  Precise studies on the Galactic bulge, globular cluster, Galactic halo and
Galactic thick disk require stellar models with alpha enhancement and various
values of helium content. These models are also important for extra-Galactic
population synthesis studies. For this purpose, we complement the existing
PARSEC models, which are based on the solar partition of heavy elements, with
alpha-enhanced partitions. We collect detailed measurements on the metal
mixture and helium abundance for the two populations of 47 Tuc (NGC 104) from
the literature, and calculate stellar tracks and isochrones with these
alpha-enhanced compositions. By fitting the precise color-magnitude diagram
with HST ACS/WFC data, from low main sequence till horizontal branch, we
calibrate some free parameters that are important for the evolution of low mass
stars like the mixing at the bottom of the convective envelope. This new
calibration significantly improves the prediction of the RGB bump brightness.
Comparison with the observed RGB and HB luminosity functions also shows that
the evolutionary lifetimes are correctly predicted. As a further result of this
calibration process, we derive the age, distance modulus, reddening, and the
red giant branch mass loss for 47 Tuc. We apply the new calibration and
alpha-enhanced mixtures of the two 47 Tuc populations ( [alpha/Fe] ~0.4 and
0.2) to other metallicities. The new models reproduce the RGB bump observations
much better than previous models. This new PARSEC database, with the newly
updated alpha-enhanced stellar evolutionary tracks and isochrones, will also be
part of the new stellar products for Gaia.


  Consider a non--linear function $G(X_t)$ where $X_t$ is a stationary Gaussian
sequence with long--range dependence. The usual reduction principle states that
the partial sums of $G(X_t)$ behave asymptotically like the partial sums of the
first term in the expansion of $G$ in Hermite polynomials. In the context of
the wavelet estimation of the long--range dependence parameter, one replaces
the partial sums of $G(X_t)$ by the wavelet scalogram, namely the partial sum
of squares of the wavelet coefficients. Is there a reduction principle in the
wavelet setting, namely is the asymptotic behavior of the scalogram for
$G(X_t)$ the same as that for the first term in the expansion of $G$ in Hermite
polynomial? The answer is negative in general. This paper provides a minimal
growth condition on the scales of the wavelet coefficients which ensures that
the reduction principle also holds for the scalogram. The results are applied
to testing the hypothesis that the long-range dependence parameter takes a
specific value.


  A network covert channel is created that uses resource names such as
addresses to convey information, and that approximates typical user behavior in
order to blend in with its environment. The channel correlates available
resource names with a user defined code-space, and transmits its covert message
by selectively accessing resources associated with the message codes. In this
paper we focus on an implementation of the channel using the Hypertext Transfer
Protocol (HTTP) with Uniform Resource Locators (URLs) as the message names,
though the system can be used in conjunction with a variety of protocols. The
covert channel does not modify expected protocol structure as might be detected
by simple inspection, and our HTTP implementation emulates transaction level
web user behavior in order to avoid detection by statistical or behavioral
analysis.


  We give a complete description of the structure of all bisimple orthodox
semigroups generated by two mutually inverse elements.


  This paper presents the computational challenge on differential geometry and
topology that was hosted within the ICLR 2022 workshop ``Geometric and
Topological Representation Learning". The competition asked participants to
provide implementations of machine learning algorithms on manifolds that would
respect the API of the open-source software Geomstats (manifold part) and
Scikit-Learn (machine learning part) or PyTorch. The challenge attracted seven
teams in its two month duration. This paper describes the design of the
challenge and summarizes its main findings.


  In this work, we study the Neumann initial-boundary value problem for a
two-species chemotaxis system with Lotka-Volterra competition and signal
production. Under a rather weak and clean condition of sub-quadratic type
damping and merely integrable initial data, we establish the global existence
of generalized solutions in an N dimensional bounded and smooth domain.


  We develop a formal theory of the weak values with emphasis on the
consistency conditions and a probabilistic interpretation in the
counter-factual processes. We present the condition for the choice of the
post-selected state to give a negative weak value of a given projection
operator and strange values of an observable in general. The general framework
is applied to Hardy's paradox and the spin $1/2$ system to explicitly address
the issues of counter-factuality and strange weak values. The counter-factual
arguments which characterize the paradox specifies the pre-selected state and a
complete set of the post-selected states clarifies how the strange weak values
emerge.


  Nearest neighbor search has found numerous applications in machine learning,
data mining and massive data processing systems. The past few years have
witnessed the popularity of the graph-based nearest neighbor search paradigm
because of its superiority over the space-partitioning algorithms. While a lot
of empirical studies demonstrate the efficiency of graph-based algorithms, not
much attention has been paid to a more fundamental question: why graph-based
algorithms work so well in practice? And which data property affects the
efficiency and how? In this paper, we try to answer these questions. Our
insight is that "the probability that the neighbors of a point o tends to be
neighbors in the KNN graph" is a crucial data property for query efficiency.
For a given dataset, such a property can be qualitatively measured by
clustering coefficient of the KNN graph. To show how clustering coefficient
affects the performance, we identify that, instead of the global connectivity,
the local connectivity around some given query q has more direct impact on
recall. Specifically, we observed that high clustering coefficient makes most
of the k nearest neighbors of q sit in a maximum strongly connected component
(SCC) in the graph. From the algorithmic point of view, we show that the search
procedure is actually composed of two phases - the one outside the maximum SCC
and the other one in it, which is different from the widely accepted single or
multiple paths search models. We proved that the commonly used graph-based
search algorithm is guaranteed to traverse the maximum SCC once visiting any
point in it. Our analysis reveals that high clustering coefficient leads to
large size of the maximum SCC, and thus provides good answer quality with the
help of the two-phase search procedure. Extensive empirical results over a
comprehensive collection of datasets validate our findings.


  We argue that quenched QCD has non-trivial phase structure for negative quark
mass, including the possibility of a parity-flavor breaking Aoki phase. This
has implications for simulations with domain-wall or overlap fermions.


  This paper is devoted to the study of reproducing kernel Hilbert spaces. We
focus on multipliers of reproducing kernel Banach and Hilbert spaces. In
particular we tried to extend this concept and prove some theorems.


  While LLMs have shown impressive capabilities in solving math or coding
problems, the ability to make scientific discoveries remains a distinct
challenge. This paper proposes a "Turing test for an AI scientist" to assess
whether an AI agent can conduct scientific research independently, without
relying on human-generated knowledge. Drawing inspiration from the historical
development of science, we propose seven benchmark tests that evaluate an AI
agent's ability to make groundbreaking discoveries in various scientific
domains. These tests include inferring the heliocentric model from celestial
observations, discovering the laws of motion in a simulated environment,
deriving the differential equation governing vibrating strings, inferring
Maxwell's equations from electrodynamics simulations, inventing numerical
methods for initial value problems, discovering Huffman coding for data
compression, and developing efficient sorting algorithms. To ensure the
validity of these tests, the AI agent is provided with interactive libraries or
datasets specific to each problem, without access to human knowledge that could
potentially contain information about the target discoveries. The ultimate goal
is to create an AI scientist capable of making novel and impactful scientific
discoveries, surpassing the best human experts in their respective fields.
These "Turing tests" serve as intermediate milestones, assessing the AI agent's
ability to make discoveries that were groundbreaking in their time. If an AI
agent can pass the majority of these seven tests, it would indicate significant
progress towards building an AI scientist, paving the way for future
advancements in autonomous scientific discovery. This paper aims to establish a
benchmark for the capabilities of AI in scientific research and to stimulate
further research in this exciting field.


  We compare two partitions of real bitangents to smooth plane quartics into
sets of 4: one coming from the closures of connected components of the
avoidance locus and another coming from tropical geometry. When both are
defined, we use the Tarski principle for real closed fields in combination with
the topology of real plane quartics and the tropical geometry of bitangents and
theta characteristics to show that they coincide.


  Conventional neural accelerators rely on isolated self-sufficient functional
units that perform an atomic operation while communicating the results through
an operand delivery-aggregation logic. Each single unit processes all the bits
of their operands atomically and produce all the bits of the results in
isolation. This paper explores a different design style, where each unit is
only responsible for a slice of the bit-level operations to interleave and
combine the benefits of bit-level parallelism with the abundant data-level
parallelism in deep neural networks. A dynamic collection of these units
cooperate at runtime to generate bits of the results, collectively. Such
cooperation requires extracting new grouping between the bits, which is only
possible if the operands and operations are vectorizable. The abundance of Data
Level Parallelism and mostly repeated execution patterns, provides a unique
opportunity to define and leverage this new dimension of Bit-Parallel Vector
Composability. This design intersperses bit parallelism within data-level
parallelism and dynamically interweaves the two together. As such, the building
block of our neural accelerator is a Composable Vector Unit that is a
collection of Narrower-Bitwidth Vector Engines, which are dynamically composed
or decomposed at the bit granularity. Using six diverse CNN and LSTM deep
networks, we evaluate this design style across four design points: with and
without algorithmic bitwidth heterogeneity and with and without availability of
a high-bandwidth off-chip memory. Across these four design points, Bit-Parallel
Vector Composability brings (1.4x to 3.5x) speedup and (1.1x to 2.7x) energy
reduction. We also comprehensively compare our design style to the Nvidia RTX
2080 TI GPU, which also supports INT-4 execution. The benefits range between
28.0x and 33.7x improvement in Performance-per-Watt.


  Motivated by the prospect of quantum simulation of quantum field theories, we
formulate the $O(N)$ nonlinear sigma model as a "qubit" model with an
$(N+1)$-dimensional local Hilbert space at each lattice site. Using an
efficient worm algorithm in the worldline formulation, we demonstrate that the
model has a second-order critical point in $(2+1)$ dimensions, where the
continuum physics of the nontrivial $O(N)$ Wilson-Fisher fixed point is
reproduced. We compute the critical exponents $\nu$ and $\eta$ for the $O(N)$
qubit models up to $N=8$, and find excellent agreement with known results in
literature from various analytic and numerical techniques for the $O(N)$
Wilson-Fisher universality class. Our models are suited for studying $O(N)$
nonlinear sigma models on quantum computers up to $N=8$ in $d=2,3$ spatial
dimensions.


