  This is an extended and pedagogically oriented version of our recent work, in
which we proposed an improvement of the splitting functions at small x which
overcomes the apparent problems encountered by the BFKL approach.


  We develop the GKM theory for the torus-equivariant cohomology of the affine
flag variety using the combinatorics of alcove walks. Dual to the usual GKM
setup, which depicts the orbits of the small torus action on a graph, alcove
walks take place in tessellations of Euclidean space. Walks in affine rank two
occur on triangulations of the plane, providing a more direct connection to
splines used for approximating surfaces. Alcove walks in GKM theory also need
not be minimal length, and can instead be randomly generated, giving rise to
more flexible implementation. This work reinterprets and recovers classical
results in GKM theory on the affine flag variety, generalizing them to both
non-minimal and folded alcove walks, all motivated by applications to splines.


  In this paper, we consider the finite temperature behaviour of the CPT-even
aether-like Lorentz-breaking term in the extended Lorentz-breaking QED and
demonstrate that its ambiguities whose presence has been shown earlier in the
zero temperature case stay also at the finite temperature.


  We introduce a topological theory to study quasiparticles in interacting
and/or disordered many-body systems, which have a finite lifetime due to
inelastic and/or elastic scattering. The one-body quasiparticle Hamiltonian
includes both the Bloch Hamiltonian of band theory and the self-energy due to
interactions, which is non-Hermitian when quasiparticle lifetime is finite. We
study the topology of non-Hermitian quasiparticle Hamiltonians in momentum
space, whose energy spectrum is complex. The interplay of band structure and
quasiparticle lifetime is found to have remarkable consequences in zero- and
small-gap systems. In particular, we predict the existence of topological
exceptional point and bulk Fermi arc in Dirac materials with two distinct
quasiparticle lifetimes.


  Gravitational field equations in Randers-Finsler space of approximate Berwald
type are investigated. A modified Friedmann equation and a new luminosity
distance-redshift relation is proposed. A best-fit to the Type Ia supernovae
(SNe) observations yields that the $\Omega_{\Lambda}$ in the $\Lambda$-CDM
model is suppressed to almost zero. This fact indicates that the astronomical
observations on the Type Ia SNe can be described well without invoking any form
of dark energy. The best-fit age of the universe is given. It is in agreement
with the age of our galaxy.


  Attributed to the ever-increasing large image datasets, Convolutional Neural
Networks (CNNs) have become popular for vision-based tasks. It is generally
admirable to have larger-sized datasets for higher network training accuracies.
However, the impact of dataset quality has not to be involved. It is reasonable
to assume the near-duplicate images exist in the datasets. For instance, the
Street View House Numbers (SVHN) dataset having cropped house plate digits from
0 to 9 are likely to have repetitive digits from the same/similar house plates.
Redundant images may take up a certain portion of the dataset without
consciousness. While contributing little to no accuracy improvement for the
CNNs training, these duplicated images unnecessarily pose extra resource and
computation consumption. To this end, this paper proposes a framework to assess
the impact of the near-duplicate images on CNN training performance, called
CE-Dedup. Specifically, CE-Dedup associates a hashing-based image deduplication
approach with downstream CNNs-based image classification tasks. CE-Dedup
balances the tradeoff between a large deduplication ratio and a stable accuracy
by adjusting the deduplication threshold. The effectiveness of CE-Dedup is
validated through extensive experiments on well-known CNN benchmarks. On one
hand, while maintaining the same validation accuracy, CE-Dedup can reduce the
dataset size by 23%. On the other hand, when allowing a small validation
accuracy drop (by 5%), CE-Dedup can trim the dataset size by 75%.


  Ice templating, also known as freeze casting, is a popular shaping route for
macroporous materials. Over the past 15 years, it has been widely applied to
various classes of materials, and in particular ceramics. Many formulation and
process parameters, often interdependent, affect the outcome. It is thus
difficult to understand the various relationships between these parameters from
isolated studies where only a few of these parameters have been investigated.
We report here the results of a meta analysis of the structural and mechanical
properties of ice templated materials from an exhaustive collection of records.
We use these results to identify which parameters are the most critical to
control the structure and properties, and to derive guidelines to optimize the
mechanical response of ice templated materials. We hope these results will be a
helpful guide to anyone interested in such materials.


  We present new solutions of the $d=5$ Einstein-Yang-Mills theory describing
black holes with squashed horizons. These configurations are asymptotically
locally flat and have a boundary topology of a fibre bundle $R\times S^1
\hookrightarrow S^{2}$. In a $d=4$ picture, they describe black hole solutions
with both nonabelian and U(1) magnetic charges.


  We discuss strangeness production close to threshold in p+A and A+A
collision. Comparing the body of available K+, K0, K-, and Lambda data with the
IQMD transport code and for some key observables as well with the HSD transport
code, we find good agreement for the large majority of the observables. The
investigation of the reaction with help of these codes reveals the complicated
interaction of the strange particles with hadronic matter which makes
strangeness production in heavy-ion collisions very different from that in
elementary interactions. We show how different strange particle observables can
be used to study the different facets of this interaction (production,
rescattering and potential interaction) which finally merge into a
comprehensive understanding of these interactions. We identify those
observables which allow for studying (almost) exclusively one of these
processes to show how future high precision experiments can improve our
quantitative understanding. Finally, we discuss how the K+ multiplicity can be
used to study the hadronic equation of state.


  The accessibility of content for all has been a key goal of the Web since its
conception. However, true accessibility -- access to relevant content in the
global context -- has been elusive for reasons that extend beyond physical
accessibility issues. Among them are the spoken languages, literacy levels,
expertise, and culture. These issues are highly significant, since information
may not reach those who are the most in need of it. For example, the minimum
wage laws that are published in legalese on government sites and the
low-literate and immigrant populations. While some organizations and volunteers
work on bridging such gaps by creating and disseminating alternative versions
of such content, Web scale solutions much be developed to take advantage of its
distributed dissemination capabilities. This work examines content
accessibility from the perspective of inclusiveness. For this purpose, a human
in the loop approach for renarrating Web content is proposed, where a
renarrator creates an alternative narrative of some Web content with the intent
of extending its reach. A renarration relates some Web content with an
alternative version by means of transformations like simplification,
elaboration, translation, or production of audio and video material. This work
presents a model and a basic architecture for supporting renarrations along
with various scenarios. We also discuss the potentials of the W3C specification
for Web Annotation Data Model towards a more inclusive and decentralized social
web.


  Techniques based on minimal graph cuts have become a standard tool for
solving combinatorial optimization problems arising in image processing and
computer vision applications. These techniques can be used to minimize
objective functions written as the sum of a set of unary and pairwise terms,
provided that the objective function is submodular. This can be interpreted as
minimizing the $l_1$-norm of the vector containing all pairwise and unary
terms. By raising each term to a power $p$, the same technique can also be used
to minimize the $l_p$-norm of the vector. Unfortunately, the submodularity of
an $l_1$-norm objective function does not guarantee the submodularity of the
corresponding $l_p$-norm objective function. The contribution of this paper is
to provide useful conditions under which an $l_p$-norm objective function is
submodular for all $p\geq 1$, thereby identifying a large class of $l_p$-norm
objective functions that can be minimized via minimal graph cuts.


  In recent years, there has been growing interest in using photonic technology
to perform the underlying linear algebra operations required by different
applications, including neuromorphic photonics, quantum computing and microwave
processing, mainly aiming at taking advantage of the silicon photonics' (SiPho)
credentials to support high-speed and energy-efficient operations. Mapping,
however, a targeted matrix with absolute accuracy into the optical domain
remains a huge challenge in linear optics, since state-of-the-art linear
optical circuit architectures are highly sensitive to fabrication
imperfections. This leads to reduced fidelity metrics that degrade faster as
the insertion losses of the constituent optical matrix node or the matrix
dimensions increase. In this work, we present for the first time a novel
coherent SiPho crossbar (Xbar) that can support on-chip fidelity restoration
while implementing linear algebra operations, realizing the first experimental
demonstration of perfect on-chip arbitrary linear optical transformations. We
demonstrate the experimental implementation of 10000 arbitrary linear
transformations in the photonic domain achieving a record high fidelity of
99.997%+-0.002, limited mainly by the statistical error enforced by the
measurement equipment. Our work represents the first integrated universal
linear optical circuit that provides almost unity and loss-independent fidelity
in the realization of arbitrary matrices, opening new avenues for exploring the
use of light in resolving universal computational tasks.


  The development and deployment of machine learning systems can be executed
easily with modern tools, but the process is typically rushed and
means-to-an-end. The lack of diligence can lead to technical debt, scope creep
and misaligned objectives, model misuse and failures, and expensive
consequences. Engineering systems, on the other hand, follow well-defined
processes and testing standards to streamline development for high-quality,
reliable results. The extreme is spacecraft systems, where mission critical
measures and robustness are ingrained in the development process. Drawing on
experience in both spacecraft engineering and AI/ML (from research through
product), we propose a proven systems engineering approach for machine learning
development and deployment. Our Technology Readiness Levels for ML (TRL4ML)
framework defines a principled process to ensure robust systems while being
streamlined for ML research and product, including key distinctions from
traditional software engineering. Even more, TRL4ML defines a common language
for people across the organization to work collaboratively on ML technologies.


  We argue that a strict relation exists between two in principle unrelated
quantities: The size of the growing domains in a coarsening system, and the
kinetic roughening of an interface. This relation is confirmed by extensive
simulations of the Ising model with different forms of quenched disorder, such
as random bonds, random fields and stochastic dilution.


  In our previous paper, we determined a unified combinatorial framework to
look at a large number of colored partition identities, and studied the five
identities corresponding to the exceptional modular equations of prime degree
of the Schroeter, Russell and Ramanujan type. The goal of this paper is to use
the master bijection of our previous work to show combinatorially several new
and highly nontrivial colored partition identities. We conclude by listing a
number of further interesting identities of the same type as conjectures.


