Donder-Weyl (DW) Hamiltonian formulation of the Palatini
action of vielbein gravity formulated in terms of the solder form and spin
connection, which are treated as independent variables. The basic geometrical
constructions necessary for the DW Hamiltonian theory of vielbein gravity are
presented. We reproduce the DW Hamilton equations in the multisymplectic and
pre-multisymplectic formulations. We also give basic examples of Hamiltonian
(n-1)-forms and related Poisson brackets.


  We propose a mechanism that allows for sizeable flavour violation in
quark-lepton currents, while suppressing flavour changing neutral currents in
quark-quark and lepton-lepton sectors. The mechanism is applied to the recently
proposed 4321 renormalizable model, which can accommodate the current
experimental anomalies in $B$-meson decays, both in charged and neutral
currents, while remaining consistent with all other indirect flavour and
electroweak precision measurements and direct searches at high-$p_T$. To
support this claim, we present an exhaustive phenomenological survey of this
fully calculable UV complete model and highlight the rich complementarity
between indirect and direct searches.


  We present a new way of embedding functional languages into the Coq proof
assistant by using meta-programming. This allows us to develop the meta-theory
of the language using the deep embedding and provides a convenient way for
reasoning about concrete programs using the shallow embedding. We connect the
deep and the shallow embeddings by a soundness theorem. As an instance of our
approach, we develop an embedding of a core smart contract language into Coq
and verify several important properties of a crowdfunding contract based on a
previous formalisation of smart contract execution in blockchains.


  The ratio of two probability densities, called a density-ratio, is a vital
quantity in machine learning. In particular, a relative density-ratio, which is
a bounded extension of the density-ratio, has received much attention due to
its stability and has been used in various applications such as outlier
detection and dataset comparison. Existing methods for (relative) density-ratio
estimation (DRE) require many instances from both densities. However,
sufficient instances are often unavailable in practice. In this paper, we
propose a meta-learning method for relative DRE, which estimates the relative
density-ratio from a few instances by using knowledge in related datasets.
Specifically, given two datasets that consist of a few instances, our model
extracts the datasets' information by using neural networks and uses it to
obtain instance embeddings appropriate for the relative DRE. We model the
relative density-ratio by a linear model on the embedded space, whose global
optimum solution can be obtained as a closed-form solution. The closed-form
solution enables fast and effective adaptation to a few instances, and its
differentiability enables us to train our model such that the expected test
error for relative DRE can be explicitly minimized after adapting to a few
instances. We empirically demonstrate the effectiveness of the proposed method
by using three problems: relative DRE, dataset comparison, and outlier
detection.


  An exact one monopole solution in a uniform self-dual background field is
obtained in the BPS limit of the SU(2) Yang-Mills-Higgs theory by using the
inverse scattering method.


  This mini-review collects theoretical results predicting the creation of
matter-wave solitons by the pseudo-spinor system of Gross-Pitaevskii equations
(GPEs) with the self-attractive cubic nonlinearity and linear
first-order-derivative terms accounting for the spin-orbit coupling (SOC). In
one dimension (1D), the so predicted bright solitons are similar to their
well-known counterparts supported by the GPE in the absence of SOC. Completely
novel results were recently obtained for 2D and 3D systems: SOC suppresses the
collapse instability of the multidimensional GPE, creating fully stable 2D
ground-state solitons and metastable 3D ones of two types: semi-vortices (SVs),
with vorticities m = 1 in one spin component and m = 0 in the other, and mixed
modes (MMs), with m = 0 and m = (+/-)1 present in both components. With the
Galilean invariance broken by SOC, moving solitons exist up to a certain
critical velocity, suffering delocalization above it. The newest result
predicts stable 2D "quantum droplets" of the MM type in the presence of the
Lee-Huang-Yang corrections to the GPE system, induced by quantum fluctuations
around the mean-field states, in the case when the inter-component attraction
dominates over the self-repulsion in each component.


