  Thermal motions in the 2D Lennard-Jones liquid near solidification are
studied at equilibrium and under shear flow conditions. At the temperatures of
the study, the liquid is significantly aggregated. On times of few to few tens
of particles vibration periods, the dominant features are particles in-cage
vibrations and the highest frequency longitudinal and transverse Hypersound. On
time-scales of hundreds to thousands of vibration periods, the liquid appears
spatially heterogeneous. On these times, slow non-oscillatory fluctuating
currents persist for surprisingly long times; the hierarchical dynamics of the
heterogeneous liquid results in changing temperature, density, and velocity
profiles across the system. Heterogeneity fades, and a crossover to
non-fluctuational Hydrodynamics is observed for smoothing times of many tens of
thousands vibration periods. On these asymptotically-large times, the liquid is
spatially homogeneous except for thin layers near the boundaries where the
degree of crystallinity increases and the mobility decreases due to
liquid-boundary interactions.


  In this paper we discuss the reliability of two computational methods
(numerical integration on Cartesian grids, and population analysis) used for
evaluating scalar quantities related to the nature of electronic transitions.
These descriptors are integrals of charge density functions built from the
detachment and attachment density matrices projected in the Euclidean space
using a finite basis of orbitals. While the numerical integration on Cartesian
grids is easily considered to be converged for medium-sized density grids, the
population analysis approximation to the numerical integration values is
diagnosed using eight diagnostic tests performed on fifty-nine molecules with a
combination of fifteen Gaussian basis sets and six exchange-correlation
functionals.


  We introduce an online outlier detection algorithm to detect outliers in a
sequentially observed data stream. For this purpose, we use a two-stage
filtering and hedging approach. In the first stage, we construct a multi-modal
probability density function to model the normal samples. In the second stage,
given a new observation, we label it as an anomaly if the value of
aforementioned density function is below a specified threshold at the newly
observed point. In order to construct our multi-modal density function, we use
an incremental decision tree to construct a set of subspaces of the observation
space. We train a single component density function of the exponential family
using the observations, which fall inside each subspace represented on the
tree. These single component density functions are then adaptively combined to
produce our multi-modal density function, which is shown to achieve the
performance of the best convex combination of the density functions defined on
the subspaces. As we observe more samples, our tree grows and produces more
subspaces. As a result, our modeling power increases in time, while mitigating
overfitting issues. In order to choose our threshold level to label the
observations, we use an adaptive thresholding scheme. We show that our adaptive
threshold level achieves the performance of the optimal pre-fixed threshold
level, which knows the observation labels in hindsight. Our algorithm provides
significant performance improvements over the state of the art in our wide set
of experiments involving both synthetic as well as real data.


  Controlled integration of metallic nanoparticles (NPs) onto photonic
nanostructures enables realization of complex devices for extreme light
confinement and enhanced light-matter interaction. This can be achieved
combining Nanoparticle-on-Mirror (NPoM) nanocavities with the light
manipulation capabilities of micron-scale metallic antennas and/or photonic
integrated waveguides. However, metallic nanoparticles are usually deposited
via drop-casting, which prevents their accurate positioning. Here we present a
methodology for precise transfer and positioning of individual NPs onto
different photonic nanostructures. The method is based on soft lithography
printing that employs elastomeric stamp-assisted transfer of individual NPs
onto a single nanostructure. It can also parallel imprint many individual NPs
with high throughput and accuracy in a single step. Raman spectroscopy confirms
enhanced light-matter interactions in the resulting NPoM-based devices. Our
method mixes top-down and bottom-up nanofabrication techniques and shows the
potential of building complex photonic nanodevices for applications ranging
from enhanced sensing and spectroscopy to signal processing.


  We prove that a Hopf algebra with a finite coradical filtration is
co-Frobenius, i. e. there is a non-zero integral on it. As a consequence, we
show that algebras of functions on quantum groups at roots of one are
co-Frobenius. We also characterize co-Frobenius Hopf algebras with coradical a
Hopf subalgebra. This characterization is in the framework of the lifting
method due to H.-J. Schneider and the first-named author. Here is our main
result. Let H be a Hopf algebra whose coradical is a Hopf subalgebra. Let gr H
be the associated graded Hopf algebra and let R be the diagram of H. Then the
following are equivalent: (1) H is co-Frobenius, (2) gr H is co-Frobenius, (3)
R is finite dimensional, (4) the coradical filtration of H is finite. This
Theorem allows to construct many new examples of co-Frobenius Hopf algebras and
opens the way to the classification of ample classes of such Hopf algebras.


  Mean-field dynamo equations are addressed with the aid of the path-integral
method. The evolution of magnetic field is treated as a three-dimensional
Wiener random process, and the mean magnetic-field equations are obtained with
the Wiener integral over all the trajectories of fluid particle. The form of
the equations is just the same as the conventional mean-field equations, but
the present equations are derived with the velocity-field realization affected
by the magnetic-field force. In this sense, the present ones are nonlinear
dynamo equations.


  We introduce the concept of attainable sets of payoffs in two-player repeated
games with vector payoffs. A set of payoff vectors is called {\em attainable}
if player 1 can ensure that there is a finite horizon $T$ such that after time
$T$ the distance between the set and the cumulative payoff is arbitrarily
small, regardless of what strategy player 2 is using. This paper focuses on the
case where the attainable set consists of one payoff vector. In this case the
vector is called an attainable vector. We study properties of the set of
attainable vectors, and characterize when a specific vector is attainable and
when every vector is attainable.


  Triangular flow $v_3$ of identified and inclusive particles in Pb+Pb
collisions at $\sqrt{s_{NN}} = 2.76$ TeV is studied as a function of centrality
and transverse momentum within the \textsc{hydjet++} model. The model enables
one to investigate the influence of both hard processes and final-state
interactions on the harmonics of particle anisotropic flow. Decays of
resonances are found to increase the magnitude of the $v_3(p_{\rm T})$
distributions at $p_{\rm T} \geq 2$ GeV/$c$ and shift their maxima to higher
transverse momenta. The $p_{\rm T}$-integrated triangular flow, however,
becomes slightly weakened for all centralities studied. The resonance decays
also modify the spectra towards the number-of-constituent-quark scaling
fulfillment for the triangular flow, whereas jets are the main source of the
scaling violation at the energies available at the CERN Large Hadron Collider
(LHC). Comparison with the corresponding spectra of elliptic flow reveals that
resonance decays and jets act in a similar manner on both $v_3(p_{\rm T})$ and
$v_2(p_{\rm T})$ behavior. Obtained results are also confronted with the
experimental data on differential triangular flow of identified hadrons, ratio
$v_3^{1/3}(p_{\rm T}) / v_2^{1/2}(p_{\rm T})$ and $p_{\rm T}$-integrated
triangular flow of charged hadrons.


  We study scalar quantum field theory on a compact manifold. The free theory
is defined in terms of functional integrals. For positive mass it is shown to
have the Markov property in the sense of Nelson. This property is used to
establish a reflection positivity result when the manifold has a reflection
symmetry. In dimension d=2 we use the Markov property to establish a sewing
operation for manifolds with boundary circles. Also in d=2 the Markov property
is proved for interacting fields.


  Parker Solar Probe (PSP) entered a region of the sub-Alfvenic solar wind
during encounter 8 and we present the first detailed analysis of low-frequency
turbulence properties in this novel region. The magnetic field and flow
velocity vectors were highly aligned during this interval. By constructing
spectrograms of the normalized magnetic helicity, cross helicity, and residual
energy, we find that PSP observed primarily Alfvenic fluctuations, a
consequence of the highly field-aligned flow that renders quasi-2D fluctuations
unobservable to PSP. We extend Taylor hypothesis to sub and super Alfvenic
flows. Spectra for the fluctuating forward and backward Elsasser variables are
presented. The observed spectra are well fitted using a spectral theory for
nearly incompressible magnetohydrodynamics assuming a wave number anisotropy.
The density spectrum is a power law that resembles neither the Elsasser spectra
nor the compressible magnetic field spectrum, suggesting that these are
advected entropic rather than magnetosonic modes and not due to the parametric
decay instability. Spectra in the neighboring modestly super Alfvenic intervals
are similar.


  Integer programming (IP) is a general optimization framework widely
applicable to a variety of unstructured and structured problems arising in,
e.g., scheduling, production planning, and graph optimization. As IP models
many provably hard to solve problems, modern IP solvers rely on many
heuristics. These heuristics are usually human-designed, and naturally prone to
suboptimality. The goal of this work is to show that the performance of those
solvers can be greatly enhanced using reinforcement learning (RL). In
particular, we investigate a specific methodology for solving IPs, known as the
Cutting Plane Method. This method is employed as a subroutine by all modern IP
solvers. We present a deep RL formulation, network architecture, and algorithms
for intelligent adaptive selection of cutting planes (aka cuts). Across a wide
range of IP tasks, we show that the trained RL agent significantly outperforms
human-designed heuristics, and effectively generalizes to 10X larger instances
and across IP problem classes. The trained agent is also demonstrated to
benefit the popular downstream application of cutting plane methods in
Branch-and-Cut algorithm, which is the backbone of state-of-the-art commercial
IP solvers.


  For numerous graph problems in the realm of parameterized algorithms, using
the size of a smallest deletion set (called a modulator) into well-understood
graph families as parameterization has led to a long and successful line of
research. Recently, however, there has been an extensive study of structural
parameters that are potentially much smaller than the modulator size. In
particular, recent papers [Jansen et al. STOC 2021; Agrawal et al. SODA 2022]
have studied parameterization by the size of the modulator to a graph family
$\mathcal{H}$ ($\textbf{mod}_{\mathcal{H}}$), elimination distance to
$\mathcal{H}$ ($\textbf{ed}_{\mathcal{H}}$), and $\mathcal{H}$-treewidth
($\textbf{tw}_{\mathcal{H}}$). While these new parameters have been
successfully exploited to design fast exact algorithms their utility
(especially that of latter two) in the context of approximation algorithms is
mostly unexplored.
  The conceptual contribution of this paper is to present novel algorithmic
meta-theorems that expand the impact of these structural parameters to the area
of FPT Approximation, mirroring their utility in the design of exact FPT
algorithms. Precisely, we show that if a covering or packing problem is
definable in Monadic Second Order Logic and has a property called Finite
Integer Index, then the existence of an FPT Approximation Scheme (FPT-AS, i.e.,
($1\pm \epsilon$)-approximation) parameterized these three parameters is in
fact equivalent. As concrete exemplifications of our meta-theorems, we obtain
FPT-ASes for well-studied graph problems such as Vertex Cover, Feedback Vertex
Set, Cycle Packing and Dominating Set, parameterized by these three parameters.


