  Bj\"orner and Wachs defined a major index for labeled plane forests and
showed that it has the same distribution as the number of inversions. We define
and study the distributions of a few other natural statistics on labeled
forests. Specifically, we introduce the notions of bottom-to-top maxima, cyclic
bottom-to-top maxima, sorting index, and cycle minima. Then we show that the
pairs (inv, Bt-max), (sor, Cyc), and (maj, Cbt-max) are equidistributed. Our
results extend the result of Bj\"orner and Wachs and generalize results for
permutations. We also introduce analogous statistics for signed labeled forests
and show equidistribution results which generalize results for signed
permutations.


  The spin polarization of electrons from multiphoton ionization of Xe by 395
nm circularly polarized laser pulses at $6\cdot10^{13}$ W/cm$^2$ has been
measured. At this photon energy of 3.14 eV the above threshold ionization peaks
connected to Xe$^+$ ions in the ground state ($J=3/2$, ionization potential
$I_p=12.1$ eV) and the first exicted state ($J=1/2$, $I_p=13.4$ eV) are clearly
separated in the electron energy distribution. These two combs of ATI peaks
show opposite spin polarizations. The magnitude of the spin polarization is a
factor of two higher for the $J=1/2$ than for the $J=3/2$ final ionic state. In
turn the data show that the ionization probability is strongly dependent on the
sign of the magnetic quantum number.


  The growing role of data-driven approaches to scientific discovery has
unveiled a large class of models that involve latent transformations with a
rigid algebraic constraint. Three-dimensional molecule reconstruction in
Cryo-Electron Microscopy (cryo-EM) is a central problem in this class. Despite
decades of algorithmic and software development, there is still little
theoretical understanding of the sample complexity of this problem, that is,
number of images required for 3-D reconstruction. Here we consider
multi-reference alignment (MRA), a simple model that captures fundamental
aspects of the statistical and algorithmic challenges arising in cryo-EM and
related problems. In MRA, an unknown signal is subject to two types of
corruption: a latent cyclic shift and the more traditional additive white
noise. The goal is to recover the signal at a certain precision from
independent samples. While at high signal-to-noise ratio (SNR), the number of
observations needed to recover a generic signal is proportional to
$1/\mathrm{SNR}$, we prove that it rises to a surprising $1/\mathrm{SNR}^3$ in
the low SNR regime. This precise phenomenon was observed empirically more than
twenty years ago for cryo-EM but has remained unexplained to date. Furthermore,
our techniques can easily be extended to the heterogeneous MRA model where the
samples come from a mixture of signals, as is often the case in applications
such as cryo-EM, where molecules may have different conformations. This
provides a first step towards a statistical theory for heterogeneous cryo-EM.


  This paper presents a method for learning And-Or models to represent context
and occlusion for car detection and viewpoint estimation. The learned And-Or
model represents car-to-car context and occlusion configurations at three
levels: (i) spatially-aligned cars, (ii) single car under different occlusion
configurations, and (iii) a small number of parts. The And-Or model embeds a
grammar for representing large structural and appearance variations in a
reconfigurable hierarchy. The learning process consists of two stages in a
weakly supervised way (i.e., only bounding boxes of single cars are annotated).
Firstly, the structure of the And-Or model is learned with three components:
(a) mining multi-car contextual patterns based on layouts of annotated single
car bounding boxes, (b) mining occlusion configurations between single cars,
and (c) learning different combinations of part visibility based on car 3D CAD
simulation. The And-Or model is organized in a directed and acyclic graph which
can be inferred by Dynamic Programming. Secondly, the model parameters (for
appearance, deformation and bias) are jointly trained using Weak-Label
Structural SVM. In experiments, we test our model on four car detection
datasets --- the KITTI dataset \cite{Geiger12}, the PASCAL VOC2007 car
dataset~\cite{pascal}, and two self-collected car datasets, namely the
Street-Parking car dataset and the Parking-Lot car dataset, and three datasets
for car viewpoint estimation --- the PASCAL VOC2006 car dataset~\cite{pascal},
the 3D car dataset~\cite{savarese}, and the PASCAL3D+ car
dataset~\cite{xiang_wacv14}. Compared with state-of-the-art variants of
deformable part-based models and other methods, our model achieves significant
improvement consistently on the four detection datasets, and comparable
performance on car viewpoint estimation.


  We consider direct-detection searches for sub-GeV dark matter via electron
scatterings in the presence of large interactions between dark and ordinary
matter. Scatterings both on electrons and nuclei in the Earth's crust,
atmosphere, and shielding material attenuate the expected local dark matter
flux at a terrestrial detector, so that such experiments lose sensitivity to
dark matter above some critical cross section. We study various models,
including dark matter interacting with a heavy and ultralight dark photon,
through an electric dipole moment, and exclusively with electrons. For a
dark-photon mediator and an electric dipole interaction, the dark
matter-electron scattering cross-section is directly linked to the dark
matter-nucleus cross section, and nuclear interactions typically dominate the
attenuation process. We determine the exclusion bands for the different
dark-matter models from several experiments - SENSEI, CDMS-HVeV, XENON10,
XENON100, and DarkSide-50 - using a combination of Monte Carlo simulations and
analytic estimates. We also derive projected sensitivities for a detector
located at different depths and for a range of exposures, and calculate the
projected sensitivity for SENSEI at SNOLAB and DAMIC-M at Modane. Finally, we
discuss the reach to high cross sections and the modulation signature of a
small balloon- and satellite-borne detector sensitive to electron recoils, such
as a Skipper-CCD. Such a detector could potentially probe unconstrained
parameter space at high cross sections for a sub-dominant component of dark
matter interacting with a massive, but ultralight, dark photon.


  Decentralized conflict resolution for autonomous vehicles is needed in many
places where a centralized method is not feasible, e.g., parking lots, rural
roads, merge lanes, etc. However, existing methods generally do not fully
utilize optimization in decentralized conflict resolution. We propose a
decentralized conflict resolution method for autonomous vehicles based on a
novel extension to the Alternating Directions Method of Multipliers (ADMM),
called Online Adaptive ADMM (OA-ADMM), and on Model Predictive Control (MPC).
OA-ADMM is tailored to online systems, where fast and adaptive real-time
optimization is crucial, and allows the use of safety information about the
physical system to improve safety in real-time control. We prove convergence in
the static case and give requirements for online convergence. Combining OA-ADMM
and MPC allows for robust decentralized motion planning and control that
seamlessly integrates decentralized conflict resolution. The effectiveness of
our proposed method is shown through simulations in CARLA, an open-source
vehicle simulator, resulting in a reduction of 47.93% in mean added delay
compared with the next best method.


  In this paper we build on the framework developed in "Subelliptic Boundary
Value Problems for the Spin_C Dirac Operator, I, II, III" to obtain a more
complete understanding of the gluing properties for indices of boundary value
problems for the SpinC-Dirac operator with sub-elliptic boundary conditions. We
extend our analytic results for sub-elliptic boundary value problems for the
SpinC-Dirac operator, and gluing results for the indices of these boundary
problems to SpinC-manifolds with several pseudoconvex (pseudoconcave) boundary
components. These results are applied to study Stein fillability for compact,
3-dimensional, contact manifolds.


  As a first step towards understanding the morphology of PdO crystals we
performed a systematic full-potential density-functional theory study of all
possible 1 x 1 terminations of the low-index surfaces of tetragonal PdO.
Applying the concept of first-principles atomistic thermodynamics we analyze
the composition, structure and stability of these PdO orientations in
equilibrium with an arbitrary oxygen environment. Within the studied subset of
1 x 1 geometries the polar PdO-terminated PdO(100) orientation turns out to be
surprisingly stable over the whole range of experimentally accessible gas phase
conditions. Setting up a constrained Wulff construction within the compiled
data set, this PdO(100)-PdO facet correspondingly dominates the obtained
polyhedron by far. The real PdO crystallite shape will however likely be
affected by surface reconstructions, which are not covered by the present
study.


  In this paper, we intend to evaluate and analyze the statefinder parameters
in $f(T)$ cosmology. Friedmann equation in $f(T)$ model is taken, and the
statefinder parameters ${r,s}$ are calculated. We consider a model of $f(T)$
which contains a constant, linear and non-linear form of torsion. We plot $r$
and $s$ in order to characterize this model in the ${r,s}$ plane. We found that
our model $f(T)=2C_1 \sqrt{-T} +\alpha T+C_2,$ predicts the decay of dark
energy in the far future while its special case namely teleparallel gravity
predicts that dark energy will overcome over all the energy content of the
Universe.


  Distributed embedded systems (DESs) are no longer the exception; they are the
rule in many application areas such as avionics, the automotive industry,
traffic systems, sensor networks, and medical devices. Formal DES specification
and verification is challenging due to state space explosion and the need to
support real-time features. This paper reports on an extensive industry-based
case study involving a DES product family for a pedestrian and car 4-way
traffic intersection in which autonomous devices communicate by asynchronous
message passing without a centralized controller. All the safety requirements
and a liveness requirement informally specified in the requirements document
have been formally verified using Real-Time Maude and its model checking
features.


  We study the superfluid to Mott-insulator transition of bosons in an optical
anizotropic lattice by employing the Bose-Hubbard model living on a
two-dimensional lattice with anizotropy parameter $\kappa$. The compressible
superfluid state and incompressible Mott-insulator (MI) lobes are efficiently
described analytically, using the quantum U(1) rotor approach. The ground state
phase diagram showing the evolution of the MI lobes is quantified for arbitrary
values of $\kappa$, corresponding to various kind of lattices: from square,
through rectangular to almost one-dimensional.


  Dimensionality reduction represents a critical preprocessing step in order to
increase the efficiency and the performance of many hyperspectral imaging
algorithms. However, dimensionality reduction algorithms, such as the Principal
Component Analysis (PCA), suffer from their computationally demanding nature,
becoming advisable for their implementation onto high-performance computer
architectures for applications under strict latency constraints. This work
presents the implementation of the PCA algorithm onto two different
high-performance devices, namely, an NVIDIA Graphics Processing Unit (GPU) and
a Kalray manycore, uncovering a highly valuable set of tips and tricks in order
to take full advantage of the inherent parallelism of these high-performance
computing platforms, and hence, reducing the time that is required to process a
given hyperspectral image. Moreover, the achieved results obtained with
different hyperspectral images have been compared with the ones that were
obtained with a field programmable gate array (FPGA)-based implementation of
the PCA algorithm that has been recently published, providing, for the first
time in the literature, a comprehensive analysis in order to highlight the pros
and cons of each option.


