  We consider the phase equilibria of a fluid confined in a deep capillary
groove of width $L$ with identical side walls and a bottom made of a different
material. All walls are completely wet by the liquid. Using density functional
theory and interfacial models, we show that the meniscus separating liquid and
gas phases at two phase capillary-coexistence meets the bottom capped end of
the groove at a capillary contact angle $\theta^{\rm cap}(L)$ which depends on
the difference between the Hamaker constants. If the bottom wall has a weaker
wall-fluid attraction than the side walls, then $\theta^{\rm cap}>0$ even
though all the isolated walls are themselves completely wet. This alters the
capillary condensation transition which is now first-order; this would be
continuous in a capped capillary made wholly of either type of material. We
show that the capillary contact angle $\theta^{\rm cap}(L)$ vanishes in two
limits, corresponding to different capillary wetting transitions. These occur
as the width i) becomes macroscopically large, and ii) is reduced to a
microscopic value determined by the difference in Hamaker constants. This
second wetting transition is characterised by large scale fluctuations and
essential critical singularities arising from marginal interfacial
interactions.


  We construct solutions to the Strominger system on a class of noncompact
Calabi-Yau 3-folds. These spaces include $\mathbb{C}^3$ and resolved conifold
$\mathcal{O}(-1,-1)$ as special examples.


  We present a new "learning-to-learn"-type approach that enables rapid
learning of concepts from small-to-medium sized training sets and is primarily
designed for web-initialized image retrieval. At the core of our approach is a
deep architecture (a Set2Model network) that maps sets of examples to simple
generative probabilistic models such as Gaussians or mixtures of Gaussians in
the space of high-dimensional descriptors. The parameters of the embedding into
the descriptor space are trained in the end-to-end fashion in the meta-learning
stage using a set of training learning problems. The main technical novelty of
our approach is the derivation of the backprop process through the mixture
model fitting, which makes the likelihood of the resulting models
differentiable with respect to the positions of the input descriptors.
  While the meta-learning process for a Set2Model network is discriminative, a
trained Set2Model network performs generative learning of generative models in
the descriptor space, which facilitates learning in the cases when no negative
examples are available, and whenever the concept being learned is polysemous or
represented by noisy training sets. Among other experiments, we demonstrate
that these properties allow Set2Model networks to pick visual concepts from the
raw outputs of Internet image search engines better than a set of strong
baselines.


  The perturbative approach to stochastic inflation is used to determine the
spectrum of density fluctuations and gravitational waves due to the coarse
grained field. The amplitude of the curvature fluctuation spectrum, the
spectral index and the running of the spectral index are in general found to be
smaller than in the standard approach to inflation. Furthermore, the amount of
non-gaussianity due to the second order perturbation is estimated.


  Two-dimensional affine A-nets in 3-space are quadrilateral meshes that
discretize surfaces parametrized along asymptotic lines. The characterizing
property of A-nets is planarity of vertex stars, so for generic A-nets the
elementary quadrilaterals are skew. We classify the simply connected affine
A-nets that can be extended to continuously differentiable surfaces by gluing
hyperboloid surface patches into the skew quadrilaterals. The resulting
surfaces are called "hyperbolic nets" and are a novel piecewise smooth
discretization of surfaces parametrized along asymptotic lines. It turns out
that a simply connected affine A-net has to satisfy one combinatorial and one
geometric condition to be extendable - all vertices have to be of even degree
and all quadrilateral strips have to be "equi-twisted". Furthermore, if an
A-net can be extended to a hyperbolic net, then there exists a 1-parameter
family of such C^1-surfaces. It is briefly explained how the generation of
hyperbolic nets can be implemented on a computer. The article uses the
projective model of Pluecker geometry to describe A-nets and hyperboloids.


  We investigate charged dilatonic black $p$-branes smeared on a transverse
circle. The system can be reduced to neutral vacuum black branes, and we
perform static perturbations for the reduced system to construct non-uniform
solutions. At each order a single master equation is derived, and the
Gregory-Laflamme critical wavelength is determined. Based on the non-uniform
solutions, we discuss thermodynamic properties of this system and argue that in
a microcanonical ensemble the non-uniform smeared branes are entropically
disfavored even near the extremality, if the spacetime dimension is $D \le 13
+p$, which is the critical dimension for the vacuum case. However, the critical
dimension is not universal. In a canonical ensemble the vacuum non-uniform
black branes are thermodynamically favorable at $D > 12+p$, whereas the
non-uniform smeared branes are favorable at $D > 14+p$ near the extremality.


  A general controller scheme for stabilizing a non-linear system, which has
its origin from the linear system theory, is proposed in this paper. The
proposed controller can stabilize the non-linear system subjected to initial
conditions. An effective way to obtain the controller parameters is presented
with the knowledge of the system model. The controller is designed for the
linear time-invariant (LTI) system, which can reject any disturbance acting on
it. Paper emphasis the idea of an integrator controller in disturbance
rejection. The concept is extended to the application to non-linear systems
where the non-linearities are assessed as the disturbance to the refined linear
part of the system. Boundedness and convergence of the non-linear system with
the controller are proved to justify system stabilization. Hardware
implementation of the controller on the 2 dof helicopter model is presented
with experimental results, which validates the proposed control scheme.


  This is the first comprehensive introduction to the authors' recent attempts
toward a better understanding of the global concepts behind spinor
representations of surfaces in 3-space. The important new aspect is a
quaternionic-valued function theory, whose "meromorphic functions" are
conformal maps into quaternions, which extends the classical complex function
theory on Riemann surfaces. The first results along these lines were presented
at the ICM 98 in Berlin. An important new invariant of the quaternionic
holomorphic theory is the Willmore energy. For quaternionic holomorphic curves
in the quaternionic projective line, i.e., the conformal 4-sphere, this energy
is the classical Willmore energy of conformal surfaces. Using these new
techniques, the article discusses the mean curvature sphere of conformal
surfaces in the 4-sphere, Willmore surfaces in the 4-sphere, Baecklund
tranformations of Willmore surfaces, super-conformal surfaces and twistor
projections, and a duality between Willmore surfaces in the 3-sphere and
minimal surfaces in hyperbolic 3-space. Finally, a new proof of Montiel's
recent classification of Willmore 2-spheres in the 4-sphere is given.


  The randomized fixe-composition with optimal decoding error exponents are
studied \cite{Raul_ISIT,Raul_journal} for the finite alphabet interference
channel (IFC) with two transmitter-receiver pairs. In this paper we investigate
the capacity region of the randomized fixed-composition coding scheme. A
complete characterization of the capacity region of the said coding scheme is
given. The inner bound is derived by showing the existence of a positive error
exponent within the capacity region. A simple universal decoding rule is given.
The tight outer bound is derived by extending a technique first developed in
\cite{Dueck_RC} for single input output channels to interference channels. It
is shown that even with a sophisticated time-sharing scheme among randomized
fixed-composition codes, the capacity region of the randomized
fixed-composition coding is not bigger than the known Han-Kobayashi
\cite{Han_Kobayashi} capacity region. This suggests that the average behavior
of random codes are not sufficient to get new capacity regions.


  This paper proposes a novel model for predicting subgraphs in dynamic graphs,
an extension of traditional link prediction. This proposed end-to-end model
learns a mapping from the subgraph structures in the current snapshot to the
subgraph structures in the next snapshot directly, i.e., edge existence among
multiple nodes in the subgraph. A new mechanism named cross-attention with a
twin-tower module is designed to integrate node attribute information and
topology information collaboratively for learning subgraph evolution. We
compare our model with several state-of-the-art methods for subgraph prediction
and subgraph pattern prediction in multiple real-world homogeneous and
heterogeneous dynamic graphs, respectively. Experimental results demonstrate
that our model outperforms other models in these two tasks, with a gain
increase from 5.02% to 10.88%.


  We remove the need to physically transport computational anyons around each
other from the implementation of computational gates in topological quantum
computing. By using an anyonic analog of quantum state teleportation, we show
how the braiding transformations used to generate computational gates may be
produced through a series of topological charge measurements.


  We point out four problems which have arisen during the recent research in
the domain of Combinatorial Physics.


  We have developed a simulation model of particle acceleration in coronal
shock waves. The model is based on a Monte Carlo method, where particles are
traced in prescribed large-scale electromagnetic fields utilizing the guiding
center approximation. The particles are scattered in the turbulence according
to quasilinear theory, with the scattering amplitude directly proportional to
the intensity of Alfv\'en waves at gyro-resonant wavenumbers. The Alfv\'en
waves are traced simultaneously with the particles, so that the wave field is
propagated outwards from the Sun using WKB propagation supplemented with a
phenomenological wavenumber diffusion term and a growth rate computed from the
net flux of the accelerated particles. We consider initial wave amplitudes
small enough to allow rapid escape of particles from the shock to the ambient
medium. Thus, in our model the Alfv\'en waves responsible for the diffusive
acceleration of particles are generated by the accelerated particles
themselves. In this work, we study the effects of non-constant shock velocity
and non-monotonic Alfv\'en velocity on particle acceleration scenarios. We
report in particular how the deceleration of a shock affects particle intensity
and turbulence power evolution in the vicinity of the shock.


  High-energy emission of extragalactic objects is known to take place in
relativistic jets, but the nature, the location, and the emission processes of
the emitting particles are still unknown. One of the models proposed to explain
the formation of relativistic ejections and their associated non-thermal
emission is the two-flow model, where the jets are supposed to be composed of
two different flows, a mildly relativistic baryonic jet surrounding a fast,
relativistically moving electron-positron plasma. Here we present the
simulation of the emission of such a structure taking into account the main
sources of photons that are present in active galactic nuclei (AGNs). We
reproduce the broadband spectra of radio-loud AGNs with a detailed model of
emission taking into account synchrotron and inverse-Compton emission by a
relativistically moving beam of electron-positron, heated by a surrounding
turbulent baryonic jet. We compute the density and energy distribution of a
relativistic pair plasma all along a jet, taking into account the synchrotron
and inverse-Compton process on the various photon sources present in the core
of the AGN, as well as the pair creation and annihilation processes. We use
semi-analytical approximations to quickly compute the inverse-Compton process
on a thermal photon distribution with any anisotropic angular distribution. The
anisotropy of the photon field is also responsible for the bulk acceleration of
the pair plasma through the "Compton rocket" effect, thus imposing the plasma
velocity along the jet. As an example, the simulated emerging spectrum is
compared to the broadband emission of 3C273. In the case of 3C273, we obtain an
excellent fit of the average broadband energy distribution by assuming physical
parameters compatible with known estimates.


