  Telecommunication networks play a critical role in modern society. With the
arrival of 5G networks, these systems are becoming even more diversified,
integrated, and intelligent. Traffic forecasting is one of the key components
in such a system, however, it is particularly challenging due to the complex
spatial-temporal dependency. In this work, we consider this problem from the
aspect of a cellular network and the interactions among its base stations. We
thoroughly investigate the characteristics of cellular network traffic and shed
light on the dependency complexities based on data collected from a densely
populated metropolis area. Specifically, we observe that the traffic shows both
dynamic and static spatial dependencies as well as diverse cyclic temporal
patterns. To address these complexities, we propose an effective
deep-learning-based approach, namely, Spatio-Temporal Hybrid Graph
Convolutional Network (STHGCN). It employs GRUs to model the temporal
dependency, while capturing the complex spatial dependency through a hybrid-GCN
from three perspectives: spatial proximity, functional similarity, and recent
trend similarity. We conduct extensive experiments on real-world traffic
datasets collected from telecommunication networks. Our experimental results
demonstrate the superiority of the proposed model in that it consistently
outperforms both classical methods and state-of-the-art deep learning models,
while being more robust and stable.


  Systems with low mechanical dissipation are extensively used in precision
measurements such as gravitational wave detection, atomic force microscopy and
quantum control of mechanical oscillators via opto- and electromechanics. The
mechanical quality factor ($Q$) of these systems determines the
thermomechanical force noise and the thermal decoherence rate of mechanical
quantum states. While the dissipation rate is typically set by the bulk
acoustic properties of the material, by exploiting dissipation dilution,
mechanical $Q$ can be engineered through geometry and increased by many orders
of magnitude. Recently, soft clamping in combination with strain engineering
has enabled room temperature quality factors approaching one billion ($10^9$)
in millimeter-scale resonators. Here we demonstrate a new approach to soft
clamping which exploits vibrations in the perimeter of polygon-shaped
resonators tethered at their vertices. In contrast to previous approaches,
which rely on cascaded elements to achieve soft clamping, perimeter modes are
soft clamped due to symmetry and the boundary conditions at the polygon
vertices. Perimeter modes reach $Q$ of 3.6 billion at room temperature while
spanning only two acoustic wavelengths -- a 4-fold improvement over the
state-of-the-art mechanical $Q$ with 10-fold smaller devices. The small size of
our devices makes them well-suited for near-field integration with
microcavities for quantum optomechanical experiments. Moreover, their
compactness allows the realization of phononic lattices. We demonstrate a
one-dimensional Su-Schrieffer-Heeger chain of high-$Q$ perimeter modes coupled
via nearest-neighbour interaction and characterize the localized edge modes.


  Steganography embraces several hiding techniques which spawn across multiple
domains. However, the related terminology is not unified among the different
domains, such as digital media steganography, text steganography,
cyber-physical systems steganography, network steganography (network covert
channels), local covert channels, and out-of-band covert channels. To cope with
this, a prime attempt has been done in 2015, with the introduction of the
so-called hiding patterns, which allow to describe hiding techniques in a more
abstract manner. Despite significant enhancements, the main limitation of such
a taxonomy is that it only considers the case of network steganography.
  Therefore, this paper reviews both the terminology and the taxonomy of hiding
patterns as to make them more general. Specifically, hiding patterns are split
into those that describe the embedding and the representation of hidden data
within the cover object.
  As a first research action, we focus on embedding hiding patterns and we show
how they can be applied to multiple domains of steganography instead of being
limited to the network scenario. Additionally, we exemplify representation
patterns using network steganography. Our pattern collection is available under
https://patterns.ztt.hs-worms.de.


  We consider the cross section for one-particle inclusive production at high
transverse momentum in hadronic collisions. We present the all-order
resummation formula that controls the logarithmically-enhanced perturbative QCD
contributions to the partonic cross section in the threshold region, at fixed
rapidity of the observed parton (hadron). The explicit resummation up to
next-to-leading logarithmic accuracy is supplemented with the computation of
the general structure of the near-threshold contributions to the
next-to-leading order cross section. This next-to-leading order computation
allows us to extract the one-loop hard-virtual amplitude that enters into the
resummation formula. This is a necessary ingredient to explicitly extend the
soft-gluon resummation beyond the next-to-leading logarithmic accuracy. These
results equally apply to both spin-unpolarized and spin-polarized scattering
processes.


  The present paradigm in design and modelling of lattice architected
mechanical metamaterials is mostly limited to traditional numerical methods
like finite element analysis. Recently, the use of machine learning and
artificial intelligence techniques have become popular and here we extend these
ideas to architected metamaterials. We show that truss based lattices have a
natural resemblance to computational graphs which serve as an input for the
rapidly emerging field of graph neural networks (GNNs). A dataset comprising
thousands of such extremely complex lattices is trained using a GNN to predict
the underlying dominant deformation mechanism viz. stretching and bending. The
trained GNN achieves > 90% accuracy on a previously unseen complex lattice
dataset. Such graph-based learning of metamaterials has the capability to
predict a range of properties, from elastic moduli to fracture toughness and
promises AI driven discovery of emergent metamaterials possessing superlative
properties.


  We investigate the arrangement of hypersurfaces on a nonsingular varieties
whose associated logarithmic vector bundle is arithmetically Cohen-Macaulay
(for short, aCM), and prove that the projective space is the only smooth
complete intersection with Picard rank one that admits an aCM logarithmic
vector bundle. We also obtain a number of results on aCM logarithmic vector
bundles over several specific varieties. As an opposite situation we
investigate the Torelli-type problem that the logarithmic cohomology determines
the arrangement.


  High-dimensional feature selection arises in many areas of modern science.
For example, in genomic research we want to find the genes that can be used to
separate tissues of different classes (e.g. cancer and normal) from tens of
thousands of genes that are active (expressed) in certain tissue cells. To this
end, we wish to fit regression and classification models with a large number of
features (also called variables, predictors). In the past decade, penalized
likelihood methods for fitting regression models based on hyper-LASSO
penalization have received increasing attention in the literature. However,
fully Bayesian methods that use Markov chain Monte Carlo (MCMC) are still in
lack of development in the literature. In this paper we introduce an MCMC
(fully Bayesian) method for learning severely multi-modal posteriors of
logistic regression models based on hyper-LASSO priors (non-convex penalties).
Our MCMC algorithm uses Hamiltonian Monte Carlo in a restricted Gibbs sampling
framework; we call our method Bayesian logistic regression with hyper-LASSO
(BLRHL) priors. We have used simulation studies and real data analysis to
demonstrate the superior performance of hyper-LASSO priors, and to investigate
the issues of choosing heaviness and scale of hyper-LASSO priors.


  We investigated the effects of synaptic depression on the macroscopic
behavior of stochastic neural networks. Dynamical mean field equations were
derived for such networks by taking the average of two stochastic variables: a
firing state variable and a synaptic variable. In these equations, their
average product is decoupled as the product of averaged them because the two
stochastic variables are independent. We proved the independence of these two
stochastic variables assuming that the synaptic weight is of the order of 1/N
with respect to the number of neurons N. Using these equations, we derived
macroscopic steady state equations for a network with uniform connections and a
ring attractor network with Mexican hat type connectivity and investigated the
stability of the steady state solutions. An oscillatory uniform state was
observed in the network with uniform connections due to a Hopf instability.
With the ring network, high-frequency perturbations were shown not to affect
system stability. Two mechanisms destabilize the inhomogeneous steady state,
leading two oscillatory states. A Turing instability leads to a rotating bump
state, while a Hopf instability leads to an oscillatory bump state, which was
previous unreported. Various oscillatory states take place in a network with
synaptic depression depending on the strength of the interneuron connections.


  We show how translational invariance can be broken by the vacuum that drives
the spontaneous symmetry breaking of extra-dimensional extensions of the
Standard Model, when delta-like interactions between brane and bulk scalar
fields are present. We explicitly build some examples of vacuum configurations,
which induce the spontaneous symmetry breaking, and have non trivial profile in
the extra coordinate.


  We investigate Eisenstein congruences between the so-called Euler systems of
Garrett--Rankin--Selberg type. This includes the cohomology classes of
Beilinson--Kato, Beilinson--Flach and diagonal cycles. The proofs crucially
rely on different known versions of the Bloch--Kato conjecture, and are based
on the study of the Perrin-Riou formalism and the comparison between the
different $p$-adic $L$-functions.


  We present monaa, a monitoring tool over a real-time property specified by
either a timed automaton or a timed regular expression. It implements a timed
pattern matching algorithm that combines 1) features suited for online
monitoring, and 2) acceleration by automata-based skipping. Our experiments
demonstrate monaa's performance advantage, especially in online usage.


  We use a mock galaxy catalogue based upon the Millennium Run simulation to
investigate the intrinsic spatial properties of compact groups of galaxies. We
find that approximately 30% of galaxy associations identified in our mock
catalogue are physically dense systems of four or more galaxies with no
interlopers, approximately half are close associations of 2, 3 or 4 galaxies
with one or more interlopers, and the remainder are not physically dense.
Genuine compact groups are preferentially brighter and more isolated than those
with interlopers; by increasing the required minimum surface brightness of a
group from the canonical value of 26mags/arcsec^2 to 22mags/arcsec^2, we can
increase the proportion of genuinely compact systems identified with no
interlopers from 29% to 75%. Of the genuine compact groups identified, more
than half consist of a single dark matter halo with all the member galaxies
deeply embedded within it. In some cases, there are other galaxies which share
the same halo (typically with mass ~ 10^13 h^{-1} M_\odot) but which are not
identified as being members of the compact group. This implies that compact
groups are associated with group environments, some or all members of which are
in the compact group. For those compact groups where all galaxies are in the
same halo, the three-dimensional velocity dispersion of the compact group
correlates broadly with the virial velocity of the dark matter halo. However,
the scale-size of the group - and hence the fraction of the halo mass which the
group samples - is completely uncorrelated with the properties of the dark
matter halo. This means that masses derived under the simple assumption of
virial equilibrium using the observed velocity dispersions and sizes of compact
groups give incorrect estimates of the true mass of the underlying dark matter.


