  Channel idle time distribution based secondary transmission strategies have
been studied intensively in the literature. Under various performance metrics,
the ultimate performance of secondary devices are eventually dictated by the
presumed channel idle time distribution. Such distributions can take any
arbitrary form in practice. In this work, we study idle time distributions in
wireless local area networks (WLAN) using large amount of the channel idle time
data collected in real-world WLAN networks. We demonstrate with experimental
data that the channel idle time distribution can be closely modeled by
hyper-exponential distribution. Furthermore, one can treat the primary packet
arrival process as a semi-Markov modulated Poisson process. Several secondary
transmission strategies are discussed under this model. It is shown that using
only one hyper-exponential distribution, the secondary user can achieve a
desirable performance when the primary packet arrival process is stationary.
However, experimental data suggests that in practice, this process is not
stationary and the secondary user can experience a large performance loss with
stationary transmission strategy. We propose a novel transmission strategy that
achieves suboptimal secondary user performance when the idle time distribution
is not stationary. The performances of secondary transmission strategies are
demonstrated using experimental data.


  Solver competitions play a prominent role in assessing and advancing the
state of the art for solving many problems in AI and beyond. Notably, in many
areas of AI, competitions have had substantial impact in guiding research and
applications for many years, and for a solver to be ranked highly in a
competition carries considerable weight. But to which extent can we expect
competition results to generalise to sets of problem instances different from
those used in a particular competition? This is the question we investigate
here, using statistical resampling techniques. We show that the rankings
resulting from the standard interpretation of competition results can be very
sensitive to even minor changes in the benchmark instance set used as the basis
for assessment and can therefore not be expected to carry over to other samples
from the same underlying instance distribution. To address this problem, we
introduce a novel approach to statistically meaningful analysis of competition
results based on resampling performance data. Our approach produces confidence
intervals of competition scores as well as statistically robust solver rankings
with bounded error. Applied to recent SAT, AI planning and computer vision
competitions, our analysis reveals frequent statistical ties in solver
performance as well as some inversions of ranks compared to the official
results based on simple scoring.


  The Density Matrix Renormalization Group (DMRG) has become a powerful
numerical method that can be applied to low-dimensional strongly correlated
fermionic and bosonic systems. It allows for a very precise calculation of
static, dynamic and thermodynamic properties. Its field of applicability has
now extended beyond Condensed Matter, and it is now successfully used in
Quantum Chemistry, Statistical Mechanics, Quantum Information Theory, Nuclear
and High Energy Physics as well. In this article, we briefly review the main
aspects of the method and present some of the most relevant applications so as
to give an overview on the scope and possibilities of DMRG. We focus on the
most important extensions of the method such as the calculation of dynamical
properties, the application to classical systems, finite temperature
simulations, phonons and disorder, field theory, time-dependent properties and
the ab initio calculation of electronic states in molecules. The recent quantum
information interpretation, the development of highly accurate time-dependent
algorithms and the possibility of using the DMRG as the impurity-solver of the
Dynamical Mean Field Method (DMFT) give new insights into its present and
potential uses. We review the numerous very recent applications of these
techniques where the DMRG has shown to be one of the most reliable and
versatile methods in modern computational physics.


  The growth of solids from sub-micron to millimeter and centimeter sizes is
the early step toward the formation of planets inside protoplanetary disks
(PPDs). However, such processes and their potential impact on the later stages
of solid growth are still poorly understood. In this work, we test the
hypothesis that most disks contain at least one ringed structure with a
relative small radius. We have carried out a large family of 1D two-fluid
(gas+dust) hydrodynamical simulations by evolving the gas and dust motion
self-consistently while allowing dust size to evolve via coagulation and
fragmentation. We investigate the joint effects of ringed structures and dust
size growth on the overall sub-millimeter and millimeter (mm) flux and spectral
index of PPDs. Ringed structures slow down the dust radial drift and speed up
the dust growth. In particular, we find that those unresolved disks with a high
fragmentation velocity ($\sim10\ {\rm m~s^{-1}}$) and a high dust surface
density ($\sim10\ {\rm g\ cm^{-2}}$ in the ring) can have mm spectral indices
as low as $\sim2.0$, consistent with mm observations of faint disks in nearby
star forming regions. Furthermore, disks with more than one ringed structure
can potentially reproduce brighter disks with spectral indices lower than
$\sim2.5$. Future multi-wavelength high-resolution observations of these low
spectral index sources can be used to test the existence of the ringed
structures in the unresolved disks and differentiate the effects of dust size
growth from optical depth.


  We present a maximum-likelihood analysis for estimating the angular
distribution of power in an anisotropic stochastic gravitational-wave
background using ground-based laser interferometers. The standard isotropic and
gravitational-wave radiometer searches (optimal for point sources) are
recovered as special limiting cases. The angular distribution can be decomposed
with respect to any set of basis functions on the sky, and the single-baseline,
cross-correlation analysis is easily extended to a network of three or more
detectors-that is, to multiple baselines. A spherical harmonic decomposition,
which provides maximum-likelihood estimates of the multipole moments of the
gravitational-wave sky, is described in detail. We also discuss: (i) the
covariance matrix of the estimators and its relationship to the detector
response of a network of interferometers, (ii) a singular-value decomposition
method for regularizing the deconvolution of the detector response from the
measured sky map, (iii) the expected increase in sensitivity obtained by
including multiple baselines, and (iv) the numerical results of this method
when applied to simulated data consisting of both point-like and di#use
sources. Comparisions between this general method and the standard isotropic
and radiometer searches are given throughout, to make contact with the existing
literature on stochastic background searches.


  The categorical compositional approach to meaning has been successfully
applied in natural language processing, outperforming other models in
mainstream empirical language processing tasks. We show how this approach can
be generalized to conceptual space models of cognition. In order to do this,
first we introduce the category of convex relations as a new setting for
categorical compositional semantics, emphasizing the convex structure important
to conceptual space applications. We then show how to construct conceptual
spaces for various types such as nouns, adjectives and verbs. Finally we show
by means of examples how concepts can be systematically combined to establish
the meanings of composite phrases from the meanings of their constituent parts.
This provides the mathematical underpinnings of a new compositional approach to
cognition.


  Analytical tools to $K$-theory; namely, self-stabilization of rapidly
decreasing matrices, linearization of cyclic loops, and the contractibility of
the pointed stable Toeplitz algebra are discussed in terms of concrete
formulas. Adaptation to the *-algebra and finite perturbation categories is
also considered. Moreover, the finite linearizability of algebraically finite
cyclic loops is demonstrated.


  Electrical resistance tomography (ERT) -based distributed surface sensing
systems, or sensing skins, offer alternative sensing techniques for structural
health monitoring, providing capabilities for distributed sensing of, for
example, damage, strain and temperature. Currently, however, the computational
techniques utilized for sensing skins are limited to planar surfaces. In this
paper, to overcome this limitation, we generalize the ERT-based surface sensing
to non-planar surfaces covering arbitrarily shaped three-dimensional
structures; We construct a framework in which we reformulate the image
reconstruction problem of ERT using techniques of Riemannian geometry, and
solve the resulting problem numerically. We test this framework in series of
numerical and experimental studies. The results demonstrate that the
feasibility of the proposed formulation and the applicability of ERT-based
sensing skins for non-planar geometries.


  GGR News:
  New version of LISA, by Karsten Danzmann
  We hear that, by David Garfinkle
  Research Briefs:
  Finally, results from Gravity Probe B, by Clifford M. Will
  Discovery of the highest mass neutron star, by Wynn C.G. Ho
  Conference reports:
  Numerical relativity beyond astrophysics, by Carsten Gundlac
  Cold materials, hot nuclei and black holes, by Vijay Balasubramanian
  Benasque workshop on gravity, by Oscar J.C. Dias


  The near-IR emission in Type 1 AGNs is thought to be dominated by the thermal
radiation from dust grains that are heated by the central engine in the
UV/optical and are almost at the sublimation temperature. A brightening of the
central source can thus further sublimate the innermost dust, leading to an
increase in the radius of the near-IR emitting region. Such changes in radius
have been indirectly probed by the measurements of the changes in the time lag
between the near-IR and UV/optical light variation. Here we report direct
evidence for such a receding sublimation region through the near-IR
interferometry of the brightest Type 1 AGN in NGC4151. The increase in radius
follows a significant brightening of the central engine with a delay of at
least a few years, which is thus the implied destruction timescale of the
innermost dust distribution. Compiling historic flux variations and radius
measurements, we also infer the reformation timescale for the inner dust
distribution to be several years in this galactic nucleus. More specifically
and quantitatively, we find that the radius at a given time seems to be
correlated with a long-term average of the flux over the previous several (~6)
years, instead of the instantaneous flux. Finally, we also report measurements
of three more Type 1 AGNs newly observed with the Keck interferometer, as well
as the second epoch measurements for three other AGNs.


  The study of our Sun holds significant importance in Space Weather research,
encompassing a diverse range of phenomena characterized by distinct temporal
and spatial scales. To address these complexities, we developed CAFE-AMR, an
implementation of an Adaptive Mesh Refinement (AMR) strategy coupled with a
Magnetohydrodynamics (MHD) equation solver, aiming to tackle Solar
Physics-related problems. CAFE-AMR employs standard fluid dynamics methods,
including Finite Volume discretization, HLL and Roe class flux formulas, linear
order reconstructors, second-order Runge-Kutta, and Corner Transport Upwind
time stepping. In this paper, we present the core structure of CAFE-AMR,
discuss and evaluate mesh refinement criteria strategies, and conduct various
tests, including simulations of idealized Solar Wind models, relevant for Space
Weather applications.


  The optimal allocation of vaccines to population subgroups over time is a
challenging health care management problem. In the context of a pandemic, the
interaction between vaccination policies adopted by multiple agents and the
cooperation (or lack thereof) creates a complex environment that affects the
global transmission dynamics of the disease. In this study, we take the
perspective of decision-making agents that aim to minimize the size of their
susceptible populations and must allocate vaccine under limited supply. We
assume that vaccine efficiency rates are unknown to agents and we propose an
optimization policy based on Thompson sampling to learn mean vaccine efficiency
rates over time. Furthermore, we develop a budget-balanced resource sharing
mechanism to promote cooperation among agents. We apply the proposed framework
to the COVID-19 pandemic. We use a raster model of the world where agents
represent the main countries worldwide and interact in a global mobility
network to generate multiple problem instances. Our numerical results show that
the proposed vaccine allocation policy achieves a larger reduction in the
number of susceptible individuals, infections and deaths globally compared to a
population-based policy. In addition, we show that, under a fixed global
vaccine allocation budget, most countries can reduce their national number of
infections and deaths by sharing their budget with countries with which they
have a relatively high mobility exchange. The proposed framework can be used to
improve policy-making in health care management by national and global health
authorities.


