  We studied dielectric properties of a polar nematic phase (NF) sandwiched
between two gold or ITO electrodes, serving as a cell surfaces. In bulk, NF is
expected to exhibit a Goldstone mode (phason), because polarization can
uniformly rotate with no energy cost. However, because the coupling between the
direction of nematic director and polarization is finite, and the confinement,
even in the absence of the aligning surface layer, induces some energy cost for
a reorientation of polarization, the phason dielectric relaxation frequency is
measured in a kHz regime. The phason mode is easily quenched by a bias electric
field, which enables fluctuations in the magnitude of polarization to be
followed in both, the ferronematic and nematic phases. This amplitude (soft)
mode is also influenced by boundary conditions. A theory describing the phase
and amplitude fluctuations in the NF phase shows that the free energy of the
system and, consequently, the dielectric response are dominated by
polarization-related terms with the flexoelectricity being relevant only at a
very weak surface anchoring. Contributions due to the nematic elastic terms are
always negligible. The model relates the observed low frequency mode to the
director fluctuations weakly coupled to polarization fluctuations.


  A complete sample of 60 serendipitous hard X-ray sources with flux in the
range $\sim 1 \times 10^{-13}$ \ecs to $\sim 4 \times 10^{-12}$ \ecs (2 - 10
keV), detected in 87 ASCA GIS2 images, was recently presented in literature.
Using this sample it was possible to extend the description of the 2-10 keV
LogN(>S)-LogS down to a flux limit of $\sim 6\times 10^{-14}$ \ecs (the
faintest detectable flux), resolving about a quarter of the Cosmic X-ray
Background. In this paper we have combined the ASCA GIS2 and GIS3 data of these
sources to investigate their X-ray spectral properties using the "hardness"
ratios and the "stacked" spectra method. Because of the sample statistical
representativeness, the results presented here, that refer to the faintest hard
X-ray sources that can be studied with the current instrumentation, are
relevant to the understanding of the CXB and of the AGN unification scheme.


  Suppose that we first apply the Lasso to a design matrix, and then update one
of its columns. In general, the signs of the Lasso coefficients may change, and
there is no closed-form expression for updating the Lasso solution exactly. In
this work, we propose an approximate formula for updating a debiased Lasso
coefficient. We provide general nonasymptotic error bounds in terms of the
norms and correlations of a given design matrix's columns, and then prove
asymptotic convergence results for the case of a random design matrix with
i.i.d.\ sub-Gaussian row vectors and i.i.d.\ Gaussian noise. Notably, the
approximate formula is asymptotically correct for most coordinates in the
proportional growth regime, under the mild assumption that each row of the
design matrix is sub-Gaussian with a covariance matrix having a bounded
condition number. Our proof only requires certain concentration and
anti-concentration properties to control various error terms and the number of
sign changes. In contrast, rigorously establishing distributional limit
properties (e.g.\ Gaussian limits for the debiased Lasso) under similarly
general assumptions has been considered open problem in the universality
theory. As applications, we show that the approximate formula allows us to
reduce the computation complexity of variable selection algorithms that require
solving multiple Lasso problems, such as the conditional randomization test and
a variant of the knockoff filter.


  We review and elaborate on properties of the string tension in
two-dimensional gauge theories. The first model we consider is massive QED in
the $m\ll e$ limit. We evaluate the leading string tension both in the
fermionic and bosonized descriptions. We discuss the next to leading
corrections in $m/e$. The next-to-leading terms in the long distance behavior
of the quark-antiquark potential, are evaluated in a certain region of external
versus dynamical charges. The finite temperature behavior is also determined.
In $QCD_2$ we review the results for the string tension of quarks in cases with
dynamical quarks in the fundamental, adjoint, symmetric and antisymmetric
representations. The screening nature of $SYM_2$ is re-derived.


  We investigate the impact of aliasing on generalization in Deep Convolutional
Networks and show that data augmentation schemes alone are unable to prevent it
due to structural limitations in widely used architectures. Drawing insights
from frequency analysis theory, we take a closer look at ResNet and
EfficientNet architectures and review the trade-off between aliasing and
information loss in each of their major components. We show how to mitigate
aliasing by inserting non-trainable low-pass filters at key locations,
particularly where networks lack the capacity to learn them. These simple
architectural changes lead to substantial improvements in generalization on
i.i.d. and even more on out-of-distribution conditions, such as image
classification under natural corruptions on ImageNet-C [11] and few-shot
learning on Meta-Dataset [26]. State-of-the art results are achieved on both
datasets without introducing additional trainable parameters and using the
default hyper-parameters of open source codebases.


  Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation
$\rho: GL(n)\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of
sections of the tensor bundle with fiber $V$ over a sufficiently small open set
$U\subset M$, in other words, $T(V)$ is the space of tensor fields of type $V$
on $M$ on which the group $\Diff (M)$ of diffeomorphisms of $M$ naturally acts.
Elsewhere, the author classified the $\Diff (M)$-invariant differential
operators $D: T(V_{1})\otimes T(V_{2})\longrightarrow T(V_{3})$ for irreducible
fibers with lowest weight. Here the result is generalized to bilinear operators
invariant with respect to the group $\Diff_{\omega}(M)$ of symplectomorphisms
of the symplectic manifold $(M, \omega)$. We classify all first order invariant
operators; the list of other operators is conjectural. Among the new operators
we mention a 2nd order one which determins an ``algebra'' structure on the
space of metrics (symmetric forms) on $M$.


  We propose a new method to characterize the geometrical texture of a granular
packing at the particle scale including the steric hindrance effect. This
method is based on the assumption of a maximum disorder (entropy) compatible
both with strain-induced anisotropy of the contact network and steric
exclusions. We show that the predicted statistics for the local configurations
is in a fairly agreement with our numerical data.


  Quasars are very important in materializing the reference frame. The excess
emission of AGNs (active galactic nuclei) in the mid infrared band can be used
to identify quasar candidates. As extremely distant and point like objects,
quasars also could be further selected by astrometry method. Increasing the
number of reliable quasar candidates is necessary in characterizing the
properties of Gaia astrometric solution and evaluating the reliability of Gaia
own quasars classification. We identify quasars by using appropriate AllWISE
[W1-W2] color and different combinations of astrometric criteria. Together with
the contamination and completeness, the magnitude, astrometric properties,
density distribution, and the morphological indexes of these selected quasars
are evaluated. We obtain a quasar candidate catalog of 1,503,373 sources, which
contains 1,186,690 candidates (78.9%) in common with the Gaia EDR3_AGN catalog
and 316,683 newly identified quasar candidates. The completeness of this
catalog is around 80% compared to LQAC5, and the purity of the overall catalog
is about 90%. We also found that the purity of quasar candidates selected by
this method will decrease in the crowded sky area and the region with less WISE
observations.


  We present an analysis of the newly observed pentaquark $P_c(4312)^+$ to shed
light on its quantum numbers. To do that, the QCD sum rule approach is used.
The measured mass of this particle is close to $\Sigma_c^{++}\bar{D}^-$
threshold and has a small width, which supports the possibility of its being a
molecular state. We consider an interpolating current in a molecular form and
analyze both the positive and negative parity states with spin-$\frac{1}{2}$.
We also consider the bottom counterpart of the state with similar molecular
form. Our mass result for the charm pentaquark state supports that, the quantum
numbers of the observed state are consistent with $J^P=\frac{1}{2}^{-}$.


  Exciton, trion and electron spin dynamics in a 20 nm wide modulation-doped
GaAs single quantum well are investigated using resonant ultrafast two-color
Kerr rotation spectroscopy. Excitons and trions are selectively detected by
resonant probe pulses while their relative spectral weight is controlled by
adjusting the gate voltage which tunes the carrier density. Tuning the carrier
density markedly influences the spin decay time of the two dimensional electron
gas. The spin decay time can be enhanced by a factor of 3 at an intermediate
carrier concentration in the quantum well, where excitons and trions coexist in
the system. In addition, we explore the capability to tune the g-factor of the
electron gas via the carrier density.


  Faults in electricity distribution networks have the potential to ignite
fires, cause electrocution, and damage the system itself. High current Low
Impedance Faults (LIF) are typically detected and mitigated via over-current,
distance, directional relays, fuses, etc. In contrast, while High Impedance
Faults (HIF) are equally hazardous, they are much more challenging to detect
due to the fault current being much lower than load currents and their
time-varying and nonlinear behaviour. Moreover, New Zealand distribution
networks are extensive and largely unmonitored beyond the substation, and
suitable HIF detection schemes are still an ongoing research challenge.
  To date, we have built a physical test facility for power system fault
analysis and developing and evaluating our sensing and fault detection system.
We have simulated LIF and HIF with different fault surface materials and
load-switching events. From the data collected, we have characterized the
unique fault behaviour for both LIF and HIF in 400V networks and trained a Deep
Learning classifier to recognize the type of fault present from its unique
signature. We have developed an outdoor pole mountable sensing system and have
installed this in Wellington Electricity's network for ongoing data collection
and evaluation.
  This paper will describe the test facility and our experience developing and
implementing the sensing system. The widest range of HIF phenomena observed was
in the fault experiments involving the tree branch. For brevity, therefore,
this paper reports on the results of just these tree-branch experiments. HIF
faults on other surface materials will be reported elsewhere. Finally, we will
detail the pole-mountable sensing system installed in Wellington Electricity's
network and the outcomes thus far.


  We report low frequency charge noise measurement on silicon substrates with
different phosphorus doping densities. The measurements are performed with
aluminum single electron transistors (SETs) at millikelvin temperatures where
the substrates are in the insulating regime. By measuring the SET Coulomb
oscillations, we find a gate voltage dependent charge noise on the more heavily
doped substrate. This charge noise, which is seen to have a 1/f spectrum, is
attributed to the electric field induced tunneling of electrons from their
phosphorus donor potentials.


  The property and gravitational field of global string of tachyon matter are
investigated in a four dimentional approximately cylindrically-symmetric
spacetime with a deficit angle. Especially, we give an exact solution of the
tachyon field in the flat spacetime background and we also find the solution of
the metric in the linearized approximation of gravity.