  We develop a renormalized continuum field theory for a directed polymer
interacting with a random medium and a single extended defect. The
renormalization group is based on the operator algebra of the pinning
potential; it has novel features due to the breakdown of hyperscaling in a
random system. There is a second-order transition between a localized and a
delocalized phase of the polymer; we obtain analytic results on its critical
pinning strength and scaling exponents. Our results are directly related to
spatially inhomogeneous Kardar-Parisi-Zhang surface growth.


  Given a von Neumann algebra $M$ with a faithful normal finite trace $\tau$
denote by $L^\Lambda(M, \tau)$ the generalized Arens algebra with respect to
$M.$ We give a complete description of all additive derivations on the algebra
$L^\Lambda(M, \tau).$ In particular each additive derivation on the algebra
$L^{\Lambda}(M, \tau),$ where $M$ is a type II von Neumann algebra, is inner.


  We first study a free particle on an $(n-1)$-sphere in an extended phase
space, where the originally second-class Hamiltonian and constraints are now in
strong involution. This allows for a Schr\"odinger representation and a
Hamilton-Jacobi formulation of the model. We thereby obtain the free particle
energy spectrum corresponding to that of a rigid rotator. We extend these
considerations to a modified version of the field theoretical O(3) nonlinear
sigma model, and obtain the corresponding energy spectrum as well as BRST
Lagrangian.


  We present a comprehensive test of the cosmic distance duality relation (DDR)
using a combination of strong gravitational lensing (SGL) time delay
measurements and Type Ia supernovae (SNe Ia) data. We investigate three
different parameterizations of potential DDR violations. To bridge the gap
between SGL and SNe Ia datasets, we implement an artificial neural network
(ANN) approach to reconstruct the distance modulus of SNe Ia. Our analysis
uniquely considers both scenarios where the absolute magnitude of SNe Ia
($M_B$) is treated as a free parameter and where it is fixed to a
Cepheid-calibrated value. Using a sample of six SGL systems and the Pantheon+
SNe Ia dataset, we find no statistically significant evidence for DDR
violations across all parameterizations. The consistency of our findings across
different parameterizations not only reinforces confidence in the standard DDR
but also demonstrates the robustness of our analytical approach.


  Vision Language Models (VLMs) have undergone a rapid evolution, giving rise
to significant advancements in the realm of multimodal understanding tasks.
However, the majority of these models are trained and evaluated on
English-centric datasets, leaving a gap in the development and evaluation of
VLMs for other languages, such as Japanese. This gap can be attributed to the
lack of methodologies for constructing VLMs and the absence of benchmarks to
accurately measure their performance. To address this issue, we introduce a
novel benchmark, Japanese Heron-Bench, for evaluating Japanese capabilities of
VLMs. The Japanese Heron-Bench consists of a variety of imagequestion answer
pairs tailored to the Japanese context. Additionally, we present a baseline
Japanese VLM that has been trained with Japanese visual instruction tuning
datasets. Our Heron-Bench reveals the strengths and limitations of the proposed
VLM across various ability dimensions. Furthermore, we clarify the capability
gap between strong closed models like GPT-4V and the baseline model, providing
valuable insights for future research in this domain. We release the benchmark
dataset and training code to facilitate further developments in Japanese VLM
research.


  This work describes the way that topological mixing and chaos in continua, as
induced by discrete dynamical systems, can or can't be understood through
topological conjugacy with symbolic dynamical systems. For example, there is no
symbolic dynamical system that is topologically conjugate to any discrete
dynamical system on an entire continuum, and there is no finer topology that
can be given to a continuum which simultaneously makes the continuum
homeomorphic to a symbolic dynamical system and contains its original topology.
However, this paper demonstrates an analytical mechanism by which the existence
of topological mixing and/or chaos can be shown through conjugacy with
qualitative dynamical systems outside the usual purview of symbolic dynamics.
Two examples of this mechanism are demonstrated on classic textbook models of
chaotic dynamics; the first proving the existence of topological mixing
everywhere in the dyadic map on the interval by showing that there exists a
qualitative system that is topologically conjugate to the dyadic map on the
interval with a finer topology than the usual Euclidean topology, and the other
following a similar approach to demonstrate the existence of Devaney chaos
everywhere in the $2$-tent map on the interval. The content is presented in a
somewhat self-contained fashion, reiterating some standard results in the
field, to aid new learners of topological mixing/chaos.


  The increasingly widespread use of 'smart' devices has raised multifarious
ethical concerns regarding their use in domestic spaces. Previous work
examining such ethical dimensions has typically either involved empirical
studies of concerns raised by specific devices and use contexts, or
alternatively expounded on abstract concepts like autonomy, privacy or trust in
relation to 'smart homes' in general. This paper attempts to bridge these
approaches by asking what features of smart devices users consider as rendering
them 'smart' and how these relate to ethical concerns. Through a multimethod
investigation including surveys with smart device users (n=120) and
semi-structured interviews (n=15), we identify and describe eight types of
smartness and explore how they engender a variety of ethical concerns including
privacy, autonomy, and disruption of the social order. We argue that this
middle ground, between concerns arising from particular devices and more
abstract ethical concepts, can better anticipate potential ethical concerns
regarding smart devices.


  Multiplex networks describe a large number of systems ranging from social
networks to the brain. These multilayer structure encode information in their
structure. This information can be extracted by measuring the correlations
present in the multiplex networks structure, such as the overlap of the links
in different layers. Many multiplex networks are also weighted, and the weights
of the links can be strongly correlated with the structural properties of the
multiplex network. For example in multiplex network formed by the citation and
collaboration networks between PRE scientists it was found that the statistical
properties of citations to co-authors are different from the one of citations
to non-co-authors, i.e. the weights depend on the overlap of the links. Here we
present a theoretical framework for modelling multiplex weighted networks with
different types of correlations between weights and overlap. To this end, we
use the framework of canonical network ensembles, and the recently introduced
concept of multilinks, showing that null models of a large variety of network
structures can be constructed in this way. In order to provide a concrete
example of how this framework apply to real data we consider a multiplex
constructed from gene expression data of healthy and cancer tissues.


  We investigate holographic superconductors in asympototically geometries with
hyperscaling violation. The mass of the scalar field decouples from the UV
dimension of the dual scalar operator and can be chosen as negative as we want,
without disturbing the Breitenlohner-Freedman bound. We first numerically find
that the scalar condenses below a critical temperature and a gap opens in the
real part of the conductivity, indicating the onset of superconductivity. We
further analytically explore the effects of the hyperscaling violation on the
superconducting transition temperature. We find that the critical temperature
increases with the increasing of hyperscaling violation.


  Multi-wavelength B, V, R, I observations of the optical afterglow of GRB
050319 were performed by the 1.05-m telescope at Kiso Observatory and the 1.0-m
telescope at Lulin Observatory from 1.31 hours to 9.92 hours after the burst.
Our R band lightcurves, combined with other published data, can be described by
the smooth broken power-law function, with $\alpha_1$ = -0.84 $\pm$0.02 to
$\alpha_2$ = -0.48$\pm$0.03, 0.04 days after the GRB. The optical lightcurves
are characterized by shallow decays-- as was also observed in the X-rays--
which may have a similar origin, related to energy injection. However, our
observations indicate that there is still a puzzle concerning the chromatic
breaks in the R band lightcurve (at 0.04 days) and the X-ray lightcurve (at
0.004 days) that remains to be solved.


  We present analysis of time-variable, shifted absorption features in far-UV
spectra of the unusual 49 Ceti debris disk. This nearly edge-on disk is one of
the brightest known, and is one of the very few containing detectable amounts
of circumstellar gas as well as dust. In our two visits of Hubble Space
Telescope STIS spectra, variable absorption features are seen on the wings of
lines arising from C II and C IV, but not for any of the other circumstellar
absorption lines. Similar variable features have long been seen in spectra of
the well-studied $\beta$ Pictoris debris disk and attributed to the transits of
star-grazing comets. We calculate the velocity ranges and apparent column
densities of the 49 Cet variable gas, which appears to be moving at velocities
of tens to hundreds of km s$^{-1}$ relative to the central star. The velocities
of the gas in the redshifted variable event in Visit 2 show that the maximum
distances of the infalling gas at the time of transit are about 0.05 to 0.2 AU
from the central star. A preliminary attempt at a composition analysis of the
redshifted event suggests that the C/O ratio in the infalling gas may be
super-solar, as it is in the bulk of the stable disk gas.


  An efficient multi-mode quantum memory is a crucial resource for
long-distance quantum communication based on quantum repeaters. We propose a
quantum memory based on spectral shaping of an inhomogeneously broadened
optical transition into an atomic frequency comb (AFC). The spectral width of
the AFC allows efficient storage of multiple temporal modes, without the need
to increase the absorption depth of the storage material, in contrast to
previously known quantum memories. Efficient readout is possible thanks to
rephasing of the atomic dipoles due to the AFC structure. Long-time storage and
on-demand readout is achieved by use of spin-states in a lambda-type
configuration. We show that an AFC quantum memory realized in solids doped with
rare-earth-metal ions could store hundreds of modes or more with close to unit
efficiency, for material parameters achievable today.


  A TeV scale decaying dark matter chiral multiplet N is introduced in addition
to the minimal supersymmetric standard model(MSSM). For a calculable abundance
of N, we introduce heavy axino decaying to N and MSSM particles including the
lightest supersymmetric particle(LSP). In the scenario that heavy axino, once
dominating the energy density of the universe, decays after the LSP decouples,
it is possible to estimate the relative cosmic abundances of N and the LSP.
Dimension 6 interactions allow the lifetime of the fermionic or the bosonic
superpartner of N in the 10^{27} s range to be compatible with the recent
astrophysical bounds. A diagrammatic strategy obtaining a suppression factor
1/M^2 is also given.


  This paper develops an inherently parallelised, fast, approximate
learning-based solution to the generic class of Capacitated Vehicle Routing
Problems with Time Windows and Dynamic Routing (CVRP-TWDR). Considering
vehicles in a fleet as decentralised agents, we postulate that using
reinforcement learning (RL) based adaptation is a key enabler for real-time
route formation in a dynamic environment. The methodology allows each agent
(vehicle) to independently evaluate the value of serving each customer, and
uses a centralised allocation heuristic to finalise the allocations based on
the generated values. We show that the solutions produced by this method are
significantly faster than exact formulations and state-of-the-art
meta-heuristics, while being reasonably close to optimal in terms of solution
quality. We describe experiments in both the static case (when all customer
demands and time windows are known in advance) as well as the dynamic case
(where customers can pop up at any time during execution). The results with a
single trained model on large, out-of-distribution test data demonstrate the
scalability and flexibility of the proposed approach.


