  The European Moon Rover System (EMRS) Pre-Phase A activity is part of the
European Exploration Envelope Programme (E3P) that seeks to develop a versatile
surface mobility solution for future lunar missions. These missions include:
the Polar Explorer (PE), In-Situ Resource Utilization (ISRU), and Astrophysics
Lunar Observatory (ALO) and Lunar Geological Exploration Mission (LGEM).
Therefore, designing a multipurpose rover that can serve these missions is
crucial. The rover needs to be compatible with three different mission
scenarios, each with an independent payload, making flexibility the key driver.
This study focuses on modularity in the rover's locomotion solution and
autonomous on-board system. Moreover, the proposed EMRS solution has been
tested at an analogue facility to prove the modular mobility concept. The tests
involved the rover's mobility in a lunar soil simulant testbed and different
locomotion modes in a rocky and uneven terrain, as well as robustness against
obstacles and excavation of lunar regolith. As a result, the EMRS project has
developed a multipurpose modular rover concept, with power, thermal control,
insulation, and dust protection systems designed for further phases. This paper
highlights the potential of the EMRS system for lunar exploration and the
importance of modularity in rover design.


  Hydrodynamic slip of a liquid at a solid surface represents a fundamental
phenomenon in fluid dynamics that governs liquid transport at small scales. For
polymeric liquids, de Gennes predicted that the Navier boundary condition
together with the theory of polymer dynamics imply extraordinarily large
interfacial slip for entangled polymer melts on ideal surfaces; this Navier-de
Gennes model was confirmed using dewetting experiments on ultra-smooth,
low-energy substrates. Here, we use capillary leveling - surface tension driven
flow of films with initially non-uniform thickness - of polymeric films on
these same substrates. Measurement of the slip length from a robust
one-parameter fit to a lubrication model is achieved. We show that at the lower
shear rates involved in leveling experiments as compared to dewetting ones, the
employed substrates can no longer be considered ideal. The data is instead
consistent with physical adsorption of polymer chains at the solid/liquid
interface. We extend the Navier-de Gennes description using one additional
parameter, namely the density of physically adsorbed chains per unit surface.
The resulting formulation is found to be in excellent agreement with the
experimental observations.


  In this paper, we show that all real zeros of the bilateral Hurwitz zeta
function $Z(s,a):=\zeta (s,a) + \zeta (s,1-a)$ with $1/4 \le a \le 1/2$ are on
only the non-positive even integers exactly same as in the case of $(2^s-1)
\zeta (s)$. We also prove that all real zeros of the bilateral periodic zeta
function $P(s,a):={\rm{Li}}_s (e^{2\pi ia}) + {\rm{Li}}_s (e^{2\pi i(1-a)})$
with $1/4 \le a \le 1/2$ are on only the negative even integers just like
$\zeta (s)$. Moreover, we show that all real zeros of the quadrilateral zeta
function $Q(s,a):=Z(s,a) + P(s,a)$ with $1/4 \le a \le 1/2$ are on only the
negative even integers. On the other hand, we prove that $Z(s,a)$, $P(s,a)$ and
$Q(s,a)$ have at least one real zero in $(0,1)$ when $0<a<1/2$ is sufficiently
small. The complex zeros of these zeta functions are also discussed when $1/4
\le a \le 1/2$ is rational or transcendental. As a corollary, we show that
$Q(s,a)$ with rational $1/4 < a < 1/3$ or $1/3 < a < 1/2$ does not satisfy the
analogue of the Riemann hypothesis even though $Q(s,a)$ satisfies the
functional equation that appeared in Hamburger's or Hecke's theorem and all
real zeros of $Q(s,a)$ are located at only the negative even integers again as
in the case of $\zeta (s)$.


  The Hausdorff dimension of spectral measure for the graph Laplacian is shown
exactly in terms of an intermittency function. The intermittency function can
be estimated by using one-dimensional discrete Schr\"{o}dinger operator method.


  Local drug delivery has received much recognition in recent years, yet it is
still unpredictable how drug efficacy depends on physicochemical properties and
delivery kinetics. The purpose of the current study is to provide a useful
mathematical model for drug release from a drug delivery device and consecutive
drug transport in biological tissue, thereby aiding the development of new
therapeutic drug by a systemic approach. In order to study the complete
process, a two-layer spatio-temporal model depicting drug transport between the
coupled media is presented. Drug release is described by considering
solubilisation dynamics of drug particle, diffusion of the solubilised drug
through porous matrix and also some other processes like reversible
dissociation / recrystallization, drug particle-receptor binding and
internalization phenomena. The model has led to a system of partial
differential equations describing the important properties of drug kinetics.
This model contributes towards the perception of the roles played by diffusion,
mass-transfer, particle binding and internalization parameters.


  American football is the most popular high school sport and is among the
leading cause of injury among adolescents. While there has been considerable
recent attention on the link between football and cognitive decline, there is
also evidence of higher than expected rates of pain, obesity, and lower quality
of life among former professional players, either as a result of repetitive
head injury or through different mechanisms. Previously hidden downstream
effects of playing football may have far-reaching public health implications
for participants in youth and high school football programs.
  Our proposed study is a retrospective observational study that compares 1,153
high school males who played varsity football with 2,751 male students who did
not. 1,951 of the control subjects did not play any sport and the remaining 800
controls played a non-contact sport. Our primary outcome is self-rated health
measured at age 65. To control for potential confounders, we adjust for
pre-exposure covariates with matching and model-based covariance adjustment. We
will conduct an ordered testing procedure designed to use the full pool of
2,751 controls while also controlling for possible unmeasured differences
between students who played sports and those who did not. We will
quantitatively assess the sensitivity of the results to potential unmeasured
confounding. The study will also assess secondary outcomes of pain, difficulty
with activities of daily living, and obesity, as these are both important to
individual well-being and have public health relevance.


  Supersymmetry predicts that gauge couplings are equal to the corresponding
gaugino-sfermion-fermion Yukawa couplings. This prediction can be tested for
the QCD sector of the MSSM by studying the processes eplus+eminus ->
squark+antisquark+gluon and eplus+eminus -> squark+antiquark+gluino at a future
linear collider. We present results for these processes at next-to-leading
order in alpha_s in the framework of the MSSM. We find sizable SUSY-QCD
corrections. The renormalization scale dependence is significantly reduced at
next-to-leading order.


  The $2$-decomposition for ribbon graphs was introduced in [Annals of
Combinatorics 15 (2011), pp 675-706]. We extend this result to half-edged
ribbon graphs and to rank $D$-weakly colored graphs [SIGMA 12 (2016), 030],
generalizing therefore the $2$-sums and tensor products of these graphs. Using
this extension for the $2$-decompositions, we provide new expansion formulas
for the Bollob\'as Riordan polynomial for half-edged ribbon graphs and also for
the polynomial invariant for weakly colored stranded graphs.


  The nanocrystalline-amorphous textures are commonly observed in the coatings
synthesized by energetic deposition.This work reports a theoretical study
towards binary Cu-C phase separation.By performing a MD simulation using the
LAMMPS instead of classical PFK methodology, we theoretically explained how the
initial pressure and Cu concentration fundamentally determines Cu
nanocrystalline's final morphology and grain size,which gives a novel insight
into binary phase separation and the evolution mechanism of
nanocrystalline-amorphous structures during energetic deposition.


  We study the dynamics of dark solitons in an incoherently pumped
exciton-polariton condensate by means of a system composed by a generalized
open-dissipative Gross-Pitaevskii equation for the polaritons' wavefunction and
a rate equation for the exciton reservoir density. Considering a perturbative
regime of sufficiently small reservoir excitations, we use the reductive
perturbation method, to reduce the system to a Korteweg-de Vries (KdV) equation
with linear loss. This model is used to describe the analytical form and the
dynamics of dark solitons. We show that the polariton field supports decaying
dark soliton solutions with a decay rate determined analytically in the weak
pumping regime. We also find that the dark soliton evolution is accompanied by
a shelf, whose dynamics follows qualitatively the effective KdV picture.


  Cardiovascular disease is a major life-threatening condition that is commonly
monitored using electrocardiogram (ECG) signals. However, these signals are
often contaminated by various types of noise at different intensities,
significantly interfering with downstream tasks. Therefore, denoising ECG
signals and increasing the signal-to-noise ratio is crucial for cardiovascular
monitoring. In this paper, we propose a deep learning method that combines a
one-dimensional convolutional layer with transformer architecture for denoising
ECG signals. The convolutional layer processes the ECG signal by various
kernel/patch sizes and generates an embedding called multi-scale patch
embedding. The embedding then is used as the input of a transformer network and
enhances the capability of the transformer for denoising the ECG signal.


  In this paper we consider several generalizations of the Borsuk-Ulam theorem
for G-spaces and apply these results to Tucker type lemmas for G-simplicial
complexes and PL-manifolds.


  In an optical superlattice of triple wells, containing two mutually
interacting atom species in adjacent wells, we show that one species can be
transported through the positions of the other species, yet avoiding
significant overlap and direct interaction. The transfer protocol is optimized
to be robust against missing atoms of either species in any lattice site, as
well as against lattice fluctuations. The degree and the duration of the
inter-species overlap during passage can be tuned, making possible controlled
large-scale interaction-induced change of internal states.


  We present a study of the spin transfer torque oscillator based on
CoFeB/MgO/CoFeB asymmetric magnetic tunnel junctions. We observe microwave
precession in junctions with different thickness of the free magnetization
layer. Taking advantage of the ferromagnetic interlayer exchange coupling
between the free and reference layer in the MTJ and perpendicular interface
anisotropy in thin CoFeB electrode we demonstrate the nanometer scale device
that can generate high frequency signal without external magnetic field
applied. The amplitude of the oscillation exceeds 10 nV/Hz^0.5 at 1.5 GHz.


  It is shown in "SIAM J. Sci. Comput. 39 (2017):B424-B441" that free-form
curves used in computer aided geometric design can usually be represented as
the solutions of linear differential systems and points and derivatives on the
curves can be evaluated dynamically by solving the differential systems
numerically. In this paper we present an even more robust and efficient
algorithm for dynamic evaluation of exponential polynomial curves and surfaces.
Based on properties that spaces spanned by general exponential polynomials are
translation invariant and polynomial spaces are invariant with respect to a
linear transform of the parameter, the transformation matrices between bases
with or without translated or linearly transformed parameters are explicitly
computed. Points on curves or surfaces with equal or changing parameter steps
can then be evaluated dynamically from a start point using a pre-computed
matrix. Like former dynamic evaluation algorithms, the newly proposed approach
needs only arithmetic operations for evaluating exponential polynomial curves
and surfaces. Unlike conventional numerical methods that solve a linear
differential system, the new method can give robust and accurate evaluation
results for any chosen parameter steps. Basis transformation technique also
enables dynamic evaluation of polynomial curves with changing parameter steps
using a constant matrix, which reduces time costs significantly than computing
each point individually by classical algorithms.