  In [19], Zheng studied the bounded derived categories of constructible
$\bar{\mathbb{Q}}_l$-sheaves on some algebraic stacks consisting of the
representations of a enlarged quiver and categorified the integrable highest
weight modules of the corresponding quantum group by using these categories. In
this paper, we shall generalize Zheng's work to highest weight modules of a
subalgebra of the double Ringel-Hall algebra associated to a quiver in a
functional version.


  Lies can have profoundly negative consequences for individuals, groups, and
even for societies. Understanding how lying evolves and when it proliferates is
therefore of significant importance for our personal and societal well-being.
To that effect, we here study the sender-receiver game in well-mixed
populations with methods of statistical physics. We use the Monte Carlo method
to determine the stationary frequencies of liars and believers for four
different lie types. We consider altruistic white lies that favor the receiver
at a cost to the sender, black lies that favor the sender at a cost to the
receiver, spiteful lies that harm both the sender and the receiver, and Pareto
white lies that favor both the sender and the receiver. We find that spiteful
lies give rise to trivial behavior, where senders quickly learn that their best
strategy is to send a truthful message, whilst receivers likewise quickly learn
that their best strategy is to believe the sender's message. For altruistic
white lies and black lies, we find that most senders lie while most receivers
do not believe the sender's message, but the exact frequencies of liars and
non-believers depend significantly on the payoffs, and they also evolve
non-monotonically before reaching the stationary state. Lastly, for Pareto
white lies we observe the most complex dynamics, with the possibility of both
lying and believing evolving with all frequencies between 0 and 1 in dependence
on the payoffs. We discuss the implications of these results for moral behavior
in human experiments.


  We show that the Heun confluent equation admits infinitely many solutions in
terms of the confluent generalized hypergeometric functions. For each of these
solutions a characteristic exponent of a regular singularity of the Heun
confluent equation is a non-zero integer and the accessory parameter obeys a
polynomial equation. Each of the solutions can be written as a linear
combination with constant coefficients of a finite number of either the Kummer
confluent hypergeometric functions or the Bessel functions.


  The aim of this work is to characterize linear maps of inner pro\-duct
infinite-dimensional vector spaces where the Moore-Penrose inverse exists. This
MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $A\in
\text{Mat}_{n\times m} ({\mathbb C})$. Moreover, a method for the computation
of the MP inverse of some endomorphisms on infinite-dimensional vector spaces
is given. As an application, we study the least norm solution of an infinite
linear system from the Moore-Penrose inverse offered.


  This paper establishes a number of constraints on the structure of large
cardinals under strong compactness assumptions. These constraints coincide with
those imposed by the Ultrapower Axiom, a principle that is expected to hold in
Woodin's hypothesized Ultimate \(L\), providing some evidence for the Ultimate
\(L\) Conjecture.
  We show that every regular cardinal above the first strongly compact that
carries an indecomposable ultrafilter is measurable, answering a question of
Silver for large enough cardinals. We show that any successor almost strongly
compact cardinal of uncountable cofinality is strongly compact, making progress
on a question of Boney, Unger, and Brooke-Taylor. We show that if there is a
proper class of strongly compact cardinals then there is no nontrivial cardinal
preserving elementary embedding from the universe of sets into an inner model,
answering a question of Caicedo granting large cardinals. Finally, we show that
if \(\kappa\) is strongly compact, then \(V\) is a set forcing extension of the
inner model \(\kappa\text{-HOD}\) consisting of sets that are hereditarily
ordinal definable from a \(\kappa\)-complete ultrafilter over an ordinal;
\(\kappa\text{-HOD}\) seems to be the first nontrivial example of a ground of
\(V\) whose definition does not involve forcing.


  Our ability to interpret and glean useful information from the large body of
observations of strongly magnetised neutron stars rests largely on our
theoretical understanding of magnetic field equilibria. We answer the following
question: is one free to arbitrarily prescribe magnetic equilibria such that
fluid degrees of freedom can balance the equilibrium equations? We examine this
question for various models for neutron star matter; from the simplest
single-fluid barotrope to more realistic non-barotropic multifluid models with
superfluid/superconducting components, muons and entropy. We do this for both
axi- and non-axisymmetric equilibria, and in Newtonian gravity and general
relativity. We show that, in axisymmetry, the most realistic model allows
complete freedom in choosing a magnetic field equilibrium whereas
non-axisymmetric equilibria are never completely arbitrary.


  We consider the problem of forecasting complex, nonlinear space-time
processes when observations provide only partial information of on the system's
state. We propose a natural data-driven framework, where the system's dynamics
are modelled by an unknown time-varying differential equation, and the
evolution term is estimated from the data, using a neural network. Any future
state can then be computed by placing the associated differential equation in
an ODE solver. We first evaluate our approach on shallow water and Euler
simulations. We find that our method not only demonstrates high quality
long-term forecasts, but also learns to produce hidden states closely
resembling the true states of the system, without direct supervision on the
latter. Additional experiments conducted on challenging, state of the art ocean
simulations further validate our findings, while exhibiting notable
improvements over classical baselines.


  Exciton polaritons are hybrid particles of excitons (bound electron-hole
pairs) and cavity photons, which are renowned for displaying Bose Einstein
condensation and other coherent phenomena at elevated temperatures. However,
their formation in semiconductor microcavities is often accompanied by the
appearance of an incoherent bath of optically dark excitonic states that can
interact with polaritons via their matter component. Here we show that the
presence of such a dark excitonic medium can "dress" polaritons with density
fluctuations to form coherent polaron-like quasiparticles, thus fundamentally
modifying their character. We employ a many-body Green's function approach that
naturally incorporates correlations beyond the standard mean-field theories
applied to this system. With increasing exciton density, we find a reduction in
the light-matter coupling that arises from the polaronic dressing cloud rather
than any saturation induced by the fermionic constituents of the exciton. In
particular, we observe the strongest effects when the spin of the polaritons is
opposite that of the excitonic medium. In this case, the coupling to light
generates an additional polaron quasiparticle - the biexciton polariton - which
emerges due to the dark-exciton counterpart of a polariton Feshbach resonance.
Our results can explain recent experiments on polariton interactions in
two-dimensional semiconductors and potentially provide a route to tailoring the
properties of exciton polaritons and their correlations.


  It is possible to reduce the discrepancy between the local measurement of the
cosmological parameter $H_0$ and the value derived from the $Planck$
measurements of the Cosmic Microwave Background (CMB) by considering
contamination of the CMB by emission from some medium around distant
extragalactic sources, such as extremely cold coarse-grain dust. Though being
distant, such a medium would still be in the foreground with respect to the
CMB, and, as any other foreground, it would alter the CMB power spectrum. This
could contribute to the dispersion of CMB temperature fluctuations. By
generating a few random samples of CMB with different dispersions, we have
checked that the increased dispersion leads to a smaller estimated value of
$H_0$, the rest of the cosmological model parameters remaining fixed. This
might explain the reduced value of the $Planck$-derived parameter $H_0$ with
respect to the local measurements. The signature of the distant foreground in
the CMB traced by SNe was previously reported by the authors of this paper --
we found a correlation between the SN redshifts, $z_{\rm SN}$, and CMB
temperature fluctuations at the SNe locations, $T_{\rm SN}$. Here we have used
the slopes of the regression lines $T_{\rm SN}\,/\,z_{\rm SN}$ corresponding to
different {\it Planck} wave bands in order to estimate the possible temperature
of the distant extragalactic medium, which turns out to be very low, about
5\,K. The most likely ingredient of this medium is coarse-grain ($grey$) dust,
which is known to be almost undetectable, except for the effect of dimming
remote extragalactic sources.


  In this paper, we argue that similarity-based privacy metrics cannot ensure
regulatory compliance of synthetic data. Our analysis and counter-examples show
that they do not protect against singling out and linkability and, among other
fundamental issues, completely ignore the motivated intruder test.


  The \emph{simplified} Wasserstein barycenter problem, also known as the
cheapest hub problem, consists in selecting one point from each of $k$ given
sets, each set consisting of $n$ points, with the aim of minimizing the sum of
distances to the barycenter of the $k$ chosen points. This problem is also
known as the cheapest hub problem. This problem is known to be NP-hard. We
compute the Wasserstein barycenter by exploiting the Euclidean distance matrix
structure to obtain a facially reduced doubly nonnegative, \DNNp, relaxation.
The facial reduction provides a natural splitting for applying the symmetric
alternating directions method of multipliers (\sADMM) to the \DNN relaxation.
The \sADMM method exploits structure in the subproblems to find strong upper
and lower bounds. In addition, we extend the problem to allow varying $n_j$
points for the $j$-th set.
  The purpose of this paper is twofold. First we want to illustrate the
strength of this \DNN relaxation with a splitting approach. Our numerical tests
then illustrate the surprising success on random problems, as we generally,
efficiently, find the provable exact solution of this NP-hard problem.
Comparisons with current commercial software illustrate this surprising
efficiency. However, we demonstrate and prove that there is a duality gap for
problems with \emph{enough} multiple optimal solutions, and that this arises
from problems with highly symmetrized structure.


  We have performed numerical studies of the Hubbard-Holstein model in two
dimensions using determinant quantum Monte Carlo (DQMC). Here we present
details of the method, emphasizing the treatment of the lattice degrees of
freedom, and then study the filling and behavior of the fermion sign as a
function of model parameters. We find a region of parameter space with large
Holstein coupling where the fermion sign recovers despite large values of the
Hubbard interaction. This indicates that studies of correlated polarons at
finite carrier concentrations are likely accessible to DQMC simulations. We
then restrict ourselves to the half-filled model and examine the evolution of
the antiferromagnetic structure factor, other metrics for antiferromagnetic and
charge-density-wave order, and energetics of the electronic and lattice degrees
of freedom as a function of electron-phonon coupling. From this we find further
evidence for a competition between charge-density-wave and antiferromagnetic
order at half-filling.