  We present an explicit formula for the canonical height of a projective toric
variety.


  The adsorption of MgO molecules on a Fe(001) surface was studied using
density functional theory (DFT) and projector augmented wave methods. The
energetically most favored configurations for different adsorption sites
considered were identified. The most preferable adsorption geometry is when the
MgO molecules are parallel to the surface, with Mg in the interstitial site and
O in on-top of the Fe atom. During the adsorption of subsequent MgO molecules
in this geometry, a sharp, non-oxidized interface is formed between the MgO
adlayer and Fe(001) surface. The adsorption of MgO perpendicular to the
surface, with oxygen incorporated in the topmost Fe layer is less probable, but
may lead to the formation of the FeO layer when stabilized with an excess of
oxygen atoms. Structural, electronic and magnetic properties of both interface
types were examined for the MgO coverage from 1/9 to 1 monolayer (ML).
Electronic and magnetic properties are sensitive to the MgO coverage. For lower
coverage of MgO, clear hybridization between the Fe 3d and O 2p states is
shown. The average magnetic moment of the surface Fe atoms is reduced with
coverage, achieving 2.78 $\mu_{\rm B}$ for 1 ML of MgO.


  Although microarrays are routine analysis tools in biomedical research, they
still yield noisy output that often requires experimental confirmation. Many
studies have aimed at optimizing probe design and statistical analysis to
tackle this problem. However, less emphasis has been placed on controlling the
noise inherent to the experimental approach. To address this problem, we
investigate here a procedure that controls for such experimental variance and
combine it with an assessment of probe performance. Two custom arrays were used
to evaluate the procedure: one based on 25mer probes from an Affymetrix design
and the other based on 60mer probes from an Agilent design. To assess
experimental variance, all probes were replicated ten times. To assess probe
performance, the probes were calibrated using a dilution series of target
molecules and the signal response was fitted to an absorption model. We found
that significant variance of the signal could be controlled by averaging across
probes and removing probes that are nonresponsive. Thus, a more reliable signal
could be obtained using our procedure than conventional approaches. We suggest
that once an array is properly calibrated, absolute quantification of signals
becomes straight forward, alleviating the need for normalization and reference
hybridizations.


  We prove that any complete immersed two-sided mean convex translating soliton
$\Sigma \subset \mathbb{R}^3$ for the mean curvature flow is convex. As a
corollary it follows that an entire mean convex graphical translating soliton
in $\mathbb{R}^3$ is the axisymmetric "bowl soliton". We also show that if the
mean curvature of $\Sigma$ tends to zero at infinity, then $\Sigma$ can be
represented as an entire graph and so is the "bowl soliton". Finally we
classify all locally strictly convex graphical translating solitons defined
over strip regions.


  Recent years have seen smart contracts are getting increasingly popular in
building trustworthy decentralized applications. Previous research has proposed
static and dynamic techniques to detect vulnerabilities in smart contracts.
These tools check vulnerable contracts against several predefined rules.
However, the emerging new vulnerable types and programming skills to prevent
possible vulnerabilities emerging lead to a large number of false positive and
false negative reports of tools. To address this, we propose Vulpedia, which
mines expressive vulnerability signatures from contracts. Vulpedia is based on
the relaxed assumption that the owner of contract is not malicious.
Specifically, we extract structural program features from vulnerable and benign
contracts as vulnerability signatures, and construct a systematic detection
method based on detection rules composed of vulnerability signatures. Compared
with the rules defined by state-of-the-arts, our approach can extract more
expressive rules to achieve better completeness (i.e., detection recall) and
soundness (i.e., precision). We further evaluate Vulpedia with four baselines
(i.e., Slither, Securify, SmartCheck and Oyente) on the testing dataset
consisting of 17,770 contracts. The experiment results show that Vulpedia
achieves best performance of precision on 4 types of vulnerabilities and
leading recall on 3 types of vulnerabilities meanwhile exhibiting the great
efficiency performance.


  To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we
propose a novel method related to the use of hyperspherical harmonics. We
suggest an appropriate extension to form a new basis of spin-angular harmonics
that is suitable for a representation of the vertex functions. We present a
numerical algorithm to solve the Bethe-Salpeter equation and investigate in
detail the properties of the solution for the scalar, pseudoscalar and vector
meson exchange kernels including the stability of bound states. We also compare
our results to the non relativistic ones and to the results given by light
front dynamics.


  Weather data collected from automated weather stations have become a crucial
component for making decisions in agriculture and in forestry. Over time,
weather stations may become out-of-order or stopped for maintenance, and
therefore, during those periods, the data values will be missing.
Unfortunately, this will cause huge problems when analysing the data. The main
aim of this study is to create high-quality historical weather datasets by
dealing efficiently with missing values. In this paper, we present a set of
missing data imputation methods and study their effectiveness. These methods
were used based on different types of missing values. The experimental results
show that two the proposed methods are very promising and can be used at larger
scale.


  We employ the $\lambda^3$ regime where a near-single-cycle laser pulse is
tightly focused, thus providing the highest possible intensity for the minimal
energy at a certain laser power. The quantum electrodynamics processes in the
course of the interaction of the ultraintense laser with a solid target are
studied via three-dimensional particle-in-cell simulations, revealing the
generation of copious $\gamma$-photons and electron-positron pairs. The
parametric study on the laser polarisation, target thickness and electron
number density shows that the radially polarised laser provides the optimal
regime for $\gamma$-photon generation. By varying the laser power in the range
of 1 to 300 petawatt we find the scaling of the laser to $\gamma$-photon energy
conversion efficiency. The laser-generated $\gamma$-photon interaction with a
high-Z target is further studied by using Monte Carlo simulations revealing
further electron-positron pair generation and radioactive nuclides creation.


  The semiclassical SU(3) Skyrme model is traditionally considered as
describing a rigid quantum rotator with the profile function being fixed by the
classical solution of the corresponding SU(2) Skyrme model. In contrast, we go
beyond the classical profile function by quantizing the SU(3) Skyrme model
canonically. The quantization of the model is performed in terms of the
collective coordinate formalism and leads to the establishment of purely
quantum corrections of the model. These new corrections are of fundamental
importance. They are crucial in obtaining stable quantum solitons of the
quantum SU(3) Skyrme model, thus making the model self-consistent and not
dependent on the classical solution of the SU(2) case. We show that such a
treatment of the model leads to a family of stable quantum solitons that
describe the baryon octet and decuplet and reproduce their masses in a
qualitative agreement with the empirical values.


  An implementation of the generalized time-dependent generator coordinated
method (TD-GCM) is developed, that can be applied to the dynamics of small- and
large-amplitude collective motion of atomic nuclei. Both the generator states
and weight functions of the GCM correlated wave function depend on time. The
initial generator states are obtained as solutions of deformation-constrained
self-consistent mean-field equations, and are evolved in time by the standard
mean-field equations of nuclear density functional theory (TD-DFT). The TD-DFT
trajectories are used as a generally non-orthogonal and overcomplete basis in
which the TD-GCM wave function is expanded. The weights, expressed in terms of
a collective wave function, obey a TD-GCM (integral) equation. In this
explorative paper, the generalized TD-GCM is applied to the excitation energies
and spreading width of giant resonances, and to the dynamics of induced
fission. The necessity of including pairing correlations in the basis of TD-DFT
trajectories is demonstrated in the latter example.


  As machine- and AI-generated content proliferates, protecting the
intellectual property of generative models has become imperative, yet verifying
data ownership poses formidable challenges, particularly in cases of
unauthorized reuse of generated data. The challenge of verifying data ownership
is further amplified by using Machine Learning as a Service (MLaaS), which
often functions as a black-box system.
  Our work is dedicated to detecting data reuse from even an individual sample.
Traditionally, watermarking has been leveraged to detect AI-generated content.
However, unlike watermarking techniques that embed additional information as
triggers into models or generated content, potentially compromising output
quality, our approach identifies latent fingerprints inherently present within
the outputs through re-generation. We propose an explainable verification
procedure that attributes data ownership through re-generation, and further
amplifies these fingerprints in the generative models through iterative data
re-generation. This methodology is theoretically grounded and demonstrates
viability and robustness using recent advanced text and image generative
models. Our methodology is significant as it goes beyond protecting the
intellectual property of APIs and addresses important issues such as the spread
of misinformation and academic misconduct. It provides a useful tool to ensure
the integrity of sources and authorship, expanding its application in different
scenarios where authenticity and ownership verification are essential.


  Technical debt denotes shortcuts taken during software development, mostly
for the sake of expedience. When such shortcuts are admitted explicitly by
developers (e.g., writing a TODO/Fixme comment), they are termed as
Self-Admitted Technical Debt or SATD. There has been a fair amount of work
studying SATD management in Open Source projects, but SATD in industry is
relatively unexplored. At the same time, there is no work focusing on
developers' perspectives towards SATD and its management. To address this, we
conducted an exploratory case study in cooperation with an industrial partner
to study how they think of SATD and how they manage it. Specifically, we
collected data by identifying and characterizing SATD in different sources
(issues, source code comments, and commits) and carried out a series of
interviews with 12 software practitioners. The results show: 1) the core
characteristics of SATD in industrial projects; 2) developers' attitudes
towards identified SATD and statistics; 3) triggers for practitioners to
introduce and repay SATD; 4) relations between SATD in different sources; 5)
practices used to manage SATD; 6) challenges and tooling ideas for SATD
management.


  With the increased adoption of E-learning platforms, keeping online learners
engaged throughout a lesson is challenging. One approach to tackle this
challenge is to probe learn-ers periodically by asking questions. The paper
presents an approach to generate questions from a given video lecture
automatically. The generated questions are aimed to evaluate learners'
lower-level cognitive abilities. The approach automatically extracts text from
video lectures to generates wh-kinds of questions. When learners respond with
an answer, the proposed approach further evaluates the response and provides
feedback. Besides enhancing learner's engagement, this approach's main benefits
are that it frees instructors from design-ing questions to check the
comprehension of a topic. Thus, instructors can spend this time productively on
other activities.