  Great advances in computing and communication technology are bringing many
benefits to society, with transformative changes and financial opportunities
being created in health care, transportation, education, law enforcement,
national security, commerce, and social interactions. Many of these benefits,
however, involve the use of sensitive personal data, and thereby raise concerns
about privacy. Failure to address these concerns can lead to a loss of trust in
the private and public institutions that handle personal data, and can stifle
the independent thought and expression that is needed for our democracy to
flourish.
  This report, sponsored by the Computing Community Consortium (CCC), suggests
a roadmap for privacy research over the next decade, aimed at enabling society
to appropriately control threats to privacy while enjoying the benefits of
information technology and data science. We hope that it will be useful to the
agencies of the Federal Networking and Information Technology Research and
Development (NITRD) Program as they develop a joint National Privacy Research
Strategy over the coming months. The report synthesizes input drawn from the
privacy and computing communities submitted to both the CCC and NITRD, as well
as past reports on the topic.


  This work investigates uncertainty-aware deep learning (DL) in tactile
robotics based on a general framework introduced recently for robot vision. For
a test scenario, we consider optical tactile sensing in combination with DL to
estimate the edge pose as a feedback signal to servo around various 2D test
objects. We demonstrate that uncertainty-aware DL can improve the pose
estimation over deterministic DL methods. The system estimates the uncertainty
associated with each prediction, which is used along with temporal coherency to
improve the predictions via a Kalman filter, and hence improve the tactile
servo control. The robot is able to robustly follow all of the presented
contour shapes to reduce not only the error by a factor of two but also smooth
the trajectory from the undesired noisy behaviour caused by previous
deterministic networks. In our view, as the field of tactile robotics matures
in its use of DL, the estimation of uncertainty will become a key component in
the control of physically interactive tasks in complex environments.


  Magnetic resonance (MR) imaging offers a wide variety of imaging techniques.
A large amount of data is created per examination which needs to be checked for
sufficient quality in order to derive a meaningful diagnosis. This is a manual
process and therefore time- and cost-intensive. Any imaging artifacts
originating from scanner hardware, signal processing or induced by the patient
may reduce the image quality and complicate the diagnosis or any image
post-processing. Therefore, the assessment or the ensurance of sufficient image
quality in an automated manner is of high interest. Usually no reference image
is available or difficult to define. Therefore, classical reference-based
approaches are not applicable. Model observers mimicking the human observers
(HO) can assist in this task. Thus, we propose a new machine-learning-based
reference-free MR image quality assessment framework which is trained on
HO-derived labels to assess MR image quality immediately after each
acquisition. We include the concept of active learning and present an efficient
blinded reading platform to reduce the effort in the HO labeling procedure.
Derived image features and the applied classifiers (support-vector-machine,
deep neural network) are investigated for a cohort of 250 patients. The MR
image quality assessment framework can achieve a high test accuracy of 93.7$\%$
for estimating quality classes on a 5-point Likert-scale. The proposed MR image
quality assessment framework is able to provide an accurate and efficient
quality estimation which can be used as a prospective quality assurance
including automatic acquisition adaptation or guided MR scanner operation,
and/or as a retrospective quality assessment including support of diagnostic
decisions or quality control in cohort studies.


  A directed acyclic hypergraph is a generalized concept of a directed acyclic
graph, where each hyperedge can contain an arbitrary number of tails and heads.
Directed hypergraphs can be used to model data flow and execution dependencies
in streaming applications. Thus, hypergraph partitioning algorithms can be used
to obtain efficient parallelizations for multiprocessor architectures. However,
an acyclicity constraint on the partition is necessary when mapping streaming
applications to embedded multiprocessors due to resource restrictions on this
type of hardware. The acyclic hypergraph partitioning problem is to partition
the hypernodes of a directed acyclic hypergraph into a given number of blocks
of roughly equal size such that the corresponding quotient graph is acyclic
while minimizing an objective function on the partition.
  Here, we contribute the first n-level algorithm for the acyclic hypergraph
partitioning problem. Our focus is on acyclic hypergraphs where hyperedges can
have one head and arbitrary many tails. Based on this, we engineer a memetic
algorithm to further reduce communication cost, as well as to improve
scheduling makespan on embedded multiprocessor architectures. Experiments
indicate that our algorithm outperforms previous algorithms that focus on the
directed acyclic graph case which have previously been employed in the
application domain. Moreover, our experiments indicate that using the directed
hypergraph model for this type of application yields a significantly smaller
makespan.


  A filtered Lie splitting scheme is proposed for the time integration of the
cubic nonlinear Schr\"odinger equation on the two-dimensional torus
$\mathbb{T}^2$. The scheme is analyzed in a framework of discrete Bourgain
spaces, which allows us to consider initial data with low regularity; more
precisely initial data in $H^s(\mathbb{T}^2)$ with $s>0$. In this way, the
usual stability restriction to smooth Sobolev spaces with index $s>1$ is
overcome. Rates of convergence of order $\tau^{s/2}$ in $L^2(\mathbb{T}^2)$ at
this regularity level are proved. Numerical examples illustrate that these
convergence results are sharp.


  We construct local, unitary gauge theories that violate Lorentz symmetry
explicitly at high energies and are renormalizable by weighted power counting.
They contain higher space derivatives, which improve the behavior of
propagators at large momenta, but no higher time derivatives. We show that the
regularity of the gauge-field propagator privileges a particular spacetime
breaking, the one into into space and time. We then concentrate on the simplest
class of models, study four dimensional examples and discuss a number of issues
that arise in our approach, such as the low-energy recovery of Lorentz
invariance.


  In this paper, we provide a new characterization of Keisler's order in terms
of saturation of Boolean ultrapowers. To do so, we apply and expand the
framework of 'separation of variables' recently developed by Malliaris and
Shelah. We also show that good ultrafilters on Boolean algebras are precisely
the ones which capture the maximum class in Keisler's order, answering a
question posed by Benda in 1974.


  We study the planar magnetic textures in an insulating magnetic film coupled
to the Dirac surface state of a topological insulator. It is shown that the
radial vortex with winding number $w=\pm1$ leads to the confinement of Dirac
states, where an exact mapping to the Schr\"{o}dinger equation of a
two-dimensional hydrogen atom is found. The fully spin polarized zero energy
bound state resembles the zeroth Landau level of Dirac electrons in a uniform
out-of-plane magnetic field. Interestingly, when the hybrid system is proximity
coupled to an $s$-wave superconductor, the existence of Majorana zero modes at
Abrikosov vortex depends only on the relative value of the magnetic exchange
coupling and the pairing strength. We conclude with a brief discussion on the
physical realization with such magnetic textures.


  The jaggedness of an order ideal I in a poset P is the number of maximal
elements in I plus the number of minimal elements of P not in I. A probability
distribution on the set of order ideals of P is toggle-symmetric if for every p
in P, the probability that p is maximal in I equals the probability that p is
minimal not in I. In this paper, we prove a formula for the expected jaggedness
of an order ideal of P under any toggle-symmetric probability distribution when
P is the poset of boxes in a skew Young diagram. Our result extends the main
combinatorial theorem of Chan-L\'opez-Pflueger-Teixidor, who used an expected
jaggedness computation as a key ingredient to prove an algebro-geometric
formula; and it has applications to homomesies, in the sense of Propp-Roby, of
the antichain cardinality statistic for order ideals in partially ordered sets.


  Phase-space representations are of increasing importance as a viable and
successful means to study exponentially complex quantum many-body systems from
first principles. This review traces the background of these methods, starting
from the early work of Wigner, Glauber and Sudarshan. We focus on modern
phase-space approaches using non-classical phase-space representations. These
lead to the Gaussian representation, which unifies bosonic and fermionic
phase-space. Examples treated include quantum solitons in optical fibers,
colliding Bose-Einstein condensates, and strongly correlated fermions on
lattices.


  The study is devoted to the development of new effective tools and methods of
ana-lytical hydrodynamics, including problems of existence, smoothness and
structure of laminar and turbulent flows. The main problem is complex
Navier-Stokes equations and turbulence in complex spaces. The necessity of
introducing complex spaces in hydrodynamics is deter-mined by the mechanism of
transition of a laminar flow into a turbulent flow. The author pro-poses a
non-traditional scenario of the transition: the cause of turbulence is in
destruction (cessation of existence) of a laminar flow. The article contains
the mathematical rationale for the necessity of development of the theory of
turbulence in the complex configurational space: the complex configurational
space is the natural area of existence of turbulence. Hydrody-namic flows are
regarded as flows on entropy manifolds that [flows] are supported by the two
symmetries: the symmetry of conservation of general entropy and the symmetry of
duality of impulse representation. The new symmetry has been introduced and
studied: the forminvari-ance of Helmholtz matrix of impulse density. The strict
foundation has been provided for the known fact of chaotic mechanics:
appearance of the new structure (a turbulent flow) is a result of interaction
of two entities: dissipation and vorticity. On the deep level the phenomenology
of turbulence in complex spaces is based on the transition from the mechanics
of a material point to the mechanics of an oriented material point, that
[transition] takes place in a current period of time.


  A new microscopic derivation of the elastic constants of amorphous solids is
presented within the framework of nonaffine lattice dynamics, which makes use
of a perturbative form of the low-frequency eigenvectors of the dynamical
matrix introduced in [V. Mazzacurati, G. Ruocco, M. Sampoli EPL 34, 681
(1996)]. The theory correctly recovers the shear modulus at jamming, $\mu \sim
(z-2d)$, including prefactors in quantitative agreement with simulations.
Furthermore, this framework allows us, for the first time, to include the
effect of internal stresses. The theory shows that the Maxwell rigidity
criterion $z=2d$ is violated with internal stress. In particular, $\mu \sim
(z-2df)$ where $f<1$ if the bonds are, on average, stretched, and the solid is
thus rigid below the Maxwell isostatic limit, while $f>1$ if the bonds are, on
average, compressed. The coefficient $f$ is derived in analytical form and
depends only on $d$ and on the average particle displacement from the
interaction energy minimum.