  Let $P=\{p_0,\ldots,p_{n-1}\}$ be a set of points in $\mathbb{R}^d$, modeling
devices in a wireless network. A range assignment assigns a range $r(p_i)$ to
each point $p_i\in P$, thus inducing a directed communication graph $G_r$ in
which there is a directed edge $(p_i,p_j)$ iff $\textrm{dist}(p_i, p_j) \leq
r(p_i)$, where $\textrm{dist}(p_i,p_j)$ denotes the distance between $p_i$ and
$p_j$. The range-assignment problem is to assign the transmission ranges such
that $G_r$ has a certain desirable property, while minimizing the cost of the
assignment; here the cost is given by $\sum_{p_i\in P} r(p_i)^{\alpha}$, for
some constant $\alpha>1$ called the distance-power gradient.
  We introduce the online version of the range-assignment problem, where the
points $p_j$ arrive one by one, and the range assignment has to be updated at
each arrival. Following the standard in online algorithms, resources given out
cannot be taken away -- in our case this means that the transmission ranges
will never decrease. The property we want to maintain is that $G_r$ has a
broadcast tree rooted at the first point $p_0$. Our results include the
following.
  - For $d=1$, a 1-competitive algorithm does not exist. In particular, for
$\alpha=2$ any online algorithm has competitive ratio at least 1.57.
  - For $d=1$ and $d=2$, we analyze two natural strategies: Upon the arrival of
a new point $p_j$, Nearest-Neighbor increases the range of the nearest point to
cover $p_j$ and Cheapest Increase increases the range of the point for which
the resulting cost increase to be able to reach $p_j$ is minimal.
  - We generalize the problem to arbitrary metric spaces, where we present an
$O(\log n)$-competitive algorithm.


  Existing synthetic datasets (FigureQA, DVQA) for reasoning over plots do not
contain variability in data labels, real-valued data, or complex reasoning
questions. Consequently, proposed models for these datasets do not fully
address the challenge of reasoning over plots. In particular, they assume that
the answer comes either from a small fixed size vocabulary or from a bounding
box within the image. However, in practice, this is an unrealistic assumption
because many questions require reasoning and thus have real-valued answers
which appear neither in a small fixed size vocabulary nor in the image. In this
work, we aim to bridge this gap between existing datasets and real-world plots.
Specifically, we propose PlotQA with 28.9 million question-answer pairs over
224,377 plots on data from real-world sources and questions based on
crowd-sourced question templates. Further, 80.76% of the out-of-vocabulary
(OOV) questions in PlotQA have answers that are not in a fixed vocabulary.
Analysis of existing models on PlotQA reveals that they cannot deal with OOV
questions: their overall accuracy on our dataset is in single digits. This is
not surprising given that these models were not designed for such questions. As
a step towards a more holistic model which can address fixed vocabulary as well
as OOV questions, we propose a hybrid approach: Specific questions are answered
by choosing the answer from a fixed vocabulary or by extracting it from a
predicted bounding box in the plot, while other questions are answered with a
table question-answering engine which is fed with a structured table generated
by detecting visual elements from the image. On the existing DVQA dataset, our
model has an accuracy of 58%, significantly improving on the highest reported
accuracy of 46%. On PlotQA, our model has an accuracy of 22.52%, which is
significantly better than state of the art models.


  We demonstrate a new method for measuring radio frequency (RF) electric
fields based on quantum interference in an atom. Using a bright resonance
prepared within an electromagnetically induced transparency window we are able
to achieve a sensitivity of ~ 30 {\mu}V cm^-1 sqrt(Hz)^-1. For this work, we
demonstrated detection of RF electric fields as small as ~ 8 {\mu}V cm^-1. The
sensitivity is currently limited by the spectral bandwidth of the lasers used
in the experiment and can be significantly improved in the future. The method
can serve as a new quantum based standard for RF electrometry. The
reproducibility, accuracy and stability of using a quantum system for measuring
RF electric fields promises to advance electrometry to the current levels of
magnetometry.


  We investigate the behaviour of a system of particles with the different
character of interaction. The approach makes it possible to describe systems of
interacting particles by statistical methods taking into account a spatial
nonhomogeneous distribution of particles, i.e. cluster formation. For these
clusters are evaluated: their size, the number of particles in a cluster, and
the temperature of phase transition to the cluster state. Three systems are
under consideration: electrons on the liquid helium surface, particles
interacting by the shielding Coulomb potential, which are found under the
influence of an elastic field (e.g. nucleons in a nucleus), and gravitating
masses with the Hubble expansion.


  A forward electromagnetic calorimeter (FoCal) based on SiW technology is
being considered as a possible upgrade to the ALICE detector. This device
should in particular feature an extremely high granularity allowing gamma/pi0
discrimination out to very high momenta. The main option considered for the
high granularity layers is the use of CMOS pixel sensors. We will discuss the
motivation and design principles of the proposed calorimeter and will then
focus on the experience gained with a full CMOS-pixel calorimeter prototype.
Preliminary results of this device show very good capabilities for shower
profile measurements, and reasonable results for linearity and resolution,
which are limited by the currently incomplete calibration.


  We consider how does the introduction of a Polyakov loop affects the
spatially inhomogeneous quark condensate. The primary result of our work is
that the existence of the spatially non-uniform chiral phase is confirmed
within the Polyakov NJL model in a chiral limit. These findings are obtained
both in a 3d-cutoff and in a Schwinger (proper time) regularization schemes.


  We consider a geometric approach to field theory in which torsion is present
beside gravity and also electrodynamics for the matter field equations, and we
develop the consequences of the torsion-spin coupling for the spinor fields; we
show that these interactions have the structure of the weak interactions acting
among leptons: we discuss the implications for the standard model of
fundamental interactions of elementary fields in the perspective of the
foundations of unification in theoretical physics.


  Refractory High-Entropy Alloys (RHEAs) hold promising potential to be used as
structural materials in future nuclear fusion reactors, where W and its alloys
are currently leading candidates. Fusion materials must be able to withstand
extreme conditions, such as (i) severe radiation-damage arising from
highly-energetic neutrons, (ii) embrittlement caused by implantation of H and
He ions, and (iii) exposure to extreme high-temperatures and thermal gradients.
Recent research demonstrated that two RHEAs - the WTaCrV and WTaCrVHf - can
outperform both coarse-grained and nanocrystalline W in terms of its radiation
response and microstructural stability. Chemical complexity and
nanocrystallinity enhance the radiation tolerance of these new RHEAs, but their
multi-element nature, including low-melting Cr, complicates bulk fabrication
and limits practical applications. We demonstrate that reducing the number of
alloying elements and yet retain high-radiation tolerance is possible within
the ternary system W-Ta-V via synthesis of two novel nanocrystalline refractory
medium-entropy alloys (RMEAs): the W$_{53}$Ta$_{44}$V$_{3}$ and
W$_{53}$Ta$_{42}$V$_{5}$ (in at.\%). We experimentally show that the radiation
response of the W-Ta-V system can be tailored by small additions of V, and such
experimental result was validated with theoretical analysis of chemical
short-range orders (CSRO) from combined ab-initio atomistic Monte-Carlo
modeling. It is predicted from computational analysis that a small change in V
concentration has a significant effect on the Ta-V CRSO between
W$_{53}$Ta$_{44}$V$_{3}$ and W$_{53}$Ta$_{42}$V$_{5}$ leading to
radiation-resistant microstructures in these RMEAs from chemistry stand-point
of views. We deviate from the original high-entropy alloy concept to show that
high radiation resistance can be achieved in systems with simplified chemical
complexity.


  In this paper, we propose a semi-supervised clustering method, CEC-IB, that
models data with a set of Gaussian distributions and that retrieves clusters
based on a partial labeling provided by the user (partition-level side
information). By combining the ideas from cross-entropy clustering (CEC) with
those from the information bottleneck method (IB), our method trades between
three conflicting goals: the accuracy with which the data set is modeled, the
simplicity of the model, and the consistency of the clustering with side
information. Experiments demonstrate that CEC-IB has a performance comparable
to Gaussian mixture models (GMM) in a classical semi-supervised scenario, but
is faster, more robust to noisy labels, automatically determines the optimal
number of clusters, and performs well when not all classes are present in the
side information. Moreover, in contrast to other semi-supervised models, it can
be successfully applied in discovering natural subgroups if the partition-level
side information is derived from the top levels of a hierarchical clustering.


  In the paper we prove the existence of probabilistic solutions to systems of
the form $-Au=F(x,u)+\mu$, where $F$ satisfies a generalized sign condition and
$\mu$ is a smooth measure. As for $A$ we assume that it is a generator of a
Markov semigroup determined by a right Markov process whose resolvent is order
compact on $L^1$. This class includes local and nonlocal operators
corresponding to Dirichlet forms as well as some operators which are not in the
variational form. To study the problem we introduce new concept of compactness
property relating the underlying Markov process to almost everywhere
convergence. We prove some useful properties of the compactness property and
provide its characterization in terms of Meyer's property (L) of Markov
processes and in terms of order compactness of the associated resolvent.


  Systematic in vivo validations of computational models of the aortic valve
remain scarce, despite successful validation against in vitro data. Utilizing a
combination of computed tomography and 4D flow magnetic resonance imaging data,
we developed patient-specific fluid-structure interaction models of the aortic
valve immersed in the aorta for five patients in the pre-transcatheter aortic
valve replacement configuration. Incorporating also an in vitro setup of the
valve, our computational models are subjected to rigorous validation against 4D
flow measurements. Our results demonstrate the models' capacity to accurately
replicate flow dynamics within established ranges of uncertainties mainly
arising from 4D flow noise. In addition, we illustrate how computational models
can serve as valuable cross-checks to reduce noise and erratic behaviour of in
vivo data. This study represents a significant step towards integrating in
silico technologies into real clinical contexts, providing a robust framework
for improving aortic stenosis diagnosis and the design of next-generation
aortic valve bioprostheses.


  This extensive review was written for the ``Encyclopedia of Complexity and
System Science'' (Springer, 2008) and addresses a broad audience ranging from
engineers to applied mathematicians, computer scientists and physicists. It
provides an extensive overview of various aspects of pedestrian dynamics,
focussing on evacuation processes. First the current status of empirical
results is critically reviewed as it forms the basis for the calibration of
models needed for quantitative predictions. Then various modeling approaches
are discussed, focussing on cellular automata models. Finally, some specific
applications to safety analysis in public buildings or public transport are
presented.