  The integration of biosensing platforms with drug delivery systems has led to
effective treatment strategies for biomedical applications. With the emergency
of nanotechnology, the manipulation of materials in the nanometer, these
biosensing and drug delivery systems have been tremendously improved due to the
exceptional properties exhibited by these materials. The conventional
approaches used to synthesize the nanomaterials including physical and chemical
methods involve the usage of harsh chemicals and hazardous reaction conditions
and hence posing a threat to health and the environment. This problem is solved
by the biological methods that involve green nanotechnology which integrates
green chemistry and engineering principles to formulate harmless and
eco-friendly nanomaterials to fight the complications affecting human health
and the environment. These biological methods use phytochemicals found in
plants and plants parts as well as microorganisms for the bioreduction of metal
ions to their corresponding nanomaterials. The plants and the microorganisms
are readily available, cost-efficient, and have biocompatibility hence offering
sustainable synthetic methods for nanomaterials. This review will therefore
focus on the plant-mediated and microbe-mediated green synthesis of different
nanomaterials, the mechanisms of these synthetic methods, the application of
the green synthesized nanomaterials in biosensing and drug delivery as well as
the challenges of the synthetic methods.


  We study convergence properties of pseudo-marginal Markov chain Monte Carlo
algorithms (Andrieu and Roberts [Ann. Statist. 37 (2009) 697-725]). We find
that the asymptotic variance of the pseudo-marginal algorithm is always at
least as large as that of the marginal algorithm. We show that if the marginal
chain admits a (right) spectral gap and the weights (normalised estimates of
the target density) are uniformly bounded, then the pseudo-marginal chain has a
spectral gap. In many cases, a similar result holds for the absolute spectral
gap, which is equivalent to geometric ergodicity. We consider also unbounded
weight distributions and recover polynomial convergence rates in more specific
cases, when the marginal algorithm is uniformly ergodic or an independent
Metropolis-Hastings or a random-walk Metropolis targeting a super-exponential
density with regular contours. Our results on geometric and polynomial
convergence rates imply central limit theorems. We also prove that under
general conditions, the asymptotic variance of the pseudo-marginal algorithm
converges to the asymptotic variance of the marginal algorithm if the accuracy
of the estimators is increased.


  Word-level Quality Estimation (QE) of Machine Translation (MT) aims to find
out potential translation errors in the translated sentence without reference.
Typically, conventional works on word-level QE are designed to predict the
translation quality in terms of the post-editing effort, where the word labels
("OK" and "BAD") are automatically generated by comparing words between MT
sentences and the post-edited sentences through a Translation Error Rate (TER)
toolkit. While the post-editing effort can be used to measure the translation
quality to some extent, we find it usually conflicts with the human judgement
on whether the word is well or poorly translated. To overcome the limitation,
we first create a golden benchmark dataset, namely \emph{HJQE} (Human Judgement
on Quality Estimation), where the expert translators directly annotate the
poorly translated words on their judgements. Additionally, to further make use
of the parallel corpus, we propose the self-supervised pre-training with two
tag correcting strategies, namely tag refinement strategy and tree-based
annotation strategy, to make the TER-based artificial QE corpus closer to
\emph{HJQE}. We conduct substantial experiments based on the publicly available
WMT En-De and En-Zh corpora. The results not only show our proposed dataset is
more consistent with human judgment but also confirm the effectiveness of the
proposed tag correcting strategies.\footnote{The data can be found at
\url{https://github.com/ZhenYangIACAS/HJQE}.}


  The NA48/2 collaboration has shown clear experimental evidence for a cusp in
the data for K -> pi pi^0 pi^0. This effect can be used to extract information
on the pi-pi scattering lengths. We address this issue using a two-loop
dispersive construction of pi pi -> pi pi and K -> pi pi pi amplitudes in the
presence of isospin breaking.


  We revisit the localization computation of the expectation values of 't Hooft
operators in $\mathcal{N}=2^*$ SU(N) theory on $\mathbb{R}^3 \times S^1$. We
show that the part of the answer arising from "monopole bubbling" on
$\mathbb{R}^3$ can be understood as an equivariant integral over a
Kronheimer-Nakajima moduli space of instantons on an orbifold of
$\mathbb{C}^2$. It can also be described as a Witten index of a certain
supersymmetric quiver quantum mechanics with $\mathcal{N}=(4,4)$ supersymmetry.
The map between the defect data and the quiver quantum mechanics is worked out
for all values of N. For the SU(2) theory, we compute several examples of these
line defect expectation values using the Witten index formula and confirm that
the expressions agree with the formula derived by Okuda, Ito and Taki. In
addition, we present a Type IIB construction -- involving D1-D3-NS5-branes --
for monopole bubbling in $\mathcal{N}=2^*$ SU(N) SYM and demonstrate how the
quiver quantum mechanics arises in this brane picture.


  Methods. We use the code MCFOST to solve the non-LTE problem of line
formation in non-axisymmetric accreting magnetospheres. We compute the
Br{\gamma} line profile originating from accretion columns for models with
different magnetic obliquities. We also derive monochromatic synthetic images
of the Br{\gamma} line emitting region across the line profile. This spectral
line is a prime diagnostics of magnetospheric accretion in young stars and is
accessible with the long baseline near-infrared interferometer GRAVITY
installed at the ESO Very Large Telescope Interferometer.
  Results. We derive Br{\gamma} line profiles as a function of rotational phase
and compute interferometric observables, visibilities and phases, from
synthetic images. The line profile shape is modulated along the rotational
cycle, exhibiting inverse P Cygni profiles at the time the accretion shock
faces the observer. The size of the line's emission region decreases as the
magnetic obliquity increases, which is reflected in a lower line flux. We apply
interferometric models to the synthetic visibilities in order to derive the
size of the line-emitting region. We find the derived interferometric size to
be more compact than the actual size of the magnetosphere, ranging from 50 to
90\% of the truncation radius. Additionally, we show that the rotation of the
non-axisymmetric magnetosphere is recovered from the rotational modulation of
the Br{\gamma}-to-continuum photo-centre shifts, as measured by the
differential phase of interferometric visibilities.


  In this paper, we study the hard uniform capacitated $k$- median problem
using local search heuristic. Obtaining a constant factor approximation for the
\ckm problem is open. All the existing solutions giving constant-factor
approximation, violate at least one of the cardinality and the capacity
constraints. All except Koruplou et al are based on LP-relaxation.
  We give $(3+\epsilon)$ factor approximation algorithm for the problem
violating the cardinality by a factor of $8/3 \approx 2.67$. There is a
trade-off between the approximation factor and the cardinality violation
between our work and the existing work. Koruplou et al gave $(1 + \alpha)$
approximation factor with $(5 + 5/\alpha)$ factor loss in cardinality using
local search paradigm. Though the approximation factor can be made arbitrarily
small, cardinality loss is at least $5$.
  On the other hand, we improve upon the results in
[capkmGijswijtL2013],[capkmshili2014], [Lisoda2016] in terms of factor-loss
though the cardinality loss is more in our case. Also, these results are
obtained using LP-rounding, some of them being strengthened, whereas local
search techniques are simple to apply and have been shown to perform well in
practice via empirical studies.
  We extend the result to hard uniform capacitated $k$-median with penalties.
To the best of our knowledge, ours is the first result for the problem.


  We generalize the notion of stable equivalence of Morita type and define what
is called "singular equivalence of Morita type with level". Such an equivalence
of induces an equivalence between singular categories. We will also prove that
a derived equivalence of standard type induces a singular equivalence of Morita
type with level.


  The rapid development of Large Language Models (LLMs) has led to great
strides in model capabilities like long-context understanding and reasoning.
However, as LLMs are able to process longer contexts, it becomes more
challenging to evaluate whether they have acquired certain capabilities, since
the length of text (e.g., 200K tokens) they can process far exceeds what humans
can reliably assess in a reasonable duration. In this paper, we propose using
complex synthetic tasks as a proxy evaluation method, and present S3Eval, a
Synthetic, Scalable, Systematic evaluation suite for LLMs evaluation. The
synthetic nature of S3Eval provides users full control over the dataset,
allowing them to systematically probe LLM capabilities by scaling text length
and varying task difficulty across diverse scenarios. The strong correlation
between S3Eval and real-world benchmarks demonstrates the soundness of using
S3Eval for evaluation of LLMs. S3Eval provides a flexible and infinite
long-context data generation method. We have generated a comprehensive dataset
called S3Eval-Standard, and experimental results have shown that it poses
significant challenges for all existing LLMs.


  Axisymmetric accretion disks in vicinity of a central compact body are
studied. For the simple models such as vertically isothermal disks as well as
adiabatic ones the exact solutions to the steady-state MHD
(magneto-hydrodynamic) system were found under the assumption that the radial
components of velocity and magnetic field are negligible. On the basis of the
exact solution one may conclude that vertically isothermal disks will be
totally isothermal. The exact solution for the case of adiabatic disk
corroborates the view that thin disk accretion must be highly non-adiabatic. An
intermediate approach, that is between the above-listed two, for the modeling
of thin accretion disks is developed. In the case of non-magnetic disk, this
approach enables to prove, with ease, that all solutions for the mid-plane
circular velocity are unstable provided the disk is non-viscous. Hence, this
approach enables to demonstrate that the pure hydrodynamic turbulence in
accretion disks is possible. It is interesting that a turbulent magnetic disk
tends to be Keplerian. This can easily be shown by assuming that the turbulent
gas tends to flow with minimal losses, i.e. to have the Euler number as small
as possible.


  We found an additional symmetry hidden in the fermion and Higgs sectors of
the Standard Model. It is connected to the centers of the SU(3) and SU(2)
subgroups of the gauge group. A lattice regularization of the whole Standard
Model is constructed that possesses this symmetry.