  For many years, the Simplified Refined Instrumental Variable method for
Continuous-time systems (SRIVC) has been widely used for identification. The
intersample behaviour of the input plays an important role in this method, and
it has been shown recently that the SRIVC estimator is not consistent if an
incorrect assumption on the intersample behaviour is considered. In this paper,
we present an extension of the SRIVC algorithm that is able to deal with
continuous-time multisine signals, which cannot be interpolated exactly through
hold reconstructions. The proposed estimator is generically consistent for any
input reconstructed through zero or first-order-hold devices, and we show that
it is generically consistent for continuous-time multisine inputs as well. The
statistical performance of the proposed estimator is compared to the standard
SRIVC estimator through extensive simulations.


  We report the Chandra Advanced CCD Imaging Spectrometer detection of the
X-ray counterpart of the high magnetic field, ~1600 year-old, 407 ms radio
pulsar J1119-6127 associated with the supernova remnant G292.2-0.5. The
powerful imaging capability of Chandra also unveiled, for the first time, a
faint 3"x6" pulsar wind nebula (PWN) at energies above ~1.2 keV. The X-ray
emission from the pulsar and its associated nebula is well described by an
absorbed power law model with a photon index of 2.2 (1.9-2.8). The
corresponding 0.5-10 keV unabsorbed X-ray luminosity is 5.5(2.2-15.5)x10^32
ergs/s (at 6 kpc). When compared to two other pulsars with similar spin and
magnetic properties, J1119-6127 stands out as being the least efficient at
turning rotational kinetic energy into X-ray emission. This study shows that
high magnetic field radio pulsars can be significant X-ray emitters and Chandra
is needed to study the emission properties of the pulsars and associated faint
PWNe.


  A rainbow matching for (not necessarily distinct) sets F_1,...,F_k of
hypergraph edges is a matching consisting of k edges, one from each F_i. The
aim of the paper is twofold - to put order in the multitude of conjectures that
relate to this concept (some of them first presented here), and to present some
partial results on one of these conjectures, that seems central among them.


  We report the first wide-field mapping of the kinematics and stellar
populations in the E3 galaxy NGC 4365. The velocity maps extend previous
long-slit work. They show two independent kinematic subsystems: the central 300
x 700 pc rotates about the projected minor axis, and the main body of the
galaxy, 3 x 4 kpc, rotates almost at right angles to this. The line-strength
maps show that the metallicity of the stellar population decreases from a
central value greater than solar, to one-half solar at a radius of 2 kpc. The
decoupled core and main body of the galaxy have the same luminosity-weighted
age, of ~14 Gyr, and the same elevated magnesium-to-iron ratio. The two
kinematically distinct components have thus shared a common star formation
history. We infer that the galaxy underwent a sequence of mergers associated
with dissipative star formation that ended >12 Gyr ago. The misalignment
between the photometric and kinematic axes of the main body is unambiguous
evidence of triaxiality. The similarity of the stellar populations in the two
components suggests that the observed kinematic structure has not changed
substantially in 12 Gyr.


  The relaxation-time limit from the Quantum-Navier-Stokes-Poisson system to
the quantum drift-diffusion equation is performed in the framework of finite
energy weak solutions. No assumptions on the limiting solution are made. The
proof exploits the suitably scaled a priori bounds inferred by the energy and
BD entropy estimates. Moreover, it is shown how from those estimates the Fisher
entropy and free energy estimates associated to the diffusive evolution are
recovered in the limit. As a byproduct, our main result also provides an
alternative proof for the existence of finite energy weak solutions to the
quantum drift-diffusion equation.


  We address the non-redundant random generation of $k$ words of length $n$ in
a context-free language. Additionally, we want to avoid a predefined set of
words. We study a rejection-based approach, whose worst-case time complexity is
shown to grow exponentially with $k$ for some specifications and in the limit
case of a coupon collector. We propose two algorithms respectively based on the
recursive method and on an unranking approach. We show how careful
implementations of these algorithms allow for a non-redundant generation of $k$
words of length $n$ in $\mathcal{O}(k\cdot n\cdot \log{n})$ arithmetic
operations, after a precomputation of $\Theta(n)$ numbers. The overall
complexity is therefore dominated by the generation of $k$ words, and the
non-redundancy comes at a negligible cost.


  Numerical analysis of a shear layer between a cool liquid n-decane
hydrocarbon and a hot oxygen gas at supercritical pressures shows that a
well-defined phase equilibrium can be established. Variable properties are
considered with the product of density and viscosity in the gas phase showing a
nearly constant result within the laminar flow region with no instabilities.
Sufficiently thick diffusion layers form around the liquid-gas interface to
support the case of continuum theory and phase equilibrium. While molecules are
exchanged for both species at all pressures, net mass flux across the interface
shifts as pressure is increased. Net vaporization occurs for low pressures
while net condensation occurs at higher pressures. For a mixture of n-decane
and oxygen, the transition occurs around 50 bar. The equilibrium values at the
interface quickly reach their downstream asymptotes. For all cases, profiles of
diffusing-advecting quantities collapse to a similar solution (i.e., function
of one independent variable). Validity of the boundary layer approximation and
similarity are shown in both phases for Reynolds numbers greater than 239 at
150 bar. Results for other pressures are also taken at high Reynolds numbers.
Thereby, the validity of the boundary layer approximation and similarity are
expected. However, at very high pressures, the similar one-dimensional profiles
vary for different problem constraints.


  We report the discovery and characterization of HD 89345b (K2-234b; EPIC
248777106b), a Saturn-sized planet orbiting a slightly evolved star. HD 89345
is a bright star ($V = 9.3$ mag) observed by the K2 mission with one-minute
time sampling. It exhibits solar-like oscillations. We conducted
asteroseismology to determine the parameters of the star, finding the mass and
radius to be $1.12^{+0.04}_{-0.01}~M_\odot$ and
$1.657^{+0.020}_{-0.004}~R_\odot$, respectively. The star appears to have
recently left the main sequence, based on the inferred age,
$9.4^{+0.4}_{-1.3}~\mathrm{Gyr}$, and the non-detection of mixed modes. The
star hosts a "warm Saturn" ($P = 11.8$~days, $R_p = 6.86 \pm 0.14~R_\oplus$).
Radial-velocity follow-up observations performed with the FIES, HARPS, and
HARPS-N spectrographs show that the planet has a mass of $35.7 \pm
3.3~M_\oplus$. The data also show that the planet's orbit is eccentric
($e\approx 0.2$). An investigation of the rotational splitting of the
oscillation frequencies of the star yields no conclusive evidence on the
stellar inclination angle. We further obtained Rossiter-McLaughlin
observations, which result in a broad posterior of the stellar obliquity. The
planet seems to conform to the same patterns that have been observed for other
sub-Saturns regarding planet mass and multiplicity, orbital eccentricity, and
stellar metallicity.


  The crystal base of the modified quantized enveloping algebras of type
$A_{+\infty}$ or $A_\infty$ is realized as a set of integral bimatrices. It is
obtained by describing the decomposition of the tensor product of a highest
weight crystal and a lowest weight crystal into extremal weight crystals, and
taking its limit using a tableaux model of extremal weight crystals. This
realization induces in a purely combinatorial way a bicrystal structure of the
crystal base of the modified quantized enveloping algebras and hence its
Peter-Weyl type decomposition generalizing the classical RSK correspondence.


  Quantum theory allows direct measurement of the average of a non-Hermitian
operator using the weak value of the positive semidefinite part of the
non-Hermitian operator. Here, we experimentally demonstrate the measurement of
weak value and average of non-Hermitian operators by a novel interferometric
technique. Our scheme is unique as we can directly obtain the weak value from
the interference visibility and the phase shift in a Mach Zehnder
interferometer without using any weak measurement or post selection. Both the
experiments discussed here were performed with laser sources, but the results
would be the same with average statistics of single photon experiments. Thus,
the present experiment opens up the novel possibility of measuring weak value
and the average value of non-Hermitian operator without weak interaction and
post-selection, which can have several technological applications.


  Calculations are performed of the cooling of neutron stars with standard and
enhanced neutrino energy losses in the presence of neutron and proton
superfluidities in the stellar cores. The effects of superfluidity on the heat
capacity and the neutrino luminosity produced by the direct and modified Urca
processes and by the neutrino bremsstrahlung emission in nucleon-nucleon
collisions are taken into account. The constraints are analyzed on the critical
temperatures $\tn$ and $\tp$ of the transition of neutrons and protons to the
superfluid state, which can be obtained from a comparison of observational data
on thermal radiation from neutron stars with theoretical cooling curves for the
standard and enhanced neutrino energy losses. Possible ranges of $\tn$ and
$\tp$ for the pulsar Geminga are discussed.


  Potential functional approximations are an intriguing alternative to density
functional approximations. The potential functional that is dual to the Lieb
density functional is defined and properties given. The relationship between
Thomas-Fermi theory as a density functional and as a potential functional is
derived. The properties of several recent semiclassical potential functionals
are explored, especially in their approach to the large particle number and
classical continuum limits. The lack of ambiguity in the energy density of
potential functional approximations is demonstrated. The density-density
response function of the semiclassical approximation is calculated and shown to
violate a key symmetry condition.


  Let $\mathfrak g_i$ be a simple complex Lie algebra, $1\leq i \leq d$, and
let $G=G_1\times...\times G_d$ be the corresponding adjoint group. Consider the
$G$-module $V=\oplus r_i\mathfrak g_i$ where $r_i\geq 1$ for all $i$. We say
that $V$ is \emph{large} if all $r_i\geq 2$ and $r_i\geq 3$ if $G_i$ has rank
1. In [Schwarz12] we showed that when $V$ is large any algebraic automorphism
$\psi$ of the quotient $Z:= V//G$ lifts to an algebraic mapping $\Psi\colon
V\to V$ which sends the fiber over $z$ to the fiber over $\psi(z)$, $z\in Z$.
(Most cases were already handled in [Kuttler11]). We also showed that one can
choose a biholomorphic lift $\Psi$ such that $\Psi(gv)=\sigma(g)\Psi(v)$, $g\in
G$, $v\in V$, where $\sigma$ is an automorphism of $G$. This leaves open the
following questions: Can one lift holomorphic automorphisms of $Z$? Which
automorphisms lift if $V$ is not large? We answer the first question in the
affirmative and also answer the second question. Part of the proof involves
establishing the following result for $V$ large. Any algebraic differential
operator of order $k$ on $Z$ lifts to a $G$-invariant algebraic differential
operator of order $k$ on $V$. We also consider the analogues of the questions
above for actions of compact Lie groups.