  Shockwaves provide a useful and rewarding route to the nonequilibrium
properties of simple fluids far from equilibrium. For simplicity, we study a
strong shockwave in a dense two-dimensional fluid. Here, our study of nonlinear
transport properties makes plain the connection between the observed local
hydrodynamic variables (like the various gradients and fluxes) and the chosen
recipes for defining (or "measuring") those variables. The range over which
nonlocal hydrodynamic averages are computed turns out to be much more
significant than are the other details of the averaging algorithms. The results
show clearly the incompatibility of microscopic time-reversible
cause-and-effect dynamics with macroscopic instantaneously-irreversible models
like the Navier-Stokes equations.


  Recently, it was suggested that the system of smeared black branes might
provide a counter example to the Gubser-Mitra conjecture. Concerning to this
issue, we have investigated the s-wave perturbation analysis to see how the
stability of such system behaves. Some partial results are reported in this
meeting.


  The Read-Rezayi (RR) parafermion states form a series of exotic non-Abelian
fractional quantum Hall (FQH) states at filling $\nu = k/(k+2)$.
Computationally, the wave functions of these states are prohibitively expensive
to generate for large systems. We introduce a series of parton states, denoted
"$\bar{2}^{k}1^{k+1}$," and show that they lie in the same universality classes
as the particle-hole-conjugate RR ("anti-RR") states. Our analytical results
imply that a $(U(1)_{k+1} \times U(2k)_{-1})/(SU(k)_{-2} \times U(1)_{-1})$
coset conformal field theory describes the edge excitations of the
$\bar{2}^{k}1^{k+1}$ state, suggesting non-trivial dualities with respect to
previously known descriptions. The parton construction allows wave functions in
anti-RR phases to be generated for hundreds of particles. We further propose
the parton sequence "$\bar{n}\bar{2}^{2}1^{4}$," with $n=1,2,3$, to describe
the FQH states observed at $\nu=2+1/2,~2+2/5$ and $2+3/8$.


  The Efimov effect is the only experimentally realized universal phenomenon
that exhibits the renormalization-group limit cycle with the three-body
parameter parametrizing a family of universality classes. Recent experiments in
ultracold atoms have unexpectedly revealed that the three-body parameter itself
is universal when measured in units of an effective range. By performing an
exact functional renormalization-group analysis with various finite-range
interaction potentials, we demonstrate that the onset of the
renormalization-group flow into the limit cycle is universal, regardless of
short-range details, which connects the missing link between the two
universalities of the Efimov physics. A close connection between the
topological property of the limit cycle and few-body physics is also
delineated.


  We report the discovery of a quasi-periodic oscillation (QPO) at 642 mHz in
an {\it XMM-Newton} observation of the ultraluminous X-ray source (ULX) IC 342
X-1. The QPO has a centroid at $\nu_{QPO} = 642 \pm 20$ mHz, a coherence factor
of $ Q = 11.6$, and an amplitude (rms) of 4.1\% with significance of
$3.6\sigma$. The energy dependence study shows that the QPO is stronger in the
energy range 0.3 - 5.0 keV. A subsequent observation (6 days later) does not
show any signature of the QPO in the power density spectrum. The broadband
energy spectra (0.3 - 40.0 keV) obtained by quasi-simultaneous observations of
{\it XMM-Newton} and {\it NuSTAR} can be well described by an absorbed {\it
diskbb} plus {\it cutoffpl} model. The best fitted spectral parameters are
power-law index ($\Gamma$) $\sim$ 1.1, cutoff energy ($E_c$) $\sim$ 7.9 keV and
disc temperature ($kT_{in}$) $\sim$ 0.33 keV, where the QPO is detected. The
unabsorbed bolometric luminosity is $\sim$ 5.34$\times$ 10$^{39}$ erg~s$^{-1}$.
Comparing with the well known X-ray binary GRS 1915+105, our results are
consistent with the mass of the compact object in IC 342 X-1 being in the range
$\sim 20 - 65 ~ M_\odot$. We discuss the possible implications of our results.


  In this article, we present a construction of a spanner on a set of $n$
points in $\mathbf{R}^d$ that we call a heavy path WSPD spanner. The
construction is parameterized by a constant $s > 2$ called the separation
ratio. The size of the graph is $O(s^dn)$ and the spanning ratio is at most $1
+ 2/s + 2/(s - 1)$. We also show that this graph has a hop spanning ratio of at
most $2\lg n + 1$.
  We present a memoryless local routing algorithm for heavy path WSPD spanners.
The routing algorithm requires a vertex $v$ of the graph to store
$O(\mathrm{deg}(v)\log n)$ bits of information, where $\mathrm{deg}(v)$ is the
degree of $v$. The routing ratio is at most $1 + 4/s + 1/(s - 1)$ and at least
$1 + 4/s$ in the worst case. The number of edges on the routing path is bounded
by $2\lg n + 1$.
  We then show that the heavy path WSPD spanner can be constructed in metric
spaces of bounded doubling dimension. These metric spaces have been studied in
computational geometry as a generalization of Euclidean space. We show that, in
a metric space with doubling dimension $\lambda$, the heavy path WSPD spanner
has size $O(s^\lambda n)$ where $s$ is the separation ratio. The spanning ratio
and hop spanning ratio are the same as in the Euclidean case.
  Finally, we show that the local routing algorithm works in the bounded
doubling dimension case. The vertices require the same amount of storage, but
the routing ratio becomes at most $1 + (2 + \frac{\tau}{\tau-1})/s + 1/(s - 1)$
in the worst case, where $\tau \ge 11$ is a constant related to the doubling
dimension.


  We propose that the real spectrum and the orthogonality of the states for
several known complex potentials of both types, PT-symmetric and
non-PT-symmetric can be understood in terms of currently proposed
$\eta$-pseudo-Hermiticity (Mostafazadeh, quant-ph/0107001) of a Hamiltonian,
provided the Hermitian linear automorphism, $\eta$, is introduced as
$e^{-\theta p}$ which affects an imaginary shift of the co-ordinate :
$e^{-\theta p} x e^{\theta p} = x+i\theta$.


  The configuration interaction (CI) is a versatile wavefunction theory for
interacting fermions but it involves an extremely long CI series. Using a
symmetric tensor decomposition (STD) method, we convert the CI series into a
compact and numerically tractable form. The converted series encompasses the
Hartree-Fock state in the first term and rapidly converges to the full-CI
state, as numerically tested using small molecules. Provided that the length of
the STD-CI series grows only moderately with the increasing complexity of the
system, the new method will serve as one of the alternative variational methods
to achieve full-CI with enhanced practicability.


  Recently, there has been increasing progress in end-to-end automatic speech
recognition (ASR) architecture, which transcribes speech to text without any
pre-trained alignments. One popular end-to-end approach is the hybrid
Connectionist Temporal Classification (CTC) and attention (CTC/attention) based
ASR architecture. However, how to deploy hybrid CTC/attention systems for
online speech recognition is still a non-trivial problem. This article
describes our proposed online hybrid CTC/attention end-to-end ASR architecture,
which replaces all the offline components of conventional CTC/attention ASR
architecture with their corresponding streaming components. Firstly, we propose
stable monotonic chunk-wise attention (sMoChA) to stream the conventional
global attention, and further propose monotonic truncated attention (MTA) to
simplify sMoChA and solve the training-and-decoding mismatch problem of sMoChA.
Secondly, we propose truncated CTC (T-CTC) prefix score to stream CTC prefix
score calculation. Thirdly, we design dynamic waiting joint decoding (DWJD)
algorithm to dynamically collect the predictions of CTC and attention in an
online manner. Finally, we use latency-controlled bidirectional long short-term
memory (LC-BLSTM) to stream the widely-used offline bidirectional encoder
network. Experiments with LibriSpeech English and HKUST Mandarin tasks
demonstrate that, compared with the offline CTC/attention model, our proposed
online CTC/attention model improves the real time factor in human-computer
interaction services and maintains its performance with moderate degradation.
To the best of our knowledge, this is the first work to provide the full-stack
online solution for CTC/attention end-to-end ASR architecture.


  We consider group-valued cocycles over dynamical systems. The base system is
a homeomorphism $f$ of a metric space satisfying a closing property, for
example a hyperbolic dynamical system or a subshift of finite type. The cocycle
$A$ takes values in the group of invertible bounded linear operators on a
Banach space and is H\"older continuous. We prove that upper and lower Lyapunov
exponents of $A$ with respect to an ergodic invariant measure $\mu$ can be
approximated in terms of the norms of the values of $A$ on periodic orbits of
$f$. We also show that these exponents cannot always be approximated by the
exponents of $A$ with respect to measures on periodic orbits. Our arguments
include a result of independent interest on construction and properties of a
Lyapunov norm for infinite dimensional setting. As a corollary, we obtain
estimates of the growth of the norm and of the quasiconformal distortion of the
cocycle in terms of the growth at the periodic points of $f$.


  Today's great challenges of energy and informational technologies are
addressed with a singular compound, the Li and Na doped few layer graphene. All
what is impossible for graphite (homogeneous and high level Na doping), and
unstable for single layer graphene, works very well for this structure. The
transformation of the Raman G line to a Fano lineshape and the emergence of
strong, metallic-like electron spin resonance (ESR) modes, attest the high
level of graphene doping in liquid ammonia for both kinds of alkali atoms. The
spin-relaxation time in our materials, deduced from the ESR line-width, is 6-8
ns, which is comparable to the longest values found in spin-transport
experiments on ultrahigh mobility graphene flakes. This could qualify our
material as promising candidate in spintronics devices. On the other hand, the
successful sodium doping, this being a highly abundant metal, could be an
encouraging alternative to lithium batteries.


  We consider solutions to the nonlinear sigma model (wave maps) with target
space S^3 and base space 3+1 Minkowski space, and we find critical behavior
separating singular solutions from nonsingular solutions. For families of
solutions with localized spatial support a self-similar solution is found at
the boundary. For other families, we find that a static solution appears to sit
at the boundary. This behavior is compared to the black hole critical phenomena
found by Choptuik.