  We present images of the SNR HB3 at both 408 MHz and 1420 MHz from the
Canadian Galactic Plane Survey mainly based on data from the Synthesis
Telescope of the Dominion Radio Astrophysical Observatory. We reproduce the
100m-Effelsberg HB3 image at 2695 MHz at large scale, and find that there
exists a background emission gradient across the HB3 area. Based on our
analysis of background emission and the boundary between W3 and HB3, we give
HB3's flux density as 68.6 +/- 11.5 Jy at 408 MHz and 44.8 +/- 12.0 Jy at 1420
MHz, after subtracting flux from compact sources within HB3. The integrated
flux-density-based spectral index between 408 MHz and 1420 MHz is 0.34 +/-
0.15. The averaged T-T plot spectral index using all subareas is 0.36. Our
measurement values are less than a previously published value of 0.6. The
408-1420 MHz spectral index varies spatially in HB3 in the range 0.1 to 0.7. We
investigate the data used by previous authors, and consider more data at 232
MHz, 3650 MHz and 3900 MHz which are not included in previous calculations.
There is evidence for two spectral indices for HB3 in the radio band, i.e.,
0.63 (38 - 610 MHz) and 0.32 (408 - 3900 MHz). This is consistent with the
spatial variations: the low frequency data mainly reflects the steeper indices
and the high frequency data mainly reflects the flatter indices.


  We suggest a categorification procedure for the SO(2N) one-variable
specialization of the two-variable Kauffman polynomial. The construction has
many similarities with the HOMFLYPT categorification: a planar graph formula
for the polynomial is converted into a complex of graded vector spaces, each of
them being the homology of a Z_2 graded differential vector space associated to
a graph and constructed using matrix factorizations. This time, however, the
elementary matrix factorizations are not Koszul; instead, they are convolutions
of chain complexes of Koszul matrix factorizations. We prove that the homotopy
class of the resulting complex associated to a diagram of a link is invariant
under the first two Reidemeister moves and conjecture its invariance under the
third move.


  Nonlinear acceleration methods are powerful techniques to speed up
fixed-point iterations. However, many acceleration methods require storing a
large number of previous iterates and this can become impractical if
computational resources are limited. In this paper, we propose a nonlinear
Truncated Generalized Conjugate Residual method (nlTGCR) whose goal is to
exploit the symmetry of the Hessian to reduce memory usage. The proposed method
can be interpreted as either an inexact Newton or a quasi-Newton method. We
show that, with the help of global strategies like residual check techniques,
nlTGCR can converge globally for general nonlinear problems and that under mild
conditions, nlTGCR is able to achieve superlinear convergence. We further
analyze the convergence of nlTGCR in a stochastic setting. Numerical results
demonstrate the superiority of nlTGCR when compared with several other
competitive baseline approaches on a few problems. Our code will be available
in the future.


  To perform any meaningful optimization task, distribution grid operators need
to know the topology of their grids. Although power grid topology
identification and verification has been recently studied, discovering
instantaneous interplay among subsets of buses, also known as higher-order
interactions in recent literature, has not yet been addressed. The system
operator can benefit from having this knowledge when re-configuring the grid in
real time, to minimize power losses, balance loads, alleviate faults, or for
scheduled maintenance. Establishing a connection between the celebrated exact
distribution flow equations and the so-called self-driven graph Volterra model,
this paper puts forth a nonlinear topology identification algorithm, that is
able to reveal both the edge connections as well as their higher-order
interactions. Preliminary numerical tests using real data on a 47-bus
distribution grid showcase the merits of the proposed scheme relative to
existing alternatives.


  The majority of contemporary object-tracking approaches do not model
interactions between objects. This contrasts with the fact that objects' paths
are not independent: a cyclist might abruptly deviate from a previously planned
trajectory in order to avoid colliding with a car. Building upon HART, a neural
class-agnostic single-object tracker, we introduce a multi-object tracking
method MOHART capable of relational reasoning. Importantly, the entire system,
including the understanding of interactions and relations between objects, is
class-agnostic and learned simultaneously in an end-to-end fashion. We explore
a number of relational reasoning architectures and show that
permutation-invariant models outperform non-permutation-invariant alternatives.
We also find that architectures using a single permutation invariant operation
like DeepSets, despite, in theory, being universal function approximators, are
nonetheless outperformed by a more complex architecture based on multi-headed
attention. The latter better accounts for complex physical interactions in a
challenging toy experiment. Further, we find that modelling interactions leads
to consistent performance gains in tracking as well as future trajectory
prediction on three real-world datasets (MOTChallenge, UA-DETRAC, and Stanford
Drone dataset), particularly in the presence of ego-motion, occlusions, crowded
scenes, and faulty sensor inputs.


  Projected Entangled Pair States (PEPS) provide a framework for the
construction of models where a single tensor gives rise to both Hamiltonian and
ground state wavefunction on the same footing. A key problem is to characterize
the behavior which emerges in the system in terms of the properties of the
tensor, and thus of the Hamiltonian. In this paper, we consider PEPS models
with $\mathbb Z_2$ on-site symmetry and study the occurence of long-range order
and spontaneous symmetry breaking. We show how long-range order is connected to
a degeneracy in the spectrum of the PEPS transfer operator, and how the latter
gives rise to spontaneous symmetry breaking under perturbations. We provide a
succinct characterization of the symmetry broken states in terms of the PEPS
tensor, and find that using the symmetry broken states we can derive a local
entanglement Hamiltonian, thereby restoring locality of the entanglement
Hamiltonian for all gapped phases.


  One of the most studied forms of attacks on the cyber-physical systems is the
replay attack. The statistical similarities of the replay signal and the true
observations make the replay attack difficult to detect. In this paper, we have
addressed the problem of replay attack detection by adding watermarking to the
control inputs and then performed resilient detection using cumulative sum
(CUSUM) test on the joint statistics of the innovation signal and the
watermarking signal. We derive the expression of the Kullback-Liebler
divergence (KLD) between the two joint distributions before and after the
replay attack, which is asymptotically inversely proportional to the detection
delay. We perform structural analysis of the derived KLD expression and suggest
a technique to improve the KLD for the systems with relative degree greater
than one. A scheme to find the optimal watermarking signal variance for a fixed
increase in the control cost to maximize the KLD under the CUSUM test is
presented. We provide various numerical simulation results to support our
theory. The proposed method is also compared with a state-of-the-art method.


  In this investigation, the distribution of the ratio of two independently
distributed xgamma (Sen et al. 2016) random variables X and Y , with different
parameters, is proposed and studied. The related distributional properties such
as, moments, entropy measures, are investigated. We have also shown a unique
characterization of the proposed distribution based on truncated incomplete
moments.


  Cryptoprimitives rely on thorough theoretical background, but often lack
basic usability features making them prone to unintentional misuse by
developers. We argue that this is true even for the state-of-the-art designs.
Analyzing 52 candidates of the current CAESAR competition has shown none of
them have an avalanche effect in authentication tag strong enough to work
properly when partially misconfigured. Although not directly decreasing their
security profile, this hints at their security usability being less than
perfect. Paper details available at crcs.cz/papers/memics2016


  The Dirichlet problem for a Monge-Ampere equation corresponding to a
nonnegative, possible degenerate cohomology class on a Kaehler manifold with
boundary is studied. C^{1,\alpha} estimates away from a divisor are obtained,
by combining techniques of Blocki, Tsuji, Yau, and pluripotential theory. In
particular, C^{1,\alpha} geodesic rays in the space of Kaehler potentials are
constructed for each test configuration


  Neural Radiance Fields (NeRF) have demonstrated impressive potential in
synthesizing novel views from dense input, however, their effectiveness is
challenged when dealing with sparse input. Existing approaches that incorporate
additional depth or semantic supervision can alleviate this issue to an extent.
However, the process of supervision collection is not only costly but also
potentially inaccurate, leading to poor performance and generalization ability
in diverse scenarios. In our work, we introduce a novel model: the
Collaborative Neural Radiance Fields (ColNeRF) designed to work with sparse
input. The collaboration in ColNeRF includes both the cooperation between
sparse input images and the cooperation between the output of the neural
radiation field. Through this, we construct a novel collaborative module that
aligns information from various views and meanwhile imposes self-supervised
constraints to ensure multi-view consistency in both geometry and appearance. A
Collaborative Cross-View Volume Integration module (CCVI) is proposed to
capture complex occlusions and implicitly infer the spatial location of
objects. Moreover, we introduce self-supervision of target rays projected in
multiple directions to ensure geometric and color consistency in adjacent
regions. Benefiting from the collaboration at the input and output ends,
ColNeRF is capable of capturing richer and more generalized scene
representation, thereby facilitating higher-quality results of the novel view
synthesis. Extensive experiments demonstrate that ColNeRF outperforms
state-of-the-art sparse input generalizable NeRF methods. Furthermore, our
approach exhibits superiority in fine-tuning towards adapting to new scenes,
achieving competitive performance compared to per-scene optimized NeRF-based
methods while significantly reducing computational costs. Our code is available
at: https://github.com/eezkni/ColNeRF.


  We calculate tidally driven mean flows in a slowly and uniformly rotating
massive main sequence star in a binary system. We treat the tidal potential due
to the companion as a small perturbation to the primary star. We compute tidal
responses of the primary as forced linear oscillations, as a function of the
tidal forcing frequency $\omega_{\rm tide}=2(\Omega_{\rm orb}-\Omega)$, where
$\Omega_{\rm orb}$ is the mean orbital angular velocity and $\Omega$ is the
angular velocity of rotation of the primary star. The amplitude of the tidal
responses is proportional to the parameter $f_0\propto (M_2/M)(a_{\rm
orb}/R)^{-3}$, where $M$ and $M_2$ are the masses of the primary and companion
stars, $R$ is the radius of the primary and $a_{\rm orb}$ is the mean orbital
separation between the stars. For a given $f_0$, the amplitudes depend on
$\omega_{\rm tide}$ and become large when $\omega_{\rm tide}$ is in resonance
with natural frequencies of the star. Using the tidal responses, we calculate
axisymmetric mean flows, assuming that the mean flows are non-oscillatory flows
driven via non-linear effects of linear tidal responses. We find that the
$\phi$-component of the mean flow velocity dominates. We also find that the
amplitudes of the mean flows are large only in the surface layers where
non-adiabatic effects are significant and that the amplitudes are confined to
the equatorial regions of the star. Depending on $M_2/M$ and $a_{\rm orb}/R$,
the amplitudes of mean flows at the surface become significant.