  Systems of neutral interacting mesons are investigated, concerning in
particular the validity of their description by an effective hamiltonian.
First, I study its connection to quantum field theory and show that the
spectrum of such systems cannot be reduced in general to the one of a single
constant effective mass matrix. Choosing nevertheless to work in this customary
formalism, one then faces several ways to diagonalize a complex matrix, which
lead to different eigenvalues and eigenvectors. Last, and it is the main
subject of this work, because K0 and its charge conjugate K0bar are also
connected, in quantum field theory, by hermitian conjugation, any constant
effective mass matrix is defined, in this basis, up to arbitrary diagonal
antisymmetric terms; I use this freedom to deform the mass matrix in various
ways and study the consequences on its spectrum. Emphasis is put on the role of
discrete symmetries throughout the paper. That the degeneracy of the
eigenvalues of the full renormalized mass matrix can be a sufficient condition
for the outcome of CP violation is outlined in an appendix. In the whole work,
the dual formalism of |in> and <out| states and bi-orthogonal basis, suitable
for non-normal matrices, is used.


  Current induced forces are not only related with the discrete nature of
electrons but also with its quantum character. It is natural then to wonder
about the effect of decoherence. Here, we develop the theory of current induced
forces including dephasing processes and we apply it to study adiabatic quantum
motors (AQMs). The theory is based on B\"uttiker's fictitious probe model which
here is reformulated for this particular case. We prove that it accomplishes
fluctuation-dissipation theorem. We also show that, in spite of decoherence,
the total work performed by the current induced forces remains equal to the
pumped charge per cycle times the voltage. We find that decoherence affects not
only the current induced forces of the system but also its intrinsic friction
and noise, modifying in a non trivial way the efficiency of AQMs. We apply the
theory to study an AQM inspired by a classical peristaltic pump where we
surprisingly find that decoherence can play a crucial role by triggering its
operation. Our results can help to understand how environmentally induced
dephasing affects the quantum behavior of nano-mechanical devices.


  In this work, we present a fully quantum theory of the plasmonic nanolaser,
based on the maser model. Theory can be applied both to the microlasers with
high Q-factor cavities and plasmonic nanolasers. We show that the latter is
essentially a thresholdless device. We obtain the statistics of quanta,
spectrum of the plasmonic radiation and the second-order coherence degree in
the steady state. The limits of the model applicability are discussed in
detail. All results are compared with the full numerical simulation.


  Since its conception, digital synthesis has significantly influenced the
advancement of music, leading to new genres and production styles. Through
existing synthesis techniques, one can recreate naturally occurring sounds as
well as generate innovative artificial timbres. However, research in audio
technology continues to pursue new methods of synthesizing sounds, keeping the
transformation of music constant. This research attempts to formulate the
framework of a new synthesis technique by redefining the popular
Proportional-Integral-Derivative (PID) algorithm used in feedback-based process
control. The framework is then implemented as a Python application to study the
available control parameters and their effect on the synthesized output.
Further, applications of this technique as an audio signal and LFO generator,
including its potentiality as an alternative to FM and Wavetable synthesis
techniques, are studied in detail. The research concludes by highlighting some
of the imperfections in the current framework and the possible research
directions to be considered to address them.


  We consider an online version of a longest path problem in an undirected and
planar graph that is motivated by a location and routing problem occurring in
the board game "Turn & Taxis". Path extensions have to be selected based on
only partial knowledge on the order in which nodes become available in later
iterations. Besides board games, online path extension problems have
applications in disaster relief management when infrastructure has to be
rebuilt after natural disasters. For example, flooding may affect large parts
of a road network, and parts of the network may become available only
iteratively and decisions may have to be made without the possibility of
planning ahead.
  We suggest and analyse selection criteria that identify promising nodes
(locations) for path extensions. We introduce the concept of tentacles of paths
as an indicator for the future extendability. Different initialization and
extension heuristics are suggested on compared to an ideal solution that is
obtained by an integer linear programming formulation assuming complete
knowledge, i.e., assuming that the complete sequence in which nodes become
available is known beforehand. All algorithms are tested and evaluated on the
original "Turn & Taxis" graph, and on an extended version of the "Turn & Taxis"
graph, with different parameter settings. The numerical results confirm that
the number of tentacles is a useful criterion when selecting path extensions,
leading to near-optimal paths at relatively low computational costs.


  We study pathwise entropy solutions for scalar conservation laws with
inhomogeneous fluxes and quasilinear multiplicative rough path dependence. This
extends the previous work of Lions, Perthame and Souganidis who considered
spatially independent and inhomogeneous fluxes with multiple paths and a single
driving singular path respectively. The approach is motivated by the theory of
stochastic viscosity solutions which relies on special test functions
constructed by inverting locally the flow of the stochastic characteristics.
For conservation laws this is best implemented at the level of the kinetic
formulation which we follow here.


  Let R be a complete discrete valuation ring with maximal ideal generated by
pi. Let f(X) in R[X] be a monic polynomial with nonzero discriminant Delta(f).
Let s >= v_pi(Delta(f)) + 1. Suppose given a factorisation of f(X) in (R/pi^s
R)[X] into several factors, not necessarily coprime in (R/pi R)[X]. We lift it
uniquely to a factorisation of f(X) in R[X]. This generalises the
Hensel-Rychlik Lemma, which covers the case of two factors. We work directly
with lifts of factorisations into several factors and avoid having to iterate
factorisations into two factors. For this purpose we define a resultant for
several polynomials in one variable as determinant of a generalised Sylvester
matrix.


  We discuss the grounded, equipotential ellipse in two-dimensional
electrostatics to illustrate different ways of extending the domain of the
potential and placing image charges such that homogeneous boundary conditions
are satisfied. In particular, we compare and contrast the Kelvin and Sommerfeld
image methods.


  We consider the long-time behavior of a diffusion process on $\mathbb{R}^d$
advected by a stationary random vector field which is assumed to be
divergence-free, dihedrally symmetric in law and have a log-correlated
potential. A special case includes $\nabla^\perp$ of the Gaussian free field in
two dimensions. We show the variance of the diffusion process at a large time
$t$ behaves like $2 c_* t (\log t)^{1/2}$, in a quenched sense and with a
precisely determined, universal prefactor constant $c_*>0$. We also prove a
quenched invariance principle under this superdiffusive scaling. The proof is
based on a rigorous renormalization group argument in which we inductively
analyze coarse-grained diffusivities, scale-by-scale. Our analysis leads to
sharp homogenization and large-scale regularity estimates on the infinitesimal
generator, which are subsequently transferred into quantitative information on
the process.


  This paper proposes a new approach to training recommender systems called
deviation-based learning. The recommender and rational users have different
knowledge. The recommender learns user knowledge by observing what action users
take upon receiving recommendations. Learning eventually stalls if the
recommender always suggests a choice: Before the recommender completes
learning, users start following the recommendations blindly, and their choices
do not reflect their knowledge. The learning rate and social welfare improve
substantially if the recommender abstains from recommending a particular choice
when she predicts that multiple alternatives will produce a similar payoff.


  In this paper, we consider mixed curvature $\mathcal{C}_{a,b}$, which is a
convex combination of Ricci curvature and holomorphic sectional curvature
introduced by Chu-Lee-Tam. We prove that if a compact complex manifold M admits
a K\"{a}hler metric with quasi-positive mixed curvature and $3a+2b\geq0$, then
it is projective. If $a,b\geq0$, then M is rationally connected. As a
corollary, the same result holds for k-Ricci curvature. We also show that any
compact K\"{a}hler manifold with quasi-positive 2-scalar curvature is
projective. Lastly, we generalize the result to the Hermitian case. In
particular, any compact Hermitian threefold with quasi-positive real
bisectional curvature have vanishing Hodge number $h^{2,0}$. Furthermore, if it
is K\"{a}hlerian, it is projective.


  Queries with similar information needs tend to have similar document clicks,
especially in biomedical literature search engines where queries are generally
short and top documents account for most of the total clicks. Motivated by
this, we present a novel architecture for biomedical literature search, namely
Log-Augmented DEnse Retrieval (LADER), which is a simple plug-in module that
augments a dense retriever with the click logs retrieved from similar training
queries. Specifically, LADER finds both similar documents and queries to the
given query by a dense retriever. Then, LADER scores relevant (clicked)
documents of similar queries weighted by their similarity to the input query.
The final document scores by LADER are the average of (1) the document
similarity scores from the dense retriever and (2) the aggregated document
scores from the click logs of similar queries. Despite its simplicity, LADER
achieves new state-of-the-art (SOTA) performance on TripClick, a recently
released benchmark for biomedical literature retrieval. On the frequent (HEAD)
queries, LADER largely outperforms the best retrieval model by 39% relative
NDCG@10 (0.338 v.s. 0.243). LADER also achieves better performance on the less
frequent (TORSO) queries with 11% relative NDCG@10 improvement over the
previous SOTA (0.303 v.s. 0.272). On the rare (TAIL) queries where similar
queries are scarce, LADER still compares favorably to the previous SOTA method
(NDCG@10: 0.310 v.s. 0.295). On all queries, LADER can improve the performance
of a dense retriever by 24%-37% relative NDCG@10 while not requiring additional
training, and further performance improvement is expected from more logs. Our
regression analysis has shown that queries that are more frequent, have higher
entropy of query similarity and lower entropy of document similarity, tend to
benefit more from log augmentation.


  For an oscillating electric dipole in the shape of a small, solid,
uniformly-polarized, spherical particle, we compute the self-field as well as
the radiated electromagnetic field in the surrounding free space. The assumed
geometry enables us to obtain the exact solution of Maxwell's equations as a
function of the dipole moment, the sphere radius, and the oscillation
frequency. The self field, which is responsible for the radiation resistance,
does not introduce acausal or otherwise anomalous behavior into the dynamics of
the bound electrical charges that comprise the dipole. Departure from
causality, a well-known feature of the dynamical response of a charged particle
to an externally applied force, is shown to arise when the charge is examined
in isolation, namely in the absence of the restraining force of an equal but
opposite charge that is inevitably present in a dipole radiator. Even in this
case, the acausal behavior of the (free) charged particle appears to be rooted
in the approximations used to arrive at an estimate of the self-force. When the
exact expression of the self-force is used, our numerical analysis indicates
that the impulse-response of the particle should remain causal.


  Strong coupling between molecular vibrations and microcavity modes has been
demonstrated to modify physical and chemical properties of the molecular
material. Here, we study the much less explored coupling between lattice
vibrations (phonons) and microcavity modes. Embedding thin layers of hexagonal
boron nitride (hBN) into classical microcavities, we demonstrate the evolution
from weak to ultrastrong phonon-photon coupling when the hBN thickness is
increased from a few nanometers to a fully filled cavity. Remarkably, strong
coupling is achieved for hBN layers as thin as 10 nm. Further, the ultrastrong
coupling in fully filled cavities yields a cavity polariton dispersion matching
that of phonon polaritons in bulk hBN, highlighting that the maximum
light-matter coupling in microcavities is limited to the coupling strength
between photons and the bulk material. The tunable cavity phonon polaritons
could become a versatile platform for studying how the coupling strength
between photons and phonons may modify the properties of polar crystals.


