  The paper develops a stochastic Agent-Based Model (ABM) mimicking the spread
of infectious diseases in geographical domains. The model is designed to
simulate the spatiotemporal spread of SARS-CoV2 disease, known as COVID-19. Our
SARS-CoV2-based ABM framework (CoV-ABM) simulates the spread at any
geographical scale, ranging from a village to a country and considers unique
characteristics of SARS-CoV2 viruses such as its persistence in the
environment. Therefore, unlike other simulators, CoV-ABM computes the density
of active viruses inside each location space to get the virus transmission
probability for each agent. It also uses the local census and health data to
create health and risk factor profiles for each individual. The proposed model
relies on a flexible timestamp scale to optimize the computational speed and
the level of detail. In our framework each agent represents a person
interacting with the surrounding space and other adjacent agents inside the
same space. Moreover, families stochastic daily tasks are formulated to get
tracked by the corresponding family members. The model also formulates the
possibility of meetings for each subset of friendships and relatives. The main
aim of the proposed framework is threefold: to illustrate the dynamics of
SARS-CoV diseases, to identify places which have a higher probability to become
infection hubs and to provide a decision-support system to design efficient
interventions in order to fight against pandemics. The framework employs SEIHRD
dynamics of viral diseases with different intervention scenarios. The paper
simulates the spread of COVID-19 in the State of Delaware, United States, with
near one million stochastic agents. The results achieved over a period of 15
weeks with a timestamp of 1 hour show which places become the hubs of
infection. The paper also illustrates how hospitals get overwhelmed as the
outbreak reaches its pick.


  The Nuker profile, characterised by an inner and outer power-law profile
smoothly merged around a break radius, is a very popular model to describe the
surface brightness profile of galactic nuclei. A disadvantage of this model for
dynamical studies is that the spatial density distribution that corresponds to
this surface brightness profile cannot be written in terms of elementary or
regular special functions. We derive a compact and elegant analytical
expression for the density of the Nuker model, based the Mellin integral
transform method. We use this expression to discuss the general behaviour and
asymptotic expansion of the density. We also discuss the special subclass of
Nuker models with an infinitely sharp break, and demonstrate that these models
are always characterised by non-monotonous and hence unphysical density
profile. We extend our study to the dynamical structure of spherical isotropic
galactic nuclei with a Nuker surface brightness profile. Based on this
analysis, we extend and refine the classification of spherical isotropic
galactic nuclei introduced by Tremaine et al. (1994). We demonstrate that both
the inner density slope and the sharpness of the break between the inner and
outer profiles critically determine the consistency and stability of the Nuker
models.


  The analysis of wave-packet dynamics may be greatly simplified when viewed in
phase-space. While harmonic oscillators are often used as a convenient platform
to study wave-packets, arbitrary state preparation in these systems is more
challenging. Here, we demonstrate a direct measurement of the Wigner
distribution of complex photon states in an anharmonic oscillator - a
superconducting phase circuit, biased in the small anharmonicity regime. We
test our method on both non-classical states composed of two energy eigenstates
and on the dynamics of a phase-locked wavepacket. This method requires a simple
calibration, and is easily applicable in our system out to the fifth level.


  Recently it has been speculated that a set of diffeomorphisms exist which act
non-trivially on the horizon of some black holes such as Kerr and Kerr-Newman
black hole. %\cite{Haco:2018ske,Haco:2019ggi}. Using this symmetry in covariant
phase space formalism one can obtain conserved charges as surface integrals on
the horizon. Kerr-Bolt spacetime is well-known for its asymptotic topology and
has been studied widely in recent years. In this work we are going to study
Kerr-Bolt black hole and provide a holographic description of it in term of
warped conformal field theory.


  High-quality frequency references are the cornerstones in position,
navigation and timing applications of both scientific and commercial domains.
Optomechanical oscillators, with direct coupling to continuous-wave light and
non-material-limited f Q product, are long regarded as a potential platform for
frequency reference in radio-frequency-photonic architectures. However, one
major challenge is the compatibility with standard CMOS fabrication processes
while maintaining optomechanical high quality performance. Here we demonstrate
the monolithic integration of photonic crystal optomechanical oscillators and
on-chip high speed Ge detectors based on the silicon CMOS platform. With the
generation of both high harmonics (up to 59th order) and subharmonics (down to
1/4), our chipset provides multiple frequency tones for applications in both
frequency multipliers and dividers. The phase noise is measured down to -125
dBc/Hz at 10 kHz offset at ~ 400 {\mu}W dropped-in powers, one of the lowest
noise optomechanical oscillators to date and in room-temperature and
atmospheric non-vacuum operating conditions. These characteristics enable
optomechanical oscillators as a frequency reference platform for
radio-frequency-photonic information processing.