  Genome-wide experiments to map the DNA-binding locations of
transcription-associated factors (TFs) have shown that the number of genes
bound by a TF far exceeds the number of possible direct target genes.
Distinguishing functional from non-functional binding is therefore a major
challenge in the study of transcriptional regulation. We hypothesized that
functional targets can be discovered by correlating binding and expression
profiles across multiple experimental conditions. To test this hypothesis, we
obtained ChIP-seq and RNA-seq data from matching cell types from the human
ENCODE resource, considered promoter-proximal and distal cumulative regulatory
models to map binding sites to genes, and used a combination of linear and
non-linear measures to correlate binding and expression data. We found that a
high degree of correlation between a gene's TF-binding and expression profiles
was significantly more predictive of the gene being differentially expressed
upon knockdown of that TF, compared to using binding sites in the cell type of
interest only. Remarkably, TF targets predicted from correlation across a
compendium of cell types were also predictive of functional targets in other
cell types. Finally, correlation across a time course of ChIP-seq and RNA-seq
experiments was also predictive of functional TF targets in that tissue.


  We analyze particular two-photon processes as possible means to explore
electronic quadrupole states in free small deformed atomic clusters. The
analysis is done in the time-dependent local density approximation (TDLDA). It
is shown that the direct two-photon population (DTP) and off-resonant
stimulated Raman (ORSR) scattering can be effectively used for excitation of
the quadrupole states in high-frequency (quadrupole plasmon) and low-frequency
(infrared) regions, respectively. In ORSR, isolated dipole particle-hole states
as well as the tail of the dipole plasmon can serve as an intermediate state. A
simultaneous study of low- and high-frequency quadrupoles, combining DTP and
ORSR, is most effective. Femtosecond pulses with intensities $I = 2\cdot
10^{10} - 2\cdot 10^{11} W/cm^2$ and pulse durations $T = 200 - 500$ fs are
found to be optimal. Since the low-lying quadrupole states are dominated by one
single electron-hole pair, their energies, being combined with the
photoelectron data for hole states, allow to get the electron spectrum above
the Fermi level and thus greatly extend our knowledge on the single particle
spectra of clusters. Besides, the developed schemes allow to estimate the
lifetime of the quadrupole states.


  We study the excited states of interacting fermions in one dimension with
particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a
combination of renormalization group methods and exact diagonalization. Absent
interactions, the entire many-body spectrum exhibits infinite-randomness
quantum critical behavior with highly degenerate excited states. We show that
though interactions are an irrelevant perturbation in the ground state, they
drastically affect the structure of excited states: even arbitrarily weak
interactions split the degeneracies in favor of thermalization (weak disorder)
or spontaneously broken particle-hole symmetry, driving the system into a
many-body localized spin glass phase (strong disorder). In both cases, the
quantum critical properties of the non-interacting model are destroyed, either
by thermal decoherence or spontaneous symmetry breaking. This system then has
the interesting and counterintuitive property that edges of the many-body
spectrum are less localized than the center of the spectrum. We argue that our
results rule out the existence of certain excited state symmetry-protected
topological orders.


  We prove that the cup product of $\Delta$-decomposable quasimorphisms, Brooks
quasimorphisms or Rolli quasimorphisms with any bounded cohomology class of
arbitrary positive degree is trivial.


  We theoretically investigate the anomalous Hall effect (AHE) that requires
neither a net magnetization nor an external magnetic field in collinear
antiferromagnets. We show that such an emergent AHE is essentially caused by a
ferroic ordering of the anisotropic magnetic dipole (AMD), which provides an
effective coupling between ordered magnetic moments and electronic motion in
the crystal. We demonstrate that the AMD is naturally induced by the
antiferromagnetic ordering, in which the magnetic moments have a quadrupole
spatial distribution. In view of the ferroic AMD ordering, we analyze the
behavior of the AHE in the orthorhombic lattice system, where the AHE is
largely enhanced by the large coupling between the AMD and the spin-orbit
interaction. From these findings, the AMD can be used as a descriptor in
general to investigate the ferromagnetic-related physical quantities in
antiferromagnets including noncollinear ones, which is detectable by using the
x-ray magneto-circular dichroism.


  We prove that for any open Riemann surface $N$ and finite subset $Z\subset
\mathbb{S}^1=\{z\in\mathbb{C}\,|\;|z|=1\},$ there exist an infinite closed set
$Z_N \subset \mathbb{S}^1$ containing $Z$ and a null holomorphic curve
$F=(F_j)_{j=1,2,3}:N\to\mathbb{C}^3$ such that the map $Y:Z_N\times N\to
\mathbb{R}^2,$ $Y(v,P)=Re(v(F_1,F_2)(P)),$ is proper.
  In particular, $Re(vF):N \to\mathbb{R}^3$ is a proper conformal minimal
immersion properly projecting into
$\mathbb{R}^2=\mathbb{R}^2\times\{0\}\subset\mathbb{R}^3,$ for all $v \in Z_N.$


  In this article we continue the classical analysis of the symmetry algebra
underlying the integrability of the spectrum in the AdS_5/CFT_4 and in the
Hubbard model. We extend the construction of the quasi-triangular Lie bialgebra
gl(2|2) by contraction and reduction studied in the earlier work to the case of
the affine algebra sl(2)^(1) times d(2,1;alpha)^(1). The reduced affine
derivation naturally measures the deviation of the classical r-matrix from the
difference form. Moreover, it implements a Lorentz boost symmetry, originally
suggested to be related to a q-deformed 2D Poincare algebra. We also discuss
the classical double construction for the bialgebra of interest and comment on
the representation of the affine structure.


  Elevated-temperature polyol-based colloidal-chemistry approach allows for the
development of size-tunable (50 and 86 nm) assemblies of maghemite iso-oriented
nanocrystals, with enhanced magnetization. 1H-Nuclear Magnetic Resonance (NMR)
relaxometric experiments show that the ferrimagnetic cluster-like colloidal
entities exhibit a remarkable enhancement (4 to 5 times) in the transverse
relaxivity, if compared to that of the superparamagnetic contrast agent
Endorem, over an extended frequency range (1-60 MHz). The marked increase of
the transverse relaxivity r2 at a clinical magnetic field strength (1.41 T),
which is 405.1 and 508.3 mM-1 s-1 for small and large assemblies respectively,
allows to relate the observed response to the raised intra-aggregate magnetic
material volume fraction. Furthermore, cell tests with murine fibroblast
culture medium confirmed the cell viability in presence of the clusters. We
discuss the NMR dispersion profiles on the basis of relaxivity models to
highlight the magneto-structural characteristics of the materials for improved
T2-weighted magnetic resonance images.


  The quantum relative entropy is frequently used as a distance, or
distinguishability measure between two quantum states. In this paper we study
the relation between this measure and a number of other measures used for that
purpose, including the trace norm distance. More precisely, we derive lower and
upper bounds on the relative entropy in terms of various distance measures for
the difference of the states based on unitarily invariant norms. The upper
bounds can be considered as statements of continuity of the relative entropy
distance in the sense of Fannes. We employ methods from optimisation theory to
obtain bounds that are as sharp as possible.


  Two improvements with respect to previous formulations are presented for the
calculation of the partition function $\mathcal{Z}$ of small, isolated and
interacting many body systems. By including anharmonicities and employing a
variational approach quantum effects can be treated even at very low
temperatures. A method is proposed of how to include collisional damping.
Finally, our approach is applied to the calculation of the decay rate of
metastable systems.


  We calculate the renormalized effective 2-, 3-, and 4-body interactions for N
neutral ultracold bosons in the ground state of an isotropic harmonic trap,
assuming 2-body interactions modeled with the combination of a zero-range and
energy-dependent pseudopotential. We work to third-order in the scattering
length a defined at zero collision energy, which is necessary to obtain both
the leading-order effective 4-body interaction and consistently include
finite-range corrections for realistic 2-body interactions. The leading-order,
effective 3- and 4-body interaction energies are U3 = -(0.85576...)(a/l)^2 +
2.7921(1)(a/l)^3 + O[(a/l)^4] and U4 = +(2.43317...)(a/l)^3 + O[(a\l)^4], where
w and l are the harmonic oscillator frequency and length, respectively, and
energies are in units of hbar*w. The one-standard deviation error 0.0001 for
the third-order coefficient in U3 is due to numerical uncertainty in estimating
a slowly converging sum; the other two coefficients are either analytically or
numerically exact. The effective 3- and 4-body interactions can play an
important role in the dynamics of tightly confined and strongly correlated
systems. We also performed numerical simulations for a finite-range boson-boson
potential, and it was comparison to the zero-range predictions which revealed
that finite-range effects must be taken into account for a realistic
third-order treatment. In particular, we show that the energy-dependent
pseudopotential accurately captures, through third order, the finite-range
physics, and in combination with the multi-body effective interactions gives
excellent agreement with the numerical simulations, validating our theoretical
analysis and predictions.


  Vertex scaling of piecewise linear metrics on surfaces introduced by Luo is a
straightforward discretization of smooth conformal structures on surfaces.
Combinatorial $\alpha$-curvature for vertex scaling of piecewise linear metrics
on surfaces is a discretization of Gaussian curvature on surfaces. In this
paper, we investigate the prescribing combinatorial $\alpha$-curvature problem
on polyhedral surfaces. Using Gu-Luo-Sun-Wu's discrete conformal theory for
piecewise linear metrics on surfaces and variational principles with
constraints, we prove some Kazdan-Warner type theorems for prescribing
combinatorial $\alpha$-curvature problem, which generalize the results obtained
by Gu-Luo-Sun-Wu on prescribing combinatorial curvatures on surfaces.
Gu-Luo-Sun-Wu conjectured that one can prove Kazdan-Warner's theorems via
approximating smooth surfaces by polyhedral surfaces. This paper takes the
first step in this direction.


  We discuss the question as to how the magnetospheric energy source feeds the
ionospheric current system.
  It is shown that a consistent application and further development of Kennel's
ideas makes it possible to successfully solve the magnetosphere-ionosphere
coupling problem in regard to the formation of auroral electrojets by steady
volume currents generated in the magnetosphere by the magnetospheric MHD
generator in the case of a simple model which, nevertheless, retains the
essential features of the reality. It is concluded that the whole of the
complicated magnetospheric ''design'' only acts to redistribute, in space and
time, currents and energy fluxes which must be supplied by external sources to
feed the dissipative processes in the ionosphere.