  A novel protocol - measurement-device-independent quantum key distribution
(MDI-QKD) - removes all attacks from the detection system, the most vulnerable
part in QKD implementations. In this paper, we present an analysis for
practical aspects of MDI-QKD. To evaluate its performance, we study various
error sources by developing a general system model. We find that MDI-QKD is
highly practical and thus can be easily implemented with standard optical
devices. Moreover, we present a simple analytical method with only two
(general) decoy states for the finite decoy-state analysis. This method can be
used directly by experimentalists to demonstrate MDI-QKD. By combining the
system model with the finite decoy-state method, we present a general framework
for the optimal choice of the intensities of the signal and decoy states.
Furthermore, we consider a common situation, namely asymmetric MDI-QKD, in
which the two quantum channels have different transmittances. We investigate
its properties and discuss how to optimize its performance. Our work is of
interest not only to experiments demonstrating MDI-QKD but also to other
non-QKD experiments involving quantum interference.


  This paper is concerned with signal detection in Gaussian noise under
quadratically convex orthosymmetric (QCO) constraints. Specifically the null
hypothesis assumes no signal, whereas the alternative considers signal which is
separated in Euclidean norm from zero, and belongs to the QCO constraint. Our
main result establishes the minimax rate of the separation radius between the
null and alternative purely in terms of the geometry of the QCO constraint --
we argue that the Kolmogorov widths of the constraint determine the critical
radius. This is similar to the estimation problem with QCO constraints, which
was first established by Donoho et al. (1990); however, as expected, the
critical separation radius is smaller compared to the minimax optimal
estimation rate. Thus signals may be detectable even when they cannot be
reliably estimated.


  For millenia, sailors have used the empirical rule that the elevation angle
of Polaris, the North Star, as measured by sextant, quadrant or astrolabe, is
approximately equal to latitude. Here, we show using elementary trigonometry
that Empirical Law 1 can be converted from a heuristic to a theorem. A second
ancient empirical law is that the distance in kilometers from the observer to
the North Pole, the geodesic distance measured along the spherical surface of
the planet, is the number of degrees of colatitude multiplied by 111.1
kilometers. Can Empirical Law 2 be similarly rendered rigorous? No; whereas as
the shape of the planet is controlled by trigonometry, the size of our world is
an accident of cosmological history. However, Empirical Law 2, can be
rigorously verified by measurements. The association of 111 km of north-south
distance to one degree of latitude trivially yields the circumference of the
globe as 40,000 km. We also extend these ideas and the parallel ray
approximation to three different ways of modeling a Flat Earth. We show that
photographs from orbit, taken by a very expensive satellite, are unnecessary to
render the Flat Earth untenable; simple mathematics proves Earth a sphere just
as well.


  The Schr\"{o}dinger problem of deducing the microscopic dynamics from the
input-output statistics data is known to admit a solution in terms of Markov
diffusions. The uniqueness of solution is found linked to the natural
boundaries respected by the underlying random motion. By choosing a reference
Smoluchowski diffusion process, we automatically fix the Feynman-Kac potential
and the field of local accelerations it induces. We generate the family of
affiliated diffusions with the same local dynamics, but different inaccessible
boundaries on finite, semi-infinite and infinite domains. For each diffusion
process a unique Feynman-Kac kernel is obtained by the constrained (Dirichlet
boundary data) Wiener path integration.As a by-product of the discussion, we
give an overview of the problem of inaccessible boundaries for the diffusion
and bring together (sometimes viewed from unexpected angles) results which are
little known, and dispersed in publications from scarcely communicating areas
of mathematics and physics.


  We propose joinwidth, a new complexity parameter for the Constraint
Satisfaction Problem (CSP). The definition of joinwidth is based on the
arrangement of basic operations on relations (joins, projections, and pruning),
which inherently reflects the steps required to solve the instance. We use
joinwidth to obtain polynomial-time algorithms (if a corresponding
decomposition is provided in the input) as well as fixed-parameter algorithms
(if no such decomposition is provided) for solving the CSP.
  Joinwidth is a hybrid parameter, as it takes both the graphical structure as
well as the constraint relations that appear in the instance into account. It
has, therefore, the potential to capture larger classes of tractable instances
than purely structural parameters like hypertree width and the more general
fractional hypertree width (fhtw). Indeed, we show that any class of instances
of bounded fhtw also has bounded joinwidth, and that there exist classes of
instances of bounded joinwidth and unbounded fhtw, so bounded joinwidth
properly generalizes bounded fhtw.
  We further show that bounded joinwidth also properly generalizes several
other known hybrid restrictions, such as fhtw with degree constraints and
functional dependencies. In this sense, bounded joinwidth can be seen as a
unifying principle that explains the tractability of several seemingly
unrelated classes of CSP instances.


  The unique capabilities of Large Language Models (LLMs), such as the natural
language text generation ability, position them as strong candidates for
providing explanation for recommendations. However, despite the size of the
LLM, most existing models struggle to produce zero-shot explanations reliably.
To address this issue, we propose a framework called Logic-Scaffolding, that
combines the ideas of aspect-based explanation and chain-of-thought prompting
to generate explanations through intermediate reasoning steps. In this paper,
we share our experience in building the framework and present an interactive
demonstration for exploring our results.


  To avoid discriminatory uses of their data, organizations can learn to map
them into a representation that filters out information related to sensitive
attributes. However, all existing methods in fair representation learning
generate a fairness-information trade-off. To achieve different points on the
fairness-information plane, one must train different models. In this paper, we
first demonstrate that fairness-information trade-offs are fully characterized
by rate-distortion trade-offs. Then, we use this key result and propose SoFaiR,
a single shot fair representation learning method that generates with one
trained model many points on the fairness-information plane. Besides its
computational saving, our single-shot approach is, to the extent of our
knowledge, the first fair representation learning method that explains what
information is affected by changes in the fairness / distortion properties of
the representation. Empirically, we find on three datasets that SoFaiR achieves
similar fairness-information trade-offs as its multi-shot counterparts.


  We review the production of gravitational waves by an electroweak first order
phase transition. The resulting signal is a good candidate for detection at
next-generation gravitational wave detectors, such as LISA. Detection of such a
source of gravitational waves could yield information about physics beyond the
Standard Model that is complementary to that accessible to current and
near-future collider experiments. We summarise efforts to simulate and model
the phase transition and the resulting production of gravitational waves.


  This paper examines a longitudinal shape evolution model in which a 3D volume
progresses through a family of elastic equilibria in response to the
time-derivative of an internal force, or yank, with an additional
regularization to ensure diffeomorphic transformations. We consider two
different models of yank and address the long time existence and uniqueness of
solutions for the equations of motion in both models. In addition, we derive
sufficient conditions for the existence of an optimal yank that best describes
the change from an observed initial volume to an observed volume at a later
time. The main motivation for this work is the understanding of processes such
as growth and atrophy in anatomical structures, where the yank could be roughly
interpreted as a metabolic event triggering morphological changes. We provide
preliminary results on simple examples to illustrate, under this model, the
retrievability of some attributes of such events.


  Aggregation of ice crystals is a key process governing precipitation.
Individual ice crystals exhibit considerable diversity of shape, and a wide
range of physical processes could influence their aggregation; despite this we
show that a simple computer model captures key features of aggregate shape and
size distribution reported recently from Cirrus clouds. The results prompt a
new way to plot the experimental size distributions leading to remarkably good
dynamical scaling. That scaling independently confirms that there is a single
dominant aggregation mechanism at play, albeit our model (based on undeflected
trajectories to contact) does not capture its form exactly.


  The human cognitive system is a remarkable exemplar of a general intelligent
system whose competence is not confined to a specific problem domain.
Evidently, general cognitive competences are a product of a prolonged and
complex process of cognitive development. Therefore, the process of cognitive
development is a primary key to understanding the emergence of intelligent
behavior. This paper develops the theoretical foundations for a model that
generalizes the process of cognitive development. The model aims to provide a
realistic scheme for the synthesis of scalable cognitive systems with an
open-ended range of capabilities. Major concepts and theories of human
cognitive development are introduced and briefly explored focusing on the
enactive approach to cognition and the concept of sense-making. The initial
scheme of human cognitive development is then generalized by introducing the
philosophy of individuation and the abstract mechanism of transduction. The
theory of individuation provides the ground for the necessary paradigmatic
shift from cognitive systems as given products to cognitive development as a
formative process of self-organization. Next, the conceptual model is specified
as a scalable scheme of networks of agents. The mechanisms of individuation are
formulated in context independent information theoretical terms. Finally, the
paper discusses two concrete aspects of the generative model -- mechanisms of
transduction and value modulating systems. These are topics of further research
towards a computationally realizable model.


  A C14 Nb0.975Fe2.025 Laves phase compound was investigated aimed at
determining the H-T magnetic phase diagram. Magnetization, M, and AC magnetic
susceptibility measurements were performed. Concerning the former field-cooled
and zero-field-cooled M-curves were recorded in the temperature range of 2-200K
and in applied magnetic field, H, up to 1000 Oe, isothermal M(H) curves at 2 K,
5 K, 50 K, 80 K and 110 K as well as hysteresis loops at several temperatures
over the field range of -10 to +10kOe. Regarding the AC susceptibility, both
real and imaginary components were registered as a function of increasing
temperature in the interval of 2 K - 150 K at the frequencies of the
oscillating field, f, from 3 Hz up to 999 Hz. An influence of the external DC
magnetic field, H, on the temperature dependence of the AC susceptibility was
investigated, too. The measurements clearly demonstrated that the magnetism of
the studied sample is weak, itinerant and has a reentrant character. Based on
the obtained results a magnetic phase diagram has been constructed in the H-T
coordinates.


  Cryptic genetic sequences have attenuated effects on phenotypes. In the
classic view, relaxed selection allows cryptic genetic diversity to build up
across individuals in a population, providing alleles that may later contribute
to adaptation when co-opted - e.g. following a mutation increasing expression
from a low, attenuated baseline. This view is described, for example, by the
metaphor of the spread of a population across a neutral network in genotype
space. As an alternative view, consider the fact that most phenotypic traits
are affected by multiple sequences, including cryptic ones. Even in a strictly
clonal population, the co-option of cryptic sequences at different loci may
have different phenotypic effects and offer the population multiple adaptive
possibilities. Here, we model the evolution of quantitative phenotypic
characters encoded by cryptic sequences, and compare the relative contributions
of genetic diversity and of variation across sites to the phenotypic potential
of a population. We show that most of the phenotypic variation accessible
through co-option would exist even in populations with no polymorphism. This is
made possible by a history of compensatory evolution, whereby the phenotypic
effect of a cryptic mutation at one site was balanced by mutations elsewhere in
the genome, leading to a diversity of cryptic effect sizes across sites rather
than across individuals. Cryptic sequences might accelerate adaptation and
facilitate large phenotypic changes even in the absence of genetic diversity,
as traditionally defined in terms of alternative alleles.