  We investigate the implications of spin symmetry for heavy quarkonia
production and decay. We first compare spin symmetry predictions for charmonia
and bottomonia radiative transitions with data and find they agree quite well.
We next use spin symmetry along with nonrelativistic QCD power counting to
determine the leading order alignment of P and D-wave orthoquarkonia that are
produced through gluon fragmentation. Finally, we discuss a mechanism which may
resolve the current factor of 30 discrepancy between theoretical predictions
and experimental measurements of prompt $\psi'$ production at the Tevatron.
This mechanism involves gluon fragmentation to a subleading Fock component in
the $\psi'$ wavefunction and yields 100\% transversely aligned $\psi'$'s to
lowest order. Observation of such a large alignment would provide strong
support for this resolution to the $\psi'$ problem.


  Semidefinite programming is an indispensable tool in computer vision, but
general-purpose solvers for semidefinite programs are often too slow and memory
intensive for large-scale problems. We propose a general framework to
approximately solve large-scale semidefinite problems (SDPs) at low complexity.
Our approach, referred to as biconvex relaxation (BCR), transforms a general
SDP into a specific biconvex optimization problem, which can then be solved in
the original, low-dimensional variable space at low complexity. The resulting
biconvex problem is solved using an efficient alternating minimization (AM)
procedure. Since AM has the potential to get stuck in local minima, we propose
a general initialization scheme that enables BCR to start close to a global
optimum - this is key for our algorithm to quickly converge to optimal or
near-optimal solutions. We showcase the efficacy of our approach on three
applications in computer vision, namely segmentation, co-segmentation, and
manifold metric learning. BCR achieves solution quality comparable to
state-of-the-art SDP methods with speedups between 4X and 35X. At the same
time, BCR handles a more general set of SDPs than previous approaches, which
are more specialized.


  A correlation is established between the molecular structure and charge
mobility of discotic mesophases of hexabenzocoronene derivatives by combining
electronic structure calculations, Molecular Dynamics, and kinetic Monte Carlo
simulations. It is demonstrated that this multiscale approach can provide an
accurate ab-initio description of charge transport in organic materials.


  We theoretically investigate the Tunneling Anisotropic Magneto-Seebeck effect
in a realistically-modeled CoPt|MgO|Pt tunnel junction using coherent transport
calculations. For comparison we study the tunneling magneto-Seebeck effect in
CoPt|MgO|CoPt as well. We find that the magneto-Seebeck ratio of CoPt|MgO|Pt
exceeds that of CoPt|MgO|CoPt for small barrier thicknesses, reaching 175% at
room temperature. This result provides a sharp contrast to the
magnetoresistance, which behaves oppositely for all barrier thicknesses and
differs by one order of magnitude between devices. Here the magnetoresistance
results from differences in transmission brought upon by changing the tunnel
junction's magnetization configuration. The magneto-Seebeck effect results from
variations in asymmetry of the energy-dependent transmission instead. We report
that this difference in origin allows for CoPt|MgO|Pt to possess strong thermal
magnetic-transport anisotropy.


  The mathematical formalism commonly used in treating nonlocal highly singular
interactions is revised. The notion of support cone is introduced which
replaces that of support for nonlocalizable distributions. Such support cones
are proven to exist for distributions defined on the Gelfand-Shilov spaces
$S^\beta$, where $0<\beta <1$ . This result leads to a refinement of previous
generalizations of the local commutativity condition to nonlocal quantum
fields. For string propagators, a new derivation of a representation similar to
that of K\"{a}llen-Lehmann is proposed. It is applicable to any initial and
final string configurations and manifests exponential growth of spectral
densities intrinsic in nonlocalizable theories.


  The production of various heavy-quark-containing baryons in electron-positron
annihilation is considered. On the basis of exact formulas that we obtained
previously within full perturbation theory, new numerical calculations of the
respective cross sections are performed, and simple approximate expressions are
then constructed for the results of these calculations. The dependence of the
total cross sections on the masses of constituent quarks is discussed. The
application of the Peterson fragmentation function and a Reggeon-type
fragmentation function to describing differential cross sections is analyzed.


  Translation of the paper ``Simplizialzerlegungen von Beschrankter Flachheit''
by Hans Freudenthal (https://doi.org/10.2307/1968813), in which Freudenthal
answers ``a question by Brouwer about the construction of an infinite series of
subdivisions of a polytope, such that the next element in the sequence is a
subdivision of the previous one and such that the subsimplices that arise do
not become arbitrarily flat.''


  This third paper,devoted to global correspondences of Langlands,bears more
particularly on geometric-shifted bilinear correspondences on mixed (bi)motives
generated under the action of the products,right by left,of differential
elliptic operators.The mathematical frame,underlying these
correspondences,deals with the categories of the Suslin-Voevodsky mixed
(bi)motives and of the Chow mixed (bi)motives which are both in one-to-one
correspondence with the functional representation spaces of the shifted
algebraic bilinear semigroups.A bilinear holomorphic and supercuspidal spectral
representation of an elliptic bioperator is then developed.


  Adversarial attacks (AAs) pose a significant threat to the reliability and
robustness of deep neural networks. While the impact of these attacks on model
predictions has been extensively studied, their effect on the learned
representations and concepts within these models remains largely unexplored. In
this work, we perform an in-depth analysis of the influence of AAs on the
concepts learned by convolutional neural networks (CNNs) using eXplainable
artificial intelligence (XAI) techniques. Through an extensive set of
experiments across various network architectures and targeted AA techniques, we
unveil several key findings. First, AAs induce substantial alterations in the
concept composition within the feature space, introducing new concepts or
modifying existing ones. Second, the adversarial perturbation itself can be
linearly decomposed into a set of latent vector components, with a subset of
these being responsible for the attack's success. Notably, we discover that
these components are target-specific, i.e., are similar for a given target
class throughout different AA techniques and starting classes. Our findings
provide valuable insights into the nature of AAs and their impact on learned
representations, paving the way for the development of more robust and
interpretable deep learning models, as well as effective defenses against
adversarial threats.


  Let $G$ be a cycle or a complete bipartite graph. We show that the binomial
edge ideal $J_{G}$ and its initial ideal with respect to the lexicographic
order have the same extremal Betti number.


  We study the effect of the induced interaction on the superfluidtransition
temperature of a spin-polarized Fermi gas. In the BCS limit, the polarization
is very small in the superfluid state, and the effect of the induced
interaction is almost the same as in the spin-balanced case. The temperature Tt
and the polarization Pt of the tricritical point are both reduced from
mean-field results by a factor about 2.22. This reduction is also significant
beyond the BCS limit. In the unitary limit, we find (Pt,Tt/TF)=(0.42,0.16), in
comparison with mean-field and experimental results.


  We propose a stochastic model of a fragmentation process, developed by taking
into account fragment lifetime as a function of their size based on the Gibrat
process. If lifetime is determined by a power function of fragment size,
numerical results indicate that size distributions at different times can be
collapsed into a single time-invariant curve by scaling size by average
fragment size (i.e., the distribution obeys the dynamical scaling law). If
lifetime is determined by a logarithmic function of fragment size, the
distribution does not obey the scaling law. The necessary and sufficient
condition that the scaling law is obeyed is obtained by a scaling analysis of
the master equation.


  Fractional quantum Hall quasiparticles are famous for having fractional
electric charge. Recent experiments report that the quasiparticles' effective
electric charge determined through tunneling current noise measurements can
depend on the system parameters such as temperature or bias voltage. Several
works proposed to understand this as a signature for edge theory properties
changing with energy scale. I consider two of such experiments and show that in
one of them the apparent dependence of the electric charge on a system
parameter is likely to be an artefact of experimental data analysis.
Conversely, in the second experiment the dependence cannot be explained in such
a way.


  We generalize the Cohen-Lenstra heuristics over function fields to \'{e}tale
group schemes $G$ (with the classical case of abelian groups corresponding to
constant group schemes). By using the results of
Ellenberg-Venkatesh-Westerland, we make progress towards the proof of these
heuristics. Moreover, by keeping track of the image of the Weil-pairing as an
element of $\wedge^2G(1)$, we formulate more refined heuristics which nicely
explain the deviation from the usual Cohen-Lenstra heuristics for abelian
$\ell$-groups in cases where $\ell\mid q-1$; the nature of this failure was
suggested already in the works of Garton, EVW, and others. On the purely large
random matrix side, we provide a natural model which has the correct moments,
and we conjecture that these moments uniquely determine a limiting probability
measure.


  Let $G$ be a finite group acting on $\mathbb{C}^N$. We study the problem of
identifyng the class in $\mathbb{C}^N / G$ of a given signal: this encompasses
several types of problems in signal processing. Some instances include certain
generalizations of phase retrieval, image recognition, the analysis of
textures, etc. In our previous work \cite{prev}, based on an algebraic
approach, we constructed a Lipschitz translation invariant transform -- the
case when $G$ is cyclic. Here, we extend our results to include all finite
Abelian groups. Moreover, we show the existence of a new transform that avoids
computing high powers of the moduli of the signal entries--which can be
computationally taxing. The new transform does not enjoy the algebraic
structure imposed in our earlier work and is thus more flexible. Other (even
lower) dimensional representations are explored, however they only provide an
almost everywhere (actually generic) recovery which is not a significant
drawback for applications. Our constructions are locally robust and provide
alternatives to other statistical and neural networks based methods.


  We classify and construct all irreducible positive energy representations of
the loop group of a compact, connected and simple Lie group and show that they
admit an intertwining action of Diff(S^{1}).


  We prove an asymptotic formula with power saving error term for a certain
triple divisor sum.


  The spinal cord (SC), which conveys information between the brain and the
peripheral nervous system, plays a key role in various neurological disorders
such as multiple sclerosis (MS) and amyotrophic lateral sclerosis (ALS), in
which both gray matter (GM) and white matter (WM) may be impaired. While
automated methods for WM/GM segmentation are now largely available, these
techniques, developed for conventional systems (3T or lower) do not necessarily
perform well on 7T MRI data, which feature finer details, contrasts, but also
different artifacts or signal dropout.
  The primary goal of this study is thus to propose a new deep learning model
that allows robust SC/GM multi-class segmentation based on ultra-high
resolution 7T T2*-w MR images. The second objective is to highlight the
relevance of implementing a specific data augmentation (DA) strategy, in
particular to generate a generic model that could be used for multi-center
studies at 7T.