  We study decompositions of length functions on integral domains as sums of
length functions constructed from overrings. We find a standard representation
when the integral domain admits a Jaffard family, when it is Noetherian and
when it is a Pr\"ufer domains such that every ideal has only finitely many
minimal primes. We also show that there is a natural bijective correspondence
between singular length functions and localizing systems.


  We explore the dynamic dS/CFT correspondence using the moving domain
wall(brane) approach in the brane cosmology. The bulk spacetimes are given by
the Schwarzschild-de Sitter (SdS) black hole and the topological-de Sitter
(TdS) solutions. We consider the embeddings of (Euclidean) moving domain walls
into the (Euclidean) de Sitter spaces. The TdS solution is better to describe
the static dS/CFT correspondence than the SdS black hole, while in the dynamic
dS/CFT correspondence the SdS solution provides situation better than that of
the TdS solution. However, we do not find a desirable cosmological scenario
from the SdS black hole space.


  Production of antihydrogen atoms by mixing antiprotons with a cold, confined,
positron plasma depends critically on parameters such as the plasma density and
temperature. We discuss non-destructive measurements, based on a novel,
real-time analysis of excited, low-order plasma modes, that provide
comprehensive characterization of the positron plasma in the ATHENA
antihydrogen apparatus. The plasma length, radius, density, and total particle
number are obtained. Measurement and control of plasma temperature variations,
and the application to antihydrogen production experiments are discussed.


  Covariate balancing methods have been widely applied to single or monotone
missing patterns and have certain advantages over likelihood-based methods and
inverse probability weighting approaches based on standard logistic regression.
In this paper, we consider non-monotone missing data under the complete-case
missing variable condition (CCMV), which is a case of missing not at random
(MNAR). Using relationships between each missing pattern and the complete-case
subsample, a weighted estimator can be used for estimation, where the weight is
a sum of ratios of conditional probability of observing a particular missing
pattern versus that of observing the complete-case pattern, given the variables
observed in the corresponding missing pattern. Plug-in estimators of the
propensity ratios, however, can be unbounded and lead to unstable estimation.
Using further relations between propensity ratios and balancing of moments
across missing patterns, we employ tailored loss functions each encouraging
empirical balance across patterns to estimate propensity ratios flexibly using
functional basis expansion. We propose two penalizations to separately control
propensity ratio model complexity and covariate imbalance. We study the
asymptotic properties of the proposed estimators and show that they are
consistent under mild smoothness assumptions. Asymptotic normality and
efficiency are also developed. Numerical simulation results show that the
proposed method achieves smaller mean squared errors than other methods.


  We solve the Einstein constraint equations for a 3 + 1 dimensional vacuum
spacetime with a space-like translational Killing field in the asymptotically
flat case.. The presence of a space-like translational Killing field allows for
a reduction of the 3 + 1 dimensional problem to a 2+1 dimensional one. The aim
of this paper is to go further in the asymptotic expansion of the solutions
than in [14]. In particular the expansion we construct involves quantities
which are the 2-dimensional equivalent of the global charges.


  Statistical methods with empirical likelihood (EL) are appealing and
effective especially in conjunction with estimating equations through which
useful data information can be adaptively and flexibly incorporated. It is also
known in the literature that EL approaches encounter difficulties when dealing
with problems having high-dimensional model parameters and estimating
equations. To overcome the challenges, we begin our study with a careful
investigation on high-dimensional EL from a new scope targeting at estimating a
high-dimensional sparse model parameters. We show that the new scope provides
an opportunity for relaxing the stringent requirement on the dimensionality of
the model parameter. Motivated by the new scope, we then propose a new
penalized EL by applying two penalty functions respectively regularizing the
model parameters and the associated Lagrange multipliers in the optimizations
of EL. By penalizing the Lagrange multiplier to encourage its sparsity, we show
that drastic dimension reduction in the number of estimating equations can be
effectively achieved without compromising the validity and consistency of the
resulting estimators. Most attractively, such a reduction in dimensionality of
estimating equations is actually equivalent to a selection among those
high-dimensional estimating equations, resulting in a highly parsimonious and
effective device for high-dimensional sparse model parameters. Allowing both
the dimensionalities of model parameters and estimating equations growing
exponentially with the sample size, our theory demonstrates that the estimator
from our new penalized EL is sparse and consistent with asymptotically normally
distributed nonzero components. Numerical simulations and a real data analysis
show that the proposed penalized EL works promisingly.


  Solutions of a 1-D free-interface problem modeling solid combustion front
propagating in combustible mixture with periodically varying concentration of
reactant exhibit classical phenomenon of mode locking. Numerical simulation
shows a variety of locked periodic, quasi-periodic and chaotic solutions.


  Based on extensive study of a dynamical systems model of the development of a
cell society, a novel theory for stem cell differentiation and its regulation
is proposed as the ``chaos hypothesis''. Two fundamental features of stem cell
systems - stochastic differentiation of stem cells and the robustness of a
system due to regulation of this differentiation - are found to be general
properties of a system of interacting cells exhibiting chaotic intra-cellular
reaction dynamics and cell division, whose presence does not depend on the
detail of the model. It is found that stem cells differentiate into other cell
types stochastically due to a dynamical instability caused by cell-cell
interactions, in a manner described by the Isologous Diversification theory.
This developmental process is shown to be stable not only with respect to
molecular fluctuations but also with respect to removal of cells. With this
developmental process, the irreversible loss of multipotency accompanying the
change from a stem cell to a differentiated cell is shown to be characterized
by a decrease in the chemical diversity in the cell and of the complexity of
the cellular dynamics. The relationship between the division speed and this
loss of multipotency is also discussed. Using our model, some predictions that
can be tested experimentally are made for a stem cell system.


  We derive an effective colour chiral action with a background gauge field.
The action describes configurations of soliton-skyrmion type. Kinetic term
constant $f_0^2$, analogue of $f_\pi ^2$, is a phenomenological dimensional
parameter of the model; $d=4$ terms are unique up to the choice of background
gauge field. The case of SU(2) colour group is discussed in detail. We study an
isolated configuration, i.e. a configuration in a background field which is the
vacuum field forming the gluon condensate. Thereby we introduce the condensate
energy as a second parameter and scale. Compared with the case of flavor
skyrmion configuration, the colour chiral action contains a piece with slowly
decreasing terms coming from the background vacuum field. Asymptotic behaviour
at large distances shows exponential decrease for the case of chromomagnetic
condensates and periodic otherwise . This defines a stability region for a
colour soliton. The mass is given by the positive definite integrand for a
soliton of purely bosonization origin. Contribution from the Yang-Mills action
of the background colour field has the sign opposite to bosonization part. The
baryon number current is not influenced by the background field and leads to
the standard baryon number $B=N_F/N_C$ . For $B=1/3$ we evaluated the estimate
from above $M\approx 460$ $Mev$ .


  Ribonucleic acid (RNA) plays a variety of crucial roles in fundamental
biological processes. Recently, RNA has become an interesting drug target,
emphasizing the need to improve our understanding of its structures and
functions. Over the years, sequencing technologies have produced an enormous
amount of unlabeled RNA data, which hides important knowledge and potential.
Motivated by the successes of protein language models, we introduce RiboNucleic
Acid Language Model (RiNALMo) to help unveil the hidden code of RNA. RiNALMo is
the largest RNA language model to date with $650$ million parameters
pre-trained on $36$ million non-coding RNA sequences from several available
databases. RiNALMo is able to extract hidden knowledge and capture the
underlying structure information implicitly embedded within the RNA sequences.
RiNALMo achieves state-of-the-art results on several downstream tasks. Notably,
we show that its generalization capabilities can overcome the inability of
other deep learning methods for secondary structure prediction to generalize on
unseen RNA families. The code has been made publicly available on
https://github.com/lbcb-sci/RiNALMo.


  Projects consist of interconnected dimensions such as objective, time,
resource and environment. Use of these dimensions in a controlled way and their
effective scheduling brings the project success. Project scheduling process
includes defining project activities, and estimation of time and resources to
be used for the activities. At this point, the project resource-scheduling
problems have begun to attract more attention after Program Evaluation and
Review Technique (PERT) and Critical Path Method (CPM) are developed one after
the other. However, complexity and difficulty of CPM and PERT processes led to
the use of these techniques through artificial intelligence methods such as
Genetic Algorithm (GA). In this study, an algorithm was proposed and developed,
which determines critical path, critical activities and project completion
duration by using GA, instead of CPM and PERT techniques used for network
analysis within the scope of project management. The purpose of using GA was
that these algorithms are an effective method for solution of complex
optimization problems. Therefore, correct decisions can be made for implemented
project activities by using obtained results. Thus, optimum results were
obtained in a shorter time than the CPM and PERT techniques by using the model
based on the dynamic algorithm. It is expected that this study will contribute
to the performance field (time, speed, low error etc.) of other studies.


  We demonstrate quantum signatures of deterministic nonlinear dynamics in the
transition to superradiance of a generalized open Dicke model with different
coupling strengths for the co- and counter-rotating light-matter interaction
terms. A first-order phase transition to coexisting normal and superradiant
phases is observed, corresponding with the emergence of switching dynamics
between these two phases, driven by quantum fluctuations. We show that this
phase coexistence gives rise to a hysteresis loop also for the quantum
mechanical system. Additionally, a transition to a superradiant oscillatory
phase can be observed clearly in quantum simulations.


  There has been much recent interest and progress on topological structures of
the non-Hermitian Bloch bands. Here, we study the topological structures of
non-Bloch bands of non-Hermitian multi-band quantum systems under open boundary
conditions, which has received limited attention in prior studies. Using a
continuity criterion and an efficient sub-GBZ algorithm, we establish a
homotopic characterization -- braiding topology, e.g., characterized by the
band's total vorticity -- for open-boundary bands and sub-GBZs. Such
topological identification is robust without topological transition and
emergent degenerate points, such as exceptional points. We further analyze the
transition's impact on bands and spectral flows, including interesting
properties unique to open boundaries, and numerically demonstrate our
conclusions with tight-binding model examples. We unveil a crucial insight that
open-boundary bands interchange their portions after encountering certain
exceptional points. Our results enrich our foundational understanding of
topological characterizations for generic non-Hermitian quantum systems.