  We present a new approach to 3D object representation where a neural network
encodes the geometry of an object directly into the weights and biases of a
second 'mapping' network. This mapping network can be used to reconstruct an
object by applying its encoded transformation to points randomly sampled from a
simple geometric space, such as the unit sphere. We study the effectiveness of
our method through various experiments on subsets of the ShapeNet dataset. We
find that the proposed approach can reconstruct encoded objects with accuracy
equal to or exceeding state-of-the-art methods with orders of magnitude fewer
parameters. Our smallest mapping network has only about 7000 parameters and
shows reconstruction quality on par with state-of-the-art object decoder
architectures with millions of parameters. Further experiments on feature
mixing through the composition of learned functions show that the encoding
captures a meaningful subspace of objects.


  For any hyperbolic twist knot in the 3-sphere, we show that the resulting
manifold by $r$-surgery on the knot has left-orderable fundamental group if the
slope $r$ satisfies the inequality $0\le r \le 4$.


  Evolution of the coalescence rate of double neutron stars (NS) and neutron
star -- black hole (BH) binaries are computed for model galaxies with different
star formation rates. Assuming gamma-ray bursts (GRB) to originate from NS+NS
or NS+BH merging in distant galaxies, theoretical logN--logS distributions and
<V/V_max> tests of gamma-ray bursts (GRB) are calculated for the first time
taking the computed merging rates into account. We use a flat cosmological
model (Omega=1) with different values of the cosmological constant Lambda and
under various assumptions about the star formation history in galaxies. The
calculated source evolution predicts a 5-10 times increase of the source
statistics at count rates 3-10 times lower than the exising BATSE sensitivity
limit. The most important parameter in fitting the 2nd BATSE catalogue is the
initial redshift of star formation, which is found to be z_*=2-5 depending on a
poorly determined average spectral index of GRB.


  We introduce a novel unsupervised approach to reconstructing a 3D volume from
only two planar projections that exploits a previous\-ly-captured 3D volume of
the patient. Such volume is readily available in many important medical
procedures and previous methods already used such a volume. Earlier methods
that work by deforming this volume to match the projections typically fail when
the number of projections is very low as the alignment becomes
underconstrained. We show how to use a generative model of the volume
structures to constrain the deformation and obtain a correct estimate.
Moreover, our method is not bounded to a specific sensor calibration and can be
applied to new calibrations without retraining. We evaluate our approach on a
challenging dataset and show it outperforms state-of-the-art methods. As a
result, our method could be used in treatment scenarios such as surgery and
radiotherapy while drastically reducing patient radiation exposure.


  We use the largest complete sample of 64 galaxy clusters (HIghest X-ray FLUx
Galaxy Cluster Sample) with available high-quality X-ray data from Chandra, and
apply 16 cool-core diagnostics to them, some of them new. We also correlate
optical properties of brightest cluster galaxies (BCGs) with X-ray properties.
To segregate cool core and non-cool-core clusters, we find that central cooling
time, t_cool, is the best parameter for low redshift clusters with high quality
data, and that cuspiness is the best parameter for high redshift clusters. 72%
of clusters in our sample have a cool core (t_cool < 7.7 h_{71}^{-1/2} Gyr) and
44% have strong cool cores (t_cool <1.0 h_{71}^{-1/2} Gyr). For the first time
we show quantitatively that the discrepancy in classical and spectroscopic mass
deposition rates can not be explained with a recent formation of the cool
cores, demonstrating the need for a heating mechanism to explain the cooling
flow problem. [Abridged]


  As the reliability of the robot's perception correlates with the number of
integrated sensing modalities to tackle uncertainty, a practical solution to
manage these sensors from different computers, operate them simultaneously, and
maintain their real-time performance on the existing robotic system with
minimal effort is needed. In this work, we present an end-to-end
software-hardware framework, namely ExtPerFC, that supports both conventional
hardware and software components and integrates machine learning object
detectors without requiring an additional dedicated graphic processor unit
(GPU). We first design our framework to achieve real-time performance on the
existing robotic system, guarantee configuration optimization, and concentrate
on code reusability. We then mathematically model and utilize our transfer
learning strategies for 2D object detection and fuse them into depth images for
3D depth estimation. Lastly, we systematically test the proposed framework on
the Baxter robot with two 7-DOF arms, a four-wheel mobility base, and an Intel
RealSense D435i RGB-D camera. The results show that the robot achieves
real-time performance while executing other tasks (e.g., map building,
localization, navigation, object detection, arm moving, and grasping)
simultaneously with available hardware like Intel onboard CPUS/GPUs on
distributed computers. Also, to comprehensively control, program, and monitor
the robot system, we design and introduce an end-user application. The source
code is available at https://github.com/tuantdang/perception_framework.


  The recent discovery of the interfacial superconductivity (SC) of the
Bi2Te3/Fe1+yTe heterostructure has attracted extensive studies due to its
potential as a novel platform for trapping and controlling Majorana fermions.
Here we present studies of another topological insulator (TI)/Fe1+yTe
heterostructure, Sb2Te3/Fe1+yTe, which also enjoys an interfacial
two-dimensional SC. The results of transport measurements support that the
reduction of excess Fe concentration of the Fe1+yTe layer not only increases
the fluctuation of its antiferromagnetic (AFM) order but also enhances the
quality of the SC of this heterostructure system. On the other hand, the
interfacial SC of this heterostructure was found to have a wider-ranging
TI-layer thickness dependence than that of the Bi2Te3/Fe1+yTe heterostructure,
which is believed to be attributed to the much higher bulk conductivity of
Sb2Te3 that enhances indirect coupling between its top and bottom topological
surface states (TSSs). Our results provide the evidence of the interplay among
the AFM order, itinerant carries from the TSSs and the induced interfacial SC
of the TI/Fe1+yTe heterostructure system.


  We propose a multi-task deep-learning approach for estimating the
check-worthiness of claims in political debates. Given a political debate, such
as the 2016 US Presidential and Vice-Presidential ones, the task is to predict
which statements in the debate should be prioritized for fact-checking. While
different fact-checking organizations would naturally make different choices
when analyzing the same debate, we show that it pays to learn from multiple
sources simultaneously (PolitiFact, FactCheck, ABC, CNN, NPR, NYT, Chicago
Tribune, The Guardian, and Washington Post) in a multi-task learning setup,
even when a particular source is chosen as a target to imitate. Our evaluation
shows state-of-the-art results on a standard dataset for the task of
check-worthiness prediction.


  The Pauli rearrangement potential given by the second-order diagram is
evaluated for a nucleon optical model potential (OMP) with $G$ matrices of the
nucleon-nucleon interaction in chiral effective field theory. The results
obtained in nuclear matter are applied for $^{40}$Ca in a local-density
approximation. The repulsive effect is of the order of 5MeV at the normal
density. The density dependence indicates that the real part of the microscopic
OMP becomes shallower in a central region, but is barely affected in a surface
area. This improves the overall resemblance of the microscopic OMP to the
empirical one.


  Soft robots are naturally designed to perform safe interactions with their
environment, like locomotion and manipulation. In the literature, there are now
many concepts, often bio-inspired, to propose new modes of locomotion or
grasping. However, a methodology for implementing motion planning of these
tasks, as exists for rigid robots, is still lacking. One of the difficulties
comes from the modeling of these robots, which is very different, as it is
based on the mechanics of deformable bodies. These models, whose dimension is
often very large, make learning and optimization methods very costly. In this
paper, we propose a proxy approach, as exists for humanoid robotics. This proxy
is a simplified model of the robot that enables frugal learning of a motion
strategy. This strategy is then transferred to the complete model to obtain the
corresponding actuation inputs. Our methodology is illustrated and analyzed on
two classical designs of soft robots doing manipulation and locomotion tasks.


  Anharmonic inter-atomic potential x to power of n, n>1, has been used in
molecular dynamics (MD) simulations of stress dynamics of FCC oriented crystal.
The model of the chain of masses and springs is found as a convenient and
accurate description of simulation results, with masses representing the
crystallographic planes. The dynamics of oscillations of two planes is found
analytically to be given by Euler beta functions, and its scaling with
non-linearity parameter and amplitude of oscillations, or applied shear
pressure is discussed on examples of time dependencies of displacements,
velocities, and forces acting on masses (planes). The dynamics of stress
penetration from the surface of the sample with multiply-planes (an anharmonic
crystal) towards its interior is confirmed to be given exactly as a series of
Bessel functions, when n=2 (Schrodinger and Pater solutions). When n<>2 the
stress dynamics (wave propagation) in bulk material remains qualitatively of
the same nature as in the linear case. In particular, results suggest that the
quasi-linear relationship between frequency and wave number is preserved. Speed
of the transverse sound component, dependent on sound wave amplitude, is found
to be a strongly decreasing function of n. The results are useful in the
analysis of any MD simulations under pressure, as they help to understand the
dynamics of pressure retarded effects, as well help design the proper
methodology of performing MD simulations, such as studies of dynamics of
dislocations.


  Feature transformation aims to generate new pattern-discriminative feature
space from original features to improve downstream machine learning (ML) task
performances. However, the discrete search space for the optimal feature
explosively grows on the basis of combinations of features and operations from
low-order forms to high-order forms. Existing methods, such as exhaustive
search, expansion reduction, evolutionary algorithms, reinforcement learning,
and iterative greedy, suffer from large search space. Overly emphasizing
efficiency in algorithm design usually sacrifices stability or robustness. To
fundamentally fill this gap, we reformulate discrete feature transformation as
a continuous space optimization task and develop an
embedding-optimization-reconstruction framework. This framework includes four
steps: 1) reinforcement-enhanced data preparation, aiming to prepare
high-quality transformation-accuracy training data; 2) feature transformation
operation sequence embedding, intending to encapsulate the knowledge of
prepared training data within a continuous space; 3) gradient-steered optimal
embedding search, dedicating to uncover potentially superior embeddings within
the learned space; 4) transformation operation sequence reconstruction,
striving to reproduce the feature transformation solution to pinpoint the
optimal feature space.