  Dexterous robotic manipulation in unstructured environments can aid in
everyday tasks such as cleaning and caretaking. Anthropomorphic robotic hands
are highly dexterous and theoretically well-suited for working in human
domains, but their complex designs and dynamics often make them difficult to
control. By contrast, parallel-jaw grippers are easy to control and are used
extensively in industrial applications, but they lack the dexterity for various
kinds of grasps and in-hand manipulations. In this work, we present DELTAHANDS,
a synergistic dexterous hand framework with Delta robots. The DELTAHANDS are
soft, easy to reconfigure, simple to manufacture with low-cost off-the-shelf
materials, and possess high degrees of freedom that can be easily controlled.
DELTAHANDS' dexterity can be adjusted for different applications by leveraging
actuation synergies, which can further reduce the control complexity, overall
cost, and energy consumption. We characterize the Delta robots' kinematics
accuracy, force profiles, and workspace range to assist with hand design.
Finally, we evaluate the versatility of DELTAHANDS by grasping a diverse set of
objects and by using teleoperation to complete three dexterous manipulation
tasks: cloth folding, cap opening, and cable arrangement. We open-source our
hand framework at https://sites.google.com/view/deltahands/.


  We obtained high temporal resolution spectroscopy of the unusual binary
system AR Sco covering nearly an orbit. The H$\alpha$ emission shows a complex
line structure similar to that seen in some polars during quiescence. Such
emission is thought to be due to long-lived prominences originating on the red
dwarf. A difference between AR Sco and these other systems is that the white
dwarf in AR Sco is rapidly spinning relative to the orbital period. "Slingshot"
prominences stable at 3 to 5 stellar radii require surface magnetic fields
between 100 and 500 G. This is comparable to the estimated WD magnetic field
strength near the surface of the secondary. Our time-resolved spectra also show
emission fluxes, line equivalent widths, and continuum color varying over the
orbit and the beat/spin periods of the system. During much of the orbit, the
optical spectral variations are consistent with synchrotron emission with the
highest energy electrons cooling between pulses. On the time-scale of the
beat/spin period we detect red and blue-shifted H$\alpha$ emission flashes that
reach velocities of 700 km/s. Red-shifted Balmer emission flashes are
correlated with the bright phases of the continuum beat pulses while
blue-shifted flashes appear to prefer the time of minimum in the beat light
curve. We propose that much of the energy generated in AR Sco comes from fast
magnetic reconnection events occurring near the inward face of the secondary
and we show that the energy generated by magnetic reconnection can account for
the observed excess luminosity from the system.


  We report on a contrasting behavior of the in-plane and out-of-plane
magnetoresistance (MR) in heavily underdoped antiferromagnetic (AF)
YBa_2Cu_3O_{6+x} (x<0.37). The out-of-plane MR (I//c) is positive over most of
the temperature range and shows a sharp increase, by about two orders of
magnitude, upon cooling through the Neel temperature T_N. A contribution
associated with the AF correlations is found to dominate the out-of-plane MR
behavior for H//c from far above T_N, pointing to the key role of spin
fluctuations in the out-of-plane transport. In contrast, the transverse
in-plane MR (I//a(b);H//c) appears to be small and smooth through T_N, implying
that the development of the AF order has little effect on the in-plane
resistivity.


  It is known that the Higgs potential in the Standard Model can drive a
successful inflation as long as the Higgs field couples non-minimally to
gravity. It is then inevitable to take into account the loop corrections of the
Standard Model particles to the Higgs potential in the Higgs inflation. In this
paper, we discuss the one-loop corrections at finite temperature to the
curvature perturbation generated during the Higgs inflation. We find that the
thermal loop effects can suppress the power of the curvature perturbation at
large scales, thus resulting in a low quadrupole of the temperature anisotropy
in the cosmic microwave background.


  In theories of Einstein gravity coupled with a dilaton and a two-form, a soft
theorem for the two-form, known as the Kalb-Ramond B-field, has so far been
missing. In this work we fill the gap, and in turn formulate a unified soft
theorem valid for gravitons, dilatons and B-fields in any tree-level scattering
amplitude involving the three massless states. The new soft theorem is fixed by
means of on-shell gauge invariance and enters at the subleading order of the
graviton's soft theorem. In contrast to the subsubleading soft behavior of
gravitons and dilatons, we show that the soft behavior of B-fields at this
order cannot be fully fixed by gauge invariance. Nevertheless, we show that it
is possible to establish a gauge invariant decomposition of the amplitudes to
any order in the soft expansion. We check explicitly the new soft theorem in
the bosonic string and in Type II superstring theories, and furthermore
demonstrate that, at the next order in the soft expansion, totally gauge
invariant terms appear in both string theories which cannot be factorized into
a soft theorem.


  Analysis and extraction of useful information from legal judgments using
computational linguistics was one of the earliest problems posed in the domain
of information retrieval. Presently, several commercial vendors exist who
automate such tasks. However, a crucial bottleneck arises in the form of
exorbitant pricing and lack of resources available in analysis of judgements
mete out by Hong Kong's Legal System. This paper attempts to bridge this gap by
providing several statistical, machine learning, deep learning and zero-shot
learning based methods to effectively analyze legal judgments from Hong Kong's
Court System. The methods proposed consists of: (1) Citation Network Graph
Generation, (2) PageRank Algorithm, (3) Keyword Analysis and Summarization, (4)
Sentiment Polarity, and (5) Paragrah Classification, in order to be able to
extract key insights from individual as well a group of judgments together.
This would make the overall analysis of judgments in Hong Kong less tedious and
more automated in order to extract insights quickly using fast inferencing. We
also provide an analysis of our results by benchmarking our results using Large
Language Models making robust use of the HuggingFace ecosystem.


  We present the main results on the energy spectrum and composition of the
highest energy cosmic rays of energy exceeding 10$^{18}$ eV obtained by the
High Resolution Fly's Eye and the Southern Auger Observatory. The current
results are somewhat contradictory and raise interesting questions about the
origin and character of these particles.


  Let X_1,X_2, . . . be a sequence of i.i.d. mean zero random variables and let
S_n the sum of the first n random variables. We show that whenever lim sup_n
|S_n|/c_n is finite with probability one and the normalizing sequence {c_n} is
sufficiently regular, the corresponding normalized partial sum process sequence
is relatively compact in C[0, 1] with canonical cluster set. Combining this
result with some LIL type results in the infinite variance case, we obtain
Strassen type results in this setting.


  Denote by $q_n(G)$ the smallest eigenvalue of the signless Laplacian matrix
of an $n$-vertex graph $G$. Brandt conjectured in 1997 that for regular
triangle-free graphs $q_n(G) \leq \frac{4n}{25}$. We prove a stronger result:
If $G$ is a triangle-free graph then $q_n(G) \leq \frac{15n}{94}<
\frac{4n}{25}$. Brandt's conjecture is a subproblem of two famous conjectures
of Erd\H{o}s:
  (1) Sparse-Half-Conjecture: Every $n$-vertex triangle-free graph has a subset
of vertices of size $\lceil\frac{n}{2}\rceil$ spanning at most $n^2/50$ edges.
  (2) Every $n$-vertex triangle-free graph can be made bipartite by removing at
most $n^2/25$ edges.
  In our proof we use linear algebraic methods to upper bound $q_n(G)$ by the
ratio between the number of induced paths with 3 and 4 vertices. We give an
upper bound on this ratio via the method of flag algebras.


  We study eta-Einstein geometry as a class of distinguished Riemannian metrics
on contact metric manifolds. In particular, we use a previous solution of the
Calabi problem for Sasakian geometry to prove the existence of eta-Einstein
structures on many different compact manifolds, including exotic spheres. We
also relate these results to the existence of Einstein-Weyl structures.


  In this paper, we demonstrate that the factorizations for tree amplitudes in
the double-cover framework, for various theories, can be generated from the
gravity amplitude in the double-cover prescription. Using our method, the
factorized formulae for amplitudes of Yang-Mills theory, special
Yang-Mills-scalar theory, and bi-adjoint scalar theory, have been derived. The
differential operators indicate some non-trivial relationships among
factorizations for above theories, as can be understood through four angles
which are factorization channels, pole-structures, gauge choices, as well as
BCFW recursions.


  We propose an extension of the BMS group, which we refer to as Weyl BMS or
BMSW for short, that includes, besides super-translations, local Weyl
rescalings and arbitrary diffeomorphisms of the 2d sphere metric. After
generalizing the Barnich-Troessaert bracket, we show that the Noether charges
of the BMSW group provide a centerless representation of the BMSW Lie algebra
at every cross section of null infinity. This result is tantamount to proving
that the flux-balance laws for the Noether charges imply the validity of the
asymptotic Einstein's equations at null infinity. The extension requires a
holographic renormalization procedure, which we construct without any
dependence on background fields. The renormalized phase space of null infinity
reveals new pairs of conjugate variables. Finally, we show that BMSW group
elements label the gravitational vacua.


  In this paper we define the triangulated category of motives over a
simplicial scheme. The morphisms between the Tate objects in this category
compute the motivic cohomology of the underlying scheme. In the last section we
consider the special case of "embedded" simplicial schemes, which correspond to
the subsheaves of the constant sheaf and naturally appear in the descent
problems for motivic cohomology such as the Bloch-Kato conjecture.


  For primordial black holes (PBHs) to form a considerable fraction of cold
dark matter, the required amplitude of primordial scalar perturbations is quite
large ($P_{\zeta}(k) \sim 10^{-2}$) if PBH is formed in radiation epoch. In
alternate cosmological histories, where additional epoch of arbitrary equation
of state precede radiation epoch, the dynamics of PBH formation and relevant
mass ranges can be different leading to lower requirement of primordial power
at smaller scales of inflation. Moreover, this alternate history can modify the
predictions for the gravitational wave (GW) spectrum, which can be probed by
upcoming GW observations. In this paper, we show that an early kination epoch
can lead to per cent level abundance ofPBH for a lower amplitude of
$P_{\zeta}(k)$ compared to PBH formation in a standard radiation epoch.
Moreover, we calculate the effect of early kination epoch on the GW spectrum
for first and second orders in perturbation theory which show enhancement in
the amplitude of the GW spectrum in a kination epoch with respect to that in a
standard radiation epoch.