  Fine-tuning pretrained language models (LMs) is a popular approach to
automatic speech recognition (ASR) error detection during post-processing.
While error detection systems often take advantage of statistical language
archetypes captured by LMs, at times the pretrained knowledge can hinder error
detection performance. For instance, presence of speech disfluencies might
confuse the post-processing system into tagging disfluent but accurate
transcriptions as ASR errors. Such confusion occurs because both error
detection and disfluency detection tasks attempt to identify tokens at
statistically unlikely positions. This paper proposes a scheme to improve
existing LM-based ASR error detection systems, both in terms of detection
scores and resilience to such distracting auxiliary tasks. Our approach adopts
the popular mixup method in text feature space and can be utilized with any
black-box ASR output. To demonstrate the effectiveness of our method, we
conduct post-processing experiments with both traditional and end-to-end ASR
systems (both for English and Korean languages) with 5 different speech
corpora. We find that our method improves both ASR error detection F 1 scores
and reduces the number of correctly transcribed disfluencies wrongly detected
as ASR errors. Finally, we suggest methods to utilize resulting LMs directly in
semi-supervised ASR training.


  In practical massive MIMO systems, a substantial portion of system resources
are consumed to acquire channel state information (CSI), leading to a
drastically lower system capacity compared with the ideal case where perfect
CSI is available. In this paper, we show that the overhead for CSI acquisition
can be largely compensated by the potential gain due to the sparsity of the
massive MIMO channel in a certain transformed domain. To this end, we propose a
novel blind detection scheme that simultaneously estimates the channel and data
by factorizing the received signal matrix. We show that by exploiting the
channel sparsity, our proposed scheme can achieve a DoF very close to the ideal
case, provided that the channel is sufficiently sparse. Specifically, the
achievable degree of freedom (DoF) has a fractional gap of only $1/T$ from the
ideal DoF, where $T$ is the channel coherence time. This is a remarkable
advance for understanding the performance limit of the massive MIMO system. We
further show that the performance advantage of our proposed scheme in the
asymptotic SNR regime carries over to the practical SNR regime. Numerical
results demonstrate that our proposed scheme significantly outperforms its
counterpart schemes in the practical SNR regime under various system
configurations.


  The inter-layer magnetoresistance in a multilayered massless Dirac fermion
system, $\alpha$-(BEDT-TTF)$_2$I$_3$, under hydrostatic pressure was
investigated. We succeeded in detecting the zero-mode (n=0) Landau level and
its spin splitting in the magnetic field normal to the 2D plane. We
demonstrated that the effective Coulomb interaction in the magnetic field
intensifies the spin splitting of zero-mode Landau carriers. At temperatures
below 2K, magnetic fields above several Tesla break the twofold valley
degeneracy.


  Maximum inner product search (MIPS) over dense and sparse vectors have
progressed independently in a bifurcated literature for decades; the latter is
better known as top-$k$ retrieval in Information Retrieval. This duality exists
because sparse and dense vectors serve different end goals. That is despite the
fact that they are manifestations of the same mathematical problem. In this
work, we ask if algorithms for dense vectors could be applied effectively to
sparse vectors, particularly those that violate the assumptions underlying
top-$k$ retrieval methods. We study IVF-based retrieval where vectors are
partitioned into clusters and only a fraction of clusters are searched during
retrieval. We conduct a comprehensive analysis of dimensionality reduction for
sparse vectors, and examine standard and spherical KMeans for partitioning. Our
experiments demonstrate that IVF serves as an efficient solution for sparse
MIPS. As byproducts, we identify two research opportunities and demonstrate
their potential. First, we cast the IVF paradigm as a dynamic pruning technique
and turn that insight into a novel organization of the inverted index for
approximate MIPS for general sparse vectors. Second, we offer a unified regime
for MIPS over vectors that have dense and sparse subspaces, and show its
robustness to query distributions.


  We show a combinatorial formula for a lower bound of the dimension of the
non-unipotent monodromy part of the first Milnor cohomology of a hyperplane
arrangement satisfying some combinatorial conditions. This gives exactly its
dimension if a stronger combinatorial condition is satisfied. We also prove a
non-combinatorial formula for the dimension of the non-unipotent part of the
first Milnor cohomology, which apparently depends on the position of the
singular points. The latter generalizes a formula previously obtained by the
second named author.


  We present a novel physics-constrained polynomial chaos expansion as a
surrogate modeling method capable of performing both scientific machine
learning (SciML) and uncertainty quantification (UQ) tasks. The proposed method
possesses a unique capability: it seamlessly integrates SciML into UQ and vice
versa, which allows it to quantify the uncertainties in SciML tasks effectively
and leverage SciML for improved uncertainty assessment during UQ-related tasks.
The proposed surrogate model can effectively incorporate a variety of physical
constraints, such as governing partial differential equations (PDEs) with
associated initial and boundary conditions constraints, inequality-type
constraints (e.g., monotonicity, convexity, non-negativity, among others), and
additional a priori information in the training process to supplement limited
data. This ensures physically realistic predictions and significantly reduces
the need for expensive computational model evaluations to train the surrogate
model. Furthermore, the proposed method has a built-in uncertainty
quantification (UQ) feature to efficiently estimate output uncertainties. To
demonstrate the effectiveness of the proposed method, we apply it to a diverse
set of problems, including linear/non-linear PDEs with deterministic and
stochastic parameters, data-driven surrogate modeling of a complex physical
system, and UQ of a stochastic system with parameters modeled as random fields.


  Pion valence, glue and sea distributions are calculated using a continuum
approach to the two valence-body bound-state problem. Since the framework is
symmetry preserving, physical features of the distributions are properly
expressed. The analysis reveals that the emergent phenomenon of dynamical
chiral symmetry breaking causes a hardening of the valence-quark distribution
function, ${q}^\pi(x)$. Nevertheless, this distribution exhibits the $x\simeq
1$ behaviour predicted by quantum chromodynamics (QCD). At the scale
$\zeta_2:=2\,$GeV, the following momentum fractions are predicted: $\langle
x_{\rm valence} \rangle = 0.48(3)$, $\langle x_{\rm glue} \rangle = 0.41(2)$,
$\langle x_{\rm sea} \rangle = 0.11(2)$. Evolving to $\zeta=5.2\,$GeV, the
result for ${q}^\pi(x)$ agrees with that computed using lattice QCD. These
outcomes should both spur improved analyses of existing experiments and
stimulate efforts to obtain new data on the pion distribution functions using
available and envisioned facilities.


  The problem of grounding VQA tasks has seen an increased attention in the
research community recently, with most attempts usually focusing on solving
this task by using pretrained object detectors. However, pre-trained object
detectors require bounding box annotations for detecting relevant objects in
the vocabulary, which may not always be feasible for real-life large-scale
applications. In this paper, we focus on a more relaxed setting: the grounding
of relevant visual entities in a weakly supervised manner by training on the
VQA task alone. To address this problem, we propose a visual capsule module
with a query-based selection mechanism of capsule features, that allows the
model to focus on relevant regions based on the textual cues about visual
information in the question. We show that integrating the proposed capsule
module in existing VQA systems significantly improves their performance on the
weakly supervised grounding task. Overall, we demonstrate the effectiveness of
our approach on two state-of-the-art VQA systems, stacked NMN and MAC, on the
CLEVR-Answers benchmark, our new evaluation set based on CLEVR scenes with
ground truth bounding boxes for objects that are relevant for the correct
answer, as well as on GQA, a real world VQA dataset with compositional
questions. We show that the systems with the proposed capsule module
consistently outperform the respective baseline systems in terms of answer
grounding, while achieving comparable performance on VQA task.


  Nonquasiparticle states above the Fermi energy are studied by first-principle
dynamical mean field calculations for a prototype half-metallic ferromagnet,
NiMnSb. We present a quantitative evaluation of the spectral weight of this
characteristic feature and discuss the possible experimental investigation
(BIS, NMR, STM and Andreev reflection) to clarify the existence of these
states.


  We present a new lattice determination of some of the parameters appearing
both in the Operator Product Expansion (OPE) analysis of the inclusive
semileptonic $B$-meson decays and in the Heavy Quark Expansion (HQE) of the
pseudoscalar (PS) and vector (V) heavy-light meson masses. We perform a lattice
QCD (LQCD) computation of PS and V heavy-light meson masses for heavy-quark
masses $m_h$ in the range from $m_c^{\rm phys}$ to $\simeq 4m_b^{\rm phys}$. We
employed the $N_f = 2+1+1$ gauge configurations of the European Twisted Mass
Collaboration (ETMC) at three values of the lattice spacing $a \simeq (0.062,
0.082, 0.089)$ fm with pion masses in the range $M_\pi \simeq (210 - 450)$ MeV.
The heavy-quark mass is simulated directly on the lattice up to $\simeq
3m_c^{\rm phys}$. The interpolation to the physical $m_b^{\rm phys}$ is
performed using the ETMC ratio method and adopting the kinetic mass scheme. We
obtain $m_b^{\rm kin}(1~\mbox{GeV}) = 4.61 (20)$ GeV
($\overline{m}_b(\overline{m}_b) = 4.26 (18)$ GeV in the $\overline{\rm MS}$
scheme). The lattice data are analyzed in terms of the HQE and the matrix
elements of dimension-4 and dimension-5 operators are extracted with good
precision, namely: $\overline{\Lambda} = 0.552 (26)$ GeV, $\mu_\pi^2 = 0.321
(32)$ GeV$^2$ and $\mu_G^2(m_b) = 0.253 (25)$ GeV$^2$. The data also allow for
an estimate of the dimension-6 operator matrix elements.


  Nominal Logic is a version of first-order logic with equality, name-binding,
renaming via name-swapping and freshness of names. Contrarily to higher-order
logic, bindable names, called atoms, and instantiable variables are considered
as distinct entities. Moreover, atoms are capturable by instantiations,
breaking a fundamental principle of lambda-calculus. Despite these differences,
nominal unification can be seen from a higher-order perspective. From this
view, we show that nominal unification can be reduced to a particular fragment
of higher-order unification problems: Higher-Order Pattern Unification. This
reduction proves that nominal unification can be decided in quadratic
deterministic time, using the linear algorithm for Higher-Order Pattern
Unification. We also prove that the translation preserves most generality of
unifiers.