  A fully massive Monte Carlo program to compute all four-fermion processes in
electron positron collisions, including Higgs boson production, is presented.
Leading higher order effects are discussed and included.


  Arbitrary order dissipative and conservative Hermite methods for the scalar
wave equation achieving $\mathcal{O}(2m)$ orders of accuracy using
$\mathcal{O}(m^d)$ degrees of freedom per node in $d$ dimensions are presented.
Stability and error analyses as well as implementation strategies for
accelerators are also given.


  The exponential scaling of the wave function is a fundamental property of
quantum systems with far reaching implications in our ability to process
quantum information. A problem where these are particularly relevant is quantum
state tomography. State tomography, whose objective is to obtain a full
description of a quantum system, can be analysed in the framework of
computational learning theory. In this model, quantum states have been shown to
be Probably Approximately Correct (PAC)-learnable with sample complexity linear
in the number of qubits. However, it is conjectured that in general quantum
states require an exponential amount of computation to be learned. Here, using
results from the literature on the efficient classical simulation of quantum
systems, we show that stabiliser states are efficiently PAC-learnable. Our
results solve an open problem formulated by Aaronson [Proc. R. Soc. A, 2088,
(2007)] and propose learning theory as a tool for exploring the power of
quantum computation.


  In this paper, we show that the linear dielectrics and magnetic materials in
matter obey a special kind of mathematical property known as Ces\`{a}ro
convergence. Then, we also show that the analytical continuation of the linear
permittivity \& permeability to a complex plane in terms of Riemann zeta
function. The metamaterials are fabricated materials with a negative refractive
index. These materials, in turn, depend on permittivity \& permeability of the
linear dielectrics and magnetic materials. Therefore, the Ces\`{a}ro
convergence property of the linear dielectrics and magnetic materials may be
used to fabricate the metamaterials.


  We present an Arakelov theoretic version of the deformation to the normal
cone. In particular, the geometric data is enriched with a deformation of a
Hermitian line bundle. We introduce numerical invariants called arithmetic
Hilbert invariants and prove the conservation of these invariants along the
deformation. In a following article, this conservation of number theorem will
allow a demonstration of the arithmetic Hilbert-Samuel theorem.


  The super-weak force is a minimal, anomaly-free U(1) extension of the
standard model, designed to explain the origin of (i) neutrino masses and
mixing matrix elements, (ii) dark matter, (iii) cosmic inflation, (iv)
stabilization of the electroweak vacuum and (v) leptogenesis. In this talk we
discuss the phenomenological status of the model and provide viable scenarios
for the physics of the items in this list.


  Online social networks are ubiquitous and user-friendly. Nevertheless, it is
vital to detect and moderate offensive content to maintain decency and empathy.
However, mining social media texts is a complex task since users don't adhere
to any fixed patterns. Comments can be written in any combination of languages
and many of them may be low-resource.
  In this paper, we present our system for the LT-EDI shared task on detecting
homophobia and transphobia in social media comments. We experiment with a
number of monolingual and multilingual transformer based models such as mBERT
along with a data augmentation technique for tackling class imbalance. Such
pretrained large models have recently shown tremendous success on a variety of
benchmark tasks in natural language processing. We observe their performance on
a carefully annotated, real life dataset of YouTube comments in English as well
as Tamil.
  Our submission achieved ranks 9, 6 and 3 with a macro-averaged F1-score of
0.42, 0.64 and 0.58 in the English, Tamil and Tamil-English subtasks
respectively. The code for the system has been open sourced.


  Self-replicability is the unique attribute observed in all the living
organisms and the question how the life was physically initiated could be
equivalent to the question how self-replicating informative polymers were
formed in the abiotic material world. It has been suggested that the present
DNA and proteins world was preceded by RNA world in which genetic information
of RNA molecules was replicated by the mutual catalytic function of RNA
molecules. However, the important question how the transition occurred from a
material world to the very early pre-RNA world remains unsolved experimentally
nor theoretically. We present an onset model of mutually catalytic
self-replicative systems formed in an assembly of polynucleotides. A
quantitative expression of the critical condition for the onset of growing
fluctuation towards self-replication in this model is obtained by analytical
and numerical calculations.


  Infectious diseases spread via pathogens such as viruses and bacteria.
Airborne pathogen transmission via droplets is an important mode for infectious
diseases. In this paper, the spreading mechanism of infectious diseases by
airborne pathogen transmission between two humans is modeled with a molecular
communication perspective. An end-to-end system model which considers the
pathogen-laden cough/sneeze droplets as the input and the infection state of
the human as the output is proposed. This model uses the gravity, initial
velocity and buoyancy for the propagation of droplets and a receiver model
which considers the central part of the human face as the reception interface
is proposed. Furthermore, the probability of infection for an uninfected human
is derived by modeling the number of propagating droplets as a random process.
The numerical results reveal that exposure time and sex of the human affect the
probability of infection. In addition, the social distance for a horizontal
cough should be at least 1.7 m and the safe coughing angle of a coughing human
to infect less people should be less than -25$^\circ$.


  We consider the linear vector space formed by the elements of the finite
fields $\mathbb{F}_q$ with $q=p^r$ over $\mathbb{F}_p$. Let
$\{a_1,\ldots,a_r\}$ be a basis of this space. Then the elements $x$ of
$\mathbb{F}_q$ have a unique representation in the form $\sum_{j=1}^r c_ja_j$
with $c_j\in\mathbb{F}_p$. Let $D_1,\ldots,D_r$ be subsets of $\mathbb{F}_p$.
We consider the set $W=W(D_1,\ldots,D_r)$ of elements of $\mathbb{F}_q$ such
that $c_j \in D_j$ for all $j=1,\ldots,r$. We give an estimate for the number
of squares in the set $W$ which implies an asymptotic formula for this quantity
in the case when the sets $D_1,\ldots,D_r$ are "large on average" and a
sufficient condition for the existence of squares in the set $W$.


  The perturbations of string-theoretic black holes are analyzed by
generalizing the method of Chandrasekhar. Attention is focussed on the case of
the recently considered charged string-theoretic black hole solutions as a
representative example. It is shown that string-intrinsic effects greatly alter
the perturbed motions of the string-theoretic black holes as compared to the
perturbed motions of black hole solutions of the field equations of general
relativity, the consequences of which bear on the questions of the scattering
behavior and the stability of string-theoretic black holes. The explicit forms
of the axial potential barriers surrounding the string-theoretic black hole are
derived. It is demonstrated that one of these, for sufficiently negative values
of the asymptotic value of the dilaton field, will inevitably become negative
in turn, in marked contrast to the potentials surrounding the static black
holes of general relativity. Such potentials may in principle be used in some
cases to obtain approximate constraints on the value of the string coupling
constant. The application of the perturbation analysis to the case of
two-dimensional string-theoretic black holes is discussed.


  This paper has inappropriate amounts of overlap with the following papers
also written by the authors or their collaborators: gr-qc/0608050,
gr-qc/0509047, gr-qc/0505078, gr-qc/0603108, gr-qc/0512080, gr-qc/0511030,
gr-qc/0606022, gr-qc/0603027, gr-qc/0603063, gr-qc/0607116, and others.


  A fundamental problem in astrophysics is the interaction between magnetic
turbulence and charged particles. It is now possible to use \emph{Ramaty High
Energy Solar Spectroscopic Imager (RHESSI)} observations of hard X-rays (HXR)
emitted by electrons to identify the presence of turbulence and to estimate the
magnitude of the magnetic field line diffusion coefficient at least in dense
coronal flaring loops.} {We discuss the various possible regimes of cross-field
transport of non-thermal electrons resulting from broadband magnetic turbulence
in coronal loops. The importance of the Kubo number $K$ as a governing
parameter is emphasized and results applicable in both the large and small Kubo
number limits are collected.} {Generic models, based on concepts and insights
developed in the statistical theory of transport, are applied to the coronal
loops and to the interpretation of hard X-ray imaging data in solar flares. The
role of trapping effects, which become important in the non-linear regime of
transport, is taken into account in the interpretation of the data.} For this
flaring solar loop, we constrain the ranges of parallel and perpendicular
correlation lengths of turbulent magnetic fields and possible Kubo numbers. We
show that a substantial amount of magnetic fluctuations with energy $\sim 1%$
(or more) of the background field can be inferred from the measurements of the
magnetic diffusion coefficient inside thick-target coronal loops.


  Liftoff variation causes errors in eddy current measurement of nonmagnetic
plates as well as magnetic plates. For nonmagnetic plates, previous work has
been carried out to address the issue. In this paper, we follow a similar
strategy, but try to reduce the lift-off effect on another index, zerocrossing
frequency for magnetic plates. This modified index, termed as the compensated
zero-crossing frequency, can be obtained from the measured multifrequency
inductance spectral data using the algorithm we developed in this paper. Since
the zero-crossing frequency can be compensated, the permeability of magnetic
plates can finally be predicted by deriving the relation between the
permeability and zero-crossing frequency from Dodd and Deeds method. We have
derived the method through mathematical manipulation and verified it by both
simulation and experimental data. The permeability error caused by liftoff can
be reduced within 7.5%.


  We report that Bi$_2$Se$_3$ thin films can be epitaxially grown on
SrTiO$_{3}$ substrates, which allow for very large tunablity in carrier density
with a back-gate. The observed low field magnetoconductivity due to weak
anti-localization (WAL) has a very weak gate-voltage dependence unless the
electron density is reduced to very low values. Such a transition in WAL is
correlated with unusual changes in longitudinal and Hall resistivities. Our
results suggest much suppressed bulk conductivity at large negative
gate-voltages and a possible role of surface states in the WAL phenomena. This
work may pave a way for realizing three-dimensional topological insulators at
ambient conditions.