  Identifying and resolving logic errors can be one of the most frustrating
challenges for novices programmers. Unlike syntax errors, for which a compiler
or interpreter can issue a message, logic errors can be subtle. In certain
conditions, buggy code may even exhibit correct behavior -- in other cases, the
issue might be about how a problem statement has been interpreted. Such errors
can be hard to spot when reading the code, and they can also at times be missed
by automated tests. There is great educational potential in automatically
detecting logic errors, especially when paired with suitable feedback for
novices. Large language models (LLMs) have recently demonstrated surprising
performance for a range of computing tasks, including generating and explaining
code. These capabilities are closely linked to code syntax, which aligns with
the next token prediction behavior of LLMs. On the other hand, logic errors
relate to the runtime performance of code and thus may not be as well suited to
analysis by LLMs. To explore this, we investigate the performance of two
popular LLMs, GPT-3 and GPT-4, for detecting and providing a novice-friendly
explanation of logic errors. We compare LLM performance with a large cohort of
introductory computing students $(n=964)$ solving the same error detection
task. Through a mixed-methods analysis of student and model responses, we
observe significant improvement in logic error identification between the
previous and current generation of LLMs, and find that both LLM generations
significantly outperform students. We outline how such models could be
integrated into computing education tools, and discuss their potential for
supporting students when learning programming.


  Biological rhythms are generated by pacemaker organs, such as the heart
pacemaker organ (the sinoatrial node) and the master clock of the circadian
rhythms (the suprachiasmatic nucleus), which are composed of a network of
autonomously oscillatory cells. Such biological rhythms have notable
periodicity despite the internal and external noise present in each cell.
Previous experimental studies indicate that the regularity of oscillatory
dynamics is enhanced when noisy oscillators interact and become synchronized.
This effect, called the collective enhancement of temporal precision, has been
studied theoretically using particular assumptions. In this study, we propose a
general theoretical framework that enables us to understand the dependence of
temporal precision on network parameters including size, connectivity, and
coupling intensity; this effect has been poorly understood to date. Our
framework is based on a phase oscillator model that is applicable to general
oscillator networks with any coupling mechanism if coupling and noise are
sufficiently weak. In particular, we can manage general directed and weighted
networks. We quantify the precision of the activity of a single cell and the
mean activity of an arbitrary subset of cells. We find that, in general
undirected networks, the standard deviation of cycle-to-cycle periods scales
with the system size $N$ as $1/\sqrt{N}$, but only up to a certain system size
$N^*$ that depends on network parameters. Enhancement of temporal precision is
ineffective when $N>N^*$. We also reveal the advantage of long-range
interactions among cells to temporal precision.


  The fractional integrals and fractional derivatives problem is tackled by
using the operator approach. The definition domain E of operators is causal
functions.Many properties of fractional integrals are given. Fractional
derivatives definition is derived from fractional integrals one. Then an
unified definition of fractional integrals and derivatives operator is obtained
according to the sign of the real part of the order s. The study utilizes many
properties of the Euler's gamma and beta functions and their extensions in R
and C. Comparison with the definitions given by other authors (Liouville,
Riemann,Liouville-Caputo)is done too.


  In the given technology-driven era, smart cities are the next frontier of
technology, aiming at improving the quality of people's lives. Many research
works focus on future smart cities with a holistic approach towards smart city
development. In this paper, we introduce such future smart cities that leverage
blockchain technology in areas like data security, energy and waste management,
governance, transport, supply chain, including emergency events, and
environmental monitoring. Blockchain, being a decentralized immutable ledger,
has the potential to promote the development of smart cities by guaranteeing
transparency, data security, interoperability, and privacy. Particularly, using
blockchain in emergency events will provide interoperability between many
parties involved in the response, will increase timeliness of services, and
establish transparency. In that case, if a current fee-based or
first-come-first-serve-based processing is used, emergency events may get
delayed in being processed due to competition, and thus, threatening people's
lives. Thus, there is a need for transaction prioritization based on the
priority of information and quick creation of blocks (variable interval block
creation mechanism). Also, since the leaders ensure transaction prioritization
while generating blocks, leader rotation and proper election procedure become
important for the transaction prioritization process to take place honestly and
efficiently. In our consensus protocol, we deploy a machine learning (ML)
algorithm to achieve efficient leader election and design a novel dynamic block
creation algorithm. Also, to ensure honest assessment from the followers on the
blocks generated by the leaders, a peer-prediction-based verification mechanism
is proposed. Both security analysis and simulation experiments are carried out
to demonstrate the robustness and accuracy of our proposed scheme.


  Let $\mathbb{K}$ be an algebraically closed field of characteristic zero and
let $\mathbb{K}_{C}[[x_{1},...,x_{e}]]$ be the ring of formal power series in
several variables with exponents in a line free cone $C$. We consider
irreducible polynomials
$f=y^n+a_1(\underline{x})y^{n-1}+\ldots+a_n(\underline{x})$ in
$\mathbb{K}_{C}[[x_{1},...,x_{e}]][y]$ whose roots are in
$\mathbb{K}_{C}[[x_{1}^{\frac{1}{n}},...,x_{e}^{\frac{1}{n}}]]$. We generalize
to these polynomials the theory of Abhyankar-Moh. In particular we associate
with any such polynomial its set of characteristic exponents and its semigroup
of values. We also prove that the set of values can be obtained using the set
of approximate roots. We finally prove that polynomials of ${\mathbb
K}[[\underline{x}]][y]$ fit in the above set for a specific line free cone (see
Section 4).


  Introduction : Mass spectrometry approaches are very attractive to detect
protein panels in a sensitive and high speed way. MS can be coupled to many
proteomic separation techniques. However, controlling technological variability
on these analytical chains is a critical point. Adequate information processing
is mandatory for data analysis to take into account the complexity of the
analysed mixture, to improve the measurement reliability and to make the
technology user friendly. Therefore we develop a hierarchical parametric
probabilistic model of the LC-MS analytical chain including the technological
variability. We introduce a Bayesian reconstruction methodology to recover the
protein biomarkers content in a robust way. We will focus on the digestion step
since it brings a major contribution to technological variability. Method : In
this communication, we introduce a hierarchical model of the LC-MS analytical
chain. Such a chain is a cascade of molecular events depicted by a graph
structure, each node being associated to a molecular state such as protein,
peptide and ion and each branch to a molecular processing such as digestion,
ionisation and LC-MS separation. This molecular graph defines a hierarchical
mixture model. We extend the Bayesian statistical framework we have introduced
previously [1] to this hierarchical description. As an example, we will
consider the digestion step. We describe the digestion process on a pair of
peptides within the targeted protein as a Bernoulli random process associated
with a cleavage probability controlled by the digestion kinetic law.


  In recent years, Knowledge Graph (KG) development has attracted significant
researches considering the applications in web search, relation prediction,
natural language processing, information retrieval, question answering to name
a few. However, often KGs are incomplete due to which Knowledge Graph
Completion (KGC) has emerged as a sub-domain of research to automatically track
down the missing connections in a KG. Numerous strategies have been suggested
to work out the KGC dependent on different representation procedures intended
to embed triples into a low-dimensional vector space. Given the difficulties
related to KGC, researchers around the world are attempting to comprehend the
attributes of the problem statement. This study intends to provide an overview
of knowledge bases combined with different challenges and their impacts. We
discuss existing KGC approaches, including the state-of-the-art Knowledge Graph
Embeddings (KGE), not only on static graphs but also for the latest trends such
as multimodal, temporal, and uncertain knowledge graphs. In addition,
reinforcement learning techniques are reviewed to model complex queries as a
link prediction problem. Subsequently, we explored popular software packages
for model training and examine open research challenges that can guide future
research.


  We present for the first time the timing and spectral analyses for a
narrow-line Seyfert 1 galaxy, SBS 1353+564, using \it{XMM-Newton} and
\it{Swift} multi-band observations from 2007 to 2019. Our main results are as
follows: 1) The temporal variability of SBS 1353+564 is random, while the
hardness ratio is relatively constant over a time span of 13 years; 2) We find
a prominent soft X-ray excess feature below 2 keV, which cannot be well
described by a simple blackbody component; 3) After comparing the two most
prevailing models for interpreting the origin of the soft X-ray excess, we find
that the relativistically smeared reflection model is unable to fit the data
above 5 keV well and the X-ray spectra do not show any reflection features,
such as the Fe K\alpha emission line. However, the warm corona model can obtain
a good fitting result. For the warm corona model, we try to use three different
sets of spin values to fit the data and derive different best-fitting parameter
sets; 4) We compare the UV/optical spectral data with the extrapolated values
of the warm corona model to determine which spin value is more appropriate for
this source, and we find that the warm corona model with non-spin can
sufficiently account for the soft X-ray excess in SBS 1353+564.


  We study the effects of including one-loop radiative corrections in a
non-supersymmetric hybrid inflationary model. These corrections can arise from
Yukawa couplings between the inflaton and right-handed neutrinos, and induce a
maximum in the potential which admits hilltop-type solutions in addition to the
standard hybrid solutions. We obtain a red-tilted spectral index $n_s$,
consistent with WMAP5 data, for sub-Planckian values of the field. This is in
contrast to the tree level hybrid analysis, in which a red-tilted spectrum is
achieved only for trans-Planckian values of the field. Successful reheating is
obtained at the end of the inflationary phase via conversion of the inflaton
and waterfall fields into right-handed neutrinos, whose subsequent decay can
explain the observed baryon asymmetry via leptogenesis.


  We study the non-equilibrium dynamics of lipid membranes with proteins that
actively pump ions across the membrane. We find that the activity leads to a
fluctuating force distribution due to electrostatic interactions arising from
variation in dielectric constant across the membrane. By applying a multipole
expansion we find effects on both the tension and bending rigidity dominated
parts of the membranes fluctuation spectrum. We discuss how our model compares
with previous studies of force-multipole models.


  The fundamental magnetic interactions of Pr$_{2}$Fe$_{17}$ are studied by
inelastic neutron scattering and anisotropy field measurements. Data analysis
confirms the presence of three magnetically inequivalent sites, and reveals an
exceptionally large value of the exchange field. The unexpected importance of
$J$-mixing effects in the description of the ground-state properties of
Pr$_{2}$Fe$_{17}$ is evidenced, and possible applications of related compounds
are envisaged.


  Effects of ion mobility and positron fraction on solitary waves of envelop of
laser field and potential of electrostatic field in weak relativistic
electron-positron-ion plasma are investigated. The parameter region for the
existence of solitary waves is obtained analytically, and the reasonable choice
of parameters is clarified. Both cases of mobile and immobile ions are
considered. It is found that the amplitudes of solitary waves in the former
case are larger compared to the latter case. For small plasma density, the
localized solitary wave solutions in terms of approximate perturbation
analytical method are consistent well with that by exact numerical
calculations. However as the plasma density increases the analytical method
loses its validity more and more. The influence of the positron fraction on the
amplitudes of solitary waves shows a monotonous increasing relation.
Implication of our results to the particle acceleration is also discussed
briefly.


