  We consider the relationship between the conjectured uniqueness of the
Moonshine Module, ${\cal V}^\natural$, and Monstrous Moonshine, the genus zero
property of the modular invariance group for each Monster group Thompson
series. We first discuss a family of possible $Z_n$ meromorphic orbifold
constructions of ${\cal V}^\natural$ based on automorphisms of the Leech
lattice compactified bosonic string. We reproduce the Thompson series for all
51 non-Fricke classes of the Monster group $M$ together with a new relationship
between the centralisers of these classes and 51 corresponding Conway group
centralisers (generalising a well-known relationship for 5 such classes).
Assuming that ${\cal V}^\natural$ is unique, we then consider meromorphic
orbifoldings of ${\cal V}^\natural$ and show that Monstrous Moonshine holds if
and only if the only meromorphic orbifoldings of ${\cal V}^\natural$ give
${\cal V}^\natural$ itself or the Leech theory. This constraint on the
meromorphic orbifoldings of ${\cal V}^\natural$ therefore relates Monstrous
Moonshine to the uniqueness of ${\cal V}^\natural$ in a new way.


  We study an infinite family of Mordell curves (i.e. the elliptic curves in
the form y^2=x^3+n, n \in Z) over Q with three explicit integral points. We
show that the points are independent in certain cases. We describe how to
compute bounds of the canonical heights of the points. Using the result we show
that any pair in the three points can always be a part of a basis of the free
part of the Mordell--Weil group.


  Due to the performance degradation of graph neural networks (GNNs) under
distribution shifts, the work on out-of-distribution (OOD) generalization on
graphs has received widespread attention. A novel perspective involves
distinguishing potential confounding biases from different environments through
environmental identification, enabling the model to escape
environmentally-sensitive correlations and maintain stable performance under
distribution shifts. However, in graph data, confounding factors not only
affect the generation process of node features but also influence the complex
interaction between nodes. We observe that neglecting either aspect of them
will lead to a decrease in performance. In this paper, we propose IENE, an OOD
generalization method on graphs based on node-level environmental
identification and extrapolation techniques. It strengthens the model's ability
to extract invariance from two granularities simultaneously, leading to
improved generalization. Specifically, to identify invariance in features, we
utilize the disentangled information bottleneck framework to achieve mutual
promotion between node-level environmental estimation and invariant feature
learning. Furthermore, we extrapolate topological environments through graph
augmentation techniques to identify structural invariance. We implement the
conceptual method with specific algorithms and provide theoretical analysis and
proofs for our approach. Extensive experimental evaluations on two synthetic
and four real-world OOD datasets validate the superiority of IENE, which
outperforms existing techniques and provides a flexible framework for enhancing
the generalization of GNNs.


  Considerable morphological phenotyping studies in nephrology have emerged in
the past few years, aiming to discover hidden regularities between clinical and
imaging phenotypes. Such studies have been largely enabled by deep learning
based image analysis to extract sparsely located targeting objects (e.g.,
glomeruli) on high-resolution whole slide images (WSI). However, such methods
need to be trained using labor-intensive high-quality annotations, ideally
labeled by pathologists. Inspired by the recent "human-in-the-loop" strategy,
we developed EasierPath, an open-source tool to integrate human physicians and
deep learning algorithms for efficient large-scale pathological image
quantification as a loop. Using EasierPath, physicians are able to (1) optimize
the recall and precision of deep learning object detection outcomes adaptively,
(2) seamlessly support deep learning outcomes refining using either our
EasierPath or prevalent ImageScope software without changing physician's user
habit, and (3) manage and phenotype each object with user-defined classes. As a
user case of EasierPath, we present the procedure of curating large-scale
glomeruli in an efficient human-in-the-loop fashion (with two loops). From the
experiments, the EasierPath saved 57 % of the annotation efforts to curate
8,833 glomeruli during the second loop. Meanwhile, the average precision of
glomerular detection was leveraged from 0.504 to 0.620. The EasierPath software
has been released as open-source to enable the large-scale glomerular
prototyping. The code can be found in https://github.com/yuankaihuo/EasierPath


  We extend Gour et al's characterization of quantum majorization via
conditional min-entropy to the context of semifinite von Neumann algebras. Our
method relies on a connection between conditional min-entropy and operator
space projective tensor norm for injective von Neumann algebras. This approach
also connects the tracial Hahn-Banach theorem of Helton, Klep and McCullough to
noncommutative vector-valued $L_1$-space.


  This study presents a framework for conducting psychological and linguistic
research through simulated conversations using large language models (LLMs).
The proposed methodology offers significant advantages, particularly for
simulating human interactions involving potential unethical language or
behaviors that would be impermissible in traditional experiments with human
participants. As a demonstration, we employed LLMs to simulate family
conversations across four parenting styles (authoritarian, authoritative,
permissive, and uninvolved). In general, we observed that the characteristics
of the four parenting styles were portrayed in the simulated conversations.
Several strategies could be used to improve the simulation quality, such as
including context awareness, employing a few-shot prompting approach or
fine-tuning models to cater to specific simulation requirements. Overall, this
study introduces a promising methodology for conducting psychological and
linguistic research through simulated conversations, while acknowledging the
current limitations and proposing potential solutions for future refinement and
improvement.


  We explore the possibility of using van dar Waals bonded heterostructures of
stacked together 2D bilayer black phosphorus (BP) for nanoscale device
applications. The electronic property of BP in AA stacking and 90{\deg} twisted
is studied with density functional theory. Further, we study the homogeneous
nanojunction architecture of BP to use its anisotropic properties. Using the
first principle simulations along with NEGF approach, we calculate quantum
transport properties of the nanojunction setup. The interlayer directionally
dependent current characteristics are explained in different setups. Our result
revealed that 90{\deg} twisted nanojucntion device would be a potential
rectifier despite having no p-n junction characteristic only due to the
intrinsic anisotropy of the material, making tunneling between armchair- and
zigzag-directional BP sheets asymmetric.


  We study correlations of observables in energy eigenstates of chaotic systems
of a large size $N$. We show that the bipartite entanglement of two subsystems
is quite strong, whereas macroscopic entanglement of the total system is
absent. It is also found that correlations, either quantum or classical, among
less than $N/2$ points are quite small. These results imply that chaotic states
are stable. Invariance of these properties under local operations is also
shown.


  Following a brief review of the principles of the strong equivalence
principle (SEP) and tests for its violation in the strong and weak
gravitational field regimes, we present preliminary results of new tests using
two long-period binary pulsars: J0407+1607 and J2016+1947. PSR J0407+1607 is in
a 669-day orbit around a $\gapp 0.2$ M$_{\odot}$ companion, while J2016+1947 is
in a 635-day orbit around a $\gapp 0.3$ M$_{\odot}$ companion. The small
eccentricities of both orbits ($e \sim 10^{-3}$) mean that these systems reduce
previous limits on SEP violation by more than a factor of 4.


  We review some previous results about the Calabi-Yau equation on the
Kodaira-Thurston manifold equipped with an invariant almost-Kaehler structure
and assuming the volume form invariant by the action of a torus. In particular,
we observe that under some restrictions the problem is reduced to a
Monge-Amp\`ere equation by using the ansatz $\tilde \omega=\Omega-dJdu+da$,
where $u$ is a $T^2$-invariant function and $a$ is a $1$-form depending on $u$.
Furthermore, we extend our analysis to non-invariant almost-complex structures
by considering some basic cases and we finally take into account a
generalization to higher dimensions.


  Connected Autonomous Vehicles (CAVs) are widely expected to improve traffic
safety and efficiency by exploiting information from surrounding vehicles via
V2V communication. A CAV typically adapts its speed based on information from
the vehicle it follows. CAVs can also use information from vehicles further
ahead within their communication range, and this results in improved traffic
safety and efficiency. In mixed traffic scenarios, however, this may not always
be possible due to the presence of human-driven vehicles that do not have
communication capabilities. Furthermore, as wireless vehicular networks are
unreliable, information from other vehicles can be delayed or lost, which
brings more challenges for CAVs in utilizing information from multiple leading
vehicles. A few studies have investigated the impact of CAVs where they use
information from multiple leading vehicles on traffic safety and efficiency,
but only in very limited scenarios (i.e., with a very small number of
vehicles).
  In contrast, this paper investigates the impact of CAV car-following control
based on multiple leading vehicles information on both mixed traffic safety and
efficiency in realistic scenarios in terms of imperfect communication, vehicle
modelling, and traffic scenario. Results show that exploiting information from
multiple, rather than a single, leading vehicles in CAV controller design
further improves both traffic safety and efficiency especially at high
penetration rates. In addition to proper tuning of CAV controller parameters
(control gains and time headways), the scale of the improvement depends on both
market penetration rate (MPR) and communication reliability. A packet error
rate (PER) of 70% leads to an increase in traffic efficiency by 4.18% (at 40%
MPR) and 12.19% (at 70% MPR), compared to the simple single leading vehicle
information based controller.


  This paper shows that $K_t$-minor-free (and $K_{s, t}$-minor-free) graphs $G$
are subgraphs of products of a tree-like graph $H$ (of bounded treewidth) and a
complete graph $K_m$. Our results include optimal bounds on the treewidth of
$H$ and optimal bounds (to within a constant factor) on $m$ in terms of the
number of vertices of $G$ and the treewidth of $G$. These results follow from a
more general theorem whose corollaries include a strengthening of the
celebrated separator theorem of Alon, Seymour, and Thomas [J. Amer. Math. Soc.
1990] and the Planar Graph Product Structure Theorem of Dujmovi\'c et al. [J.
ACM 2020].