  We propose a variance reduction framework for variational inference using the
Multilevel Monte Carlo (MLMC) method. Our framework is built on reparameterized
gradient estimators and "recycles" parameters obtained from past update history
in optimization. In addition, our framework provides a new optimization
algorithm based on stochastic gradient descent (SGD) that adaptively estimates
the sample size used for gradient estimation according to the ratio of the
gradient variance. We theoretically show that, with our method, the variance of
the gradient estimator decreases as optimization proceeds and that a learning
rate scheduler function helps improve the convergence. We also show that, in
terms of the \textit{signal-to-noise} ratio, our method can improve the quality
of gradient estimation by the learning rate scheduler function without
increasing the initial sample size. Finally, we confirm that our method
achieves faster convergence and reduces the variance of the gradient estimator
compared with other methods through experimental comparisons with baseline
methods using several benchmark datasets.


  Copula-based methods provide a flexible approach to build missing data
imputation models of multivariate data of mixed types. However, the choice of
copula function is an open question. We consider a Bayesian nonparametric
approach by using an infinite mixture of elliptical copulas induced by a
Dirichlet process mixture to build a flexible copula function. A slice sampling
algorithm is used to sample from the infinite dimensional parameter space. We
extend the work on prior parallel tempering used in finite mixture models to
the Dirichlet process mixture model to overcome the mixing issue in multimodal
distributions. Using simulations, we demonstrate that the infinite mixture
copula model provides a better overall fit compared to their single component
counterparts, and performs better at capturing tail dependence features of the
data. Simulations further show that our proposed model achieves more accurate
imputation especially for continuous variables and better inferential results
in some analytic models. The proposed model is applied to a medical data set of
acute stroke patients in Australia.


  We consider the nonlinear, inverse problem of identifying the stored energy
function of a hyperelastic material from full knowledge of the displacement
field as well as from surface sensor measurements. The displacement field is
represented as a solution of Cauchy's equation of motion, which is a nonlinear,
elastic wave equation. Hyperelasticity means that the first Piola-Kirchhoff
stress tensor is given as the gradient of the stored energy function. We assume
that a dictionary of suitable functions is available and the aim is to recover
the stored energy with respect to this dictionary. The considered inverse
problem is of vital interest for the development of structural health
monitoring systems which are constructed to detect defects in elastic materials
from boundary measurements of the displacement field, since the stored energy
encodes the mechanical peroperties of the underlying structure. In this article
we develope a numerical solver for both settings using the attenuated Landweber
method. We show that the parameter-to-solution map satisfies the local
tangential cone condition. This result can be used to prove local convergence
of the attenuated Landweber method in case that the full displacement field is
measured. In our numerical experiments we demonstrate how to construct an
appropriate dictionary and show that our algorithm is well suited to localize
damages in various situations.


  The fracture behavior of brittle and ductile materials can be strongly
influenced by thermal fluctuations, especially in micro- and nano-devices as
well as in rubberlike and biological materials. However, temperature effects,
in particular on the brittle-to-ductile transition, still require a deeper
theoretical investigation. As a step in this direction we propose a theory,
based on equilibrium statistical mechanics, able to describe the temperature
dependent brittle fracture and brittle-to-ductile transition in prototypical
discrete systems consisting in a lattice with breakable elements. Concerning
the brittle behavior, we obtain closed form expressions for the
temperature-dependent fracture stress and strain, representing a generalized
Griffith criterion, ultimately describing the fracture as a genuine phase
transition. With regard to the brittle-to-ductile transition, we obtain a
complex critical scenario characterized by a threshold temperature between the
two fracture regimes (brittle and ductile), an upper and a lower yield
strength, and a critical temperature corresponding to the complete breakdown.
To show the effectiveness of the proposed models in describing thermal fracture
behaviors at small scales, we successfully compare our theoretical results with
molecular dynamics simulations of Si and GaN nanowires.


  Few-shot classification is a challenge in machine learning where the goal is
to train a classifier using a very limited number of labeled examples. This
scenario is likely to occur frequently in real life, for example when data
acquisition or labeling is expensive. In this work, we consider the problem of
post-labeled few-shot unsupervised learning, a classification task where
representations are learned in an unsupervised fashion, to be later labeled
using very few annotated examples. We argue that this problem is very likely to
occur on the edge, when the embedded device directly acquires the data, and the
expert needed to perform labeling cannot be prompted often. To address this
problem, we consider an algorithm consisting of the concatenation of transfer
learning with clustering using Self-Organizing Maps (SOMs). We introduce a
TensorFlow-based implementation to speed-up the process in multi-core CPUs and
GPUs. Finally, we demonstrate the effectiveness of the method using standard
off-the-shelf few-shot classification benchmarks.


  First we present the general equation form of a thermal explosion in a vessel
with boundary values, later use central difference method and Newton iteration
method to solve the relevant partial differential equations in one-dimensional
and two-dimensional forms, finally we use numerical experiments to verify the
order of convergence of the central difference scheme and provide the
experiment results.


  Traditionally, measuring the center-of-mass (c.m.) velocity of an atomic
ensemble relies on measuring the Doppler shift of the absorption spectrum of
single atoms in the ensemble. Mapping out the velocity distribution of the
ensemble is indispensable when determining the c.m. velocity using this
technique. As a result, highly sensitive measurements require preparation of an
ensemble with a narrow Doppler width. Here, we use a dispersive measurement of
light passing through a moving room temperature atomic vapor cell to determine
the velocity of the cell in a single shot with a short-term sensitivity of 5.5
$\mu$m s$^{-1}$ Hz$^{-1/2}$. The dispersion of the medium is enhanced by
creating quantum interference through an auxiliary transition for the probe
light under electromagnetically induced transparency condition. In contrast to
measurement of single atoms, this method is based on the collective motion of
atoms and can sense the c.m. velocity of an ensemble without knowing its
velocity distribution. Our results improve the previous measurements by 3
orders of magnitude and can be used to design a compact motional sensor based
on thermal atoms.


  Process Outcome Prediction entails predicting a discrete property of an
unfinished process instance from its partial trace. High-capacity outcome
predictors discovered with ensemble and deep learning methods have been shown
to achieve top accuracy performances, but they suffer from a lack of
transparency. Aligning with recent efforts to learn inherently interpretable
outcome predictors, we propose to train a sparse Mixture-of-Experts where both
the ``gate'' and ``expert'' sub-nets are Logistic Regressors. This
ensemble-like model is trained end-to-end while automatically selecting a
subset of input features in each sub-net, as an alternative to the common
approach of performing a global feature selection step prior to model training.
Test results on benchmark logs confirmed the validity and efficacy of this
approach.


  We investigate the electronic properties of the LaAlO3/SrTiO3 interface using
density functional theory. In contrast to previous studies, which relied on
(semi-)local functionals and the GGA+U method, we here use a recently developed
hybrid functional to determine the electronic structure. This approach offers
the distinct advantage of accessing both the metallic and insulating
multilayers on a parameter-free equal footing. As compared to calculations
based on semilocal GGA functionals, our hybrid functional calculations lead to
a considerably increased band gap for the insulating systems. The details of
the electronic structure show substantial deviations from those obtained by GGA
calculations. This casts severe doubts on all previous results based on
semilocal functionals. In particular, corrections using rigid band shifts
("scissors operator") cannot lead to valid results.


  We consider inertial manifolds and their approximation for a class of partial
differential equations with a nonlocal Laplacian operator
$-(-\Delta)^{\frac{\alpha}{2}}$, with $0<\alpha<2$. The nonlocal or fractional
Laplacian operator represents an anomalous diffusion effect. We first establish
the existence of an inertial manifold and highlight the influence of the
parameter $\alpha$. Then we approximate the inertial manifold when a small
normal diffusion $\varepsilon \Delta$ (with $\varepsilon \in (0, 1)$) enters
the system, and obtain the estimate for the Hausdorff semi-distance between the
inertial manifolds with and without normal diffusion.


  We focus on the influence of the Coriolis acceleration on the stochastic
excitation of oscillation modes in convective regions of rotating stars. Our
aim is to estimate the asymmetry between excitation rates of prograde and
retrograde modes. We extend the formalism derived for obtaining stellar $p$-
and $g$-mode amplitudes (Samadi & Goupil 2001, Belkacem et al. 2008) to include
the effect of the Coriolis acceleration. We then study the special case of
uniform rotation for slowly rotating stars by performing a perturbative
analysis. This allows us to consider the cases of the Sun and the CoRoT target
HD 49933. We find that, in the subsonic regime, the influence of rotation as a
direct contribution to mode driving is negligible in front of the Reynolds
stress contribution. In slow rotators, the indirect effect of the modification
of the eigenfunctions on mode excitation is investigated by performing a
perturbative analysis of the excitation rates. It turns out that the excitation
of solar $p$ modes is affected by rotation with excitation rates asymmetries
between prograde and retrograde modes of the order of several percents. Solar
low-order $g$ modes are also affected by uniform rotation and their excitation
rates asymmetries are found to reach up to 10 %. The CoRoT target HD 49933 is
rotating faster than the Sun ($\Omega / \Omega_\odot \approx 8$) and we show
that the resulting excitation rates asymmetry is about 10 % for the excitation
rates of $p$ modes. We have then demonstrated that $p$ and $g$ mode excitation
rates are modified by uniform rotation through the Coriolis acceleration. Study
of the effect of differential rotation is dedicated to a forthcoming paper.


  Topological indices are a class of numerical invariants that predict certain
physical and chemical properties of molecules. Recently, two novel topological
indices, named as Sombor index and reduced Sombor index, were introduced by
Gutman, defined as $$SO(G)=\sum_{uv\in E(G)}\sqrt{d_{G}^{2}(u)+d_{G}^{2}(v)},$$
$$SO_{red}(G)=\sum_{uv\in E(G)}\sqrt{(d_{G}(u)-1)^{2}+(d_{G}(v)-1)^{2}},$$
where $d_{G}(u)$ denotes the degree of vertex $u$ in $G$.
  In this paper, our aim is to order the chemical trees, chemical unicyclic
graphs, chemical bicyclic graphs and chemical tricyclic graphs with respect to
Sombor index and reduced Sombor index. We determine the first fourteen minimum
chemical trees, the first four minimum chemical unicyclic graphs, the first
three minimum chemical bicyclic graphs, the first seven minimum chemical
tricyclic graphs. At last, we consider the applications of reduced Sombor index
to octane isomers.