  We construct the Seiberg-Witten theory on 3-manifolds with Euclidean ends
(connected sums of $\R^3$ and a compact manifold) with perturbations which
approximate $*dx_3$ at infinity, and describe the structure of the moduli
spaces. The setup is inspired by Taubes's program of relating the 4-dimensional
Seiberg-Witten invariant with `singular Gromov invariants' and has related
applications.


  We show that for an arbitrary stable theory T, a group G is profinite if and
only if G occurs as a Galois group of some Galois extension inside a monster
model of T.
  We prove that any PAC substructure of the monster model of T has projective
absolute Galois group. Moreover, any projective profinite group G is isomorphic
to the absolute Galois group of some substructure P of the monster model. If T
is omega-stable, then P can be chosen to be PAC.
  Finally, we provide a description of some Galois groups of existentially
closed substructures with G-action in the terms of the universal Frattini
cover. Such structures might be understood as a new examples of PAC structures.


  Although an intimate relation between entropy and diffusion has been
advocated for many years and even seems to have been verified in theory and
experiments, a quantitatively reliable study, and any derivation of an
algebraic relation between the two does not seem to exist. Here we explore the
nature of this entropy-diffusion relation in three deterministic systems where
an accurate estimate of both can be carried out. We study three deterministic
model systems, (a) the motion of a single point particle with constant energy
in a two-dimensional periodic potential energy landscape, (b) the same in
regular Lorentz gas where a point particle with constant energy moves between
collisions with hard disc scatterers and (c) motion of a point particle among
the boxes with small apertures. These models, introduced by Zwanzig, exhibit
diffusive motion in the limit where ergodicity is shown to exist. We then
explore the diffusion-entropy relation by an accurate calculation of both
diffusion and entropy for the aforementioned model systems. We estimate the
self-diffusion coefficient of the particle by employing computer simulations
and entropy by quadrature using Boltzmann's formula. We observe an interesting
crossover in the diffusion-entropy relation in some specific regions which is
attributed to the emergence of correlated returns. The crossover could herald a
breakdown of the Rosenfeld-like exponential scaling between the two, as
observed at low temperatures. Later, we modify the scaling relation to account
for the correlated motions and present a detailed analysis of the dynamical
entropy obtained via Lyapunov exponent which is rather an important quantity in
the study of deterministic systems.


  Probability forecasts for binary events play a central role in many
applications. Their quality is commonly assessed with proper scoring rules,
which assign forecasts a numerical score such that a correct forecast achieves
a minimal expected score. In this paper, we construct e-values for testing the
statistical significance of score differences of competing forecasts in
sequential settings. E-values have been proposed as an alternative to p-values
for hypothesis testing, and they can easily be transformed into conservative
p-values by taking the multiplicative inverse. The e-values proposed in this
article are valid in finite samples without any assumptions on the data
generating processes. They also allow optional stopping, so a forecast user may
decide to interrupt evaluation taking into account the available data at any
time and still draw statistically valid inference, which is generally not true
for classical p-value based tests. In a case study on postprocessing of
precipitation forecasts, state-of-the-art forecasts dominance tests and
e-values lead to the same conclusions.


  Many models of market dynamics make use of the idea of conservative wealth
exchanges among economic agents. A few years ago an exchange model using
extremal dynamics was developed and a very interesting result was obtained: a
self-generated minimum wealth or poverty line. On the other hand, the wealth
distribution exhibited an exponential shape as a function of the square of the
wealth. These results have been obtained both considering exchanges between
nearest neighbors or in a mean field scheme. In the present paper we study the
effect of distributing the agents on a complex network. We have considered
archetypical complex networks: Erd\"{o}s-R\'enyi random networks and scale-free
networks. The presence of a poverty line with finite wealth is preserved but
spatial correlations are important, particularly between the degree of the node
and the wealth. We present a detailed study of the correlations, as well as the
changes in the Gini coefficient, that measures the inequality, as a function of
the type and average degree of the considered networks.


  Recently, a surprising low-temperature behavior has been revealed in a
two-leg ladder Ising model with trimer rungs (Weiguo Yin, arXiv:2006.08921).
Motivated by these findings, we study this model from another perspective and
demonstrate that the reported observations are related to a critical phenomenon
in the standard Ising chain. We also discuss a related curiosity, namely, the
emergence of a power-law behavior characterized by quasicritical exponents.


  In this work, we show how the knowledge of the first few terms of the
Euler-Heisenberg Lagrangian's weak-field expansion in a magnetic field
background is enough to reconstruct the pair-production rate in a strong
electric field background. To this end, we study its associated truncated Borel
sum using Pad\'e approximants, as advocated in a recent work by Costin and
Dunne, J. Phys. A52, 445205 (2019).


  Heckman introduced $N$ operators on the space of polynomials in $N$
variables, such that these operators form a covariant set relative to
permutations of the operators and variables, and such that Jack symmetric
polynomials are eigenfunctions of the power sums of these operators. We
introduce the analogues of these $N$ operators for Macdonald symmetric
polynomials, by using Cherednik operators. The latter operators pairwise
commute, and Macdonald polynomials are eigenfunctions of their power sums. We
compute the limits of our operators at $N\to\infty$. These limits yield the
same Lax operator for Macdonald symmetric functions as constructed in our
previous work.


  The gases of the interstellar medium (ISM) possess orders of magnitude more
mass than those of all the stars combined and are thus the prime component of
the baryonic universe. With L-band surface sensitivity even better than the
planned phase one Square-Kilometer-Array (SKA1), the Five-hundred-meter
Aperture Spherical radio Telescope (FAST) promises unprecedented insights into
two of the primary components of ISM, namely, the atomic hydrogen (HI) and the
hydroxyl molecule (OH). We discuss here the evolving landscape of our
understanding of ISM, particularly, its complex phases, the magnetic fields
within, the so-called dark molecular gas (DMG), high velocity clouds, and the
connection between local and distant ISM. We lay out, in broad strokes, several
expected FAST projects, including an all northern-sky high-resolution HI survey
(22,000 deg$^2$, 3\arcmin\ FWHM beam, 0.2 km/s), targeted OH mapping, searching
for absorption or masing signals, and etc. Currently under commissioning, the
commensal observing mode of FAST will be capable of simultaneously obtaining HI
and pulsar data streams, making large-scale surveys in both science areas more
efficient.


  We construct positive singular solutions for the problem $-\Delta u=\lambda
\exp (e^u)$ in $B_1\subset \mathbb{R}^n$ ($n\geq 3$), $u=0$ on $\partial B_1$,
having a prescribed behaviour around the origin. Our study extends the one in
Y. Miyamoto [Y. Miyamoto, A limit equation and bifurcation diagrams of
semilinear elliptic equations with general supercritical growth. J.
Differential Equations \textbf{264} (2018), 2684--2707] for such
nonlinearities. Our approach is then carried out to elliptic equations
featuring iterated exponentials.


  Neural Processes (NPs; Garnelo et al., 2018a,b) are a rich class of models
for meta-learning that map data sets directly to predictive stochastic
processes. We provide a rigorous analysis of the standard maximum-likelihood
objective used to train conditional NPs. Moreover, we propose a new member to
the Neural Process family called the Gaussian Neural Process (GNP), which
models predictive correlations, incorporates translation equivariance, provides
universal approximation guarantees, and demonstrates encouraging performance.


  This is a personal view of some problems on minimal surfaces, Ricci flow,
polyhedral geometric structures, Haken 4-manifolds, contact structures and
Heegaard splittings, singular incompressible surfaces after the
Hamilton-Perelman revolution.


  We present a model-independent framework to determine finite-volume
corrections of matrix elements of spatially-separated current-current
operators. We define these matrix elements in terms of Compton-like amplitudes,
i.e. amplitudes coupling single-particle states via two current insertions. We
show that the infrared behavior of these matrix elements is dominated by the
single-particle pole, which is approximated by the elastic form factors of the
lowest-lying hadron. Therefore, given lattice data on the relevant elastic form
factors, the finite-volume effects can be estimated non-perturbatively and
without recourse to effective field theories. For illustration purposes, we
investigate the implications of the proposed formalism for a class of scalar
theories in two and four dimensions.


  A recent successful observation of a dense and deeply bound \bar{K} nuclear
system, K^-pp, in the p + p \rightarrow K^+ + K^-pp reaction in a DISTO
experiment indicates that the double-\bar{K} dibaryon, K^-K^-pp, which was
predicted to be a dense nuclear system, can also be formed in p+p collisions.
We find theoretically that the K^- -K^- repulsion plays no significant role in
reducing the density and binding energy of K^-K^-pp and that, when two
\Lambda(1405) resonances are produced simultaneously in a short-range p+p
collision, they act as doorways to copious formation of K^-K^-pp, if and only
if K^-K^-pp is a dense object, as predicted.


  A fast and simple Monte Carlo program is presented that simulates single
Bremsstrahlung in Bhabha scattering, e+e- --> e+e-gamma, without constraints on
scattering angles. This allows the study of this process at arbitrarily small,
or even vanishing, scattering angles. Experimental cuts can be imposed on an
event-by-event basis, allowing for detailed studies of the process as a
limitation to beam lifetimes, or a luminosity-measuring device, in e+e- storage
rings. As an application, we show that the easy introduction of a cutoff
parameter, corresponding to the characteristic distance between particles in
the bunches, gives a reduced cross section that is in good agreement with
observation.


  The modifications of hadronic masses and decay widths at finite temperature
and baryon density are investigated using a phenomenological model of hadronic
interactions in the Relativistic Hartree Approximation. We consider an
exhaustive set of hadronic reactions and vector meson decays to estimate the
photon emission from hot and dense hadronic matter. The reduction in the vector
meson masses and decay widths is seen to cause an enhancement in the photon
production. It is observed that the effect of $\rho$-decay width on photon
spectra is negligible. The effects on dilepton production from pion
annihilation are also indicated.


  Invasive ductal carcinoma is a prevalent, potentially deadly disease
associated with a high rate of morbidity and mortality. Its malignancy is the
second leading cause of death from cancer in women. The mammogram is an
extremely useful resource for mass detection and invasive ductal carcinoma
diagnosis. We are proposing a method for Invasive ductal carcinoma that will
use convolutional neural networks (CNN) on mammograms to assist radiologists in
diagnosing the disease. Due to the varying image clarity and structure of
certain mammograms, it is difficult to observe major cancer characteristics
such as microcalcification and mass, and it is often difficult to interpret and
diagnose these attributes. The aim of this study is to establish a novel method
for fully automated feature extraction and classification in invasive ductal
carcinoma computer-aided diagnosis (CAD) systems. This article presents a tumor
classification algorithm that makes novel use of convolutional neural networks
on breast mammogram images to increase feature extraction and training speed.
The algorithm makes two contributions.