  Let $k$ be a field of characteristic zero, let $G$ be a connected reductive
algebraic group over $k$ and let $\mathfrak{g}$ be its Lie algebra. Let $k(G)$,
respectively, $k(\mathfrak{g})$, be the field of $k$-rational functions on $G$,
respectively, $\mathfrak{g}$. The conjugation action of $G$ on itself induces
the adjoint action of $G$ on $\mathfrak{g}$. We investigate the question
whether or not the field extensions $k(G)/k(G)^G$ and
$k(\mathfrak{g})/k(\mathfrak{g})^G$ are purely transcendental. We show that the
answer is the same for $k(G)/k(G)^G$ and $k(\mathfrak{g})/k(\mathfrak{g})^G$,
and reduce the problem to the case where $G$ is simple. For simple groups we
show that the answer is positive if $G$ is split of type ${\sf A}_{n}$ or ${\sf
C}_n$, and negative for groups of other types, except possibly ${\sf G}_{2}$. A
key ingredient in the proof of the negative result is a recent formula for the
unramified Brauer group of a homogeneous space with connected stabilizers.
  As a byproduct of our investigation we give an affirmative answer to a
question of Grothendieck about the existence of a rational section of the
categorical quotient morphism for the conjugating action of $G$ on itself. The
results and methods of this paper have played an important part in recent A.
Premet's negative solution (arxiv:0907.2500) of the Gelfand--Kirillov
conjecture for finite-dimensional simple Lie algebras of every type, other than
${\sf A}_n$, ${\sf C}_n$, and ${\sf G}_2$.


  The electronic structure of Cu hexafluoroacetylacetonate, crystallized with a
stable nitronyl nitroxide radical [Ovcharenko et al., Russ. Chem. Bull. 53,
2406 (2004)], is calculated from first principles within the density functional
theory using the SIESTA method, in two magnetic configurations reflecting
parallel or antiparallel setting of S=1/2 spins of Cu(II) ions to those of
organic radicals. For a given (high-temperature) crystal structure, the
interaction is found to be predominanty antiferromagnetic, and its magnitude
estimated to be 67 inv.cm. This preference is discussed in terms of calculated
electronic properties (densities of states, molecular orbitals).


  This paper studies the Nash stability in hedonic coalition formation games.
We address the following issue: for a general problem formulation, is there any
utility allocation method ensuring a Nash-stable partition? We propose the
definition of the Nash-stable core. We study the conditions for having a
non-empty Nash-stable core. More precisely, we show how relaxed efficiency in
utility sharing method allows to ensure a non-empty Nash-stable core.


  We construct a semiparametric estimator in case-control studies where the
gene and the environment are assumed to be independent. A discrete or
continuous parametric distribution of the genes is assumed in the model. A
discrete distribution of the genes can be used to model the mutation or
presence of certain group of genes. A continuous distribution allows the
distribution of the gene effects to be in a finite-dimensional parametric
family and can hence be used to model the gene expression levels. We leave the
distribution of the environment totally unspecified. The estimator is derived
through calculating the efficiency score function in a hypothetical setting
where a close approximation to the samples is random. The resulting estimator
is proved to be efficient in the hypothetical situation. The efficiency of the
estimator is further demonstrated to hold in the case-control setting as well.


  We give a complete answer for the existence of Kawamata type semiorthogonal
decompositions of derived categories of nodal del Pezzo threefolds. More
precisely, we show that nodal non smooth $V_d$ with $1\leq d \leq 4$ have no
Kawamata type decomposition and that all nodal $V_5$ admit a Kawamata
decomposition. For the proof we go through the classification of singular del
Pezzo threefolds, compute divisor class groups of nodal del Pezzo threefolds of
small degree and use projection from a line to construct Kawamata
semiorthogonal decompositions for $d = 5$. In the $V_6$ case such a
decomposition has been previously constructed by Kawamata.


  Numerical nonlinear algebra is applied to maximum likelihood estimation for
Gaussian models defined by linear constraints on the covariance matrix. We
examine the generic case as well as special models (e.g. Toeplitz, sparse,
trees) that are of interest in statistics. We study the maximum likelihood
degree and its dual analogue, and we introduce a new software package
LinearCovarianceModels.jl for solving the score equations. All local maxima can
thus be computed reliably. In addition we identify several scenarios for which
the estimator is a rational function.


  The hypothesis of an extended red emission (ERE) in diffuse Galactic light
(DGL) has been put forward in 1998 by Gordon, Witt and Friedmann who found that
scattered starlight was not enough to explain the amount of DGL in the R band,
in some high Galactic latitude directions. This paper re-investigates, for high
Galactic latitudes, the brightnesses and colours of DGL, integrated star and
galaxy light (ISGL), and of the total extrasolar light (ISGL+DGL) measured by
Pioneer. Under the traditional assumption that DGL is forward scattering of
background starlight by interstellar dust on the line of sight, ISGL and
Pioneer have very close colours, as it is found by Gordon, Witt and Friedmann.
Pioneer observations at high |b| thus accept an alternative and simple
interpretation, with no involvement of ERE in DGL.


  This paper presents a multi-agent reinforcement learning algorithm to
represent strategic bidding behavior in freight transport markets. Using this
algorithm, we investigate whether feasible market equilibriums arise without
any central control or communication between agents. Studying behavior in such
environments may serve as a stepping stone towards self-organizing logistics
systems like the Physical Internet. We model an agent-based environment in
which a shipper and a carrier actively learn bidding strategies using policy
gradient methods, posing bid- and ask prices at the individual container level.
Both agents aim to learn the best response given the expected behavior of the
opposing agent. A neutral broker allocates jobs based on bid-ask spreads.
  Our game-theoretical analysis and numerical experiments focus on behavioral
insights. To evaluate system performance, we measure adherence to Nash
equilibria, fairness of reward division and utilization of transport capacity.
We observe good performance both in predictable, deterministic settings (~95%
adherence to Nash equilibria) and highly stochastic environments (~85%
adherence). Risk-seeking behavior may increase an agent's reward share, as long
as the strategies are not overly aggressive. The results suggest a potential
for full automation and decentralization of freight transport markets.


  Determination of whether the Harrison--Zel'dovich spectrum for primordial
scalar perturbations is consistent with observations is sensitive to
assumptions about the reionization scenario. In light of this result, we
revisit constraints on inflationary models using more general reionization
scenarios. While the bounds on the tensor-to-scalar ratio are largely
unmodified, when different reionization schemes are addressed, hybrid models
are back into the inflationary game. In the general reionization picture, we
reconstruct both the shape and amplitude of the inflaton potential. We find a
broader spectrum of potential shapes when relaxing the simple reionization
restriction. An upper limit of $10^{16}$ GeV to the amplitude of the potential
is found, regardless of the assumptions on the reionization history.


  In this work, we introduce the unsupervised Optimum-Path Forest (OPF)
classifier for learning visual dictionaries in the context of Barrett's
esophagus (BE) and automatic adenocarcinoma diagnosis. The proposed approach
was validated in two datasets (MICCAI 2015 and Augsburg) using three different
feature extractors (SIFT, SURF, and the not yet applied to the BE context
A-KAZE), as well as five supervised classifiers, including two variants of the
OPF, Support Vector Machines with Radial Basis Function and Linear kernels, and
a Bayesian classifier. Concerning MICCAI 2015 dataset, the best results were
obtained using unsupervised OPF for dictionary generation using supervised OPF
for classification purposes and using SURF feature extractor with accuracy
nearly to 78% for distinguishing BE patients from adenocarcinoma ones.
Regarding the Augsburg dataset, the most accurate results were also obtained
using both OPF classifiers but with A-KAZE as the feature extractor with
accuracy close to 73%. The combination of feature extraction and
bag-of-visual-words techniques showed results that outperformed others obtained
recently in the literature, as well as we highlight new advances in the related
research area. Reinforcing the significance of this work, to the best of our
knowledge, this is the first one that aimed at addressing computer-aided BE
identification using bag-of-visual-words and OPF classifiers, being this
application of unsupervised technique in the BE feature calculation the major
contribution of this work. It is also proposed a new BE and adenocarcinoma
description using the A-KAZE features, not yet applied in the literature.


  Motivated by the various theoretical studies regarding the efficient
capturing of dark matter by neutron stars, we explore the possible indirect
effects of captured dark matter on the cooling mechanism of a neutron star. The
equation of states for different configurations of dark matter admixed star at
finite temperature is obtained using the relativistic mean-field formalism with
the IOPB-I parameter set. We show that the variation in the dark matter
momentum vastly modifies the neutrino emissivity through specific neutrino
generating processes of the star. The specific heat and the thermal
conductivity of a dark matter admixed star have also been investigated to
explore the propagation of cooling waves in the interior of the star. The
dependence of theoretical surface temperature cooling curves on the equation of
state and chemical composition of the stellar matter has also been discussed
along with the observational data of thermal radiation from various sources. We
observed that the dark matter admixed canonical stars with $k_{f}^{\rm DM} >
0.04$ comply with the fast cooling scenario. Further, the metric for internal
thermal relaxation epoch has also been calculated with different dark matter
momentum and we deduced that increment of dark matter segment amplify the
cooling and internal relaxation rates of the star.


  The first ever numerical solution of five-body Faddeev-Yakubovsky equations
is presented in this work. Modern realistic Nucleon-Nucleon Hamiltonians have
been tested when describing low energy elastic neutron scattering on $^4$He
nucleus. Obtained results have been compared with those available in the
literature and based on solution of the Schr\"odinger equation.


  A semi-empirical three-dimensional model of turbulence in the approximation
of the far turbulent wake behind a body of revolution in a passive stratified
medium is considered. The sought quantities are the kinetic turbulent energy,
kinetic energy dissipation rate, averaged density defect and density
fluctuation variance. The full group of transformations admitted by this model
is found. The model is reduced to the system of the ordinary differential
equations due to similarity presentations obtained and B-determining equations
method. System of ordinary differential equations satisfying natural boundary
conditions was solved numerically. The solutions obtained agree with
experimental data.


  Rejoinder to "Likelihood Inference for Models with Unobservables: Another
View" by Youngjo Lee and John A. Nelder [arXiv:1010.0303]


  We investigate supersymmetric QCD with N_c+1 flavors using an extension of
the recently proposed relation between gauge theories and matrix models. The
impressive agreement between the two sides provides a beautiful confirmation of
the extension of the gauge theory-matrix model relation to this case.


  We prove uniqueness of tangent cones for forced mean curvature flow, at both
closed self-shrinkers and round cylindrical self-shrinkers, in any codimension.
The corresponding results for mean curvature flow in Euclidean space were
proven by Schulze and Colding-Minicozzi respectively. We adapt their methods to
handle the presence of the forcing term, which vanishes in the blow-up limit
but complicates the analysis along the rescaled flow. Our results naturally
include the case of mean curvature flows in Riemannian manifolds.