  This work presents a novel modeling and analysis framework for graph
sequences which addresses the challenge of detecting and contextualizing
anomalies in labelled, streaming graph data. We introduce a generalization of
the BTER model of Seshadhri et al. by adding flexibility to community
structure, and use this model to perform multi-scale graph anomaly detection.
Specifically, probability models describing coarse subgraphs are built by
aggregating probabilities at finer levels, and these closely related
hierarchical models simultaneously detect deviations from expectation. This
technique provides insight into a graph's structure and internal context that
may shed light on a detected event. Additionally, this multi-scale analysis
facilitates intuitive visualizations by allowing users to narrow focus from an
anomalous graph to particular subgraphs or nodes causing the anomaly.
  For evaluation, two hierarchical anomaly detectors are tested against a
baseline Gaussian method on a series of sampled graphs. We demonstrate that our
graph statistics-based approach outperforms both a distribution-based detector
and the baseline in a labeled setting with community structure, and it
accurately detects anomalies in synthetic and real-world datasets at the node,
subgraph, and graph levels. To illustrate the accessibility of information made
possible via this technique, the anomaly detector and an associated interactive
visualization tool are tested on NCAA football data, where teams and
conferences that moved within the league are identified with perfect recall,
and precision greater than 0.786.


  A detailed stochastic model of single-gene auto-regulation is established and
its solutions are explored when mRNA dynamics is fast compared with protein
dynamics and in the opposite regime. The model includes all the sources of
randomness that are intrinsic to the auto-regulation process and it considers
both transcriptional and post transcriptional regulation. The timescale
separation allows the derivation of analytic expressions for the equilibrium
distributions of protein and mRNA. These distributions are generally well
described in the continuous approximation, which is used to discuss the
qualitative features of the protein equilibrium distributions as a function of
the biological parameters in the fast mRNA regime. The performance of the
timescale approximation is assessed by comparison with simulations of the full
stochastic system, and a good quantitative agreement is found for a wide range
of parameter values. We show that either unimodal or bimodal equilibrium
protein distributions can arise, and we discuss the auto-regulation mechanisms
associated with bimodality.


  Communicating with each other in a distributed manner and behaving as a group
are essential in multi-agent reinforcement learning. However, real-world
multi-agent systems suffer from restrictions on limited-bandwidth
communication. If the bandwidth is fully occupied, some agents are not able to
send messages promptly to others, causing decision delay and impairing
cooperative effects. Recent related work has started to address the problem but
still fails in maximally reducing the consumption of communication resources.
In this paper, we propose Event-Triggered Communication Network (ETCNet) to
enhance the communication efficiency in multi-agent systems by sending messages
only when necessary. According to the information theory, the limited bandwidth
is translated to the penalty threshold of an event-triggered strategy, which
determines whether an agent at each step sends a message or not. Then the
design of the event-triggered strategy is formulated as a constrained Markov
decision problem, and reinforcement learning finds the best communication
protocol that satisfies the limited bandwidth constraint. Experiments on
typical multi-agent tasks demonstrate that ETCNet outperforms other methods in
terms of the reduction of bandwidth occupancy and still preserves the
cooperative performance of multi-agent systems at the most.


  The authors study the classical Lagrange inversion theorem--an antecedent of
the modern implicit function theorem--in the smooth case. Examples are given to
show that the result is sharp.


  We report on the well-posedness of the Feynman problem for the Klein-Gordon
equation on asymptotically Minkowski spacetimes. The main result is the
invertibility of the Klein-Gordon operator with Feynman conditions at infinite
times. Furthermore, the inverse is shown to coincide with the
Duistermaat-H\"ormander Feynman parametrix modulo smoothing terms.


  The electronic structure of thin films of FeTe grown on Bi$_2$Te$_3$ is
investigated using angle-resolved photoemission spectroscopy, scanning
tunneling microscopy and first principles calculations. As a comparison, data
from cleaved bulk \FeTe taken under the same experimental conditions is also
presented. Due to the substrate and thin film symmetry, FeTe thin films grow on
Bi$_2$Te$_3$ in three domains, rotated by 0$^{\circ}$, 120$^{\circ}$, and
240$^{\circ}$. This results in a superposition of photoemission intensity from
the domains, complicating the analysis. However, by combining bulk and thin
film data, it is possible to partly disentangle the contributions from three
domains. We find a close similarity between thin film and bulk electronic
structure and an overall good agreement with first principles calculations,
assuming a p-doping shift of 65~meV for the bulk and a renormalization factor
of around 2. By tracking the change of substrate electronic structure upon film
growth, we find indications of an electron transfer from the FeTe film to the
substrate. No significant change of the film's electronic structure or doping
is observed when alkali atoms are dosed onto the surface. This is ascribed to
the film's high density of states at the Fermi energy. This behavior is also
supported by the ab-initio calculations.


  The famous Minkowski inequality provides a sharp lower bound for the mixed
volume $V(K,M[n-1])$ of two convex bodies $K,M\subset\mathbb{R}^n$ in terms of
powers of the volumes of the individual bodies $K$ and $M$. The special case
where $K$ is the unit ball yields the isoperimetric inequality. In the plane,
Betke and Weil (1991) found a sharp upper bound for the mixed area of $K$ and
$M$ in terms of the perimeters of $K$ and $M$. We extend this result to general
dimensions by proving a sharp upper bound for the mixed volume $V(K,M[n-1])$ in
terms of the mean width of $K$ and the surface area of $M$. The equality case
is completely characterized. In addition, we establish a stability improvement
of this and related geometric inequalities of isoperimetric type.


  We examine the characteristic features of reversible and quantum computations
in the presence of supplementary external information, known as advice. In
particular, we present a simple, algebraic characterization of languages
recognized by one-way reversible finite automata augmented with deterministic
advice. With a further elaborate argument, we prove a similar but slightly
weaker result for bounded-error one-way quantum finite automata with advice.
Immediate applications of those properties lead to containments and separations
among various language families when they are assisted by appropriately chosen
advice. We further demonstrate the power and limitation of randomized advice
and quantum advice when they are given to one-way quantum finite automata.


  Equilibrium atomic configurations and electron energy structure of ethanol
adsorbed on the Si (111) surface are studied by the first-principles density
functional theory. Geometry optimization is performed by the total energy
minimization method. Several equilibrium atomic configurations of ethanol, both
undissociated and dissociated, on the Si (111) surface are found. Reaction
pathways and predicted transition states are discussed in comparison with
available experimental data in terms of the feasibility of the reactions
occurring. Analysis of atom and orbital resolved projected density of states
indicate substantial modifications of the Si surface valence and conduction
bands due to the adsorption of ethanol affecting the electrical properties of
the surface.


  Let $F$ be a $p$-adic field, $G = \text{GL}_{2n}(F)$ and $\theta_0$ be the
exterior automorphism of $G$ that fixes a pinning of a Borel pair. Consider the
set $\widetilde{G} = G \theta_0$ on which $G$ acts by conjugacy and the orbital
integral $J_{\widetilde{G}}(\theta_0, f)$ at $\theta_0$. We prove a
Plancherel-Harish-Chandra type formula for this orbital integral, namely as an
integral over the irreducible tempered auto-dual representations of $G$ that we
call "symplectic" (meaning their Langlands parameter factors through
$\text{Sp}_{2n}(\mathbb{C})$). This solves a problem raised by G. Chenevier and
L. Clozel. Our method uses the endoscopic transfer to $\text{SO}_{2n+1}$. Along
the way, we also prove that the Plancherel measure is constant on $L$-packets.


  Several properties of the M31 disk, namely: opacity, extinction law and
gas-to-dust ratio are studied by means of optical and near-infrared photometry
of ten globular clusters and galaxies seen through the disk. The individual
extinctions of these objects were estimated with respect to several sets of
theoretical spectral energy distributions for globulars and galaxies. Seven
targets are consistent with reddened globulars, two - with starburst galaxies
and one - with an elliptical. The extinction estimates agree with
semi-transparent disk (Av ~ 1) in the inter-arm regions. The total-to-selective
extinction ratio in those regions 2.75 is lower on average than the typical
Galactic value of Rv=3.1. We also obtained a gas-to-dust ratio, similar to that
in the the Milky way. It shows no correlation with the distance from the M31
center.


  While attaining external field control of bimolecular chemical reactions has
long been a coveted goal of physics and chemistry, the role of hyperfine
interactions and dc magnetic fields in achieving such control has remained
elusive. We develop an extended coupled-channel statistical theory of
barrierless atom-diatom chemical reactions, and apply it to elucidate the
effects of magnetic fields and hyperfine interactions on the ultracold chemical
reaction Li($^2\text{S}_{1/2}$) + CaH($^2\Sigma^+$) $\to$ LiH($^1\Sigma^+$) +
Ca($^1\text{S}_{0}$) on a newly developed set of ab initio potential energy
surfaces. We observe large field effects on the reaction cross sections,
opening up the possibility of controlling ultracold barrierless chemical
reactions by tuning selected hyperfine states of the reactants with an external
magnetic field.


  We study equivariant projective compactifications of reductive groups
obtained by closing the image of a group in the space of operators of a
projective representation. We describe the structure and the mutual position of
their orbits under the action of the doubled group by left/right
multiplications, the local structure in a neighborhood of a closed orbit, and
obtain some conditions of normality and smoothness of a compactification. Our
methods of research use the theory of equivariant embeddings of spherical
homogeneous spaces and of reductive algebraic semigroups.


  Study of primary stars lying in Sirius-like systems with various masses of WD
companions and orbital separations is one of the key aspects to understand the
origin and nature of Barium (Ba) stars. In this paper, based on high resolution
and high S/N spectra, we present systematic analysis of photospheric abundances
for 18 FGK primary stars of Sirius-like systems including six giants and 12
dwarfs. Atmospheric parameters, stellar masses, and abundances of 24 elements
(C, Na, Mg, Al, Si, S, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Sr, Y, Zr, Ba,
La, Ce and Nd) are determined homogeneously. The abundance patterns in these
sample stars show that most of the elements in our sample follow the behavior
of field stars with similar metallicity. As expected, s-process elements in
four known Ba giants show overabundance. A weak correlation was found between
anomalies of s-process elemental abundance and orbital separation, suggesting
the orbital separation of the binaries could not be the main constraint to
differentiate strong Ba stars from mild Ba stars. Our study shows that the
large mass (>0.51 M ) of a WD companion in a binary system is not a sufficient
condition to form a Ba star, even if the separation between the two components
is small. Although not sufficient it seems to be a necessary condition since Ba
stars with lower mass WDs in the observed sample were not found. Our results
support that [s/Fe] and [hs/ls] ratios of Ba stars are anti-correlated with the
metallicity. However, the different levels of s-process overabundance among Ba
stars may not to be dominated mainly by the metallicity.