  In string-inspired supergravity theory, K\"{a}hler metric of chiral matter
fields often has a pole. Such K\"{a}hler metric is interesting from the
viewpoint of the framework of the pole inflation, where the scalar potential
can be stretched out to be flat around the pole for a canonically normalized
field and inflation can be realized. However, when K\"{a}hler metric has a
pole, the scalar potential can also have a pole at the same point in
supergravity theory. We study such supergravity models with the pole, and
provide numerical analysis of inflationary dynamics and resultant density
perturbation. In contrast with usual pole inflation models, inflation in this
supergravity based model occurs not on the pole but region apart from the pole.
We show that the existence of the pole in the scalar potential is crucial
nevertheless. We also examine attractor behavior of our model.


  In this paper, we study attitude synchronization for elements in the unit
sphere of R3 and for elements in the 3D rotation group, for a network with
switching topology. The agents angular velocities are assumed to be the control
inputs, and a switching control law for each agent is devised that guarantees
synchronization, provided that all elements are initially contained in a given
region, unknown to the network. The control law is decentralized and it does
not require a common orientation frame among all agents. We refer to
synchronization of unit vectors in R3 as incomplete synchronization, and of 3D
rotation matrices as complete synchronization. Our main contribution lies on
showing that these two problems can be analyzed under a common framework, where
all elements' dynamics are transformed into unit vectors dynamics on a sphere
of appropriate dimension.


  Data-driven prediction is becoming increasingly widespread as the volume of
data available grows and as algorithmic development matches this growth. The
nature of the predictions made, and the manner in which they should be
interpreted, depends crucially on the extent to which the variables chosen for
prediction are Markovian, or approximately Markovian. Multiscale systems
provide a framework in which this issue can be analyzed. In this work kernel
analog forecasting methods are studied from the perspective of data generated
by multiscale dynamical systems. The problems chosen exhibit a variety of
different Markovian closures, using both averaging and homogenization;
furthermore, settings where scale-separation is not present and the predicted
variables are non-Markovian, are also considered. The studies provide guidance
for the interpretation of data-driven prediction methods when used in practice.


  The scheme for accurate quantitative treatment of the radiation from a
crystalline undulator in presence of the dechanneling and the photon
attenuation is presented. The number of emitted photons and the brilliance of
electromagnetic radiation generated by ultra-relativistic positrons channeling
in a crystalline undulator are calculated for various crystals, positron
energies and different bending parameters. It is demonstrated that with the use
of high-energy positron beams available at present in modern colliders it is
possible to generate the crystalline undulator radiation with energies from
hundreds of keV up to tens of MeV region. The brilliance of the undulator
radiation within this energy range is comparable to that of conventional light
sources of the third generation but for much lower photon energies.


  It is argued that the ten dimensional solution that corresponds to the
compactification of $E_8 \times E_8$ heterotic string theory on a half-flat
manifold is the product space-time $R^{1,2} \times Z_7$ where $Z_7$ is a
generalized cylinder with $G_2$ riemannian holonomy. Standard embedding on
$Z_7$ then implies an embedding on the half-flat manifold which involves the
torsionful connection rather than the Levi-Civita connection. This leads to the
breakdown of $E_8 \times E_8$ to $E_6 \times E_8$, as in the case of the
standard embedding on Calabi-Yau manifolds, which agrees with the result
derived recently by Gurrieri, Lukas and Micu (arXiv:0709.1932) using a
different approach. Green-Schwarz anomaly cancellation is then implemented via
the torsionful connection on half-flat manifolds.


  We consider data structures for graphs where we maintain a subset of the
nodes called sites, and allow proximity queries, such as asking for the closest
site to a query node, and update operations that enable or disable nodes as
sites. We refer to a data structure that can efficiently react to such updates
as reactive. We present novel reactive proximity data structures for graphs of
polynomial expansion, i.e., the class of graphs with small separators, such as
planar graphs and road networks. Our data structures can be used in several
logistical problems and geographic information systems dealing with real-time
data, such as emergency dispatching. We experimentally compare our data
structure to Dijkstra's algorithm in a system emulating random queries in a
real road network.


  The problem of antiproton scattering on the molecular Hydrogen is
investigated by means of wave packet dynamics. The electronically potential
energy surfaces of the antiproton H2 system are presented within this work.
Excitation and dissociation probabilities of the molecular Hydrogen for
collision energies in the ultra low energy regime below 10 eV are computed.


  Several guiding principles for thought processes are proposed and a
neural-network-type model implementing these principles is presented and
studied. We suggest to consider thinking within an associative network built-up
of overlapping memory states. We consider a homogeneous associative network as
biological considerations rule out distinct conjunction units between the
information (the memories) stored in the brain. We therefore propose that
memory states have a dual functionality: They represent on one side the stored
information and serve, on the other side, as the associative links in between
the different dynamical states of the network which consists of transient
attractors.
  We implement these principles within a generalized winners-take-all neural
network with sparse coding and an additional coupling to local reservoirs. We
show that this network is capable to generate autonomously a self-sustained
time-series of memory states which we identify with a thought process. Each
memory state is associatively connected with its predecessor.
  This system shows several emerging features, it is able (a) to recognize
external patterns in a noisy background, (b) to focus attention autonomously
and (c) to represent hierarchical memory states with an internal structure.


  We analyze interacting one-dimensional bosons in the continuum, subject to a
periodic sinusoidal potential of arbitrary depth. Variation of the lattice
depth tunes the system from the Bose-Hubbard limit for deep lattices, through
the sine-Gordon regime of weak lattices, to the complete absence of a lattice.
Using the Bose-Fermi mapping between strongly interacting bosons and weakly
interacting fermions, we derive the phase diagram in the parameter space of
lattice depth and chemical potential. This extends previous knowledge from
tight-binding (Bose-Hubbard) studies in a new direction which is important
because the lattice depth is a readily adjustable experimental parameter.
Several other results (equations of state, energy gaps, profiles in harmonic
trap) are presented as corollaries to the physics contained in this phase
diagram. Generically, both incompressible (gapped) and compressible phases
coexist in a trap; this has implications for experimental measurements.


  This work studies the variational quantum eigensolver algorithm, designed to
determine the ground state of a quantum mechanical system by combining
classical and quantum hardware. Methods of reducing the number of required
qubit manipulations, prone to induce errors, for the variational quantum
eigensolver are studied. We formally justify the qubit removal process as
sketched by Bravyi, Gambetta, Mezzacapo and Temme [arXiv:1701.08213 (2017)].
Furthermore, different classical optimization and entangling methods, both gate
based and native, are surveyed by computing ground state energies of H$_2$ and
LiH. This paper aims to provide performance-based recommendations for
entangling methods and classical optimization methods. Analyzing the VQE
problem is complex, where the optimization algorithm, the method of entangling,
and the dimensionality of the search space all interact. In specific cases
however, concrete results can be shown, and an entangling method or
optimization algorithm can be recommended over others. In particular we find
that for high dimensionality (many qubits and/or entanglement depth) certain
classical optimization algorithms outperform others in terms of energy error.


  The production of $J/\psi$ mesons in proton-proton collisions at a
centre-of-mass energy of $\sqrt{s}=13$ TeV is studied with the \lhcb detector.
Cross-section measurements are performed as a function of the transverse
momentum $p_\mathrm{T}$ and the rapidity $y$ of the $J/\psi$ meson in the
region $p_\mathrm{T}<14\mathrm{GeV}/c$ and $2.0<y<4.5$, for both prompt
$J/\psi$ mesons and $J/\psi$ mesons from $b$-hadron decays. The production
cross-sections integrated over the kinematic coverage are $15.03\pm 0.03\pm
0.94$ $\mu$b for prompt $J/\psi$ and $2.25\pm 0.01\pm 0.14$ $\mu$b for $J/\psi$
from $b$-hadron decays, assuming zero polarization of the $J/\psi$ meson. The
first uncertainties are statistical and the second systematic. The
cross-section reported for $J/\psi$ mesons from $b$-hadron decays is used to
extrapolate to a total $b\bar{b}$ cross-section. The ratios of the
cross-sections with respect to $\sqrt{s}=8$ TeV are also determined.


  We address the problem of cross-modal fine-grained action retrieval between
text and video. Cross-modal retrieval is commonly achieved through learning a
shared embedding space, that can indifferently embed modalities. In this paper,
we propose to enrich the embedding by disentangling parts-of-speech (PoS) in
the accompanying captions. We build a separate multi-modal embedding space for
each PoS tag. The outputs of multiple PoS embeddings are then used as input to
an integrated multi-modal space, where we perform action retrieval. All
embeddings are trained jointly through a combination of PoS-aware and
PoS-agnostic losses. Our proposal enables learning specialised embedding spaces
that offer multiple views of the same embedded entities.
  We report the first retrieval results on fine-grained actions for the
large-scale EPIC dataset, in a generalised zero-shot setting. Results show the
advantage of our approach for both video-to-text and text-to-video action
retrieval. We also demonstrate the benefit of disentangling the PoS for the
generic task of cross-modal video retrieval on the MSR-VTT dataset.