  A comparison of the COBE, Diffuse Infrared Background Experiment (DIRBE)
all-sky survey with the locations of known galaxies in the IRAS Catalog of
Extragalactic Objects and the Center for Astrophysics Catalog of Galaxies led
to the detection of as many as 56 galaxies. In this paper, we present the
photometric analysis of these detections and an analysis of their dust
properties. The sample is dominated by late-type spirals and active galaxies,
and their far-IR continuua between 25-240 microns suggest a single dust
component dominating the far-IR emission. We show that for the spirals,
T(dust)= 27.6 K, and for the active galaxies, T(dust) = 35.5 K. Estimates of
the ratio of the mass of the dust component detected at T(dust) = 20 - 30 K to
a hypothetical component with T(dust) = 15 K provide modest constraints to the
Very Cold Dust (VCD) component present in the galaxies detected at 140 and 240
microns. VCD components with less than times the mass of the 20-30 K dust are
consistent with all of the upper limits.


  We propose a twist condition, inspired by the classical Poincar\'e-Birkhoff
theorem on area-preserving maps of the annulus, which applies to asymptotically
linear Hamiltonian diffeomorphisms of linear phase space. When an
asymptotically linear Hamiltonian diffeomorphism, non-degenerate and unitary at
infinity, satisfies this twist condition, we show that it has infinitely many
periodic points.


  Understanding where and when human mobility is associated with disease
infection is crucial for implementing location-based health care policy and
interventions. Previous studies on COVID-19 have revealed the correlation
between human mobility and COVID-19 cases. However, the spatiotemporal
heterogeneity of such correlation is not yet fully understood. In this study,
we aim to identify the spatiotemporal heterogeneities in the relationship
between human mobility flows and COVID-19 cases in U.S. counties. Using
anonymous mobile device location data, we compute an aggregate measure of
mobility that includes flows within and into each county. We then compare the
trends in human mobility and COVID-19 cases of each county using dynamic time
warping (DTW). DTW results highlight the time periods and locations (counties)
where mobility may have influenced disease transmission. Also, the correlation
between human mobility and infections varies substantially across geographic
space and time in terms of relationship, strength, and similarity.


  We present a large catalog of $N_G \approx 200$ loose groups of galaxies
selected from the Perseus-Pisces redshift Survey.


  Integrating reconfigurable intelligent surfaces (RISs) in emerging
communication systems is a fast-growing research field that has recently earned
much attention. While implementing RISs near the base station (BS), i.e.,
BS-side RIS, or user equipment (UE), i.e., UE-side RIS, exhibits optimum
performance, understanding the differences between these two deployments in
terms of the system design perspective needs to be clarified. Critical design
parameters, such as RIS size, phase shift adjustment, control link, and element
type (passive/active), require greater clarity across these scenarios.
Overlooking the intricacies of such critical design parameters in light of 6G
demands endangers practical implementation, widening the gap between
theoretical insights and practical applications. In this regard, our study
investigates the impact of each RIS deployment strategy on the anticipated 6G
requirements and offers tailored RIS design recommendations to fulfill these
forward-looking requirements. Through this, we clarify the practical
distinctions and propose a comprehensive framework for differentiating between
BS-side and UE-side RIS scenarios in terms of their design parameters.
Highlighting the unique needs of each and the potential challenges ahead, we
aim to fuse the theoretical underpinnings of RIS with tangible implementation
considerations, propelling progress in both the academic sphere and the
industry.


  This paper introduces a novel approach to post-Optical Character Recognition
Correction (POC) for handwritten Cyrillic text, addressing a significant gap in
current research methodologies. This gap is due to the lack of large text
corporas that provide OCR errors for further training of language-based POC
models, which are demanding in terms of corpora size. Our study primarily
focuses on the development and application of a synthetic handwriting
generation engine based on B\'ezier curves. Such an engine generates highly
realistic handwritten text in any amounts, which we utilize to create a
substantial dataset by transforming Russian text corpora sourced from the
internet. We apply a Handwritten Text Recognition (HTR) model to this dataset
to identify OCR errors, forming the basis for our POC model training. The
correction model is trained on a 90-symbol input context, utilizing a
pre-trained T5 architecture with a seq2seq correction task. We evaluate our
approach on HWR200 and School_notebooks_RU datasets as they provide significant
challenges in the HTR domain. Furthermore, POC can be used to highlight errors
for teachers, evaluating student performance. This can be done simply by
comparing sentences before and after correction, displaying differences in
text. Our primary contribution lies in the innovative use of B\'ezier curves
for Cyrillic text generation and subsequent error correction using a
specialized POC model. We validate our approach by presenting Word Accuracy
Rate (WAR) and Character Accuracy Rate (CAR) results, both with and without
post-OCR correction, using real open corporas of handwritten Cyrillic text.
These results, coupled with our methodology, are designed to be reproducible,
paving the way for further advancements in the field of OCR and handwritten
text analysis. Paper contributions can be found in
https://github.com/dbrainio/CyrillicHandwritingPOC


  Since the introduction of the Hermitian adjacency matrix for digraphs,
interest in so-called complex unit gain graphs has surged. In this work, we
consider gain graphs whose spectra contain the minimum number of two distinct
eigenvalues. Analogously to graphs with few distinct eigenvalues, a great deal
of structural symmetry is required for a gain graph to attain this minimum.
This allows us to draw a surprising parallel to well-studied systems of lines
in complex space, through a natural correspondence to unit-norm tight frames.
We offer a full classification of two-eigenvalue gain graphs with degree at
most $4$, or with multiplicity at most $3$. Intermediate results include an
extensive review of various relevant concepts related to lines in complex
space, including SIC-POVMs, MUBs and geometries such as the Coxeter-Todd
lattice, and many examples obtained as induced subgraphs by employing a
technique parallel to the dismantling of association schemes. Finally, we touch
on an innovative application of simulated annealing to find examples by
computer.


  We prove that the Fermat-type equation $x^3 + y^3 = z^p$ has no solutions
$(a,b,c)$ satisfying $abc \ne 0$ and $\gcd(a,b,c)=1$ when $-3$ is not a square
mod~$p$. This improves to approximately $0.844$ the Dirichlet density of the
set of prime exponents to which the previous equation is known to not have such
solutions. For the proof we develop a criterion of independent interest to
decide if two elliptic curves with certain type of potentially good reduction
at 2 have symplectically or anti-symplectically isomorphic $p$-torsion modules.


  In this paper, we propose some estimation techniques to estimate the
elementary chirp model parameters, which are encountered in sonar, radar,
acoustics, and other areas. We derive asymptotic theoretical properties of
least squares estimators and approximate least squares estimators for the
one-component elementary chirp model. It is proved that the proposed estimators
are strongly consistent and follow the normal distribution asymptotically. We
also suggest how to obtain proper initial values for these methods. The problem
of finding initial values is a difficult problem when the number of components
in the model is large, or when the signal-to-noise ratio is low, or when two
frequency rates are close to each other. We propose sequential procedures to
estimate the multiple-component elementary chirp model parameters. We prove
that the theoretical properties of sequential least squares estimators and
sequential approximate least squares estimators coincide with those of least
squares estimators and approximate least squares estimators, respectively. To
evaluate the performance of the proposed estimators, numerical experiments are
performed. It is observed that the proposed sequential estimators perform well
even in situations where least squares estimators do not perform well. We
illustrate the performance of the proposed sequential algorithm on a bat data.


  The existence of hydrodynamic attractors in rapidly expanding relativistic
systems has shed light on the success of relativistic hydrodynamics in
describing heavy-ion collisions at zero chemical potential. As the search for
the QCD critical point continues, it is important to investigate how out of
equilibrium effects influence the trajectories on the QCD phase diagram. In
this proceedings, we study a Bjorken expanding hydrodynamic system based on
DMNR equations of motion with initial out of equilibrium effects and finite
chemical potential in a system with a critical point. We find that the initial
conditions are not unique for a specific freeze-out point, but rather the
system can evolve to the same final state freeze-out point with a wide range of
initial baryon chemical potential, $\mu_B$. For the same initial energy density
and baryon density, depending on how far out of equilibrium the system begins,
the initial $\mu_B$ can vary by $\Delta \mu_B\sim 350$ MeV. Our results
indicate that knowledge of the out-of-equilibrium effects in the initial state
provide vital information that influences the search for the QCD critical
point.


  We show how changes in unitarity-preserving boundary conditions allow
continuous interpolation among the Hilbert spaces of quantum mechanics on
topologically distinct manifolds. We present several examples, including a
computation of entanglement entropy production. We discuss approximate
realization of boundary conditions through appropriate interactions, thus
suggesting a route to possible experimental realization. We give a theoretical
application to quantization of singular Hamiltonians, and give tangible form to
the "many worlds" interpretation of wave functions.


  We analyze $D \to P V$, $D \to PP$ and $D \to VV$ decays within a model
developed to describe the semileptonic decays $D \to V l \nu_l$ and $D\to P l
\nu_l$. This model combines the heavy quark effective Lagrangian and chiral
perturbation theory. We determine amplitudes for decays in which the direct
weak annihilation of the initial $D$ meson is absent or negligible, and in
which the final state interactions are small. This analysis reduces the
arbitrariness in the choice of model parameters. The calculated decay widths
are in good agreement with the experimental results.


  A weaker Haag, Narnhofer and Stein prescription as well as a weaker Hessling
Quantum Equivalence Principle for the behaviour of thermal Wightman functions
on an event horizon are analysed in the case of an extremal
Reissner-Nordstr\"{o}m black hole in the limit of a large mass. In order to
avoid the degeneracy of the metric in the stationary coordinates on the
horizon, a method is introduced which employs the invariant length of geodesics
which pass the horizon. First the method is checked for a massless scalar field
on the event horizon of the Rindler wedge, extending the original procedure of
Haag, Narnhofer and Stein onto the {\em whole horizon} and recovering the same
results found by Hessling. Afterwards the HNS prescription and Hessling's
prescription for a massless scalar field are analysed on the whole horizon of
an extremal Reissner-Nordstr\"{o}m black hole in the limit of a large mass. It
is proved that the weak form of the HNS prescription is satisfyed for all the
finite values of the temperature of the KMS states, i.e., this principle does
not determine any Hawking temperature. It is found that the
Reissner-Nordstr\"{o}m vacuum, i.e., $T=0$ does satisfy the weak HNS
prescription and it is the only state which satisfies weak Hessling's
prescription, too. Finally, it is suggested that all the previously obtained
results should be valid dropping the requirements of a massless field and of a
large mass black hole.