  This paper develops and summarizes the work of building the autonomous
integrated system including perception system and vehicle dynamic controller
for a formula student autonomous racecar. We propose a system framework
combining X-by-wired modification, perception & motion planning and vehicle
dynamic control as a template of FSAC racecar which can be easily replicated. A
LIDAR-vision cooperating method of detecting traffic cone which is used as
track mark is proposed. Detection algorithm of the racecar also implements a
precise and high rate localization method which combines the GPS-INS data and
LIDAR odometry. Besides, a track map including the location and color
information of the cones is built simultaneously. Finally, the system and
vehicle performance on a closed loop track is tested. This paper also briefly
introduces the Formula Student Autonomous Competition (FSAC).


  We investigate low-energy fluctuations in the real kink crystal phase of
dense quark matter within the Nambu--Jona-Lasinio model. The modulated chiral
condensate breaks both the translational symmetry and chiral symmetry
spontaneously, which leads to the appearance of phonons and pions that are
dominant degrees of freedom in the infrared. Using the Ginzburg-Landau
expansion near the Lifshitz point, we derive elastic free energies for phonons
and pions in dependence on the temperature and chemical potential. We show that
the one-dimensional modulation is destroyed by thermal fluctuations of phonons
at nonzero temperature, and compute the exponent that characterizes the
anisotropic algebraic decay of quasicondensate correlations at long distance.
We also estimate finite-volume effects on the stability of the real kink
crystal and briefly discuss the possibility of its existence in neutron stars.


  We present computational and experimental results on how artificial
intelligence (AI) learns to control an Acrobot using reinforcement learning
(RL). Thereby the experimental setup is designed as an embedded system, which
is of interest for robotics and energy harvesting applications. Specifically,
we study the control of angular velocity of the Acrobot, as well as control of
its total energy, which is the sum of the kinetic and the potential energy. By
this means the RL algorithm is designed to drive the angular velocity or the
energy of the first pendulum of the Acrobot towards a desired value. With this,
libration or full rotation of the unactuated pendulum of the Acrobot is
achieved. Moreover, investigations of the Acrobot control are carried out,
which lead to insights about the influence of the state space discretization,
the episode length, the action space or the mass of the driven pendulum on the
RL control. By further numerous simulations and experiments the effects of
parameter variations are evaluated.


  We explore the zero-temperature behavior of an assembly of bosons interacting
through a zero-range, attractive potential. Because the two-body interaction
admits a bound state, the many-body model is best described by a Hamiltonian
that includes the coupling between atomic and molecular components. Due to the
positive scattering length, the low-density collection is expected to remain
stable against collapse despite the attraction between particles. Although a
variational many-body analysis indicates a collapsing solution with only a
molecular component to its condensate at low density, the expected atomic
condensate solution can be obtained if the chemical potential is allowed to be
complex valued. In addition to revealing two discrete eigenfrequencies
associated with the molecular case, an expansion in small oscillations
quantifies the imaginary part of the chemical potential as proportional to a
coherent decay rate of the atomic condensate into a continuum of collective
phonon excitations about the collapsing lower state.


  Superconductivity (SC) in twisted bilayer graphene (tBLG) has been explored
by varying carrier concentrations, twist angles, and screening strength, with
the aim of uncovering its origin and possible connections to strong electronic
correlations in narrow bands and various resulting broken symmetries. However,
the link between the tBLG band structure and the onset of SC and other orders
largely remains unclear. In this study, we address this crucial gap by
examining in-situ band structure tuning of a near magic-angle ($\theta
\approx0.95^0$) tBLG device with displacement field ($D$) and reveal remarkable
competition between SC and other broken symmetries. At zero $D$, the device
exhibits superconducting signatures without the resistance peak at
half-filling, a characteristic signature with a strong electronic correlation.
As $D$ increases, the SC is suppressed, accompanied by the appearance of a
resistance peak at half-filling. Hall density measurements reveal that at zero
$D$, SC arises around the van Hove singularity (vHs) from an isospin or
spin-valley unpolarized band. At higher $D$, the suppression of SC coincides
with broken isospin symmetry near half-filling with lifted degeneracy ($g_d
\sim 2$). Additionally, when SC is suppressed at higher $D$, density waves
around the superconducting dome are seen. These findings, with our theoretical
calculations, highlight the competition between SC and other orders, and the
stabilization of the latter by the electric field enhanced nesting in the band
structure of tBLG.


  We aim to tackle sparse-view reconstruction of a 360 3D scene using priors
from latent diffusion models (LDM). The sparse-view setting is ill-posed and
underconstrained, especially for scenes where the camera rotates 360 degrees
around a point, as no visual information is available beyond some frontal views
focused on the central object(s) of interest. In this work, we show that
pretrained 2D diffusion models can strongly improve the reconstruction of a
scene with low-cost fine-tuning. Specifically, we present SparseSplat360
(Sp2360), a method that employs a cascade of in-painting and artifact removal
models to fill in missing details and clean novel views. Due to superior
training and rendering speeds, we use an explicit scene representation in the
form of 3D Gaussians over NeRF-based implicit representations. We propose an
iterative update strategy to fuse generated pseudo novel views with existing 3D
Gaussians fitted to the initial sparse inputs. As a result, we obtain a
multi-view consistent scene representation with details coherent with the
observed inputs. Our evaluation on the challenging Mip-NeRF360 dataset shows
that our proposed 2D to 3D distillation algorithm considerably improves the
performance of a regularized version of 3DGS adapted to a sparse-view setting
and outperforms existing sparse-view reconstruction methods in 360 scene
reconstruction. Qualitatively, our method generates entire 360 scenes from as
few as 9 input views, with a high degree of foreground and background detail.


  To explore the static properties of the one-dimensional anyon-Hubbard model
for a mean density of one particle per site, we apply perturbation theory with
respect to the ratio between kinetic energy and interaction energy in the Mott
insulating phase. The strong-coupling results for the ground-state energy, the
single-particle excitation energies, and the momentum distribution functions up
to 6th order in hopping are benchmarked against the numerically exact
(infinite) density-matrix renormalization group technique. Since these analytic
expressions are valid for any fractional phase $\theta$ of anyons, they will be
of great value for a sufficiently reliable analysis of future experiments,
avoiding extensive and costly numerical simulations.


  We extend the construction of the relativistic Toda chains as integrable
systems on the Poisson submanifolds in Lie groups beyond the case of A-series.
For the simply-laced case this is just a direct generalization of the
well-known relativistic Toda chains, and we construct explicitly the set of the
Ad-invariant integrals of motion on symplectic leaves, which can be described
by the Poisson quivers being just the blown up Dynkin diagrams. We also
demonstrate how to get the set of "minimal" integrals of motion, using the
co-multiplication rules for the corresponding Lie algebras. In the non
simply-laced case the corresponding Bogoyavlensky-Coxeter-Toda systems are
constructed using the Fock-Goncharov folding of the corresponding Poisson
submanifolds. We discuss also how this procedure can be extended for the affine
case beyond A-series, and consider explicitly an example from the affine
D-series.


  Quantum compiling, a process that decomposes the quantum algorithm into a
series of hardware-compatible commands or elementary gates, is of fundamental
importance for quantum computing. We introduce an efficient algorithm based on
deep reinforcement learning that compiles an arbitrary single-qubit gate into a
sequence of elementary gates from a finite universal set. It generates
near-optimal gate sequences with given accuracy and is generally applicable to
various scenarios, independent of the hardware-feasible universal set and free
from using ancillary qubits. For concreteness, we apply this algorithm to the
case of topological compiling of Fibonacci anyons and obtain near-optimal
braiding sequences for arbitrary single-qubit unitaries. Our algorithm may
carry over to other challenging quantum discrete problems, thus opening up a
new avenue for intriguing applications of deep learning in quantum physics.


  The cloud-in-cloud problem is studied in the context of the extension to
non-Gaussian density fields of the Press-Schechter approach for the calculation
of the mass function. As an example of a non-Gaussian probability distribution
functions (PDFs) we consider the Chi-square, with various degrees of freedom.
We generate density fields in cubic boxes with periodic boundary conditions and
then determine the number of points considered collapsed at each scale through
an hierarchy of smoothing windows. We find that the mass function we obtain
differs from that predicted using the Extended Press-Schechter formalism,
particularly for low values of $\sigma$ and for those PDFs most distinct from a
Gaussian.


  To measure the spin period of the white dwarf in V1033 Cas with high
precision, we performed extensive photometry. Observations were obtained over
34 nights in 2017. The total duration of the observations was 143 h. We found
that the spin period of the white dwarf is equal to 563.11633+/-0.00010 s.
Using this period, we derived the oscillation ephemeris with a long validity of
100 years. The spin oscillation semi-amplitude was stable and was equal to
95.5+/-1.3 mmag. This is a very large semi-amplitude of the spin oscillation
among intermediate polars, which have similar and lesser spin periods. This
large semi-amplitude suggests that the system is noticeably inclined. The spin
pulse profile was sinusoidal with high accuracy. This may mean that the spin
oscillation is produced by a single accretion curtain whereas the second
accretion curtain may be obscured by the accretion disc. Despite the large
amount of our observations, we did not detect sidebands. The semi-amplitudes of
the undetected sideband oscillations do not exceed 10 mmag. The absence of
sideband oscillations seems puzzling. We detected the orbital variability of
V1033 Cas with a period of 4.0243+/-0.0028 h and with a semi-amplitude of
55+/-4 mmag. The orbital variability semi-amplitude seems large and also
suggests that the system is noticeably inclined. Using our oscillation
ephemeris and the times of spin pulse maximum obtained in the past, we found
that the spin period is very stable. dP/dt is most probably less than -4 X
10^(-12). This contradicts the assumption that the white dwarf in V1033 Cas is
not spinning at equilibrium. Our spin period and our oscillation ephemeris can
be used for further investigations of the stability of the spin period in V1033
Cas.


  We derive generalized Langevin equations for the translational and rotational
motion of a heated Brownian particle from the fluctuating hydrodynamics of its
non-isothermal solvent. The temperature gradient around the particle couples to
the hydrodynamic modes excited by the particle itself so that the resulting
noise spectrum is governed by a frequency-dependent temperature. We show how
the effective temperatures at which the article coordinates and (angular)
velocities appear to be thermalized emerge from this central quantity.