  Knowledge distillation aims to enhance the performance of a lightweight
student model by exploiting the knowledge from a pre-trained cumbersome teacher
model. However, in the traditional knowledge distillation, teacher predictions
are only used to provide the supervisory signal for the last layer of the
student model, which may result in those shallow student layers lacking
accurate training guidance in the layer-by-layer back propagation and thus
hinders effective knowledge transfer. To address this issue, we propose
Deeply-Supervised Knowledge Distillation (DSKD), which fully utilizes class
predictions and feature maps of the teacher model to supervise the training of
shallow student layers. A loss-based weight allocation strategy is developed in
DSKD to adaptively balance the learning process of each shallow layer, so as to
further improve the student performance. Extensive experiments on CIFAR-100 and
TinyImageNet with various teacher-student models show significantly
performance, confirming the effectiveness of our proposed method. Code is
available at:
$\href{https://github.com/luoshiya/DSKD}{https://github.com/luoshiya/DSKD}$


  Variants of Triplet networks are robust entities for learning a
discriminative embedding subspace. There exist different triplet mining
approaches for selecting the most suitable training triplets. Some of these
mining methods rely on the extreme distances between instances, and some others
make use of sampling. However, sampling from stochastic distributions of data
rather than sampling merely from the existing embedding instances can provide
more discriminative information. In this work, we sample triplets from
distributions of data rather than from existing instances. We consider a
multivariate normal distribution for the embedding of each class. Using
Bayesian updating and conjugate priors, we update the distributions of classes
dynamically by receiving the new mini-batches of training data. The proposed
triplet mining with Bayesian updating can be used with any triplet-based loss
function, e.g., triplet-loss or Neighborhood Component Analysis (NCA) loss.
Accordingly, Our triplet mining approaches are called Bayesian Updating Triplet
(BUT) and Bayesian Updating NCA (BUNCA), depending on which loss function is
being used. Experimental results on two public datasets, namely MNIST and
histopathology colorectal cancer (CRC), substantiate the effectiveness of the
proposed triplet mining method.


  Person Re-Identification (Re-Id) in occlusion scenarios is a challenging
problem because a pedestrian can be partially occluded. The use of local
information for feature extraction and matching is still necessary. Therefore,
we propose a Pose-guided inter-and intra-part relational transformer (Pirt) for
occluded person Re-Id, which builds part-aware long-term correlations by
introducing transformers. In our framework, we firstly develop a pose-guided
feature extraction module with regional grouping and mask construction for
robust feature representations. The positions of a pedestrian in the image
under surveillance scenarios are relatively fixed, hence we propose an
intra-part and inter-part relational transformer. The intra-part module creates
local relations with mask-guided features, while the inter-part relationship
builds correlations with transformers, to develop cross relationships between
part nodes. With the collaborative learning inter- and intra-part
relationships, experiments reveal that our proposed Pirt model achieves a new
state of the art on the public occluded dataset, and further extensions on
standard non-occluded person Re-Id datasets also reveal our comparable
performances.


  Risk-limiting audits (RLAs) are expected to strengthen the public confidence
in the correctness of an election outcome. We hypothesize that this is not
always the case, in part because for large margins between the winner and the
runner-up, the number of ballots to be drawn can be so small that voters lose
confidence. We conduct a user study with 105 participants resident in the US.
Our findings confirm the hypothesis, showing that our study participants felt
less confident when they were told the number of ballots audited for RLAs. We
elaborate on our findings and propose recommendations for future use of RLAs.


  Designing and optimizing neural network architectures typically requires
extensive expertise, starting with handcrafted designs and then manual or
automated refinement. This dependency presents a significant barrier to rapid
innovation. Recognizing the complexity of automatically generating neural
network architecture from scratch, we introduce Younger, a pioneering dataset
to advance this ambitious goal. Derived from over 174K real-world models across
more than 30 tasks from various public model hubs, Younger includes 7,629
unique architectures, and each is represented as a directed acyclic graph with
detailed operator-level information. The dataset facilitates two primary design
paradigms: global, for creating complete architectures from scratch, and local,
for detailed architecture component refinement. By establishing these
capabilities, Younger contributes to a new frontier, Artificial
Intelligence-Generated Neural Network Architecture (AIGNNA). Our experiments
explore the potential and effectiveness of Younger for automated architecture
generation and, as a secondary benefit, demonstrate that Younger can serve as a
benchmark dataset, advancing the development of graph neural networks. We
release the dataset and code publicly to lower the entry barriers and encourage
further research in this challenging area.


  We report the growth of self-assembled Bi2Se3 quantum dots (QDs) by molecular
beam epitaxy on GaAs substrates using the droplet epitaxy technique. The QD
formation occurs after anneal of Bismuth droplets under Selenium flux.
Characterization by atomic force microscopy, scanning electron microscopy,
X-ray diffraction, high-resolution transmission electron microscopy and X-ray
reflectance spectroscopy is presented. The quantum dots are crystalline, with
hexagonal shape, and have average dimensions of 12 nm height (12 quintuple
layers) and 46 nm width, and a density of $8.5 \cdot 10^9 cm^{-2}$. This
droplet growth technique provides a means to produce topological insulator QDs
in a reproducible and controllable way, providing convenient access to a
promising quantum material with singular spin properties.


  We establish a comparison between Rakib--Sivashinsky and
Michelson-Sivashinsky quasilinear parabolic differential equations governing
the weak thermal limit of upward flame front propagating in a channel. For the
former equation, we give a complete description of all steady solutions and
present their local and global stability analysis. For the latter,
multi-coalescent unstable steady solutions are introduced and shown to be
exponentially more numerous than the previous known coalescente solutions. This
fact is argued to be responsible for the disagreement of the observed dynamics
in numerical experiments with the exact (linear) stability analysis and also
gives the ingredients to describe the quasi-stable behavior of parabolic
steadily propagating flame with centered tip.


  Healthcare data is a valuable resource for research, analysis, and
decision-making in the medical field. However, healthcare data is often
fragmented and distributed across various sources, making it challenging to
combine and analyze effectively. Record linkage, also known as data matching,
is a crucial step in integrating and cleaning healthcare data to ensure data
quality and accuracy. Apache Spark, a powerful open-source distributed big data
processing framework, provides a robust platform for performing record linkage
tasks with the aid of its machine learning library. In this study, we developed
a new distributed data-matching model based on the Apache Spark Machine
Learning library. To ensure the correct functioning of our model, the
validation phase has been performed on the training data. The main challenge is
data imbalance because a large amount of data is labeled false, and a small
number of records are labeled true. By utilizing SVM and Regression algorithms,
our results demonstrate that research data was neither over-fitted nor
under-fitted, and this shows that our distributed model works well on the data.


  In this paper we consider the zero-flux chemotaxis-system \begin{equation*}
\begin{cases} u_{t}=\Delta u-\nabla \cdot (u \chi(v)\nabla v) &
\textrm{in}\quad \Omega\times (0,\infty), \\ 0=\Delta v-v+g(u) &
\textrm{in}\quad \Omega\times (0,\infty),\\ \end{equation*} in a smooth and
bounded domain $\Omega$ of $\mathbb{R}^2$. The chemotactic sensitivity $\chi$
is a general nonnegative function from $C^1((0,\infty))$ whilst $g$, the
production of the chemical signal $v$, belongs to $C^1([0,\infty))$ and
satisfies $\lambda_1\leq g(s)\leq \lambda_2(1+s)^\beta$, for all $s\geq 0$,
$0\leq\beta\leq \frac{1}{2}$ and $0<\lambda_1\leq \lambda_2.$ It is established
that no chemotactic collapse for the cell distribution $u$ occurs in the sense
that any arbitrary nonnegative and sufficiently regular initial data $u(x,0)$
emanates a unique pair of global and uniformly bounded functions $(u,v)$ which
classically solve the corresponding initial-boundary value problem. Finally, we
illustrate the range of dynamics present within the chemotaxis system by means
of numerical simulations.


  Decomposition of tomographic reconstructions has many different practical
application. We propose two new reconstruction methods that combines the task
of tomographic reconstruction with object decomposition. We demonstrate these
reconstruction methods in the context of decomposing directional objects into
various directional components. Furthermore we propose a method for estimating
the main direction in a directional object, directly from the measured computed
tomography data. We demonstrate all the proposed methods on simulated and real
samples to show their practical applicability. The numerical tests show that
decomposition and reconstruction can combined to achieve a highly useful
fibre-crack decomposition.


  Localized bases play an important role in understanding electronic structure.
In periodic insulators, a natural choice of localized basis is given by the
Wannier functions which depend a choice of unitary transform known as a gauge
transformation. Over the past few decades, there have been many works which
have focused on optimizing the choice of gauge so that the corresponding
Wannier functions are maximally localized or reflect some symmetry of the
underlying system. In this work, we consider fully non-periodic materials where
the usual Wannier functions are not well defined and gauge optimization is
impossible. To tackle the problem of calculating exponentially localized
generalized Wannier functions in both periodic and non-periodic system we
discuss the "Iterated Projected Position (IPP)" algorithm. The IPP algorithm is
based on matrix diagonalization and therefore unlike optimization based
approaches it does not require initialization and cannot get stuck at a local
minimum. Furthermore, the IPP algorithm is guaranteed by a rigorous analysis to
produce exponentially localized functions under certain mild assumptions. We
numerically demonstrate that the IPP algorithm can be used to calculate
exponentially localized bases for the Haldane model, the Kane-Mele model (in
both $\mathbb{Z}_2$ invariant even and $\mathbb{Z}_2$ invariant odd phases),
and the $p_x + i p_y$ model on a quasi-crystal lattice.


  Search for the bottom squarks (sbottoms) at the Large Hadron Collider (LHC)
has recently assumed a heightened focus in the hunt for Supersymmetry (SUSY).
The popular framework of the Next-to-Minimal Supersymmetric Standard Model
(NMSSM) could conceive a naturally light sbottom which could easily be
consistent with available constraints from the experiments at the LHC.
Phenomenology of such sbottoms could in principle be as striking as that for a
light top squark (stop) thanks to a rather nontrivial neutralino sector (with
appreciable mixing among the neutral higgsinos and the singlino) that the
scenario gives rise to. Nonetheless, finding such sbottoms might require a
moderately large amount of data ($\sim 300$ $\text{fb}^{-1}$) at the 13 TeV run
of the LHC. A multi-channel analysis establishing a generic depletion of events
in the usual $2b$-$jets$ +$\text{\sout{E}}_T$ final state while registering, in
conjunction, characteristically significant rates in various multi-lepton final
states accompanied by $b$-$jets$ might point not only to the presence of light
sbottom(s) but could also shed crucial light on their compositions and the
(singlino) nature of the lightest SUSY particle (LSP).