  This work focuses on the task of query-based meeting summarization in which
the summary of a context (meeting transcript) is generated in response to a
specific query. When using Large Language Models (LLMs) for this task, usually
a new call to the LLM inference endpoint/API is triggered for each new query,
even if the context stays the same. However, repeated calls to the LLM
inference endpoints would significantly increase the costs of using them in
production, making LLMs impractical for many real-world use cases. To address
this problem, in this paper, we investigate whether combining the queries for
the same input context in a single prompt to minimize repeated calls can be
successfully used in meeting summarization. In this regard, we conduct
extensive experiments by comparing the performance of various popular LLMs:
GPT-4, Gemini, Claude-3, LLaMA-2, Mistral, Phi-3, and Qwen-2 in single-query
and multi-query settings. We observe that 100% reliability in generating the
response in the expected format is usually limited to certain closed-source
LLMs, with most open-source LLMs lagging behind (except a few 7B parameters
LLMs like Mistral and Phi-3). We conclude that multi-query prompting could be
useful to significantly optimize the inference costs in meeting summarization.


  A $(3+1)$-dimensional Einstein-Gauss-Bonnet theory of gravity has been
recently formulated in [D. Glavan and C. Lin, Phys. Rev. Lett. {\bf 124},
081301 (2020)] which is different from the pure Einstein theory, i.e., bypasses
the Lovelock's theorem and avoids Ostrogradsky instability. The theory was
formulated in $D > 4$ dimensions and its action consists of the
Einstein-Hilbert term with a cosmological constant, while the Gauss-Bonnet term
multiplied by a factor $1/(D-4)$. Then, the four-dimensional theory is defined
as the limit $D \to 4$. Here we generalize this approach to the
four-dimensional Einstein-Lovelock theory and formulate the most general static
$4D$ black-hole solution allowing for a $\Lambda$-term (either positive or
negative) and the electric charge $Q$. As metric functions cannot be found in a
closed form in the general case, we develop and share publicly the code which
constructs the metric functions for every given set of parameters.


  Usually the study of energy-transfer in the light harvesting complex is
limited by a single-exciton motion along the antenna. Starting from the
many-body Schr\"odinger equation, we derived Lindblad-type Master equations
describing the cyclic exciton-electron dynamics of the light harvesting
complex, originated from charge reduction of a donor. These equations,
resembling the Master equations for the electric current in mesoscopic systems,
go beyond the single-exciton description by accounting for the multi-exciton
states accumulated in the antenna, as well as the charge-separation,
fluorescence and initial photo-absorption. Although these effects take place on
very different time-scales, we demonstrate that their inclusion is necessary
for a consistent description of the exciton dynamics. We applied our results to
evaluate the energy (exciton) current and for the fluorescent current depending
on the light-intensity.


  We examine different methods to implement coherent detection in the
subcarrier wave quantum key distribution (SCW QKD) systems. For classical
wavefields, we present the models describing homodyne-type and heterodyne-type
coherent detection schemes needed to extract information from the quadrature
phase-coded multimode signals used in SCW QKD. Practical feasibility of the
proposed schemes is corroborated by the experiments.


  All-loop planar scattering amplitudes in maximally supersymmetric Yang-Mills
theory can be formulated geometrically in terms of the "amplituhedron". We
study the mathematical structures of the one-loop amplituhedron, and present a
new formula for its canonical measure, or the one-loop Grassmannian measure
formula. Using the recently proposed momentum-twistor diagrams, we show that
there is a correspondence between the cells of one-loop amplituhedron, BCFW
terms or equivalently on-shell diagrams, and residues of the one-loop
Grassmannian formula. In particular, for the first non-trivial case of one-loop
NMHV, these structures are naturally associated with a nice geometric picture
as polygons in projective space, as we discuss in various illustrative
examples.


  We consider the two-dimensional non-relativistic Coulomb problem with the aid
of the momentum space construction of the associated Green's function. Our
presentation has precursors in three dimensions. It is mainly Schwinger's
approach which we advocate and project onto two dimensions.


  We determine the spin-lifetime anisotropy of spin-polarized carriers in
graphene. In contrast to prior approaches, our method does not require large
out-of-plane magnetic fields and thus it is reliable for both low- and
high-carrier densities. We first determine the in-plane spin lifetime by
conventional spin precession measurements with magnetic fields perpendicular to
the graphene plane. Then, to evaluate the out-of-plane spin lifetime, we
implement spin precession measurements under oblique magnetic fields that
generate an out-of-plane spin population. We find that the spin-lifetime
anisotropy of graphene on silicon oxide is independent of carrier density and
temperature down to 150 K, and much weaker than previously reported. Indeed,
within the experimental uncertainty, the spin relaxation is isotropic.
Altogether with the gate dependence of the spin lifetime, this indicates that
the spin relaxation is driven by magnetic impurities or random spin-orbit or
gauge fields.