  Since COVID-19 was first identified in December 2019, various public health
interventions have been implemented across the world. As different measures are
implemented at different countries at different times, we conduct an assessment
of the relative effectiveness of the measures implemented in 18 countries and
regions using data from 22/01/2020 to 02/04/2020. We compute the top one and
two measures that are most effective for the countries and regions studied
during the period. Two Explainable AI techniques, SHAP and ECPI, are used in
our study; such that we construct (machine learning) models for predicting the
instantaneous reproduction number ($R_t$) and use the models as surrogates to
the real world and inputs that the greatest influence to our models are seen as
measures that are most effective. Across-the-board, city lockdown and contact
tracing are the two most effective measures. For ensuring $R_t<1$, public
wearing face masks is also important. Mass testing alone is not the most
effective measure although when paired with other measures, it can be
effective. Warm temperature helps for reducing the transmission.


  Efficient global optimization is the problem of minimizing an unknown
function f, using as few evaluations f(x) as possible. It can be considered as
a continuum-armed bandit problem, with noiseless data and simple regret.
Expected improvement is perhaps the most popular method for solving this
problem; the algorithm performs well in experiments, but little is known about
its theoretical properties. Implementing expected improvement requires a choice
of Gaussian process prior, which determines an associated space of functions,
its reproducing-kernel Hilbert space (RKHS). When the prior is fixed, expected
improvement is known to converge on the minimum of any function in the RKHS. We
begin by providing convergence rates for this procedure. The rates are optimal
for functions of low smoothness, and we modify the algorithm to attain optimal
rates for smoother functions. For practitioners, however, these results are
somewhat misleading. Priors are typically not held fixed, but depend on
parameters estimated from the data. For standard estimators, we show this
procedure may never discover the minimum of f. We then propose alternative
estimators, chosen to minimize the constants in the rate of convergence, and
show these estimators retain the convergence rates of a fixed prior.


  In this paper, we investigate Hamiltonian path problem in the context of
split graphs, and produce a dichotomy result on the complexity of the problem.
Our main result is a deep investigation of the structure of $K_{1,4}$-free
split graphs in the context of Hamiltonian path problem, and as a consequence,
we obtain a polynomial-time algorithm to the Hamiltonian path problem in
$K_{1,4}$-free split graphs. We close this paper with the hardness result: we
show that, unless P=NP, Hamiltonian path problem is NP-complete in
$K_{1,5}$-free split graphs by reducing from Hamiltonian cycle problem in
$K_{1,5}$-free split graphs. Thus this paper establishes a "thin complexity
line" separating NP-complete instances and polynomial-time solvable instances.


  Using the MOPED algorithm we determine non-parametrically the Stellar Mass
Function of 96,545 galaxies from the Sloan Digital Sky Survey data release one.
By using the reconstructed spectrum due to starlight we can eliminate
contamination from either emission lines or AGN components. Our results give
excellent agreement with previous works, but extend their range by more than
two decades in mass to 10^{7.5} < M_s/h^{-2}M_\odot < 10^{12}. We present both
a standard Schechter fit and a fit modified to include an extra, high-mass
contribution, possibly from cluster cD galaxies. The Schechter fit parameters
are $\phi^*=(7.7\pm 0.8)\times 10^{-3} h^3 Mpc^{-3}$, $M^*=(7.53 \pm 0.04)
\times 10^{10} h^{-2}M_\odot$ and $\alpha=-1.167\pm 0.004$. Our sample also
yields an estimate for the contribution from baryons in stars to the critical
density of $\Omega_{b*}h=(2.40 \pm 0.04) \times 10^{-3}$, in good agreement
with other indicators. Error bars are statistical and a Salpeter IMF is assumed
throughout. We find no evolution of the mass function in the redshift range
$0.05 < z < 0.34$ indicating that almost all present day stars were already
formed at $z \sim 0.34$ with little or no star formation activity since then
and that the evolution seen in the luminosity function must be largely due to
stellar fading.


  We construct average spectra of host galaxies of slower, faster, bluer, and
redder Type Ia Supernovae (SNe Ia) from the SDSS-II supernova survey. The
average spectrum of slower declining (broader light-curve width or higher
stretch) SN Ia hosts shows stronger emission lines compared to the average
spectrum of faster declining (narrower light-curve width or lower stretch) SN
Ia hosts. Using pPXF, we find that hosts of slower declining SNe Ia have
metallicities that are, on average, 0.24 dex lower than average metallicities
of faster declining SN Ia hosts. Similarly, redder SN Ia hosts have slightly
higher metallicities than bluer SN Ia hosts. Lick index analysis of metallic
lines and Balmer lines show that faster declining SN Ia hosts have relatively
higher metal content and have relatively older stellar populations compared
with slower declining SN Ia hosts. We calculate average $\rm H_{\alpha}$ Star
Formation Rate (SFR), stellar mass, and the specific-SFR (sSFR) of host
galaxies in these subgroups of SNe Ia. We find that slower declining SN Ia
hosts have significantly higher ($>5\sigma$) sSFR than faster declining SN Ia
hosts. A Kolmogorov-Smirnov test shows that these two types of hosts originate
from different parent distributions. Our results, when compared with the models
of \cite{childress14}, indicate that slower declining SNe Ia, being hosted in
actively star-forming galaxies, are young (prompt) SNe Ia, originating from
similar progenitor age groups.


  We analyze the 0.5-10 keV spectra of six Seyfert 2 galaxies observed with the
X-ray satellite ASCA: Mrk 3, Mrk 348, Mrk 1210, Mrk 477, NGC 7212, and Was 49b.
These galaxies were selected based on their possession of optical polarized
broad lines. In the 2-10 keV band, their spectra are heavily absorbed, with
2-10 keV absorption-corrected X-ray luminosities ranging from 10^{42} to
10^{43} erg/s. The observed X-ray emission is generally only about one tenth
that predicted based on their known infrared and H_beta luminosities. This
apparent X-ray weakness can be understood if a considerable fraction of the
nuclear activity is completely blocked from view by thick matter along our line
of sight to the nucleus.
  All of these galaxies possess significant soft X-ray emission whose origin
appears to be scattered light from their nuclear emission. Based on this
hypothesis, we estimate a typical scattering efficiency for X-rays to be about
10%. This efficiency is larger than the few % found for ordinary Seyfert 2
galaxies with no report of optical polarized broad lines. A large scattering
efficiency is best explained by an apparent weakness of the hard X-ray
luminosity rather than unusually strong scattered light in the soft band. The
difference of the apparent weakness is probably associated with viewing angle.


  For a (possibly large) realized limit sketch $\mathcal{S}$ such that every
$\mathcal{S}$-model is small in a suitable sense we show that the category of
cocontinuous functors $\mathsf{Mod}(\mathcal{S}) \to \mathcal{C}$ into a
cocomplete category $\mathcal{C}$ is equivalent to the category
$\mathsf{Mod}_{\mathcal{C}}(\mathcal{S}^{\mathrm{op}})$ of $\mathcal{C}$-valued
$\mathcal{S}^{\mathrm{op}}$-models. From this result we deduce universal
properties of several examples of cocomplete categories appearing in practice.
It can be applied in particular to infinitary Lawvere theories, generalizing
the well-known case of finitary Lawvere theories. We also look at a large limit
sketch that models $\mathsf{Top}$, study the corresponding notion of an
internal net-based topological space object, and deduce from our main result
that cocontinuous functors $\mathsf{Top} \to \mathcal{C}$ into a cocomplete
category $\mathcal{C}$ correspond to net-based cotopological space objects
internal to $\mathcal{C}$. Finally, we describe a limit sketch that models
$\mathsf{Top}^{\mathrm{op}}$ and deduce from our main result that continuous
functors $\mathsf{Top} \to \mathcal{C}$ into a complete category $\mathcal{C}$
correspond to frame-based topological space objects internal to $\mathcal{C}$.
Thus, we characterize $\mathsf{Top}$ both as a cocomplete and as a complete
category. Thereby we get two new conceptual proofs of Isbell's classification
of cocontinuous functors $\mathsf{Top} \to \mathsf{Top}$ in terms of
topological topologies.


  The explanation of the apparent universality of thermodynamics points toward
the extension of the usual conceptual background of the second law. Arguments
are collected that a basic guiding idea of stability of thermodynamic
equilibrium combined with a proper interpretation of the entropy principle may
provide the necessary solid foundation with verifiable consequences.


  We study Hall-Littlewood polynomials using an integrable lattice model of
$t$-deformed bosons. Working with row-to-row transfer matrices, we review the
construction of Hall-Littlewood polynomials (of the $A_n$ root system) within
the framework of this model. Introducing appropriate double-row transfer
matrices, we extend this formalism to Hall-Littlewood polynomials based on the
$BC_n$ root system, and obtain a new combinatorial formula for them. We then
apply our methods to prove a series of refined Cauchy and Littlewood identities
involving Hall-Littlewood polynomials. The last two of these identities are
new, and relate infinite sums over hyperoctahedrally symmetric Hall-Littlewood
polynomials with partition functions of the six-vertex model on finite domains.


  We study the nonperturbative dynamics of nonsupersymmetric asymptotically
free gauge theories with fermionic matter in distinct representations of the
SO(N) and Sp(2N) gauge groups. We use different analytic methods to unveil the
associated conformal windows for the relevant matter representations. We
propose a direct test for confronting and establishing the validity of the
analytic methods used to constrain the conformal windows. By comparing the
resulting windows for SU, Sp and SO a pleasing universal picture emerges.


  The Hartree-Fock approximation of Quantum Electrodynamics provides a rigorous
framework for the description of relativistic electrons in external fields.
This nonlinear model takes into account the infinitely many virtual electrons
of Dirac's vacuum as well as the Coulomb interactions between all the
particles. The state of the system is an infinite-rank projection satisfying a
nonlinear equation. In this paper, we construct solutions to this equation, in
the regime of weak interactions (that is, small coupling constant $\alpha$),
and strong external fields (that is, large atomic charge $Z$ such that $\alpha
Z:=\kappa$ stays fixed). In this regime, we are able to remove the ultraviolet
cut-off $\Lambda$ as soon as $\alpha\log\Lambda$ stays fixed. As an application
of this result, we compare the critical strength $\kappa_c(\alpha)$ of the
external potential needed to produce an additional particle in the vacuum, when
$\alpha=0$ or $\alpha>0$. We prove that
$\lim_{\alpha\to0}\kappa_c(\alpha)/\kappa_c(0)> 1$, and we identify the limit
exactly. Because of the dielectric behavior of Dirac's vacuum, static
electron/positron pair production occurs in the interacting case for a stronger
field that in the non-interacting case, which is a mere consequence of charge
renormalization.