  We present an updated version of the ABMP16 nucleon PDFs, which is tuned by
using recent precise data on $W$- and $Z/\gamma^*$-production at the LHC and
the final HERA data on DIS $c$- and $b$-quark production and by imposing a
stringent $Q^2$-cut on the inclusive DIS data in order to avoid the impact of
higher twist terms at small $x$ at HERA. The new $W$- and $Z$-boson production
data, in particular the updated version of the ATLAS data at the c.m.s. energy
7 TeV, are well accommodated into the present fit. The strange sea distribution
obtained is consistent with the average of the up and down quark ones at small
$x$. However, it is still suppressed with respect to the non-strange one by a
factor of $\sim 0.5$ at moderate $x$. The small-$x$ gluon distribution is
enhanced as compared to the previous ABMP16 fit, in line with updated data on
the DIS $c$-quark production. Finally, a good description of the non-resonant
$\gamma^*/Z$-production data, which are included into the ABM analysis for the
first time, is achieved provided the photon-initiated lepton pair production is
taken into account.


  Presented here is a simple method for cross-validated genome-wide association
studies (cvGWAS). Focusing on phenotype prediction, the method is able to
reveal a significant amount of missing heritability by properly selecting a
small number of loci with implicit predictive ability. The results provide new
insights into the missing heritability problem and the underlying genetic
architecture of complex traits.


  We investigate the effect of strong magnetic fields on the adiabatic radial
oscillations of hadronic stars. We describe magnetized hadronic matter within
the framework of the relativistic nonlinear Walecka model and integrate the
equations of relativistic radial oscillations to determine the fundamental
pulsation mode. We consider that the magnetic field increases, in a density
dependent way, from the surface, where it has a typical magnetar value of
$10^{15}$ G, to the interior of the star where it can be as large as $3 \times
10^{18}$ G. We show that magnetic fields of the order of $10^{18}$ G at the
stellar core produce a significant change in the frequency of neutron star
pulsations with respect to unmagnetized objects. If radial pulsations are
excited in magnetar flares, they can leave an imprint in the flare lightcurves
and open a new window for the study of highly magnetized ultradense matter.


  Deep convolutional neural networks have shown outstanding performance in
medical image segmentation tasks. The usual problem when training supervised
deep learning methods is the lack of labeled data which is time-consuming and
costly to obtain. In this paper, we propose a novel uncertainty-guided
semi-supervised learning based on a student-teacher approach for training the
segmentation network using limited labeled samples and a large number of
unlabeled images. First, a teacher segmentation model is trained from the
labeled samples using Bayesian deep learning. The trained model is used to
generate soft segmentation labels and uncertainty maps for the unlabeled set.
The student model is then updated using the softly segmented samples and the
corresponding pixel-wise confidence of the segmentation quality estimated from
the uncertainty of the teacher model using a newly designed loss function.
Experimental results on a retinal layer segmentation task show that the
proposed method improves the segmentation performance in comparison to the
fully supervised approach and is on par with the expert annotator. The proposed
semi-supervised segmentation framework is a key contribution and applicable for
biomedical image segmentation across various imaging modalities where access to
annotated medical images is challenging


  Within quantum mechanics which works with parity-pseudo-Hermitian
Hamiltonians we study the tunneling in a symmetric double well formed by two
delta functions with complex conjugate strengths. The model is exactly solvable
and exhibits several interesting features. Besides an amazingly robust absence
of any PT symmetry breaking, we observe a quasi-degeneracy of the levels which
occurs all over the energy range including the high-energy domain. This pattern
is interpreted as a manifestation of certain "quantum beats".


  We study the dual model with capital injection under the additional condition
that the dividend strategy is absolutely continuous. We consider a
refraction-reflection strategy that pays dividends at the maximal rate whenever
the surplus is above a certain threshold, while capital is injected so that it
stays positive. The resulting controlled surplus process becomes the spectrally
positive version of the refracted-reflected process recently studied by P\'erez
and Yamazaki (2015). We study various fluctuation identities of this process
and prove the optimality of the refraction-reflection strategy. Numerical
results on the optimal dividend problem are also given.


  We study the final equilibrium states of the Parker instability arising from
an initially unstable cylindrical equilibrium configuration of gas in the
presence of a radial gravitational field and a longitudinal magnetic field. The
aim of this work is to compare the properties of the nonlinear final equilibria
with those found in a system with Cartesian geometry. Maps of the density and
magnetic field lines, when the strength of the gravitational field is constant,
are given in both geometries. In the axisymmetric model, the magnetic field
tends to expand in radius, forming magnetic arcades, while knots of gas are
formed because the plasma drains radially and strangulates the magnetic field
lines, leading to the formation of magnetic bottlenecks. We find that the
magnetic buoyancy and the drainage of gas along field lines are less efficient
under axial symmetry than in a Cartesian atmosphere. As a consequence, the
column density enhancement arising in gas condensations in the
axially-symmetric model is smaller than in Cartesian geometry. The
magnetic-to-gas pressure ratio in the final state takes more extreme values in
the Cartesian model. Models with non-uniform radial gravity are also discussed.


  We present atmospheric parameters and abundances for chemical elements from
carbon to barium in metal-poor stars in Segue 1 (seven stars), Coma Berenices
(three stars), and Triangulum II (one star) ultra-faint dwarf galaxies (UFDs).
The effective temperatures rely on new photometric observations in the visible
and infra-red bands, obtained with the 2.5 m telescope of the SAI MSU Caucasian
observatory. Abundances of up to fourteen chemical elements were derived under
the non-local thermodynamic equilibrium (NLTE) line formation, and LTE
abundances were obtained for up to five more elements. For the first time we
present abundance of oxygen in Seg 1 S1 and S4, silicon in ComaBer S2 and Tri
II S40, potassium in Seg 1 S1-S6 and ComaBer S1-S3, and barium in Seg 1 S7.
Three stars in Segue 1, two stars in Coma Berenices, and Triangulum II star
have very low [Na/Mg] of -1.08 to -1.67 dex, which is usually attributed in the
literature to an odd-even effect produced by nucleosynthesis in massive
metal-free stars. We interpret this chemical property as a footprint of first
stars, which is not blurred due to a small number of nucleosynthesis events
that contributed to chemical abundance patterns of the sample stars. Our NLTE
abundances of Sr and Ba in Coma Berenices, Segue 1, and Triangulum II report on
lower [Sr/Ba] abundance ratio in the UFDs compared to that in classical dwarf
spheroidal galaxies and the Milky Way halo. However, in UFDs, just as in
massive galaxies, [Sr/Ba] is not constant and it can be higher than the pure
r-process ratio. We suggest a hypothesis of Sr production in metal-poor
binaries at the earliest epoch of galactic evolution.


  We studied the stellar populations of 40 early-type galaxies using medium
resolution long-slit spectroscopy along their major axes (and along the minor
axis for two of them), from 10^7 Msol to 10^12 Msol (-9.2 > M_B > -22.4 mag).
All the studied galaxies lie on the mass-metallicity and age-mass relations.
The transition type dwarfs deviate from the latter relation having younger mean
age, and the low-mass dwarf spheroidals have older ages, marking a
discontinuity in the relation, possibly due to selection effects.
  In all mass regimes, the mean metallicity gradients are approximately -0.2
and the mean age gradients +0.1 dex per decade of radius. The individual
gradients are widely spread: $ -0.1 < \nabla_{\rm Age} < 0.4 $ and $-0.54 <
\nabla_{[{\rm Fe/H}]} < +0.2 $. We do not find evidence for a correlation
between the metallicity gradient and luminosity, velocity dispersion, central
age or age gradient. Likewise, we do not find a correlation between the age
gradient and any other parameter in bright early-type galaxies. In faint
early-types with $M_B \gtrsim -17$ mag, on the other hand, we find a
correlation between the age gradient and luminosity: the age gradient becomes
more positive for fainter galaxies.
  We conclude that various physical mechanisms can lead to similar gradients
and that these gradients are robust against the environmental effects. In
particular, the gradients observed in dwarfs galaxies certainly survived the
transformation of the progenitors through tidal harassment or/and ram-pressure
stripping. The diversity of metallicity gradients amongst dwarf elliptical
galaxies may reflect a plurality of progenitors' morphologies. The dwarfs with
steep metallicity gradients could have originated from blue compact dwarfs and
those with flat profiles from dwarf irregulars and late type spirals.
(Abridged)


  Magnetic and lattice excitations in the quantum antiferromagnet
(C$_4$H$_{12}$N$_2$)Cu$_2$Cl$_6$ (PHCC) are studied across two pressure-induced
phase transition at $P_c=4.3~\mathrm{kbar}$ and $P_1=13.4~\mathrm{kbar}$ using
Raman spectroscopy. It is confirmed that neither transition is a result of a
structural transformation. Magnetic scattering is detected. It shows a
pronounced pressure dependence and undergoes substantial changes at both
transitions. The results are in clear contradiction with previous neutron
studies, which detected only minor changes of the magnon spectrum at $P_1$. A
number of phonons show anomalous frequency shifts at low temperatures. This
effect is pressure dependent and for two of the observed phonons dramatically
reverses sign at around $P_1$. The anomalous behavior is attributed to strong
magnetoelastic coupling in PHCC.


  A small quantum scattering system (the microsystem) is studied in interaction
with a large quantum system (the macrosystem) described by unknown stochastic
variables. The interaction between the two systems is diagonal for the
microsystem in a certain basis, and it leads to an imprint on the macrosystem.
Moreover, the interaction is assumed to involve only small transfers of energy
and momentum between the two systems (as compared to typical energies/momenta
within the microsystem). This makes it suitable to carry out the analysis in
scattering theory, where the transition amplitude for the whole system
factorizes. The interaction taking place within the macrosystem is assumed to
depend on the stochastic variables in such a way that, on the average, no
particular channel is favoured. The result is then, in the thermodynamic limit
of the macrosystem, that the whole system bifurcates and the microsystem ends
up in a state described by one of the basis vectors (in the mentioned basis).
The macrosystem ends up in an entangled state tied to this basis vector. For
the ensemble of macrosystems, the interaction with the microsystem leads, on
the average, to the usual decoherence and diagonal density matrix for the
microsystem. The macrosystem can be interpreted as representing a measurement
device for performing a measurement on the microsystem. The whole discussion is
carried out within quantum mechanics itself without any modification or
generalization.


  Magnetic resonance imaging (MRI) is a widely used biomedical imaging modality
that derives much of its contrast from microscale magnetic field gradients in
biological tissues. However, the connection between these sub-voxel field
patterns and MRI contrast has not been studied experimentally. Here, we
describe a new method to map subcellular magnetic fields in mammalian cells and
tissues using nitrogen vacancy diamond magnetometry and connect these maps to
voxel-scale MRI contrast, providing insights for in vivo imaging and contrast
agent design.