  Let $\eta=\{\eta(t);t\in [0,1]\}$ be a mean zero continuous Gaussian process
with covariance $U=\{U(s,t),s,t\in [ 0,1]\},$ with $U(0,0)>0$. Let
$\{\eta_{i};i=1,\ldots, k\}$ be independent copies of $\eta$ and set $
Y_{k}(t)=\sum_{i=1}^{k} \eta^2_{i}(t), t\in [ 0,1].$ The stochastic process
$Y_{k } =\{Y_{k }(t),t\in [ 0,1] \}$ is referred to as a chi--square process of
order $k $ with kernel $U$. Let $\phi(t)$ be a positive function on
$[0,\delta]$ for some $\delta>0$. If \[\limsup_{t\to 0}\frac{ \eta(t)-\eta(0)}{
\phi(t) }=1 \qquad a.s., \] then for all integers $k\ge 1$, \[ \limsup_{t\to 0}
\frac{Y_{k }(t)-Y_{k }(0)} { \phi (t)} = 2 Y^{1/2}_{k}(0) \qquad a.s.\] Set \[
\sigma^2(u,v)=E(\eta(u)-\eta(v))^2\quad\text{and}\quad
\widetilde\sigma^2(x)=\sup_{|u-v|\le x}\sigma^2(u,v).\] Assume that $\inf_{t\in
[0,1]}U(t,t)>0$ and, \[ \lim_{x\to0}\widetilde\sigma^2(x)\log 1/x =0. \] Let
$\varphi(t)$ be a positive function on $[0,1]$. Then if \[ \lim_{h\to
0}\sup_{\stackrel{|u-v|\le h }{ u,v\in\Delta}}\frac{ \eta(u)-\eta(v)}{
\varphi(|u-v|) }=1 \qquad a.s.\] for all intervals $\Delta\subset [0,1]$, it
follows that for all intervals $\Delta\subset [0,1]$ and all integers $k\ge 1$,
\[ \lim_{h\to 0}\sup_{\stackrel{|u-v|\le h }{ u,v\in\Delta}} \frac{Y_{k
}(u)-Y_{k }(v) }{ \varphi (|u-v|)} = 2 \sup_{u\in\Delta}Y_{k }^{1/2}(u),
\hspace{.2 in}a.s.\]


  Motivated by the experimental search for the QCD critical point we perform
simulations of a stochastic field theory with purely relaxational dynamics
(model A). We verify the expected dynamic scaling of correlation functions.
Using a finite size scaling analysis we obtain the dynamic critical exponent
$z=2.026(56)$. We investigate time dependent correlation functions of higher
moments $M^n(t)$ of the order parameter $M(t)$ for $n=1,2,3,4$. We obtain
dynamic scaling with the same critical exponent $z$ for all $n$, but the
relaxation constant depends on $n$. We also study the relaxation of $M^n(t)$
after a quench, where the simulation is initialized in the high temperature
phase, and the dynamics is studied at the critical temperature $T_c$. We find
that the evolution does not follow simple scaling with the dynamic exponent
$z$, and that it involves an early time rise followed by late stage relaxation.


  A preliminary investigation is made of possible applications in quantum
theory of the topos formed by the collection of all $M$-sets, where $M$ is a
monoid. Earlier results on topos aspects of quantum theory can be rederived in
this way. However, the formalism also suggests a new way of constructing a
`neo-realist' interpretation of quantum theory in which the truth values of
propositions are determined by the actions of the monoid of strings of finite
projection operators. By these means, a novel topos perspective is gained on
the concept of state-vector reduction.


  Foundational material on complex Lie supergroups and their radial operators
is presented. In particular, Berezin's recursion formula for describing the
radial parts of fundamental operators in general linear and ortho-symplectic
cases is proved. Local versions of results which are suitable for applications
for computing characters which are only defined on proper subdomains or
covering spaces thereof are established.


  We revisit the proof of Landau damping near stable homogenous equilibria of
Vlasov-Poisson systems with screened interactions in the whole space
$\mathbb{R}^d$ (for $d\geq3$) that was first established by Bedrossian,
Masmoudi and Mouhot. Our proof follows a Lagrangian approach and relies on
precise pointwise in time dispersive estimates in the physical space for the
linearized problem that should be of independent interest. This allows to cut
down the smoothness of the initial data required in Bedrossian at al. (roughly,
we only need Lipschitz regularity). Moreover, the time decay estimates we prove
are essentially sharp, being the same as those for free transport, up to a
logarithmic correction.


  Estimating the execution time of software components is often mandatory when
evaluating the non-functional properties of software-intensive systems. This
particularly holds for real-time embedded systems, e.g., in the context of
industrial automation. In practice it is however very hard to obtain reliable
execution time estimates which are accurate, but not overly pessimistic with
respect to the typical behavior of the software.
  This article proposes two new concepts to ease the use of execution time
analysis for industrial control applications: (1) a method based on recurring
occurrences of code sequences for automatically creating a timing model of a
given processor and (2) an interactive way to integrate execution time analysis
into the development environment, thus making timing analysis results easily
accessible for software developers. The proposed methods are validated by an
industrial case study, which shows that a significant amount of code reuse is
present in a set of representative industrial control applications.


  Samarium has two stable valence states, 2+ and 3+, which coexist in many
compounds forming spatially homogeneous intermediate valence states. We study
the valence state of samarium when incorporated in a single crystalline EuO
thin film which crystallizes in a $fcc$-structure similar to that of the
intermediate valence SmO, but with a larger lattice constant. Due to the
increased lattice spacing, a stabilization of the larger Sm$^{2+}$ ion is
expected. Surprisingly, the samarium incorporated in
Sm$_{\mathrm{x}}$Eu$_{\mathrm{1-x}}$O thin films shows a predominantly
trivalent character, as determined by x-ray photoelectron spectroscopy and
magnetometry measurements. We infer that the O$^{2-}$ ions in the EuO lattice
have enough room to move locally, so as to reduce the Sm-O distance and
stabilize the Sm$^{3+}$ valence.


  In this letter, the wavelet transform is used to decompose the classical
linearly polarized plane light wave into a series of discrete Morlet wavelets.
It is found that the energy of the light wave can be discrete, associated with
its discrete wavelet structure.It is also found that the changeable energy of a
basic plane light wave packet or wave train of wave vector
$\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}\over
k} $ and with discrete wavelet structure can be with the form of ${H_{0k}} =
n{p_{0k}}\omega$ $(n = 1,2,3,...)$, where $n$ is the parameter of discrete
wavelet structure, $\omega $ is the idler frequency of the light wave packet or
wave train, and ${p_{0k}}$ is a constant to be determined.This is consistent
with the energy division of $P$ portions in Planck radiation theory, where $P$
is an integer. Finally, the random light wave packets with $n=1$ are used to
simulate the Mach-Zehnder interference of single photons, showing the
wave-particle duality of light.


  We consider the average number B_m(t) of bonds traversed exactly m times by a
t step simple random walk. We determine B_m(t) explicitly in the scaling limit
t -> oo with m/sqrt(t) fixed in dimension d=1 and m/log(t) fixed in dimension
d=2. The scaling function is an erfc in d=1 and an exponential in d=2.


  The ribosome is one of the largest and most complex macromolecular machines
in living cells. It polymerizes a protein in a step-by-step manner as directed
by the corresponding nucleotide sequence on the template messenger RNA (mRNA)
and this process is referred to as `translation' of the genetic message encoded
in the sequence of mRNA transcript. In each successful chemo-mechanical cycle
during the (protein) elongation stage, the ribosome elongates the protein by a
single subunit, called amino acid, and steps forward on the template mRNA by
three nucleotides called a codon. Therefore, a ribosome is also regarded as a
molecular motor for which the mRNA serves as the track, its step size is that
of a codon and two molecules of GTP and one molecule of ATP hydrolyzed in that
cycle serve as its fuel. What adds further complexity is the existence of
competing pathways leading to distinct cycles, branched pathways in each cycle
and futile consumption of fuel that leads neither to elongation of the nascent
protein nor forward stepping of the ribosome on its track. We investigate a
model formulated in terms of the network of discrete chemo-mechanical states of
a ribosome during the elongation stage of translation. The model is analyzed
using a combination of stochastic thermodynamic and kinetic analysis based on a
graph-theoretic approach. We derive the exact solution of the corresponding
master equations. We represent the steady state in terms of the cycles of the
underlying network and discuss the energy transduction processes. We identify
the various possible modes of operation of a ribosome in terms of its average
velocity and mean rate of GTP hydrolysis. We also compute entropy production as
functions of the rates of the interstate transitions and the thermodynamic cost
for accuracy of the translation process.


  The purpose of this work is simulation of magnetised plasmas in the ITER
project framework. In this context, kinetic Vlasov-Poisson like models are used
to simulate core turbulence in the tokamak in a toroidal geometry. This leads
to heavy simulations because a 6D dimensional problem has to be solved, even if
reduced to a 5D in so called gyrokinetic models. Accurate schemes, parallel
algorithms need to be designed to bear these simulations. This paper describes
the numerical studies to improve robustness of the conservative PSM scheme in
the context of its development in the GYSELA code. In this paper, we only
consider the 4D drift-kinetic model which is the backbone of the 5D gyrokinetic
models and relevant to build a robust and accurate numerical method.


  In quantum field theory, heavy particles with mass $M$ much greater than the
temperature $T$ give not only effects suppressed by the Boltzmann factor
$e^{-M/T}$, but also effects suppressed by powers of $T/M$. We show that
power-suppressed terms in equilibrium observables arise from effective
interactions among light particles due to virtual heavy particles. We study a
model introduced by Matsumoto and Yoshimura in which study a model introduced
by Matsumoto and Yoshimura in which heavy bosons interact only through a term
that allows pair annihilation into light particles. We construct an effective
Lagrangian for the light field by integrating out the heavy field, and use it
to calculate the leading power-suppressed terms in the energy density. The
thermal average of the Hamiltonian density for the heavy field includes a term
proportional to $T^6/M^2$, but we show that this term can be eliminated by a
field redefinition and therefore cannot have any physical significance.


  The generalized equipartition theorem known as the conjugate variables
theorem (Phys. Rev. E 86, 051136 [2012]), originally obtained in the context of
statistical inference of continuous random variables, is extended in this work
to the case of discrete variables. Using this new set of theorems we derive
novel thermodynamic identities for the canonical ensemble connecting
temperature with measurable observables.


  We study the transport properties of a voltage-biased Josephson junction
where the BCS superconducting leads are coupled via the edges of a quantum Hall
sample. In this scenario, an out of equilibrium Josephson current develops,
which is numerically studied within the Floquet-Keldysh Green's function
formalism. We particularly focus on the time-averaged current as a function of
both the bias voltage and the magnetic flux threading the sample and analyze
the resonant multiple Andreev reflection processes that lead to an enhancement
of the quasiparticle transmission. We find that a full tomography of the dc
current in the voltage-flux plane allows for a complete spectroscopy of the
one-way edge modes and could be used as a hallmark of chiral edge mediated
transport in these hybrid devices.


  A novel Lattice Boltzmann method is derived using the Principle of Minimum
Cross Entropy (MinxEnt) via the minimization of Kullback-Leibler Divergence
(KLD). By carrying out the actual single step Newton-Raphson minimization
(MinxEnt-LBM) a more accurate and stable Lattice Boltzmann Method can be
implemented. To demonstrate this, 1D shock tube and 2D lid-driven cavity flow
simulations are carried out and compared to Single Relaxation Time LBM, Two
Relaxation Time LBM, Multiple Relaxation Time LBM and Eherenfest Step LBM.