  In this paper, we derive a probability density function that generalizes the
Burr XII distribution. The cumulative distribution function and the $n^{th}$
moment of the generalized distribution are obtained while the distribution of
some order statistics of the distribution are established. A theorem that
relate the new distribution to another statistical distribution is established.


  Q-conditional symmetries (nonclassical symmetries) for the general class of
two-component reaction-diffusion systems with non-constant diffusivities are
studied. Using the recently introduced notion of Q-conditional symmetries of
the first type, an exhausted list of reaction-diffusion systems admitting such
symmetry is derived. The results obtained for the reaction-diffusion systems
are compared with those for the scalar reaction-diffusion equations. The
symmetries found for reducing reaction-diffusion systems to two-dimensional
dynamical systems, i.e., ODE systems, and finding exact solutions are applied.
As result, multiparameter families of exact solutions in the explicit form for
a nonlinear reaction-diffusion system with an arbitrary diffusivity are
constructed. Finally, the application of the exact solutions for solving a
biologically and physically motivated system is presented.


  A phenomenological approach for neutron production in fast muon interactions
has been considered. Linear approximation for photonuclear production mechanism
at shallow depth has been deduced. Present calculations were compared with
experimental and theoretical results.


  In some recent papers a loss-gain electronic circuit has been introduced and
analyzed within the context of PT-quantum mechanics. In this paper we show that
this circuit can be analyzed using the formalism of the so-called
pseudo-fermions. In particular we discuss the time behavior of the circuit, and
we construct two biorthogonal bases associated to the Liouville matrix $\Lc$
used in the treatment of the dynamics. We relate these bases to $\Lc$ and
$\Lc^\dagger$, and we also show that a self-adjoint Liouville-like operator
could be introduced in the game. Finally, we describe the time evolution of the
circuit in an {\em Heisenberg-like} representation, driven by a non
self-adjoint hamiltonian.


  In this paper we study how the use of a more continuous set of basis
functions affects the cost of solving systems of linear equations resulting
from a discretized Galerkin weak form. Specifically, we compare performance of
linear solvers when discretizing using $C^0$ B-splines, which span traditional
finite element spaces, and $C^{p-1}$ B-splines, which represent maximum
continuity. We provide theoretical estimates for the increase in cost of the
matrix-vector product as well as for the construction and application of
black-box preconditioners. We accompany these estimates with numerical results
and study their sensitivity to various grid parameters such as element size $h$
and polynomial order of approximation $p$. Finally, we present timing results
for a range of preconditioning options for the Laplace problem. We conclude
that the matrix-vector product operation is at most $\slfrac{33p^2}{8}$ times
more expensive for the more continuous space, although for moderately low $p$,
this number is significantly reduced. Moreover, if static condensation is not
employed, this number further reduces to at most a value of 8, even for high
$p$. Preconditioning options can be up to $p^3$ times more expensive to setup,
although this difference significantly decreases for some popular
preconditioners such as Incomplete LU factorization.


  The predictabilities of the three alpha-decay half-life formulae, the Royer
GLDM, the Viola-Seaborg and the Sobiczewski-Parkhomenko formulae, have been
evaluated by developing a method based on the ansatz of standard experimental
benchmarking. The coefficients of each formula were re-derived using the
reliable data of the alpha-standards nuclei. The modified formulae that
resulted were used to evaluate the accuracies of the formulae towards the
prediction of half-lives of a set of nuclides with well-studied alpha-
spectroscopic data as well as a set of exotic alpha-emitters. Further, a simple
linear optimization of the modified formulae allowed adjustments for the
insufficient statistics of the primary data set without changing the modified
formulae. While the three modified formulae showed equivalent results for all
the medium heavy nuclei except the odd-odd, the modified GLDM showed relatively
the best figures of merit for the odd-odd and superheavy nuclides.


  Low dimensional magnetic systems (such as spin-chain) are extensively studied
due to their exotic magnetic properties. Here, we would like to address that
such systems should also be interesting in the field of dielectric,
ferroelectricity and magnetodielectric coupling. As a prototype example, we
have investigated a one-dimensional (1D) helical-chain metal-organic hybrid
system with a chiral structure which shows a broad hump in magnetic
susceptibility around 55 K (Tmax). The complex dielectric constant exactly
traces this feature, which suggests intrinsic magnetodielectric coupling in
this chiral system. The dipolar ordering at Tmax occurs due to
lattice-distortion which helps to minimize the magnetic energy accompanied by
1D-magnetic ordering or vice-versa. This experimental demonstration initiates a
step to design and investigate hybrid organic-inorganic magnetic systems
consisting of chiral structure towards ferroelectricity and magnetodielectric
coupling.


  Let A be a BP*-algebra with identity e, P_{1}(A) be the set of all positive
linear functionals f on A such that f(e) = 1, and let M_{s}(A) be the set of
all nonzero hermitian multiplicative linear functionals on A. We prove that
M_{s}(A) is the set of extreme points of P_{1}(A). We also prove that, if
M_{s}(A) is equicontinuous, then every positive linear functional on A is
continuous. Finally, we give an example of a BP*-algebra whose topological dual
is not included in the vector space generated by P_{1}(A), which gives a
negative answer to a question posed by M. A. Hennings.


  We define orbifold mapping class groups (with marked points) and study them
using their action on certain orbifold analogs of arcs and simple closed
curves. Moreover, we establish a Birman exact sequence for suitable subgroups
of orbifold mapping class groups. The short exact sequence allows us to deduce
finite presentations of these groups. This is the basis for a similar
discussion of orbifold braid groups in [6].


  When a water droplet is deposited within a sparsely miscible liquid medium
such as certain oils, the droplet surprisingly vanishes, even in a confined
geometry. Such a phenomenon has crucial consequences for multiphase flows in
which confined nano- and/or picoliter droplets are considered. We report here
experiments of microdroplet dissolution in microchannels that reveal an
enhancement of the shrinkage of confined water microdroplets in oil due to the
permeability of the walls - made of polydimethilsiloxane (PDMS) - and a delay
when collective effects are present. The system is first modelled assuming that
the dissolution of the droplets in its surrounding liquid follows the
Epstein-Plesset solution of the diffusion equation. The dissolution of small
isolated droplets can indeed be described by this solution of the diffusion
equation, while the vanishing of droplets larger than a certain critical value
and those closer to other droplets requires numerical simulations which take
into account the boundary conditions of the confined system, the neighbouring
droplets and interestingly, the evaporative water vapour flux through the PDMS.
Our results thus reveal the important role of the water solubility in oil and
most remarkably, of the water vapour transport through permeable walls.


  This paper uses W. M. Schmidt's idea formulated in 1967 to generalise the
classical theory of Diophantine approximation to subspaces of $\mathbb{R}^n$.
Given two subspaces of $\mathbb{R}^n$ $A$ and $B$ of respective dimensions $d$
and $e$ with $d+e\leqslant n$, the proximity between $A$ and $B$ is measured by
$t=\min(d,e)$ canonical angles $0\leqslant \theta_1\leqslant \cdots\leqslant
\theta_t\leqslant \pi/2$; we set $\psi_j(A,B)=\sin\theta_j$. If $B$ is a
rational subspace, his complexity is measured by its height
$H(B)=\mathrm{covol}(B\cap\mathbb{Z}^n)$. We denote by $\mu_n(A\vert e)_j$ the
exponent of approximation defined as the upper bound (possibly equal to
$+\infty$) of the set of $\beta>0$ such that for infinitely many rational
subspaces $B$ of dimension $e$, the inequality $\psi_j(A,B)\leqslant
H(B)^{-\beta}$ holds. We are interested in the minimal value
$\mathring{\mu}_n(d\vert e)_j$ taken by $\mu_n(A\vert e)_j$ when $A$ ranges
through the set of subspaces of dimension $d$ of $\mathbb{R}^n$ such that for
all rational subspaces $B$ of dimension $e$ one has $\dim(A\cap B)<j$. We show
that if $A$ is included in a rational subspace $F$ of dimension $k$, its
exponent in $\mathbb{R}^n$ is the same as its exponent in $\mathbb{R}^k$ via a
rational isomorphism $F\to\mathbb{R}^k$. This allows us to deduce new upper
bounds for $\mathring{\mu}_n(d\vert e)_j$. We also study the values taken by
$\mu_n(A\vert e)_e$ when $A$ is a subspace of $\mathbb{R}^n$ satisfying
$\dim(A\cap B)<e$ for all rational subspaces $B$ of dimension $e$.


  We derive the nonlinear k_\perp-factorization for the spectrum of jets in
high-mass diffractive deep inelastic scattering as a function of three hard
scales - the virtuality of the photon Q^2, the transverse momentum of the jet
and the saturation scale Q_A. In contrast to all other hard reactions studied
so far, we encounter a clash between the two definitions of the glue in the
pomeron -- from the inclusive spectrum of leading quarks and the small-\beta
evolution of the diffractive cross section. This clash casts a further shadow
on customary applications of the familiar collinear factorization to a pQCD
analysis of diffractive deep inelastic scattering.


  Loss of plasticity is a phenomenon in which neural networks lose their
ability to learn from new experience. Despite being empirically observed in
several problem settings, little is understood about the mechanisms that lead
to loss of plasticity. In this paper, we offer a consistent explanation for
loss of plasticity: Neural networks lose directions of curvature during
training and that loss of plasticity can be attributed to this reduction in
curvature. To support such a claim, we provide a systematic investigation of
loss of plasticity across continual learning tasks using MNIST, CIFAR-10 and
ImageNet. Our findings illustrate that loss of curvature directions coincides
with loss of plasticity, while also showing that previous explanations are
insufficient to explain loss of plasticity in all settings. Lastly, we show
that regularizers which mitigate loss of plasticity also preserve curvature,
motivating a simple distributional regularizer that proves to be effective
across the problem settings we considered.


  In this paper, we consider the achievable sum secrecy rate in full-duplex
wiretap channel in the presence of an eavesdropper and imperfect channel state
information (CSI). We assume that the users participating in full-duplex
communication and the eavesdropper have single antenna each. The users have
individual transmit power constraints. They also transmit jamming signals to
improve the secrecy rates. We obtain the achievable perfect secrecy rate region
by maximizing the sum secrecy rate. We also obtain the corresponding optimum
powers of the message signals and the jamming signals. Numerical results that
show the impact of imperfect CSI on the achievable secrecy rate region are
presented.