  We give error estimates in Peng's central limit theorem for not necessarily
nondegenerate case. The exposition uses the language of the classical
probability theory instead of the language of the theory of sublinear
expectations. We only consider the one-dimensional case. The higher dimensional
extension is straightforward.


  This work addresses challenges arising from extracting entities from textual
data, including the high cost of data annotation, model accuracy, selecting
appropriate evaluation criteria, and the overall quality of annotation. We
present a framework that integrates Entity Set Expansion (ESE) and Active
Learning (AL) to reduce the annotation cost of sparse data and provide an
online evaluation method as feedback. This incremental and interactive learning
framework allows for rapid annotation and subsequent extraction of sparse data
while maintaining high accuracy. We evaluate our framework on three publicly
available datasets and show that it drastically reduces the cost of sparse
entity annotation by an average of 85% and 45% to reach 0.9 and 1.0 F-Scores
respectively. Moreover, the method exhibited robust performance across all
datasets.


  In this paper, we propose a method to automatically identify future events in
Lebanon's economy from Arabic texts. Challenges are threefold: first, we need
to build a corpus of Arabic texts that covers Lebanon's economy; second, we
need to study how future events are expressed linguistically in these texts;
and third, we need to automatically identify the relevant textual segments
accordingly. We will validate this method on a constructed corpus form the web
and show that it has very promising results. To do so, we will be using SLCSAS,
a system for semantic analysis, based on the Contextual Explorer method, and
"AlKhalil Morpho Sys" system for morpho-syntactic analysis.


  We present the prospects for studying quantum correlated charm decays at the
\psi(3770) using 0.5--1.0 ab^{-1} of data at SuperB. The impact of studying
such double tagged decays upon measurements in other charm environments will be
discussed.


  We consider the decoding problem or the problem of finding low weight
codewords for rank metric codes. We show how additional information about the
codeword we want to find under the form of certain linear combinations of the
entries of the codeword leads to algorithms with a better complexity. This is
then used together with a folding technique for attacking a McEliece scheme
based on LRPC codes. It leads to a feasible attack on one of the parameters
suggested in \cite{GMRZ13}.


  We investigated the temporally evolving network structures of the Japanese
and Korean stock markets through the minimum spanning trees composed of listed
stocks. We tested the validity of conventional grouping by industrial
categories, and found a common trend of decrease for Japan and Korea. This
phenomenon supports the increasing external effects on the markets due to the
globalization of both countries. At last the Korean market are grouped with the
MSCI Korea Index, a good reference for foreigners' trading, in the early 2000s
\cite{Jung2006}. In the Japanese market, this tendency is strengthened more and
more by burst of the bubble in 1990's.


  We design an adaptive finite element method to approximate the solutions of
quasi-linear elliptic problems. The algorithm is based on a Ka\v{c}anov
iteration and a mesh adaptation step is performed after each linear solve. The
method is thus \emph{inexact} because we do not solve the discrete nonlinear
problems exactly, but rather perform one iteration of a fixed point method
(Ka\v{c}anov), using the approximation of the previous mesh as an initial
guess. The convergence of the method is proved for any \emph{reasonable}
marking strategy and starting from any initial mesh. We conclude with some
numerical experiments that illustrate the theory.


  The five-dimensional Ising model with free boundary conditions has recently
received a renewed interest in a debate concerning the finite-size scaling of
the susceptibility near the critical temperature. We provide evidence in favour
of the conventional scaling picture, where the susceptibility scales as
$O(L^2)$ inside a critical scaling window of width $O(1/L^2)$. Our results are
based on Monte Carlo data gathered on system sizes up to $L=79$ (ca. three
billion spins) for a wide range of temperatures near the critical point. We
analyse the magnetisation distribution, the susceptibility and also the scaling
and distribution of the size of the Fortuin-Kasteleyn cluster containing the
origin. The probability of this cluster reaching the boundary determines the
correlation length, and its behaviour agrees with the mean field critical
exponent $\delta=3$, that the scaling window has width $O(1/L^2)$.


  Natural Language Inference is an important task for Natural Language
Understanding. It is concerned with classifying the logical relation between
two sentences. In this paper, we propose several text generative neural
networks for generating text hypothesis, which allows construction of new
Natural Language Inference datasets. To evaluate the models, we propose a new
metric -- the accuracy of the classifier trained on the generated dataset. The
accuracy obtained by our best generative model is only 2.7% lower than the
accuracy of the classifier trained on the original, human crafted dataset.
Furthermore, the best generated dataset combined with the original dataset
achieves the highest accuracy. The best model learns a mapping embedding for
each training example. By comparing various metrics we show that datasets that
obtain higher ROUGE or METEOR scores do not necessarily yield higher
classification accuracies. We also provide analysis of what are the
characteristics of a good dataset including the distinguishability of the
generated datasets from the original one.


  A sharp version of a recent inequality of Kovalev and Yang on the ratio of
the $(H^1)^\ast$ and $H^4$ norms for certain polynomials is obtained. The
inequality is applied to establish a sharp and tractable sufficient condition
for the Wirtinger derivatives at the origin for harmonic self-maps of the unit
disc which fix the origin.


  Motivated by wavelet analysis, we prove that there is a one-to-one
correspondence between the following data: Solutions to $R(h)=h$ where $R$ is a
certain non-positive Ruelle transfer operator; Operators that intertwine a
certain class of representations of the $C^*$-algebra $\mathfrak{A}_N$ on two
unitary generators $U$, $V$ subject to the relation $$UVU^{-1}=V^N$$ This
correspondence enables us to give a criterion for the biorthogonality of a pair
of scaling functions and calculate all solutions of the equation $R(h)=h$ in
some concrete cases.


  In recent years, soft prompt learning methods have been proposed to fine-tune
large-scale vision-language pre-trained models for various downstream tasks.
These methods typically combine learnable textual tokens with class tokens as
input for models with frozen parameters. However, they often employ a single
prompt to describe class contexts, failing to capture categories' diverse
attributes adequately. This study introduces the Partitioned Multi-modal Prompt
(PMPO), a multi-modal prompting technique that extends the soft prompt from a
single learnable prompt to multiple prompts. Our method divides the visual
encoder depths and connects learnable prompts to the separated visual depths,
enabling different prompts to capture the hierarchical contextual depths of
visual representations. Furthermore, to maximize the advantages of multi-prompt
learning, we incorporate prior information from manually designed templates and
learnable multi-prompts, thus improving the generalization capabilities of our
approach. We evaluate the effectiveness of our approach on three challenging
tasks: new class generalization, cross-dataset evaluation, and domain
generalization. For instance, our method achieves a $79.28$ harmonic mean,
averaged over 11 diverse image recognition datasets ($+7.62$ compared to CoOp),
demonstrating significant competitiveness compared to state-of-the-art
prompting methods.


  We give a brief introduction to Luttinger liquids and to the phenomena of
electronic transport or conductance in quantum wires. We explain why the
subject of transport in Luttinger liquids is relevant and fascinating and
review some important results on tunneling through barriers in a
one-dimensional quantum wire and the phenomena of persistent currents in
mesoscopic rings. We give a brief description of our own work on transport
through doubly-crossed Luttinger liquids and transport in the Schulz-Shastry
exactly solvable Luttinger-like model.


  The aim of this note is to study the dynamo properties of the
magnetohydrodynamics system at vanishing Rm. Improving the analysis of a former
study, we shall establish a generic Lyapunov instability result.


  A classical problem in ergodic continuous time control consists of studying
the limit behavior of the optimal value of a discounted cost functional with
infinite horizon as the discount factor $\lambda$ tends to zero. In the
literature, this problem has been addressed under various controllability or
ergodicity conditions ensuring that the rescaled value function converges
uniformly to a constant limit. In this case the limit can be characterized as
the unique constant such that a suitable Hamilton-Jacobi equation has at least
one continuous viscosity solution. In this paper, we study this problem without
such conditions, so that the aforementioned limit needs not be constant. Our
main result characterizes the uniform limit (when it exists) as the maximal
subsolution of a system of Hamilton-Jacobi equations. Moreover, when such a
subsolution is a viscosity solution, we obtain the convergence of optimal
values as well as a rate of convergence. This mirrors the analysis of the
discrete time case, where we characterize the uniform limit as the supremum
over a set of sub-invariant half-lines of the dynamic programming operator. The
emerging structure in both discrete and continuous time models shows that the
supremum over sub-invariato half-lines with respect to the Lax-Oleinik
semigroup/dynamic programming operator, captures the behavior of the limit cost
as discount vanishes.


  Recently, several authors have investigated topological phenomena in
periodically-driven systems of non-interacting particles. These phenomena are
identified through analogies between the Floquet spectra of driven systems and
the band structures of static Hamiltonians. Intriguingly, these works have
revealed that the topological characterization of driven systems is richer than
that of static systems. In particular, in driven systems in two dimensions
(2D), robust chiral edge states can appear even though the Chern numbers of all
the bulk Floquet bands are zero. Here we elucidate the crucial distinctions
between static and driven 2D systems, and construct a new topological invariant
that yields the correct edge state structure in the driven case. We provide
formulations in both the time and frequency domains, which afford additional
insight into the origins of the "anomalous" spectra which arise in driven
systems. Possible realizations of these phenomena in solid state and cold
atomic systems are discussed.


  Sparse linear algebra kernels play a critical role in numerous applications,
covering from exascale scientific simulation to large-scale data analytics.
Offloading linear algebra kernels on one GPU will no longer be viable in these
applications, simply because the rapidly growing data volume may exceed the
memory capacity and computing power of a single GPU. Multi-GPU systems nowadays
being ubiquitous in supercomputers and data-centers present great potentials in
scaling up large sparse linear algebra kernels. In this work, we design a novel
sparse matrix representation framework for multi-GPU systems called MSREP, to
scale sparse linear algebra operations based on our augmented sparse matrix
formats in a balanced pattern. Different from dense operations, sparsity
significantly intensifies the difficulty of distributing the computation
workload among multiple GPUs in a balanced manner. We enhance three mainstream
sparse data formats -- CSR, CSC, and COO, to enable fine-grained data
distribution. We take sparse matrix-vector multiplication (SpMV) as an example
to demonstrate the efficiency of our MSREP framework. In addition, MSREP can be
easily extended to support other sparse linear algebra kernels based on the
three fundamental formats (i.e., CSR, CSC and COO).