  Let $P$ be a set of $n$ points in strictly convex position in the plane. Let
$D_n$ be the graph whose vertex set is the set of all line segments with
endpoints in $P$, where disjoint segments are adjacent. The chromatic number of
this graph was first studied by Araujo, Dumitrescu, Hurtado, Noy, and Urrutia
[2005] and then by Dujmovi\'c and Wood [2007]. Improving on their estimates, we
prove the following exact formula: $$\chi(D_n) = n - \left\lfloor \sqrt{2n +
\tfrac{1}{4}} - \tfrac{1}{2}\right\rfloor.$$


  We give an explicit expression of the normalized characters of the symmetric
group in terms of the contents of the partition labelling the representation.


  In addition to buoyancy- and magnetic tension-driven instabilities, magnetic
flux rings are also susceptible to an instability induced by the hydrodynamic
drag force. We investigate the influence of the toroidal shape and equilibrium
condition on the thresholds of the friction-induced instability and on their
relevance for emerging magnetic flux in solar-like stars. Analytical
instability criteria are derived for axial symmetric perturbations and for flux
rings in the equatorial plane by analysing the sequence of principal minors of
the coefficient matrices of dispersion polynomials. The general case of
non-equatorial flux rings is investigated numerically by considering flux tubes
in the solar overshoot region. The friction-induced instability occurs when an
eigenmode reverses its direction of propagation due to advection, typically
from the retrograde to the prograde direction. Since the reversal requires a
certain relative velocity difference between plasma inside the flux tube and
the environment, the instability criterion depends on the location and field
strength of the flux ring. The friction-induced instability sets in at lower
field strengths than buoyancy- and tension-driven instabilities. Its threshold
is independent of the strength of friction, but the growth rates depend on the
strength of the frictional coupling between flux tube and environment. The
friction-induced instability lowers the critical magnetic field strength beyond
which flux tubes are subject to growing perturbations. Whereas buoyancy- and
tension-driven instabilities depend on the magnetic field strength alone, the
dependence of hydrodynamic drag on the tube diameter gives rise to an
additional dependence of growth times on the magnetic flux.


  We use broadband sensitive LOFAR observations in the 25-80 MHz frequency
range to study the single-pulse emission properties of the mode-switching
pulsar B0943+10. We review the derivation of magnetospheric geometry,
originally based on low-frequency radio data, and show that the geometry is
less constrained than previously thought. This may be used to help explain the
large fractional amplitudes of the observed thermal X-ray pulsations from the
polar cap, which contradict the almost aligned rotator model of PSR B0943+10.
We analyse the properties of drifting subpulses in the Bright mode and report
on the minutes-long variations of the drift period. We searched for the
periodic amplitude modulation of drifting subpulses, which is a vital argument
for constraining several important system parameters: the degree of aliasing,
the orientation of the line-of-sight vector with respect to magnetic and spin
axes, the angular velocity of the carousel, and thus, the gradient of the
accelerating potential in the polar gap. The periodic amplitude modulation was
not detected, indicating that it may be a rare or narrow-band phenomenon. Based
on our non-detection and review of available literature, we chose to leave the
aliasing order unconstrained and derived the number of sparks under different
assumptions about the aliasing order and geometry angles. Contrary to the
previous findings, we did not find a large (of the order of 10%) gradual
variation of the separation between subpulses throughout Bright mode. We
speculate that this large variation may be due to the incorrect accounting for
the curvature of the line of sight within the on-pulse window. Finally, we
report on the frequency-dependent drift phase delay, which is similar to the
delay reported previously for PSR B0809+74. We provide a quantitative
explanation of the observed frequency-dependent drift phase delay within the
carousel model.


  Five observations of the hard X-ray spectrum of Her X-1 from \xte show that
the $\sim 41$ keV energy of the cyclotron scattering line is constant within
statistics of a few percent per observtion. Comparison with other observations
over many years indicates strongly that the centroid energy of this absorption
line has increased some time between 1991 and 1993 by 23%, from 34 keV to 41
keV. Moreover, the cutoff energy of the spectral continuum increased at the
same time from 16 keV to 20 keV, which is, within the statistical error of 5%,
in direct proportion to the centroid. This may be a sign thatboth these
characteristics of the spectrum are controlled in the same way by the magnetic
field strength in the region of scattering.