  A graceful k-coloring of a non-empty graph $G=(V,E)$ is a proper vertex
coloring $f:V(G)\rightarrow\lbrace 1,2,...,k \rbrace$, $k\geq 2$, which induces
a proper edge coloring $f^{*}:E(G)\rightarrow\lbrace 1, 2, . . . , k-1 \rbrace
$ defined by $f^{*}(uv) = |f(u)-f(v)|$, where $u,v\in V(G)$. The minimum $k$
for which $G$ has a graceful $k$-coloring is called graceful chromatic number,
$\chi_{g}(G)$. The graceful chromatic number for a few variants of ladder
graphs are investigated in this article.


  We present a comprehensive analysis of electroweak, flavor, and collider
bounds on the complete set of dimension-six SMEFT operators in the
$U(2)^5$-symmetric limit. This operator basis provides a consistent framework
to describe a wide class of new physics models and, in particular, the
motivated class of models where the new degrees of freedom couple mostly to the
third generation. By analyzing observables from all three sectors, and
consistently including renormalization group evolution, we provide bounds on
the effective scale of all 124 $U(2)^5$-invariant operators. The relation
between flavor-conserving and flavor-violating observables is analyzed taking
into account the leading $U(2)^5$ breaking in the Yukawa sector, which is
responsible for heavy-light quark mixing. We show that under simple, motivated,
and non-tuned hypotheses for the parametric size of the Wilson coefficients at
the high scale, all present bounds are consistent with an effective scale as
low as 1.5 TeV. We also show that a future circular $e^+ e^-$ collider program
such as FCC-ee would push most of these bounds by an order of magnitude. This
would rule out or provide clear evidence for a wide class of compelling new
physics models that are fully compatible with present data.


  This paper presents a general class of quantile regression models for
positive continuous data. In this class of models we consider that the response
variable has a IRON distribution. We provide inference and diagnostic tools for
this class of models. An R package, called IRON, was implemented. This package
provides estimation and inference for the parameters and tools useful to check
the fit of models. The methods are also illustrated with an application to
modeling household income in Chile.


  Enhancing evacuee safety is a key factor in reducing the number of injuries
and deaths that result from earthquakes. One way this can be achieved is by
training occupants. Virtual Reality (VR) and Serious Games (SGs), represent
novel techniques that may overcome the limitations of traditional training
approaches. VR and SGs have been examined in the fire emergency context,
however, their application to earthquake preparedness has not yet been
extensively examined. We provide a theoretical discussion of the advantages and
limitations of using VR SGs to investigate how building occupants behave during
earthquake evacuations and to train building occupants to cope with such
emergencies. We explore key design components for developing a VR SG framework:
(a) what features constitute an earthquake event, (b) which building types can
be selected and represented within the VR environment, (c) how damage to the
building can be determined and represented, (d) how non-player characters (NPC)
can be designed, and (e) what level of interaction there can be between NPC and
the human participants. We illustrate the above by presenting the Auckland City
Hospital, New Zealand as a case study, and propose a possible VR SG training
tool to enhance earthquake preparedness in public buildings.


  Recent work has shown that deep reinforcement-learning agents can learn to
follow language-like instructions from infrequent environment rewards. However,
this places on environment designers the onus of designing language-conditional
reward functions which may not be easily or tractably implemented as the
complexity of the environment and the language scales. To overcome this
limitation, we present a framework within which instruction-conditional RL
agents are trained using rewards obtained not from the environment, but from
reward models which are jointly trained from expert examples. As reward models
improve, they learn to accurately reward agents for completing tasks for
environment configurations---and for instructions---not present amongst the
expert data. This framework effectively separates the representation of what
instructions require from how they can be executed. In a simple grid world, it
enables an agent to learn a range of commands requiring interaction with blocks
and understanding of spatial relations and underspecified abstract
arrangements. We further show the method allows our agent to adapt to changes
in the environment without requiring new expert examples.


  The dynamics of belief and knowledge is one of the major components of any
autonomous system that should be able to incorporate new pieces of information.
In order to apply the rationality result of belief dynamics theory to various
practical problems, it should be generalized in two respects: first it should
allow a certain part of belief to be declared as immutable; and second, the
belief state need not be deductively closed. Such a generalization of belief
dynamics, referred to as base dynamics, is presented in this paper, along with
the concept of a generalized revision algorithm for knowledge bases (Horn or
Horn logic with stratified negation). We show that knowledge base dynamics has
an interesting connection with kernel change via hitting set and abduction. In
this paper, we show how techniques from disjunctive logic programming can be
used for efficient (deductive) database updates. The key idea is to transform
the given database together with the update request into a disjunctive
(datalog) logic program and apply disjunctive techniques (such as minimal model
reasoning) to solve the original update problem. The approach extends and
integrates standard techniques for efficient query answering and integrity
checking. The generation of a hitting set is carried out through a hyper
tableaux calculus and magic set that is focused on the goal of minimality. The
present paper provides a comparative study of view update algorithms in
rational approach. For, understand the basic concepts with abduction, we
provide an abductive framework for knowledge base dynamics. Finally, we
demonstrate how belief base dynamics can provide an axiomatic characterization
for insertion a view atom to the database. We give a quick overview of the main
operators for belief change, in particular, belief update versus database
update.


  Motivated by the recent works of us [1], we establish a correspondence
between f(R)-gravity with the power-law entropy corrected holographic dark
energy (PLECHDE) and new agegraphic dark energy (PLECNADE) models. We
reconstruct corresponding f(R)-gravities and obtain the equation of state
parameters. We show that the selected f(R)-gravity models can accommodate the
transition from the quintessence state to the phantom regime as indicated by
the recent observations.


  This article discusses self-organization in cold atoms via light-mediated
interactions induced by feedback from a single retro-reflecting mirror.
Diffractive dephasing between the pump beam and the spontaneous sidebands
selects the lattice period. Spontaneous breaking of the rotational and
translational symmetry occur in the 2D plane transverse to the pump. We
elucidate how diffractive ripples couple sites on the self-induced atomic
lattice. The nonlinear phase shift of the atomic cloud imprinted onto the
optical beam is the parameter determining coupling strength. The interaction
can be tailored to operate either on external degrees of freedom leading to
atomic crystallization for thermal atoms and supersolids for a quantum
degenerate gas, or on internal degrees of freedom like populations of the
excited state or Zeeman sublevels. Using the light polarization degrees of
freedom on the Poincar{\'e} sphere (helicity and polarization direction),
specific irreducible tensor components of the atomic Zeeman states can be
coupled leading to spontaneous magnetic ordering of states of dipolar and
quadrupolar nature. The requirements for critical interaction strength are
compared for the different situations. Connections and extensions to
longitudinally pumped cavities, counterpropagating beam schemes and the CARL
instability are discussed.


  Ultrafast laser pump-probe spectroscopy is an important and growing field of
physical chemistry that allows the measurement of chemical dynamics on their
natural timescales, but undergraduate laboratory courses lack examples of such
spectroscopy and the interpretation of the dynamics that occur. Here we develop
and implement an ultrafast pump probe spectroscopy experiment for the
undergraduate physical chemistry laboratory course at the University of
California Berkeley. The goal of the experiment is to expose students to
concepts in solid-state chemistry and ultrafast spectroscopy via classic
coherent phonon dynamics principles developed by researchers over multiple
decades. The experiment utilizes a modern high-repetition-rate 800 nm
femtosecond Ti:Sapphire laser, split pulses with a variable time delay, and
sensitive detection of transient reflectivity signals using the lock-in
technique. The experiment involves minimal intervention from students and is
therefore easy and safe to implement in the laboratory. Students first perform
an intensity autocorrelation measurement on the femtosecond laser pulses to
obtain their temporal duration. Then, students measure the pump-probe
reflectivity of a single-crystal antimony sample to determine the period of
coherent phonon oscillations initiated by an ultrafast pulse excitation, which
is analyzed by fitting to a sine wave. Students who completed the experiment
in-person obtained good experimental results, and students who took the course
remotely due to the COVID-19 pandemic were provided with the data they would
have obtained during the experiment to analyze. Evaluation of student written
and oral reports reveals that the learning goals were met, and that students
gained an appreciation for the field of ultrafast laser-induced chemistry.


  A "shear" is a unipotent translate of a cuspidal geodesic ray in the quotient
of the hyperbolic plane by a non-uniform discrete subgroup of PSL(2,R),
possibly of infinite co-volume. We prove the regularized equidistribution of
shears under large translates with effective (that is, power saving) rates. We
also give applications to weighted second moments of GL(2) automorphic
L-functions, and to counting lattice points on locally affine symmetric spaces.


  Upper limits on neutrino masses from cosmology have been reported recently to
reach the impressive sub-eV level, which is competitive with future terrestrial
neutrino experiments. In this brief overview of the latest limits from
cosmology I point out some of the caveats that should be borne in mind when
interpreting the significance of these limits.


  In the present work we focus on future experiments using cluster abundance
observations to constraint the Dark Energy equation of state parameter, w. To
obtain tight constraints from this kind of experiment, a reliable sample of
galaxy clusters must be obtained from deep and wide-field images. We therefore
present the computational environment (2DPHOT) that allow us to build the
galaxy catalog from the images and the Voronoi Tessellation cluster finding
algorithm that we use to identify the galaxy clusters on those catalogs. To
test our pipeline with data similar in quality to what will be gathered by
future wide field surveys, we process images from the Deep fields obtained as
part of the LEGACY Survey (four fields of one square degree each, in five
bands, with depth up to r'=25). We test our cluster finder by determining the
completeness and purity of the finder when applied to mock galaxy catalogs made
for the Dark Energy Survey cluster finder comparison project by Risa Wechsler
and Michael Busha. This procedure aims to understand the selection function of
the underlying dark matter halos.