  In many different fields interactions between objects play a critical role in
determining their behavior. Graph neural networks (GNNs) have emerged as a
powerful tool for modeling interactions, although often at the cost of adding
considerable complexity and latency. In this paper, we consider the problem of
spatial interaction modeling in the context of predicting the motion of actors
around autonomous vehicles, and investigate alternatives to GNNs. We revisit 2D
convolutions and show that they can demonstrate comparable performance to graph
networks in modeling spatial interactions with lower latency, thus providing an
effective and efficient alternative in time-critical systems. Moreover, we
propose a novel interaction loss to further improve the interaction modeling of
the considered methods.


  Predicting the survival time of a cancer patient based on his/her genome-wide
gene expression remains a challenging problem. For certain types of cancer, the
effects of gene expression on survival are both weak and abundant, so
identifying nonzero effects with reasonable accuracy is difficult. As an
alternative to methods that use variable selection, we propose a Gaussian
process accelerated failure time model to predict survival time using
genome-wide or pathway-wide gene expression data. Using a Monte Carlo EM
algorithm, we jointly impute censored log-survival time and estimate model
parameters. We demonstrate the performance of our method and its advantage over
existing methods in both simulations and real data analysis. The real data that
we analyze were collected from 513 patients with kidney renal clear cell
carcinoma and include survival time, demographic/clinical variables, and
expression of more than 20,000 genes. Our method is widely applicable as it can
accommodate right, left, and interval censored outcomes; and provides a natural
way to combine multiple types of high-dimensional -omics data. An R package
implementing our method is available online.


  We study the thermal boundary conduction in one-dimensional harmonic and
$\phi^{4}$ lattices, both of which consist of two segments coupled by a
harmonic interaction. For the ballistic interfacial heat transport through the
harmonic lattice, we use both theoretical calculation and molecular dynamics
simulation to study the heat flux and temperature jump at the interface as to
gain insights of the Kapitza resistance at the atomic scale. In the weak
coupling regime, the heat current is proportional to the square of the coupling
strength for the harmonic model as well as anharmonic models. Interestingly,
there exists a negative temperature jump between the interfacial particles in
particular parameter regimes. A nonlinear response of the boundary temperature
jump to the externally applied temperature difference in the $\phi^{4}$ lattice
is observed. To understand the anomalous result, we then extend our studies to
a model in which the interface is represented by a relatively small segment
with gradually changing spring constants, and find that the negative
temperature jump still exist. Finally, we show that the local velocity
distribution at the interface is so close to the Gaussian distribution that the
existence/absence of local equilibrium state seems unable to determine by
numerics in this way.


  Context: We study the structure and evolution of circumstellar discs around
evolved binaries and their impact on the evolution of the central system. Aims:
To study in detail the binary nature of RUCen and ACHer, as well as the
structure and mineralogy of the circumstellar environment. Methods: We combine
multi-wavelength observations with a 2D radiative transfer study. Our radial
velocity program studies the central stars, while our Spitzer spectra and
broad-band SEDs are used to constrain mineralogy, grain sizes and physical
structure of the circumstellar environment. Results: We determine the orbital
elements of RUCen showing that the orbit is highly eccentric with a rather long
period of 1500 days. The infrared spectra of both objects are very similar and
the spectral dust features are dominated by Mg-rich crystalline silicates. The
small peak-to-continuum ratios are interpreted as being due to large grains.
Our model contains two components with a cold midplain dominated by large
grains, and the near- and mid-IR which is dominated by the emission of smaller
silicates. The infrared excess is well modelled assuming a hydrostatic passive
irradiated disc. The profile-fitting of the dust resonances shows that the
grains must be very irregular. Conclusions: These two prototypical RVTauri
pulsators with circumstellar dust are binaries where the dust is trapped in a
stable disc. The mineralogy and grain sizes show that the dust is highly
processed, both in crystallinity and grain size. The cool crystals show that
either radial mixing is very efficient and/or that the thermal history at grain
formation has been very different from that in outflows. The physical processes
governing the structure of these discs are similar to those observed in
protoplanetary discs around young stellar objects.


  Let F be a square integrable Maass form on the Siegel upper half space of
rank 2 for the Siegel modular group Sp(4, Z) with Laplace eigenvalue lambda.
If, in addition, F is a joint eigenfunction of the Hecke algebra, we show a
power-saving sup-norm bound in terms of lambda (relative to the generic bound)
for F restricted to a compact set. As an auxiliary result of independent
interest we prove new uniform bounds for spherical functions on semisimple Lie
groups.


  We show that in quadratic gravity sufficiently light objects must be
horizonless and construct explicit analytic examples of horizonless
ultracompact objects (UCOs), which are more compact than Schwarzschild black
holes. Due to the quadratic terms, gravity becomes soft and eventually vanishes
in the high-energy limit leading to a "linearization mechanism": light objects
can be described by the linearized theory when their Schwarzschild radius is
smaller than the Compton wavelength of the new gravitational degrees of
freedom. As a result, we can analytically describe UCOs with a mass-to-radius
ratio higher than for a Schwarzschild black hole. The corresponding spacetime
is regular everywhere. We show that the Ostrogradsky instabilities can be
avoided and discuss the relation with the Higgs vacuum metastability. Due to
the lack of a horizon, light UCOs do not evaporate. Therefore, they may play
the role of dark matter. We briefly discuss their phenomenology.


  We report low-temperature thermal-expansion measurements on single crystals
of the {\it layered} heavy fermion system \cri ($0.3\leq x \leq 0.6$) and
compare it with a previous study on the related {\it cubic} system \ci [R.
K\"{u}chler {\it et al.}, Phys. Rev. Lett. {\bf 96}, 256403 (2006)]. Both
systems display a quantum critical point as proven by a divergent Gr\"uneisen
ratio. Most remarkably, the three-dimensional itinerant model explains quantum
criticality in {\it both} systems, suggesting that the crystalline anisotropy
in \cri is unimportant. This is ascribed to the effect of weak disorder in
these doped systems.


  It has recently been argued that soft-collinear effective theory for
processes involving both soft and collinear partons contains a new
soft-collinear mode, which can communicate between the soft and collinear
sectors of the theory. The formalism incorporating the corresponding fields
into the effective Lagrangian is extended to include external current and
four-quark operators relevant to weak interactions. An explicit calculation of
the anomalous dimensions of these operators reveals that soft-collinear modes
are needed for correctly describing the ultraviolet behavior of the effective
theory.


  The shell-type supernova remnant (SNR) RCW 86, possibly associated with the
historical supernova SN 185, with its relatively large size (about 40' in
diameter) and the presence of non-thermal X-rays is a promising target for
gamma-ray observations. The high sensitivity, good angular resolution of a few
arc minutes and the large field of view of the High Energy Stereoscopic System
(H.E.S.S.) make it ideally suited for the study of the gamma-ray morphology of
such extended sources. H.E.S.S. observations have indeed led to the discovery
of the SNR RCW 86 in very high energy (VHE; E > 100 GeV) gamma-rays. With 31
hours of observation time, the source is detected with a statistical
significance of 8.5 sigma and is significantly more extended than the H.E.S.S.
point spread function. Morphological studies have been performed and show that
the gamma-ray flux does not correlate perfectly with the X-ray emission. The
flux from the remnant is ~10% of the flux from the Crab nebula, with a similar
photon index of about 2.5. Possible origins of the very high energy gamma-ray
emission, via either Inverse Compton scattering by electrons or the decay of
neutral pions produced by proton interactions, are discussed on the basis of
spectral features obtained both in the X-ray and gamma-ray regimes.


  The fixed-point theory and its applications to various areas of science are
well known. In this paper we present some existence and uniqueness theorems for
fixed circles of self-mappings on metric spaces with geometric interpretation.
We verify our results by illustrative examples.


  We derive an analytic connection between the screened self-consistent
effective potential from density functional theory (DFT) and atomic effective
pseudopotentials (AEPs). The motivation to derive AEPs is to address structures
with thousands to hundred thousand atoms, as given in most nanostructures. The
use of AEPs allows to bypass a self-consistent procedure and to address
eigenstates around a certain region of the spectrum (e.g., around the band
gap). The bulk AEP construction requires two simple DFT calculations of
slightly deformed elongated cells. The ensuing AEPs are given on a fine
reciprocal space grid, including the small reciprocal vector components, are
free of parameters, and involve no fitting procedure. We further show how to
connect the AEPs of different bulk materials, which is necessary to obtain
accurate band offsets. We derive a total of 20 AEPs for III-V, II-VI and group
IV semiconductors and demonstrate their accuracy and transferability by
comparison to DFT calculations of strained bulk structures, quantum wells with
varying thickness, and semiconductor alloys.


  Cichorek et al. [Phys. Rev. Lett. 94, 107002 (2005)] reported enhancements of
the lower critical field Hc1(T) and critical current in superconducting
PrOs4Sb12 below a transition temperature Tc3 ~ 0.6 K, and speculated that this
reflects a transition between superconducting phases. Features have been
observed near Tc3 in other properties, but not in the specific heat. We report
muon spin rotation measurements of the penetration depth in the vortex state of
PrOs4Sb12 near Hc1(T), that to high accuracy exhibit no anomaly Tc3 and
therefore cast doubt on the putative phase transition.


  If two random variables X and A are functionally related via f(X)=A for some
strictly monotone continuously differentiable function f:R->R, the distribution
of X may easily be computed from the distribution of A.


  In a previous paper (q-alg/9501022) we suggested some algorithms that could
be useful in solving the problem of knot classification. Here we continue this
discussion by answering questions raised in that paper and by commenting on
practical aspects related to running these algorithms as computer programs.
Further on, we reach a solution by improving on the efficiency of these
algorithms, and by introducing new ones.