  Anomaly detection on attributed networks aims to find the nodes whose
behaviors are significantly different from other majority nodes. Generally,
network data contains information about relationships between entities, and the
anomaly is usually embodied in these relationships. Therefore, how to
comprehensively model complex interaction patterns in networks is still a major
focus. It can be observed that anomalies in networks violate the homophily
assumption. However, most existing studies only considered this phenomenon
obliquely rather than explicitly. Besides, the node representation of normal
entities can be perturbed easily by the noise relationships introduced by
anomalous nodes. To address the above issues, we present a novel contrastive
learning framework for anomaly detection on attributed networks,
\textbf{SCALA}, aiming to improve the embedding quality of the network and
provide a new measurement of qualifying the anomaly score for each node by
introducing sparsification into the conventional method. Extensive experiments
are conducted on five benchmark real-world datasets and the results show that
SCALA consistently outperforms all baseline methods significantly.


  We study classical spin ice under uniaxial strain along the $[111]$
crystallographic axis. Remarkably, such strain preserves the extensive ice
degeneracy and the corresponding classical Coulomb phase. The emergent monopole
excitations remain thermodynamically deconfined exactly as in the isotropic
case. However, their motion under local heat bath dynamics depends
qualitatively on the sign of the strain. In the low-temperature limit for
negative strain, the monopoles diffuse, while for positive strain, they
localize. Introducing additional ring exchange dynamics into the ice background
transforms the localized monopoles into sub-dimensional excitations whose
motion is restricted to diffusion in the $(111)$-plane. The phenomena we
identify are experimentally accessible in rare-earth pyrochlores under uniaxial
pressure as well as in tripod kagome materials. The diffusive versus localized
nature of the monopoles manifests in characteristic magnetic noise spectra,
which we compute.


  With the tremendous advances in the architecture and scale of convolutional
neural networks (CNNs) over the past few decades, they can easily reach or even
exceed the performance of humans in certain tasks. However, a recently
discovered shortcoming of CNNs is that they are vulnerable to adversarial
attacks. Although the adversarial robustness of CNNs can be improved by
adversarial training, there is a trade-off between standard accuracy and
adversarial robustness. From the neural architecture perspective, this paper
aims to improve the adversarial robustness of the backbone CNNs that have a
satisfactory accuracy. Under a minimal computational overhead, the introduction
of a dilation architecture is expected to be friendly with the standard
performance of the backbone CNN while pursuing adversarial robustness.
Theoretical analyses on the standard and adversarial error bounds naturally
motivate the proposed neural architecture dilation algorithm. Experimental
results on real-world datasets and benchmark neural networks demonstrate the
effectiveness of the proposed algorithm to balance the accuracy and adversarial
robustness.


  In this paper, we present a crash frequency data augmentation method based on
Conditional Generative Adversarial Networks to improve crash frequency models.
The proposed method is evaluated by comparing the performance of Base SPFs
(developed using original data) and Augmented SPFs (developed using original
data plus synthesised data) in terms of hotspot identification performance,
model prediction accuracy, and dispersion parameter estimation accuracy. The
experiments are conducted using simulated and real-world crash data sets. The
results indicate that the synthesised crash data by CGAN have the same
distribution as the original data and the Augmented SPFs outperforms Base SPFs
in almost all aspects especially when the dispersion parameter is low.


  We present a new proof of the caloric smoothing related to the fractional
Gauss-Weierstrass semi-group in Triebel-Lizorkin spaces. This property will be
used to prove existence and uniqueness of mild and strong solutions of the
Cauchy problem for a fractional nonlinear heat equation.


  We consider triad dynamics as it was recently considered by Antal \emph{et
al.} [T. Antal, P. L. Krapivsky, and S. Redner, Phys. Rev. E {\bf 72}, 036121
(2005)] as an approach to social balance. Here we generalize the topology from
all-to-all to a regular one of a two-dimensional triangular lattice. The
driving force in this dynamics is the reduction of frustrated triads in order
to reach a balanced state. The dynamics is parameterized by a so-called
propensity parameter $p$ that determines the tendency of negative links to
become positive. As a function of $p$ we find a phase transition between
different kind of absorbing states. The phases differ by the existence of an
infinitely connected (percolated) cluster of negative links that forms whenever
$p\leq p_c$. Moreover, for $p\leq p_c$, the time to reach the absorbing state
grows powerlike with the system size $L$, while it increases logarithmically
with $L$ for $p > p_c$. From a finite-size scaling analysis we numerically
determine the critical exponents $\beta$ and $\nu$ together with $\gamma$,
$\tau$, $\sigma$. The exponents satisfy the hyperscaling relations. We also
determine the fractal dimension $d_f$ that fulfills a hyperscaling relation as
well. The transition of triad dynamics between different absorbing states
belongs to a universality class with new critical exponents. We generalize the
triad dynamics to four-cycle dynamics on a square lattice. In this case, again
there is a transition between different absorbing states, going along with the
formation of an infinite cluster of negative links, but the usual scaling and
hyperscaling relations are violated.


  We present the Bayesian consensus filter (BCF) for tracking a moving target
using a networked group of sensing agents and achieving consensus on the best
estimate of the probability distributions of the target's states. Our BCF
framework can incorporate nonlinear target dynamic models, heterogeneous
nonlinear measurement models, non-Gaussian uncertainties, and higher-order
moments of the locally estimated posterior probability distribution of the
target's states obtained using Bayesian filters. If the agents combine their
estimated posterior probability distributions using a logarithmic opinion pool,
then the sum of Kullback--Leibler divergences between the consensual
probability distribution and the local posterior probability distributions is
minimized. Rigorous stability and convergence results for the proposed BCF
algorithm with single or multiple consensus loops are presented. Communication
of probability distributions and computational methods for implementing the BCF
algorithm are discussed along with a numerical example.


  Atlas-type models are constant-parameter models of uncorrelated stocks for
equity markets with a stable capital distribution, in which the growth rates
and variances depend on rank. The simplest such model assigns the same,
constant variance to all stocks; zero rate of growth to all stocks but the
smallest; and positive growth rate to the smallest, the Atlas stock. In this
paper we study the basic properties of this class of models, as well as the
behavior of various portfolios in their midst. Of particular interest are
portfolios that do not contain the Atlas stock.


  In this paper we consider a family of non local functionals of
convolution-type depending on a small parameter $\varepsilon>0$ and
$\Gamma$-converging to local functionals defined on Sobolev spaces as
$\varepsilon\to 0$. We study the asymptotic behaviour of the functionals when
the order parameter is subject to Dirichlet conditions on a periodically
perforated domains, given by a periodic array of small balls of radius
$r_\delta$ centered on a $\delta$--periodic lattice, being $\delta > 0$ an
additional small parameter and $r_\delta=o(\delta)$. We highlight differences
and analogies with the local case, according to the interplay between the three
scales $\varepsilon$, $\delta$ and $r_\delta$. A fundamental tool in our
analysis turns out to be a non local variant of the classical
Gagliardo-Nirenberg-Sobolev inequality in Sobolev spaces which may be of
independent interest and useful for other applications.


  We introduce the notion of unbounded locally solid Riesz spaces, and
investigate its fundamental properties.


  The unzipping of vortex lines using magnetic-force microscopy from extended
defects is studied theoretically. We study both the unzipping isolated vortex
from common defects, such as columnar pins and twin-planes, and the unzipping
of a vortex from a plane in the presence of other vortices. We show, using
analytic and numerical methods, that the universal properties of the unzipping
transition of a single vortex depend only on the dimensionality of the defect
in the presence and absence of disorder. For the unzipping of a vortex from a
plane populated with many vortices is shown to be very sensitive to the
properties of the vortices in the two-dimensional plane. In particular such
unzipping experiments can be used to measure the ``Luttinger liquid parameter''
of the vortices in the plane. In addition we suggest a method for measuring the
line tension of the vortex directly using the experiments.


  We explore the possibility of utilizing the prompt muon fluxes at very high
energies in order to discriminate various models/parametrizations of low-x QCD
behaviour of hadronic cross-sections relevant at such energies. We find that
the pair meter technique for measuring high energy prompt muons can be very
efficient in such an endeavor. As a by product, it allows to cleanly probe the
change in composition of the primary cosmic rays expected at high energies.


  This paper describes an agent-based model of a finite group of agents in a
single population who each choose which convention to advocate, and which
convention to practice. Influences or dependencies in agents choice exists in
the form of guru effects and what others practice. With payoffs being dependent
on cumulative rewards or actual standings in society, we illustrate the
evolutionary dynamics of the phase structure of each group in the population
via simulations.


  We consider a situation where an $N$-level system (NLS) is coupled
successively to two heat baths with different temperatures without being
necessarily thermalized and approaches a steady state. For this situation we
apply a general Jarzinski-type equation and conclude that heat and entropy is
flowing from the hot bath to the cold one. The Clausius relation between
increase of entropy and transfer of heat divided by a suitable temperature
assumes the form of two inequalities. Our approach is illustrated by an
analytical example. For the linear regime, i.~e., for small temperature
differences between the two heat baths we derive an expression for the heat
conduction coefficient.


  Quantum state transfer from flying photons to stationary matter qubits is an
important element in the realization of quantum networks. Self-assembled
semiconductor quantum dots provide a promising solid-state platform hosting
both single photon and spin, with an inherent light-matter interface. Here, we
develop a method to coherently and actively control the single-photon frequency
bins in superposition using electro-optic modulators, and measure the
spin-photon entanglement with a fidelity of $0.796\pm0.020$. Further, by
Greenberger-Horne-Zeilinger-type state projection on the frequency, path and
polarization degrees of freedom of a single photon, we demonstrate quantum
state transfer from a single photon to a single electron spin confined in an
InGaAs quantum dot, separated by 5 meters. The quantum state mapping from the
photon's polarization to the electron's spin is demonstrated along three
different axis on the Bloch sphere, with an average fidelity of $78.5\%$.


  Those articles (versions) explore a non conventional pregeometrical model
encompassing quantics and geometrodynamics (a stochastic graph relational
theory).
  Some key points are :
  1) the use of simple boolean atom-like far subquantum entities connected with
action links deriving from probabilistic laws (acteons).
  2) the concept of structures as correlated nets of relations.
  3) the relational definition of locus and processual definition of distances,
with implied consequences on how the physical universe should be conceived in
such a model.
  Added versions improve and extend the idea on mathematical grounds.