  We study a competitive optimization version of $\alpha'(G)$, the maximum size
of a matching in a graph $G$. Players alternate adding edges of $G$ to a
matching until it becomes a maximal matching. One player (Max) wants that
matching to be large; the other (Min) wants it to be small. The resulting sizes
under optimal play when Max or Min starts are denoted $\Max(G)$ and $\Min(G)$,
respectively. We show that always $|\Max(G)-\Min(G)|\le 1$. We obtain a
sufficient condition for $\Max(G)=\alpha'(G)$ that is preserved under cartesian
product. In general, $\Max(G)\ge \frac23\alpha'(G)$, with equality for many
split graphs, while $\Max(G)\ge\frac34\alpha'(G)$ when $G$ is a forest.
Whenever $G$ is a 3-regular $n$-vertex connected graph, $\Max(G) \ge n/3$, and
there are such examples with $\Max(G)\le 7n/18$. For an $n$-vertex path or
cycle, the answer is roughly $n/7$.


  The molecular constitutive models, like FENE-P for polymer solutions, are
known to have convergence issues at relatively larger flow rates. In this
study, we investigate the possibility of a numerically efficient GNF-based
approximation of FENE-P, which would closely approximate the flow field.
Firstly, we compare the flow fields predicted by FENE-P and an equivalent GNF
model. For these studies, we considered the flow around a sphere and selected
the Carreau-Yasuda model as the representative GNF. This is made equivalent to
the FENE-P by selecting parameters to equalize the viscosity-shear rate
dependence. Our results show severe deficiencies of the GNF model, owing to its
inability to account for chain stretching, particularly near the stagnation
points. Next, the effect of extensional components on the local viscosity was
added by formulating an equivalent GNF-X [Journal of Rheology 64, 493 (2020)]
model. Even this failed to capture the asymmetry in the stress and flow
profiles and predicted very large stresses at both stagnation points, relative
to FENE-P. Hence, we proposed a novel modified formalism (denoted as GNF-XM)
that was able to capture all trends successfully. The drag coefficients from
GNF-XM agreed well with FENE-P predictions for all flow rates considered.
Significantly, the computational times required to solve the flow field with
GNF-XM is about an order of magnitude lower than that of FENE-P, especially at
higher flow rates. Thus, we have successfully formulated a highly efficient
GNF-based approximation to the FENE-P, whose formalism can be extended to other
similarly complicated constitutive models.


  We are proud to present the papers from the 17th Refinement Workshop,
co-located with FM 2015 held in Oslo, Norway on June 22nd, 2015.
  Refinement is one of the cornerstones of a formal approach to software
engineering: the process of developing a more detailed design or implementation
from an abstract specification through a sequence of mathematically-based steps
that maintain correctness with respect to the original specification.
  This 17th workshop continued a 20+ year tradition under the auspices of the
British Computer Society (BCS) FACS special interest group.
  This is the third volume that has appeared as an EPTCS proceedings, and we
would like to thank the editorial board (and in particular Rob van Glabbeek)
for their help and cooperation in making this happen.
  The organisers would like to thank everyone: the authors, BCS-FACS, EPTCS,
and the organisers of FM 2015 for their help in organising this workshop, the
participants of the workshop, and the reviewers involved in selecting the
papers.


  Consider the following evolution model, proposed in \cite{BS} by Bak and
Sneppen. Put $N$ vertices on a circle, spaced evenly. Each vertex represents a
certain species. We associate with each vertex a random variable, representing
the `state' or `fitness' of the species, with values in $[0,1]$. The dynamics
proceeds as follows. Every discrete time step, we choose the vertex with
minimal fitness, and assign to this vertex, and to its two neighbours, three
new independent fitnesses with a uniform distribution on $[0,1]$. A conjecture
of physicists, based on simulations, is that in the stationary regime, the
one-dimensional marginal distributions of the fitnesses converges, when $N \to
\infty$, to a uniform distribution on $(f,1)$, for some threshold $f<1$.
  In this paper we consider a discrete version of this model, proposed in
\cite{BK}. In this discrete version, the fitness of a vertex can be either 0 or
1. The system evolves according to the following rules. Each discrete time
step, we choose an arbitrary vertex with fitness 0. If all the vertices have
fitness 1, then we choose an arbitrary vertex with fitness 1. Then we update
the fitnesses of this vertex and of its two neighbours by three new independent
fitnesses, taking value 0 with probability $0<q<1$, and 1 with probability
$p=1-q$. We show that if $q$ is close enough to one, then the mean average
fitness in the stationary regime is bounded away from 1, uniformly in the
number of vertices. This is a small step in the direction of the conjecture
mentioned above, and also settles a conjecture mentioned in \cite{BK}.
  Our proof is based on a reduction to a continuous time particle system.


  We calculate the Casimir force and free energy for plane metallic mirrors at
non-zero temperature. Numerical evaluations are given with temperature and
conductivity effects treated simultaneously. The results are compared with the
approximation where both effects are treated independently and the corrections
simply multiplied. The deviation between the exact and approximated results
takes the form of a temperature dependent function for which an analytical
expression is given. The knowledge of this function allows simple and accurate
estimations at the % level.


  For any given algebra of local observables in Minkowski space an associated
scaling algebra is constructed on which renormalization group (scaling)
transformations act in a canonical manner. The method can be carried over to
arbitrary spacetime manifolds and provides a framework for the systematic
analysis of the short distance properties of local quantum field theories. It
is shown that every theory has a (possibly non-unique) scaling limit which can
be classified according to its classical or quantum nature. Dilation invariant
theories are stable under the action of the renormalization group. Within this
framework the problem of wedge (Bisognano-Wichmann) duality in the scaling
limit is discussed and some of its physical implications are outlined.


  In this Letter, we systematically investigate the Leidenfrost temperature for
hot solid substrates with various thermal diffusivities and surface
roughnesses. Based on the experimental results, we build a phenomenological
model that considers the thermal diffusivity of a solid substrate and derive a
relationship between the surface roughness and the resulting vapor film
thickness. The generality of this model is supported by experimental data for
different liquids and solid substrates. Our model thus allows for a theoretical
prediction of the Leidenfrost temperature and develops a comprehensive
understanding of the Leidenfrost effect.


  We present an algorithm for creating high resolution anatomically plausible
images consistent with acquired clinical brain MRI scans with large inter-slice
spacing. Although large data sets of clinical images contain a wealth of
information, time constraints during acquisition result in sparse scans that
fail to capture much of the anatomy. These characteristics often render
computational analysis impractical as many image analysis algorithms tend to
fail when applied to such images. Highly specialized algorithms that explicitly
handle sparse slice spacing do not generalize well across problem domains. In
contrast, we aim to enable application of existing algorithms that were
originally developed for high resolution research scans to significantly
undersampled scans. We introduce a generative model that captures fine-scale
anatomical structure across subjects in clinical image collections and derive
an algorithm for filling in the missing data in scans with large inter-slice
spacing. Our experimental results demonstrate that the resulting method
outperforms state-of-the-art upsampling super-resolution techniques, and
promises to facilitate subsequent analysis not previously possible with scans
of this quality. Our implementation is freely available at
https://github.com/adalca/papago .


  Despite incredible recent advances in machine learning, building machine
learning applications remains prohibitively time-consuming and expensive for
all but the best-trained, best-funded engineering organizations. This expense
comes not from a need for new and improved statistical models but instead from
a lack of systems and tools for supporting end-to-end machine learning
application development, from data preparation and labeling to
productionization and monitoring. In this document, we outline opportunities
for infrastructure supporting usable, end-to-end machine learning applications
in the context of the nascent DAWN (Data Analytics for What's Next) project at
Stanford.


  A Restricted Boltzmann Machine (RBM) is an unsupervised machine-learning
bipartite graphical model that jointly learns a probability distribution over
data and extracts their relevant statistical features. As such, RBM were
recently proposed for characterizing the patterns of coevolution between amino
acids in protein sequences and for designing new sequences. Here, we study how
the nature of the features learned by RBM changes with its defining parameters,
such as the dimensionality of the representations (size of the hidden layer)
and the sparsity of the features. We show that for adequate values of these
parameters, RBM operate in a so-called compositional phase in which visible
configurations sampled from the RBM are obtained by recombining these features.
We then compare the performance of RBM with other standard representation
learning algorithms, including Principal or Independent Component Analysis,
autoencoders (AE), variational auto-encoders (VAE), and their sparse variants.
We show that RBM, due to the stochastic mapping between data configurations and
representations, better capture the underlying interactions in the system and
are significantly more robust with respect to sample size than deterministic
methods such as PCA or ICA. In addition, this stochastic mapping is not
prescribed a priori as in VAE, but learned from data, which allows RBM to show
good performance even with shallow architectures. All numerical results are
illustrated on synthetic lattice-protein data, that share similar statistical
features with real protein sequences, and for which ground-truth interactions
are known.


  In this paper, new determined BVR_cI_c light curves and radial velocities of
V781 Tau are presented. By analyzing the light curves and radial velocities
simultaneously, we found that V781 Tau is a W-subtype medium contact binary
star with a mass ratio of q=2.207+-0.005 and a contact degree of
f=21.6(+-1.0)%. The difference between the two light maxima was explained by a
dark spot on the less massive primary component. The orbital period change of
V781 Tau was also investigated. A secular decrease at a rate of
$-6.01(+-2.28)*10^{-8} d/yr and a cyclic modulation with a period of 44.8+-5.7
yr and an amplitude of 0.0064+-0.0011 day were discovered. The continuous
period decrease may be caused by angular momentum loss due to magnetic stellar
wind. Applegate mechanism failed to explain the cyclic modulation. It is highly
possible that the cyclic oscillation is the result of the light travel time
effect by a third companion.


  We present a renormalization group analysis for the hyperbolic sine-Gordon
(sinh-Gordon) model in two dimensions. We derive the renormalization group
equations based on the dimensional regularization method and the Wilson method.
The same equations are obtained using both these methods. We have two
parameters $\alpha$ and $\beta\equiv \sqrt{t}$ where $\alpha$ indicates the
strength of interaction of a real salar field and $t=\beta^2$ is related with
the normalization of the action. We show that $\alpha$ is renormalized to zero
in the high-energy region, that is, the sinh-Gordon theory is an asymptotically
free theory. We also show a non-renormalization property that the beta function
of $t$ vanishes in two dimensions.