  In sparse estimation, such as fused lasso and convex clustering, we apply
either the proximal gradient method or the alternating direction method of
multipliers (ADMM) to solve the problem. It takes time to include matrix
division in the former case, while an efficient method such as FISTA (fast
iterative shrinkage-thresholding algorithm) has been developed in the latter
case. This paper proposes a general method for converting the ADMM solution to
the proximal gradient method, assuming that assumption that the derivative of
the objective function is Lipschitz continuous. Then, we apply it to sparse
estimation problems, such as sparse convex clustering and trend filtering, and
we show by numerical experiments that we can obtain a significant improvement
in terms of efficiency.


  (adapted)Considering recent observations challenging the traditional magnetar
model, we explore the wind braking of magnetars. There is evidence for strong
multipole magnetic fields in active magnetars, but the dipole field inferred
from spin down measurements may be strongly biased by a particle wind. Recent
challenging observations of magnetars may be explained naturally in the wind
braking scenario: (1) The supernova energies of magnetars are of normal value;
(2) The non-detection in Fermi observations of magnetars; (3) The problem posed
by the low-magnetic field soft gamma-ray repeaters; (4) The relation between
magnetars and high magnetic field pulsars; (5) A decreasing period derivative
during magnetar outbursts. Transient magnetars may still be magnetic dipole
braking. This may explain why low luminosity magnetars are more likely to have
radio emissions. In the wind braking scenario, magnetars are neutron stars with
strong multipole field. For some sources, a strong dipole field may be no
longer needed. A magnetism-powered pulsar wind nebula and a braking index
smaller than three are the two predictions of the wind braking model.


  A massively parallel method to build large transition rate matrices from
temperature accelerated molecular dynamics trajectories is presented. Bayesian
Markov model analysis is used to estimate the expected residence time in the
known state space, providing crucial uncertainty quantification for higher
scale simulation schemes such as kinetic Monte Carlo or cluster dynamics. The
estimators are additionally used to optimize where exploration is performed and
the degree of temperature ac- celeration on the fly, giving an autonomous,
optimal procedure to explore the state space of complex systems. The method is
tested against exactly solvable models and used to explore the dynamics of C15
interstitial defects in iron. Our uncertainty quantification scheme allows for
accurate modeling of the evolution of these defects over timescales of several
seconds.


  The study of optical phenomena on the subwavelength scale is becoming
increasingly important in photonics, particularly in the fields of
nanoemitters, photonic crystals and plasmonics. Subwavelength field patterns
are evanescent and must thus be investigated with near-field techniques. The
light powers emitted by nanoscale sources are extremely low, undermining the
traditional approach of scattering a near field to a large (thus noisy)
far-field detector. Nanoscale detectors, providing direct sensing in the
near-field with small noise due to a small active area, are needed in
high-sensitivity, high-resolution near-field imaging and in quantum
nanophotonic circuits. Here we report the first nanoscale ~50x50nm2) detector
displaying single-photon sensitivity and a nanosecond response. These
nanodetectors can also be operated in multi-photon mode, where the detection
threshold can be set at N=1, 2, 3 or 4 photons, thus allowing the mapping of
photon number statistics on the nanoscale.


  Conventional caustic methods in real or Fourier space produced accelerating
optical beams only with convex trajectories. We develop a superposition caustic
method capable of winding light beams along non-convex trajectories. We
ascertain this method by constructing a one-dimensional (1D) accelerating beam
moving along a sinusoidal trajectory, and subsequently extending to
two-dimensional (2D) accelerating beams along arbitrarily elliptical helical
trajectories. We experimentally implement the method with a compact and robust
integrated optics approach by fabricating micro-optical structures on quartz
glass plates to perform the spatial phase and amplitude modulation to the
incident light, generating beam trajectories highly consistent with prediction.
The theoretical and implementation methods can in principle be extended to the
construction of accelerating beams with a wide variety of non-convex
trajectories, thereby opening up a new route of manipulating light beams for
fundamental research and practical applications.


  For a $\beta$ ensemble on $\Sigma^{(N)}=\{(x_1,\ldots,x_N)\mathbb
R^N|x_1\le\cdots\le x_N\}$ with real analytic potential and general $\beta>0$,
under the assumption that its equilibrium measure is supported on $q$ intervals
where $q>1$, we prove the following rigidity property for its particles. First,
in the bulk of the spectrum, with overwhelming probability, the distance
between a particle and its classical position is of order $O(N^{-1+\epsilon})$.
Second, if $k$ is close to 1 or close to $N$, i.e., near the extreme edges of
the spectrum, then with overwhelming probability, the distance between the
$k$-th largest particle and its classical position is of order
$O(N^{-\frac{2}{3}+\epsilon}\min(k,N+1-k)^{-\frac{1}{3}})$. Here $\epsilon>0$
is an arbitrarily small constant. Our main idea is to decompose the multi-cut
$\beta$ ensemble as a product of probability measures on spaces with lower
dimensions and show that each of these measures is very close to a $\beta$
ensemble in one-cut regime for which the rigidity of particles is known.


  The PandaX-II experiment employed a 580kg liquid xenon detector to search for
the interactions between dark matter particles and the target xenon atoms. The
accidental coincidences of isolated signals result in a dangerous background
which mimic the signature of the dark matter. We performed a detailed study on
the accidental coincidence background in PandaX-II, including the possible
origin of the isolated signals, the background level and corresponding
background suppression method. With a boosted-decision-tree algorithm, the
accidental coincidence background is reduced by 70% in the dark matter signal
region, thus the sensitivity of dark matter search at PandaX-II is improved.


  In many scientific research fields, understanding and visualizing a black-box
function in terms of the effects of all the input variables is of great
importance. Existing visualization tools do not allow one to visualize the
effects of all the input variables simultaneously. Although one can select one
or two of the input variables to visualize via a 2D or 3D plot while holding
other variables fixed, this presents an oversimplified and incomplete picture
of the model. To overcome this shortcoming, we present a new visualization
approach using an interpretable architecture neural network (IANN) to visualize
the effects of all the input variables directly and simultaneously. We propose
two interpretable structures, each of which can be conveniently represented by
a specific IANN, and we discuss a number of possible extensions. We also
provide a Python package to implement our proposed method. The supplemental
materials are available online.


  Broken rotational and translational symmetries are the hallmarks of solid
state materials. In contrast, quantum liquids and gases do not exhibit such
properties. However, if we regard the logarithm of the absolute square of a
quantum liquid as an energy ${\cal E}= -{\rm ln}|\Psi|^2$, a geometric pattern
naturally occurs at the minimum, i.e. the optimal configuration. Such geometric
patterns have recently been studied for non-interacting fermions, and have been
named "Pauli crystals". However, such patterns exist in all interacting gases
(Bose or Fermi), independent of statistics. Here, we present an algorithm to
determine the optimal configurations of quantum clusters solely from the images
of their densities and without theoretical inputs. We establish its validity by
recovering a number of exact results, showing that it can identify the changes
in the cluster's ground state which corresponds to phase transitions in bulk
systems.


  In this paper, we revisit the communication vs. distributed computing
trade-off, studied within the framework of MapReduce in [1]. An implicit
assumption in the aforementioned work is that each server performs all possible
computations on all the files stored in its memory. Our starting observation is
that, if servers can compute only the intermediate values they need, then
storage constraints do not directly imply computation constraints. We examine
how this affects the communication-computation trade-off and suggest that the
trade-off be studied with a predetermined storage constraint. We then proceed
to examine the case where servers need to perform computationally intensive
tasks, and may not have sufficient time to perform all computations required by
the scheme in [1]. Given a threshold that limits the computational load, we
derive a lower bound on the associated communication load, and propose a
heuristic scheme that achieves in some cases the lower bound.


  We consider the 2D incompressible Navier-Stokes equations with Dirichlet
boundary condition in the exterior of one obstacle. Assuming that the
circulation at infinity of the velocity is sufficiently small, we prove that
the large time behavior of the corresponding solution to the initial-boundary
value problem is described by the Lamb-Oseen vortex. The later is the
well-known explicit self-similar solution to the Navier-Stokes system in the
whole space $\R^2$.


  In this article we prove that if $ X $ is a normed space and $ U $ is a
polygonally-connected subset of $ X $ with $M:=\{S_i:\ i\in I\}\subset
\mathcal{P}\left( U\right) $, a non-empty arbitrary family of discrete,
non-empty subsets of $ U, $ then the property of polygonal-connectedness is
also preserved in the resulting set $ U\setminus\left( \bigcup_{i\in I}
S_i\right),$ under appropriate conditions.


  The main part of this paper is a big table containing what we believe to be a
complete list of all fourth order equations of Calabi--Yau type known so far.
In the text preceding the tables we explain what a differential equation of
Calabi--Yau type is and we briefly discuss how we found these equations. We
also describe an electronic version of this list.


  We estimate on a compact interval densities with isolated irregularities,
such as discontinuities or discontinuities in some derivatives. From
independent and identically distributed observations we construct a kernel
estimator with non-constant bandwidth, in particular in the vicinity of
irregularities. It attains faster rates, for the risk $L_{p}, p\geq 1$, than
usual estimators with a fixed global bandwidth. Optimality of the rate found is
established by a lower bound result. We then propose an adaptive method
inspired by Lepski's method for automatically selecting the variable bandwidth,
without any knowledge of the regularity of the density nor of the points where
the regularity breaks down. The procedure is illustrated numerically on
examples.


  We propose an alternative mechanism of baryogenesis in which a scalar baryon
undergoes a percolating first-order phase transition in the early Universe. The
potential barrier that divides the phases contains explicit B and CP violation
and the corresponding instanton that mediates decay is therefore asymmetric.
The nucleation and growth of these asymmetric bubbles dynamically generates
baryons, which thermalize after percolation; bubble collision dynamics can also
add to the asymmetry yield. We present an explicit toy model that undergoes
bubble baryogenesis, and numerically study the evolution of the baryon
asymmetry through bubble nucleation and growth, bubble collisions, and washout.
We discuss more realistic constructions, in which the scalar baryon and its
potential arise amongst the color-breaking minima of the MSSM, or in the
supersymmetric neutrino seesaw mechanism. Phenomenological consequences, such
as gravitational waves, and possible applications to asymmetric dark-matter
generation are also discussed.