  This study compares the media discourses about Euroscepticism in 2014 across
six countries (United Kingdom, Ireland, France, Spain, Sweden, and Denmark). We
assess the extent to which the mass media's reporting of Euroscepticism
indicates the Europeanization of public spheres. Using a mixed-methods approach
combining LDA topic modeling and qualitative coding, we find that approximately
70 per cent of print articles mentioning "Euroscepticism" or "Eurosceptic" are
framed in a non-domestic (i.e. European) context. In five of the six cases
studied, articles exhibiting a European context are strikingly similar in
content, with the British case as the exception. However, coverage of British
Euroscepticism drives Europeanization in other Member States. Bivariate
logistic regressions further reveal three macro-level structural variables that
significantly correlate with a Europeanized media discourse: newspaper type
(tabloid or broadsheet), presence of a strong Eurosceptic party, and
relationship to the EU budget (net contributor or receiver of EU funds).


  In this paper, the local inertial coordinate system is calculated through
coordinate transformations from laboratory coordinate system. We derived the
same free falling equations as those in General Relativity. However, the
definitions of second and higher order covariant derivatives are different. Our
results are different from the classic view of the principle of equivalence,
and suggest that all the laws of physics in gravitational field can be given by
doing coordinate transformations from local inertial coordinate system to lab
coordinate system.


  This article conceives a unified representation for near-field and far-field
holographic multiple-input multiple-output (HMIMO) channels, addressing a
practical design dilemma: "Why does the angular-domain representation no longer
function effectively?" To answer this question, we pivot from the angular
domain to the wavenumber domain and present a succinct overview of its
underlying philosophy. In re-examining the Fourier plane-wave series expansion
that recasts spherical propagation waves into a series of plane waves
represented by Fourier harmonics, we characterize the HMIMO channel employing
these Fourier harmonics having different wavenumbers. This approach, referred
to as the wavenumebr-domain representation, facilitates a unified view across
the far-field and the near-field. Furthermore, the limitations of the DFT basis
are demonstrated when identifying the sparsity inherent to the HMIMO channel,
motivating the development of a wavenumber-domain basis as an alternative. We
then present some preliminary applications of the proposed wavenumber-domain
basis in signal processing across both the far-field and near-field, along with
several prospects for future HMIMO system designs based on the wavenumber
domain.


  The article is the translation of authors paper, printed earlier in
inaccessible edition and devoted to the formulation of basic concepts of
dynamic description of particles' statistic ensemble in a gravitational field.
Later on, the results of this article were used by numbers of authors in papers
of relativistic kinetics.


  Simulations of large-scale dynamical systems require expensive computations.
Low-dimensional parametrization of high-dimensional states such as Proper
Orthogonal Decomposition (POD) can be a solution to lessen the burdens by
providing a certain compromise between accuracy and model complexity. However,
for really low-dimensional parametrizations (for example for controller design)
linear methods like the POD come to their natural limits so that nonlinear
approaches will be the methods of choice. In this work we propose a
convolutional autoencoder (CAE) consisting of a nonlinear encoder and an affine
linear decoder and consider combinations with k-means clustering for improved
encoding performance. The proposed set of methods is compared to the standard
POD approach in two cylinder-wake scenarios modeled by the incompressible
Navier-Stokes equations.


  The alternative approach to QCD analysis of the photon structure function
$F_2^{\gamma}$ is presented. It differs from the conventional one by the
presence of the terms which in conventional approach appear in higher orders.
We show that this difference concerns also the photonic parton distribution
functions. In the alternative approach, the complete LO analysis of
$F_2^{\gamma}$ can be performed as all required quantities are known. At the
NLO, however, one of the coefficient function is so far not available and thus
only the photonic parton distribution function can be computed and compared to
those of standard approach. We discuss the numerical difference of these
approaches at the LO and the NLO approximation and show that in case of
$F_2^{\gamma}$ this difference is non-negligible and may play an important role
in the analysis on photon data of the future experiments.


  It has long been known that a single-layer fully-connected neural network
with an i.i.d. prior over its parameters is equivalent to a Gaussian process
(GP), in the limit of infinite network width. This correspondence enables exact
Bayesian inference for infinite width neural networks on regression tasks by
means of evaluating the corresponding GP. Recently, kernel functions which
mimic multi-layer random neural networks have been developed, but only outside
of a Bayesian framework. As such, previous work has not identified that these
kernels can be used as covariance functions for GPs and allow fully Bayesian
prediction with a deep neural network.
  In this work, we derive the exact equivalence between infinitely wide deep
networks and GPs. We further develop a computationally efficient pipeline to
compute the covariance function for these GPs. We then use the resulting GPs to
perform Bayesian inference for wide deep neural networks on MNIST and CIFAR-10.
We observe that trained neural network accuracy approaches that of the
corresponding GP with increasing layer width, and that the GP uncertainty is
strongly correlated with trained network prediction error. We further find that
test performance increases as finite-width trained networks are made wider and
more similar to a GP, and thus that GP predictions typically outperform those
of finite-width networks. Finally we connect the performance of these GPs to
the recent theory of signal propagation in random neural networks.


  Motivated by recent experiments on rotating Bose-Einstein condensates, we
investigate a rotating, polarized Fermi gas trapped in an anharmonic potential.
We apply a semiclassical expansion of the density of states in order to
determine how the thermodynamic properties depend on the rotation frequency.
The accuracy of the semiclassical approximation is tested and shown to be
sufficient for describing typical experiments. At zero temperature, rotating
the gas above a given frequency $\Omega_{\rm DO}$ leads to a `donut'-shaped
cloud which is analogous to the hole found in two-dimensional Bose-Einstein
condensates. The free expansion of the gas after suddenly turning off the trap
is considered and characterized by the time and rotation frequency dependence
of the aspect ratio. Temperature effects are also taken into account and both
low- and high-temperature expansions are presented for the relevant
thermodynamical quantities. In the high-temperature regime a virial theorem
approach is used to study the delicate interplay between rotation and
anharmonicity.


  Slow dynamics in an amorphous quasi-two-dimensional complex plasma, comprised
of microparticles of two different sizes, was studied experimentally. The
motion of individual particles was observed using video microscopy, and the
self-part of the intermediate scattering function as well as the mean-squared
particle displacement was calculated. The long-time structural relaxation
reveals the characteristic behavior near the glass transition. Our results
suggest that binary complex plasmas can be an excellent model system to study
slow dynamics in classical supercooled fluids.


  We show that the magnetization in color-flavor locked superconductors can be
so strong that homogeneous quark matter becomes metastable for a wide range of
magnetic field values. This indicates that magnetic domains or other type of
magnetic inhomogeneities can be present in the quark cores of magnetars.


  In this work, we investigate black hole (BH) physics in the context of
quantum corrections. These quantum corrections were introduced recently by
replacing classical geodesics with quantal (Bohmian) trajectories and hence
form a quantum Raychaudhuri equation (QRE). From the QRE, we derive a modified
Schwarzschild metric, and use that metric to investigate BH singularity and
thermodynamics. We find that these quantum corrections change the picture of
Hawking radiation greatly when the size of BH approaches the Planck scale. They
prevent the BH from total evaporation, predicting the existence of a quantum BH
remnant, which may introduce a possible resolution for the catastrophic
behavior of Hawking radiation as the BH mass approaches zero. Those corrections
also turn the spacelike singularity of the black hole to be timelike, and hence
this may ameliorate the information loss problem.


  We study a spontaneous symmetry breaking mechanism for a topological quantum
field theory based on the twisted $\mathcal{N} = 2$ super-Yang-Mills theory.
Specifically, by employing Fujikawa's Becchi-Rouet-Stora-Tyutin mechanism,
local degrees of freedom are released. In fact, a trivial potential in the
equivariant cohomology is introduced. Such potential displays a nontrivial
vacuum solution which induces the breaking of the gauge symmetry without
explicitly breaking the original fermionic scalar supersymmetry of topological
Witten's action. The result is that not only massive vector bosons emerge, but
also fermionic massive fields states appear. Such a result shows that the
introduction of a topological phase in quantum field theory could provide a
mechanism of mass generation for fermions together with Higgs bosons.


  The standard proof of the equivalence of Fourier type on R^d and on the torus
T^d is usually stated in terms of an implicit constant, defined as the minimum
of a sum of powers of sinc functions. In this note we compute this minimum
explicitly.


  We calculate inclusive cross section for $f_2(1270)$ tensor meson production
via color singlet gluon-gluon fusion in the $k_t$-factorization approach with
unintegrated gluon distribution functions (UGDFs). The process may be
potentially interesting in the context of searches for saturation effects. The
energy-momentum tensor, equivalent to helicity-2 coupling, and helicity-0
coupling are used for the $g^* g^* \to f_2(1270)$ vertex. Two somewhat
different parametrizations of helicity-2 and helicity-0 tensorial structure
from the literature are used in our calculations. Some parameters are extracted
from $\gamma \gamma \to f_2(1270) \to \pi \pi$ reactions. Different modern
UGDFs from the literature are used. The results strongly depend on the
parametrization of the $g^* g^* \to f_2(1270)$ form factor. Our results for
transverse momentum distributions of $f_2$ are compared to preliminary ALICE
data. We can obtain agreement with the data only at larger $f_2(1270)$
transverse momenta only for some parametrizations of the $g^* g^* \to
f_2(1270)$ form factor. No obvious sign of the onset of saturation is possible.
At low transverse momenta one needs to include also the $\pi\pi$ final-state
rescattering. The agreement with the ALICE data can be obtained by adjusting
probability of formation and survival of $f_2(1270)$ in a harsh quark-gluon and
multipion environment. The pomeron-pomeron fusion mechanism is discussed in
addition and results are quantified.


  New optical photometric and spectroscopic data of the bright hypernova SN
2002ap are presented. The obtained BVRI light curves as well as the optical
spectra agree well with other published data series. The distance has been
inferred by applying the Expanding Photosphere Method for the data around
maximum. The derived 6.7 Mpc is in good agreement with recent photometric
distances of M74. However, the total (random plus systematic) uncertainty of
the EPM-distance is at least 4.5 Mpc (about 70 %). The physical parameters of
the SN have been determined via simplified analytic models of the light and
velocity curves. It is confirmed that SN 2002ap was a less energetic hypernova,
the kinetic energy was 4 - 8 10^51 erg, and the reddening-free absolute
bolometric magnitude reached -16.63 mag (corresponding to L_bol = 3.47 10^8
L_solar), about 2 magnitude less than the prototype hypernova SN 1998bw.