  We study the spectral properties of the Laplace operator associated to a
hyperbolic surface in the presence of a unitary representation of the
fundamental group. Following the approach by Guillop\'e and Zworski, we
establish a factorization formula for the twisted scattering determinant and
describe the behavior of the scattering matrix in a neighborhood of $1/2$.


  An algorithm to estimate motion from satellite imagery is presented. Dense
displacement fields are computed from time-separated images of of significant
convective activity using a Bayesian formulation of the motion estimation
problem. Ordinarily this motion estimation problem is ill-posed; there are far
too many degrees of freedom than necessary to represent the motion. Therefore,
some form of regularization becomes necessary and by imposing smoothness and
non-divergence as desirable properties of the estimated displacement vector
field, excellent solutions are obtained. Our approach provides a marked
improvement over other methods in conventional use. In contrast to correlation
based approaches, the displacement fields produced by our method are dense,
spatial consistency of the displacement vector field is implicit, and
higher-order and small-scale deformations can be easily handled. In contrast
with optic-flow algorithms, we can produce solutions at large separations of
mesoscale features between large time-steps or where the deformation is rapidly
evolving.


  In this paper, we investigate the pointwise space-time behavior of two-phase
fluid model derived by Choi \cite{Choi} [SIAM J. Math. Anal., 48(2016), pp.
3090-3122], which is the compressible damped Euler equations coupled with
compressible Naiver-Stokes equations. Based on Green's function method together
with frequency analysis and nonlinear coupling of different wave patterns, it
shows that both of two densities and momentums obey the generalized Huygens'
principle as the compressible Navier-Stokes equations \cite{LW}, however, it is
different from the compressible damped Euler equations \cite{Wang2}. The main
contributions include seeking suitable combinations to avoid the singularity
from the Hodge decomposition in the low frequency part of the Green's function,
overcoming the difficulty of the non-conservation arising from the damped
mechanism of the system, and developing the detailed description of the
singularities in the high frequency part of the Green's function. Finally, as a
byproduct, we extend $L^2$-estimate in \cite{Wugc} [SIAM J. Math. Anal.,
52(2020), pp. 5748-5774] to $L^p$-estimate with $p>1$.


  We consider the variational principle in the covariant formulation of
modified teleparallel theories with second order field equations. We vary the
action with respect to the spin connection and obtain a consistency condition
relating the spin connection with the tetrad. We argue that since the spin
connection can be calculated using an additional reference tetrad, modified
teleparallel theories can be interpreted as effectively bigravity theories. We
conclude with discussion about the relation of our results and those obtained
in the usual, non-covariant, formulation of teleparallel theories and present
the solution to the problem of choosing the tetrad in $f(T)$ gravity theories.


  It is well known that a direct sum of CLS-modules is not, in general, a
CLS-module. It is proved that if $M=M_1\oplus M_2$, where $M_1$ and $M_2$ are
CLS-modules such that $M_1$ and $M_2$ are relatively ojective (or $M_1$ is
$M_2$-ejective), then $M$ is a CLS-module and some known results are
generalized. Tercan [8] proved that if a module $M=M_{1}\oplus M_{2}$ where
$M_{1}$ and $M_{2}$ are CS-modules such that $M_{1}$ is $M_{2}$-injective, then
$M$ is a CS-module if and only if $Z_{2}(M)$ is a CS-module. Here we will show
that Tercan's claim is not true.


  We establish the $L^2$-solvability of Dirichlet, Neumann and regularity
problems for divergence-form heat (or diffusion) equations with
H\"older-continuous diffusion coefficients, on bounded Lipschitz domains in
$\mathbb{R}^n$. This is achieved through the demonstration of invertibility of
the relevant layer-potentials which is in turn based on Fredholm theory and a
new systematic approach which yields suitable parabolic Rellich-type estimates.