  We consider some aspects of the perturbation to the luminosity distance
$d(z)$ that are of relevance for SN1a cosmology and for future peculiar
velocity surveys at non-negligible redshifts.
  1) Previous work has shown that the correction to the lowest order
perturbation $\delta d / d = -\delta v / c z$ has the peculiar characteristic
that it appears to depend on the absolute state of motion of sources, rather
than on their motion relative to that of the observer. The resolution of this
apparent violation of the equivalence principle is that it is necessary to
allow for evolution of the velocities with time, and also, when considering
perturbations on the scale of the observer-source separation, to include the
gravitational redshift effect. We provide an expression for $\delta d / d$ that
provides a physically consistent way to measure peculiar velocities and
determine their impact for SN1a cosmology.
  2) We then calculate the perturbation to the redshift as a function of source
flux density, which has been proposed as an alternative probe of large-scale
motions. We show how the inclusion of surface brightness modulation modifies
the relation between $\delta z(m)$ and the peculiar velocity, and that, while
the noise properties of this method might appear promising, the velocity signal
is swamped by the effect of galaxy clustering for most scales of interest.
  3) We show how, in linear theory, peculiar velocity measurements are biased
downwards by the effect of smaller scale motions or by measurement errors (such
as in photometric redshifts). Our results nicely explain the effects seen in
simulations by Koda et al.\ 2013.
  We critically examine the prospects for extending peculiar velocity studies
to larger scales with near-term future surveys.


  The rotational spectrum of the formaldehyde isotopologue H$_2$C$^{17}$O was
investigated between 0.56 and 1.50 THz using a sample of natural isotopic
composition. In addition, transition frequencies were determined for
H$_2$C$^{18}$O and H$_2$C$^{16}$O between 1.37 and 1.50 THz. The data were
combined with critically evaluated literature data to derive improved sets of
spectroscopic parameters which include $^{17}$O or H nuclear hyperfine
structure parameters.


  We present a set of Lorentz invariant kinematic variables for reconstructing
mass of semi-invisible decaying particles pair-produced at lepton colliders,
$m_{\rm RC}^{\rm min}$, $m_{\rm RC}^{\rm max}$ and $m_{\rm LSP}^{\rm max}$,
with analytical formulas. They give the minimal and maximum bounds of the
decaying particle mass and upper bound of the invisible particle mass. In the
search of new physics, these variables can greatly enhance the statistical
significance of signal. For the process of smuon pair production at
$\sqrt{s}=240~{\rm GeV}$ lepton collider of 5 ab$^{-1}$, the cross section
detection limit is pushed by one order, and the expected exclusion and
discovery limits are set above $\sqrt{s}\big/2$ and go into the off-shell
region. Moreover, these variables can also be used to improve the precision of
$W$-boson mass measurement in full leptonic decayed channel. At future lepton
collider, the precision can reach to $2\sim 3$ MeV level.


  Mathematical models in epidemiology are an indispensable tool to determine
the dynamics and important characteristics of infectious diseases. Apart from
their scientific merit, these models are often used to inform political
decisions and intervention measures during an ongoing outbreak. However,
reliably inferring the dynamics of ongoing outbreaks by connecting complex
models to real data is still hard and requires either laborious manual
parameter fitting or expensive optimization methods which have to be repeated
from scratch for every application of a given model. In this work, we address
this problem with a novel combination of epidemiological modeling with
specialized neural networks. Our approach entails two computational phases: In
an initial training phase, a mathematical model describing the epidemic is used
as a coach for a neural network, which acquires global knowledge about the full
range of possible disease dynamics. In the subsequent inference phase, the
trained neural network processes the observed data of an actual outbreak and
infers the parameters of the model in order to realistically reproduce the
observed dynamics and reliably predict future progression. With its flexible
framework, our simulation-based approach is applicable to a variety of
epidemiological models. Moreover, since our method is fully Bayesian, it is
designed to incorporate all available prior knowledge about plausible parameter
values and returns complete joint posterior distributions over these
parameters. Application of our method to the early Covid-19 outbreak phase in
Germany demonstrates that we are able to obtain reliable probabilistic
estimates for important disease characteristics, such as generation time,
fraction of undetected infections, likelihood of transmission before symptom
onset, and reporting delays using a very moderate amount of real-world
observations.