  Rich experimental data accumulated in the past few years in the hadronic
$Z^0$ decays allow one to check the quark combinatorics relations for a new
type of processes, namely: quark jets in the decays $Z^0 \to q\bar q \to
hadrons$. In this paper we review quark combinatorics rules for the yields of
vector and pseudoscalar mesons, $V/P$, in the central and fragmentation regions
of the hadronic $Z^0$ decays. It is stressed that in the central region a
direct verification of quark combinatorics rules is rather problematic because
of a considerable background related to the decay of highly excited resonances;
however such a verification is possible in the fragmentation region, at
$x_{hadron} \sim 0.5-1$, where the contribution of resonance decays is
suppressed due to the rapid decrease of spectra with increasing $x_{hadron}$.
It is shown that the experimental data in the fragmentation region for
$\rho^0/\pi^0$ and $p/\pi^+$ are in a reasonable agreement with the predictions
of quark combinatorics. The ratios of the heavy meson yields, $B^*/B$ and
  $D^*/D$, are also discussed: the data demonstrate a good agreement with the
quark combinatorial results. We analyse the structure of the suppression
parameters for strange and heavy quark productions in soft processes and
estimate their order of magnitudes in the multiperipheral processes; the ratio
$K^{\pm}/\pi^{\pm}$ at $x_{hadron}\sim 0.5-0.8$ and production probabilities of
the $c\bar c$ and $b \bar b$ mesons are in a good agreement with the estimates.


  The pion-nucleon bremsstrahlung $\pi+N\Longrightarrow\gamma'+\pi'+N'$ is
studied in a new form of current conservation. According to this condition, the
internal and external particle radiation parts of the $\pi N$ radiation
amplitude have opposite signs, i.e., they contain terms which must cancel each
other.
  Therefore, one has a screening of the internal and external particle
radiation in the $\pi N$ bremsstrahlung. In particular, it is shown that the
double $\Delta$ exchange diagram with the $\Delta-\gamma' \Delta'$ vertex
cancel against the appropriate longitudinal part of the external particle
radiation diagrams. Consequently, a model independent relation between the
magnetic dipole moments of the $\Delta^+$ and $\Delta^{++}$ resonances and the
anomalous magnetic moment of the proton $\mu_p$ is obtained, where
$\mu_{\Delta}$ is expressed by $\mu_p$ as $\mu_{\Delta^+}={{M_{\Delta}}\over
{m_p}} \mu_p$ and $\mu_{\Delta^{++}}={3\over 2}\mu_{\Delta^+}$ in agreement
with the values extracted from the fit for the experimental cross section of
the $\pi^+ p\to\gamma'\pi^+ p$ reaction.


  We present the NIR luminosity (LF) and stellar mass functions (SMF) of
galaxies in the core of the Shapley supercluster at z=0.048, based on new
K-band observations in conjunction with B- and R-band photometry and a
subsample of ~650 galaxies spectroscopically confirmed supercluster members,
allowing to investigate the galaxies down to M_K^*+6 and M=10^8.75 M_sun. For
the 3 deg^2 field the K-band LF is described by a Schechter function with
M_K^*=-24.96+-0.10 and \alpha=-1.42+-0.03. We investigate the effect of
environment by deriving the LF in three regions selected according to the local
galaxy density, and observe a significant increase in the faint-end slope going
from the high- (\alpha=-1.33) to the low-density (\alpha=-1.49) environments.
The SMF is fitted well by a Schechter function with log_10(M^*)=11.16+-0.04 and
\alpha=-1.20+-0.02. The SMF of supercluster galaxies is also characterised by
an excess of massive galaxies that are associated to the cluster BCGs. While
the value of M* depends on environment the slope of the galaxy SMF does not
vary with the environment. By comparing our findings with cosmological
simulations, we conclude that the environmental dependences of the LF are not
primary due to variations in the merging histories, but to processes which are
not treated in the semi-analytical models, such as tidal stripping or
harassment. In field regions the SMF shows a sharp upturn below M=10^9 M_sun,
close to our mass limit, suggesting that the upturns seen in our K-band LFs,
but not in the SMF, are due to this dwarf population. The environmental
variations seen in the faint-end of the K-band LF suggests that dwarf galaxies,
which are easier to strip than their more massive counterparts, are affected by
tidal/gas stripping upon entering the supercluster.


  Image denoising has recently taken a leap forward due to machine learning.
However, image denoisers, both expert-based and learning-based, are mostly
tested on well-behaved generated noises (usually Gaussian) rather than on
real-life noises, making performance comparisons difficult in real-world
conditions. This is especially true for learning-based denoisers which
performance depends on training data. Hence, choosing which method to use for a
specific denoising problem is difficult.
  This paper proposes a comparative study of existing denoisers, as well as an
extensible open tool that makes it possible to reproduce and extend the study.
MWCNN is shown to outperform other methods when trained for a real-world image
interception noise, and additionally is the second least compute hungry of the
tested methods. To evaluate the robustness of conclusions, three test sets are
compared. A Kendall's Tau correlation of only 60% is obtained on methods
ranking between noise types, demonstrating the need for a benchmarking tool.


  The inverse problem of electrical impedance tomography is severely ill-posed.
In particular, the resolution of images produced by impedance tomography
deteriorates as the distance from the measurement boundary increases. Such
depth dependence can be quantified by the concept of distinguishability of
inclusions. This paper considers the distinguishability of perfectly conducting
ball inclusions inside a unit ball domain, extending and improving known
two-dimensional results to an arbitrary dimension $d \geq 2$ with the help of
Kelvin transformations. The obtained depth-dependent distinguishability bounds
are also proven to be optimal.


  Motivated by experiments and formal asymptotic expansions in the physics
literature, Maor and Shachar (J. Elasticity 134 (2019), 149-173) studied the
behaviour of a model elastic energy of maps between manifolds with incompatible
metrics. For thin objects they analysed the scaling of the minimal elastic
energy as a function of the thickness. In particular they showed that for maps
from a ball of radius h in an oriented Riemannian manifold to Euclidean space,
the infimum of a model elastic energy per unit volume scales like the fourth
power of h and after rescaling one gets convergence to a quadratic expression
in the curvature tensor R(p), where p denotes the centre of the ball. In this
paper we show the same result for general compact oriented Riemannian targets
with R(p) replaced by a suitable difference of the curvature tensors in the
target and the domain, thus answering Open Question 1 in the paper by Maor and
Shachar. The result extends noncompact targets provided they satisfy a uniform
regularity condition. A key idea in the proof is to use Lipschitz
approximations to define a suitable notion of convergence.


  In this paper, we present a learning-based approach that allows a robot to
quickly follow a reference path defined in joint space without exceeding limits
on the position, velocity, acceleration and jerk of each robot joint. Contrary
to offline methods for time-optimal path parameterization, the reference path
can be changed during motion execution. In addition, our approach can utilize
sensory feedback, for instance, to follow a reference path with a bipedal robot
without losing balance. With our method, the robot is controlled by a neural
network that is trained via reinforcement learning using data generated by a
physics simulator. From a mathematical perspective, the problem of tracking a
reference path in a time-optimized manner is formalized as a Markov decision
process. Each state includes a fixed number of waypoints specifying the next
part of the reference path. The action space is designed in such a way that all
resulting motions comply with the specified kinematic joint limits. The reward
function finally reflects the trade-off between the execution time, the
deviation from the desired reference path and optional additional objectives
like balancing. We evaluate our approach with and without additional objectives
and show that time-optimized path tracking can be successfully learned for both
industrial and humanoid robots. In addition, we demonstrate that networks
trained in simulation can be successfully transferred to a real robot.


  We prove smoothing estimates in Morrey-Campanato spaces for a Helmholtz
equation $$
  -Lu+zu=f,
  \qquad
  -Lu:=\nabla^{b}(a(x)\nabla^{b}u)-c(x)u,
  \qquad
  \nabla^{b}:=\nabla+ib(x) $$ with fully variable coefficients, of limited
regularity, defined on the exterior of a starshaped compact obstacle in
$\mathbb{R}^{n}$, $n\ge3$, with Dirichlet boundary conditions. The principal
part of the operator is a long range perturbation of a constant coefficient
operator, while the lower order terms have an almost critical decay. We give
explicit conditions on the size of the perturbation which prevent trapping.
  As an application, we prove smoothing estimates for the Schr\"{o}dinger flow
$e^{itL}$ and the wave flow $e^{it \sqrt{L}}$ with variable coefficients on
exterior domains and Dirichlet boundary conditions.


  We describe updates to the \redmapper{} algorithm, a photometric red-sequence
cluster finder specifically designed for large photometric surveys. The updated
algorithm is applied to $150\,\mathrm{deg}^2$ of Science Verification (SV) data
from the Dark Energy Survey (DES), and to the Sloan Digital Sky Survey (SDSS)
DR8 photometric data set. The DES SV catalog is locally volume limited, and
contains 786 clusters with richness $\lambda>20$ (roughly equivalent to
$M_{\rm{500c}}\gtrsim10^{14}\,h_{70}^{-1}\,M_{\odot}$) and $0.2<z<0.9$. The DR8
catalog consists of 26311 clusters with $0.08<z<0.6$, with a sharply increasing
richness threshold as a function of redshift for $z\gtrsim 0.35$. The
photometric redshift performance of both catalogs is shown to be excellent,
with photometric redshift uncertainties controlled at the $\sigma_z/(1+z)\sim
0.01$ level for $z\lesssim0.7$, rising to $\sim0.02$ at $z\sim0.9$ in DES SV.
We make use of \emph{Chandra} and \emph{XMM} X-ray and South Pole Telescope
Sunyaev-Zeldovich data to show that the centering performance and
mass--richness scatter are consistent with expectations based on prior runs of
\redmapper{} on SDSS data. We also show how the \redmapper{} \photoz{} and
richness estimates are relatively insensitive to imperfect star/galaxy
separation and small-scale star masks.