  We propose a novel adaptive design for clinical trials with time-to-event
outcomes and covariates (which may consist of or include biomarkers). Our
method is based on the expected entropy of the posterior distribution of a
proportional hazards model. The expected entropy is evaluated as a function of
a patient's covariates, and the information gained due to a patient is defined
as the decrease in the corresponding entropy. Candidate patients are only
recruited onto the trial if they are likely to provide sufficient information.
Patients with covariates that are deemed uninformative are filtered out. A
special case is where all patients are recruited, and we determine the optimal
treatment arm allocation. This adaptive design has the advantage of potentially
elucidating the relationship between covariates, treatments, and survival
probabilities using fewer patients, albeit at the cost of rejecting some
candidates. We assess the performance of our adaptive design using data from
the German Breast Cancer Study group and numerical simulations of a biomarker
validation trial.


  We present Bernstein-Sato identities for scalar-, spinor- and differential
form-valued distribution kernels on Euclidean space associated to conformal
symmetry breaking operators. The associated Bernstein-Sato operators lead to
partially new formulae for conformal symmetry breaking differential operators
on functions, spinors and differential forms.


  In a 1983 paper with Frank Warner, we proved that the space of all great
circle fibrations of the 3-sphere S^3 deformation retracts to the subspace of
Hopf fibrations, and so has the homotopy type of a pair of disjoint
two-spheres. Since that time, no generalization of this result to higher
dimensions has been found, and so we narrow our sights here and show that in an
infinitesimal sense explained below, the space of all smooth oriented great
circle fibrations of the 2n+1 sphere S^(2n+1) deformation retracts to its
subspace of Hopf fibrations. The tools gathered to prove this also serve to
show that every germ of a smooth great circle fibration of S^(2n+1) extends to
such a fibration of all of S^(2n+1), a result previously known only for S^3 .


  By doubling the target space of a canonical Courant algebroid and
subsequently projecting down to a specific subbundle, we identify the data of
double field theory (DFT) and hence define its algebroid structure. We specify
the properties of the DFT algebroid. We show that one of the Courant algebroid
properties plays the role of the strong constraint in the context of DFT. The
DFT algebroid is a special example when properties of a Courant algebroid are
relaxed in a specific and dependent manner. When otherwise, we uncover
additional structures.


  We wish to understand how irreducible representations of a group G behave
when restricted to a subgroup G' (the branching problem). Our primary concern
is with representations of reductive Lie groups, which involve both algebraic
and analytic approaches. We divide branching problems into three stages:
  (A) abstract features of the restriction;
  (B) branching laws (irreducible decompositions of the restriction); and
  (C) construction of symmetry breaking operators on geometric models.
  We could expect a simple and detailed study of branching problems in Stages B
and C in the settings that are {\it{a priori}} known to be "nice" in Stage A,
and conversely, new results and methods in Stage C that might open another
fruitful direction of branching problems including Stage A.
  The aim of this article is to give new perspectives on the subjects, to
explain the methods based on some recent progress, and to raise some
conjectures and open questions.


  The present article studies the extension of two deterministic models for
describing the novel coronavirus pandemic crisis, the SIR model and the SEIR
model. The models were studied and compared to real data in order to support
the validity of each description and extract important information regarding
the pandemic, such as the basic reproductive number R0, which might provide
useful information concerning the rate of increase of the pandemic predicted by
each model. We next proceed to making predictions and comparing more complex
models derived from the SEIR model with the SIRD model, in order to find the
most suitable one for describing and predicting the pandemic crisis. Aiming to
answer the question if the simple SIRD model is able to make reliable
predictions and deliver suitable information compared to more complex models.


  Attitude determination is a popular application of Global Navigation
Satellite Systems (GNSS). Many methods have been developed to solve the
attitude determination problem with different performance offerings. We develop
a constrained wrapped least-squares (C-WLS) method for high-accuracy attitude
determination. This approach is built on an optimization model that leverages
prior information related to the antenna array and the integer nature of the
carrier-phase ambiguities in an innovative way. The proposed approach adopts an
efficient search strategy to estimate the vehicle's attitude parameters using
ambiguous carrier-phase observations directly, without requiring prior
carrier-phase ambiguity fixing. The performance of the proposed method is
evaluated via simulations and experimentally utilizing data collected using
multiple GNSS receivers. The simulation and experimental results demonstrate
excellent performance, with the proposed method outperforming the ambiguity
function method, the constrained LAMBDA and multivariate constrained LAMBDA
methods, three prominent attitude determination algorithms.


  Photonic brain-inspired platforms are emerging as novel analog computing
devices, enabling fast and energy-efficient operations for machine learning.
These artificial neural networks generally require tailored optical elements,
such as integrated photonic circuits, engineered diffractive layers,
nanophotonic materials, or time-delay schemes, which are challenging to train
or stabilize. Here we present a neuromorphic photonic scheme - photonic extreme
learning machines - that can be implemented simply by using an optical encoder
and coherent wave propagation in free space. We realize the concept through
spatial light modulation of a laser beam, with the far field that acts as
feature mapping space. We experimentally demonstrated learning from data on
various classification and regression tasks, achieving accuracies comparable to
digital extreme learning machines. Our findings point out an optical machine
learning device that is easy-to-train, energetically efficient, scalable and
fabrication-constraint free. The scheme can be generalized to a plethora of
photonic systems, opening the route to real-time neuromorphic processing of
optical data.


  We analyze the density of roots of random polynomials where each complex
coefficient is constructed of a random modulus and a fixed, deterministic
phase. The density of roots is shown to possess a singular component only in
the case for which the phases increase linearly with the index of coefficients.
This means that, contrary to earlier belief, eigenvectors of a typical quantum
chaotic system with some antiunitary symmetry will not display a clustering
curve in the stellar representation. Moreover, a class of time-reverse
invariant quantum systems is shown, for which spectra display fluctuations
characteristic of orthogonal ensemble, while eigenvectors confer to predictions
of unitary ensemble.


  We discuss the motion of neutral and charged particles in a plane
electro-magnetic wave and its accompanying gravitational field.


  We present a conjecture regarding the expectation of the maxima of $L^2$
norms of sub-vectors of a Gaussian vector; this has application to nonlinear
reconstruction.


  Study of stable isotopy classes of a finite collection of immersed circles
without triple or higher intersections on closed oriented surfaces is
considered as a planar analogue of virtual knot theory, a far reaching
generalisation of classical knot theory. Recent works have established
Alexander and Markov theorems in the planar setting. In the classical case, the
role of groups is played by twin groups, a class of right-angled Coxeter
groups. A new class of groups called virtual twin groups, that extends twin
groups in a natural way, plays the role of groups in the virtual case. The
virtual twin group $VT_n$ contains the pure virtual twin group $PVT_n$, a
planar analogue of the pure Artin braid group. In this paper, we prove that the
pure virtual twin group $PVT_n$ is an irreducible right-angled Artin group with
trivial center and give it's precise presentation. We show that $PVT_n$ has a
decomposition as an iterated semi-direct product of infinite rank free groups.
We give a complete description of the automorphism group of $PVT_n$ and
establish splitting of natural exact sequences of automorphism groups. As
applications, we show that $VT_n$ is residually finite and $PVT_n$ has the
$R_\infty$-property.


  The notion of analyticity is studied in the context of hypercomplex numbers.
A critical review of the problems arising from the conventional approach is
given. We describe a local analyticity condition which yields the desired type
of hypercomplex solutions. The result is the definition of a generalized
complex analyticity to hypercomplex space.
  02.10.Tq/Vr, 02.30.-f/Dk, 02.90.+p


  Based on the largest catalogs currently available, comprising 6090 contact
binaries (CBs) and 2167 open clusters, we determine the near-infrared $JHK_{\rm
s}$ CB period--luminosity (PL) relations, for the first time achieving the low
levels of intrinsic scatter that make these relations viable as competitive
distance calibrators. To firmly establish our distance calibration on the basis
of open cluster CBs, we require that (i) the CB of interest must be located
inside the core radius of its host cluster; (ii) the CB's proper motion must be
located within the $2\sigma$ distribution of that of its host open cluster; and
(iii) the CB's age, $t$, must be comparable to that of its host cluster, i.e.,
$\Delta \log (t\mbox{ yr}^{-1}) <0.3$. We thus select a calibration sample of
66 CBs with either open cluster distances or accurate space-based parallaxes.
The resulting near-infrared PL relations, for both late-type (i.e., W Ursae
Majoris-type) and---for the first time---early-type CBs, are as accurate as the
well-established $JHK_{\rm s}$ Cepheid PL relations, (characterized by
single-band statistical uncertainties of $\sigma < 0.10$ mag). We show that CBs
can be used as viable distance tracers, yielding distances with uncertainties
of better than 5\% for 90\% of the 6090 CBs in our full sample. By combining
the full $JHK_{\rm s}$ photometric data set, CBs can trace distances with an
accuracy, $\sigma=0.05 \mbox{ (statistical)} \pm0.03 \mbox{ (systematic)}$ mag.
The 102 CBs in the Large Magellanic Cloud are used to determine a distance
modulus to the galaxy of $(m-M_V)_0^{\rm LMC}=18.41\pm0.20$ mag.


  After a brief review of the first phase of development of Quantum-Gravity
Phenomenology, I argue that this research line is now ready to enter a more
advanced phase: while at first it was legitimate to resort to heuristic
order-of-magnitude estimates, which were sufficient to establish that
sensitivity to Planck-scale effects can be achieved, we should now rely on
detailed analyses of some reference test theories. I illustrate this point in
the specific example of studies of Planck-scale modifications of the
energy/momentum dispersion relation, for which I consider two test theories.
Both the photon-stability analyses and the Crab-nebula synchrotron-radiation
analyses, which had raised high hopes of ``beyond-Plankian'' experimental
bounds, turn out to be rather ineffective in constraining the two test
theories. Examples of analyses which can provide constraints of rather wide
applicability are the so-called ``time-of-flight analyses'', in the context of
observations of gamma-ray bursts, and the analyses of the cosmic-ray spectrum
near the GZK scale.