  We use a recently developed interpretable and unsupervised machine-learning
method, the tensorial kernel support vector machine (TK-SVM), to investigate
the low-temperature classical phase diagram of a generalized
Heisenberg-Kitaev-$\Gamma$ ($J$-$K$-$\Gamma$) model on a honeycomb lattice.
Aside from reproducing phases reported by previous quantum and classical
studies, our machine finds a hitherto missed nested zigzag-stripy order and
establishes the robustness of a recently identified modulated $S_3 \times Z_3$
phase, which emerges through the competition between the Kitaev and $\Gamma$
spin liquids, against Heisenberg interactions. The results imply that, in the
restricted parameter space spanned by the three primary exchange interactions
-- $J$, $K$, and $\Gamma$, the representative Kitaev material $\alpha$-${\rm
RuCl}_3$ lies close to the boundaries of several phases, including a simple
ferromagnet, the unconventional $S_3 \times Z_3$ and nested zigzag-stripy
magnets. A zigzag order is stabilized by a finite $\Gamma^{\prime}$ and/or
$J_3$ term, whereas the four magnetic orders may compete in particular if
$\Gamma^{\prime}$ is anti-ferromagnetic.


  A search has been made for a contribution of the changing cosmic ray
intensity to the global warming observed in the last century. The cosmic ray
intensity shows a strong 11 year cycle due to solar modulation and the overall
rate has decreased since 1900. These changes in cosmic ray intensity are
compared to those of the mean global surface temperature to attempt to quantify
any link between the two. It is shown that, if such a link exists, the changing
cosmic ray intensity contributes less than 8% to the increase in the mean
global surface temperature observed since 1900.


  Item-item collaborative filtering (CF) models are a well known and studied
family of recommender systems, however current literature does not provide any
theoretical explanation of the conditions under which item-based
recommendations will succeed or fail.
  We investigate the existence of an ideal item-based CF method able to make
perfect recommendations. This CF model is formalized as an eigenvalue problem,
where estimated ratings are equivalent to the true (unknown) ratings multiplied
by a user-specific eigenvalue of the similarity matrix. Preliminary experiments
show that the magnitude of the eigenvalue is proportional to the accuracy of
recommendations for that user and therefore it can provide reliable measure of
confidence.


  Consider a countably infinite collection of interacting queues, with a queue
located at each point of the $d$-dimensional integer grid, having independent
Poisson arrivals, but dependent service rates. The service discipline is of the
processor sharing type,with the service rate in each queue slowed down, when
the neighboring queues have a larger workload. The interactions are translation
invariant in space and is neither of the Jackson Networks type, nor of the
mean-field type. Coupling and percolation techniques are first used to show
that this dynamics has well defined trajectories. Coupling from the past
techniques are then proposed to build its minimal stationary regime. The rate
conservation principle of Palm calculus is then used to identify the stability
condition of this system, where the notion of stability is appropriately
defined for an infinite dimensional process. We show that the identified
condition is also necessary in certain special cases and conjecture it to be
true in all cases. Remarkably, the rate conservation principle also provides a
closed form expression for the mean queue size. When the stability condition
holds, this minimal solution is the unique translation invariant stationary
regime. In addition, there exists a range of small initial conditions for which
the dynamics is attracted to the minimal regime. Nevertheless, there exists
another range of larger though finite initial conditions for which the dynamics
diverges, even though stability criterion holds.


  We prove the conjectured limiting normality for the number of crossings of a
uniformly chosen set partition of [n] = {1,2,...,n}. The arguments use a novel
stochastic representation and are also used to prove central limit theorems for
the dimension index and the number of levels.


  We consider high density quark matter in the large $\N_c$ and $\N_f$ limit
with $\N_f/\N_c$ fixed. In this limit, the color superconductivity disappears.
We discuss that the chiral density wave state is also absent in the limit, if
we assume the existence of the non-perturbative magnetic screening effect as
indicated by recent lattice study. We argue that ferromagnetism can become a
candidate for the ground state if quarks are massive.


  We present geometrical and kinematical analysis of Moreton waves and EIT
waves observed on June 3, 2012 and Moreton waves observed on July 6, 2012. The
Moreton waves were recorded in H$\alpha$ images of Global Oscillation Network
Group (GONG) archive and EIT waves obtained from SDO/AIA observations,
especially in 193 nm channel. The observed wave of June 3 has angular span of
about $70^{\circ}$ with a broad wave front associated to NOAA active region
11496. It was found that the speed of the wave that started propagating at
17.53 UT is between 950 to 1500 km/s. Related to this wave occurrence, there
was solar type II and III radio bursts. The speed of the EIT in this respect
about 247 km/sec. On the other hand, the wave of July 6 may be associated to
X1.1 class flare that occurred at 23.01 UT around the 11514 active region. From
the kinematical analysis, the wave propagated with the initial velocity of
about 1180 km/s which is in agreement with coronal shock velocity derived from
type II radio burst observation, $v\sim1200$ km/s.


  We perform photometric (the Lomb-Scargle periodogram, autocorrelation, and
wavelet) and asteroseismic analyses of 92 Kepler solar-like main-sequence stars
to understand the reliability of the measured stellar rotation periods. We
focus on the 70 stars without reported stellar companions, and classify them
into four groups according to the quarter-to-quarter variance of the
Lomb-Scargle period and the precision of the asteroseismic period. We present
detailed individual comparison among photometric and asteroseismic constraints
for these stars. We find that most of our targets exhibit significant
quarter-to-quarter variances in the photometric periods, suggesting that the
photometrically estimated period should be regarded as a simplified
characterization of the true stellar rotation period, especially under the
presence of the latitudinal differential rotation. On the other hand, there are
a fraction of stars with a relatively small quarter-to-quarter variance in the
photometric periods, most of which have consistent values for asteroseismically
and photometrically estimated rotation periods. We also identify over ten stars
whose photometric and asteroseismic periods significantly disagree, which would
be potentially interesting targets for further individual investigations.


  Composing fashion outfits involves deep understanding of fashion standards
while incorporating creativity for choosing multiple fashion items (e.g.,
Jewelry, Bag, Pants, Dress). In fashion websites, popular or high-quality
fashion outfits are usually designed by fashion experts and followed by large
audiences. In this paper, we propose a machine learning system to compose
fashion outfits automatically. The core of the proposed automatic composition
system is to score fashion outfit candidates based on the appearances and
meta-data. We propose to leverage outfit popularity on fashion oriented
websites to supervise the scoring component. The scoring component is a
multi-modal multi-instance deep learning system that evaluates instance
aesthetics and set compatibility simultaneously. In order to train and evaluate
the proposed composition system, we have collected a large scale fashion outfit
dataset with 195K outfits and 368K fashion items from Polyvore. Although the
fashion outfit scoring and composition is rather challenging, we have achieved
an AUC of 85% for the scoring component, and an accuracy of 77% for a
constrained composition task.


  We present the second release of the Meta-catalogue of X-Ray detected
Clusters of galaxies (hereafter MCXC-II). The MCXC-II has been compiled from
publicly available ROSAT All Sky Survey-based (NORAS, REFLEX, BCS, SGP, NEP,
MACS, CIZA, RXGCC) and serendipitous (160SD, 400SD, SHARC, WARPS, and EMSS)
cluster catalogues. Redshifts were systematically checked and updated if
necessary, and additional redshift information (type and origin) added. The
X-ray data were standardised to an overdensity of 500 using a new procedure
based on the use of the original flux and aperture measurements available in
the input catalogues. MCXC-II contains 2221 entries, essentially completing the
census of ROSAT cluster detections by including objects from the REFLEX-II and
RXGCC surveys, in addition to providing a complete and fully-homogenised
sub-catalogue of all published MACS clusters. Duplicate entries from overlaps
between the survey areas of the individual input catalogues were carefully
handled. For each cluster the MCXC-II provides three identifiers, a redshift,
coordinates, membership in the original catalogue, and standardised [0.1-2.4]
keV band luminosity $L_{500}$, total mass $M_{500}$, and radius $R_{500}$.
Uncertainties on $L_{500}$ were computed from the flux errors in the original
catalogues. MCXC-II additionally furnishes information on overlaps between the
input catalogues, gives the luminosity and its uncertainty when measurements
from different surveys are available, and provides notes on individual objects.


  Homogeneous photometric data (Johnson V, B-V, V-K, Cousins V-I and Stromgren
b-y), radial velocities, and abundances of Fe, O, Mg, Si, Ca, Ti, Cr and Ni are
presented for 99 stars with high precision parallaxes measured by the Hipparcos
satellite. These data have been previously used to assist the derivation of
accurate distances and ages of galactic globular clusters. Magnitudes and
colours for the programme stars were obtained combining and standardizing
carefully selected literature data available in the Simbad data-base and V and
B-V values measured by the Hipparcos/Tycho mission. Comparison of colours for
our targets suggests: (i) ground-based and Tycho B-V's agree well for colours
bluer than 0.75 mag, but have a lot of scatter for redder colours; (ii) the
Hipparcos V-I colours have a very large scatter and a zero point offset of
+0.02 mag compared to the literature values. The programme stars have metal
abundances in the range -2.5<[Fe/H]<0.2. The spectroscopic observational data
set consists of high dispersion (15,000<R<60,000), high S/N(>200) spectra
obtained at the Asiago and McDonald Observatories for 66 stars. The analysis is
carried out following the same precepts used in previous papers of this series
and includes corrections for departures from LTE in the formation of the O
lines. The main results are: (i) the equilibrium of ionization of Fe is well
satisfied in late F-early K-dwarfs; (ii) Oxygen and alpha-elements are
overabundant by about 0.3 dex. This large homogeneous abundance data set has
been used to recalibrate the abundance scales of Schuster and Nissen (1989, AA,
221, 65), Carney et al. (1994, AJ, 107, 2240), and Ryan and Norris (1991, AJ,
101, 1835).


  In the paper we consider the energy and its flux in the Bonnor spacetime. We
construct some non-local expressions from the Einstein canonical
energy-momentum pseudotensor of the gravitational field which show that the
gravitational energy and its flux in this spacetime are different from zero and
do not vanish even outside of the material source (a stationary beam of the
null dust) of this spacetime.


  Near the horizon, the obvious symmetries of a black hole spacetime---the
horizon-preserving diffeomorphisms---are enhanced to a larger symmetry group
with a BMS${}_3$ algebra. Using dimensional reduction and covariant phase space
techniques, I investigate this augmented symmetry, and show that it is strong
enough to determine the black hole entropy.