  In this study, we have proposed a new type of tactile sensor that is capable
of detecting the stiffness of soft objects. The sensor consists of a brass
cylinder with an axial bore. An iron core can easily move inside the bore.
Three peripheral bobbins were machined in the cylinder around which three coils
have been wound. One of the coils was excited with an alternating current which
caused a voltage to be induced in two other coils. A return spring was used to
return the core to its initial position after it has been moved. The sensor was
pressed against the surface of the object whose stiffness was going to be
measured. The position of the core in this state was depended on the stiffness
of the given object and the spring constant and was measured by measuring the
change in the induced voltage in secondary coils. The proposed sensor was
capable of measuring two contact parameters namely the applied force and the
stiffness of the object. Using the data of this sensor, three different
objects, made of polyurethane, silicon rubber and paraffin gel were
discriminated. Thus, this sensor could be used in robot hands and minimally
invasive surgery tools to improve their operation.


  We report on a new constraint on gravitylike short-range forces, in which the
interaction charge is mass, obtained by measuring the angular distribution of 5
A neutrons scattering off atomic xenon gas. Around 10^7 scattering events were
collected at the 40 m small angle neutron scattering beam line located at the
HANARO research reactor of the Korean Atomic Energy Research Institute. The
extracted coupling strengths of new forces in the Yukawa-type parametrization
are g^2 = (0.2 \pm 6.8 \pm 2.0) \times 10^-15 GeV^2 and g^2 = (-5.3 \pm 9.0 +
2.7 -2.8) \times 10^-17 GeV^2 for interaction ranges of 0.1 and 1.0 nm,
respectively. These strengths correspond to 95% confidence level limits of g^2
< (1.4 \pm 0.2) \times 10^-14 GeV^-2 and g^2 < (1.3 \pm 0.2) \times 10^-16
GeV^-2, improving the current limits for interaction ranges between 4 and 0.04
nm by a factor of up to 10.


  We study the problem of distribution testing when the samples can only be
accessed using a locally differentially private mechanism and focus on two
representative testing questions of identity (goodness-of-fit) and independence
testing for discrete distributions. We are concerned with two settings: First,
when we insist on using an already deployed, general-purpose locally
differentially private mechanism such as the popular RAPPOR or the recently
introduced Hadamard Response for collecting data, and must build our tests
based on the data collected via this mechanism; and second, when no such
restriction is imposed, and we can design a bespoke mechanism specifically for
testing. For the latter purpose, we introduce the Randomized Aggregated Private
Testing Optimal Response (RAPTOR) mechanism which is remarkably simple and
requires only one bit of communication per sample.
  We propose tests based on these mechanisms and analyze their sample
complexities. Each proposed test can be implemented efficiently. In each case
(barring one), we complement our performance bounds for algorithms with
information-theoretic lower bounds and establish sample optimality of our
proposed algorithm. A peculiar feature that emerges is that our sample-optimal
algorithm based on RAPTOR uses public-coins, and any test based on RAPPOR or
Hadamard Response, which are both private-coin mechanisms, requires
significantly more samples.


  We consider the nonlinear Klein-Gordon equation
$\partial_t^2u(x,t)-\partial_x^2u(x,t)+\alpha u(x,t)=\pm|u(x,t)|^{p-1}u(x,t)$
on a periodic metric graph (necklace graph) for $p>1$ with Kirchhoff conditions
at the vertices. Under suitable assumptions on the frequency we prove the
existence and regularity of infinitely many spatially localized time-periodic
solutions (breathers) by variational methods. We compare our results with
previous results obtained via spatial dynamics and center manifold techniques.
Moreover, we deduce regularity properties of the solutions and show that they
are weak solutions of the corresponding initial value problem. Our approach
relies on the existence of critical points for indefinite functionals, the
concentration compactness principle, and the proper set-up of a functional
analytic framework. Compared to earlier work for breathers using variational
techniques, a major improvement of embedding properties has been achieved. This
allows in particular to avoid all restrictions on the exponent $p>1$ and to
achieve higher regularity.


  We report localization of fractional quantum Hall (QH) quasiparticles on
graphene antidots. By studying coherent tunneling through the localized QH edge
modes on the antidot, we measured the QH quasiparticle charges to be
approximately $\pm e/3$ at fractional fillings of $\nu = \pm 1/3$. The Dirac
spectrum in graphene allows large energy scales and robust quasiparticle
localization against thermal excitation. The capability of localizing
fractional quasiparticles on QH antidots brings promising opportunities for
realizing anyon braiding and novel quantum electronics.


  We introduce the Treebank of Learner English (TLE), the first publicly
available syntactic treebank for English as a Second Language (ESL). The TLE
provides manually annotated POS tags and Universal Dependency (UD) trees for
5,124 sentences from the Cambridge First Certificate in English (FCE) corpus.
The UD annotations are tied to a pre-existing error annotation of the FCE,
whereby full syntactic analyses are provided for both the original and error
corrected versions of each sentence. Further on, we delineate ESL annotation
guidelines that allow for consistent syntactic treatment of ungrammatical
English. Finally, we benchmark POS tagging and dependency parsing performance
on the TLE dataset and measure the effect of grammatical errors on parsing
accuracy. We envision the treebank to support a wide range of linguistic and
computational research on second language acquisition as well as automatic
processing of ungrammatical language. The treebank is available at
universaldependencies.org. The annotation manual used in this project and a
graphical query engine are available at esltreebank.org.


  The ongoing discussion whether thermodynamic properties can be extracted from
a (possibly approximate) quantum mechanical time evolution using time averages
is fed with an instructive example. It is shown for the harmonic oscillator how
the Hilbert space or an appropriately defined phase space must be populated in
terms of coherent states in order to obtain the quantum result respectively the
classical one.


  In this paper, we propose a feasible scheme for generating the
Schr\"{o}dinger cat states of a macroscopic mechanical resonator in pulsed
cavity optomechanics. Starting with cooling the mechanical oscillator to its
ground state, a red and a blue pulses with different powers are simultaneously
employed to drive the cavity to achieve squeezed mechanical states.
Subsequently, a second red pulse is utilized to generate the macroscopic
mechanical quantum superpositions, conditioned on the detection of cavity
output photons. Finally, after being stored in the resonator for a period of
time, the mechanical state is mapped, with a third red pulse, to the cavity
output field used for state verification. Our approach is generic and can also
be used to produce other kinds of non-Gaussian mechanical states, like
optical-catalysis nonclassical states.


  In this paper we study the existence of multiple nontrivial positive weak
solutions to the following system of problems. \begin{align*} \begin{split}
-\Delta_{p}u-\Delta_q u &= \lambda
f(x)|u|^{r-2}u+\nu\frac{1-\alpha}{2-\alpha-\beta}h(x)
|u|^{-\alpha}|v|^{1-\beta}\,\,\mbox{in}\,\,\Omega,\\ -\Delta_{p}v-\Delta_q v &=
\mu g(x)|v|^{r-2}v+\nu\frac{1-\beta}{2-\alpha-\beta}h(x)
|u|^{1-\alpha}|v|^{-\beta}\,\,\mbox{in}\,\,\Omega,\\
u,v&>0\,\,\mbox{in}\,\,\Omega,\\ u= v &= 0\,\, \mbox{on}\,\, \partial\Omega
\end{split} \end{align*} where (C):~$0<\alpha<1,\;0<\beta<1,$
$2-\alpha-\beta<q<\frac{N(p-1)}{N-p}<p<r<p^*$, with $p^*=\frac{Np}{N-p}$. We
will guarantee the existence of a solution in the Nehari manifold. Further by
using the Lusternik-Schnirelman category we will prove the existence of at
least $\text{cat}(\Omega)+1$ number of solutions.


  Research on intelligent tutoring systems has been exploring data-driven
methods to deliver effective adaptive assistance. While much work has been done
to provide adaptive assistance when students seek help, they may not seek help
optimally. This had led to the growing interest in proactive adaptive
assistance, where the tutor provides unsolicited assistance upon predictions of
struggle or unproductivity. Determining when and whether to provide
personalized support is a well-known challenge called the assistance dilemma.
Addressing this dilemma is particularly challenging in open-ended domains,
where there can be several ways to solve problems. Researchers have explored
methods to determine when to proactively help students, but few of these
methods have taken prior hint usage into account. In this paper, we present a
novel data-driven approach to incorporate students' hint usage in predicting
their need for help. We explore its impact in an intelligent tutor that deals
with the open-ended and well-structured domain of logic proofs. We present a
controlled study to investigate the impact of an adaptive hint policy based on
predictions of HelpNeed that incorporate students' hint usage. We show
empirical evidence to support that such a policy can save students a
significant amount of time in training, and lead to improved posttest results,
when compared to a control without proactive interventions. We also show that
incorporating students' hint usage significantly improves the adaptive hint
policy's efficacy in predicting students' HelpNeed, thereby reducing training
unproductivity, reducing possible help avoidance, and increasing possible help
appropriateness (a higher chance of receiving help when it was likely to be
needed). We conclude with suggestions on the domains that can benefit from this
approach as well as the requirements for adoption.


  We have realised a 4-beam pyramidal magneto-optical trap ideally suited for
future microfabrication. Three mirrors split and steer a single incoming beam
into a tripod of reflected beams, allowing trapping in the four-beam overlap
volume. We discuss the influence of mirror angle on cooling and trapping,
finding optimum efficiency in a tetrahedral configuration. We demonstrate the
technique using an ex-vacuo mirror system to illustrate the previously
inaccessible supra-plane pyramid MOT configuration. Unlike standard pyramidal
MOTs both the pyramid apex and its mirror angle are non-critical and our MOT
offers improved molasses free from atomic shadows in the laser beams. The MOT
scheme naturally extends to a 2-beam refractive version with high optical
access. For quantum gas experiments, the mirror system could also be used for a
stable 3D tetrahedral optical lattice.