  We prove that all finite W-algebras associated with nilpotent elements e in a
complex semisimple Lie algebra g have finite-dimensional representations. In
order to obtain this result we establish a connection between primitive ideals
of U(g) attached to the nilpotent orbit containing e and finite-dimensional
representations of the reduced enveloping algebra assiciated with e over an
algebraically closed field of finite characteristic.


  Adversarial Robustness Distillation (ARD) is a novel method to boost the
robustness of small models. Unlike general adversarial training, its robust
knowledge transfer can be less easily restricted by the model capacity.
However, the teacher model that provides the robustness of knowledge does not
always make correct predictions, interfering with the student's robust
performances. Besides, in the previous ARD methods, the robustness comes
entirely from one-to-one imitation, ignoring the relationship between examples.
To this end, we propose a novel structured ARD method called Contrastive
Relationship DeNoise Distillation (CRDND). We design an adaptive compensation
module to model the instability of the teacher. Moreover, we utilize the
contrastive relationship to explore implicit robustness knowledge among
multiple examples. Experimental results on multiple attack benchmarks show
CRDND can transfer robust knowledge efficiently and achieves state-of-the-art
performances.


  Cross-Impact Balance Analysis (CIB) is a widely used method to build
scenarios and help researchers to formulate policies in different fields, such
as management sciences and social sciences. During the development of the CIB
method over the years, some derivative methods were developed to expand its
application scope, including a method called dynamic CIB. However, the workflow
of dynamic CIB is relatively complex. In this article, we provide another
approach to extend CIB in multiple timespans based on the concept 'scenario
weight' and simplify the workflow to bring convenience to the policy makers.


  We propose a new encoding of the first-order connection method as a Boolean
satisfiability problem. The encoding eschews tree-like presentations of the
connection method in favour of matrices, as we show that tree-like calculi have
a number of drawbacks in the context of satisfiability solving. The matrix
setting permits numerous global refinements of the basic connection calculus.
We also show that a suitably-refined calculus is a decision procedure for the
Bernays-Sch\"onfinkel class.


  The most accurate measurements of magnetic fields in star-forming gas are
based on the Zeeman observations analyzed by Crutcher et al. (2010). We show
that their finding that the 3D magnetic field scales approximately as
density$^{0.65}$ can also be obtained from analysis of the observed
line-of-sight fields. We present two large-scale AMR MHD simulations of several
thousand $M_\odot$ of turbulent, isothermal, self-gravitating gas, one with a
strong initial magnetic field (Alfven Mach number $M_{A,0}= 1$) and one with a
weak initial field ($M_{A,0}=10$). We construct samples of the 100 most massive
clumps in each simulation and show that they exhibit a power-law relation
between field strength and density in excellent agreement with the observed
one. Our results imply that the average field in molecular clumps in the
interstellar medium is $<B_{tot}> \sim 42 n_{H,4}^{0.65} \mu$G. Furthermore,
the median value of the ratio of the line-of-sight field to density$^{0.65}$ in
the simulations is within a factor of about (1.3, 1.7) of the observed value
for the strong and weak field cases, respectively. The median value of the
mass-to-flux ratio, normalized to the critical value, is 70% of the
line-of-sight value. This is larger than the 50% usually cited for spherical
clouds because the actual mass-to-flux ratio depends on the volume-weighted
field, whereas the observed one depends on the mass-weighted field. Our results
indicate that the typical molecular clump in the ISM is significantly
supercritical (~ factor of 3). The results of our strong-field model are in
very good quantitative agreement with the observations of Li et al. (2009),
which show a strong correlation in field orientation between small and large
scales. Because there is a negligible correlation in the weak-field model, we
conclude that molecular clouds form from strongly magnetized (although
magnetically supercritical) gas.


  We present an update of a phenomenological model for the spin dependent
structure functions $g_1(x,Q^2)$ of the proton and neutron. This model is based
on a broken SU(6) wavefunction parametrized by the unpolarized structure
functions. The two free parameters of the model are choosen to fulfill the
Bjorken and Ellis--Jaffe sum rules. The model respects isospin symmetry and has
zero strange sea polarization. Using new values for $F/D$ from hyperon beta
decay the resulting $Q^2$ dependent asymmetries $A_1$ are in perfect agreement
with the existing data. Therefore we do not see any evidence for a ``spin
crisis''. With two choices for $g_2$ the $Q^2$ dependence of $A_1(x,Q^2)$ and
$A_2(x,Q^2)\sqrt{Q^2}/M$ is predicted and shown to be small for both cases.