  Two setups with interlocked magnetic flux tubes are used to study the
evolution of magnetic energy and helicity on magnetohydrodynamical (MHD)
systems like plasmas. In one setup the initial helicity is zero while in the
other it is finite. To see if it is the actual linking or merely the helicity
content that influences the dynamics of the system we also consider a setup
with unlinked field lines as well as a field configuration in the shape of a
trefoil knot. For helical systems the decay of magnetic energy is slowed down
by the helicity which decays slowly. It turns out that it is the helicity
content, rather than the actual linking, that is significant for the dynamics.


  We investigate the delocalization of operators in non-chaotic quantum systems
whose interactions are encoded in an underlying graph or network. In
particular, we study how fast operators of different sizes delocalize as the
network connectivity is varied. We argue that these delocalization properties
are well captured by Krylov complexity and show, numerically, that efficient
delocalization of large operators can only happen within sufficiently connected
network topologies. Finally, we demonstrate how this can be used to furnish a
deeper understanding of the quantum charging advantage of a class of SYK-like
quantum batteries.


  Sampling, grouping, and aggregation are three important components in the
multi-scale analysis of point clouds. In this paper, we present a novel
data-driven sampler learning strategy for point-wise analysis tasks. Unlike the
widely used sampling technique, Farthest Point Sampling (FPS), we propose to
learn sampling and downstream applications jointly. Our key insight is that
uniform sampling methods like FPS are not always optimal for different tasks:
sampling more points around boundary areas can make the point-wise
classification easier for segmentation. Towards this end, we propose a novel
sampler learning strategy that learns sampling point displacement supervised by
task-related ground truth information and can be trained jointly with the
underlying tasks. We further demonstrate our methods in various point-wise
analysis tasks, including semantic part segmentation, point cloud completion,
and keypoint detection. Our experiments show that jointly learning of the
sampler and task brings better performance than using FPS in various
point-based networks.


  In this article, we demonstrate the common fixed point theorems for three
transformations on vector S-metric space by utilizing weakly compatible and
point of coincidence. Moreover, some of our results generalize the existing
results in the literature.


  We consider the degree/diameter problem for graphs embedded in a surface,
namely, given a surface $\Sigma$ and integers $\Delta$ and $k$, determine the
maximum order $N(\Delta,k,\Sigma)$ of a graph embeddable in $\Sigma$ with
maximum degree $\Delta$ and diameter $k$. We introduce a number of
constructions which produce many new largest known planar and toroidal graphs.
We record all these graphs in the available tables of largest known graphs.
Given a surface $\Sigma$ of Euler genus $g$ and an odd diameter $k$, the
current best asymptotic lower bound for $N(\Delta,k,\Sigma)$ is given by
\[\sqrt{\frac{3}{8}g}\Delta^{\lfloor k/2\rfloor}.\] Our constructions produce
new graphs of order \[\begin{cases}6\Delta^{\lfloor k/2\rfloor}& \text{if
$\Sigma$ is the Klein bottle}\\
\(\frac{7}{2}+\sqrt{6g+\frac{1}{4}}\)\Delta^{\lfloor k/2\rfloor}&
\text{otherwise,}\end{cases}\] thus improving the former value by a factor of
4.


  The chapter provides an introduction to the basic concepts of Algebraic
Topology with an emphasis on motivation from applications in the physical
sciences. It finishes with a brief review of computational work in algebraic
topology, including persistent homology.


  We present a density functional theory (DFT) for lattice models with local
electron-electron (e-e) and electron-phonon (e-ph) interactions.
Exchange-correlation potentials are derived via dynamical mean field theory for
the infinite-dimensional Bethe lattice, and analytically for an isolated
Hubbard-Holstein site. These potentials exhibit discontinuities as a function
of the density, which depend on the relative strength of the e-e and e-ph
interactions. By comparing to exact benchmarks, we show that the DFT formalism
gives a good description of the linear conductance and real-time dynamics.


  Considering light transport in disordered media, the medium is often treated
as an effective medium requiring accurate evaluation of an effective refractive
index. Because of its simplicity, the Maxwell-Garnett (MG) mixing rule is
widely used, although its restriction to particles much smaller than the
wavelength is rarely satisfied. Using 3D finite-difference time-domain
simulations, we show that the MG theory indeed fails for large particles.
Systematic investigation of size effects reveals that the effective refractive
index can be instead approximated by a quadratic polynomial whose coefficients
are given by an empirical formula. Hence, a simple mixing rule is derived which
clearly outperforms established mixing rules for composite media containing
large particles, a common condition in natural disordered media.


  We model the transport of an unknown quantum state on one dimensional qubit
lattices by means of a quantum cellular automata evolution. We do this by first
introducing a class of discrete noisy dynamics, in the first excitation sector,
in which a wide group of classical stochastic dynamics is embedded within the
more general formalism of quantum operations. We then extend the Hilbert space
of the system to accommodate a global vacuum state, thus allowing for the
transport of initial on-site coherences besides excitations, and determine the
dynamical constraints that define the class of noisy quantum cellular automata
in this subspace. We then study the transport performance through numerical
simulations, showing that for some instances of the dynamics perfect quantum
state transfer is attainable. Our approach provides one with a natural
description of both unitary and open quantum evolutions, where the homogeneity
and locality of interactions allow one to take into account several forms of
quantum noise in a plausible scenario.


  Fictitious play (FP) is one of the most fundamental game-theoretical learning
frameworks for computing Nash equilibrium in $n$-player games, which builds the
foundation for modern multi-agent learning algorithms. Although FP has provable
convergence guarantees on zero-sum games and potential games, many real-world
problems are often a mixture of both and the convergence property of FP has not
been fully studied yet. In this paper, we extend the convergence results of FP
to the combinations of such games and beyond. Specifically, we derive new
conditions for FP to converge by leveraging game decomposition techniques. We
further develop a linear relationship unifying cooperation and competition in
the sense that these two classes of games are mutually transferable. Finally,
we analyze a non-convergent example of FP, the Shapley game, and develop
sufficient conditions for FP to converge.


  We consider the structure of finite $p$-groups $G$ having precisely three
characteristic subgroups, namely $1$, $\Phi(G)$ and $G$. The structure of $G$
varies markedly depending on whether $G$ has exponent $p$ or $p^2$, and, in
both cases, the study of such groups raises deep problems in representation
theory. We present classification theorems for 3- and 4-generator groups, and
we also study the existence of such $r$-generator groups with exponent $p^2$
for various values of $r$. The automorphism group induced on the Frattini
quotient is, in various cases, related to a maximal linear group in
Aschbacher's classification scheme.


  The standard Large Deviation Theory (LDT) mirrors the Boltzmann-Gibbs (BG)
factor which describes the thermal equilibrium of short-range Hamiltonian
systems, the velocity distribution of which is Maxwellian. It is generically
applicable to systems satisfying the Central Limit Theorem (CLT), among others.
When we focus instead on stationary states of typical complex systems (e.g.,
classical long-range Hamiltonian systems), both the CLT and LDT need to be
generalized. We focus here on a scale-invariant stochastic process involving
strongly-correlated exchangeable random variables which, through the Laplace-de
Finetti theorem, is known to yield a long-tailed $Q$-Gaussian $N\to\infty$
attractor in the space of distributions ($1 < Q<3)$. We present strong
numerical indications that the corresponding LDT probability distribution is
given by $P(N,z)=P_0\,e_q^{-r_q(z)N}=P_0[1-(1-q)r_q(z)N]^{1/(1-q)}$ with
$q=2-1/Q \in (1,5/3)$. The rate function $r_q(z)$ seemingly equals the relative
nonadditive $q_r$-entropy per particle, with $q_r \simeq \frac{7}{10} +
\frac{6}{10}\frac{1}{Q-1}$, thus exhibiting a singularity at $Q=1$ and
recovering the BG value $q_r=1$ in the $Q \to 3$ limit. Let us emphasize that
the extensivity of $r_q(z)N$ appears to be verified, consistently with what is
expected, from the Legendre structure of thermodynamics, for a total entropy.
The present analysis of a relatively simple model somewhat mirroring spin-1/2
long-range-interacting ferromagnets (e.g., with strongly anisotropic XY
coupling) might be helpful for a deeper understanding of nonequilibrium systems
with global correlations and other complex systems.


  We propose an eclipsing light-curve diagnosis for black-hole accretion flows.
When emission from an inner accretion disk around a black hole is occulted by a
companion star, the observed light curve becomes asymmetric at ingress and
egress on a time scale of 0.1-1 seconds. This light-curve analysis provides a
means of verifying the relativistic properties of the accretion flow, based on
the special/general relativistic effects of black holes. The ``skewness'' for
the eclipsing light curve of a thin disk is $\sim 0.08$, whereas that of a slim
disk is $\sim 0$, since the innermost part is self-occulted by the disk's outer
rim.


  Let G be a finite group with Sylow p-subgroup P. We show that the character
table of G determines whether P has maximal nilpotency class and whether P is a
minimal non-abelian group. The latter result is obtained from a precise
classification of the corresponding groups G in terms of their composition
factors. For p-constrained groups G we prove further that the character table
determines whether P can be generated by two elements.


  Let $k$ be a field with resolution of singularities, and $X$ a separated
$k$-scheme of finite type with structure map $g$. We show that the slice
filtration in the motivic stable homotopy category commutes with pullback along
$g$. Restricting the field further to the case of characteristic zero, we are
able to compute the slices of Weibel's homotopy invariant $K$-theory extending
the result of Levine, and also the zero slice of the sphere spectrum extending
the result of Levine and Voevodsky. We also show that the zero slice of the
sphere spectrum is a strict cofibrant ring spectrum
$\mathbf{HZ}_{X}^{\slicefilt}$ which is stable under pullback and that all the
slices have a canonical structure of strict modules over
$\mathbf{HZ}_{X}^{\slicefilt}$. If we consider rational coefficents and assume
that $X$ is geometrically unibranch then relying on the work of Cisinski and
D{\'e}glise, we get that the zero slice of the sphere spectrum is given by
Voevodsky's rational motivic cohomology spectrum $\mathbf{HZ}_{X}\otimes
\mathbb Q$ and that the slices have transfers. This proves several conjectures
of Voevodsky.