  We compare the time evolution of entanglement measures after local operator
excitation in the critical Ising model with predictions from conformal field
theory. For the spin operator and its descendants we find that Renyi entropies
of a block of spins increase by a constant that matches the logarithm of the
quantum dimension of the conformal family. However, for the energy operator we
find a small constant contribution that differs from the conformal field theory
answer equal to zero. We argue that the mismatch is caused by the subtleties in
the identification between the local operators in conformal field theory and
their lattice counterpart. Our results indicate that evolution of entanglement
measures in locally excited states not only constraints this identification,
but also can be used to extract non-trivial data about the conformal field
theory that governs the critical point. We generalize our analysis to the Ising
model away from the critical point, states with multiple local excitations, as
well as the evolution of the relative entropy after local operator excitation
and discuss universal features that emerge from numerics.


  We propose an optomechanical nano-gravimeter based on exceptional points. The
system is a coupled cavity optomechanical system, in which the gain and loss
are applied by driving the cavities with a blue detuned and red detuned
electromagnetic field, respectively. When the gain and loss reach a balance,
the system will show the degeneracy of exceptional points, and any perturbation
will cause an eigenfrequencies split, which is proportional to the square root
of the perturbation strength. Compared with the traditional optomechanical
sensors, the sensitivity is greatly enhanced. This work paves the way for the
design of optomechanical ultrasensitive force sensors that can be applied to
detect non-Newtonian effects, high-order weak interactions, and so on.


  We rewrite the Klein-Gordon (KG) equation in an arbitrary space-time
transforming it into a generalized Schr\"odinger equation. Then we take the
weak field limit and show that this equation has some differences with the
traditional Schr\"odinger equation plus a gravitational field. Thus, this
procedure shows that the Schr\"odinger equation derived in a covariant manner
is different from the traditional one. With this new Schr\"odinger equation, we
study the KG equation in a Newtonian space-time to describe the behavior of a
scalar particle in an inertial system. We give some examples where it is
possible to study the energy levels, effective potential and the wave function
of the systems, these results contain the gravitational effects due to the
curvature of space-time. We show that it is possible to verify experimentally
these effects in a laboratory using non-inertial reference frames.


  The spot pricing scheme has been considered to be resource-efficient for
providers and cost-effective for consumers in the Cloud market. Nevertheless,
unlike the static and straightforward strategies of trading on-demand and
reserved Cloud services, the market-driven mechanism for trading spot service
would be complicated for both implementation and understanding. The largely
invisible market activities and their complex interactions could especially
make Cloud consumers hesitate to enter the spot market. To reduce the
complexity in understanding the Cloud spot market, we decided to reveal the
backend information behind spot price variations. Inspired by the methodology
of reverse engineering, we developed a Predator-Prey model that can simulate
the interactions between demand and resource based on the visible spot price
traces. The simulation results have shown some basic regular patterns of market
activities with respect to Amazon's spot instance type m3.large. Although the
findings of this study need further validation by using practical data, our
work essentially suggests a promising approach (i.e.~using a Predator-Prey
model) to investigate spot market activities.


  In recent years, social virtual reality (VR), sometimes described as the
"metaverse," has become widely available. With its potential comes risks,
including risks to privacy. To understand these risks, we study the
identifiability of participants' motion in VR in a dataset of 232 VR users with
eight weekly sessions of about thirty minutes each, totaling 764 hours of
social interaction. The sample is unique as we are able to study the effect of
user, session, and time independently. We find that the number of sessions
recorded greatly increases identifiability, and duration per session increases
identifiability as well, but to a lesser degree. We also find that greater
delay between training and testing sessions reduces identifiability.
Ultimately, understanding the identifiability of VR activities will help
designers, security professionals, and consumer advocates make VR safer.


  Let $D$ be an integral domain with quotient field $K$. A star-operation
$\star$ on $D$ is a closure operation $A \longmapsto A^\star$ on the set of
nonzero fractional ideals, $F(D)$, of $D$ satisfying the properties:
$(xD)^\star = xD$ and $(xA)^\star = xA^\star$ for all $x \in K^\ast$ and $A \in
F(D)$. Let ${\M S}$ be a multiplicatively closed set of ideals of $D$. For $A
\in F(D)$ define $A_{\M S} = \{x \in K \mid xI \subseteq{A}$, for some $I \in
{\M S}\}$. Then $D_{\M S}$ is an overring of $D$ and $A_{\M S}$ is a fractional
ideal of $D_{\M S}$. Let ${\M S}$ be a multiplicative set of finitely generated
nonzero ideals of $D$ and $A \in F(D)$, then the map $A \longmapsto A_{\M S}$
is a finite character star-operation if and only if for each $I \in {\M S}$,
$I_v = D$. We give an example to show that this result is not true if the
ideals are not assumed to be finitely generated. In general, the map $A
\longmapsto A_{\M S}$ is a star-operation if and only if $\bar {\M S}$, the
saturation of ${\M S}$, is a localizing GV-system. We also discuss
star-operations given of the form $A \longmapsto \cap AD_\alpha$, where $D =
\cap D_\alpha$.


  Precision measurements, now and at a future linear electron-positron collider
(ILC), can provide indirect information about the possible scale of
supersymmetry. We illustrate the present-day and possible future ILC
sensitivities within the constrained minimal supersymmetric extension of the
Standard Model (CMSSM), in which there are three independent soft
supersymmetry-breaking parameters m_{1/2}, m_0 and A_0. We analyze the present
and future sensitivities separately for M_W, sin^2(theta_eff), (g-2)_mu, BR(b
-> s gamma), BR(B_s -> mu+ mu-), M_h and Higgs branching ratios. We display the
observables as functions of m_{1/2}, fixing m_0 so as to obtain the cold dark
matter density allowed by WMAP and other cosmological data for specific values
of A_0, tan beta and mu > 0. In a second step, we investigate the combined
sensitivity of the currently available precision observables, M_W,
sin^2(theta_eff), (g-2)_mu and BR(b -> s gamma), by performing a chi^2
analysis. The current data are in very good agreement with the CMSSM prediction
for tan beta = 10, with a clear preference for relatively small values of
m_{1/2} \sim 300 GeV. In this case, there would be good prospects for observing
supersymmetry directly at both the LHC and the ILC, and some chance already at
the Tevatron collider. For tan beta = 50, the quality of the fit is worse, and
somewhat larger m_{1/2} values are favoured. With the prospective ILC
accuracies the sensitivity to indirect effects of supersymmetry greatly
improves. This may provide indirect access to supersymmetry even at scales
beyond the direct reach of the LHC or the ILC.


  In this work we rigorously analyse assumptions inherent to black-box
optimisation hyper-parameter tuning tasks. Our results on the Bayesmark
benchmark indicate that heteroscedasticity and non-stationarity pose
significant challenges for black-box optimisers. Based on these findings, we
propose a Heteroscedastic and Evolutionary Bayesian Optimisation solver (HEBO).
HEBO performs non-linear input and output warping, admits exact marginal
log-likelihood optimisation and is robust to the values of learned parameters.
We demonstrate HEBO's empirical efficacy on the NeurIPS 2020 Black-Box
Optimisation challenge, where HEBO placed first. Upon further analysis, we
observe that HEBO significantly outperforms existing black-box optimisers on
108 machine learning hyperparameter tuning tasks comprising the Bayesmark
benchmark. Our findings indicate that the majority of hyper-parameter tuning
tasks exhibit heteroscedasticity and non-stationarity, multi-objective
acquisition ensembles with Pareto front solutions improve queried
configurations, and robust acquisition maximisers afford empirical advantages
relative to their non-robust counterparts. We hope these findings may serve as
guiding principles for practitioners of Bayesian optimisation. All code is made
available at https://github.com/huawei-noah/HEBO.


  Prediction sets capture uncertainty by predicting sets of labels rather than
individual labels, enabling downstream decisions to conservatively account for
all plausible outcomes. Conformal inference algorithms construct prediction
sets guaranteed to contain the true label with high probability. These
guarantees fail to hold in the face of distribution shift, which is precisely
when reliable uncertainty quantification can be most useful. We propose a novel
algorithm for constructing prediction sets with PAC guarantees in the label
shift setting. This method estimates the predicted probabilities of the classes
in a target domain, as well as the confusion matrix, then propagates
uncertainty in these estimates through a Gaussian elimination algorithm to
compute confidence intervals for importance weights. Finally, it uses these
intervals to construct prediction sets. We evaluate our approach on five
datasets: the CIFAR-10, ChestX-Ray and Entity-13 image datasets, the tabular
CDC Heart dataset, and the AGNews text dataset. Our algorithm satisfies the PAC
guarantee while producing smaller, more informative, prediction sets compared
to several baselines.


  The Aldous--Broder algorithm provides a way of sampling a uniformly random
spanning tree for finite connected graphs using simple random walk. Namely,
start a simple random walk on a connected graph and stop at the cover time. The
tree formed by all the first-entrance edges has the law of a uniform spanning
tree. Here we show that the tree formed by all the last-exit edges also has the
law of a uniform spanning tree. This answers a question of Tom Hayes and Cris
Moore from 2010. The proof relies on a bijection that is related to the BEST
theorem in graph theory. We also give other applications of our results,
including new proofs of the reversibility of loop-erased random walk, of the
Aldous--Broder algorithm itself, and of Wilson's algorithm.


  The lattice fluid model of the system with short range and long range Coulomb
interactions is suggested. In the framework of the collective variables method,
the screening of the Coulomb interactions in the bulk is considered. It is
shown that the Debye length includes additional concentration dependence
inversely proportional to the square root of the mean concentration of vacant
sites like what is known at the plane boundary. The Coulomb interaction
contribution to the free energy of the system is calculated in the approach
close to the mean spherical approximation and is given in an analytical form.
The influence of the variation of the crystal field near the system boundary on
the structure and characteristics of the electric double layer is investigated.
As compared to the system with equal crystal potentials at the lattice sites
throughout the system the pronounced difference for the electric capacitance
appears at low absolute values of the surface potential and it is more
pronounced for negative electric potentials. The capacitance diverges as the
potential values at which the electric field tends to zero and attains negative
values in regions of the surface potentials depending on their polarity and
values of the surface crystal potential. Negative values of the capacitance may
indicate the thermodynamic instability of the system that can result from
neglecting the short range interaction contribution.


  We examine instances of modularity of (rigid) Calabi-Yau manifolds whose
periods are expressed in terms of hypergeometric functions. The $p$-th
coefficients $a(p)$ of the corresponding modular form can be often read off, at
least conjecturally, from the truncated partial sums of the underlying
hypergeometric series modulo a power of $p$ and from Weil's general bounds
$|a(p)|\le2p^{(m-1)/2}$, where $m$ is the weight of the form. Furthermore, the
critical $L$-values of the modular form are predicted to be $\mathbb
Q$-proportional to the values of a related basis of solutions to the
hypergeometric differential equation.