  This paper presents the analysis of the data acquired during the first
physics run of the Taiwan Axion Search Experiment with Haloscope (TASEH), a
search for axions using a microwave cavity at frequencies between 4.70750 and
4.79815 GHz. The data were collected from October 13, 2021 to November 15,
2021, and are referred to as the CD102 data. The analysis of the TASEH CD102
data excludes models with the axion-two-photon coupling $|g_{a\gamma\gamma}|
\gtrsim 8.2\times 10^{-14}$ GeV$^{-1}$, a factor of eleven above the benchmark
KSVZ model for the mass range 19.4687 < ma < 19.8436 $\mu$eV.


  Distance based algorithms are a common technique in the construction of
phylogenetic trees from taxonomic sequence data. The first step in the
implementation of these algorithms is the calculation of a pairwise distance
matrix to give a measure of the evolutionary change between any pair of the
extant taxa. A standard technique is to use the log det formula to construct
pairwise distances from aligned sequence data. We review a distance measure
valid for the most general models, and show how the log det formula can be used
as an estimator thereof. We then show that the foundation upon which the log
det formula is constructed can be generalized to produce a previously unknown
estimator which improves the consistency of the distance matrices constructed
from the log det formula. This distance estimator provides a consistent
technique for constructing quartets from phylogenetic sequence data under the
assumption of the most general Markov model of sequence evolution.


  The elliptic integral and its various generalizations are playing very
important and basic role in different branches of modern mathematics. It is
well known that they cannot be represented by the elementary transcendental
functions. Therefore, there is a need for sharp computable bounds for the
family of integrals. In this paper, by virtue of two new tools, we study
monotonicity and convexity of certain combinations of the complete elliptic
integrals of the first kind, and obtain new sharp bounds and inequalities for
them. In particular, we prove that the function $\mathcal{K}\left( \sqrt{%
x}\right) /\ln \left( c/\sqrt{1-x}\right) $ is concave on $\left( 0,1\right) $
if and only if $c=e^{4/3}$, where $\mathcal{K}$ denotes the complete elliptic
integrals of the first kind.


  We introduce a notion of bimodule in the setting of enriched
$\infty$-categories, and use this to construct a double $\infty$-category of
enriched $\infty$-categories where the two kinds of 1-morphisms are functors
and bimodules. We then consider a natural definition of natural transformations
in this context, and show that in the underlying $(\infty,2)$-category of
enriched $\infty$-categories with functors as 1-morphisms the 2-morphisms are
given by natural transformations.


  Existing work on risk-sensitive reinforcement learning - both for symmetric
and downside risk measures - has typically used direct Monte-Carlo estimation
of policy gradients. While this approach yields unbiased gradient estimates, it
also suffers from high variance and decreased sample efficiency compared to
temporal-difference methods. In this paper, we study prediction and control
with aversion to downside risk which we gauge by the lower partial moment of
the return. We introduce a new Bellman equation that upper bounds the lower
partial moment, circumventing its non-linearity. We prove that this proxy for
the lower partial moment is a contraction, and provide intuition into the
stability of the algorithm by variance decomposition. This allows
sample-efficient, on-line estimation of partial moments. For risk-sensitive
control, we instantiate Reward Constrained Policy Optimization, a recent
actor-critic method for finding constrained policies, with our proxy for the
lower partial moment. We extend the method to use natural policy gradients and
demonstrate the effectiveness of our approach on three benchmark problems for
risk-sensitive reinforcement learning.


  Nonlocal terms in the Einstein Hilbert(EH) action appears as IR corrections
in effective theory of quantum gravity. Here we have considered such an action
keeping the terms which are quadratic in Ricci Scalar. We obtain the solution
for a spherical symmetric. We conduct an analysis for linearised gravity action
and find the Newtonian potentials of linearized gravity action and count the
degrees of freedom. Finally we reproduce the results for few known examples
found in literature.


  Face anti-spoofing is essential to prevent face recognition systems from a
security breach. Much of the progresses have been made by the availability of
face anti-spoofing benchmark datasets in recent years. However, existing face
anti-spoofing benchmarks have limited number of subjects ($\le\negmedspace170$)
and modalities ($\leq\negmedspace2$), which hinder the further development of
the academic community. To facilitate face anti-spoofing research, we introduce
a large-scale multi-modal dataset, namely CASIA-SURF, which is the largest
publicly available dataset for face anti-spoofing in terms of both subjects and
visual modalities. Specifically, it consists of $1,000$ subjects with $21,000$
videos and each sample has $3$ modalities (i.e., RGB, Depth and IR). We also
provide a measurement set, evaluation protocol and training/validation/testing
subsets, developing a new benchmark for face anti-spoofing. Moreover, we
present a new multi-modal fusion method as baseline, which performs feature
re-weighting to select the more informative channel features while suppressing
the less useful ones for each modal. Extensive experiments have been conducted
on the proposed dataset to verify its significance and generalization
capability. The dataset is available at
https://sites.google.com/qq.com/chalearnfacespoofingattackdete


  We prove that an infinitesimally Hilbertian CD(0,N) space containing a line
splits as the product of $R$ and an infinitesimally Hilbertian CD(0,N-1) space.
By `infinitesimally Hilbertian' we mean that the Sobolev space
$W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When
coupled with a curvature-dimension bound, this condition is known to be stable
with respect to measured Gromov-Hausdorff convergence.


  The matrix theory description of the discrete light cone quantization of $M$
theory on a $T^{2}$ is studied. In terms of its super Yang- Mills description,
we identify symmetries of the equations of motion corresponding to independent
rescalings of one of the world sheet light cone coordinates, which show how the
$S$ duality of Type IIB string theory is realized as a Nahm-type
transformation. In the $M$ theory description this corresponds to a simple
$9-11$ flip.


  We discuss in this Letter the association of the candidate magnetar CXOU
J171405.7-381031 with the supernova remnant CTB 37B. The recent detection of
the period derivative of the object allowed an estimation of a young
characteristic age of only $\sim 1000 yr$. This value is too small to be
compatible even with the minimum radius of the remnant $\geq 10 pc$, the value
corresponding to the {\it lower} limit of the estimated distance of $10.2 \pm
3.5 kpc$, unless the true distance happens to be even smaller than the lower
limit. We argue that a consistent scenario for the remnant origin, in which the
latter is powered by the energy injected by a young magnetar, is indeed more
accurate to explain the young age, and points out to its non-standard (i.e.
magnetar-driven) nature.


  We improve and subsume the conditions of Johansson and \"Oberg [18] and
Berbee [2] for uniqueness of a g-measure, i.e., a stationary distribution for
chains with complete connections. In addition, we prove that these unique
g-measures have Bernoulli natural extensions. In particular, we obtain a unique
g-measure that has the Bernoulli property for the full shift on finitely many
states under any one of the following additional assumptions. (1)
$$\sum_{n=1}^\infty (\var_n \log g)^2<\infty,$$ (2) For any fixed $\epsilon>0$,
$$\sum_{n=1}^\infty e^{-(\{1}{2}+\epsilon) (\var_1 \log g+...+\var_n \log
g)}=\infty,$$ (3) $$\var_n \log g=\ordo{\{1}{\sqrt{n}}}, \quad n\to \infty.$$
That the measure is Bernoulli in the case of (1) is new. In (2) we have an
improved version of Berbee's condition (concerning uniqueness and
Bernoullicity) [2], allowing the variations of log g to be essentially twice as
large. Finally, (3) is an example that our main result is new both for
uniqueness and for the Bernoulli property. We also conclude that we have
convergence in the Wasserstein metric of the iterates of the adjoint transfer
operator to the g-measure.


  We present a concentration inequality for linear functionals of
noncommutative polynomials in random matrices. Our hypotheses cover most
standard ensembles, including Gaussian matrices, matrices with independent
uniformly bounded entries and unitary or orthogonal matrices.


  This paper investigates a wireless-powered hybrid reflecting intelligent
surface (hybrid RIS)-assisted multiple access system, where the RIS can harvest
energy from energy station (ES) transmitted radio frequency signal (RF), and
each reflecting element can flexibly switch between active mode, passive mode,
and idle mode. The objective is to minimize the maximum energy consumption of
the users by jointly optimizing the operating modes of each reflecting element,
the amplification factor of active elements, the transmit power, and
transmission time allocation, subject to quality-of-service (QoS) of each user
and the available energy constraint of RIS. In the formulated optimization
problem, the operating modes of each reflecting element are highly coupled with
the amplification coefficient of the active reflecting elements, making it a
challenging mixed-integer programming problem. To solve this problem, a
hierarchical optimization method based on deep reinforcement learning is
proposed, where the operating modes of each reflecting element and the
amplification coefficient of active elements are obtained by solving the outer
sub-problem using proximal policy optimization (PPO), and the transmit power
and transmission time allocation are obtained by solving the inner sub-problem
using convex optimization methods. Simulation results show that compared to the
baseline scheme, the proposed scheme can reduce user energy consumption by $70
\%$.


  In kesterite CZTSSe solar cell research, an asymmetric crystallization
profile is often obtained after annealing, resulting in a bilayered or
double-layered absorber. So far, only segregated pieces of research exist to
characterize this double layer, its formation dynamics and its effect on the
performance of devices. Here, we review the existing research on double-layered
kesterites and evaluate the different mechanisms proposed. Using a
cosputtering-based approach, we show that the two layers can differ
significantly in morphology, composition and optoelectronic properties, and
complement the results with a statistical dataset of over 850 individual CZTS
solar cells. By reducing the absorber thickness from above 1000 nm to 300 nm,
we show that the double layer segregation is alleviated. In turn, we see a
progressive improvement in the device performance for lower thickness, which
alone would be inconsistent with the known case of ultrathin CIGS solar cells.
By comparing the results with CZTS grown on monocrystalline Si substrates,
without a native Na supply, we show that the alkali metal supply does not
determine the double layer formation, but merely reduces the threshold for its
occurrence. Instead, we propose that the main formation mechanism is the early
migration of Cu to the surface during annealing and formation of Cu2-xS phases,
in a self-regulating process akin to the Kirkendall effect. We comment on the
generality of the mechanism proposed, comparing our results to other synthesis
routes, including our own in-house results from solution processing and pulsed
laser deposition of sulfide and oxide-based targets. Although the double layer
occurrence largely depends on the kesterite synthesis route, the common factors
determining the double layer occurrence appear to be the presence of metallic
Cu and/or a chalcogen deficiency in the precursor matrix.