  We calculate the form factor $M(q^2)$ for the Dalitz decay $J/\psi\to
\gamma^*(q^2)\eta_{(N_f=1)}$ with $\eta_{(N_f)}$ being the SU($N_f$) flavor
singlet pseudoscalar meson. The difference among the partial widths
$\Gamma(J/\psi\to \gamma \eta_{(N_f)})$ at different $N_f$ can be attributed in
part to the $\mathbf{U}_A(1)$ anomaly that induces a $N_f$ scaling. $M(q^2)$'s
in $N_f=1,2$ are both well described by the single pole model
$M(q^2)=M(0)/(1-q^2/\Lambda^2)$. Combined with the known experimental results
of the Dalitz decays $J/\psi\to Pe^+e^-$, the pseudoscalar mass $m_P$
dependence of the pole parameter $\Lambda$ is approximated by
$\Lambda(m_P^2)=\Lambda_1(1-m_P^2/\Lambda_2^2)$ with
$\Lambda_1=2.64(4)~\mathrm{GeV}$ and $\Lambda_2=2.97(33)~\mathrm{GeV}$. These
results provide inputs for future theoretical and experimental studies on the
Dalitz decays $J/\psi\to Pe^+e^-$.


  The time division multiple access (TDMA) technique has been applied in
automotive multiple-input multiple-output (MIMO) radar. However, it suffers
from the transmit energy loss, and as a result the parameter estimation
performance degradation when the number of transmit elements increases. To
tackle these problem, a transmit beamspace (TB) Doppler division multiple
access (DDMA) approach is proposed. First, a phase modulation matrix with empty
Doppler spectrum is introduced. By exploiting the empty Doppler spectrum, a
test function based on sequential detection is developed to mitigate the
Doppler ambiguity in DDMA waveform. Then, a discrete Fourier transform
(DFT)-based TB in slow-time is formed.The proposed method can achieve waveform
diversity in Doppler domain and generate a TB in slow-time that concentrates
the transmitted power in a fixed spatial region to improve the transmit energy
distribution for automotive MIMO radar, which is favored by medium/long range
radar (MRR/LRR) applications. As compared to the conventional TDMA technique,
the proposed TB DDMA approach can fully exploit the transmission capabilities
of all transmit elements to ensure that the emitted power is efficiently used
and inherits easy implementation. Moreover, the proposed TB DDMA method avoids
the trade-off between the active time for each transmit antenna and the frame
time. Simulation results verify the effectiveness of the proposed TB DDMA
approach for automotive MIMO radar.


  We present phase space distributions and multiplicities of K+, K- and phi
mesons produced in Ar+KCl reactions at a kinetic beam energy of 1.756 AGeV and
measured with the HADES spectrometer. The inverse slope parameters and yields
of kaons supplement the systematics of previous measurements. The percentage of
K- mesons coming fromphi decay is found to be 18+- 7%.


  Pulsar radio emission undergoes dispersion due to the presence of free
electrons in the interstellar medium (ISM). The dispersive delay in the arrival
time of pulsar signal changes over time due to the varying ISM electron column
density along the line of sight. Correcting for this delay accurately is
crucial for the detection of nanohertz gravitational waves using Pulsar Timing
Arrays. In this work, we present in-band and inter-band DM estimates of four
pulsars observed with uGMRT over the timescale of a year using two different
template alignment methods. The DMs obtained using both these methods show only
subtle differences for PSR 1713+0747 and J1909$-$3744. A considerable offset is
seen in the DM of PSR J1939+2134 and J2145$-$0750 between the two methods. This
could be due to the presence of scattering in the former and profile evolution
in the latter. We find that both methods are useful but could have a systematic
offset between the DMs obtained. Irrespective of the template alignment methods
followed, the precision on the DMs obtained is about $10^{-3}$ pc cm$^{-3}$
using only BAND3 and $10^{-4}$ pc cm$^{-3}$ after combining data from BAND3 and
BAND5 of the uGMRT. In a particular result, we have detected a DM excess of
about $5\times10^{-3}$ pc cm$^{-3}$ on 24 February 2019 for PSR J2145$-$0750.
This excess appears to be due to the interaction region created by fast solar
wind from a coronal hole and a coronal mass ejection (CME) observed from the
Sun on that epoch. A detailed analysis of this interesting event is presented.


  We modify and extend an earlier proposal by Brown and Teitelboim to relax the
effective cosmological term by nucleation of branes coupled to a three-index
gauge potential. Microscopic considerations from string/M theory suggest two
major innovations in the framework. First, the dependence of brane properties
on the compactification of extra dimensions may generate a very small quantized
unit for jumps in the effective cosmological term. Second, internal degrees of
freedom for multiply coincident branes may enhance tunneling rates by
exponentially large density of states factors. These new features essentially
alter the relaxation dynamics. By requiring stability on the scale of the
lifetime of the universe, rather than absolute stability, we derive a
non-trivial relation between the supersymmetry breaking scale and the value of
the cosmological term. It is plausibly, though not certainly, satisfied in
Nature.


  We report the magnetic, magnetoelastic, and magnetotransport properties of
single crystals of polar magnets $R$AuGe ($R=$ Dy, Ho, and Gd), grown by Au-Ge
self-flux. Magnetization and magnetostriction measurements reveal multi-step
metamagnetic transitions for the $c$-axis magnetic field ($H\parallel c$) for
DyAuGe and HoAuGe, suggesting magnetic frustration in the triangular lattice of
$R$ ions. The magnetic phase diagrams have clarified a close connection between
the magnetoelastic property and the emergence of the intermediate metamagentic
phase. The magnetic-field dependence of the resistivity and Hall resistivity
reveal the semimetallic transport dominated by hole-type carriers, consistent
with the behavior in a nonmagnetic analogue YAuGe. We also identify a signature
of an anomalous Hall effect (AHE) proportional to the field-induced
magnetization in $R=$ Dy, Ho, and Gd. GdAuGe shows magnetic and transport
behavior as reported in a previous study using Bi-flux grown single crystals,
while the self-flux grown crystal shows larger magnetoresistance ($\sim$ 345\%,
at 1.8 K and 9 T) due to higher hole-type carrier mobility ($\sim$ 6400
cm$^2$/Vs). Using the two-band model analysis considering the mobility change
during the magnetization process, we extract the anomalous Hall conductivity:
$\sim 1200$ S/cm and $\sim 530$ S/cm for $R=$ Dy and Ho, respectively, at 1.8 K
with 9 T for $H\parallel c$. The magnitude of conductivity suggests a
contribution of intrinsic origin, possibly related to the Berry curvature in
the electron bands induced by the time-reversal symmetry breaking and the polar
lattice.


  We compute the canonical class of certain Rees algebras. Our formula
generalizes that of Herzog and Vasconcelos. Its proof relies on the fact that
the formation of the canonical module commutes with subintersections in
important cases. As an application we treat the classical determinantal ideals
and the corresponding algebras of minors.


  We give the full description of all degenerations of complex five dimensional
noncommutative Heisenberg algebras. As a corollary, we have the full
description of all degenerations of four dimensional anticommutative $3$-ary
algebras.


  We review the blackfold description of the fully localized orthogonal M2-M5
intersection in eleven-dimensional supergravity which constitutes the direct
gravitational analogue of the Howe-Lambert-West self-dual string soliton
solution. We emphasize the preliminary implications of this description for the
physics of the M2-M5 system and the novel research directions that it opens.
This report contains several new results. As an extension of previous work we
report new results on deformations of the M2-M5-KKW intersection that describe
self-dual ring intersections. Extremal non-supersymmetric configurations of
this type probe novel aspects of the M2-M5 system and allow us to explore
further the merits and limitations of the blackfold description of black brane
intersections. In particular, we provide an example of a situation where an
effective description of extremal non-supersymmetric spike configurations is
shown to capture correctly features of the exact solutions beyond its strict
regime of validity. This observation hints at the existence of improved
convergence properties in the underlying derivative expansion scheme without
the necessary presence of supersymmetry.


  Recently, self-supervised pretraining has achieved impressive results in
end-to-end (E2E) automatic speech recognition (ASR). However, the dominant
sequence-to-sequence (S2S) E2E model is still hard to fully utilize the
self-supervised pre-training methods because its decoder is conditioned on
acoustic representation thus cannot be pretrained separately. In this paper, we
propose a pretrained Transformer (Preformer) S2S ASR architecture based on
hybrid CTC/attention E2E models to fully utilize the pretrained acoustic models
(AMs) and language models (LMs). In our framework, the encoder is initialized
with a pretrained AM (wav2vec2.0). The Preformer leverages CTC as an auxiliary
task during training and inference. Furthermore, we design a one-cross decoder
(OCD), which relaxes the dependence on acoustic representations so that it can
be initialized with pretrained LM (DistilGPT2). Experiments are conducted on
the AISHELL-1 corpus and achieve a $4.6\%$ character error rate (CER) on the
test set. Compared with our vanilla hybrid CTC/attention Transformer baseline,
our proposed CTC/attention-based Preformer yields $27\%$ relative CER
reduction. To the best of our knowledge, this is the first work to utilize both
pretrained AM and LM in a S2S ASR system.


  The recently reported coexistence of an oscillatory magnetic order with the
wave vector Q=0.241 \AA^{-1} and superconductivity in TmNi2B2C is analyzed
theoretically. It is shown that the oscillatory magnetic order and
superconductivity interact predominantly via the exchange interaction between
localized moments (LM's) and conduction electrons, while the electromagnetic
interaction between them is negligible. In the coexistence phase of the clean
TmNi2B2C the quasiparticle spectrum should have a line of zeros at the Fermi
surface, giving rise to the power law behavior of thermodynamic and transport
properties. Two scenarios of the origin of the oscillatory magnetic order in
TmNi2B2C are analyzed: a) due to superconductivity and b) independently on
superconductivity. Experiments in magnetic field are proposed in order to
choose between them.


  Rare-earth ion doped crystals are state-of-the-art platforms for processing
quantum information, particularly thanks to their excellent optical and spin
coherence properties at cryogenic temperatures. Experimental observations have
shown that the application of a static magnetic bias field significantly
improves the coherence times in the rare-earth ions ensemble, but only a few
studies have focused on its the dependency as a function of both magnetic field
direction and amplitude. This is especially true for magnetic field amplitudes
under the mT, and for low magnetic dipole moment ions. In this paper, we
investigate the relationship between the magnetic field parameters and the
decoherence caused by magnetic dipole-dipole coupling with the nearest
neighbors nuclear spins in the crystal. The primary non-Kramers rare-earth ions
investigated here are europium and praseodymium, but we also extend our study
to the ytterbium Kramers ion due to its low magnetic dipole in the mT range. We
perform theoretical investigations and simulations of the energy structure and
coherence time evolution and identify good correspondences between experimental
and simulated spin echo data. This work allows us to pinpoint the most relevant
decoherence mechanisms in the considered magnetic field regime, and to predict
favorable magnetic configurations.