  An analytical benchmark is proposed for graphene and carbon nanotubes, that
may serve to test whatsoever molecular dynamics code implemented with REBO
potentials. By exploiting the benchmark, we checked results produced by LAMMPS
(Large-scale Atomic/Molecular Massively Parallel Simulator) when adopting the
second generation Brenner potential, we made evident that the code in its
current implementation produces results which are offset from those of the
benchmark by a significant amount, and provide evidence of the reason.


  Microwave emission of solar flares is formed primarily by incoherent
gyrosynchrotron radiation generated by accelerated electrons in coronal
magnetic loops. The resulting emission depends on many factors, including
pitch-angle distribution of the emitting electrons and the source geometry. In
this work, we perform systematic simulations of solar microwave emission using
recently developed tools (GS Simulator and fast gyrosynchrotron codes) capable
of simulating maps of radio brightness and polarization as well as spatially
resolved emission spectra. A 3D model of a symmetric dipole magnetic loop is
used. We compare the emission from isotropic and anisotropic (of loss-cone
type) electron distributions. We also investigate effects caused by
inhomogeneous distribution of the emitting particles along the loop. It is
found that effect of the adopted moderate electron anisotropy is the most
pronounced near the footpoints and it also depends strongly on the loop
orientation. Concentration of the emitting particles at the loop top results in
a corresponding spatial shift of the radio brightness peak, thus reducing
effects of the anisotropy. The high-frequency (around 50 GHz) emission spectral
index is specified mainly by the energy spectrum of the emitting electrons;
however, at intermediate frequencies (around 10-20 GHz), the spectrum shape is
strongly dependent on the electron anisotropy, spatial distribution, and
magnetic field nonuniformity. The implications of the obtained results for the
diagnostics of the energetic electrons in solar flares are discussed.


  In this paper we develop a simple theory to study the effects of ionic size
on ionic distributions around a charged spherical particle. We include a
correction to the regular Poisson-Boltzmann equation in order to take into
account the size of ions in a mean-field regime. The results are compared with
Monte Carlo simulations and a Density Functional Theory based on the
Fundamental Measure approach and a second-order bulk expansion which accounts
for electrostatic correlations. The agreement is very good even for multivalent
ions. Our results show that the theory can be applied with very good accuracy
in the description of ions with high effective ionic radii and low
concentration, interacting with a colloid or nanoparticle in an electrolyte
solution.


  For a large class of semiclassical operators $P(h)-z$ which includes
Schr\"odinger operators on manifolds with boundary, we construct the Quantum
Monodromy operator $M(z)$ associated to a periodic orbit $\gamma$ of the
classical flow. Using estimates relating $M(z)$ and $P(h)-z$, we prove
semiclassical estimates for small complex perturbations of $P(h) -z$ in the
case $\gamma$ is semi-hyperbolic. As our main application, we give logarithmic
lower bounds on the mass of eigenfunctions away from semi-hyperbolic orbits of
the associated classical flow.
  As a second application of the Monodromy Operator construction, we prove if
$\gamma$ is an elliptic orbit, then $P(h)$ admits quasimodes which are
well-localized near $\gamma$.


  We analyze four-lepton contact interactions that lead to lepton flavor
violating processes, with violation of individual family lepton number but
total lepton number conserved. In an effective Lagrangian framework, the
assumption of gauge invariance leads to relations among branching ratios and
cross sections of lepton flavor violating processes. In this paper, we work out
how to use these relations systematically. We also study the consequences of
loop-induced processes.


  Tensors play a vital role in machine learning (ML) and often exhibit
properties best explored while maintaining high-order. Efficiently performing
ML computations requires taking advantage of sparsity, but generalized hardware
support is challenging. This paper introduces FLAASH, a flexible and modular
accelerator design for sparse tensor contraction that achieves over 25x speedup
for a deep learning workload. Our architecture performs sparse high-order
tensor contraction by distributing sparse dot products, or portions thereof, to
numerous Sparse Dot Product Engines (SDPEs). Memory structure and job
distribution can be customized, and we demonstrate a simple approach as a proof
of concept. We address the challenges associated with control flow to navigate
data structures, high-order representation, and high-sparsity handling. The
effectiveness of our approach is demonstrated through various evaluations,
showcasing significant speedup as sparsity and order increase.