  In this paper we classify and give Kazhdan-Lusztig type character formulas
for equivariantly irreducible representations of Lie algebras of reductive
algebraic groups over a field of large positive characteristic. The
equivariance is with respect to a group whose connected component is a torus.
Character computation is done in two steps. First, we treat the case of
distinguished $p$-characters: those that are not contained in a proper Levi.
Here we essentially show that the category of equivariant modules we consider
is a cell quotient of an affine parabolic category $\mathcal{O}$. For this, we
prove an equivalence between two categorifications of a parabolically induced
module over the affine Hecke algebra conjectured by the first named author. For
the general nilpotent $p$-character, we get character formulas by explicitly
computing the duality operator on a suitable equivariant K-group.


  We show that the $1/N_c$ rotational corrections to $g_A$, derived using the
semiclassical quantization scheme in the NJL model, possess correct properties
under charge conjugation.


  Some fast radio bursts (FRBs) exhibit repetitive behaviors and their origins
remain enigmatic. It has been argued that repeating FRBs could be produced by
the interaction between a neutron star and an asteroid belt. Here we consider
the systems in which an asteroid belt dwells around a massive star, while a
neutron star, as a companion of the massive star, interacts with the belt
through gravitational force. Various orbital configurations are assumed for the
system. Direct N-body simulations are performed to investigate the dynamical
evolution of the asteroids belt. It is found that a larger orbital eccentricity
of the neutron star will destroy the belt more quickly, with a large number of
asteroids being scattered out of the system. A non-zero mutual inclination
angle suppresses the ejection rate of asteroids, but it also leads to a
reduction in the collision rate of asteroids with the neutron star since many
asteroids are essentially scattered into the 3D space. Among the various
configurations, a clear periodicity is observed in the collision events for the
case with an orbital eccentricity of 0.7 and mutual inclination of $0^{\circ}$.
It is found that such a periodicity can be sustained for at least 8 neutron
star orbital periods, supporting this mechanism as a possible explanation for
periodically repeating FRBs. Our studies also suggest that the active stage of
these kinds of FRB sources should be limited, since the asteroid belt would
finally be destroyed by the neutron star after multiple passages.


  We consider a local phenomenological model to explain a non-local gravity
scenario which has been proposed to address dark energy issues. This non-local
gravity action has been seen to fit the data as well as $\Lambda$-CDM and
therefore demands a more fundamental local treatment. The induced gravity model
coupled with higher-derivative gravity is exploited for this proposal, as this
perturbatively renormalizable model has a well-defined ultraviolet (UV)
description where ghosts are evaded. We consider a generalised version of this
model where we consider two coupled scalar fields and their non-minimal
coupling with gravity. In this simple model, one of the scalar field acquires a
Vacuum Expectation Value (VEV), thereby inducing a mass for one of the scalar
fields and generating Newton's constant. The induced mass however is seen to be
always above the running energy scale thereby leading to its decoupling. The
residual theory after decoupling becomes a platform for driving the accelerated
expansion under certain conditions. Integrating out the residual scalar
generates a non-local gravity action. The leading term of which is the
non-local gravity action used to fit the data of dark energy.


  Model-free time-to-event regression under confounding presents challenges due
to biases introduced by causal and censoring sampling mechanisms. This
phenomenology poses problems for classical non-parametric estimators like
Beran's or the k-nearest neighbours algorithm. In this study, we propose a
natural framework that leverages the structure of reproducing kernel Hilbert
spaces (RKHS) and, specifically, the concept of kernel mean embedding to
address these limitations. Our framework has the potential to enable
statistical counterfactual modeling, including counterfactual prediction and
hypothesis testing, under right-censoring schemes. Through simulations and an
application to the SPRINT trial, we demonstrate the practical effectiveness of
our method, yielding coherent results when compared to parallel analyses in
existing literature. We also provide a theoretical analysis of our estimator
through an RKHS-valued empirical process. Our approach offers a novel tool for
performing counterfactual survival estimation in observational studies with
incomplete information. It can also be complemented by state-of-the-art
algorithms based on semi-parametric and parametric models.


  We present state-of-the-art results on morphosyntactic tagging across
different varieties of Arabic using fine-tuned pre-trained transformer language
models. Our models consistently outperform existing systems in Modern Standard
Arabic and all the Arabic dialects we study, achieving 2.6% absolute
improvement over the previous state-of-the-art in Modern Standard Arabic, 2.8%
in Gulf, 1.6% in Egyptian, and 8.3% in Levantine. We explore different training
setups for fine-tuning pre-trained transformer language models, including
training data size, the use of external linguistic resources, and the use of
annotated data from other dialects in a low-resource scenario. Our results show
that strategic fine-tuning using datasets from other high-resource dialects is
beneficial for a low-resource dialect. Additionally, we show that high-quality
morphological analyzers as external linguistic resources are beneficial
especially in low-resource settings.


  A quantile binary classifier uses the rule: Classify x as +1 if P(Y = 1|X =
x) >= t, and as -1 otherwise, for a fixed quantile parameter t {[0, 1]. It has
been shown that Support Vector Machines (SVMs) in the limit are quantile
classifiers with t = 1/2 . In this paper, we show that by using asymmetric cost
of misclassification SVMs can be appropriately extended to recover, in the
limit, the quantile binary classifier for any t. We then present a principled
algorithm to solve the extended SVM classifier for all values of t
simultaneously. This has two implications: First, one can recover the entire
conditional distribution P(Y = 1|X = x) = t for t {[0, 1]. Second, we can build
a risk-agnostic SVM classifier where the cost of misclassification need not be
known apriori. Preliminary numerical experiments show the effectiveness of the
proposed algorithm.


  Video harmonization aims to adjust the foreground of a composite video to
make it compatible with the background. So far, video harmonization has only
received limited attention and there is no public dataset for video
harmonization. In this work, we construct a new video harmonization dataset
HYouTube by adjusting the foreground of real videos to create synthetic
composite videos. Moreover, we consider the temporal consistency in video
harmonization task. Unlike previous works which establish the spatial
correspondence, we design a novel framework based on the assumption of color
mapping consistency, which leverages the color mapping of neighboring frames to
refine the current frame. Extensive experiments on our HYouTube dataset prove
the effectiveness of our proposed framework. Our dataset and code are available
at https://github.com/bcmi/Video-Harmonization-Dataset-HYouTube.


  In this paper we study the properties of the periodic orbits of \"x + V'_x(t,
x) = 0 with x \in S1 and V(t, x) a T0 periodic potential. Called {\rho} \in
(1/T0)Q the frequency of windings of an orbit in S1 we show that exists an
infinite number of periodic solutions with a given {\rho}. We give a lower
bound on the number of periodic orbits with a given period and {\rho} by means
of the Morse theory.


  We review various ways of obtaining consistency between the idea of
supersymmetric grand unification and an apparent low value of $\alpha_s \sim
0.112$ indicated by several low energy experiments. We argue that to reconcile
the low value of $\alpha_s$ with the predictions of supersymmetric GUTs, we
need to go beyond the standard minimal supersymmetric GUT scenario and invoke
new physics either at $10^{11}-10^{12}$ GeV, or at the GUT scale.


  Recently, several papers have been devoted to the analysis of lamplighter
random walks, in particular when the underlying graph is the infinite path
$\mathbb{Z}$. In the present paper, we develop a spectral analysis for
lamplighter random walks on finite graphs. In the general case, we use the
$C_2$-symmetry to reduce the spectral computations to a series of eigenvalue
problems on the underlying graph. In the case the graph has a transitive
isometry group $G$, we also describe the spectral analysis in terms of the
representation theory of the wreath product $C_2\wr G$. We apply our theory to
the lamplighter random walks on the complete graph and on the discrete circle.
These examples were already studied by Haggstrom and Jonasson by probabilistic
methods.


  Recently, semantic search has been successfully applied to e-commerce product
search and the learned semantic space(s) for query and product encoding are
expected to generalize to unseen queries or products. Yet, whether
generalization can conveniently emerge has not been thoroughly studied in the
domain thus far. In this paper, we examine several general-domain and
domain-specific pre-trained Roberta variants and discover that general-domain
fine-tuning does not help generalization, which aligns with the discovery of
prior art. Proper domain-specific fine-tuning with clickstream data can lead to
better model generalization, based on a bucketed analysis of a publicly
available manual annotated query-product pair da


  We construct a consistent self-coupling for the vector-tensor multiplet in N
= 2 harmonic central charge superspace.


  Four different spin structures of two electrons and of two holes situated on
the lowest Landau levels (LLLs) are taken into account to investigate possible
bound states of the two-dimensional magnetic biexciton formed of two
magnetoexcitons with opposite wave vectors and antiparallel dipole moments. The
singlet and triplet states of the spins of two electrons and of two holes
separately, as well as of two para- and two ortho-magnetoexcitons are
considered. The general expressions describing the binding energy of the bound
states and the normalization conditions characterized by the effective spin
parameter for the corresponding wave functions are derived. The most favorable
of the four considered spin configurations happened to be the triplet-triplet
spin structure of two electrons and of two holes. In its frame a metastable
bound state with activation barrier comparable with two ionization potentials
of the magnetoexciton is revealed .


  We propose and theoretically and numerically investigate narrowband
integrated filters consisting of identical resonant dielectric ridges on the
surface of a single-mode dielectric slab waveguide. The proposed composite
structures operate near a bound state in the continuum (BIC) and enable
spectral filtering of transverse-electric-polarized guided modes propagating in
the waveguide. We demonstrate that by proper choice of the distances between
the ridges, flat-top reflectance profiles with steep slopes and virtually no
sidelobes can be obtained using just a few ridges. In particular, the structure
consisting of two ridges can optically implement the second-order Butterworth
filter, whereas at a larger number of ridges, excellent approximations to
higher-order Butterworth filters can be achieved. Owing to the BIC supported by
the ridges constituting the composite structure, the flat-top reflection band
can be made arbitrarily narrow without increasing the structure size. In
addition to the filtering properties, the investigated structures support
another type of BICs - Fabry-P\'erot BICs arising when the distances between
the adjacent ridges meet the Fabry-P\'erot resonance condition. In the vicinity
of the Fabry-P\'erot BICs, an effect similar to the electromagnetically induced
transparency is observed, namely, sharp transmittance peaks against the
background of a wide transmittance dip.