  As it was proposed and recently verified experimentally, the mechanism of
Feshbach resonance in a condensate can create a second condensate component of
molecules that coexists with the atomic condensate. In this work we investigate
signatures of the presence of the molecular condensate through the equilibrium
properties and collective excitations of the hybrid system of atoms and
molecules, subjected to a trap, employing a time-dependent variational ansatz.
We show that the shape of the condensate changes significantly by the presence
of the molecules and that modes unique to this hybrid system appear at
observable frequencies.


  Identifying coherent spatiotemporal patterns generated by complex dynamical
systems is a central problem in many science and engineering disciplines. Here,
we combine ideas from the theory of operator-valued kernels with
delay-embedding techniques in dynamical systems to develop of a method for
objective identification of spatiotemporal coherent patterns, without prior
knowledge of the state space and/or the dynamical laws of the system generating
the data. A key aspect of this method is that it operates on a space of
vector-valued observables using a kernel measure of similarity that takes into
account both temporal and spatial degrees of freedom (in contrast, classical
kernel techniques such as PCA utilize aggregate measures of similarity between
'snapshots'). As a result, spectral decomposition of data via our approach
yields a significantly more efficient and physically meaningful representation
of complex spatiotemporal signals than conventional methods based on
scalar-valued kernels. We demonstrate this behavior with applications to an
oscillator model and sea surface temperature data from a climate model.


  Few-shot anomaly detection (FSAD) is essential in industrial manufacturing.
However, existing FSAD methods struggle to effectively leverage a limited
number of normal samples, and they may fail to detect and locate inconspicuous
anomalies in the spatial domain. We further discover that these subtle
anomalies would be more noticeable in the frequency domain. In this paper, we
propose a Dual-Path Frequency Discriminators (DFD) network from a frequency
perspective to tackle these issues. Specifically, we generate anomalies at both
image-level and feature-level. Differential frequency components are extracted
by the multi-frequency information construction module and supplied into the
fine-grained feature construction module to provide adapted features. We
consider anomaly detection as a discriminative classification problem,
wherefore the dual-path feature discrimination module is employed to detect and
locate the image-level and feature-level anomalies in the feature space. The
discriminators aim to learn a joint representation of anomalous features and
normal features in the latent space. Extensive experiments conducted on MVTec
AD and VisA benchmarks demonstrate that our DFD surpasses current
state-of-the-art methods. Source code will be available.


  We propose to learn energy-based model (EBM) in the latent space of a
generator model, so that the EBM serves as a prior model that stands on the
top-down network of the generator model. Both the latent space EBM and the
top-down network can be learned jointly by maximum likelihood, which involves
short-run MCMC sampling from both the prior and posterior distributions of the
latent vector. Due to the low dimensionality of the latent space and the
expressiveness of the top-down network, a simple EBM in latent space can
capture regularities in the data effectively, and MCMC sampling in latent space
is efficient and mixes well. We show that the learned model exhibits strong
performances in terms of image and text generation and anomaly detection. The
one-page code can be found in supplementary materials.


  In this paper, we propose a semi-Lagrangian discontinuous Galerkin method
coupled with Runge-Kutta exponential integrators (SLDG-RKEI) for nonlinear
Vlasov dynamics. The commutator-free Runge-Kutta (RK) exponential integrators
(EI) were proposed by Celledoni, et al. (FGCS, 2003). In the nonlinear
transport setting, the RKEI can be used to decompose the evolution of the
nonlinear transport into a composition of a sequence of linearized dynamics.
The resulting linearized transport equations can be solved by the
semi-Lagrangian (SL) discontinuous Galerkin (DG) method proposed in Cai, et al.
(JSC, 2017). The proposed method can achieve high order spatial accuracy via
the SLDG framework, and high order temporal accuracy via the RK EI. Due to the
SL nature, the proposed SLDG-RKEI method is not subject to the CFL condition,
thus they have the potential in using larger time-stepping sizes than those in
the Eulerian approach. Inheriting advantages from the SLDG method, the proposed
SLDG-RKEI schemes are mass conservative, positivity-preserving, have no
dimensional splitting error, perform well in resolving complex solution
structures, and can be evolved with adaptive time-stepping sizes. We show the
performance of the SLDG-RKEI algorithm by classical test problems for the
nonlinear Vlasov-Poisson system, as well as the Guiding center Vlasov model.
Though that it is not our focus of this paper to explore the SLDG-RKEI scheme
for nonlinear hyperbolic conservation laws that develop shocks, we show some
preliminary results on schemes' performance on the Burgers' equation.


  We consider the class of groups whose word problem is poly-context-free; that
is, an intersection of finitely many context-free languages. We show that any
group which is virtually a finitely generated subgroup of a direct product of
free groups has poly-context-free word problem, and conjecture that the
converse also holds. We prove our conjecture for several classes of soluble
groups, including metabelian groups and torsion-free soluble groups, and
present progress towards resolving the conjecture for soluble groups in
general. Some of the techniques introduced for proving languages not to be
poly-context-free may be of independent interest.


  In this study, we demonstrated experimentally and theoretically that oxygen
vacancies are responsible for the charge transport in HfO$_2$. Basing on the
model of phonon-assisted tunneling between traps, and assuming that the
electron traps are oxygen vacancies, good quantitative agreement between the
experimental and theoretical data of current-voltage characteristics were
achieved. The thermal trap energy of 1.25 eV in HfO$_2$ was determined based on
the charge transport experiments.


  The (1+1)-dimensional higher-order Broer-Kaup (HBK) system is studied by
consistent tanh expansion (CTE) method in this paper.It is proved that the HBK
system is CTE solvable. Some exact interaction solutions among different
nonlinear excitations such as solitons, rational waves, periodic waves and
corresponding images are explicitly given.


  The deep-learning-based tunnel accident detection (TAD) system (Lee 2019) has
installed a system capable of monitoring 9 CCTVs at XX site in November, 2018.
The initial deep-learning training was started by studying 70,914 labeled
images and label data. However, sunlight, the tail light of a vehicle, and the
warning light of the working vehicle were recognized as a fire, and many
pedestrians were detected in the lane of the tunnel or a black elongated black
object. To solve these problems, as shown in Fig. 1, the false detection data
detected in the field were trained with labeled data and reapplied in the
field. As a result, false detection of pedestrians and fire could be
significantly reduced.


  In the early 1970's, Richard Stanley and Kenneth Johnson introduced and laid
the groundwork for studying the order polynomial of partially ordered sets
(posets). Decades later, Hamaker, Patrias, Pechenik, and Williams introduced
the term "doppelgangers": equivalence classes of posets under the equivalence
relation given by equality of the order polynomial. We provide necessary and
sufficient conditions on doppelgangers through application of both old and
novel tools, including new recurrences and the Ur-operation: a new generalized
poset operation. In addition, we prove that the doppelgangers of posets P of
bounded height $|P|-k$ may be classified up to systems of $k$ diophantine
equations in $2^{O(k^2)}$ time, and similarly that the order polynomial of such
posets may be computed in $O(|P|)$ time.


  It is already well-understood that many delay differential equations with
only a single constant delay exhibit a change in stability according to the
value of the delay in relation to a critical delay value. Finding a formula for
the critical delay is important to understanding the dynamics of delayed
systems and is often simple to obtain when the system only has a single
constant delay. However, if we consider a system with multiple constant delays,
there is no known way to obtain such a formula that determines for what values
of the delays a change in stability occurs. In this paper, we present some
single-delay approximations to a multi-delay system obtained via a Taylor
expansion as well as formulas for their critical delays which are used to
approximate where the change in stability occurs in the multi-delay system. We
determine when our approximations perform well and we give extra analytical and
numerical attention to the two-delay and three-delay settings.


  We complete the existing literature on the kinetic theory of systems with
long-range interactions. Starting from the BBGKY hierarchy, or using projection
operator technics or a quasilinear theory, a general kinetic equation can be
derived when collective effects are neglected. This equation (which is not
well-known) applies to possibly spatially inhomogeneous systems, which is
specific to systems with long-range interactions. Interestingly, the structure
of this kinetic equation bears a clear physical meaning in terms of generalized
Kubo relations. Furthermore, this equation takes a very similar form for
stellar systems and two-dimensional point vortices providing therefore a
unified description of the kinetic theory of these systems. If we assume that
the system is spatially homogeneous (or axisymmetric for point vortices), this
equation can be simplified and reduces to the Landau equation (or its
counterpart for point vortices). Our formalism thus offers a simple derivation
of Landau-type equations. We also use this general formalism to derive a
kinetic equation, written in angle-action variables, describing spatially
inhomogeneous systems with long-range interactions. This new derivation solves
the shortcomings of our previous derivation [P.H. Chavanis, Physica A 377, 469
(2007)]. Finally, we consider a test particle approach and derive general
expressions for the diffusion and friction (or drift) coefficients of a test
particle evolving in a bath of field particles. We make contact with the
expressions previously obtained in the literature. As an application of the
kinetic theory, we argue that the relaxation time is shorter for inhomogeneous
(or high-dimensional) systems than for homogeneous (or low-dimensional) systems
because there are potentially more resonances.


  Energy disaggregation or nonintrusive load monitoring (NILM), is a
single-input blind source discrimination problem, aims to interpret the mains
user electricity consumption into appliance level measurement. This article
presents a new approach for power disaggregation by using a deep recurrent long
short term memory (LSTM) network combined with convolutional neural networks
(CNN). Deep neural networks have been shown to be a significant way for these
types of problems because of their complexity and huge number of trainable
paramters. Hybrid method that proposed in the article could significantly
increase the overall accuracy of NILM because it benefits from both network
advantages. The proposed method used sequence-to-sequence learning, where the
input is a window of the mains and the output is a window of the target
appliance. The proposed deep neural network approach has been applied to
real-world household energy dataset "REFIT". The REFIT electrical load
measurements dataset described in this paper includes whole house aggregate
loads and nine individual appliance measurements at 8-second intervals per
house, collected continuously over a period of two years from 20 houses around
the UK. The proposed method achieve significant performance, improving accuracy
and F1-score measures by 95.93% and 80.93% ,respectively which demonstrates the
effectiveness and superiority of the proposed approach for home energy
monitoring. Comparison of proposed method and other recently published method
has been presented and discussed based on accuracy, number of considered
appliances and size of the deep neural network trainable parameters. The
proposed method shows remarkable performance compare to other previous methods.