  We consider minimizers of the following mass critical Hartree minimization
problem:
  \[ e_\lambda(N):=\underset{\{u\in H^1(R^d),\,\|u\|^2_2=N\}}{\inf}
E_\lambda(u),\,\ d\ge 3, \] where the Hartree energy functional $E_\lambda(u)$
is defined by \[
  E_\lambda(u):=\int_{R ^d}|\nabla u(x)|^2dx+\lambda \int_{R
^d}g(x)u^2(x)dx-\frac{1}{2} \int_{R ^d}\int_{R ^d}
\frac{u^2(x)u^2(y)}{|x-y|^2}dxdy,\,\ \lambda>0,\] and the steep potential
$g(x)$ satisfies $0=g(0)=\inf _{R^d}g(x)\le g(x)\le 1$ and $1-g(x)\in
L^{\frac{d}{2}}(R^d)$. We prove that there exists a constant $N^*>0$,
independent of $\lambda g(x)$, such that if $N\ge N^*$, then $e_\lambda(N)$
does not admit minimizers for any $\lambda >0$; if $0<N<N^*$, then there exists
a constant $\lambda ^*(N)>0$ such that $e_\lambda(N)$ admits minimizers for any
$\lambda >\lambda ^*(N)$, and $e_\lambda(N)$ does not admit minimizers for
$0<\lambda <\lambda ^*(N)$. For any given $0<N<N^*$, the limit behavior of
positive minimizers for $e_\lambda(N)$ is also studied as $\lambda\to\infty$,
where the mass concentrates at the bottom of $g(x)$.


  In the present paper we characterize the surjective isometries of the space
of compact, convex subsets of proper, geodesically complete CAT(0)-spaces in
which geodesics do not split, endowed with the Hausdorff metric. Moreover, an
analogue characterization of the surjective isometries of the space of compact
subsets of a proper, uniquely geodesic, geodesically complete metric space in
which geodesics do not split, when endowed with the Hausdorff metric, is given.


  When the interaction between a molecular system and confined light modes in
an optical or plasmonic cavity is strong enough to overcome the dissipative
process, hybrid light-matter states (polaritons) become the fundamental
excitations in the system. The mixing between the light and matter characters
modifies the photophysical and photochemical properties. Especially, it was
reported that these polaritons can be employed to control photochemical
reactions, charge and energy transfer, and other processes. In addition,
according to recent studies, vibrational strong coupling can be employed to
resonantly enhance the thermally-activated chemical reactions. In this work, a
theoretical model and an efficient numerical method for studying the dynamics
of molecules strongly interacting with quantum light are developed based on
non-adiabatic excited-state molecular dynamics. The methodology was employed to
study the \textit{cis-trans} photoisomerization of a realistic molecule in a
cavity. Numerical simulations demonstrate that the photochemical reactions can
be controlled by tuning the properties of the cavity. In the calculated
example, the isomerization is suppressed when polaritonic states develop a
local minimum on the lower polaritonic state. Moreover, the observed reduction
of isomerization is tunable via the photon energy and light-molecule coupling
strength. But the fluctuation in transition dipole screens the effect of
light-matter, which makes it harder to tune the photochemical properties via
the coupling strength. These insights suggest quantum control of photochemical
reactions is possible by specially designed photonic or plasmonic cavities.


  In Natural Language Processing (NLP), binary classification algorithms are
often evaluated using the F1 score. Because the sample F1 score is an estimate
of the population F1 score, it is not sufficient to report the sample F1 score
without an indication of how accurate it is. Confidence intervals are an
indication of how accurate the sample F1 score is. However, most studies either
do not report them or report them using methods that demonstrate poor
statistical properties. In the present study, I review current analytical
methods (i.e., Clopper-Pearson method and Wald method) to construct confidence
intervals for the population F1 score, propose two new analytical methods
(i.e., Wilson direct method and Wilson indirect method) to do so, and compare
these methods based on their coverage probabilities and interval lengths, as
well as whether these methods suffer from overshoot and degeneracy. Theoretical
results demonstrate that both proposed methods do not suffer from overshoot and
degeneracy. Experimental results suggest that both proposed methods perform
better, as compared to current methods, in terms of coverage probabilities and
interval lengths. I illustrate both current and proposed methods on two
suggestion mining tasks. I discuss the practical implications of these results,
and suggest areas for future research.