  In a Bernal-stacked graphene bilayer, an electronic state in Landau level $%
N=0$ is described by its guiding-center index $X$ (in the Landau gauge) and by
its valley, spin, and orbital indices $\xi =\pm K,\sigma =\pm 1,$ and $%
n=0,1.$ When Coulomb interaction is taken into account, the chiral
two-dimensional electron gas (C2DEG) in this system can support a variety of
quantum Hall ferromagnetic (QHF)\ ground states where the spins and/or valley
pseudospins and/or orbital pseudospins collectively align in space. In this
work, we give a comprehensive account of the phase diagram of the C2DEG at
integer filling factors $\nu \in [-3,3] $ in Landau level N=0 when an
electrical potential difference $\Delta_{B}$ between the two layers is varied.
We consider states with or without layer, spin, or orbital coherence. For each
phase, we discuss the behavior of the transport gap as a function of
$\Delta_{B},$ the spectrum of collective excitations and the optical absorption
due to orbital pseudospin-wave modes. We also study the effect of an external
in-plane electric field on a coherent state that has both valley and spin
coherence and show that it is possible, in such a state, to control the spin
polarization by varying the strength of the external in-plane electric field.


  Algebraic curves in Hilbert modular surfaces that are totally geodesic for
the Kobayashi metric have very interesting geometric and arithmetic properties,
e.g. they are rigid. There are very few methods known to construct such
algebraic geodesics that we call Kobayashi curves.
  We give an explicit way of constructing Kobayashi curves using determinants
of derivatives of theta functions. This construction also allows to calculate
the Euler characteristics of the Teichmueller curves constructed by McMullen
using Prym covers.


  We give simple criteria to identify the exponential order of magnitude of the
absolute value of the determinant for wide classes of random matrix models, not
requiring the assumption of invariance. These include Gaussian matrices with
covariance profiles, Wigner matrices and covariance matrices with
subexponential tails, Erd\H{o}s-R\'enyi and $d$-regular graphs for any
polynomial sparsity parameter, and non-mean-field random matrix models, such as
random band matrices for any polynomial bandwidth. The proof builds on recent
tools, including the theory of the Matrix Dyson Equation as developed in
[Ajanki, Erd\H{o}s, Kr\"uger 2019].
  We use these asymptotics as an important input to identify the complexity of
classes of Gaussian random landscapes in our companion papers [Ben Arous,
Bourgade, McKenna 2021; McKenna 2021].


  We consider the classical problem of particle diffusion in $d$-dimensional
radially-symmetric systems with absorbing boundaries. A key quantity to
characterise such diffusive transport is the evolution of the proportion of
particles remaining in the system over time, which we denote by
$\mathcal{P}(t)$. Rather than work with analytical expressions for
$\mathcal{P}(t)$ obtained from solution of the corresponding continuum model,
which when available take the form of an infinite series of exponential terms,
single-term low-parameter models are commonly proposed to approximate
$\mathcal{P}(t)$ to ease the process of fitting, characterising and
interpreting experimental release data. Previous models of this form have
mainly been developed for circular and spherical systems with an absorbing
boundary. In this work, we consider circular, spherical, annular and
spherical-shell systems with absorbing, reflecting and/or semi-absorbing
boundaries. By proposing a moment matching approach, we develop several simple
one and two parameter exponential and Weibull models for $\mathcal{P}(t)$, each
involving parameters that depend explicitly on the system dimension,
diffusivity, geometry and boundary conditions. The developed models, despite
their simplicity, agree very well with values of $\mathcal{P}(t)$ obtained from
stochastic model simulations and continuum model solutions.


  We extract K-matrix poles from our fits to elastic pion-nucleon scattering
and eta-nucleon production data in order to test a recently proposed method for
the determination of resonance properties, based on the trace of the K-matrix.
We have considered issues associated with the separation of background and
resonance contributions, the correspondence between K-matrix and T-matrix
poles, and the complicated behavior of eigenphases.


  We present results obtained from a series of 5~\AA\ resolution spectra of the
X-ray Nova GRO~J0422+32 obtained in 1993~October, when the system was
approximately 2 magnitudes above quiescence, with ${\rm R \sim 19}$. The data
were obtained in an effort to measure the orbital radial velocity curve of the
secondary, but detection of the narrow photospheric absorption lines needed to
do this proved elusive. Instead we found wide absorption bands reminiscent of
M~star photospheric features. The parameters determined by fitting accretion
disk line profiles (Smak profiles) to the H$\alpha$ line are similar to those
found in several strong black-hole candidates. Measurements of the velocity of
the H$\alpha$ line are consistent with an orbital period of 5.1~hours and a
velocity semi-amplitude of the primary of $34 \pm 6$~\kms. These measurements,
when combined with measurements of the velocity semi-amplitude of the secondary
made by others, indicate that the mass ratio $q \sim 0.09$. If the secondary
follows the empirical mass-radius relation found for CVs, the low $q$ implies a
primary mass of $M_x \sim 5.6$\mo, and a rather low (face-on) inclination. The
H$\alpha$ EW is found to be modulated on the orbital period with a phasing that
implies a partial eclipse of the disk by the secondary, but simultaneous R~band
photometry shows no evidence for such an eclipse.


  Much unstructured data has been produced with the growth of the Internet and
social media. A significant volume of textual data includes users' opinions
about products in online stores and social media. By exploring and categorizing
them, helpful information can be acquired, including customer satisfaction,
user feedback about a particular event, predicting the sale of a specific
product, and other similar cases. In this paper, we present an approach for
sentiment analysis with a deep learning model and use it to recommend products.
A two-channel convolutional neural network model has been used for opinion
mining, which has five layers and extracts essential features from the data. We
increased the number of comments by applying the SMOTE algorithm to the initial
dataset and balanced the data. Then we proceed to cluster the aspects. We also
assign a weight to each cluster using tensor decomposition algorithms that
improve the recommender system's performance. Our proposed method has reached
91.6% accuracy, significantly improved compared to previous aspect-based
approaches.


  Hubble Space Telescope (HST) spectra of the extreme ultraviolet (EUV), the
optically thick emission from the innermost accretion flow onto the central
supermassive black hole, indicate that RLQs tend to be EUV weak compared to the
radio quiet quasars (RQQs); yet the remainder of the optically thick thermal
continuum is indistinguishable. The deficit of EUV emission in RLQs has a
straightforward interpretation as a missing or a suppressed innermost region of
local energy dissipation in the accretion flow. This article is an examination
of the evidence for a distribution of magnetic flux tubes in the innermost
accretion flow that results in magnetically arrested accretion (MAA) and
creates the EUV deficit. These same flux tubes and possibly the interior
magnetic flux that they encircle are the source of the jet power as well. In
the MAA scenario, islands of large scale magnetic vertical flux perforate the
innermost accretion flow of RLQs. The first prediction of the theory that is
supported by the HST data is that the strength of the (large scale poloidal
magnetic fields) jets in the MAA region is regulated by the ram pressure of the
accretion flow in the quasar environment. The second prediction that is
supported by the HST data is that the rotating magnetic islands remove energy
from the accretion flow as a Poynting flux dominated jet in proportion to the
square of the fraction of the EUV emitting gas that is displaced by these
islands.


  We establish a link between vorticity wave interaction and
$\mathcal{PT}$-symmetry breaking in shear flow instabilities. The minimal
dynamical system for two coupled counter-propagating vorticity waves is shown
to be a non-Hermitian system that exhibits a saddle-node exceptional point. The
mechanism of phase-locking and mutual growth of vorticity waves is then related
to the Krein collision and the breaking of $\mathcal{PT}$-symmetry through the
exceptional point. The key parameter that leads the system to spontaneous
$\mathcal{PT}$-symmetry breaking is the ratio between frequency detuning and
coupling strength of the vorticity waves. The critical behavior near the
exceptional point is described as a transition between phase-locking and
phase-slip dynamics of the vorticity waves. The phase-slip dynamics lead to
non-modal, transient growth of perturbations in the regime of unbroken
$\mathcal{PT}$-symmetry, and the phase-slip frequency $\Omega \propto
|k-k_c|^{1/2}$ shares the same critical exponent with the phase rigidity of
system eigenvectors. The results can be readily extended to the interaction of
multiple vorticity waves with multiple exceptional points and rich transient
dynamics.


  Computing asymptotics of the recurrence coefficients of X1-Jacobi polynomials
we investigate the limit of Christoffel function. We also study the relation
between the normalized counting measure based on the zeros of the modified
average characteristic polynomial and the Christoffel function in limit. The
proofs of corresponding theorems with respect to ordinary orthogonal
polynomials are based on the three-term recurrence relation. The main point is
that exceptional orthogonal polynomials possess at least five-term formulae and
so the Christoffel-Darboux formula also fails. It seems that these difficulties
can be handled in combinatorial way.


  Theoretically, stars have been formed from the collapse of cores in the
molecular clouds. Historically, the core had been assumed as an singular
isothermal sphere (SIS), and the collapse had been investigated by a
self-similar manner. This is while the rotation and magnetic field lead to
non-symmetric collapse so that a spheroid shape may be occurred. Here, the
resultant of the centrifugal force and magnetic field gradient is assumed to be
in the normal direction of the rotational axis, and its components are supposed
to be a fraction $\beta$ of the local gravitational force. In this research, a
collapsing SIS core is considered to find the importance of the parameter
$\beta$ for oblateness of the mass shells which are above the head of the
expansion wave. We apply the Adomian decomposition method to solve the system
of nonlinear partial differential equations because the collapse does not occur
in a spherical symmetry with self-similar behavior. In this way, we obtain a
semi-analytical relation for the mass infall rate $\dot{M}$ of the shells at
the envelope. Near the rotational axis, the $\dot{M}$ decreases with increasing
of the non-dimensional radius $\xi$, while a direct relation is observed
between $\dot{M}$ and $\xi$ in the equatorial regions. Also, the values of
$\dot{M}$ in the polar regions are greater than the equatorial values, and this
difference is more often at smaller values of $\xi$. Overall, the results show
that before reaching the head of expansion wave, the visible shape of the
molecular cloud cores can evolve to oblate spheroids. The ratio of major to
minor axes of oblate cores increases with increasing the parameter $\beta$, and
its value can approach to the apparently observed elongated shapes of cores in
the maps of molecular clouds such as Taurus and Perseus.


  We consider a multidimensional inhomogeneous birth-death process (BDP) and
obtain bounds on the rate of convergence for the corresponding one-dimensional
processes.