  Richard Feynman's observation that quantum mechanical effects could not be
simulated efficiently on a computer led to speculation that computation in
general could be done more efficiently if it used quantum effects. This
speculation appeared justified when Peter Shor described a polynomial time
quantum algorithm for factoring integers.
  In quantum systems, the computational space increases exponentially with the
size of the system which enables exponential parallelism. This parallelism
could lead to exponentially faster quantum algorithms than possible
classically. The catch is that accessing the results, which requires
measurement, proves tricky and requires new non-traditional programming
techniques.
  The aim of this paper is to guide computer scientists and other
non-physicists through the conceptual and notational barriers that separate
quantum computing from conventional computing. We introduce basic principles of
quantum mechanics to explain where the power of quantum computers comes from
and why it is difficult to harness. We describe quantum cryptography,
teleportation, and dense coding. Various approaches to harnessing the power of
quantum parallelism are explained, including Shor's algorithm, Grover's
algorithm, and Hogg's algorithms. We conclude with a discussion of quantum
error correction.


  Cytology is the branch of pathology which deals with the microscopic
examination of cells for diagnosis of carcinoma or inflammatory conditions.
Automation in cytology started in the early 1950s with the aim to reduce manual
efforts in diagnosis of cancer. The inflush of intelligent technological units
with high computational power and improved specimen collection techniques
helped to achieve its technological heights. In the present survey, we focus on
such image processing techniques which put steps forward towards the automation
of cytology. We take a short tour to 17 types of cytology and explore various
segmentation and/or classification techniques which evolved during last three
decades boosting the concept of automation in cytology. It is observed, that
most of the works are aligned towards three types of cytology: Cervical, Breast
and Lung, which are discussed elaborately in this paper. The user-end systems
developed during that period are summarized to comprehend the overall growth in
the respective domains. To be precise, we discuss the diversity of the
state-of-the-art methodologies, their challenges to provide prolific and
competent future research directions inbringing the cytology-based commercial
systems into the mainstream.


  The consistent theoretical description of gravitational Hall-MHD (G-Hall-MHD)
equilibria is of fundamental importance for understanding the phenomenology of
accretion disks (AD) around compact objects (black holes, neutron stars, etc.).
The very existence of these equilibria is actually suggested by observations,
which show evidence of quiescent, and essentially non-relativistic, AD plasmas
close to compact stars, thus indicating that accretion disks may be
characterized by slowly varying EM and fluid fields. These (EM) fields, in
particular the electric field, may locally be extremely intense, so that AD
plasmas are likely to be locally non-neutral and therefore characterized by the
presence of Hall currents. This suggests therefore that such equilibria should
be described in the framework of the Hall-MHD theory. Extending previous
approaches, holding for non-rotating plasmas or based on specialized
single-species model equilibria which ignore the effect of space-time
curvature, the purpose of this work is the formulation of a generalized
Grad-Shafranov (GGS) equation suitable for the investigation of G-Hall-MHD
equilibria in AD's where non-relativistic plasmas are present. For this purpose
the equilibria are assumed to be generated by a strong axisymmetric stellar
magnetic field and by the gravitating plasma characterizing the AD.


  It is shown that the space-time with a conical singularity, which describes a
thin cosmic string, is hyperbolic in the sense that a unique H^1 solution
exists to the initial value problem for the wave equation with a certain class
of initial data.


  Many social, technological and biological interactions involve network
relationships whose outcome intimately depends on the structure of the network
and on the strengths of the connections. Yet, although much information is now
available concerning the structure of many networks, the strengths are more
difficult to measure. Here we show that, for one particular social network,
notably the e-mail network, a suitable measure of the strength of the
connections can be available. We also propose a simple mechanism, based on
positive feedback and reciprocity, that can explain the observed behavior and
that hints toward specific dynamics of formation and reinforcement of network
connections. Network data from contexts different from social sciences indicate
that power-law, and generally broad, distributions of the connection strength
are ubiquitous, and the proposed mechanism has a wide range of applicability.


  Carrier envelope phase (CEP) stabilized pulses of intense 800 nm light of 5
fs duration are used to probe the dissociation dynamics of dications of
isotopically-substituted water, HOD. HOD$^{2+}$ dissociates into either H$^+$ +
OD$^+$ or D$^+$ + OH$^+$. The branching ratio for these two channels is
CEP-dependent; the OD$^+$/OH$^+$ ratio (relative to that measured with
CEP-unstabilized pulses) varies from 150% to over 300% at different CEP values,
opening prospects of isotope-dependent control over molecular bond breakage.
The kinetic energy released as HOD$^{2+}$ Coulomb explodes is also
CEP-dependent. Formidable theoretical challenges are identified for proper
insights into the overall dynamics which involve non-adiabatic field ionization
from HOD to HOD$^+$ and, thence, to HOD$^{2+}$ via electron rescattering.


  In this work we examine the nucleation from NaCl aqueous solutions within
nano-confined environments, employing enhanced sampling molecular dynamics
simulations integrated with machine learning-derived reaction coordinates.
Through our simulations, we successfully induce phase transitions between
solid, liquid, and a hydrated phase, typically observed at lower temperatures
in bulk environments. Interestingly, nano-confinement serves to stabilize the
solid phase and elevate melting points. Our simulations explain these findings
by underscoring the significant role of water, alongside ion aggregation and
subtle, anistropic dielectric behavior, in driving nucleation within
nano-constrained environments. This letter thus provides a framework for
sampling, analyzing and understanding nucleation processes under
nano-confinement.


  In this article, we study the twisting procedure of orbifold cohomology. We
introduce local system and construct twisted orbifold cohomology. Then, we
generalize Vafa-Witten's notion of discrete torsion to general orbifold and
examine its relation to local system. Finally, some examples are computed.


  The polar codes are proven to be capacity-achieving and are shown to have
equivalent or even better finite-length performance than the turbo/LDPC codes
under some improved decoding algorithms over the additive white Gaussian noise
(AWGN) channels. Polar coding is based on the so-called channel polarization
phenomenon induced by a transform over the underlying binary-input channel. The
channel polarization is found to be universal in many signal processing
problems and has been applied to the coded modulation schemes. In this paper,
the channel polarization is further extended to the multiple antenna
transmission following a multilevel coding principle. The multiple-input
multile-output (MIMO) channel under quadrature amplitude modulation (QAM) are
transformed into a series of synthesized binary-input channels under a
three-stage channel transform. Based on this generalized channel polarization,
the proposed space-time polar coded modulation (STPCM) scheme allows a joint
optimization of the binary polar coding, modulation and MIMO transmission. In
addition, a practical solution of polar code construction over the fading
channels is also provided, where the fading channels are approximated by an
AWGN channel which shares the same capacity with the original. The simulations
over the MIMO channel with uncorrelated Rayleigh fast fading show that the
proposed STPCM scheme can outperform the bit-interleaved turbo coded scheme in
all the simulated cases, where the latter is adopted in many existing
communication systems.


  In [10], Wears defined and studied algebraic T-solitons. In this paper, we
give the definition of algebraic Schouten solitons as a special T-soliton and
classify algebraic Schouten solitons associated to Levi-Civita connections,
canonical connections and Kobayashi-Nomizu connections on three-dimensional
Lorentzian Lie groups with some product structure.


  We introduce a novel latent vector space model that jointly learns the latent
representations of words, e-commerce products and a mapping between the two
without the need for explicit annotations. The power of the model lies in its
ability to directly model the discriminative relation between products and a
particular word. We compare our method to existing latent vector space models
(LSI, LDA and word2vec) and evaluate it as a feature in a learning to rank
setting. Our latent vector space model achieves its enhanced performance as it
learns better product representations. Furthermore, the mapping from words to
products and the representations of words benefit directly from the errors
propagated back from the product representations during parameter estimation.
We provide an in-depth analysis of the performance of our model and analyze the
structure of the learned representations.


  An obstacle affecting any proposal for a topological quantum computer based
on Ising anyons is that quasiparticle braiding can only implement a finite
(non-universal) set of quantum operations. The computational power of this
restricted set of operations (often called stabilizer operations) has been
studied in quantum information theory, and it is known that no
quantum-computational advantage can be obtained without the help of an
additional non-stabilizer operation. Similarly, a bipartite two-qubit system
based on Ising anyons cannot exhibit non-locality (in the sense of violating a
Bell inequality) when only topologically protected stabilizer operations are
performed. To produce correlations that cannot be described by a local hidden
variable model again requires the use of a non-stabilizer operation. Using
geometric techniques, we relate the sets of operations that enable universal
quantum computing (UQC) with those that enable violation of a Bell inequality.
Motivated by the fact that non-stabilizer operations are expected to be highly
imperfect, our aim is to provide a benchmark for identifying UQC-enabling
operations that is both experimentally practical and conceptually simple. We
show that any (noisy) single-qubit non-stabilizer operation that, together with
perfect stabilizer operations, enables violation of the simplest two-qubit Bell
inequality can also be used to enable UQC. This benchmarking requires finding
the expectation values of two distinct Pauli measurements on each qubit of a
bipartite system.


  For a closed oriented 3-manifold Y, we define an absolute grading on the
Heegaard Floer homology groups of Y by homotopy classes of oriented 2-plane
fields. We show that this absolute grading refines the relative one and that it
is compatible with the maps induced by cobordisms. We also prove that if {\xi}
is a contact structure on Y, then the grading of the contact invariant c({\xi})
is the homotopy class of {\xi}.


  In this article we develop a multi-grid multi-level Monte Carlo (MGMLMC)
method for the stochastic Stokes-Darcy interface model with random hydraulic
conductivity both in the porous media domain and on the interface. Because the
randomness through the interface affects the flow in the Stokes domain, we
investigate the coupled stochastic Stokes-Darcy model to improve the fidelity
as this model also considers the second and third porosity of the free flow.
Then we prove the existence and uniqueness of the weak solution of the
variational form. For the numerical solution, we adopt the Monte Carlo (MC)
method and finite element method (FEM), for the discrete form in the
probability space and physical space, respectively. In the traditional
single-level Monte Carlo (SLMC) method, more accurate numerical approximate
requires both larger number of samples in probability space and smaller mesh
size in the physical space. Then the computational cost increase significantly
as the mesh size becomes smaller for the more accurate numerical approximate.
Therefore we adopt the multi-level Monte Carlo (MLMC) method to dramatically
reduce the computational cost in the probability space, because the number of
samples decays fast while the mesh size decreases. We also develop a strategy
to calculate the number of samples needed in MLMC method for the stochastic
Stokes-Darcy model. Furthermore MLMC naturally provides the hierarchial grids
and sufficient information on these grids for multi-grid (MG) method, which can
in turn improve the efficiency of MLMC. In order to fully make use of the
dynamical interaction between this two methods, we propose the multi-grid
multi-level Monte Carlo method for more efficiently solving the stochastic
model. Numerical examples are provided to verify and illustrate the proposed
method and the theoretical conclusions.