  Despite their importance in many biological, ecological and physical
processes, microorganismal fluid flows under tight confinement have not been
investigated experimentally. Strong screening of Stokelets in this geometry
suggests that the flow fields of different microorganisms should be universally
dominated by the 2D source dipole from the swimmer's finite-size body.
Confinement therefore is poised to collapse differences across microorganisms,
that are instead well-established in bulk. Here we combine experiments and
theoretical modelling to show that, in general, this is not correct. Our
results demonstrate that potentially minute details like microswimmers'
spinning and the physical arrangement of the propulsion appendages have in fact
a leading role in setting qualitative topological properties of the
hydrodynamic flow fields of micro-swimmers under confinement. This is well
captured by an effective 2D model, even under relatively weak confinement.
These results imply that active confined hydrodynamics is much richer than in
bulk, and depends in a subtle manner on size, shape and propulsion mechanisms
of the active components.


  Free massive higher spin fields in weak background gravitational fields are
discussed. Contrary to the spin one case, higher spin fields should have
nontrivial non-minimal couplings to the curvature. A precise analysis is given
for the spin 2 case, and it is shown that two conditions should be satisfied
among five non-minimal coupling constants, which we derive both in the
Hamiltonian and Lagrangian formalisms. It is checked that the linearized limit
of the massive gravity theory indeed has the non-minimal couplings that satisfy
the conditions. We also discuss the form of the non-minimal couplings for the
spin 3 case.


  We perform a von Neumann stability analysis on a common discretization of the
Einstein equations. The analysis is performed on two formulations of the
Einstein equations, namely, the standard ADM formulation and the
conformal-traceless (CT) formulation. The eigenvalues of the amplification
matrix are computed for flat space as well as for a highly nonlinear plane wave
exact solution. We find that for the flat space initial data, the condition for
stability is simply $\frac {\Delta t}{\Delta z} \leq 1$. However, a von Neumann
analysis for highly nonlinear plane wave initial data shows that the standard
ADM formulation is unconditionally unstable, while the conformal-traceless (CT)
formulation is stable for $0.25 \leq \frac {\Delta t}{\Delta z} < 1$.


  In this addendum we present the stand-alone C++ program MSSMEFTHiggs3L, which
implements the 3-loop FlexibleEFTHiggs approach to calculate the lightest
CP-even Higgs boson pole mass in the real MSSM at N$^3$LL and N$^3$LO with
$x_q$ resummation, presented in JHEP 07 (2020) 197 (arXiv:2003.04639).


  We prove Strichartz estimates on general flat d-torus for arbitrary d. Using
these estimates, we prove local wellposedness for the cubic nonlinear
Schr\"odinger equations in appropriate Sobolev spaces. In dimensions 2 and 3,
we prove polynomial bounds on the possible growth of Sobolev norms of smooth
solutions.


  We study estimators with generalized lasso penalties within the computational
sufficiency framework introduced by Vu (2018, arXiv:1807.05985). By
representing these penalties as support functions of zonotopes and more
generally Minkowski sums of line segments and rays, we show that there is a
natural reflection group associated with the underlying optimization problem. A
consequence of this point of view is that for large classes of estimators
sharing the same penalty, the penalized least squares estimator is
computationally minimal sufficient. This means that all such estimators can be
computed by refining the output of any algorithm for the least squares case. An
interesting technical component is our analysis of coordinate descent on the
dual problem. A key insight is that the iterates are obtained by reflecting and
averaging, so they converge to an element of the dual feasible set that is
minimal with respect to a ordering induced by the group associated with the
penalty. Our main application is fused lasso/total variation denoising and
isotonic regression on arbitrary graphs. In those cases the associated group is
a permutation group.


  Artificial neural network (ANN) provides superior accuracy for nonlinear
alternating current (AC) state estimation (SE) in smart grid over traditional
methods. However, research has discovered that ANN could be easily fooled by
adversarial examples. In this paper, we initiate a new study of adversarial
false data injection (FDI) attack against AC SE with ANN: by injecting a
deliberate attack vector into measurements, the attacker can degrade the
accuracy of ANN SE while remaining undetected. We propose a population-based
algorithm and a gradient-based algorithm to generate attack vectors. The
performance of these algorithms is evaluated through simulations on IEEE 9-bus,
14-bus and 30-bus systems under various attack scenarios. Simulation results
show that DE is more effective than SLSQP on all simulation cases. The attack
examples generated by DE algorithm successfully degrade the ANN SE accuracy
with high probability.


  We compute the fake degrees of representations of classical Weyl groups in
terms of domino tableaux.


  Optimizing charging protocols is critical for reducing battery charging time
and decelerating battery degradation in applications such as electric vehicles.
Recently, reinforcement learning (RL) methods have been adopted for such
purposes. However, RL-based methods may not ensure system (safety) constraints,
which can cause irreversible damages to batteries and reduce their lifetime. To
this end, this work proposes an adaptive and safe RL framework to optimize fast
charging strategies while respecting safety constraints with a high
probability. In our method, any unsafe action that the RL agent decides will be
projected into a safety region by solving a constrained optimization problem.
The safety region is constructed using adaptive Gaussian process (GP) models,
consisting of static and dynamic GPs, that learn from online experience to
adaptively account for any changes in battery dynamics. Simulation results show
that our method can charge the batteries rapidly with constraint satisfaction
under varying operating conditions.


  We consider T--shaped, two--dimensional quantum waveguides containing
attractive or repulsive impurities with a smooth, realistic shape, and study
how the resonance behavior of the total conductance depends upon the strength
of the defect potential and the geometry of the device. The resonance
parameters are determined locating the relevant S-matrix poles in the Riemann
energy surface. The total scattering operator is obtained from the S-matrices
of the various constituent segments of the device through the *-product
composition rule. This allows for a numerically stable evaluation of the
scattering matrix and of the resonance parameters.


  Starting with a subclass of the four-dimensional spaces possessing two
commuting Killing vectors and a non-trivial Killing tensor, we fully integrate
Einstein's vacuum equation with a cosmological constant. Although most of the
solutions happen to be already known, we have found a solution that, as far as
we could search for, has not been attained before. We also characterize the
geometric properties of this new solution, it is a Kundt spacetime of Petrov
type II possessing a null Killing vector field and an isometry algebra that is
three-dimensional and abelian. In particular, such solution becomes a pp-wave
spacetime when the cosmological constant is set to zero.


  Stardust grains recovered from meteorites provide high-precision snapshots of
the isotopic composition of the stellar environment in which they formed.
Attributing their origin to specific types of stars, however, often proves
difficult. Intermediate-mass stars of 4-8 solar masses are expected to
contribute a large fraction of meteoritic stardust. However, no grains have
been found with characteristic isotopic compositions expected from such stars.
This is a long-standing puzzle, which points to serious gaps in our
understanding of the lifecycle of stars and dust in our Galaxy. Here we show
that the increased proton-capture rate of $^{17}$O reported by a recent
underground experiment leads to $^{17}$O/$^{16}$O isotopic ratios that match
those observed in a population of stardust grains, for proton-burning
temperatures of 60-80 million K. These temperatures are indeed achieved at the
base of the convective envelope during the late evolution of intermediate-mass
stars of 4-8 solar masses, which reveals them as the most likely site of origin
of the grains. This result provides the first direct evidence that these stars
contributed to the dust inventory from which the Solar System formed.


  In this paper, the boundary flex control problem of non stationary equation
governing the coupled mass and heat flow of a viscous incompressible fluid in a
generalized Boussinesq approximation by assuming that viscosity and heat
conductivity are dependent on temperature has been studied. The boundary
condition for velocity of fluid is non -standard boundary condition:
specifically the case where dynamical pressure is given on some part of the
boundary and the boundary condition for temperature of fluid is mixed boundary
condition has been considered. The optimal condition has been derived. Then,
Pontryagin's maximum principle in the special case has been derived.


  Particle dynamics in Earth's outer radiation belt can be modelled using a
diffusion framework, where large-scale electron movements are captured by a
diffusion equation across a single adiabatic invariant, $L^{*}$ $``(L)"$. While
ensemble models are promoted to represent physical uncertainty, as yet there is
no validated method to analyse radiation belt ensembles. Comparisons are
complicated by the domain dependent diffusion, since diffusion coefficient
$D_{LL}$ is dependent on $L$. We derive two tools to analyse ensemble members:
time to monotonicity $t_m$ and mass/energy moment quantities $\mathcal{N},
\mathcal{E}$. We find that the Jacobian ($1/L^2$) is necessary for radiation
belt error metrics. Components of $\partial\mathcal{E}/\partial t$ are
explicitly calculated to compare the effects of outer and inner boundary
conditions, and loss, on the ongoing diffusion. Using $t_m$, $\mathcal{N}$ and
$\mathcal{E}$, we find that: (a) different physically motivated choices of
outer boundary condition and location result in different final states and
different rates of evolution; (b) the gradients of the particle distribution
affect evolution more significantly than $D_{LL}$; (c) the enhancement
location, and the amount of initial background particles, are both significant
factors determining system evolution; (d) loss from pitch-angle scattering is
generally dominant; it mitigates but does not remove the influence of both
initial conditions and outer boundary settings, which are due to the
$L$-dependence of $D_{LL}$. We anticipate this study will promote renewed focus
on the distribution gradients, on the location and nature of the outer boundary
in radiation belt modelling, and provide a foundation for systematic ensemble
modelling.


  We report the spin to charge current conversation in an intrinsic topological
insulator (TI) $(Bi_{0.22}Sb_{0.78})_2Te_3$ film at room temperature. The spin
currents are generated in a thin layer of permalloy (Py) by two different
processes, spin pumping (SPE) and spin Seebeck effects (SSE). In the first we
use microwave-driven ferromagnetic resonance of the Py film to generate a SPE
spin current that is injected into the TI $(Bi_{0.22}Sb_{0.78})_2Te_3$ layer in
direct contact with Py. In the second we use the SSE in the longitudinal
configuration in Py without contamination by the Nernst effect made possible
with a thin NiO layer between the Py and $(Bi_{0.22}Sb_{0.78})_2Te_3$ layers.
The spin-to-charge current conversion is attributed to the inverse Edelstein
effect (IEE) made possible by the spin-momentum locking in the electron Fermi
contours due to the Rashba field. The measurements by the two techniques yield
very similar values for the IEE parameter, which are larger than the reported
values in the previous studies on topological insulators.