  Cellular-based networks are expected to offer connectivity for massive
Internet of Things (mIoT) systems. However, their Random Access CHannel (RACH)
procedure suffers from unreliability, due to the collision from the
simultaneous massive access. Despite that this collision problem has been
treated in existing RACH schemes, these schemes usually organize IoT devices'
transmission and re-transmission along with fixed parameters, thus can hardly
adapt to time-varying traffic patterns. Without adaptation, the RACH procedure
easily suffers from high access delay, high energy consumption, or even access
unavailability. With the goal of improving the RACH procedure, this paper
targets to optimize the RACH procedure in real-time by maximizing a long-term
hybrid multi-objective function, which consists of the number of access success
devices, the average energy consumption, and the average access delay. To do
so, we first optimize the long-term objective in the number of access success
devices by using Deep Reinforcement Learning (DRL) algorithms for different
RACH schemes, including Access Class Barring (ACB), Back-Off (BO), and
Distributed Queuing (DQ). The converging capability and efficiency of different
DRL algorithms including Policy Gradient (PG), Actor-Critic (AC), Deep
Q-Network (DQN), and Deep Deterministic Policy Gradients (DDPG) are compared.
Inspired by the results from this comparison, a decoupled learning strategy is
developed to jointly and dynamically adapt the access control factors of those
three access schemes. This decoupled strategy first leverage a Recurrent Neural
Network (RNN) model to predict the real-time traffic values of the network
environment, and then uses multiple DRL agents to cooperatively configure
parameters of each RACH scheme.


  We present new 144-MHz LOFAR observations of the prototypical `X-shaped'
radio galaxy NGC 326, which show that the formerly known wings of the radio
lobes extend smoothly into a large-scale, complex radio structure. We argue
that this structure is most likely the result of hydrodynamical effects in an
ongoing group or cluster merger, for which pre-existing X-ray and optical data
provide independent evidence. The large-scale radio structure is hard to
explain purely in terms of jet reorientation due to the merger of binary black
holes, a previously proposed explanation for the inner structure of NGC 326.
For this reason, we suggest that the simplest model is one in which the
merger-related hydrodynamical processes account for all the source structure,
though we do not rule out the possibility that a black hole merger has
occurred. Inference of the black hole-black hole merger rate from observations
of X-shaped sources should be carried out with caution in the absence of deep,
sensitive low-frequency observations. Some X-shaped sources may be signposts of
cluster merger activity, and it would be useful to investigate the environments
of these objects more generally.


  We establish a general inequality on the Poisson space, yielding an upper
bound for the distance in total variation between the law of a regular random
variable with values in the integers and a Poisson distribution. Several
applications are provided, in particular: (i) to deduce a set of sufficient
conditions implying that a sequence of (suitably shifted) multiple Wiener-It\^o
integrals converges in distribution to a Poisson random variable, and (ii) to
compute explicit rates of convergence for the Poisson approximation of
statistics associated with geometric random graphs with sparse connections
(thus refining some findings by Lachi\`eze-Rey and Peccati (2011)). This is the
first paper studying Poisson approximations on configuration spaces by
combining the Malliavin calculus of variations and the Chen-Stein method.


  Understanding rapid solidification behavior at velocities relevant to
additive manufacturing (AM) is critical to controlling microstructure
selection. Although in-situ visualization of solidification dynamics is now
possible, systematic studies under AM conditions with microstructural outcomes
compared to solidification theory remain lacking. Here we measure solid-liquid
interface velocities of Ni-Mo-Al alloy single crystals under AM conditions with
synchrotron X-ray imaging, characterize the microstructures, and show
discrepancies with classical theories regarding the onset velocity for absolute
stability of a planar solid-liquid interface. Experimental observations reveal
cellular/dendritic microstructures can persist at velocities larger than the
expected absolute stability limit, where banded structure formation should
theoretically appear. We show that theory and experimental observations can be
reconciled by properly accounting for the effect of solute trapping and kinetic
undercooling on the velocity-dependent solidus and liquidus temperatures of the
alloy. Further theoretical developments and accurate assessments of key
thermophysical parameters - like liquid diffusivities, solid-liquid interface
excess free energies, and kinetic coefficients - remain needed to
quantitatively investigate such discrepancies and pave the way for the
prediction and control of microstructure selection under rapid solidification
conditions.


  At high energies, in particle-capture processes between ions and atoms,
classical kinematic requirements show that generally double collision Thomas
processes dominate. However, for certain mass-ratios these processes are
kinematically forbidden. This paper explores the possibility of capture for
such processes by triple or higher order collision processes.


  We present a theoretical analysis of the properties of low-dimensional
quantum antiferromagnets in applied magnetic fields. In a nonlinear sigma model
description, we use a spin stiffness analysis, a 1/N expansion, and a
renormalization group approach to describe the broken-symmetry regimes of
finite magnetization, and, in cases of most interest, a low-field regime where
symmetry is restored by quantum fluctuations. We compute the magnetization,
critical fields, spin correlation functions, and decay exponents accessible by
nuclear magnetic resonance experiments. The model is relevant to many systems
exhibiting Haldane physics, and provides good agreement with data for the
two-chain spin ladder compound CuHpCl.


  Several new physics scenarios, motivated e.g. by dark matter, feature new
electroweakly charged states where the lightest particle in the multiplet is
stable and neutral. In such cases direct searches at LHC are notoriously
difficult, while electroweak precision tests both at hadron and lepton
colliders offer the possibility to indirectly probe those states. In this work,
we assess the sensitivity of the high-luminosity phase of the LHC on new
electroweak multiplets via the modification of neutral and charged Drell-Yan
processes, and compare the reach of future hadron and lepton colliders
presently under consideration.


  First-principles simulations of electronic properties of hybrid
inorganic/organic interfaces are challenging, as common density-functional
theory (DFT) approximations target specific material classes like bulk
semiconductors or gas-phase molecules. Taking as a prototypical example
anthracene physisorbed on monolayer MoS$_2$, we assess the ability of different
\textit{ab initio} schemes to describe the electronic structure using
semi-local and hybrid DFT. For the latter, an unconstrained three-parameter
range-separation scheme is employed. Comparisons against many-body perturbation
theory results indicate that DFT is substantially unable to make reliable
predictions about interfacial properties. Hybrid functionals, while improving
the accuracy of the MoS$_2$ band structure, do not systematically enhance the
description of hybrid systems with respect to semi-local functionals. Neither
approach provides a good starting point for $G_0W_0$, which, consequently,
cannot provide much information beyond the correct energy level alignment. We
show that non-empirically parametrized electrostatic screening models can
accomplish the same task at negligible computational costs. Such schemes can
include substrates of hybrid interfaces in good agreement with experimental
data. Our results indicate that currently, fully atomistic, many-body
simulations of weakly interacting hybrid systems are not worth the required
computational resources. In contrast, ab-initio-parametrized effective models
mimicking the environment offer a scalable alternative without compromising
accuracy and predictivity.


  We propose a scheme for generating entangled states for two superconducting
quantum interference devices in a thermal cavity with the assistance of a
microwave pulse.


  We present a detailed spectral and imaging analysis of the central $15''$
radius ($\sim 7.5 \text{ kpc}$) region of the merger galaxy NGC 6240 that makes
use of all the available \textit{Chandra}-ACIS data ($0.3 - 3 \text{ keV}$
effective exposure of $\sim 190 \text{ ks}$). This region shows extended X-ray
structures with lower energy counterparts imaged in CO, [O III] and H$\alpha$
line emission. We find both photo-ionized phases of possible nuclear excitation
and thermal shock-excited emission in the different large-scale components: the
north-west "loop" detected in H$\alpha$, the region surrounding the two nuclei,
the large outflow region to the north-east detected in [O III], and the
southern X-ray extensions. The latter could be the ionization cone of the
northern nucleus, with the N counterpart being obscured by the galaxy disk. The
radial distribution of the X-ray surface brightness suggests a confined hot
interstellar medium at $r < 2.5 \text{ kpc}$, with a free-flowing wind at
larger radii; if the confinement is magnetic, we estimate B-field values of
$\sim 100\,\mu \text{G}$ , similar to those measured in the halo of M82. The
thermal gas of the extended halo at $kT \sim 1 \text{ keV}$ absorbs soft X-rays
from the AGN, but not the extreme ultraviolet radiation leading to a rapid
increase in $F_{\text{[O III]}}/F_{\text{X}}$ beyond $\sim 3 \text{ kpc}$. The
$\alpha$ element to Fe abundance ratios of the thermal components in the
different regions of the extended X-ray emission are generally compatible with
SNe II yields, confirming the importance of the active star formation in NGC
6240.


  In this note we prove (under mild hypotheses) that $f$ is a nontrivial
character of $\mathbb{F}_p$ if and only if the Fourier transform of $f$ has
magnitude 1 somewhere in $\mathbb{F}_p^\times$. This implies a converse to a
theorem of Gauss on the magnitude of the Gauss sum, in addition to other
consequences.


  We present Uncertainty-aware Cascaded Stereo Network (UCS-Net) for 3D
reconstruction from multiple RGB images. Multi-view stereo (MVS) aims to
reconstruct fine-grained scene geometry from multi-view images. Previous
learning-based MVS methods estimate per-view depth using plane sweep volumes
with a fixed depth hypothesis at each plane; this generally requires densely
sampled planes for desired accuracy, and it is very hard to achieve
high-resolution depth. In contrast, we propose adaptive thin volumes (ATVs); in
an ATV, the depth hypothesis of each plane is spatially varying, which adapts
to the uncertainties of previous per-pixel depth predictions. Our UCS-Net has
three stages: the first stage processes a small standard plane sweep volume to
predict low-resolution depth; two ATVs are then used in the following stages to
refine the depth with higher resolution and higher accuracy. Our ATV consists
of only a small number of planes; yet, it efficiently partitions local depth
ranges within learned small intervals. In particular, we propose to use
variance-based uncertainty estimates to adaptively construct ATVs; this
differentiable process introduces reasonable and fine-grained spatial
partitioning. Our multi-stage framework progressively subdivides the vast scene
space with increasing depth resolution and precision, which enables scene
reconstruction with high completeness and accuracy in a coarse-to-fine fashion.
We demonstrate that our method achieves superior performance compared with
state-of-the-art benchmarks on various challenging datasets.