  In pool-based active learning, the learner is given an unlabeled data set and
aims to efficiently learn the unknown hypothesis by querying the labels of the
data points. This can be formulated as the classical Optimal Decision Tree
(ODT) problem: Given a set of tests, a set of hypotheses, and an outcome for
each pair of test and hypothesis, our objective is to find a low-cost testing
procedure (i.e., decision tree) that identifies the true hypothesis. This
optimization problem has been extensively studied under the assumption that
each test generates a deterministic outcome. However, in numerous applications,
for example, clinical trials, the outcomes may be uncertain, which renders the
ideas from the deterministic setting invalid. In this work, we study a
fundamental variant of the ODT problem in which some test outcomes are noisy,
even in the more general case where the noise is persistent, i.e., repeating a
test gives the same noisy output. Our approximation algorithms provide
guarantees that are nearly best possible and hold for the general case of a
large number of noisy outcomes per test or per hypothesis where the performance
degrades continuously with this number. We numerically evaluated our algorithms
for identifying toxic chemicals and learning linear classifiers, and observed
that our algorithms have costs very close to the information-theoretic minimum.


  The polarized synchrotron data of the northern C-BASS survey show a
surprisingly low linear polarization fraction, $\Pi\simeq 3\%$, while the
magnetic field polarization features coherent structures over rather large
angular scales. The low polarization degree points to a strong dominance of the
turbulent magnetic field -- in agreement with the observation that the total
synchrotron intensity is much larger than expected from the regular component
in current models for the Galactic magnetic field (GMF). In contrast, studies
of cosmic ray propagation employing these GMF models suggest that cosmic rays
propagate anisotropically, what in turn requires weak turbulent fields. As a
solution to this contradicting requirements, we suggest that the GMF consists
of three components with different levels of turbulence: a disk dominated by
the turbulent field, a halo dominated by the regular field, plus an extended
turbulent halo field.


  Platforms for all-optical computing possess photonic circuits made of
silicon-based channels, metal wires or optical fibers, etc. However, such solid
waveguides suffer from the lack of reversibility and reconfigurability if
facing the next generation of light-guiding-light (LGL) computing scheme, which
envisions circuitry-free and rapidly reconfigurable systems powered by dynamic
interactions between light beams. Here, we proposed the ubiquitous air as a
restorable LGL signal manipulation medium with transient air-plasma waveguide
circuits. Briefly, by focusing femtosecond laser beams in the free space, the
created atmospherical plasma filament array via photoionization was able to
guide terahertz (THz) pulses along its epsilon-near-zero (ENZ) zone with a
1/f-profile spectral response. Consequently, this achieved a time-domain
integration of the THz pulse in broad bandwidth. When the pumping laser was
sequentially turned off and on, this multi-filament air-plasma structure was
erased and rebuilt within nano- and femto-seconds, respectively, allowing rapid
and repeated rearrangements of the all-optical stage. Furthermore, this
air-based LGL information processing approach is promising to pave the way
towards all-optical calculations during free-space directional transmission of
THz waves, by which means the delivered THz signal can be remotely controlled.


  Clustering is a widely used unsupervised learning technique involving an
intensive discrete optimization problem. Associative Memory models or AMs are
differentiable neural networks defining a recursive dynamical system, which
have been integrated with various deep learning architectures. We uncover a
novel connection between the AM dynamics and the inherent discrete assignment
necessary in clustering to propose a novel unconstrained continuous relaxation
of the discrete clustering problem, enabling end-to-end differentiable
clustering with AM, dubbed ClAM. Leveraging the pattern completion ability of
AMs, we further develop a novel self-supervised clustering loss. Our
evaluations on varied datasets demonstrate that ClAM benefits from the
self-supervision, and significantly improves upon both the traditional Lloyd's
k-means algorithm, and more recent continuous clustering relaxations (by upto
60% in terms of the Silhouette Coefficient).


  We study in detail the structure of phase space in the neighborhood of stable
periodic orbits in a rotating 3D potential of galactic type. We have used the
color and rotation method to investigate the properties of the invariant tori
in the 4D spaces of section. We compare our results with those of previous
works and we describe the morphology of the rotational, as well as of the tube
tori in the 4D space. We find sticky chaotic orbits in the immediate
neighborhood of sets of invariant tori surrounding 3D stable periodic orbits.
Particularly useful for galactic dynamics is the behavior of chaotic orbits
trapped for long time between 4D invariant tori. We find that they support
during this time the same structure as the quasi-periodic orbits around the
stable periodic orbits, contributing however to a local increase of the
dispersion of velocities. Finally we find that the tube tori do not appear in
the 3D projections of the spaces of section in the axisymmetric Hamiltonian we
examined.


  Under the potential outcomes framework, causal effects are defined as
comparisons between potential outcomes under treatment and control. To infer
causal effects from randomized experiments, Neyman proposed to test the null
hypothesis of zero average causal effect (Neyman's null), and Fisher proposed
to test the null hypothesis of zero individual causal effect (Fisher's null).
Although the subtle difference between Neyman's null and Fisher's null has
caused lots of controversies and confusions for both theoretical and practical
statisticians, a careful comparison between the two approaches has been lacking
in the literature for more than eighty years. We fill in this historical gap by
making a theoretical comparison between them and highlighting an intriguing
paradox that has not been recognized by previous researchers. Logically,
Fisher's null implies Neyman's null. It is therefore surprising that, in actual
completely randomized experiments, rejection of Neyman's null does not imply
rejection of Fisher's null for many realistic situations, including the case
with constant causal effect. Furthermore, we show that this paradox also exists
in other commonly-used experiments, such as stratified experiments,
matched-pair experiments, and factorial experiments. Asymptotic analyses,
numerical examples, and real data examples all support this surprising
phenomenon. Besides its historical and theoretical importance, this paradox
also leads to useful practical implications for modern researchers.


  We analyze how a probing particle modifies the infrared electromagnetic near
field of a sample. The particle, described by electric and magnetic
polarizabilities, represents the tip of an apertureless scanning optical
near-field microscope (SNOM). We show that the interaction with the sample can
be accounted for by ascribing to the particle dressed polarizabilities that
combine the effects of image dipoles with retardation. When calculated from
these polarizabilities, the SNOM signal depends only on the fields without the
perturbing tip. If the studied surface is not illuminated by an external source
but heated instead, the signal is closely related to the projected
electromagnetic local density of states (EM-LDOS). Our calculations provide the
link between the measured far-field spectra and the sample's optical
properties.We also analyze the case where the probing particle is hotter than
the sample and evaluate the impact of the dressed polarizabilities on
near-field radiative heat transfer. We show that such a heated probe above a
surface performs a surface spectroscopy, in the sense that the spectrum of the
heat current is closely related to the local electromagnetic density of states.
The calculations agree well with available experimental data.


  We investigate the growth optimal strategy over a finite time horizon for a
stock and bond portfolio in an analytically solvable multiplicative Markovian
market model. We show that the optimal strategy consists in holding the amount
of capital invested in stocks within an interval around an ideal optimal
investment. The size of the holding interval is determined by the intensity of
the transaction costs and the time horizon.


  This work presents author's explicit methods of constructing abelian
extensions of complete discrete valuation fields. His approach to explicit
equations of a cyclic extension of degree p^n which contains a given cyclic
extension of degree p is explained.


  It is demonstrated how perturbative O(alpha_s^2) relativistic corrections to
the non-relativistic stable heavy quark-antiquark production cross section in
e^+e^- annihilation based on a Coulombic QCD potential can be systematically
calculated using the concept of effective field theories. The O(alpha_s^2)
corrections from the relativistic energy-momentum relation, the relativistic
phase space corrections and the O(alpha_s^2) corrections involving the group
theoretical factors C_F^2 and C_F T are determined explicitly. For the case of
$t\bar t$ production the sum of these corrections amounts to 3% - 7% over the
whole threshold regime and is insensitive to variations in the top width.
Perturbative O(alpha_s^2) corrections to the leptonic decay width of heavy
quark-antiquark $^3S_1$ vector resonances are extracted.


  Aims. We analyse the effects of a first generation of fast rotating massive
stars on the dynamical and chemical properties of globular clusters. Methods.
We use stellar models of fast rotating massive stars, losing mass through a
slow mechanical equatorial winds to produce material rich in H-burning
products. We propose that stars with high Na and low O abundances (hereafter
anomalous stars) are formed from matter made of slow winds of individual
massive stars and of interstellar matter. The proportion of slow wind and of
interstellar material is fixed in order to reproduce the observed Li-Na
anticorrelation in NGC 6752. Results. In the case that globular clusters,
during their lifetime, did not lose any stars, we found that to reproduce the
observed ratio of normal to anomalous stars, a flat initial mass function (IMF)
is needed, with typically a slope x=0.55 (a Salpeter's IMF has x=1.35). In the
case that globular clusters suffer from an evaporation of normal stars, the IMF
slope can be steeper: to have x=1.35, about 96% of the normal stars would be
lost. We make predictions for the distribution of stars as a function of their
[O/Na] and obtain quite reasonable agreement with that one observed for NGC
6752. Predictions for the number fraction of stars with different values of
helium, of the 12C/13C and 16O/17O ratios are discussed, as well as the
expected relations between values of [O/Na] and those of helium, of [C/N], of
12C/13C and of 16O/17O. Future observations might test these predictions. We
also provide predictions for the present day mass of the clusters expressed in
units of mass of the gas used to form stars, and for the way the present day
mass is distributed between the first and second generation of stars and the
stellar remnants.


  Retention of plasma-implanted D is studied in W targets damaged by a Cu ion
beam at up to 0.2 dpa with sample temperatures between 300 K and 1200 K. At a D
plasma ion fluence of $10^{24}/m^2$ on samples damaged to 0.2 dpa at 300 K, the
retained D retention inventory is $4.6x10^{20} D/m^2$, about ~5.5 times higher
than in undamaged samples. The retained inventory drops to $9x10^{19} D/m^2$
for samples damaged to 0.2 dpa at 1000 K, consistent with onset of vacancy
annealing at a rate sufficient to overcome the elevated rate of ion beam
damage; at a damage temperature of 1200 K retention is nearly equal to values
seen in undamaged materials. A nano-scale technique provides thermal
conductivity measurements from the Cu- ion beam displacement damaged region. We
find the thermal conductivity of W damaged to 0.2 dpa at room temperature drops
from the un-irradiated value of 182 +/- 3.3 W/m-K to 53 +/- 8 W/m-K.