  In this paper, we study asymptotic behaviors of a subcritical branching
killed Brownian motion with drift $-\rho$ and offspring distribution
$\{p_k:k\ge 0\}$. Let $\widetilde{\zeta}^{-\rho}$ be the extinction time of
this subcritical branching killed Brownian motion, $\widetilde{M}_t^{-\rho}$
the maximal position of all the particles alive at time $t$ and
$\widetilde{M}^{-\rho}:=\max_{t\ge 0}\widetilde{M}_t^{-\rho}$ the all time
maximal position. Let $\mathbb{P}_x$ be the law of this subcritical branching
killed Brownian motion when the initial particle is located at $x\in
(0,\infty)$. Under the assumption $\sum_{k=1}^\infty k (\log k) p_k <\infty$,
we establish the decay rates of $\mathbb{P}_x(\widetilde{\zeta}^{-\rho}>t)$ and
$\mathbb{P}_x(\widetilde{M}^{-\rho}>y)$ as $t$ and $y$ tend to $\infty$
respectively. We also establish the decay rate of
$\mathbb{P}_x(\widetilde{M}_t^{-\rho}>z(t,\rho))$ as $t\to\infty$, where
$z(t,\rho)=\sqrt{t}z-\rho t$ for $\rho\leq 0$ and $z(t,\rho)=z$ for $\rho>0$.
As a consequence, we obtain a Yaglom-type limit theorem.


  In recent years, tensors have been applied to different applications in
science and engineering fields. In order to establish theory about tail bounds
of the tensors summation behavior, this work extends previous work by
considering the tensors summation tail behavior of the top $k$-largest singular
values of a function of the tensors summation, instead of the largest/smallest
singular value of the tensors summation directly (identity function) explored
in Shih Yu's work: Convenient tail bounds for sums of random tensors.
Majorization and antisymmetric tensor product tools are main techniques
utilized to establish inequalities for unitarily norms of multivariate tensors.
The Laplace transform method is integrated with these inequalities for
unitarily norms of multivariate tensors to give us tail bounds estimation for
Ky Fan $k$-norm for a function of the tensors summation. By restricting
different random tensor conditions, we obtain generalized tensor Chernoff and
Bernstein inequalities.


  In today's world, the rapid expansion of IoT networks and the proliferation
of smart devices in our daily lives, have resulted in the generation of
substantial amounts of heterogeneous data. These data forms a stream which
requires special handling. To handle this data effectively, advanced data
processing technologies are necessary to guarantee the preservation of both
privacy and efficiency. Federated learning emerged as a distributed learning
method that trains models locally and aggregates them on a server to preserve
data privacy. This paper showcases two illustrative scenarios that highlight
the potential of federated learning (FL) as a key to delivering efficient and
privacy-preserving machine learning within IoT networks. We first give the
mathematical foundations for key aggregation algorithms in federated learning,
i.e., FedAvg and FedProx. Then, we conduct simulations, using Flower Framework,
to show the \textit{efficiency} of these algorithms by training deep neural
networks on common datasets and show a comparison between the accuracy and loss
metrics of FedAvg and FedProx. Then, we present the results highlighting the
trade-off between maintaining privacy versus accuracy via simulations -
involving the implementation of the differential privacy (DP) method - in
Pytorch and Opacus ML frameworks on common FL datasets and data distributions
for both FedAvg and FedProx strategies.


  We perform measurements, numerical simulations, and quantitative comparisons
with available theory on solitary wave propagation in a linear chain of beads
without static preconstrain. By designing a nonintrusive force sensor to
measure the impulse as it propagates along the chain, we study the solitary
wave reflection at a wall. We show that the main features of solitary wave
reflection depend on wall mechanical properties. Since previous studies on
solitary waves have been performed at walls without these considerations, our
experiment provides a more reliable tool to characterize solitary wave
propagation. We find, for the first time, precise quantitative agreements.


  We calculate, within pQCD parton model at leading orders, the expression of
the longitudinal polarization of Lambda baryons produced in polarized
semi-inclusive DIS, including weak interaction effects. We present some
numerical estimates in few cases for which data are or will soon be available
and discuss how to gather new information on polarized fragmentation functions.


  Atom interferometry is an exciting tool to probe fundamental physics. It is
considered especially apt to test the universality of free fall by using two
different sorts of atoms. The increasing sensitivity required for this kind of
experiment sets severe requirements on its environments, instrument control,
and systematic effects. This can partially be mitigated by going to space as
was proposed, for example, in the Spacetime Explorer and Quantum Equivalence
Principle Space Test (STE-QUEST) mission. However, the requirements on the
instrument are still very challenging. For example, the specifications of the
STE-QUEST mission imply that the Feshbach coils of the atom interferometer are
allowed to change their radius only by about 260 nm or 2.6E-4% due to thermal
expansion although they consume an average power of 22 W. Also Earth's magnetic
field has to be suppressed by a factor of 10E5. We show in this article that
with the right design such thermal and magnetic requirements can indeed be met
and that these are not an impediment for the exciting physics possible with
atom interferometers in space.