  Compartment models with delay terms are widely used across a range of
disciplines. The motivation to include delay terms varies across different
contexts. In epidemiological and pharmacokinetic models, the delays are often
used to represent an incubation period. In this work, we derive a compartment
model with delay terms from an underlying non-Markov stochastic process. Delay
terms arise when waiting times are drawn from a delay exponential distribution.
This stochastic process approach allows us to preserve the physicality of the
model, gaining understanding into the conditions under which delay terms can
arise. By providing the conditions under which the delay exponential function
is a probability distribution, we establish a critical value for the delay
terms. An exact stochastic simulation method is introduced for the generalized
model, enabling us to utilize the simulation in scenarios where intrinsic
stochasticity is significant, such as when the population size is small. We
illustrate the applications of the model and validate our simulation algorithm
on examples drawn from epidemiology and pharmacokinetics.


  We prove sharp inequalities of Hardy type for functions in the Sobolev space
$W^{1,p}$ on the unit sphere $\mathbb{S}^{n-1}$ in $\mathbb{R}^{n}$. We achieve
this in both the subcritical and critical cases. The method we use to show
optimality takes into account all the constants involved in our inequalities.


  For two one-forms and the Dirac operator, Dabrowski etc. recovered the
spectral Einstein functionals by computing their noncommutative residue in
Theorem 4.1 \cite{DL}. In this paper, we generalize the results of Dabrowski
etc. to the cases of four dimensional spin manifolds with boundary.


  We prove that a submaximal plane curve (i.e., an irreducible counterexample
to Nagata's conjecture) with r singular points has sequence of multiplicities
(m, n, ..., n) with m<sn for every integer with ((s-1)(s+2))^2 > 6.76(r-1).


  The author considers the effects of the CP-violating phases, e. g. arg(A_t)
and arg(mu) on the e^+ e^- --> {tilde t}_1 {tilde t}_1^* (H_1) processes. The
third generation squark trilinear terms give significant contributions to the
Higgs potential at the one-loop level. This results in the changes of the stop
masses and the lighter stop - the lighter anti-stop - the lightest Higgs
coupling. The author shows the coupling and the loop effects on the processes.
And the author will discuss the determination method of soft parameters.


  For a holographically defined finite temperature theory, we derive an
off-shell constitutive relation for a global $U(1)$ current driven by a weak
external non-dynamical electromagnetic field. The constitutive relation
involves an all order gradient expansion resummed into three momenta-dependent
transport coefficient functions: diffusion, electric conductivity, and
"magnetic" conductivity. These transport functions are first computed
analytically in the hydrodynamic limit, up to third order in the derivative
expansion, and then numerically for generic values of momenta. We also compute
a diffusion memory function, which, as a result of all order gradient
resummation, is found to be causal.


  Deep learning techniques have gained a lot of traction in the field of NLP
research. The aim of this paper is to predict the age and gender of an
individual by inspecting their written text. We propose a supervised BERT-based
classification technique in order to predict the age and gender of bloggers.
The dataset used contains 681284 rows of data, with the information of the
blogger's age, gender, and text of the blog written by them. We compare our
algorithm to previous works in the same domain and achieve a better accuracy
and F1 score. The accuracy reported for the prediction of age group was 84.2%,
while the accuracy for the prediction of gender was 86.32%. This study relies
on the raw capabilities of BERT to predict the classes of textual data
efficiently. This paper shows promising capability in predicting the
demographics of the author with high accuracy and can have wide applicability
across multiple domains.


  In this paper, we obtain a priori estimates for the set of anti-symmetric
solutions to a fractional Laplacian equation in a bounded domain using a
blowing-up and rescaling argument. In order to establish a contradiction to
possible blow-ups, we apply a certain variation of the moving planes method in
order to prove a monotonicity result for the limit equation after rescaling.


  We determine the paint cost spectrum for perfect $k$-ary trees.
  A coloring of the vertices of a graph $G$ with $d$ colors is said to be
\emph{$d$-distinguishing} if only the trivial automorphism preserves the color
classes. The smallest such $d$ is the distinguishing number of $G$ and is
denoted $\mbox{dist}(G).$ The \emph{paint cost of $d$-distinguishing $G$},
denoted $\rho^d(G)$, is the minimum size of the complement of a color class
over all $d$-distinguishing colorings. A subset $S$ of the vertices of $G$ is
said to be a \emph{fixing set} for $G$ if the only automorphsim that fixes the
vertices in $S$ pointwise is the trivial automorphism. The cardinality of a
smallest fixing set is denoted $\mbox{fix}(G)$. In this paper, we explore the
breaking of symmetry in perfect $k$-ary trees by investigating what we define
as the \emph{paint cost spectrum} of a graph $G$: $(\mbox{dist}(G);
\rho^{\mbox{dist}(G)}(G), \rho^{\mbox{dist}(G)+1}(G), \dots,
\rho^{\mbox{fix}(G)+1}(G))$ and the \emph{paint cost ratio} of $G$, which is
defined to be the fraction of paint costs in the paint cost spectrum equal to
$\mbox{fix}(G)$. We determine both the paint cost spectrum and the paint cost
ratio completely for perfect $k$-ary trees.
  We also prove a lemma that is of interest in its own right: given an
$n$-tuple, $n \geq 2$ of distinct elements of an ordered abelian group and $1
\leq k \leq n! -1$, there exists a $k \times n$ row permuted matrix with
distinct column sums.


  Recent years have seen a substantial development of quantitative methods,
mostly led by the computer science community with the goal of developing better
machine learning applications, mainly focused on predictive modeling. However,
economic, management, and technology forecasting research has so far been
hesitant to apply predictive modeling techniques and workflows. In this paper,
we introduce a machine learning (ML) approach to quantitative analysis geared
towards optimizing the predictive performance, contrasting it with standard
practices inferential statistics, which focus on producing good parameter
estimates. We discuss the potential synergies between the two fields against
the backdrop of this, at first glance, target-incompatibility. We discuss
fundamental concepts in predictive modeling, such as out-of-sample model
validation, variable and model selection, generalization, and hyperparameter
tuning procedures. We are providing a hands-on predictive modeling introduction
for a quantitative social science audience while aiming at demystifying
computer science jargon. We use the illustrative example of patent quality
estimation - which should be a familiar topic of interest in the Scientometrics
community - guiding the reader through various model classes and procedures for
data pre-processing, modeling, and validation. We start off with more familiar
easy to interpret model classes (Logit and Elastic Nets), continues with less
familiar non-parametric approaches (Classification Trees, Random Forest,
Gradient Boosted Trees), and finally presents artificial neural network
architectures, first a simple feed-forward and then a deep autoencoder geared
towards rare-event prediction.


  This paper develops an accurate, efficient filter (called the `TT filter')
for tracking multiple targets using a spatially-distributed network of
amplitude sensors that estimate distance but not direction. Several innovations
are included in the algorithm that increase accuracy and reduce complexity. For
initial target acquisition once tracking begins, a constrained Hessian search
is used to find the maximum likelihood (ML) target vector, based on the
measurement model and a Gaussian approximation of the prior. The Hessian at the
ML vector is used to give an initial approximation of the negative log
likelihood for the target vector distribution: corrections are applied if the
Hessian is not positive definite due to the near-far problem. Further
corrections are made by applying a transformation that matches the known
nonlinearity introduced by distance-only sensors. A set of integration points
is constructed using this information, which are used to estimate the mean and
moments of the target vector distribution. Results show that the TT filter
gives superior accuracy and lower complexity than previous alternatives such as
Kalman-based or particle filters.


  For multi-component superconductors, it is known that the presence of
symmetry breaking fields can lead to multiple superconducting phase
transitions. This phenomenon is best illustrated in UPt$_3$. Motivated by
recent small angle neutron scattering experiments on the vortex state of
UPt$_3$, the London theory in the vicinity of such phase transitions is
determined. It is found that the form of this London theory is in general quite
different than that for conventional superconductors. This is due to the
existence of a diverging correlation length associated with these phase
transitions. One striking consequence is that non-trivial vortex lattices exist
arbitrarily close to H$_{c1}$. It is also found that the penetration depth
develops a novel temperature dependence and anisotropy. Results of this theory
for UPt$_3$ are derived. Possible applications to CeIn$_3$,
U$_{1-x}$Th$_x$Be$_{13}$, electron doped cuprate superconductors,
Sr$_2$RuO$_4$, and MgCNi$_3$ are also discussed.


  Many real world problems can be defined as optimisation problems in which the
aim is to maximise an objective function. The quality of obtained solution is
directly linked to the pertinence of the used objective function. However,
designing such function, which has to translate the user needs, is usually
fastidious. In this paper, a method to help user objective functions designing
is proposed. Our approach, which is highly interactive, is based on man machine
dialogue and more particularly on the comparison of problem instance solutions
by the user. We propose an experiment in the domain of cartographic
generalisation that shows promising results.


  Higher intensity of strong-coupling stimulated Brillouin scattering (SC-SBS)
amplification is achieved by supplementary Raman amplification. In the new
scheme, a Raman pump laser first amplifies the seed pulse in the homogeneous
plasma, then a SC-SBS pump laser continues the amplification in the
inhomogeneous plasma in order to suppress the spontaneous instability of pump
lasers. The intensity of seed laser gets higher and the duration of seed laser
gets shorter than that in the pure SC-SBS scheme with the same incident energy,
while the energy conversion effciency is not significantly reduced. We also
found that the SC-SBS amplification is seeded by the \pi pulse of Raman
amplification. The results obtained from envelope coupling equations, Vlasov
simulations and two-dimensional particle-in-cell(PIC) simulations agree with
each other. This scheme is a simple and effective way to improve the SC-SBS
amplification and is easy to implement in experiments.


  The manipulation of quantum "resources" such as entanglement, coherence and
magic states lies at the heart of quantum science and technology, empowering
potential advantages over classical methods. In practice, a particularly
important kind of manipulation is to "purify" the quantum resources, since they
are inevitably contaminated by noise and thus often lose their power or become
unreliable for direct usage. Here we prove fundamental limitations on how
effectively generic noisy resources can be purified enforced by the laws of
quantum mechanics, which universally apply to any reasonable kind of quantum
resource. More explicitly, we derive nontrivial lower bounds on the error of
converting any full-rank noisy state to any target pure resource state by any
free protocol (including probabilistic ones)---it is impossible to achieve
perfect resource purification, even probabilistically. Our theorems indicate
strong limits on the efficiency of distillation, a widely used type of resource
purification routine that underpins many key applications of quantum
information science. In particular, this general result induces the first
explicit lower bounds on the resource cost of magic state distillation, a
leading scheme for realizing scalable fault-tolerant quantum computation.
Implications for the standard error-correction-based methods are specifically
discussed.