  The good Boussinesq equation has several modified versions such as the
modified Boussinesq equation, Mikhailov-Lenells equation and Hirota-Satsuma
equation. This work builds the full relations among these equations by Miura
transformation and invertible linear transformations and draws a pyramid
diagram to demonstrate such relations. The direct and inverse spectral analysis
shows that the solution of Riemann-Hilbert problem for Hirota-Satsuma equation
has simple pole at origin, the solution of Riemann-Hilbert problem for the good
Boussinesq equation has double pole at origin, while the solution of
Riemann-Hilbert problem for the modified Boussinesq equation and
Mikhailov-Lenells equation doesn't have singularity at origin. Further, the
large-time asymptotic behaviors of the Hirota-Satsuma equation with Schwartz
class initial value is studied by Deift-Zhou nonlinear steepest descent
analysis. In such initial condition, the asymptotic expressions of the
Hirota-Satsuma equation and good Boussinesq equation away from the origin are
proposed and it is displayed that the leading term of asymptotic formulas match
well with direct numerical simulations.


  The field of Explainable Artificial Intelligence (XAI) aims to improve the
interpretability of black-box machine learning models. Building a heatmap based
on the importance value of input features is a popular method for explaining
the underlying functions of such models in producing their predictions.
Heatmaps are almost understandable to humans, yet they are not without flaws.
Non-expert users, for example, may not fully understand the logic of heatmaps
(the logic in which relevant pixels to the model's prediction are highlighted
with different intensities or colors). Additionally, objects and regions of the
input image that are relevant to the model prediction are frequently not
entirely differentiated by heatmaps. In this paper, we propose a framework
called TbExplain that employs XAI techniques and a pre-trained object detector
to present text-based explanations of scene classification models. Moreover,
TbExplain incorporates a novel method to correct predictions and textually
explain them based on the statistics of objects in the input image when the
initial prediction is unreliable. To assess the trustworthiness and validity of
the text-based explanations, we conducted a qualitative experiment, and the
findings indicated that these explanations are sufficiently reliable.
Furthermore, our quantitative and qualitative experiments on TbExplain with
scene classification datasets reveal an improvement in classification accuracy
over ResNet variants.


  A short review on theoretical implications of non-thermal emission (radio,
extreme ultraviolet, high energy X-ray) from the intra-cluster medium is given.
The origin of cluster radio halos and cluster radio relics is discussed within
the framework of a network of processes producing a non-thermal electron
population. Emphasis is given to the role of old, remnant, presently invisible
relativistic plasma released by former radio galaxies.


  We present the measurement of the absolute branching fractions of $B^{+} \to
X_{c\bar{c}} K^{+}$ and $B^{+} \to \bar{D}^{(\ast) 0} \pi^{+} $ decays, using a
data sample of $772\times10^{6}$ $B\bar{B}$ pairs collected at the
$\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy
$e^{+}e^{-}$ collider. Here, $X_{c\bar{c}}$ denotes $\eta_{c}$, $J/\psi$,
$\chi_{c0}$, $\chi_{c1}$, $\eta_{c}(2S)$, $\psi(2S)$, $\psi(3770)$, $X(3872)$,
and $X(3915)$. We do not observe significant signals for $X(3872)$ nor
$X(3915)$, and set the 90$\%$ confidence level upper limits: ${\cal B}(B^{+}
\to X(3872) K^{+} )<2.7 \times 10^{-4}$ and ${\cal B}(B^{+} \to X(3915) K^{+}
)<2.9 \times 10^{-4}$. These represent the most stringent upper limit for
${\cal B}(B^{+} \to X(3872) K^{+} )$ to date and the first measurement for
${\cal B}(B^{+} \to X(3915) K^{+} )$. The measured branching fractions for
$\eta_{c}$ and $\eta_{c}(2S)$ are the most precise to date: ${\cal B}(B^{+} \to
\eta_{c} K^{+} )=(12.3\pm0.8\pm0.7) \times 10^{-4}$ and ${\cal B}(B^{+} \to
\eta_{c}(2S)K^{+}) =(4.9\pm1.1\pm0.3) \times 10^{-4}$ , where the first and
second uncertainties are statistical and systematic, respectively.


  Monocular multi-object detection and localization in 3D space has been proven
to be a challenging task. The MoNet3D algorithm is a novel and effective
framework that can predict the 3D position of each object in a monocular image
and draw a 3D bounding box for each object. The MoNet3D method incorporates
prior knowledge of the spatial geometric correlation of neighbouring objects
into the deep neural network training process to improve the accuracy of 3D
object localization. Experiments on the KITTI dataset show that the accuracy
for predicting the depth and horizontal coordinates of objects in 3D space can
reach 96.25\% and 94.74\%, respectively. Moreover, the method can realize the
real-time image processing at 27.85 FPS, showing promising potential for
embedded advanced driving-assistance system applications. Our code is publicly
available at https://github.com/CQUlearningsystemgroup/YicongPeng.


  we introduce deductive association networks(DANs), a network that performs
deductive reasoning. To have high-dimensional thinking, combining various
axioms and putting the results back into another axiom is necessary to produce
new relationships and results. For example, it would be given two propositions:
"Socrates is a man." and "All men are mortals." and two propositions could be
used to infer the new proposition, "Therefore Socrates is mortal.". To
evaluate, we used MNIST Dataset, a handwritten numerical image dataset, to
apply it to the group theory and show the results of performing deductive
learning.


  Superconductive quantum circuits (SQCs) comprise quantized energy levels that
may be coupled via microwave electromagnetic fields. Described in this way, one
may draw a close analogy to atoms with internal (electronic) levels coupled by
laser light fields. In this Letter, we present a superconductive analog to
electromagnetically induced transparency (S-EIT) that utilizes SQC designs of
present day experimental consideration. We discuss how S-EIT can be used to
establish macroscopic coherence in such systems and, thereby, utilized as a
sensitive probe of decoherence.


  A search for pair-produced third generation scalar leptoquarks is presented,
using proton-proton collisions at sqrt(s)= 7 TeV at the LHC. The data were
recorded with the ATLAS detector and correspond to an integrated luminosity of
4.7 fb-1. Each leptoquark is assumed to decay to a tau lepton and a b-quark
with a branching fraction equal to 100%. No statistically significant excess
above the Standard Model expectation is observed. Third generation leptoquarks
are therefore excluded at 95% confidence level for masses less than 534 GeV.


  As well known, if the Higgs boson were not observed at LHC, the technicolor
model would be the most favorable candidate responsible for the symmetry
breaking. To overcome some defects in the previous model, some extended
versions have been proposed. In the TC2 model typical signature is existence of
heavy $H_{TC}$ and technipion $\Pi$. A direct proof of validity of the model is
to produce them at accelerator. Thus we study the production rates of $ e^ + e^
- \to H_{TC} \Pi ^0 $ and $e^ + e^ - \to \Pi ^ + \Pi ^ -$ at ILC in the
topcolor-assisted technicolor (TC2) model. In fact, there is a flood of models
belonging to new physics which can result in products with characteristics
similar to $H_{TC}+\Pi$ of the TC2 model. Therefore to distinguish this model
from others one may need to investigate some details by calculating the cross
section to NLO. We indeed find that the NLO corrections are significant, namely
the ratio $\delta \equiv (\sigma_{NLO} - \sigma_{LO})/\sigma_{LO} $ in $ e^ +
e^ - \to H_{TC} \Pi ^0 $ exceeds 100% within a plausible parameter space.


  Monolithic Active Pixel Sensors (MAPS) combine the sensing part and the
front-end electronics in the same silicon layer, making use of CMOS technology.
Profiting from the progresses of this commercial process, MAPS have been
undergoing significant advances over the last decade in terms of integration
densities, radiation hardness and readout speed. The first application of MAPS
in high energy physics has been the PXL detector, installed in 2014 as the
vertexer of the STAR experiment at BNL. In the same years, ALICE Collaboration
started the development of a new MAPS with improved performances, to assemble a
new detector to replace the Inner Tracking System used during LHC Run 1 and 2.
This effort lead to the ALPIDE sensor, today successfully equipped in a large
variety of systems. Starting from 2019, profiting from the experience acquired
during the design of the ALPIDE sensor, the ALICE Collaboration embarked on a
new development phase, the ITS3 project. Here the goal is to design the first
truly cylindrical detector based on wafer-size sensors in 65 nm CMOS node. This
new detector is expected to take data during LHC Run 4. ALICE Collaboration
submitted a proposal for a new experiment, to be installed in place of the
present detector system before the LHC Run 5. Building on the experience on
MAPS acquired in the recent years, the idea is to design a compact all silicon
detector, that will give unprecedented insight into the quark-gluon plasma
characterization.


  We derive a standard quantum limit for probing mechanical energy quantization
in a class of systems with mechanical modes parametrically coupled to external
degrees of freedom. To resolve a single mechanical quantum, it requires a
strong-coupling regime -- the decay rate of external degrees of freedom is
smaller than the parametric coupling rate. In the case for cavity-assisted
optomechanical systems, e.g. the one proposed by Thompson et al., zero-point
motion of the mechanical oscillator needs to be comparable to linear dynamical
range of the optical system which is characterized by the optical wavelength
divided by the cavity finesse.


  Sensing is a universal task in science and engineering. Downstream tasks from
sensing include inferring full state estimates of a system (system
identification), control decisions, and forecasting. These tasks are
exceptionally challenging to achieve with limited sensors, noisy measurements,
and corrupt or missing data. We propose a SHallow REcurrent Decoder (SHRED)
neural network structure for sensing which incorporates (i) a recurrent neural
network (LSTM) to learn a latent representation of the temporal dynamics of the
sensors, and (ii) a shallow decoder that learns a mapping between this latent
representation and the high-dimensional state space. By explicitly accounting
for the time-history, or trajectory, of the sensor measurements, SHRED enables
accurate reconstructions with far fewer sensors, outperforms existing
techniques when more measurements are available, and is agnostic towards sensor
placement. In addition, a compressed representation of the high-dimensional
state is directly obtained from sensor measurements, which provides an
on-the-fly compression for modeling physical and engineering systems.
Forecasting is also achieved from the sensor time-series data alone, producing
an efficient paradigm for predicting temporal evolution with an exceptionally
limited number of sensors. In the example cases explored, including turbulent
flows, complex spatio-temporal dynamics can be characterized with exceedingly
limited sensors that can be randomly placed with minimal loss of performance.