  Graphene samples can have a very high carrier mobility if influences from the
substrate and the environment are minimized. Embedding a graphene sheet into a
heterostructure with hexagonal boron nitride (hBN) on both sides was shown to
be a particularly efficient way of achieving a high bulk mobility.
Nanopatterning graphene can add extra damage and drastically reduce sample
mobility by edge disorder. Preparing etched graphene nanostructures on top of
an hBN substrate instead of SiO2 is no remedy, as transport characteristics are
still dominated by edge roughness. Here we show that etching fully encapsulated
graphene on the nanoscale is more gentle and the high mobility can be
preserved. To this end, we prepared graphene antidot lattices where we observe
magnetotransport features stemming from ballistic transport. Due to the short
lattice period in our samples we can also explore the boundary between the
classical and the quantum transport regime.


  In this work, using self-consistent tight-binding calculations, for the first
time, we show that a direct to indirect bandgap transition is possible in an
armchair graphene nanoribbon by the application of an external bias along the
width of the ribbon, opening up the possibility of new device applications.
With the help of Dirac equation, we qualitatively explain this bandgap
transition using the asymmetry in the spatial distribution of the perturbation
potential produced inside the nanoribbon by the external bias. This is followed
by the verification of the bandgap trends with a numerical technique using
Magnus expansion of matrix exponentials. Finally, we show that the carrier
effective masses possess tunable sharp characters in the vicinity of the
bandgap transition points.


  The discovery of large number of Cepheid variables in far-off galaxies offers
a unique opportunity to determine the accurate distance of the host galaxy
through their period-luminosity relation. The main aim of the present study is
to identify short-period and relatively faint Cepheids in the crowded field of
M31 disk which was observed as part of the Nainital Microlensing Survey. The
Cousins R and I-band photometric observations were obtained with a 1-m
telescope on more than 150 nights over the period between November 1998 to
January 2002. The data was analysed using the pixel technique and the mean
magnitudes of the Cepheids were determined by correlating their pixel fluxes
with the corresponding PSF-fitted photometric magnitudes. Here, we report
identification of 39 short-period Cepheid variables in the M31 disk. Most of
the Cepheids are found with R (mean) ~ 20-21 mag and the dense phase coverage
of our observations enabled us to identify Cepheids with periods as short as
3.4 days The frequency-period distribution of these Cepheids peaks at logP ~
0.9 and 1.1 days.


  We show that the zero field normal-state resistivity above Tc for various
levels of electron doping-both for underdoped, optimally, and overdoped
LaO1-xFxFeAs, i.e. (x=0.05-0.075 and 0.1-0.2) and underdoped SmO1-xFxFeAs
(x=0.06- 0.1) members of the 1111-iron-pnictide superconductor family-can be
scaled in a broad temperature range from 20 to 300 K onto a single universal
curve. The scaling was performed using the energy scale Delta, the resistivity
rho(Delta) and the residual resistivity rho0 as scaling parameters as well as
applying a recently proposed model-independent scaling method (H. G. Luo, Y. H.
Su, and T. Xiang, Phys. Rev. B 77, 014529 (2008)). The scaling parameters have
been calculated and the compositional variation of Delta has been determined.
The existence of a universal metallic rho(T) curve is interpreted as an
indication of a single mechanism which dominates the scattering of the charge
carriers in LaO1-xFxFeAs (x= 0.05 to 0.075 and 0.1 to 0.2) and SmO1-xFxFeAs (x
= 0.06 to 0.1) .


  In this paper, we show that it is possible for a commutative ring with
identity to be non-atomic (that is, there exist non-zero nonunits that cannot
be factored into irreducibles) and yet have a strongly atomic polynomial
extension. In particular, we produce a commutative ring with identity, R, that
is antimatter (that is, R has no irreducibles whatsoever) such that R[t] is
strongly atomic. What is more, given any nonzero nonunit f(t) in R[t] then
there is a factorization of f(t) into irreducibles of length no more than
deg(f(t)) + 2.


  Non-linear d-dimensional vector $\sigma$-models are studied in the large
N-limit. It is found that a two-point correlation function obeys a standard
Schrodinger equation for a free quantum particle moving in the
$\delta$-function quantum well. The threshold problem for bound states in this
equation is shown to be equivalent to a critical behavior of these models above
and below the Curie point.
  The SU(N)- symmetric Ginzburg-Landau (GL) $\sigma$-model subject to a uniform
magnetic field H is considered in the large-N limit within the Schrodinger
equation approach. A upper critical magnetic field line $H_{c2}(T)$ of type-II
superconductors for an arbitrary external H is obtained without exploiting the
lowest Landau level (LLL) approximation. Both low-H perturbation expansion
terms and exponentially small corrections to the LLL approximation are
calculated.
  Correspondences between the one-particle quantum mechanics and critical
phenomena as well as some applications of the above method to other models of
statistical mechanics are also discussed.


  A comparative XMM-Newton archival data spectral study of the ultraluminous
X-ray source (ULX) M33 X-8 has been performed by using both the standard disk
model and the newly developed slim disk models. The results of this analysis
tend to confirm the hypothesis that M33 X-8 is an X-ray binary with a
stellar-mass black hole accreting at super-Eddington rate.


  The $\gamma$-ray strength function and the nuclear level density of
$^{167}$Ho have been extracted using the Oslo method from a
$^{164}\text{Dy}(\alpha,p\gamma)^{167}$Ho experiment carried out at the Oslo
Cyclotron Laboratory. The level density displays a shape that is compatible
with %can be approximated with the constant temperature model in the
quasicontinuum, while the strength function shows structures indicating the
presence of both a scissors and a pygmy dipole resonance. Using our present
results as well as data from a previous
$^{163}\text{Dy}(\alpha,p\gamma)^{166}$Ho experiment, the
$^{165}\text{Ho}(n,\gamma)$ and $^{166}\text{Ho}(n,\gamma)$ MACS uncertainties
have been constrained. The possible influence of the low-lying, long-lived
6~keV isomer $^{166}$Ho in the $s$ process is investigated in the context of a
2~$M_\odot$, [Fe/H]=-0.5 AGB star. We show that the newly obtained
$^{165}\text{Ho}(n,\gamma)$ MACS affects the final $^{165}$Ho abundance, while
the $^{166}\text{Ho}(n,\gamma)$ MACS only impacts the enrichment of
$^{166,167}$Er to a limited degree due to the relatively rapid $\beta$ decay of
the thermalized $^{166}$Ho at typical $s$-process temperatures.


  We present a second order accurate in time numerical scheme for curve
shortening flow in the plane that is unconditionally monotone. It is a variant
of threshold dynamics, a class of algorithms in the spirit of the level set
method that represent interfaces implicitly. The novelty is monotonicity: it is
possible to preserve the comparison principle of the exact evolution while
achieving second order in time consistency. As a consequence of monotonicity,
convergence to the viscosity solution of curve shortening is ensured by
existing theory.


  Hybridization of atomic orbitals is a widely appreciated phenomenon whose
impact on the structure and properties of, for example, organic molecules is
well-established. Here, we demonstrate that hybridization also dramatically
impacts the shapes of small alkali metal clusters. The seemingly similar and
valence-iso-electronic LiNa4- and LiK4- clusters adopt very different global
minimum structures: LiNa4- is a planar C2v (1A1) species distorted from the
perfect pentagon due to the pseudo Jahn-Teller effect, and LiK4- is a planar
square D4h (1A1g) species with Li being in the centre. This effect is rooted in
the different degrees of the 2s-2p hybridization in Li in response to binding
to Na versus K. Li inside the Na cluster exhibits a strong 2s-2p mixing, to
achieve stronger covalent bonding. In contrast, Li inside of the K cluster does
not show any hybridization, and the LiK4- cluster is reminiscent of an ionic
salt. These differences are tied to the relative electronegativities of Li, Na,
and K, and overlap of the valence atomic orbitals of Li with those of Na versus
those of K. Atomic orbital hybridization is thus a pronounced effect in
clusters, the understanding of which is important for the use of clusters in
material science or catalysis, and designing clusters of desired shapes.


  Given the remarkable achievements in image generation through diffusion
models, the research community has shown increasing interest in extending these
models to video generation. Recent diffusion models for video generation have
predominantly utilized attention layers to extract temporal features. However,
attention layers are limited by their memory consumption, which increases
quadratically with the length of the sequence. This limitation presents
significant challenges when attempting to generate longer video sequences using
diffusion models. To overcome this challenge, we propose leveraging state-space
models (SSMs). SSMs have recently gained attention as viable alternatives due
to their linear memory consumption relative to sequence length. In the
experiments, we first evaluate our SSM-based model with UCF101, a standard
benchmark of video generation. In addition, to investigate the potential of
SSMs for longer video generation, we perform an experiment using the MineRL
Navigate dataset, varying the number of frames to 64, 200, and 400. In these
settings, our SSM-based model can considerably save memory consumption for
longer sequences, while maintaining competitive FVD scores to the
attention-based models. Our codes are available at
https://github.com/shim0114/SSM-Meets-Video-Diffusion-Models.


  In this paper, we present a workflow for the simulation of drone operations
exploiting realistic background environments constructed within Unreal Engine 4
(UE4). Methods for environmental image capture, 3D reconstruction
(photogrammetry) and the creation of foreground assets are presented along with
a flexible and user-friendly simulation interface. Given the geographical
location of the selected area and the camera parameters employed, the scanning
strategy and its associated flight parameters are first determined for image
capture. Source imagery can be extracted from virtual globe software or
obtained through aerial photography of the scene (e.g. using drones). The
latter case is clearly more time consuming but can provide enhanced detail,
particularly where coverage of virtual globe software is limited. The captured
images are then used to generate 3D background environment models employing
photogrammetry software. The reconstructed 3D models are then imported into the
simulation interface as background environment assets together with appropriate
foreground object models as a basis for shot planning and rehearsal. The tool
supports both free-flight and parameterisable standard shot types along with
programmable scenarios associated with foreground assets and event dynamics. It
also supports the exporting of flight plans. Camera shots can also be designed
to provide suitable coverage of any landmarks which need to appear in-shot.
This simulation tool will contribute to enhanced productivity, improved safety
(awareness and mitigations for crowds and buildings), improved confidence of
operators and directors and ultimately enhanced quality of viewer experience.


  Homogeneous isotropic cosmological models built in the framework of the
Poincar\'e gauge theory of gravity based on general expression of gravitational
Lagrangian with indefinite parameters are analyzed. Special points of
cosmological solutions for flat cosmological models at asymptotics and
conditions of their stability in dependence of indefinite parameters are found.
Procedure of numerical integration of the system of gravitational equations at
asymptotics is considered. Numerical solution for accelerating Universe without
dark energy is obtained.