  We have constructed a new formalism for describing a situation with
{\color{red} several (dual) strings} present at a time, a {\color{red} string
field theory}, by means of a constituent / a strings from objects picture
similar to, but importantly different from the "bits" by Charles
Thorn\cite{Thorn}. Our "objects" (essentially the bits) represent rather a
making a lattice in the {\color{red} light cone variables} on the string. The
remarkable feature and simplicity of our formalism is, that the "objects" do
{\color{red} NOT interact}, basically just run or sit trivially fixed.
{\color{red} Scattering is a fake} in our formalism. This opens also up for
hoping for generalizations inspired by hadrons with their partons all having
Bjorken variable $x=0$, and thus infinitely many constituents. The p-adic
string is an example.


  We have carried out temperature-dependent x-ray diffraction and Raman
scattering experiments on powder $Cs_3Bi_2Br_9$. Trigonal to monoclinic
structural transition at around 95 K is discussed and shown to be driven by the
softening of the soft mode. We propose a model to describe the dynamics of the
incomplete soft-mode. Raman scattering experiments demonstrate the origin of
the soft mode to the rocking motions of Br atoms that participate to form
$BiBr_6$ octahedra, which correlates the reported theoretical calculations.
Some of the Raman mode frequencies exhibit anomalous temperature dependence due
to strong anharmonic phonon-phonon coupling. Temperature-dependent x-ray
diffraction analysis estimate the volume thermal expansion coefficient in
trigonal phase to be $13.54\times10^{-5} K^{-1}$. In the trigonal phase, the
broadening of the full width at half maximum (FWHM) with increase in
temperature for $E_g$ and $A_{1g}$ modes is accompanied by decaying of one
optical phonon into two acoustic phonons. The volume thermal expansion rather
than anharmonic phonon-phonon interaction dominates the frequency shift for the
Raman modes in trigonal phase. In the monoclinic phase, the strength of four
phonon processes to the frequency shift and linewidth broadening is much
smaller than that for three phonon processes for some of the modes. The
observed temperature dependence of FWHM of certain Raman modes in both phases
suggests unusual electron-phonon coupling in the crystal.


  Coupling of black hole mass to the cosmic expansion has been suggested as a
possible path to understanding the dark energy content of the Universe. We test
this hypothesis by comparing the supermassive black hole (SMBH) mass density at
$z=0$ to the total mass accreted in AGN since $z=6$, to constrain how much of
the SMBH mass density can arise from cosmologically-coupled growth, as opposed
to growth by accretion. Using an estimate of the local SMBH mass density of
$\approx 1.0\times10^{6}\,$M$_{\odot}\,$Mpc$^{-1}$, a radiative accretion
efficiency, $\eta$: $0.05<\eta<0.3$, and the observed AGN luminosity density at
$z\approx 4$, we constrain the value of the coupling constant between the scale
size of the Universe and the black hole mass, $k$, to lie in the range
$0<k\stackrel{<}{_{\sim}}2$, below the value of $k=3$ needed for black holes to
be the source term for dark energy. Initial estimates of the gravitational wave
background using pulsar timing arrays, however, favor a higher SMBH mass
density at $z=0$. We show that if we adopt such a mass density at $z=0$ of
$\approx 7.4\times 10^{6}\,$M$_{\odot}\,$Mpc$^{-1}$, this makes $k=3$ viable
even for low radiative efficiencies, and may exclude non-zero cosmological
coupling. We conclude that, although current estimates of the SMBH mass density
based on the black hole mass -- bulge mass relation probably exclude $k=3$, the
possibility remains open that, if the GWB is due to SMBH mergers, $k>2$ is
preferred.


  Motivation: Technical debt is a metaphor that describes not-quite-right code
introduced for short-term needs. Developers are aware of it and admit it in
source code comments, which is called Self- Admitted Technical Debt (SATD).
Therefore, SATD indicates weak code that developers are aware of. Problem
statement: Inspecting source code is time-consuming; automatically inspecting
source code for its vulnerabilities is a crucial aspect of developing software.
It helps practitioners reduce the time-consuming process and focus on
vulnerable aspects of the source code. Proposal: Accurately identify and better
understand the semantics of self-admitted technical debt (SATD) by leveraging
NLP and NL-PL approaches to detect vulnerabilities and the related SATD.
Finally, a CI/CD pipeline will be proposed to make the vulnerability discovery
process easily accessible to practitioners.


  We present the photometric and spectroscopic evolution of the type Ic
supernova LSQ14efd, discovered by the La Silla QUEST survey and followed by
PESSTO. LSQ14efd was discovered few days after explosion and the observations
cover up to ~100 days. The early photometric points show the signature of the
cooling of the shock break-out event experienced by the progenitor at the time
of the supernova explosion, one of the first for a type Ic supernova. A
comparison with type Ic supernova spectra shows that LSQ14efd is quite similar
to the type Ic SN 2004aw. These two supernovae have kinetic energies that are
intermediate between standard Ic explosions and those which are the most
energetic explosions known (e.g. SN 1998bw). We computed an analytical model
for the light-curve peak and estimated the mass of the ejecta 6.3 +/- 0.5 Msun,
a synthesized nickel mass of 0.25 Msun and a kinetic energy of Ekin = 5.6 +/-
0.5 x 10^51 erg. No connection between LSQ14efd and a GRB event could be
established. However we point out that the supernova shows some spectroscopic
similarities with the peculiar SN-Ia 1999ac and the SN-Iax SN 2008A. A
core-collapse origin is most probable considering the spectroscopic,
photometric evolution and the detection of the cooling of the shock break-out.


  Large language models (LLM) not only have revolutionized the field of natural
language processing (NLP) but also have the potential to reshape many other
fields, e.g., recommender systems (RS). However, most of the related work
treats an LLM as a component of the conventional recommendation pipeline (e.g.,
as a feature extractor), which may not be able to fully leverage the generative
power of LLM. Instead of separating the recommendation process into multiple
stages, such as score computation and re-ranking, this process can be
simplified to one stage with LLM: directly generating recommendations from the
complete pool of items. This survey reviews the progress, methods, and future
directions of LLM-based generative recommendation by examining three questions:
1) What generative recommendation is, 2) Why RS should advance to generative
recommendation, and 3) How to implement LLM-based generative recommendation for
various RS tasks. We hope that this survey can provide the context and guidance
needed to explore this interesting and emerging topic.


  In this paper, we present the optimal use of coded signals in diverging wave
transmission for fast ultrasonic imaging. The performance of coded imaging with
diverging waves, quantified by SNR, CNR, speckle power and target signal
strength, is optimized in terms of code length, wave profile, aperture size and
field of view. We obtained one frame in 200 microseconds using coded diverging
wave transmission, equivalent to very high 5000 frames/s rate, where the
imaging depth is 7.5 cm. The performances of coded diverging wave transmission
and conventional single focused phased array imaging are compared on a single
frame basis. Complementary Golay sequences with code lengths ranging from 2 to
10 bits are used to code the signal. The signal strength and SNR obtained using
synthetic transmit aperture and conventional single focused phased array
imaging techniques, respectively, are used as reference in the performance
analysis. We present a method to determine the optimum diverging wave profile
to maximize the SNR across the entire viewing sector, which matches the
received signal strength distribution to that of synthetic transmit aperture
imaging. Optimum diverging wave profiles are determined for different sector
angles and for different array apertures. For 90{\deg} sector, the SNR of 8-bit
coded signal with optimized diverging wave profile is higher than that of
conventional single focused phased array imaging at all depths and regions
except the focal region, where it is 2-8 dB lower.


  Satellite-based QKD offers the potential to share highly secure encryption
keys between optical ground stations all over the planet. SpooQySats is a
programme for establishing the space worthiness of highly-miniaturised,
polarization entangled, photon pair sources using CubeSat nanosatellites. The
sources are being developed iteratively with an early version in orbit already
and improved versions soon to be launched. Once fully developed, the photon
pair sources can be deployed on more advanced satellites that are equipped with
optical links. These can allow for very secure uplinks and downlinks and can be
used to establish a global space-based quantum key distribution network. This
would enable highly secure symmetric encryption keys to be shared between
optical ground stations all over the planet.


  A singularly perturbed convection-diffusion problem posed on the unit square
in $\mathbb{R}^2$, whose solution has exponential boundary layers, is solved
numerically using the local discontinuous Galerkin (LDG) method with piecewise
polynomials of degree at most $k>0$ on three families of layer-adapted meshes:
Shishkin-type, Bakhvalov-Shishkin-type and Bakhvalov-type.On Shishkin-type
meshes this method is known to be no greater than $O(N^{-(k+1/2)})$ accurate in
the energy norm induced by the bilinear form of the weak formulation, where $N$
mesh intervals are used in each coordinate direction. (Note: all bounds in this
abstract are uniform in the singular perturbation parameter and neglect
logarithmic factors that will appear in our detailed analysis.) A delicate
argument is used in this paper to establish $O(N^{-(k+1)})$ energy-norm
superconvergence on all three types of mesh for the difference between the LDG
solution and a local Gauss-Radau projection of the exact solution into the
finite element space. This supercloseness property implies a new $N^{-(k+1)}$
bound for the $L^2$ error between the LDG solution on each type of mesh and the
exact solution of the problem; this bound is optimal (up to logarithmic
factors). Numerical experiments confirm our theoretical results.


  This paper deals with the detection problem of extragalactic point-sources in
multi-frequency, microwave sky maps that will be obtainable in future cosmic
microwave background radiation (CMB) experiments with instruments capable of
very high spatial resolution. With spatial resolutions that can be of order of
0.1-1.0 arcsec or better, the extragalactic point-sources will appear isolated.
The same holds also for the compact structures due to the Sunyaev-Zeldovich
(SZ) effect (both thermal and kinetic). This situation is different from the
maps obtainable with instruments as WMAP or PLANCK where, because of the
smaller spatial resolution (approximately 5-30 arcmin), the point-sources and
the compact structures due to the SZ effect form a uniform noisy background
(the "confusion noise"). Hence, the point-source detection techniques developed
in the past are based on the assumption that all the emissions that contribute
to the microwave background can be modeled with homogeneous and isotropic
(often Gaussian) random fields and make use of the corresponding spatial
power-spectra. In the case of very high resolution observations such an
assumption cannot be adopted since it still holds only for the CMB. Here, we
propose an approach based on the assumption that the diffuse emissions that
contribute to the microwave background can be locally approximated by
two-dimensional low order polynomials. In particular, two sets of numerical
techniques are presented containing two different algorithms each. The
performance of the algorithms is tested with numerical experiments that mimic
the physical scenario expected for high Galactic latitude observations with the
Atacama Large Millimeter/Submillimeter Array (ALMA).