  The effect of a random magnetic field in the convective zone of the Sun on
resonant neutrino spin oscillations, i.e. transitions of the type
$\nu_{eL}\to\tilde\nu_{\mu R}$, is considered. The average survival probability
and the expected experimental signals in the existing solar neutrino
experiments are computed as a function of the level of the noise and magnitude
of a constant magnetic field in the convective zone. From comparison with
observed detection rates we conclude that the RSFP solutions to the SNP with
negligible mixing angle are stable under the presence of low or moderate levels
of noise. Detection rates, specially in the Homestake experiment, are however
sensitive to large levels of noise. As a consequence, an upper limit on small
scale magnetic fluctuations is obtained from the combined solar data:
$\surd\langle B^2\rangle< 140-200 $ kG for the scale $L_0\sim 1000 $ km and
transition moment $\mu=10^{-11} \mu_B$.


  This article takes up the challenge of extending the classical Real
Nullstellensatz of Dubois and Risler to left ideals in a *-algebra A. After
introducing the notions of non-commutative zero sets and real ideals, we
develop three themes related to our basic question: does an element p of A
having zero set containing the intersection of zero sets of elements from a
finite set S of A belong to the smallest real ideal containing S? Firstly, we
construct some general theory which shows that if a canonical topological
closure of certain objects are permitted, then the answer is yes, while at the
purely algebraic level it is no. Secondly for every finite subset S of the free
*-algebra R<x,x*> of polynomials in g indeterminates and their formal adjoints,
we give an implementable algorithm which computes the smallest real ideal
containing S and prove that the algorithm succeeds in a finite number of steps.
Lastly we provide examples of noncommutative real ideals for which a purely
algebraic non-commutative real Nullstellensatz holds. For instance, this
includes the real (left) ideals generated by a finite sets S in the *-algebra
of n by n matrices whose entries are polynomials in one-variable. Further,
explicit sufficient conditions on a left ideal in R<x,x*> are given which cover
all the examples of such ideals of which we are aware and significantly more.


  We provide a sufficient condition for the numerical range of a nilpotent
matrix N to be circular in terms of the existence of cycles in an undirected
graph associated with N. We prove that if we add to this matrix N a diagonal
real matrix D, the matrix D + N has convex numerical range. For 3 x 3 nilpotent
matrices, we strength further our results and obtain necessary and sufficient
conditions for circularity and convexity of the numerical range.


  In this paper we study the gravitational instability in presence of
viscosity. In particular, the standard Jeans Mechanism is analyzed taking into
account bulk-viscosity effects in the first-order Newtonian dynamics. We show
how the perturbation evolution is damped by dissipative processes and the
top-down fragmentation mechanism is suppressed for strong viscous effects. The
critical value of the Jeans Mass remains unchanged also in presence of bulk
viscosity.


  We derive the general formulas for a special configuration of the sequential
warped product semi-Riemannian manifold to be Einstein, where the base-manifold
is the product of two manifolds both equipped with a conformal metrics.
Subsequently we study the case in which these two manifolds are conformal to a
$n_1$-dimensional and $n_2$-dimensional pseudo-Euclidean space, respectively.
For the latter case, we prove the existence of a family of solutions that are
invariant under the action of a $(n_1-1)$-dimensional group of transformations
to the case of positive constant Ricci curvature ($\lambda>0$).


  This paper describes Picky, a probabilistic agenda-based chart parsing
algorithm which uses a technique called {\em probabilistic prediction} to
predict which grammar rules are likely to lead to an acceptable parse of the
input. Using a suboptimal search method, Picky significantly reduces the number
of edges produced by CKY-like chart parsing algorithms, while maintaining the
robustness of pure bottom-up parsers and the accuracy of existing probabilistic
parsers. Experiments using Picky demonstrate how probabilistic modelling can
impact upon the efficiency, robustness and accuracy of a parser.


  We solve the equation $f(x,y)^3 + g(x,y)^3 = x^3 + y^3$ for homogeneous $f, g
\in \mathbb C(x,y)$, completing an investigation begun by Vi\`ete in 1591. The
usual addition law for elliptic curves and composition give rise to two binary
operations on the set of solutions. We show that a particular subset of the set
of solutions is ring-isomorphic to $\mathbb Z[e^{2 \pi i / 3}]$.


  We study the effects of inhomogeneities on the evolution of the Universe, by
considering a range of cosmological models with discretized matter content.
This is done using exact and fully relativistic methods that exploit the
symmetries in and about submanifolds of spacetimes that themselves possess no
continuous global symmetries. These methods allow us to follow the evolution of
our models throughout their entire history, far beyond what has previously been
possible. We find that while some space-like curves collapse to anisotropic
singularities in finite time, others remain non-singular forever. The resulting
picture is of a cosmological spacetime in which some behaviour remains close to
Friedmann-like, while other behaviours deviate radically. In particular, we
find that large-scale acceleration is possible without any violation of the
energy conditions.


  We report a deep learning (DL) framework viz. deep autoencoder that
autonomously discovers an appropriate order parameter from molecular dynamics
(MD) simulation data to characterize the coil to globule phase transition of a
polymer. The deep autoencoder encodes the 3N dimensional MD trajectory of a
polymer in a one-dimensional feature space and, subsequently, decodes the
one-dimensional feature to its original 3N dimensional polymer trajectory. The
feature space representation of a polymer provides a new order parameter that
accurately describes the coil to globule phase transition as a function of
temperature. This method is very generic and extensible to identify flexible
order parameters to characterize wide range of phase transitions that take
place in polymers and other soft materials. Moreover, this MD-DL approach is
computational very efficient than a pure MD based characterization of phase
transition, and has potential implications in accelerating phase prediction.


  We argue that the decays of radioactive nuclei related to $^{44}$Ti and
$^{56}$Ni ejected during supernova explosions can provide a vast pool of mildly
relativistic positrons and electrons which are further accelerated to
ultrarelativistic energies by reverse and forward shocks. This interesting link
between two independent processes - the radioactivity and the particle
acceleration - can be a clue for solution of the well known theoretical problem
of electron injection in supernova remnants. In the case of the brightest radio
source Cas A, we demonstrate that the radioactivity can supply adequate number
of energetic electrons and positrons for interpretation of observational data
provided that they are stochastically pre-accelerated in the upstream regions
of the forward and reverse shocks.


  We derive a simplified general expression for the two-body scalar Casimir
energy in generalized separable coordinate systems. We apply this technique to
the case of radial semi-transparent planes in the annular region between two
concentric Dirichlet cylinders. This situation is explored both analytically
and numerically.


  We study the superfluid transition in a quasi-two-dimensional Fermi gas with
a magnetic field tuning through a Feshbach resonance. Using an effective
two-dimensional Hamiltonian with renormalized interaction between atoms and
dressed molecules, we investigate the Berezinskii-Kosterlitz-Thouless
transition temperature by studying the phase fluctuation effect. We also take
into account the trapping potential in the radial plane, and discuss the number
and superfluid density distributions. These results can be compared to
experimental outcomes for gases prepared in one-dimensional optical lattices.


  The magnetic structure of the intermetallic antiferromagnet Sm2IrIn8 was
determined using x-ray resonant magnetic scattering (XRMS). Below TN = 14.2,
Sm2IrIn8 has a commensurate antiferromagnetic structure with a propagation
vector (1/2,0,0). The Sm magnetic moments lie in the ab plane and are rotated
roughly 18 degrees away from the a axis. The magnetic structure of this
compound was obtained by measuring the strong dipolar resonant peak whose
enhancement was of over two orders of magnitude at the L2 edge. At the L3 edge
both quadrupolar and dipolar features were observed in the energy line shape.
The magnetic structure and properties of Sm2IrIn8 are found to be consistent
with the general trend already seen for the Nd-, Tb- and the Ce-based compounds
from the RmMnIn3m+2n family (R = rare earth; M=Rh or Ir, m = 1, 2; n = 0, 1),
where the crystalline electrical field (CEF) effects determine the direction of
magnetic moments and the TN evolution in the series. The measured Neel
temperature for Sm2IrIn8 is slightly suppressed when compared to the TN of the
parent cubic compound SmIn3.


  We describe the mathematical underpinnings of the biorthogonal von Neumann
method for quantum mechanical simulations (PvB). In particular, we present a
detailed discussion of the important issue of non-orthogonal projection onto
subspaces of biorthogonal bases, and how this differs from orthogonal
projection. We present various representations of the Schr\"odinger equation in
the reduced basis and discuss their relative merits. We conclude with
illustrative examples and a discussion of the outlook and challenges ahead for
the PvB representation.


  We study geometric and topological properties of singularities on the
boundaries of $\varepsilon$-neighbourhoods $E_\varepsilon = \{x \in
\mathbb{R}^2 : \textrm{dist}(x, E) \leq \varepsilon \}$ of planar sets $E
\subset \mathbb{R}^2$. We develop a novel technique for analysing the boundary
and obtain, for a compact set $E$ and $\varepsilon > 0$, a classification of
singularities (i.e. non-smooth points) on $\partial E_\varepsilon$ into eight
categories. We also show that the set of singularities is either countable or
the disjoint union of a countable set and a closed, totally disconnected,
nowhere dense set.


  We demonstrate the suppression of crosstalk between two dielectric
nanowaveguides by placing an auxiliary linear waveguide between loaded
waveguides spaced by one wavelength. The total cross-sectional dimension of the
system containing two transmission lines is less than two microns that is
hundred times smaller than a cross-section of a system made of dielectric
fiber. The propagating modes in these waveguides are the sum and the difference
of symmetric and antisymmetric modes of the coupled system. Crosstalk is
suppressed by matching the wavenumbers of these modes. The analytically
obtained results are confirmed by numerical simulation.


  Both syntax-phonology and syntax-semantics interfaces in Higher Order Grammar
(HOG) are expressed as axiomatic theories in higher-order logic (HOL), i.e. a
language is defined entirely in terms of provability in the single logical
system. An important implication of this elegant architecture is that the
meaning of a valid expression turns out to be represented not by a single, nor
even by a few "discrete" terms (in case of ambiguity), but by a "continuous"
set of logically equivalent terms. The note is devoted to precise formulation
and proof of this observation.