  To fully empower sensor networks with cognitive Internet of Things (IoT)
technology, efficient medium access control protocols that enable the
coexistence of cognitive sensor networks with current wireless infrastructure
are as essential as the cognitive power in data fusion and processing due to
shared wireless spectrum. Cognitive radio (CR) is introduced to increase
spectrum efficiency and support such an endeavor, which thereby becomes a
promising building block toward facilitating cognitive IoT. In this paper,
primary users (PUs) refer to devices in existing wireless infrastructure, and
secondary users (SUs) refer to cognitive sensors. For interference control
between PUs and SUs, SUs adopt dynamic spectrum access and power adjustment to
ensure sufficient operation of PUs, which inevitably leads to increasing
latency and poses new challenges on the reliability of IoT communications.
  To guarantee operations of primary systems while simultaneously optimizing
system performance in cognitive radio ad hoc networks (CRAHNs), this paper
proposes interference-aware flooding schemes exploiting global timeout and
vaccine recovery schemes to control the heavy buffer occupancy induced by
packet replications. The information delivery dynamics of SUs under the
proposed interference-aware recovery-assisted flooding schemes is analyzed via
epidemic models and stochastic geometry from a macroscopic view of the entire
system. The simulation results show that our model can efficiently capture the
complicated data delivery dynamics in CRAHNs in terms of end-to-end
transmission reliability and buffer occupancy. This paper sheds new light on
analysis of recovery-assisted flooding schemes in CRAHNs and provides
performance evaluation of cognitive IoT services built upon CRAHNs.


  An exact reduced dynamical map along with its operator sum representation is
derived for a central spin interacting with a thermal spin environment. The
dynamics of the central spin shows high sustainability of quantum traits such
as coherence and entanglement in the low-temperature regime. However, for
sufficiently high temperature and when the number of bath particles approaches
the thermodynamic limit, this feature vanishes and the dynamics closely mimics
Markovian evolution. The properties of the long-time-averaged state and the
trapped information of the initial state for the central qubit are also
investigated in detail, confirming that the nonergodicity of the dynamics can
be attributed to the finite temperature and finite size of the bath. It is
shown that if a certain stringent resonance condition is satisfied, the
long-time-averaged state retains quantum coherence, which can have far reaching
technological implications in engineering quantum devices. An exact time-local
master equation of the canonical form is derived. With the help of this master
equation, the nonequilibrium properties of the central spin system are studied
by investigating the detailed balance condition and irreversible entropy
production rate. The result reveals that the central qubit thermalizes only in
the limit of very high temperature and large number of bath spins.


  Archetypal analysis and non-negative matrix factorization (NMF) are staples
in a statisticians toolbox for dimension reduction and exploratory data
analysis. We describe a geometric approach to both NMF and archetypal analysis
by interpreting both problems as finding extreme points of the data cloud. We
also develop and analyze an efficient approach to finding extreme points in
high dimensions. For modern massive datasets that are too large to fit on a
single machine and must be stored in a distributed setting, our approach makes
only a small number of passes over the data. In fact, it is possible to obtain
the NMF or perform archetypal analysis with just two passes over the data.


  The cornerstone of autonomous vehicles (AV) is a solid perception system,
where camera encoders play a crucial role. Existing works usually leverage
pre-trained Convolutional Neural Networks (CNN) or Vision Transformers (ViTs)
designed for general vision tasks, such as image classification, segmentation,
and 2D detection. Although those well-known architectures have achieved
state-of-the-art accuracy in AV-related tasks, e.g., 3D Object Detection, there
remains significant potential for improvement in network design due to the
nuanced complexities of industrial-level AV dataset. Moreover, existing public
AV benchmarks usually contain insufficient data, which might lead to inaccurate
evaluation of those architectures.To reveal the AV-specific model insights, we
start from a standard general-purpose encoder, ConvNeXt and progressively
transform the design. We adjust different design parameters including width and
depth of the model, stage compute ratio, attention mechanisms, and input
resolution, supported by systematic analysis to each modifications. This
customization yields an architecture optimized for AV camera encoder achieving
8.79% mAP improvement over the baseline. We believe our effort could become a
sweet cookbook of image encoders for AV and pave the way to the next-level
drive system.


  AI faces a trifecta of grand challenges the Energy Wall, the Alignment
Problem and the Leap from Narrow AI to AGI. Contemporary AI solutions consume
unsustainable amounts of energy during model training and daily operations.
Making things worse, the amount of computation required to train each new AI
model has been doubling every 2 months since 2020, directly translating to
increases in energy consumption. The leap from AI to AGI requires multiple
functional subsystems operating in a balanced manner, which requires a system
architecture. However, the current approach to artificial intelligence lacks
system design; even though system characteristics play a key role in the human
brain from the way it processes information to how it makes decisions.
Similarly, current alignment and AI ethics approaches largely ignore system
design, yet studies show that the brains system architecture plays a critical
role in healthy moral decisions. In this paper, we argue that system design is
critically important in overcoming all three grand challenges. We posit that
system design is the missing piece in overcoming the grand challenges. We
present a Systematic AI Approach for AGI that utilizes system design principles
for AGI, while providing ways to overcome the energy wall and the alignment
challenges.


  We introduce a method, dubbed the flux-fusion anomaly test, to detect certain
anomalous symmetry fractionalization patterns in two-dimensional symmetry
enriched topological (SET) phases. We focus on bosonic systems with Z2
topological order, and symmetry group of the form G = U(1) $\rtimes$ G', where
G' is an arbitrary group that may include spatial symmetries and/or time
reversal. The anomalous fractionalization patterns we identify cannot occur in
strictly d=2 systems, but can occur at surfaces of d=3 symmetry protected
topological (SPT) phases. This observation leads to examples of d=3 bosonic
topological crystalline insulators (TCIs) that, to our knowledge, have not
previously been identified. In some cases, these d=3 bosonic TCIs can have an
anomalous superfluid at the surface, which is characterized by non-trivial
projective transformations of the superfluid vortices under symmetry. The basic
idea of our anomaly test is to introduce fluxes of the U(1) symmetry, and to
show that some fractionalization patterns cannot be extended to a consistent
action of G' symmetry on the fluxes. For some anomalies, this can be described
in terms of dimensional reduction to d=1 SPT phases. We apply our method to
several different symmetry groups with non-trivial anomalies, including G =
U(1) X Z2T and G = U(1) X Z2P, where Z2T and Z2P are time-reversal and d=2
reflection symmetry, respectively.


  Stochastic approximation (SA) algorithms have been widely applied in
minimization problems when the loss functions and/or the gradient information
are only accessible through noisy evaluations. Stochastic gradient (SG)
descent---a first-order algorithm and a workhorse of much machine learning---is
perhaps the most famous form of SA. Among all SA algorithms, the second-order
simultaneous perturbation stochastic approximation (2SPSA) and the second-order
stochastic gradient (2SG) are particularly efficient in handling
high-dimensional problems, covering both gradient-free and gradient-based
scenarios. However, due to the necessary matrix operations, the per-iteration
floating-point-operations (FLOPs) cost of the standard 2SPSA/2SG is $O(p^3)$,
where $p$ is the dimension of the underlying parameter. Note that the $O(p^3)$
FLOPs cost is distinct from the classical SPSA-based per-iteration $O(1)$ cost
in terms of the number of noisy function evaluations. In this work, we propose
a technique to efficiently implement the 2SPSA/2SG algorithms via the symmetric
indefinite matrix factorization and show that the FLOPs cost is reduced from
$O(p^3)$ to $O(p^2)$. The formal almost sure convergence and rate of
convergence for the newly proposed approach are directly inherited from the
standard 2SPSA/2SG. The improvement in efficiency and numerical stability is
demonstrated in two numerical studies.


  We quantify resilience with metrics extracted from the historical outage data
that is routinely recorded by many distribution utilities. The outage data is
coordinated with wind data to relate average outage rates in an area to wind
speed measured at a nearby weather station. A past investment in wind hardening
would have reduced the outage rates, and the effect of this on metrics can be
calculated by sampling a reduced number of the historical outages and
recomputing the metrics. This quantifies the impact that the hardening would
have had on customers. This is a tangible way to relate an investment in wind
resilience to the benefits it would have had on the lived experience of
customers that could help make the case for the investment to the public and
regulators. We also quantify the impact of earlier or faster restoration on
customer metrics and compare this to the impact of investment in hardening.
Overall this is a new and straightforward approach to quantify resilience and
justify resilience investments to stakeholders that is directly driven by
utility data. The approach driven by data avoids complicated models or modeling
assumptions.


  When a sufficiently large far-field training data is presented, jointly
optimizing a multichannel frontend and an end-to-end (E2E) Automatic Speech
Recognition (ASR) backend shows promising results. Recent literature has shown
traditional beamformer designs, such as MVDR (Minimum Variance Distortionless
Response) or fixed beamformers can be successfully integrated as the frontend
into an E2E ASR system with learnable parameters. In this work, we propose the
self-attention channel combinator (SACC) ASR frontend, which leverages the
self-attention mechanism to combine multichannel audio signals in the magnitude
spectral domain. Experiments conducted on a multichannel playback test data
shows that the SACC achieved a 9.3% WERR compared to a state-of-the-art fixed
beamformer-based frontend, both jointly optimized with a ContextNet-based ASR
backend. We also demonstrate the connection between the SACC and the
traditional beamformers, and analyze the intermediate outputs of the SACC.


  We study a dissipative version of the contact process, with mean-field
interaction, which admits a simple epidemiological interpretation. The
propagation of chaos and the corresponding normal fluctuations reveal that the
noise present in the finite-size system induces oscillations with a nearly
deterministic period and a randomly varying amplitude. This is reminiscent of
the emergence of pandemic waves in real epidemics.