  We study the second-order asymptotics of information transmission using
random Gaussian codebooks and nearest neighbor (NN) decoding over a
power-limited stationary memoryless additive non-Gaussian noise channel. We
show that the dispersion term depends on the non-Gaussian noise only through
its second and fourth moments, thus complementing the capacity result
(Lapidoth, 1996), which depends only on the second moment. Furthermore, we
characterize the second-order asymptotics of point-to-point codes over
$K$-sender interference networks with non-Gaussian additive noise.
Specifically, we assume that each user's codebook is Gaussian and that NN
decoding is employed, i.e., that interference from the $K-1$ unintended users
(Gaussian interfering signals) is treated as noise at each decoder. We show
that while the first-order term in the asymptotic expansion of the maximum
number of messages depends on the power of the interferring codewords only
through their sum, this does not hold for the second-order term.


  In this study, we propose an alternative way to simulate particle suspensions
using the lattice Boltzmann method. The main idea is to impose the non-slip
boundary condition in the lattice sites located on the particle boundaries. The
focus on the lattice sites, instead of the links between them, as done in the
more used methods, represents a great simplification in the algorithm. A fully
description of the method will be presented, in addition to simulations
comparing the proposed method with other methods and, also, with experimental
results.


  (abridged) We present the Significant Cosmic Holes in Universe (SCHU) method
for identifying cosmic voids and loops of filaments in cosmological datasets
and assigning their statistical significance using techniques from topological
data analysis. Persistent homology is used to find different dimensional holes.
For dark matter halo catalogs and galaxy surveys, the 0-, 1-, and 2-dimensional
holes can be identified with clusters, loops of filaments, and voids. The
procedure overlays halos/galaxies on a 3D grid, and a distance-to-measure (DTM)
function is calculated at each point of the grid. A filtration is generated
over the lower-level sets of the DTM across increasing threshold values. The
filtered simplicial complex can be used to summarize the birth/death times of
the different dimension homology group generators (i.e., the holes).
Persistence diagrams are produced from the dimension and birth/death times of
each homology group generator. Using the persistence diagrams and bootstrap
sampling, we explain how $p$-values can be assigned to each homology group
generator. The homology group generators on a persistence diagram are not, in
general, uniquely located back in the original dataset volume so we propose a
method for finding a representation of the homology group generators. This
method provides a novel, statistically rigorous approach for locating
informative generators in cosmological datasets, which may be useful for
providing complementary cosmological constraints on the effects of, for
example, the sum of the neutrino masses. The method is tested on a Voronoi foam
simulation, and then applied to a subset of the SDSS galaxy survey and a
cosmological simulation. Lastly, we calculate Betti functions for two of the
MassiveNuS simulations and discuss implications for using the persistent
homology of the density field to help break degeneracy in the cosmological
parameters.


  Research on formulae production in spreadsheets has established the practice
as high risk yet unrecognised as such by industry. There are numerous software
applications that are designed to audit formulae and find errors. However these
are all post creation, designed to catch errors before the spreadsheet is
deployed. As a general conclusion from EuSpRIG 2003 conference it was decided
that the time has come to attempt novel solutions based on an understanding of
human factors. Hence in this paper we examine one such possibility namely a
novel example driven modelling approach. We discuss a control experiment that
compares example driven modelling against traditional approaches over several
progressively more difficult tests. The results are very interesting and
certainly point to the value of further investigation of the example driven
potential. Lastly we propose a method for statistically analysing the problem
of overconfidence in spreadsheet modellers.


  The hydrodynamic stability of accretion disks is considered. The particular
question is whether the combined action of a (stable) vertical density
stratification and a (stable) radial differential rotation gives rise to a new
instability for nonaxisymmetric modes of disturbances. The existence of such an
instability is not suggested by the well-known Solberg-Hoiland criterion. It is
also not suggested by a local analysis for disturbances in general
stratifications of entropy and angular momentum which is presented in our
Section 2 confirming the results of the Solberg-Hoiland criterion also for
nonaxisymmetric modes within the frame of ideal hydrodynamics but only in the
frame of a short-wave approximation for small m. As a necessary condition for
stability we find that only conservative external forces are allowed to
influence the stable disk. As magnetic forces are never conservative, linear
disk instabilities should only exist in the magnetohydrodynamical regime which
indeed contains the magnetorotational instability as a much-promising
candidate. To overcome some of the used approximations in a numerical
approach,the equations of the compressible adiabatic hydrodynamics are
integrated imposing initial nonaxisymmetric velocity perturbations with m=1 to
m=200.
  Only solutions with decaying kinetic energy are found. The system always
settles in a vertical equilibrium stratification according to pressure balance
with the gravitational potential of the central object. keywords: accretion
disks -- hydrodynamic instabilities -- turbulence


  We study the design of interactive clustering algorithms for data sets
satisfying natural stability assumptions. Our algorithms start with any initial
clustering and only make local changes in each step; both are desirable
features in many applications. We show that in this constrained setting one can
still design provably efficient algorithms that produce accurate clusterings.
We also show that our algorithms perform well on real-world data.


  Resilience is defined as the ability of a network to resist, adapt, and
quickly recover from disruptions, and to continue to maintain an acceptable
level of services from users' perspective. With the advent of future radio
networks, including advanced 5G and upcoming 6G, critical services become
integral to future networks, requiring uninterrupted service delivery for end
users. Unfortunately, with the growing network complexity, user mobility and
diversity, it becomes challenging to scale current resilience management
techniques that rely on local optimizations to large dense network deployments.
This paper aims to address this problem by globally optimizing the resilience
of a dense multi-cell network based on multi-agent deep reinforcement learning.
Specifically, our proposed solution can dynamically tilt cell antennas and
reconfigure transmit power to mitigate outages and increase both coverage and
service availability. A multi-objective optimization problem is formulated to
simultaneously satisfy resiliency constraints while maximizing the service
quality in the network area in order to minimize the impact of outages on
neighbouring cells. Extensive simulations then demonstrate that with our
proposed solution, the average service availability in terms of user throughput
can be increased by up to 50-60% on average, while reaching a coverage
availability of 99% in best cases.


  In hadronic collisions at high energies, the top-quark may be treated as a
parton inside a hadron. Top-quark initiated processes become increasingly
important since the top-quark luminosity can reach a few percent of the
bottom-quark luminosity. In the production of a heavy particle $H$ with mass
$m_H > m_t$, treating the top-quark as a parton allows us to resum large
logarithms $\log(m_{H}^{2}/m_{t}^{2}$) arising from collinear splitting in the
initial state. We quantify the effect of collinear resummation at the 14-TeV
LHC and a future 100-TeV hadron collider, focusing on the top-quark open-flavor
process $gg\to t\bar t H$ in comparison with $t\bar t \to H$ and $tg\rightarrow
tH$ at the leading order (LO) in QCD. We employ top-quark parton distribution
functions with appropriate collinear subtraction and power counting. We find
that (1) Collinear resummation enhances the inclusive production of a heavy
particle with $m_H\approx$ 5 TeV (0.5 TeV) by more than a factor of two
compared to the open-flavor process at a 100-TeV (14-TeV) collider; (2)
Top-quark mass effects are important for scales $m_H$ near the top-quark
threshold, where the cross section is largest. We advocate a modification of
the ACOT factorization scheme, dubbed m-ACOT, to consistently treat heavy-quark
masses in hadronic collisions; (3) The scale uncertainty of the total cross
section in m-ACOT is of about 20 percent at the LO. While a higher-order
calculation is indispensable for a precise prediction, the LO cross section is
well described by the process $t\bar t\to H$ using an effective factorization
scale significantly lower than $m_H$. We illustrate our results by the example
of a heavy spin-0 particle. Our main results also apply to the production of
particles with spin-1 and 2.


  We consider deformations of the $SU(3)$ Affine Toda theory (AT) and
investigate the integrability properties of the deformed theories. We find that
for some special deformations all conserved quantities change to being
conserved only asymptotically, {\it i.e.} in the process of the scattering of
two solitons these charges do vary in time, but they return, after the
scattering, to the values they had prior to the scattering. This phenomenon,
which we have called quasi-integrability, is related to special properties of
the two-soliton solutions under space-time parity transformations. Some
properties of the AT solitons are discussed, especially those involving
interesting static multi-soliton solutions. We support our analytical studies
with detailed numerical ones in which the time evolution has been simulated by
the 4th order Runge-Kutta method. We find that for some perturbations the
solitons repel and for the others they form a quasi-bound state. When we send
solitons towards each other they can repel when they come close together with
or without `flipping' the fields of the model. The solitons radiate very little
and appear to be stable. These results support the ideas of
quasi-integrability, {\it i.e.} that many effects of integrability also
approximately hold for the deformed models.


  The expression of the quantum Ruijsenaars-Schneider Hamiltonian is obtained
in the framework of the dynamical $R$-matrix formalism. This generalizes to the
case of $U_q(sl_n)$ the result obtained by O. Babelon, D. Bernard and E. Billey
for $U_q(sl_2)$ which is the higher difference Lame operator. The general
method involved is the universal $R$-matrix construction.


  Code annotations is a widely used feature in Java systems to configure custom
metadata on programming elements. Their increasing presence creates the need
for approaches to assess and comprehend their usage and distribution. In this
context, software visualization has been studied and researched to improve
program comprehension in different aspects. This study aimed at designing a
software visualization approach that graphically displays how code annotations
are distributed and organized in a software system and developing a tool, as a
reference implementation of the approach, to generate views and interact with
users. We conducted an empirical evaluation through questionnaires and
interviews to evaluate our visualization approach considering four aspects:
effectiveness for program comprehension, perceived usefulness, perceived ease
of use, and suitability for the intended audience. The resulting data was used
to perform a qualitative and quantitative analysis. The tool identifies package
responsibilities providing visual information about their annotations at
different levels. Using the developed tool, the participants achieved a high
correctness rate in the program comprehension tasks and performed very well in
questions about the overview of the system under analysis. Finally,
participants perceived that the tool outperforms existing approaches for code
inspection when searching for information related to code annotations. The
results show that the visualization approach using the developed tool is
effective in program comprehension tasks related to code annotations, which can
also be used to identify responsibilities in the application packages.
Moreover, it was evaluated as suitable for newcomers to overview the usage of
annotations in the system and for architects to perform a deep analysis that
can potentially detect misplaced annotations and abnormal growths on their
usage.