  Many problems in computational neuroscience, neuroinformatics, pattern/image
recognition, signal processing and machine learning generate massive amounts of
multidimensional data with multiple aspects and high dimensionality. Tensors
(i.e., multi-way arrays) provide often a natural and compact representation for
such massive multidimensional data via suitable low-rank approximations. Big
data analytics require novel technologies to efficiently process huge datasets
within tolerable elapsed times. Such a new emerging technology for
multidimensional big data is a multiway analysis via tensor networks (TNs) and
tensor decompositions (TDs) which represent tensors by sets of factor
(component) matrices and lower-order (core) tensors. Dynamic tensor analysis
allows us to discover meaningful hidden structures of complex data and to
perform generalizations by capturing multi-linear and multi-aspect
relationships. We will discuss some fundamental TN models, their mathematical
and graphical descriptions and associated learning algorithms for large-scale
TDs and TNs, with many potential applications including: Anomaly detection,
feature extraction, classification, cluster analysis, data fusion and
integration, pattern recognition, predictive modeling, regression, time series
analysis and multiway component analysis.
  Keywords: Large-scale HOSVD, Tensor decompositions, CPD, Tucker models,
Hierarchical Tucker (HT) decomposition, low-rank tensor approximations (LRA),
Tensorization/Quantization, tensor train (TT/QTT) - Matrix Product States
(MPS), Matrix Product Operator (MPO), DMRG, Strong Kronecker Product (SKP).


  We present simulation results of the ground state structure and dynamics of
quantum droplets in one-dimensional spin-orbit coupled binary Bose-Einstein
condensates. We have considered two cases for this analysis, such as (i) the
mean-field term has a vanishingly small contribution utilizing the equal and
opposite inter- and intraspecies interaction and (ii) unequal inter- and
intraspecies interaction. For both cases, it shows remarkably different natures
of the quantum droplet. In the former case, it exhibits bright sech-like
droplet nature, while in the latter case, we find the flattened sech-like shape
of the droplet. Further, we analyze the effect of velocity perturbation on the
dynamics in both cases. For the first case, we find a systematic change from
the solitonic droplet nature to the breathing droplet which finally has a
moving droplet feature upon increasing the velocity. However, the second case
shows similar dynamics except having more dynamically stable features than the
first. Finally, we present various dynamics that ensued in the quantum droplet
due to the quenching of the interaction parameters, coupling parameters or
allowing the droplet to undergo collisions.


  In this paper, describing function method is used to analyze the
characteristics and parameters selection of differentiators. Nonlinear
differentiator is an effective compensation to linear differentiator, and
hybrid differentiator consisting of linear and nonlinear parts is the
combination of both advantages of linear and nonlinear differentiators. The
merits of the hybrid differentiator include its simplicity, rapid convergence
at all times, and restraining noises effectively. The methods are confirmed by
some examples.


  We studied the crystal structure and spin state of MnP under high pressure
with synchrotron X-ray diffraction and X-ray emission spectroscopy. MnP has an
exceedingly strong anisotropy in compressibility, with the primary compressible
direction along the b axis of the Pnma structure. X-ray emission spectroscopy
reveals a pressure-driven quenching of the spin state in MnP. Firstprinciples
calculations suggest that the strongly anisotropic compression behavior
significantly enhances the dispersion of the Mn d-orbitals and the splitting of
the d orbital levels compared to the hypothetical isotropic compression
behavior. Thus, we propose spin quenching results mainly from the significant
enhancement of the itinerancy of d electrons and partly from spin rearrangement
occurring in the split d-orbital levels near the Fermi level. This explains the
fast suppression of magnetic ordering in MnP under high pressure. The spin
quenching lags behind the occurrence of superconductivity at ~8 GPa implying
that spin fluctuations govern the electron pairing for superconductivity.


  Let $k$ be a nonperfect separably closed field. Let $G$ be a (possibly
non-connected) reductive group defined over $k$. We study rationality problems
for Serre's notion of complete reducibility of subgroups of $G$. In our
previous work, we constructed examples of subgroups $H$ of $G$ that are
$G$-completely reducible but not $G$-completely reducible over $k$ (and vice
versa). In this paper, we give a theoretical underpinning of those
constructions. To illustrate our result, we present a new such example in a
non-connected reductive group of type $D_4$ in characteristic $2$. Then using
Geometric Invariant Theory, we generalize the theoretical result above
obtaining a new result on the structure of $G(k)$-(and $G$-) orbits in an
arbitrary affine $G$-variety. We translate our result into the language of
spherical buildings to give a topological viewpoint. A problem on centralizers
of completely reducible subgroups and a problem concerning the number of
conjugacy classes are also considered.


  Accurate and automated segmentation of multi-structure (i.e., kidneys, renal
tu-mors, arteries, and veins) from 3D CTA is one of the most important tasks
for surgery-based renal cancer treatment (e.g., laparoscopic partial
nephrectomy). This paper briefly presents the main technique details of the
multi-structure seg-mentation method in MICCAI 2022 KIPA challenge. The main
contribution of this paper is that we design the 3D UNet with the large context
information cap-turing capability. Our method ranked eighth on the MICCAI 2022
KIPA chal-lenge open testing dataset with a mean position of 8.2. Our code and
trained models are publicly available at
https://github.com/fengjiejiejiejie/kipa22_nnunet.


  Let $G=(V(G),E(G))$ be a graph. A function $f:V(G)\rightarrow
\mathbb{P}(\{1,2\})$ is a $2$-rainbow dominating function if for every vertex
$v$ with $f(v)=\emptyset$, $f\big{(}N(v)\big{)}=\{1,2\}$. An outer-independent
$2$-rainbow dominating function (OI$2$RD function) of $G$ is a $2$-rainbow
dominating function $f$ for which the set of all $v\in V(G)$ with
$f(v)=\emptyset$ is independent. The outer independent $2$-rainbow domination
number (OI$2$RD number) $\gamma_{oir2}(G)$ is the minimum weight of an OI$2$RD
function of $G$.
  In this paper, we first prove that $n/2$ is a lower bound on the OI$2$RD
number of a connected claw-free graph of order $n$ and characterize all such
graphs for which the equality holds, solving an open problem given in an
earlier paper. In addition, a study of this parameter for some graph products
is carried out. In particular, we give a closed (resp. an exact) formula for
the OI$2$RD number of rooted (resp. corona) product graphs and prove upper
bounds on this parameter for the Cartesian product and direct product of two
graphs.


  In this paper, we remove certain hypothesis in the theorem of
Bertolini-Darmon on the rationality of Stark-Heegner points over narrow genus
class fields of real quadratic fields. Along the way, we establish that certain
normalized special values of $L$-functions are squares of rational numbers, a
result that is of independent interest, and can be regarded as instances of the
rank zero case of the Birch and Swinnerton-dyer conjecture modulo squares.


  We simulate a theory with two dynamical O($a$) improved Wilson quarks whose
mass $M$ ranges from a factor eight up to a factor two below the charm quark
mass and at three values of the lattice spacing ranging from 0.066 to 0.034 fm.
This theory is a prototype to study the decoupling of heavy quarks. We measure
the mass and cut-off dependence of ratios of gluonic observables defined from
the Wilson flow or the static potential. The size of the 1/$M$ corrections can
be determined and disentangled from the lattice artifacts. The difference with
the pure gauge theory is at the percent level when two quarks with a mass of
the charm quark are present.


  Point-like Liouville integrable dynamical defects are introduced in the
context of the Landau-Lifshitz and Principal Chiral (Faddeev-Reshetikhin)
models. Based primarily on the underlying quadratic algebra we identify the
first local integrals of motion, the associated Lax pairs as well as the
relevant sewing conditions around the defect point. The involution of the
integrals of motion is shown taking into account the sewing conditions.


  A hierarchy of pairwise commuting Hamiltonians for the quantum periodic
Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors
of these Hamiltonians are Jack symmetric functions of infinitely many variables
$x_1,x_2,\ldots$. This construction provides explicit expressions for the
Hamiltonians in terms of the power sum symmetric functions
$p_n=x_1^n+x_2^n+\cdots$ and is based on our recent results from [Comm. Math.
Phys. 324 (2013), 831-849, arXiv:1212.2781].


  Decentralized partially observable Markov decision process (DEC-POMDP) models
sequential decision making problems by a team of agents. Since the planning of
DEC-POMDP can be interpreted as the maximum likelihood estimation for the
latent variable model, DEC-POMDP can be solved by the EM algorithm. However, in
EM for DEC-POMDP, the forward--backward algorithm needs to be calculated up to
the infinite horizon, which impairs the computational efficiency. In this
paper, we propose the Bellman EM algorithm (BEM) and the modified Bellman EM
algorithm (MBEM) by introducing the forward and backward Bellman equations into
EM. BEM can be more efficient than EM because BEM calculates the forward and
backward Bellman equations instead of the forward--backward algorithm up to the
infinite horizon. However, BEM cannot always be more efficient than EM when the
size of problems is large because BEM calculates an inverse matrix. We
circumvent this shortcoming in MBEM by calculating the forward and backward
Bellman equations without the inverse matrix. Our numerical experiments
demonstrate that the convergence of MBEM is faster than that of EM.


  Entropic arguments are shown to play a central role in the foundations of
quantum theory. We prove that probabilities are given by the modulus squared of
wave functions, and that the time evolution of states is linear and also
unitary.


  Motivated by the cosmic censorship conjecture in mathematical relativity, we
establish the precise mass lower bound for an asymptotically flat Riemannian
3-manifold with nonnegative scalar curvature and minimal surface boundary, in
terms of angular momentum and charge. In particular this result does not
require the restrictive assumptions of simple connectivity and completeness,
which are undesirable from both a mathematical and physical perspective.


  Shape Invariant potentials in the sense of [Gendenshte\"{\i}n L.\'E., JETP
Lett. 38, (1983) 356] which depend on more than two parameters are not know to
date. In [Cooper F., Ginocchio J.N. and Khare A., Phys. Rev. {\bf 36 D}, (1987)
2458] was posed the problem of finding a class of Shape Invariant potentials
which depend on n parameters transformed by translation, but it was not solved.
We analyze the problem using some properties of the Riccati equation and we
find the general solution.