  There is a growing interest in techniques for detecting whether a logic
specification is satisfied too easily, or vacuously. For example, the
specification "every request is eventually followed by an acknowledgment" is
satisfied vacuously by a system that never generates any requests. Vacuous
satisfaction misleads users of model-checking into thinking that a system is
correct.
  There are several existing definitions of vacuity. Originally, Beer et al.
formalized vacuity as insensitivity to syntactic perturbation. However, this
definition is only reasonable for vacuity in a single occurrence. Armoni et al.
argued that vacuity must be robust -- not affected by semantically invariant
changes, such as extending a model with additional atomic propositions. They
show that syntactic vacuity is not robust for LTL, and propose an alternative
definition -- trace vacuity.
  In this article, we continue this line of research. We show that trace
vacuity is not robust for branching time logic. We refine it to apply uniformly
to linear and branching time logic and to not suffer from the common pitfalls
of prior definitions. Our new definition -- bisimulation vacuity -- is a proper
non-trivial extension of both syntactic and trace vacuity. We discuss the
complexity of detecting bisimulation vacuity, and give efficient algorithms to
detect vacuity for several practically-relevant subsets of CTL*.


  We introduce the concept of a Background-subtracted Solar Activity Map
(BaSAM) as a new quantitative tool to assess and visualize the temporal
variation of the photospheric magnetic field and the UV 160 nm intensity. The
method utilizes data of the Solar Dynamics Observatory (SDO) and is applicable
to both full-disk observations and regions-of-interest. We illustrate and
discuss the potential of BaSAM resorting to datasets representing solar minimum
and maximum conditions: (1) Contributions of quiet-Sun magnetic fields, i.e.
the network and (decaying) plage, to solar activity can be better determined
when their variation is measured with respect to the background given by "deep"
magnetograms. (2) Flaring and intermittent brightenings are easily appraised in
BaSAMs of the UV intensity. (3) Both magnetic-field and intensity variations
demonstrated that the flux system of sunspots is well connected to the
surrounding supergranular cells. In addition, producing daily full-disk BaSAMs
for the entire mission time of SDO provides a unique tool to analyze solar
cycle variations, showing how vigorous or frail are the variations of
magnetic-field and intensity features.


  This paper considers the problem of designing maximum distance separable
(MDS) codes over small fields with constraints on the support of their
generator matrices. For any given $m\times n$ binary matrix $M$, the GM-MDS
conjecture, due to Dau et al., states that if $M$ satisfies the so-called MDS
condition, then for any field $\mathbb{F}$ of size $q\geq n+m-1$, there exists
an $[n,m]_q$ MDS code whose generator matrix $G$, with entries in $\mathbb{F}$,
fits $M$ (i.e., $M$ is the support matrix of $G$). Despite all the attempts by
the coding theory community, this conjecture remains still open in general. It
was shown, independently by Yan et al. and Dau et al., that the GM-MDS
conjecture holds if the following conjecture, referred to as the TM-MDS
conjecture, holds: if $M$ satisfies the MDS condition, then the determinant of
a transformation matrix $T$, such that $TV$ fits $M$, is not identically zero,
where $V$ is a Vandermonde matrix with distinct parameters. In this work, we
generalize the TM-MDS conjecture, and present an algebraic-combinatorial
approach based on polynomial-degree reduction for proving this conjecture. Our
proof technique's strength is based primarily on reducing inherent
combinatorics in the proof. We demonstrate the strength of our technique by
proving the TM-MDS conjecture for the cases where the number of rows ($m$) of
$M$ is upper bounded by $5$. For this class of special cases of $M$ where the
only additional constraint is on $m$, only cases with $m\leq 4$ were previously
proven theoretically, and the previously used proof techniques are not
applicable to cases with $m > 4$.


  We study an isoperimetric problem described by a functional that consists of
the standard Gaussian perimeter and the norm of the barycenter. This second
term has a repulsive effect, and it is in competition with the perimeter.
Because of that, in general the solution is not the half-space. We characterize
all the minimizers of this functional, when the volume is close to one, by
proving that the minimizer is either the half-space or the symmetric strip,
depending on the strength of the repulsive term. As a corollary, we obtain that
the symmetric strip is the solution of the Gaussian isoperimetric problem among
symmetric sets when the volume is close to one.


  Let F be a field of characteristic not 2 and assume all algebras are over F.
We establish several conjugacy theorems for the special linear Lie algebra sl_2
over an F-algebra which is a UFD. We find the structure of the full
automorphism group as well as conditions for when two such algebras are
isomorphic. We also study the structure of their derivation algebras. Often we
work with more general coordinates when this if feasible.


  The similarity of the observed mass densities of baryons and cold dark matter
may be a sign they have a related origin. The baryon-to-dark matter ratio can
be understood in the MSSM with right-handed (RH) neutrinos if CDM is due to a d
= 4 flat direction condensate of very weakly coupled RH sneutrino LSPs and the
baryon asymmetry is generated by Affleck-Dine leptogenesis along a d = 4
(H_{u}L)^2 flat direction. Observable signatures of the model include CDM and
baryon isocurvature perturbations and distinctive long-lived NLSP
phenomenology.


  Cogent is a restricted functional language designed to reduce the cost of
developing verified systems code. Because of its sometimes-onerous
restrictions, such as the lack of support for recursion and its strict
uniqueness type system, Cogent provides an escape hatch in the form of a
foreign function interface (FFI) to C code. This poses a problem when verifying
Cogent programs, as imported C components do not enjoy the same level of static
guarantees that Cogent does. Previous verification of file systems implemented
in Cogent merely assumed that their C components were correct and that they
preserved the invariants of Cogent's type system. In this paper, we instead
prove such obligations. We demonstrate how they smoothly compose with existing
Cogent theorems, and result in a correctness theorem of the overall Cogent-C
system. The Cogent FFI constraints ensure that key invariants of Cogent's type
system are maintained even when calling C code. We verify reusable higher-order
and polymorphic functions including a generic loop combinator and array
iterators and demonstrate their application to several examples including
binary search and the BilbyFs file system. We demonstrate the feasibility of
verification of mixed Cogent-C systems, and provide some insight into
verification of software comprised of code in multiple languages with differing
levels of static guarantees.


  Reinforcement Learning from Human Feedback (RLHF) has enabled significant
advancements within language modeling for powerful, instruction-following
models. However, the alignment of these models remains a pressing challenge as
the policy tends to overfit the learned ``proxy" reward model past an
inflection point of utility as measured by a ``gold" reward model that is more
performant -- a phenomenon known as overoptimisation. Prior work has mitigated
this issue by computing a pessimistic statistic over an ensemble of reward
models, which is common in Offline Reinforcement Learning but incredibly costly
for language models with high memory requirements, making such approaches
infeasible for sufficiently large models. To this end, we propose using a
shared encoder but separate linear heads. We find this leads to similar
performance as the full ensemble while allowing tremendous savings in memory
and time required for training for models of similar size.


  New spectroscopic orbits of inner subsystems in 14 hierarchies are determined
from long-term monitoring with the optical echelle spectrometer, CHIRON. Their
main components are nearby solar-type stars belonging to nine triple systems
(HIP 3645, 14307, 36165, 79980, 103735, 103814, 104440, 105879, 109443) and
five quadruples of 2+2 hierarchy (HIP 41171, 49336, 75663, 78163, and 117666).
The inner periods range from 254 days to 18 yr. Inner subsystems in HIP 3645,
14313, 79979, 103735, 104440, and 105879 are resolved by speckle
interferometry, and their combined spectro-interferometric orbits are derived
here. Astrometric orbits of HIP 49336 Aa,Ab and HIP 117666 Aa,Ab are determined
from wobble in the observed motion of the outer pairs. Comparison with three
spectroscopic orbits found in the Gaia DR3 archive reveals that Gaia
under-estimated the amplitudes (except for HIP 109443), while the periods match
approximately. This work contributes new data on the architecture of nearby
hierarchical systems, complementing their statistics.


  Contrastive learning has made considerable progress in computer vision,
outperforming supervised pretraining on a range of downstream datasets.
However, is contrastive learning the better choice in all situations? We
demonstrate two cases where it is not. First, under sufficiently small
pretraining budgets, supervised pretraining on ImageNet consistently
outperforms a comparable contrastive model on eight diverse image
classification datasets. This suggests that the common practice of comparing
pretraining approaches at hundreds or thousands of epochs may not produce
actionable insights for those with more limited compute budgets. Second, even
with larger pretraining budgets we identify tasks where supervised learning
prevails, perhaps because the object-centric bias of supervised pretraining
makes the model more resilient to common corruptions and spurious
foreground-background correlations. These results underscore the need to
characterize tradeoffs of different pretraining objectives across a wider range
of contexts and training regimes.


  We extend the idea of quantum phase transitions of light in atom-photon
system with Dicke-Bose-Hubbard model for arbitrary number of two-level atoms.
The formulations of eigenenergies, effective Rabi frequencies, and critical
chemical potentials for two atoms are derived. With a self-consistent method,
we obtain a complete phase diagram for two two-level atoms on resonance, which
indicates the transition from Mott insulator to superfluidity and with a mean
excitations diagram for confirmation. We illustrate the generality of the
method by constructing the dressed-state basis for arbitrary number of
two-level atoms. In addition, we show that the Mott insulator lobes in the
phase diagrams will smash out with the increase of atom numbers. The results of
this work provide a step for studying the effects with combinations of
Dicke-like and Hubbard-like models to simulate strongly correlated electron
systems using photons.


  This text is the rejoinder following the discussion of a survey paper about
minimal penalties and the slope heuristics (Arlot, 2019. Minimal penalties and
the slope heuristics: a survey. Journal de la SFDS). While commenting on the
remarks made by the discussants, it provides two new results about the slope
heuristics for model selection among a collection of projection estimators in
least-squares fixed-design regression. First, we prove that the slope
heuristics works even when all models are significantly biased. Second, when
the noise is Gaussian with a general dependence structure, we compute
expectations of key quantities, showing that the slope heuristics certainly is
valid in this setting also.


  We give a sharp bound for the Lebesgue constant associated to Leja sequences
in the complex unit disk, confirming a conjecture made by Calvi and Phung in
2011