  While Bayesian neural networks (BNNs) provide a sound and principled
alternative to standard neural networks, an artificial sharpening of the
posterior usually needs to be applied to reach comparable performance. This is
in stark contrast to theory, dictating that given an adequate prior and a
well-specified model, the untempered Bayesian posterior should achieve optimal
performance. Despite the community's extensive efforts, the observed gains in
performance still remain disputed with several plausible causes pointing at its
origin. While data augmentation has been empirically recognized as one of the
main drivers of this effect, a theoretical account of its role, on the other
hand, is largely missing. In this work we identify two interlaced factors
concurrently influencing the strength of the cold posterior effect, namely the
correlated nature of augmentations and the degree of invariance of the employed
model to such transformations. By theoretically analyzing simplified settings,
we prove that tempering implicitly reduces the misspecification arising from
modeling augmentations as i.i.d. data. The temperature mimics the role of the
effective sample size, reflecting the gain in information provided by the
augmentations. We corroborate our theoretical findings with extensive empirical
evaluations, scaling to realistic BNNs. By relying on the framework of group
convolutions, we experiment with models of varying inherent degree of
invariance, confirming its hypothesized relationship with the optimal
temperature.


  We introduce a novel laser-scanning optical microscopy technique that employs
optical-frequency-comb (OFC) lasers. This method facilitates multimodal
spectroscopic imaging by analyzing interferograms produced via a dual-comb
spectroscopic approach. Such interferograms capture comprehensive light
information, including amplitude, phase, polarization, frequency, and time of
flight information, enabling multimodal imaging from a single measurement. We
demonstrate the potential of this technique across several spectroscopic
imaging applications.


  We present a framework for the study of muon density patterns on the ground
due to showers produced in the atmosphere by cosmic rays incident at high
zenith angles. As a checking procedure predictions of a model based on such a
framework are compared to simulation results.


  SMC AB 6 is the shortest-period (6.5d) Wolf-Rayet (WR) binary in the Small
Magellanic Cloud, and is therefore crucial for the study of binary interaction
and formation of WR stars at low metallicity. The WR component in AB 6 was
previously found to be very luminous (logL=6.3[Lsun]) compared to its reported
orbital mass (8Msun), placing it significantly above the Eddington limit.
Through spectroscopy and orbital analysis of newly acquired optical data taken
with UVES, we aim to understand the peculiar results reported for this system
and explore its evolutionary history.
  Results: We find that AB 6 contains at least four stars. The 6.5d period WR
binary comprises the WR primary (WN3:h, star A) and a rather rapidly rotating
early O-type companion (O5.5 V, star B). Static N and He lines suggest the
presence of an emission line star (O5.5 I(f), star C). Finally, narrow
absorption lines portraying a long-term radial velocity variation show the
existence of a fourth star (O7.5 V, star D). Star D appears to form a second
140d period binary together with a fifth stellar member, which is a B-type
dwarf or a black hole. It is not clear that these additional components are
bound to the WR binary. The WR star is found to be less luminous than
previously thought (logL = 5.9[Lsun]) and, adopting 41Msun for star B, more
massive (18Msun). Correspondingly, the WR star does not exceed the Eddington
limit. We derive the initial masses of 60 and 40Msun for stars A and B and an
age of 3.9 Myr for the system. The WR binary likely experienced nonconservative
mass transfer in the past supported by the relatively rapid rotation of star B.
  Conclusion: Our study shows that AB 6 is a multiple -- probably quintuple --
system. This finding resolves the previously reported puzzle of the WR primary
exceeding the Eddington limit and suggests that the WR star exchanged mass with
its companion in the past.


  The work provides an exhaustive comparison of some representative families of
topology optimization methods for 3D structural optimization, such as the Solid
Isotropic Material with Penalization (SIMP), the Level-set, the Bidirectional
Evolutionary Structural Optimization (BESO), and the Variational Topology
Optimization (VARTOP) methods. The main differences and similarities of these
approaches are then highlighted from an algorithmic standpoint. The comparison
is carried out via the study of a set of numerical benchmark cases using
industrial-like fine-discretization meshes (around 1 million finite elements),
and Matlab as the common computational platform, to ensure fair comparisons.
Then, the results obtained for every benchmark case with the different methods
are compared in terms of computational cost, topology quality, achieved minimum
value of the objective function, and robustness of the computations
(convergence in objective function and topology). Finally, some quantitative
and qualitative results are presented, from which, an attempt of qualification
of the methods, in terms of their relative performance, is done.


  We prove lower bounds for the fraction of edges of an $r$-graph which can be
covered by the union of $k$ 1-factors. The special case $r=3$ yields some known
results for cubic graphs. Furthermore, we introduce the concept of
$k$-overfull-free $r$-graphs and achieve better bounds for these graphs.


  We review a time-dependent version of the Schrieffer-Wolff transformation
that accounts for real-time control of system parameters, soon to be rendered
possible on a broad basis due to technical progress. The dispersive regime of
$N$ multilevel systems coupled to a cavity via a Jaynes-Cummings interaction is
extended to the most general case. As a concrete example we rigorously apply
the technique to dispersive two-qubit gates in a superconducting architecture,
showing that fidelities based on previous models are off by up to $10^{-2}$,
which is certainly relevant for high-fidelity gates compatible with
fault-tolerant quantum information devices. A closed analytic form for the
error depending on the target evolution closes our work.


  The distributed computing literature considers multiple options for modeling
communication. Most simply, communication is categorized as either synchronous
or asynchronous. Synchronous communication assumes that messages get delivered
within a publicly known timeframe and that parties' clocks are synchronized.
Asynchronous communication, on the other hand, only assumes that messages get
delivered eventually. A more nuanced approach, or a middle ground between the
two extremes, is given by the partially synchronous model, which is arguably
the most realistic option. This model comes in two commonly considered flavors:
  (i) The Global Stabilization Time (GST) model: after an (unknown) amount of
time, the network becomes synchronous. This captures scenarios where network
issues are transient.
  (ii) The Unknown Latency (UL) model: the network is, in fact, synchronous,
but the message delay bound is unknown.
  This work formally establishes that any time-agnostic property that can be
achieved by a protocol in the UL model can also be achieved by a (possibly
different) protocol in the GST model. By time-agnostic, we mean properties that
can depend on the order in which events happen but not on time as measured by
the parties. Most properties considered in distributed computing are
time-agnostic. The converse was already known, even without the time-agnostic
requirement, so our result shows that the two network conditions are, under one
sensible assumption, equally demanding.


  An expression is given for the electronic polarization of an insulating
crystal within the ultrasoft pseudopotential scheme. The pseudopotential
charge-augmentation terms modify the usual Berry-phase expression, and also
give rise to a second term that takes the form of a conventional expectation
value.


  The charge asymmetry has been measured using $19,039~W$ decays recorded by
the CDF detector during the 1992-93 run of the Tevatron Collider. The asymmetry
is sensitive to the ratio of $d$ and $u$ quark distributions to $x<0.01$ at
$Q^2 \approx M_W^2$, where nonperturbative effects are minimal. It is found
that of the two current sets of parton distributions, those of Martin, Roberts
and Stirling (MRS) are favored over the sets most recently produced by the CTEQ
collaboration. The $W$ asymmetry data provide a stronger constraints on $d/u$
ratio than the recent measurements of $F_2^{\mu n}/F_2^{\mu p}$ which are
limited by uncertainties originating from deutron corrections.


  In this paper, we show the surprisingly good properties of plain vision
transformers for body pose estimation from various aspects, namely simplicity
in model structure, scalability in model size, flexibility in training
paradigm, and transferability of knowledge between models, through a simple
baseline model dubbed ViTPose. Specifically, ViTPose employs the plain and
non-hierarchical vision transformer as an encoder to encode features and a
lightweight decoder to decode body keypoints in either a top-down or a
bottom-up manner. It can be scaled up from about 20M to 1B parameters by taking
advantage of the scalable model capacity and high parallelism of the vision
transformer, setting a new Pareto front for throughput and performance.
Besides, ViTPose is very flexible regarding the attention type, input
resolution, and pre-training and fine-tuning strategy. Based on the
flexibility, a novel ViTPose+ model is proposed to deal with heterogeneous body
keypoint categories in different types of body pose estimation tasks via
knowledge factorization, i.e., adopting task-agnostic and task-specific
feed-forward networks in the transformer. We also empirically demonstrate that
the knowledge of large ViTPose models can be easily transferred to small ones
via a simple knowledge token. Experimental results show that our ViTPose model
outperforms representative methods on the challenging MS COCO Human Keypoint
Detection benchmark at both top-down and bottom-up settings. Furthermore, our
ViTPose+ model achieves state-of-the-art performance simultaneously on a series
of body pose estimation tasks, including MS COCO, AI Challenger, OCHuman, MPII
for human keypoint detection, COCO-Wholebody for whole-body keypoint detection,
as well as AP-10K and APT-36K for animal keypoint detection, without
sacrificing inference speed.


  Heavy Ball (HB) nowadays is one of the most popular momentum methods in
non-convex optimization. It has been widely observed that incorporating the
Heavy Ball dynamic in gradient-based methods accelerates the training process
of modern machine learning models. However, the progress on establishing its
theoretical foundation of acceleration is apparently far behind its empirical
success. Existing provable acceleration results are of the quadratic or
close-to-quadratic functions, as the current techniques of showing HB's
acceleration are limited to the case when the Hessian is fixed. In this work,
we develop some new techniques that help show acceleration beyond quadratics,
which is achieved by analyzing how the change of the Hessian at two consecutive
time points affects the convergence speed. Based on our technical results, a
class of Polyak-\L{}ojasiewicz (PL) optimization problems for which provable
acceleration can be achieved via HB is identified. Moreover, our analysis
demonstrates a benefit of adaptively setting the momentum parameter.
  (Update: 08/29/2023) Erratum is added in Appendix J. This is an updated
version that fixes an issue in the previous version. An additional condition
needs to be satisfied for the acceleration result of HB beyond quadratics in
this work, which naturally holds when the dimension is one or, more broadly,
when the Hessian is diagonal. We elaborate on the issue in Appendix J.