  We discuss the evolution of cosmological magnetic fields from the early
universe to the present. We review different scenarios for magnetogenesis in
the early universe and follow the subsequent evolution of these fields as the
universe recombines. We then focus on the role primordial fields play after
recombination in the seeding of stellar and galactic fields and the formation
of structure. Cosmological magnetic fields in the intergalactic medium trace
the turbulent history of the universe and may contain fossils of the early
universe. We conclude by discussing observational probes of cosmological
magnetic fields including the study of extragalactic cosmic rays.


  A hot and dense partonic system can be produced in the early stage of a
relativistic heavy ion collision. How it equilibrates is important for the
extraction of Quark-Gluon Plasma properties. We study the chemical and kinetic
equilibrations of the Quark-Gluon Plasma using a radiative transport model.
Thermal and Color-Glass-Condensate motivated initial conditions are used. We
observe that screened parton interactions always lead to partial pressure
isotropization. Different initial pressure anisotropies result in the same
asymptotic evolution. Comparison of evolutions with and without radiative
processes shows that chemical equilibration interacts with kinetic
equilibration and radiative processes can contribute significantly to pressure
isotropization.


  In this paper, we introduce a new approach for constructing robust
well-balanced numerical methods for the one-dimensional Saint-Venant system
with and without the Manning friction term. Following the idea presented in [R.
Abgrall, Commun. Appl. Math. Comput. 5(2023), pp. 370-402], we first combine
the conservative and non-conservative (primitive) formulations of the studied
conservative hyperbolic system in a natural way. The solution is globally
continuous and described by a combination of point values and average values.
The point values and average values will then be evolved by two different forms
of PDEs: a conservative version of the cell averages and a possibly
non-conservative one for the points. We show how to deal with both the
conservative and non-conservative forms of PDEs in a well-balanced manner. The
developed schemes are capable of exactly preserving both the still-water and
moving-water equilibria. Compared with existing well-balanced methods, this new
class of scheme is nonlinear-equations-solver-free. This makes the developed
schemes less computationally costly and easier to extend to other models. We
demonstrate the behavior of the proposed new scheme on several challenging
examples.


  Apportionment is the problem of distributing $h$ indivisible seats across
states in proportion to the states' populations. In the context of the US House
of Representatives, this problem has a rich history and is a prime example of
interactions between mathematical analysis and political practice. Grimmett
(2004) suggested to apportion seats in a randomized way such that each state
receives exactly their proportional share $q_i$ of seats in expectation (ex
ante proportionality) and receives either $\lfloor q_i \rfloor$ or $\lceil q_i
\rceil$ many seats ex post (quota). However, there is a vast space of
randomized apportionment methods satisfying these two axioms, and so we
additionally consider prominent axioms from the apportionment literature. Our
main result is a randomized method satisfying quota, ex ante proportionality
and house monotonicity - a property that prevents paradoxes when the number of
seats changes and which we require to hold ex post. This result is based on a
generalization of dependent rounding on bipartite graphs, which we call
cumulative rounding and which might be of independent interest, as we
demonstrate via applications beyond apportionment.


  While building a universal quantum computer remains challenging, devices of
restricted power such as the so-called one pure qubit model have attracted
considerable attention. An important step in the construction of these limited
quantum computational devices is the understanding of whether the verification
of the computation within these models could be also performed in the
restricted scheme. Encoding via blindness (a cryptographic protocol for
delegated computing) has proven successful for the verification of universal
quantum computation with a restricted verifier. In this paper, we present the
adaptation of this approach to the one pure qubit model, and present the first
feasible scheme for the verification of delegated one pure qubit model of
quantum computing.


  The Schr\"odinger cat state is important in quantum optics because of its
non-Gaussian properties. This paper proposes the use of degenerate parametric
scattering and measurement of the number of photons in the pump mode to
conditionally prepare the Schr\"odinger cat state. This method ensures the
preparation of SC in systems with weak parametric non-linear interaction.
Comparison with the existing whispering mode gallery microresonator from
lithium niobate indicates the possible applicability of this method.


  We prove that with high probability over the choice of a random graph $G$
from the Erd\H{o}s-R\'enyi distribution $G(n,1/2)$, a natural
$n^{O(\varepsilon^2 \log n)}$-time, degree $O(\varepsilon^2 \log n)$
sum-of-squares semidefinite program cannot refute the existence of a valid
$k$-coloring of $G$ for $k = n^{1/2 +\varepsilon}$. Our result implies that the
refutation guarantee of the basic semidefinite program (a close variant of the
Lov\'asz theta function) cannot be appreciably improved by a natural $o(\log
n)$-degree sum-of-squares strengthening, and this is tight up to a $n^{o(1)}$
slack in $k$. To the best of our knowledge, this is the first lower bound for
coloring $G(n,1/2)$ for even a single round strengthening of the basic SDP in
any SDP hierarchy.
  Our proof relies on a new variant of instance-preserving non-pointwise
complete reduction within SoS from coloring a graph to finding large
independent sets in it. Our proof is (perhaps surprisingly) short, simple and
does not require complicated spectral norm bounds on random matrices with
dependent entries that have been otherwise necessary in the proofs of many
similar results [BHK+16, HKP+17, KB19, GJJ+20, MRX20].
  Our result formally holds for a constraint system where vertices are allowed
to belong to multiple color classes; we leave the extension to the formally
stronger formulation of coloring, where vertices must belong to unique colors
classes, as an outstanding open problem.


  In reference gr-qc/0104036 a four-dimensional effective theory of gravity
embeddable in a five-dimensional "distorted" Randall-Sundrum brane scenario was
derived. The present paper is aimed at the application of such a theory to
describe physics in an open Friedmann-Robertson-Walker (Weyl-symmetric)
universe. It is shown that regular bouncing universes arise for a given range
of the free parameter of the theory.


  Spin excitations that soften near the onset of magnetic order have long been
known to act as `paramagnon' pairing glue that can drive spin-triplet
superconductivity. Recent findings of superconductivity in graphene bilayers
and trilayers, occurring in the proximity of different itinerant ordered phases
polarized in isospin (spin and valley), have motivated us to conduct a
comprehensive investigation of an isospin extension of the paramagnon pairing
mechanism in the vicinity of spin/isospin orders. In each case, we identify a
soft mode, associated with the order parameter fluctuations, that mediates
pairing interaction. We develop an approach that relates the soft mode
described through summation of the contributions most strongly divergent at the
onset of spin/valley isospin orders. This interaction is not always attractive,
but if it is, it gives rise to an enhancement of superconducting $T_c$ in an
appropriate pairing channel. In the cases when the pairing interaction is
attractive, it leads to the formation of a superconducting state which can be
either spin-triplet and valley-singlet or vice versa, depending on the specific
isospin order type. These findings demonstrate that the occurrence of
superconductivity in the vicinity of an itinerant magnetic phase is a generic
phenomenon, closely mirroring experimental observations.


  We study t-structures generated by sets of objects which satisfy a condition
weaker than the compactness. We also study weight structures cogenerated by
sets of objects satisfying the dual condition. Under some appropriate
hypothesis, it turns out that the weight structure is right adjacent to the
t-structure.


  Long-tailed classification poses a challenge due to its heavy imbalance in
class probabilities and tail-sensitivity risks with asymmetric misprediction
costs. Recent attempts have used re-balancing loss and ensemble methods, but
they are largely heuristic and depend heavily on empirical results, lacking
theoretical explanation. Furthermore, existing methods overlook the decision
loss, which characterizes different costs associated with tailed classes. This
paper presents a general and principled framework from a
Bayesian-decision-theory perspective, which unifies existing techniques
including re-balancing and ensemble methods, and provides theoretical
justifications for their effectiveness. From this perspective, we derive a
novel objective based on the integrated risk and a Bayesian deep-ensemble
approach to improve the accuracy of all classes, especially the "tail".
Besides, our framework allows for task-adaptive decision loss which provides
provably optimal decisions in varying task scenarios, along with the capability
to quantify uncertainty. Finally, We conduct comprehensive experiments,
including standard classification, tail-sensitive classification with a new
False Head Rate metric, calibration, and ablation studies. Our framework
significantly improves the current SOTA even on large-scale real-world datasets
like ImageNet.


  Accelerated charges emit both electromagnetic and gravitational radiation.
Classically, it was found that the electromagnetic energy spectrum radiated by
an electron in a monochromatic plane wave is proportional to the corresponding
gravitational one. Quantum mechanically, it was shown that the amplitudes of
graviton photoproduction and Compton scattering are proportional to each other
at tree level. Here, by combining strong-field QED and quantum gravity, we
demonstrate that the amplitude of nonlinear graviton photoproduction in an
arbitrary plane wave is proportional to the corresponding amplitude of
nonlinear Compton scattering. Also, introducing classical amplitudes we prove
that the proportionality relies on the semiclassical nature of the electron's
motion in a plane wave and on energy-momentum conservation laws, leading to the
same proportionality constant in the classical and quantum case. These results
deepen the intertwine between gravity and electromagnetism into both a
nonlinear and a quantum level.


  Preliminary results on the measurement of four selected properties of the top
quark are presented. The relative fraction of $t\bar{t}$ production through
gluon fusion has been measured in the $t\bar{t}$ dilepton decay channel by the
CDF Collaboration as $F_{gg}=0.53^{+0.36}_{-0.38}$. Using an integrated
luminosity of 2.7 fb$^{-1}$ collected with the CDF II detector, we also
determine the $t\bar{t}$ differential cross section with respect to values up
to $\sim$1 TeV of the $t\bar{t}$ invariant mass. We present a model-independent
measurement of the helicity of $W$ bosons produced in top quark decays, using
an integrated luminosity of up to 2.7 fb$^{-1}$ collected by the D0 detector,
and find the fraction of longitudinal $W$ bosons $f_0=0.49\pm0.14$, and the
fraction of right-handed $W$ bosons $f_+=0.11\pm0.08$. Finally, we measure the
parton level forward-backward asymmetry of pair produced top quarks using an
integrated luminosity of 3.2 fb$^{-1}$ collected with the CDF II detector, and
find $A_{FB}=0.19\pm0.07$. All results are consistent with the predictions of
the standard model.