  Transient structural changes of Al$_2$O$_3$ on subatomic length scales
following irradiation with an intense x-ray laser pulse (photon energy: 8.70
keV; pulse duration: 6 fs; fluence: 8$\times$10$^2$ J/cm$^{2}$) have been
investigated by using an x-ray pump x-ray probe technique. The measurement
reveals that aluminum and oxygen atoms remain in their original positions by
$\sim$20 fs after the intensity maximum of the pump pulse, followed by
directional atomic displacements at the fixed unit cell parameters. By
comparing the experimental results and theoretical simulations, we interpret
that electron excitation and relaxation triggered by the pump pulse modifies
the potential energy surface and drives the directional atomic displacements.
Our results indicate that high-resolution x-ray structural analysis with the
accuracy of 0.01 \AA is feasible even with intense x-ray pulses by making the
pulse duration shorter than the timescale needed to complete electron
excitation and relaxation processes, which usually take up to a few tens of
femtoseconds.


  We calculate the branching ratios of pure annihilation type decays
$B^0\rightarrow D_{s}^{-}K_{2}^{*+}$ and $B_s\rightarrow \bar{D}a_{2}$ using
the perturbative QCD approach based on $k_T$ factorization. The branching
ratios are predicted to be $(60.6_{-16.5\,-10.4\,-2.1}^{+17.3\,+4.3\,+3.2})
\times 10^{-6}$ for $B^0\rightarrow D_{s}^{-}K_{2}^{*+}$,
$(1.1_{-0.4\,-0.2\,-0.1}^{+0.4\,+0.1\,+0.1})\times 10^{-6}$ for $B_s\rightarrow
\bar{D}a_{2}^{0}$ and $(2.3_{-0.8\,-0.4\,-0.1}^{+0.8\,+0.2\,+0.1})\times
10^{-6}$ for $B_{s}\rightarrow D^{-}a_{2}^{+}$.
  They are large enough to be measured in the ongoing experiment. Due to the
shortage of contributions from penguin operators, there are no direct CP
asymmetries for these decays in the standard model. We also derive simple
relations among these decay channels to reduce theoretical uncertainties for
the experiments to test the accuracy of theory and search of new physics
signal.


  Transport properties of dense QCD matter is discussed. Using the Kubo formula
for conductivity, we discuss some topological aspects of quark matter during
chiral transition. The close relation to Weyl semimetal is pointed out and
anomalous Hall effect is demonstrated to be possible there. In particular, it
is shown that the spectral asymmetry of the quasi-particles plays an important
role for the Hall conductivity in the magnetic field.


  Service virtualisation is a supporting tool for DevOps to generate
interactive service models of dependency systems on which a system-under-test
relies. These service models allow applications under development to be
continuously tested against production-like conditions. Generating these
virtual service models requires expert knowledge of the service protocol, which
may not always be available. However, service models may be generated
automatically from network traces. Previous work has used the Needleman-Wunsch
algorithm to select a response from the service model to play back for a live
request. We propose an extension of the Needleman-Wunsch algorithm, which uses
entropy analysis to automatically detect the critical matching fields for
selecting a response. Empirical tests against four enterprise protocols
demonstrate that entropy weighted matching can improve response accuracy.


  One-dimensional particle-in-cell simulation is used to simulate the
capacitively coupled argon plasma for a range of driving frequency from 13.56
MHz to 100 MHz. The argon chemistry set can, selectively, include two
metastable levels enabling multi-step ionization and metastable pooling. The
results show that the plasma density decreases when metastable atoms are
included with higher discrepancy at higher excitation frequency. The
contribution of multistep ionization to overall density increases with
excitation frequency. The electron temperature increases with the inclusion of
metastable atoms and decreases with excitation frequency. At lower excitation
frequency, the density of Ar** (3p5 4p, 13.1 eV) is higher than Ar* (3p5 4s,
11.6 eV), whereas, at higher excitation frequencies the Ar* (3p5 4s, 11.6 eV)
is the dominant metastable atom. The metastable and electron temperature
profile evolve from a parabolic profile at lower excitation frequency to a
saddle type profile at higher excitation frequency. With metastable, the
electron energy distribution function (EEDF) changes its shape from Druyvesteyn
type, at low excitation frequency, to bi-Maxwellian, at high frequency plasma
excitation, however a three-temperature EEDF is observed without metastable
atoms.


  We propose to use the Balescu-Lenard-Vlasov (BLV) equation to describe
relativistic heavy ion collisions. We use an inter-quark Richardson's potential
consistent with the indications of Lattice QCD calculations. The color degrees
of freedom are explicitly taken into account.
  We explicitly demonstrate that the Vlasov approach alone is insufficient in
the hadronization region.
  In order to overcome this problem we prepare the initial condition for many
events using molecular dynamics with frictional cooling and a Thomas-Fermi
approximation to the Fermi motion.
  These events are averaged and propagated in time using the Vlasov approach.
The fluctuations are used to evaluate the collision term and in turn the number
of q-$\bar q$ created.


Introducing the discussion paper by Sz\'{e}kely and Rizzo


  We consider a new type of mappings in metric spaces which can be
characterized as mappings contracting perimeters of triangles. It is shown that
such mappings are continuous. The fixed-point theorem for such mappings is
proved and the classical Banach fixed-point theorem is obtained like a simple
corollary. An example of a mapping contractive perimeters of triangles which is
not a contraction mapping is constructed.


  We advance an exact, explicit form for the solutions to the fractional
diffusion-advection equation. Numerical analysis of this equation shows that
its solutions resemble power-laws.


  In this paper, we establish the existence of $p$-energy norms and the
corresponding $p$-energy measures for scale-irregular Vicsek sets, which may
lack self-similarity. We also investigate the characterizations of $p$-energy
norms in terms of Besov-Lipschitz norms, with their weak monotonicity and the
corresponding Bourgain-Brezis-Mironescu convergence.


  We propose a CFT unitary description of the gravitational collapse. The
starting point is the model of a black hole in AdS proposed by Maldacena in
arXiv: 0106112 [hep-th]. We show that by proposing a two-copies version of the
AdS/CFT conjecture, the process of formation of black holes so as other
spacetimes with horizons may be described as an unitary process in the dual
field theory. In doing this, we construct a well defined framework to describe
general spacetimes as entangled states, in terms of the spectrum of states on
the exact Anti-de-Sitter background. As application, we show how the
description of the Hawking-Page transition results simplified in this formalism
and some novel aspects may be observed. Finally, a simplified analysis based on
weakly coupled bulk fields is discussed.


  We extend results on generic strange duality for K3 surfaces by showing that
the proposed isomorphism holds over an entire Noether-Lefschetz divisor in the
moduli space of quasipolarized K3s. We interpret the statement globally as an
isomorphism of sheaves over this divisor, and also describe the global
construction over the space of polarized K3s.


  Iterative methods based on matrix splittings are useful in solving large
sparse linear systems. In this direction, proper splittings and its several
extensions are used to deal with singular and rectangular linear systems. In
this article, we introduce a new iteration scheme called three-step alternating
iterations using proper splittings and group inverses to find an approximate
solution of singular linear systems, iteratively. A preconditioned alternating
iterative scheme is also proposed to relax some sufficient conditions and to
obtain faster convergence as well. We then show that our scheme converges
faster than the existing one. The theoretical findings are then validated
numerically.


  Acid-base reactions are ubiquitous in nature. Understanding their mechanisms
is crucial in many fields, from biochemistry to industrial catalysis.
Unfortunately, experiments only give limited information without much insight
into the molecular behaviour. Atomistic simulations could complement
experiments and shed precious light on microscopic mechanisms. The large free
energy barriers connected to proton dissociation however make the use of
enhanced sampling methods mandatory. Here we perform an ab initio molecular
dynamics (MD) simulation and enhance sampling with the help of methadynamics.
This has been made possible by the introduction of novel descriptors or
collective variables (CVs) that are based on a conceptually new outlook on
acid-base equilibria. We test successfully our approach on three different
aqueous solutions of acetic acid, ammonia, and bicarbonate. These are
representative of acid, basic, and amphoteric behaviour.


  Reflecting intelligent surface (RIS) has emerged as a promising technology
for enhancing wireless communication performance and enabling new applications
in 6G networks with potentially low energy consumption and hardware complexity
thanks to their passive nature. Despite the significant growth of the
literature on RIS in recent years, covering various aspects of this technology,
challenges and issues regarding the practical implementation of RIS have been
less addressed. This issue is even more severe at D-band frequencies due to the
inherent challenges. This paper aims to connect the requirements and
aspirations from the link-level side to the actually achievable RIS hardware
with the focus on the various models for RIS. In order to obtain a realistic
hardware scenario while maintaining a manageable parameter set, a static
reflect array with similar reflection behavior as the reconfigurable one is
employed. The results of the study enable an improved RIS design process due to
more realistic models. The special focus of this paper is on the hardware
impairments, in particular, (i) the effect of specular reflection, and (ii) the
beam squint effect.


  Algorithms are now routinely used to make consequential decisions that affect
human lives. Examples include college admissions, medical interventions or law
enforcement. While algorithms empower us to harness all information hidden in
vast amounts of data, they may inadvertently amplify existing biases in the
available datasets. This concern has sparked increasing interest in fair
machine learning, which aims to quantify and mitigate algorithmic
discrimination. Indeed, machine learning models should undergo intensive tests
to detect algorithmic biases before being deployed at scale. In this paper, we
use ideas from the theory of optimal transport to propose a statistical
hypothesis test for detecting unfair classifiers. Leveraging the geometry of
the feature space, the test statistic quantifies the distance of the empirical
distribution supported on the test samples to the manifold of distributions
that render a pre-trained classifier fair. We develop a rigorous hypothesis
testing mechanism for assessing the probabilistic fairness of any pre-trained
logistic classifier, and we show both theoretically as well as empirically that
the proposed test is asymptotically correct. In addition, the proposed
framework offers interpretability by identifying the most favorable
perturbation of the data so that the given classifier becomes fair.


  We report on the extension of the experiments (P. M. Walmsley et al., Phys.
Rev. Lett. 99, 265302 (2007)) on the decay of quasiclassical turbulence
generated by an impulsive spin-down from angular velocity Omega to rest of
superfluid 4He in a cubic container at temperatures 0.15 K - 1.6 K. The density
of quantized vortex lines L is measured by scattering negative ions. Following
the spin-down, the maximal density of vortices is observed after time t ~ 10
Omega^-1. By observing the propagation of ions along the axis of the initial
rotation, the transient dynamics of the turbulence spreading from the perimeter
of the container into its central region is investigated. Nearly homogeneous
turbulence develops after time t ~ 100 Omega^-1 and decays as L proportional to
t^(-3/2). The effective kinematic viscosity in T=0 limit is nu = 0.003 kappa,
where kappa=10^-3 cm^2 / s is the circulation quantum.