  In this paper, a generalized variable-coefficient KdV equation (vcKdV)
arising in fluid mechanics, plasma physics and ocean dynamics is investigated
by using symmetry group analysis. Two basic generators are determined, and for
every generator in the optimal system the admissible forms of the coefficients
and the corresponding reduced ordinary differential equation are obtained. The
search for solutions to those reduced ordinary differential equations yields
many new solutions for the generalized vcKdV equation.


  Approximating the partition function of the ferromagnetic Ising model with
general external fields is known to be #BIS-hard in the worst case, even for
bounded-degree graphs, and it is widely believed that no polynomial-time
approximation scheme exists. This motivates an average-case question: are there
classes of instances for which polynomial-time approximation schemes exist? We
investigate this question for the random field Ising model on graphs with
maximum degree $\Delta$. We establish the existence of fully polynomial-time
approximation schemes and samplers with high probability over the random fields
if the external fields are IID Gaussians with variance larger than a constant
depending only on the inverse temperature and $\Delta$. The main challenge
comes from the positive density of vertices at which the external field is
small. These regions, which may have connected components of size $\Theta(\log
n)$, are a barrier to algorithms based on establishing a zero-free region, and
cause worst-case analyses of Glauber dynamics to fail. The analysis of our
algorithm is based on percolation on a self-avoiding walk tree.


  The dynamics of units (molecules) with slowly relaxing internal states is
studied as an iterated function system (IFS) for the situation common in e.g.
biological systems where these units are subjected to frequent collisional
interactions. It is found that an increase in the collision frequency leads to
successive discrete states that can be analyzed as partial steps to form a
Cantor set. By considering the interactions among the units, a self-consistent
IFS is derived, which leads to the formation and stabilization of multiple such
discrete states. The relevance of the results to dynamical multiple states in
biomolecules in crowded conditions is discussed.


  Software testing is one of the important ways to ensure the quality of
software. It is found that testing cost more than 50% of overall project cost.
Effective and efficient software testing utilizes the minimum resources of
software. Therefore, it is important to construct the procedure which is not
only able to perform the efficient testing but also minimizes the utilization
of project resources. The goal of software testing is to find maximum defects
in the software system. More the defects found in the software ensure more
efficiency is the software testing Different techniques have been proposed to
detect the defects in software and to utilize the resources and achieve good
results. As world is continuously moving toward data driven approach for making
important decision. Therefore, in this research paper we performed the machine
learning analysis on the publicly available datasets and tried to achieve the
maximum accuracy. The major focus of the paper is to apply different machine
learning techniques on the datasets and find out which technique produce
efficient result. Particularly, we proposed an ensemble learning models and
perform comparative analysis among KNN, Decision tree, SVM and Na\"ive Bayes on
different datasets and it is demonstrated that performance of Ensemble method
is more than other methods in term of accuracy, precision, recall and F1-score.
The classification accuracy of ensemble model trained on CM1 is 98.56%,
classification accuracy of ensemble model trained on KM2 is 98.18% similarly,
the classification accuracy of ensemble learning model trained on PC1 is
99.27%. This reveals that Ensemble is more efficient method for making the
defect prediction as compared other techniques.


  Energy spectra of antineutrinos coming from $^{232}$Th and $^{233}$U
neutron-induced fission are calculated, relevant inverse beta decay
$\bar{{\nu}_e}+p \to n + e^{+}$ positron spectra and total cross sections are
found. This study is stimulated by a hypothesis that a self-sustained nuclear
chain reaction is burning at the center of the Earth ("Georeactor"). The
Georeactor, according to the author of this idea, provides energy necessary to
sustain the Earth's magnetic field. The Georeactor's nuclear fuel is $^{235}$U
and, probably, $^{232}$Th and $^{233}$U. Results of present study may appear to
be useful in future experiments aimed to test the Georector hypothesis and to
estimate its fuel components as a part of developments in geophysics and
astrophysics based on observations of low energy antineutrinos in Nature.


  This paper extends the algorithm schemes proposed in \cite{Nesterov2007a} and
\cite{Nesterov2007b} to the minimization of the sum of a composite objective
function and a convex function. Two proximal point-type schemes are provided
and their global convergence is investigated. The worst case complexity bound
is also estimated under certain Lipschitz conditions and nondegeneratedness.
The algorithm is then accelerated to get a faster convergence rate for the
strongly convex case.


  This paper aims to characterize boundedness of composition operators on Besov
spaces $B^s_{p,q}$ of higher order derivatives $s>1+1/p$ on the one-dimensional
Euclidean space. In contrast to the lower order case $0<s<1$, there were a few
results on the boundedness of composition operators for $s>1$. We prove a
relation between the composition operators and pointwise multipliers of Besov
spaces, and effectively use the characterizations of the pointwise multipliers.
As a result, we obtain necessary and sufficient conditions for the boundedness
of composition operators for general $p$, $q$, and $s$ such that $1<p\le
\infty$, $0<q\le \infty$, and $s>1+1/p$. In this paper, we treat, as a map that
induces the composition operator, not only a homeomorphism on the real line but
also a continuous map whose number of elements of inverse images at any one
point is bounded above. We also show a similar characterization of the
boundedness of composition operators on Sobolev spaces.


  Topological ordered states are exotic quantum states of matter that defy the
usual description in terms of symmetry breaking and local order parameters. The
type or order they feature is of non-local, topological nature, and it allows
such systems to present unusual and interesting behaviours, like robust
degeneracy, and anyonic excitations. Here we focus on the behaviour of such
systems away from equilibrium. After a sudden change of the Hamiltonian - the
so called quantum quench - quantum many body systems show thermalization,
unless the quench is integrable. We show how in topologically ordered systems
out of equilibrium behaviour do not follow the usual thermalization behaviour.


  In this paper, we consider a distributed remote source coding problem, where
a sequence of observations of source vectors is available at the encoder. The
problem is to specify the optimal rate for encoding the observations subject to
a covariance matrix distortion constraint and in the presence of side
information at the decoder. For this problem, we derive lower and upper bounds
on the rate-distortion function (RDF) for the Gaussian case, which in general
do not coincide. We then provide some cases, where the RDF can be derived
exactly. We also show that previous results on specific instances of this
problem can be generalized using our results. We finally show that if the
distortion measure is the mean squared error, or if it is replaced by a certain
mutual information constraint, the optimal rate can be derived from our main
result.


  We study the blowup behavior for the focusing energy-supercritical semilinear
wave equation in 3 space dimensions without symmetry assumptions on the data.
We prove the stability of the ODE blowup profile.


  The sharply quantized transport observed in the integer quantum Hall effect
can be explained via a simple one-dimensional model with a time-periodic,
adiabatically varying potential in which electronic charge is pumped from one
side of the system to the other. This so-called `Thouless pump' captures the
topological physics of the quantum Hall effect using the notion of dimensional
reduction: The time-varying potential mathematically maps onto a momentum
coordinate in a conceptual second dimension. Importantly, this assumes an
electronic system in equilibrium and in its ground state, that is, with
uniformly filled bands below a Fermi energy. Here, we theoretically propose and
experimentally demonstrate quantized nonlinear Thouless pumping of photons with
a band that is decidedly not uniformly occupied. In our system, nonlinearity
acts to quantize transport via soliton formation and spontaneous symmetry
breaking bifurcations. Quantization follows from the fact that the
instantaneous soliton solutions centered upon a given unit cell are identical
after each pump cycle, up to translation invariance; this is an entirely
different mechanism from traditional Thouless pumping of fermions in
equilibrium. Our result shows that nonlinearity and interparticle interactions
can induce quantized transport and topological behavior even where the linear
limit does not.


  We derive the first and second variation formula for the Green's function
pole's value of Paneitz operator on the standard three sphere. In particular it
is shown that the first variation vanishes and the second variation is
nonpositively definite. Moreover, the second variation vanishes only at the
direction of conformal deformation. We also introduce a new invariant of the
Paneitz operator and illustrate its close relation with the second eigenvalue
and Sobolev inequality of Paneitz operator.


  We study the algebraic structure and representation theory of the Hopf
algebras ${}_J\mathcal{O}(G)_J$ when $G$ is an affine algebraic unipotent group
over $\mathbb{C}$ with $\mathrm{dim}(G) = n$ and $J$ is a Hopf $2$-cocycle for
$G$. The cotriangular Hopf algebras ${}_J\mathcal{O}(G)_J$ have the same
coalgebra structure as $\mathcal{O}(G)$ but a deformed multiplication. We show
that they are involutive $n$-step iterated Hopf Ore extensions of derivation
type. The 2-cocycle $J$ has as support a closed subgroup $T$ of $G$, and
${}_J\mathcal{O}(G)_J$ is a crossed product $S \#_{\sigma}U(\mathfrak{t})$,
where $\mathfrak{t}$ is the Lie algebra of $T$ and $S$ is a deformed coideal
subalgebra. The simple ${}_J\mathcal{O}(G)_J$-modules are stratified by a
family of factor algebras ${}_J\mathcal{O}(Z_g)_J$, parametrised by the double
cosets $TgT$ of $T$ in $G$. The finite dimensional simple
${}_J\mathcal{O}(G)_J$-modules are all 1-dimensional, so form a group $\Gamma$,
which we prove to be an explicitly determined closed subgroup of $G$. A
selection of examples illustrate our results.


  Using standard cosmological model we show that the cores of ultra-compact
radio sources observed with ground-based Very Long Baseline Interferometry
(VLBI) on the angular scales of milliarcseconds cannot be used as a reasonable
standard unit of linear size. "Luminosity - linear size" correlation obtained
by many authors for ultra compact radio sources has different origin than that
for the radio galaxies and quasars on the angular scales of arcminutes. It is
just the manifestation of the fact that ground-based VLBI networks are unable
to resolve VLBI-cores and the Malmquist bias presents. Thus, the cores of
compact radio sources can't be used as "standard rods" at least with resolution
offered by ground-based VLBI. This conclusion is illustrated on 15 GHz VLBA
sample of radio sources.