  Diffusion of innovation can be interpreted as a social spreading phenomena
governed by the impact of media and social interactions. Although these
mechanisms have been identified by quantitative theories, their role and
relative importance are not entirely understood, since empirical verification
has so far been hindered by the lack of appropriate data. Here we analyse a
dataset recording the spreading dynamics of the world's largest Voice over
Internet Protocol service to empirically support the assumptions behind models
of social contagion. We show that the rate of spontaneous service adoption is
constant, the probability of adoption via social influence is linearly
proportional to the fraction of adopting neighbours, and the rate of service
termination is time-invariant and independent of the behaviour of peers. By
implementing the detected diffusion mechanisms into a dynamical agent-based
model, we are able to emulate the adoption dynamics of the service in several
countries worldwide. This approach enables us to make medium-term predictions
of service adoption and disclose dependencies between the dynamics of
innovation spreading and the socioeconomic development of a country.


  The unlabeled sensing problem is to solve a noisy linear system of equations
under unknown permutation of the measurements. We study a particular case of
the problem where the permutations are restricted to be r-local, i.e. the
permutation matrix is block diagonal with r x r blocks. Assuming a Gaussian
measurement matrix, we argue that the r-local permutation model is more
challenging compared to a recent sparse permutation model. We propose a
proximal alternating minimization algorithm for the general unlabeled sensing
problem that provably converges to a first order stationary point. Applied to
the r-local model, we show that the resulting algorithm is efficient. We
validate the algorithm on synthetic and real datasets. We also formulate the
1-d unassigned distance geometry problem as an unlabeled sensing problem with a
structured measurement matrix.


  In a previous paper (hep-th/0509071), it was shown that quantum 1/J
corrections to the BMN spectrum in an effective Landau-Lifshitz (LL) model
match with the results from the one-loop gauge theory, provided one chooses an
appropriate regularization. In this paper we continue this study for the
conjectured Bethe ansatz for the long range spin chain representing
perturbative planar N=4 Super Yang-Mills in the SU(2) sector, and the ``quantum
string" Bethe ansatz for its string dual. The comparison is carried out for
corrections to BMN energies up to 3rd order in the effective expansion
parameter $\tl=\lambda/J^2$. After determining the ``gauge-theory'' LL action
to order $\tl^3$, which is accomplished indirectly by fixing the coefficients
in the LL action so that the energies of circular strings match with the
energies found using the Bethe ansatz, we find perfect agreement. We interpret
this as further support for an underlying integrability of the system. We then
consider the ``string-theory'' LL action which is a limit of the classical
string action representing fast string motion on an S^3 subspace of S^5 and
compare the resulting $\tl^3/J^2$ corrections to the prediction of the
``string'' Bethe ansatz. As in the gauge case, we find precise matching. This
indicates that the LL Hamiltonian supplemented with a normal ordering
prescription and zeta-function regularization reproduces the full superstring
result for the $1/J^2$ corrections, and also signifies that the string Bethe
ansatz does describe the quantum BMN string spectrum to order $1/J^2$. We also
comment on using the quantum LL approach to determine the non-analytic
contributions in $\lambda$ that are behind the strong to weak coupling
interpolation between the string and gauge results.


  We generalize an already proposed protocol for quantum state transfer to spin
chains of arbitrary spin. An arbitrary unknown $d-$ level state is transferred
through a chain with rather good fidelity by the natural dynamics of the chain.
We compare the performance of this protocol for various values of $d$. A
by-product of our study is a much simpler method for picking up the state at
the destination as compared with the one proposed previously. We also discuss
entanglement distribution through such chains and show that the quality of
entanglement transition increases with the number of levels $d$.


  It is shown how to set up, conduct, and analyze large simulation studies with
the new R package simsalapar = simulations simplified and launched parallel. A
simulation study typically starts with determining a collection of input
variables and their values on which the study depends, such as sample sizes,
dimensions, types and degrees of dependence, estimation methods, etc.
Computations are desired for all com- binations of these variables. If
conducting these computations sequentially is too time- consuming, parallel
computing can be applied over all combinations of select variables. The final
result object of a simulation study is typically an array. From this array,
sum- mary statistics can be derived and presented in terms of (flat contingency
or LATEX) tables or visualized in terms of (matrix-like) figures. The R package
simsalapar provides several tools to achieve the above tasks. Warnings and
errors are dealt with correctly, various seeding methods are available, and run
time is measured. Furthermore, tools for analyzing the results via tables or
graphics are pro- vided. In contrast to rather minimal examples typically found
in R packages or vignettes, an end-to-end, not-so-minimal simulation problem
from the realm of quantitative risk management is given. The concepts presented
and solutions provided by simsalapar may be of interest to students,
researchers, and practitioners as a how-to for conducting real- istic,
large-scale simulation studies in R. Also, the development of the package
revealed useful improvements to R itself, which are available in R 3.0.0.


  In this paper, we provide Algebraic-Coding necessary and sufficient
conditions for the Maximum Distance Separable Conjecture to hold.


  In this article we determine a generating set of rational invariants of
minimal cardinality for the action of the orthogonal group $\mathrm{O}_3$ on
the space $\mathbb{R}[x,y,z]_{2d}$ of ternary forms of even degree $2d$. The
construction relies on two key ingredients: On one hand, the Slice Lemma allows
us to reduce the problem to dermining the invariants for the action on a
subspace of the finite subgroup $\mathrm{B}_3$ of signed permutations. On the
other hand, our construction relies in a fundamental way on specific bases of
harmonic polynomials. These bases provide maps with prescribed
$\mathrm{B}_3$-equivariance properties. Our explicit construction of these
bases should be relevant well beyond the scope of this paper. The expression of
the $\mathrm{B}_3$-invariants can then be given in a compact form as the
composition of two equivariant maps. Instead of providing (cumbersome) explicit
expressions for the $\mathrm{O}_3$-invariants, we provide efficient algorithms
for their evaluation and rewriting. We also use the constructed
$\mathrm{B}_3$-invariants to determine the $\mathrm{O}_3$-orbit locus and
provide an algorithm for the inverse problem of finding an element in
$\mathbb{R}[x,y,z]_{2d}$ with prescribed values for its invariants. These are
the computational issues relevant in brain imaging.


  The Russia-based Internet Research Agency (IRA) carried out a broad
information campaign in the U.S. before and after the 2016 presidential
election. The organization created an expansive set of internet properties: web
domains, Facebook pages, and Twitter bots, which received traffic via purchased
Facebook ads, tweets, and search engines indexing their domains. We investigate
the scope of IRA activities in 2017, joining data from Facebook and Twitter
with logs from the Internet Explorer 11 and Edge browsers and the Bing.com
search engine. The studies demonstrate both the ease with which malicious
actors can harness social media and search engines for propaganda campaigns,
and the ability to track and understand such activities by fusing content and
activity resources from multiple internet services. We show how cross-platform
analyses can provide an unprecedented lens on attempts to manipulate opinions
and elections in democracies.


  For the sake of saving time and costs the feedback control based on
discrete-time observations is used to stabilize the switching diffusion
systems. Response lags are required by most of physical systems and play a key
role in the feedback control. The aim of this paper is to design delay feedback
control functions based on the discrete-time observations of the system states
and the Markovian states in order for the controlled switching diffusion system
(SDS) to be exponentially stable in $p$th moment and probability one as well as
stable in $H_\infty$. The designed control principles are implementable to
stablize quasi-linear and highly nonlinear SDSs. For quasi-linear SDSs the
criteria are sharp that under the control with high strength the controlled
SDSs will be stable (bounded) while under the weaker control they will be
unstable (unbounded) in mean square. The sample and moment Lyapunov exponents
are estimated which have close relationship with the time delays.


  It is known that the $S(n,k)$ Stirling numbers as well as the ordered
Stirling numbers $k!S(n,k)$ form log-concave sequences. Although in the first
case there are many estimations about the mode, for the ordered Stirling
numbers such estimations are not known. In this short note we study this
problem and some of its generalizations.


  There exists an intriguing relation between genus zero correlation functions
in the H^+_3 WZNW model and in Liouville field theory. We provide a path
integral derivation of the correspondence and then use our new approach to
generalize the relation to surfaces of arbitrary genus g. In particular we
determine the correlation functions of N primary fields in the WZNW model
explicitly through Liouville correlators with N+2g-2 additional insertions of
certain degenerate fields. The paper concludes with a list of interesting
further extensions and a few comments on the relation to the geometric
Langlands program.


  Two approaches for determining Hilbert functions of fat point subschemes of
$\mathbb P^2$ are demonstrated. A complete determination of the Hilbert
functions which occur for 9 double points is given using the first approach,
extending results obtained in a previous paper using the second approach. In
addition the second approach is used to obtain a complete determination of the
Hilbert functions for $n\geq 9$ $m$-multiple points for every $m$ if the points
are smooth points of an irreducible plane cubic curve. Additional results are
obtained using the first approach for $n\geq 9$ double points when the points
lie on an irreducible cubic (but now are not assumed to be smooth points of the
cubic).


  The idea of coded caching for content distribution networks was introduced by
Maddah-Ali and Niesen, who considered the canonical $(N, K)$ cache network in
which a server with $N$ files satisfy the demands of $K$ users (equipped with
independent caches of size $M$ each). Among other results, their work provided
a characterization of the exact rate memory tradeoff for the problem when
$M\geq\frac{N}{K}(K-1)$. In this paper, we improve this result for large caches
with $M\geq \frac{N}{K}(K-2)$. For the case
$\big\lceil\frac{K+1}{2}\big\rceil\leq N \leq K$, we propose a new coded
caching scheme, and derive a matching lower bound to show that the proposed
scheme is optimal. This extends the characterization of the exact rate memory
tradeoff to the case $M\geq \frac{N}{K}\Big(K-2+\frac{(K-2+1/N)}{(K-1)}\Big)$.
For the case $1\leq N\leq \big\lceil\frac{K+1}{2}\big\rceil$, we derive a new
lower bound, which demonstrates that the scheme proposed by Yu et al. is
optimal and thus extend the characterization of the exact rate memory tradeoff
to the case $M\geq \frac{N}{K}(K-2)$.