  Some scales of spaces of ultra-differentiable functions are introduced,
having good stability properties with respect to infinitely many derivatives
and compositions. They are well-suited for solving non-linear functional
equations by means of hard implicit function theorems. They comprise Gevrey
functions and thus, as a limiting case, analytic functions. Using majorizing
series, we manage to characterize them in terms of a real sequence M bounding
the growth of derivatives. In this functional setting, we prove two fundamental
results of Hamiltonian perturbation theory: the invariant torus theorem, where
the invariant torus remains ultra-differentiable under the assumption that its
frequency satisfies some arithmetic condition which we call BR M , and which
generalizes the Bruno-R{\"u}ssmann condition ; and Nekhoroshev's theorem, where
the stability time depends on the ultra-differentiable class of the
pertubation, through the same sequence M. Our proof uses periodic averaging,
while a substitute of the analyticity width allows us to bypass analytic
smoothing. We also prove converse statements on the destruction of invariant
tori and on the existence of diffusing orbits with ultra-differentiable
perturbations, by respectively mimicking a construction of Bessi (in the
analytic category) and Marco-Sauzin (in the Gevrey non-analytic category). When
the perturbation space satisfies some additional condition (we then call it
matching), we manage to narrow the gap between stability hypotheses (e.g. the
BR M condition) and instability hypotheses, thus circumbscribing the stability
threshold. The formulas relating the growth M of derivatives of the
perturbation on the one hand, and the arithmetics of robust frequencies or the
stability time on the other hand, bring light to the competition between
stability properties of nearly integrable systems and the distance to
integrability. Due to our method of proof using width of regularity as a
regularizing parameter, these formulas are closer to optimal as the the
regularity tends to analyticity.


  We give a counterexample to a conjecture of S.E. Morris by showing that there
is a compact plane set X such that R(X) has no non-zero, bounded point
derivations but such that R(X) is not weakly amenable. We also give an example
of a separable uniform algebra A such that every maximal ideal of A has a
bounded approximate identity but such that A is not weakly amenable.


  We give an explicit expression for the primitive E8-invariant tensor with
eight symmetric indices. The result is presented in a manifestly
Spin(16)/Z2-covariant notation.


  We have calculated self-consistent equilibria of a collisionless relativistic
electron-positron gas in the vicinity of a magnetic $X-$point. For the
considered conditions, pertinent to extra-galactic jets, we find that leptons
are accelerated up to Lorentz factors $\Gamma_0 = \kappa e B_0L {\cal E}^2
/mc^2 \gg 1$, where $B_0$ is the typical magnetic field strength, ${\cal
E}\equiv E_0/B_0$, with $E_0$ the reconnection electric field, $L$ is the
length scale of the magnetic field, and $\kappa \approx 12$. The acceleration
is due to the dominance of the electric field over the magnetic field in a
region around the $X-$point. The distribution function of the accelerated
leptons is found to be approximately $dn/d\gamma \propto \gamma^{-1}$ for
$\gamma \lesssim \Gamma_0$. The apparent distribution function may be steeper
than $\gamma^{-1}$ due to the distribution of $\Gamma_0$ values and/or the
radiative losses. Self-consistent equilibria are found only for plasma inflow
rates to the $X-$point less than a critical value.


  In this paper, we study the heat engine where charged AdS black holes
surrounded by dark energy is the working substance and the mechanical work is
done via $PdV$ term in the first law of black hole thermodynamics in the
extended phase space. We first investigate the effects of a kind of dark energy
(quintessence field in this paper) on the efficiency of the RN-AdS black holes
as heat engine defined as a rectangle closed path in the $P-V$ plane. We get
the exact efficiency formula and find that quintessence field can improve the
heat engine efficiency which will increase as the field density $\rho_q$ grows.
At some fixed parameters, we find that bigger volume difference between the
smaller black holes($V_1$) and the bigger black holes($V_2$ ) will lead to a
lower efficiency, while the bigger pressure difference $P_1-P_4$ will make the
efficiency higher but it is always smaller than 1 and will never be beyond
Carnot efficiency which is the maximum value of the efficiency constrained by
thermodynamics laws, this is consistent to the heat engine in traditional
thermodynamics. After making some special choices for thermodynamical
quantities, we find that the increase of electric charge $Q$ and normalization
factor $a$ can also promote heat engine efficiency which would infinitely
approach the Carnot limit when $Q$ or $a$ goes to infinity.


  The non-convex complementarity constraints present a fundamental
computational challenge in energy constrained optimization problems. In this
work, we present a new, linear, and robust battery optimization formulation
that sidesteps the need for battery complementarity constraints and integers
and prove analytically that the formulation guarantees that all energy
constraints are satisfied which ensures that the optimized battery dispatch is
physically realizable. In addition, we bound the worst-case model mismatch and
discuss conservativeness. Simulation results further illustrate the
effectiveness of this approach.


  For $m, d \in {\mathbb N}$, a jittered sampling point set $P$ having $N =
m^d$ points in $[0,1)^d$ is constructed by partitioning the unit cube $[0,1)^d$
into $m^d$ axis-aligned cubes of equal size and then placing one point
independently and uniformly at random in each cube. We show that there are
constants $c \ge 0$ and $C$ such that for all $d$ and all $m \ge d$ the
expected non-normalized star discrepancy of a jittered sampling point set
satisfies \[c \,dm^{\frac{d-1}{2}} \sqrt{1 + \log(\tfrac md)} \le {\mathbb E}
D^*(P) \le C\, dm^{\frac{d-1}{2}} \sqrt{1 + \log(\tfrac md)}.\]
  This discrepancy is thus smaller by a factor of
$\Theta\big(\sqrt{\frac{1+\log(m/d)}{m/d}}\,\big)$ than the one of a uniformly
distributed random point set of $m^d$ points. This result improves both the
upper and the lower bound for the discrepancy of jittered sampling given by
Pausinger and Steinerberger (Journal of Complexity (2016)). It also removes the
asymptotic requirement that $m$ is sufficiently large compared to $d$.


  We present results of optical and infrared photometric monitoring of the
eclipsing low-mass X-ray binary V395 Car (2S 0921-630). Our observations reveal
a clear, repeating orbital modulation with an amplitude of about one magnitude
in B, and V and a little less in J. Combining our data with archival
observations spanning about 20 years, we derive an updated ephemeris with
orbital period 9.0026+/-0.0001d. We attribute the modulation to a combination
of the changing aspect of the irradiated face of the companion star and
eclipses of the accretion disk around the neutron star. Both appear to be
necessary as a secondary eclipse of the companion star is clearly seen. We
model the B, V, and J lightcurves using a simple model of an accretion disk and
companion star and find a good fit is possible for binary inclinations of
82.2+/-1.0 degrees. We estimate the irradiating luminosity to be about 8x10^35
erg/s, in good agreement with X-ray constraints.


  Mariana trench is the deepest place on the Earth. It crosses four tectonic
plates of the Pacific Ocean: Mariana, Caroline, Pacific and Philippine. The
formation of the trench is caused by the complex interconnection of various
environmental factors. The aim of this study was to describe and characterize
various impact factors affecting formation of the Mariana trench geomorphology
and continental margin environments using R programming language and
mathematical algorithms of correlation methods written on R code. To record the
system of geological, tectonic, geographic, oceanological and bathymetric
features affecting Mariana trench , a combination of statistical methods, GIS
and R programming codes were applied. The questions answered are as follows:
which factors are the most influencing for the Mariana trench morphology, and
to what extend do they affect its development? Is sedimental thickness of the
ocean trench basement more important factors for the trench formation comparing
to the steepness slope angle and aspect degree? Three methods of computing were
tested: Pearson correlation, Spearman correlation, Kendall correlation,
numerical correlogram, correlation matrix and cross-correlatios to analyze
environmental impact factors. The correlogram matrices are computed and
visualized by R scripting libraries. Complex usage of programming tools,
mathematical statistics and geospatial analysis enabled to get a differentiated
understandings of the hadal environments of the Mariana trench. The results
revealed following three types of factors having the highest score: geometric
(tg{\deg} slope angle), geologic (sedimental thickness) and tectonic structure.
The results furthermore indicated that tectonic plates, sedimental thickness of
the trench basement and igneous volcanic areas causing earthquakes play the
most essential role in the geomorphology of the trench.


  We propose a theory for the underdoped hole-doped cuprates, focusing on the
"nodal-anti-nodal dichotomy" observed in recent experiments. Our theory begins
with an ordered antiferromagnetic Fermi liquid with electron and hole pockets.
We argue that it is useful to consider a quantum transition at which the loss
of antiferromagnetic order leads to a hypothetical metallic "algebraic charge
liquid" (ACL) with pockets of charge -e and +e fermions, and an emergent U(1)
gauge field; the instabilities of the ACL lead to the low temperature phases of
the underdoped cuprates. The pairing instability leads to a superconductor with
the strongest pairing within the -e Fermi pockets, a d-wave pairing signature
for electrons, and very weak nodal-point pairing of the +e fermions near the
Brillouin zone diagonals. The influence of an applied magnetic field is
discussed using a proposed phase diagram as a function of field strength and
doping. We describe the influence of gauge field and pairing fluctuations on
the quantum Shubnikov-de Haas oscillations in the normal states induced by the
field. For the finite temperature pseudogap region, our theory has some
similarities to the phenomenological two-fluid model of -2e bosons and +e
fermions proposed by Geshkenbein, Ioffe, and Larkin [cond-mat/9609209], which
describes anomalous aspects of transverse transport in a magnetic field.


  Quantum materials are defined by the emergence of new properties resulting
from collective quantum effects and by holding promise for their quantum
applications. Novel superconductors, from high-Tc cuprates and iron-based
superconductors to twisted monolayers, exhibit a higher level of emergent
complexity, with a multiband electronic structure playing a pivotal role in
their comprehension and potential applications. Here, we provide a brief
overview of key multiband effects in these superconductors and topological
semimetals, offering guidelines for the theory-assisted development of new
quantum materials and devices.


  Q-balls generically exist in the supersymmetric extensions of the standard
model. Taking into account the additional sources of CP violation, which are
naturally accomodated by the supersymmetric models, it is shown that the Q-ball
matter depends additively on individual CP phases, whereas mass per unit charge
in the Q-ball depends only on the relative phases. There are regions of the
parameter space where there is no stable Q-ball solution in the CP-conserving
limit whereas finite CP phases induce a stable Q-ball.