  Giant multipole resonances in Nd and Sm isotopes are studied by employing the
quasiparticle-random-phase approximation on the basis of the Skyrme
energy-density-functional method. Deformation effects on giant resonances are
investigated in these isotopes which manifest a typical nuclear shape change
from spherical to prolate shapes. The peak energy, the broadening, and the
deformation splitting of the isoscalar giant monopole (ISGMR) and quadrupole
(ISGQR) resonances agree well with measurements. The magnitude of the peak
splitting and the fraction of the energy-weighted strength in the lower peak of
the ISGMR reflect the nuclear deformation. The experimental data on ISGMR,
ISGDR, and ISGQR are consistent with the nuclear-matter incompressibility $K
\simeq 210-230$ MeV and the effective mass $m^*_0/m \simeq 0.8-0.9$. However,
the high-energy octupole resonance (HEOR) in $^{144}$Sm seems to indicates a
smaller effective mass, $m^*_0/m \simeq 0.7-0.8$. A further precise measurement
of HEOR is desired to determine the effective mass.


  A completely new approach to the Ising model in 1 to 5 dimensions is
developed. We employ $p,q$-binomial coefficients, a generalisation of the
binomial coefficients, to describe the magnetisation distributions of the Ising
model. For the complete graph this distribution corresponds exactly to the
limit case $p=q$. We take our investigation to the simple $d$-dimensional
lattices for $d=1,2,3,4,5$ and fit $p,q$-binomial distributions to our data,
some of which are exact but most are sampled. For $d=1$ and $d=5$ the
magnetisation distributions are remarkably well-fitted by $p,q$-binomial
distributions. For $d=4$ we are only slightly less successful, while for
$d=2,3$ we see some deviations (with exceptions!) between the $p,q$-binomial
and the Ising distribution. We begin the paper by giving results on the
behaviour of the $p,q$-distribution and its moment growth exponents given a
certain parameterization of $p,q$. Since the moment exponents are known for the
Ising model (or at least approximately for $d=3$) we can predict how $p,q$
should behave and compare this to our measured $p,q$. The results speak in
favour of the $p,q$-binomial distribution's correctness regarding their general
behaviour in comparison to the Ising model. The full extent to which they
correctly model the Ising distribution is not settled though.


  In the first part of this paper we revisit the history of theoretical
predictions for HB luminosities in old Population II stellar clusters, starting
from the results of `old' evolutionary computations to introduce in various
steps all the available `new' physics. We discuss the influence of physical
ingredients on selected evolutionary parameters, finally presenting models
which incorporate all the most recent updating of the relevant physics. The
evolutionary behavior of such models is extensively investigated for selected
choices about the cluster metallicity, discussing theoretical predictions
concerning both cluster isochrones and the calibration of the parameter R in
terms of the original amount of He in stellar matter. One finds that the `new'
physics has a relevant influence on both these parameters, moving in particular
cluster ages to a much better agreement with current cosmological evaluations.
This scenario is implemented by a further set of stellar models where element
diffusion is taken into account. The comparison between theoretical scenarios
with or without diffusion is presented and discussed. A discussion of current
observational constraints to the light of the updated theory closes the paper.


  Consider the two related problems of sensor selection and sensor fusion. In
the first, given a set of sensors, one wishes to identify a subset of the
sensors, which while small in size, captures the essence of the data gathered
by the sensors. In the second, one wishes to construct a fused sensor, which
utilizes the data from the sensors (possibly after discarding dependent ones)
in order to create a single sensor which is more reliable than each of the
individual ones. In this work, we rigorously define the dependence among
sensors in terms of joint empirical measures and incremental parsing. We show
that these measures adhere to a polymatroid structure, which in turn
facilitates the application of efficient algorithms for sensor selection. We
suggest both a random and a greedy algorithm for sensor selection. Given an
independent set, we then turn to the fusion problem, and suggest a novel
variant of the exponential weighting algorithm. In the suggested algorithm, one
competes against an augmented set of sensors, which allows it to converge to
the best fused sensor in a family of sensors, without having any prior data on
the sensors' performance.


  Large language models (LLMs) are susceptible to a variety of risks, from
non-faithful output to biased and toxic generations. Due to several limiting
factors surrounding LLMs (training cost, API access, data availability, etc.),
it may not always be feasible to impose direct safety constraints on a deployed
model. Therefore, an efficient and reliable alternative is required. To this
end, we present our ongoing efforts to create and deploy a library of
detectors: compact and easy-to-build classification models that provide labels
for various harms. In addition to the detectors themselves, we discuss a wide
range of uses for these detector models - from acting as guardrails to enabling
effective AI governance. We also deep dive into inherent challenges in their
development and discuss future work aimed at making the detectors more reliable
and broadening their scope.


  We derive some additional results on the Bienyam\'e-Galton-Watson branching
process with $\theta -$linear fractional branching mechanism, as studied in
\cite{Sag}. This includes: the explicit expression of the limit laws in both
the sub-critical cases and the super-critical cases with finite mean, the
long-run behavior of the population size in the critical case, limit laws in
the super-critical cases with infinite mean when the $\theta $-process is
either regular or explosive, results regarding the time to absorption, an
expression of the probability law of the $\theta $-branching mechanism
involving Bell polynomials, the explicit computation of the stochastic
transition matrix of the $\theta -$process, together with its powers.


  We establish unique continuation for various discrete nonlinear wave
equations. For example, we show that if two solutions of the Toda lattice
coincide for one lattice point in some arbitrarily small time interval, then
they coincide everywhere. Moreover, we establish analogous results for the
Toda, Kac-van Moerbeke, and Ablowitz-Ladik hierarchies. Although all these
equations are integrable, the proof does not use integrability and can be
adapted to other equations as well.


  We derive an unbiased information theoretic energy landscape for chromosomes
at metaphase using a maximum entropy approach that accurately reproduces the
details of the experimentally measured pair-wise contact probabilities between
genomic loci. Dynamical simulations using this landscape lead to cylindrical,
helically twisted structures reflecting liquid crystalline order. These
structures are similar to those arising from a generic ideal homogenized
chromosome energy landscape. The helical twist can be either right or left
handed so chiral symmetry is broken spontaneously. The ideal chromosome
landscape when augmented by interactions like those leading to topologically
associating domain (TAD) formation in the interphase chromosome reproduces
these behaviors. The phase diagram of this landscape shows the helical fiber
order and the cylindrical shape persist at temperatures above the onset of
chiral symmetry breaking which is limited by the TAD interaction strength.


  The best known inner bound on the two-receiver general broadcast channel
without a common message is due to Marton [3]. This result was subsequently
generalized in [p. 391, Problem 10(c) 2] and [4] to broadcast channels with a
common message. However the latter region is not computable (except in certain
special cases) as no bounds on the cardinality of its auxiliary random
variables exist. Nor is it even clear that the inner bound is a closed set. The
main obstacle in proving cardinality bounds is the fact that the traditional
use of the Carath\'{e}odory theorem, the main known tool for proving
cardinality bounds, does not yield a finite cardinality result. One of the main
contributions of this paper is the introduction of a new tool based on an
identity that relates the second derivative of the Shannon entropy of a
discrete random variable (under a certain perturbation) to the corresponding
Fisher information. In order to go beyond the traditional Carath\'{e}odory type
arguments, we identify certain properties that the auxiliary random variables
corresponding to the extreme points of the inner bound need to satisfy. These
properties are then used to establish cardinality bounds on the auxiliary
random variables of the inner bound, thereby proving the computability of the
region, and its closedness.
  Lastly, we establish a conjecture of \cite{NairZizhou} that Marton's inner
bound and the recent outer bound of Nair and El Gamal do not match in general.


  We consider a class of 2d $\sigma$-models on products of group spaces that
provide new examples of a close connection between integrability and stability
under the RG flow. We first study the integrable $G \times G$ model derived
from the affine Gaudin construction (for which the 1-loop $\beta$-functions
were found in arXiv:2010.07879) and show that its condition of integrability is
preserved also by the 2-loop RG flow. We then investigate the RG flow in the
gauged $G \times G /H$ model, in particular the integrable $T^{1,1}$ model
found in arXiv:2010.05573. We also construct a new class of integrable $G
\times G /H$ models in the case when the subgroup $H$ is abelian. In the
simplest case of $G=SU_2$, $H=U_1$ this leads to an integrable $\sigma$-model
on the $T^{1,q}$ space (with a particular $B$-field). This model is also shown
to be stable under the 2-loop RG flow, and we relate this property to its
invariance under T-duality in an isometric $U_1$ direction. This $T^{1,q}$
model may be interpreted as an integrable deformation of the GMM model (of two
coupled WZW theories with generic levels) away from the conformal point.


  We present a new method to measure the guided, radiated and total decay rates
in one-dimensional waveguides. It is also theoretically shown that large
modifications of the total decay rate can be achieved in realistic EDFAs and
EDWAs with effective mode area radii smaller than ~ 1 micrometer.


  We present two studies exploring how blind or low-vision (BLV) family members
engage with their sighted children's artwork, strategies to support
understanding and interpretation, and the potential role of technology, such as
AI, therein. Our first study involved 14 BLV individuals, and the second
included five groups of BLV individuals with their children. Through
semi-structured interviews with AI descriptions of children's artwork and
multi-sensory design probes, we found that BLV family members value artwork
engagement as a bonding opportunity, preferring the child's storytelling and
interpretation over other nonvisual representations. Additionally, despite some
inaccuracies, BLV family members felt that AI-generated descriptions could
facilitate dialogue with their children and aid self-guided art discovery. We
close with specific design considerations for supporting artwork engagement in
mixed visual-ability families, including enabling artwork access through
various methods, supporting children's corrections of AI output, and
distinctions in context vs. content and interpretation vs. description of
children's artwork.


  Potocek and Ferenczi [Phys. Rev. A 92, 023829 (2015)] provided an analysis of
the experimental evidence obtained by Danan et al. [Phys. Rev. Lett. 111,
240402 (2013)] for the surprising behaviour of photons passing through an
interferometer, in particular, motion on disconnected paths. Potocek and
Ferenczi reproduced the results of the experiment, but when analyzing its
modification, they claimed that the reasoning of Danan et al., which led to
disconnected paths, is erroneous. It is argued here that the criticism of
Potocek and Ferenczi is unfounded.


  In the present article, we deal with the overconvergence of the
Sz?asz-Durrmeyer-Chlodowsky operators. Here we study the approximation
properties e.g. upper estimates, Voronovskaja type result for these operators
attached to analytic functions in compact disks. Also, we discuss the exact
order in simultaneous approximation by these operators and its derivatives and
the asymptotic result with quantitative upper estimate. In such a way, we put
in evidence the overconvergence phenomenon for the Sz?asz-Durrmeyer-Chlodowsky
operators, namely the extensions of approximation properties with exact
quantitative estimates and orders of these convergencies to sets in the complex
plane that contain the interval [0,\infty).