  We have investigated STM images of the (110) cross-sectional surface of
Mn-doped GaAs using first principles total-energy pseudopotential calculations.
We focus on configurations with Mn interstitial in the uppermost surface
layers. In particular, we have found that Mn impurities, surrounded by Ga or As
atoms, introduce in both cases strong local distortions in the GaAs(110)
surface, with bond length variations up to 8 % on surface and non-negligible
relaxations effects propagating up to the third sub-surface layer. In both
cases interstitial Mn induces a spin-polarization on its nearest neighbors,
giving rise to a ferromagnetic Mn-As and to antiferromagnetic Mn-Ga
configuration.


  Understanding human activities and movements on the Web is not only important
for computational social scientists but can also offer valuable guidance for
the design of online systems for recommendations, caching, advertising, and
personalization. In this work, we demonstrate that people tend to follow
routines on the Web, and these repetitive patterns of web visits increase their
browsing behavior's achievable predictability. We present an
information-theoretic framework for measuring the uncertainty and theoretical
limits of predictability of human mobility on the Web. We systematically assess
the impact of different design decisions on the measurement. We apply the
framework to a web tracking dataset of German internet users. Our empirical
results highlight that individual's routines on the Web make their browsing
behavior predictable to 85% on average, though the value varies across
individuals. We observe that these differences in the users' predictabilities
can be explained to some extent by their demographic and behavioral attributes.


  We show that starting with either the non-extensive Tsallis entropy in Wang's
formalism or the extensive Renyi entropy, it is possible to construct the
equilibrium statistical mechanics with non-Gibbs canonical distribution
functions. The transformation formulas between Tsallis statistics and Renyi
statistics are presented. The one-particle distribution function in Renyi
statistics with extensive entropy for the classical ideal gas at finite
particle number develops a power-law tail for high momenta.


  The task of following-the-leader is implemented using a hierarchical Deep
Neural Network (DNN) end-to-end driving model to match the direction and speed
of a target pedestrian. The model uses a classifier DNN to determine if the
pedestrian is within the field of view of the camera sensor. If the pedestrian
is present, the image stream from the camera is fed to a regression DNN which
simultaneously adjusts the autonomous vehicle's steering and throttle to keep
cadence with the pedestrian. If the pedestrian is not visible, the vehicle uses
a straightforward exploratory search strategy to reacquire the tracking
objective. The classifier and regression DNNs incorporate grouped convolutions
to boost model performance as well as to significantly reduce parameter count
and compute latency. The models are trained on the Intelligence Processing Unit
(IPU) to leverage its fine-grain compute capabilities in order to minimize
time-to-train. The results indicate very robust tracking behavior on the part
of the autonomous vehicle in terms of its steering and throttle profiles, while
requiring minimal data collection to produce. The throughput in terms of
processing training samples has been boosted by the use of the IPU in
conjunction with grouped convolutions by a factor ~3.5 for training of the
classifier and a factor of ~7 for the regression network. A recording of the
vehicle tracking a pedestrian has been produced and is available on the web.
This is a preprint of an article published in SN Computer Science. The final
authenticated version is available online at:
https://doi.org/https://doi.org/10.1007/s42979-021-00572-1.


  The dielectric anomalies of window-type glasses at low temperatures ($T<$ 1
K) are rather successfully explained by the two-level systems (2LS) tunneling
model (TM). However, the magnetic effects discovered in the multisilicate
glasses in recent times \cite{ref1}-\cite{ref3}, and also some older data from
mixed (SiO$_2$)$_{1-x}$(K$_2$O)$_x$ and (SiO$_2$)$_{1-x}$(Na$_2$O)$_x$ glasses
\cite{ref4}, indicate the need for a suitable generalization of the 2LS TM. We
show that, not only for the magnetic effects \cite{ref3,ref5} but also for the
mixed glasses in the absence of a field, the right extension of the 2LS TM is
provided by the (anomalous) multilevel tunneling systems approach proposed by
one of us. It appears that new 2LS develop via dilution near the hull of the
SiO$_4$-percolating clusters in the mixed glasses.


  Given a set $X$, a collection $\mathcal{F} \subset \mathcal{P}(X)$ is said to
be $k$-Sperner if it does not contain a chain of length $k+1$ under set
inclusion and it is saturated if it is maximal with respect to this
probability. Gerbner et al. proved that the smallest saturated $k$-Sperner
system contains at least $2^{k/2-1}$ elements, and later, Morrison, Noel, and
Scott showed that the smallest such set contains no more than $2^{0.976723k}$
elements. We improve both the upper and lower bounds, showing that the size of
the smallest saturated $k$-Sperner system lies between $\sqrt{k}2^{k/2}$ and
$2^{0.961471k}$.


  Heterogeneous comprehensive learning particle swarm optimization (HCLPSO) is
a type of evolutionary algorithm with enhanced exploration and exploitation
capabilities. The low-discrepancy sequence (LDS) is more uniform in covering
the search space than random sequences. In this paper, making use of the good
uniformity of LDS to improve HCLPSO is researched. Numerical experiments are
performed to show that it is impossible to effectively improve the search
ability of HCLPSO by only using LDS to generate the initial population.
However, if we properly choose some random sequences from the HCLPSO velocities
updating formula and replace them with the deterministic LDS, we can obtain a
more efficient algorithm. Compared with the original HCLPSO under the same
accuracy requirement, the HCLPSO updating the velocities with the deterministic
LDS can significantly reduce the iterations required for finding the optimal
solution, without decreasing the success rate.


  Cross sections for the production of two isolated muons up to high di-muon
masses are measured in ep collisions at HERA with the H1 detector in a data
sample corresponding to an integrated luminosity of 71 pb^-1 at a centre of
mass energy of sqrt{s} = 319 GeV. The results are in good agreement with
Standard Model predictions, the dominant process being photon-photon
interactions. Additional muons or electrons are searched for in events with two
high transverse momentum muons using the full data sample corresponding to 114
pb^-1, where data at sqrt{s} = 301 GeV and sqrt{s} = 319 GeV are combined. Both
the di-lepton sample and the tri-lepton sample agree well with the predictions.


  This paper invented a new rolling control mechanism of two section
articulated-wing ornithopter, which is analogues to aileron control in plane,
however, similar control mechanism leads to opposite result, indicating the
ornithopter supposed to go left now go right instead. This research gives a
qualitative dynamics model which explains this new phenomenon. Because of wing
folding, the differential rotation of outer-section wing (analogues to aileron
in plane, left aileron up and right aileron down make left turn) around pitch
axis becomes common mode rotation around yaw axis,leading its rotating torque
changing from left-handed rotation (using left-handed as example, right-handed
is the same) around roll axis to a common mode force pointing to front-right
(northeast, NE) direction from first player's view of the ornithopter.Because
most of the flapping movement is in the upper hemisphere from ornithopter's
view, the NE force is above on the center of mass of the orthopter, generating
a right-handed moment around roll axis. Therefore, the ornithopter supposed to
go left now goes right. This phenomenon is a unique and only observed in two
section articulated-wing ornithopter by far. Many field tests conducted by
authors confirm it is highly repetitive.


  Given a nonsymmetric operad $\mathcal{O}$, we first construct two new
nonsymmetric operads $\mathcal{O}^{\mathrm{comp}}$ and
$\mathcal{O}^{\mathrm{Dend}}$. These operads are respectively useful to study
compatible and split Loday-algebras. As an application of the operad
$\mathcal{O}^{\mathrm{comp}}$, we show that the cohomology of a compatible
associative algebra carries a Gerstenhaber structure. We give an application of
the operad $\mathcal{O}^\mathrm{Dend}$ to dendriform algebras and find
generalizations to other Loday-algebras. In the end, we construct another
operad $\mathrm{Fam}(\mathcal{O}^\Omega)^\mathrm{Dend}$ to study
dendriform-family algebras recently introduced in the literature. We also
define and study homotopy dendriform-family algebras.


  Wide field-of-view (FoV) cameras efficiently capture large portions of the
scene, which makes them attractive in multiple domains, such as automotive and
robotics. For such applications, estimating depth from multiple images is a
critical task, and therefore, a large amount of ground truth (GT) data is
available. Unfortunately, most of the GT data is for pinhole cameras, making it
impossible to properly train depth estimation models for large-FoV cameras. We
propose the first method to train a stereo depth estimation model on the widely
available pinhole data, and to generalize it to data captured with larger FoVs.
Our intuition is simple: We warp the training data to a canonical, large-FoV
representation and augment it to allow a single network to reason about diverse
types of distortions that otherwise would prevent generalization. We show
strong generalization ability of our approach on both indoor and outdoor
datasets, which was not possible with previous methods.


  We study the time dependence of R\'{e}nyi/entanglement entropies of locally
excited states created by fields with integer spins $s \leq 2$ in $4$
dimensions. For spins 0, 1 these states are characterised by localised energy
densities of a given width which travel as a spherical wave at the speed of
light. For the spin 2 case, in the absence of a local gauge invariant stress
tensor, we probe these states with the Kretschmann scalar and show they
represent localised curvature densities which travel at the speed of light. We
consider the reduced density matrix of the half space with these excitations
and develop methods which include a convenient gauge choice to evaluate the
time dependence of R\'{e}nyi/entanglement entropies as these quenches enter the
half region. In all cases, the entanglement entropy grows in time and saturates
at $\log 2 $. In the limit, the width of these excitations tends to zero, the
growth is determined by order $2s+1$ polynomials in the ratio of the distance
from the co-dimension-2 entangling surface and time. The polynomials
corresponding to quenches created by the fields can be organised in terms of
their representations under the $SO(2)_T\times SO(2)_L$ symmetry preserved by
the presence of the co-dimension 2 entangling surface. For fields transforming
as scalars under this symmetry, the order $2s+1$ polynomial is completely
determined by the spin.


  We study the uniqueness and robustness of acoustic signatures in the cosmic
microwave background by allowing for the possibility that they are generated by
some as yet unknown source of gravitational perturbations. The acoustic {\it
pattern} of peak locations and relative heights predicted by the standard
inflationary cold dark matter model is essentially unique and its confirmation
would have deep implications for the causal structure of the early universe. A
generic pattern for isocurvature initial conditions arises due to backreaction
effects but is not robust to exotic source behavior inside the horizon. If
present, the acoustic pattern contains unambiguous information on the curvature
of the universe even in the general case. By classifying the behavior of the
unknown source, we determine the minimal observations necessary for robust
constraints on the curvature. The diffusion damping scale provides an entirely
model independent cornerstone upon which to build such a measurement. The peak
spacing, if regular, supplies a precision test.