  Suppose $\alpha$ is a rotationally symmetric norm on
$L^{\infty}\left(\mathbb{T}\right) $ and $\beta$ is a "nice" norm on
$L^{\infty}\left(\Omega,\mu \right) $ where $\mu$ is a $\sigma$-finite measure
on $\Omega$. We prove a version of Beurling's invariant subspace theorem for
the space $L^{\beta}\left(\mu,H^{\alpha}\right) .$ Our proof uses the recent
version of Beurling's theorem on $H^{\alpha}\left(\mathbb{T}\right) $ proved by
the first author and measurable cross-section techniques. Our result
significantly extends a result of H. Rezaei, S. Talebzadeh, and D. Y. Shin.


  Traditional dynamic security assessment faces challenges as power systems are
experiencing a transformation to inverter-based-resource (IBR) dominated
systems, for which electromagnetic transient (EMT) dynamics have to be
considered. However, EMT simulation is time-consuming especially for a large
power grid because the mathematical model based on detailed component modeling
is highly stiff and needs to be integrated at tiny time steps due to numerical
stability. This paper proposes a heterogeneous multiscale method (HMM) to
address the simulation of a power system considering EMT dynamics as a
multiscale problem. The method aims to accurately simulate the macroscopic
dynamics of the system even when EMT dynamics are dominating. By force
estimation using a kernel function, the proposed method automatically generates
a macro model on the fly of simulation based on the micro model of EMT
dynamics. It can flexibly switch between the micro- and macro-models to capture
important EMT dynamics during some time intervals while skipping over other
time intervals of less interest to achieve a superior simulation speed. The
method is illustrated by a case study on a two-machine EMT model to demonstrate
its potential for power system simulation.


  Power grids, as well as neuronal networks with synaptic plasticity, describe
real-world systems of tremendous importance for our daily life. The
investigation of these seemingly unrelated types of dynamical networks has
attracted increasing attention over the last decade. In this work, we exploit
the recently established relation between these two types of networks to gain
insights into the dynamical properties of multifrequency clusters in power grid
networks. For this, we consider the model of Kuramoto-Sakaguchi phase
oscillators with inertia and describe the emergence of multicluster states.
Building on this, we provide a new perspective on solitary states in power grid
networks by introducing the concept of pseudo coupling weights.


  The purpose of physics is to describe nature from elementary particles all
the way up to cosmological objects like cluster of galaxies and black holes.
Although a unified description for all this spectrum of events is desirable,
this would be highly impractical. To not get lost in unnecessary details,
effective descriptions are mandatory. Here we analyze the dynamics that may
emerge from a full quantum description when one does not have access to all the
degrees of freedom of a system. More concretely, we describe the properties of
the dynamics that arise from quantum mechanics if one has access only to a
coarse-grained description of the system. We obtain that the effective maps are
not necessarily of Kraus form, due to correlations between accessible and
nonaccessible degrees of freedom, and that the distance between two effective
states may increase under the action of the effective map. We expect our
framework to be useful for addressing questions such as the thermalization of
closed quantum systems, as well as the description of measurements in quantum
mechanics.


  Multipath communication not only allows improved throughput but can also be
used to leverage different path characteristics to best fulfill each
application's objective. In particular, certain delay-sensitive applications,
such as real time voice and video communications, can usually withstand packet
loss and aim to maximize throughput while keeping latency at a reasonable
level. In such a context, one hard problem is to determine along which path the
data should be transmitted or retransmitted. In this paper, we formulate this
problem as a linear optimization, show bounds on the performance that can be
obtained in a multipath paradigm, and show that path diversity is a strong
asset for improving network performance. We also discuss how these theoretical
limits can be approached in practice and present simulation results.


  Smartphone usage while driving is unanimously considered to be a really
dangerous habit due to strong correlation with road accidents. In this paper,
the problem of detecting whether the driver is using the phone during a trip is
addressed. To do this, high-frequency data from the triaxial inertial
measurement unit (IMU) integrated in almost all modern phone is processed
without relying on external inputs so as to provide a self-contained approach.
By resorting to a frequency-domain analysis, it is possible to extract from the
raw signals the useful information needed to detect when the driver is using
the phone, without being affected by the effects that vehicle motion has on the
same signals. The selected features are used to train a Support Vector Machine
(SVM) algorithm. The performance of the proposed approach are analyzed and
tested on experimental data collected during mixed naturalistic driving
scenarios, proving the effectiveness of the proposed approach.


  Thanks to space-borne experiments such as the AMS-02 and PAMELA missions in
low-Earth orbit, along with the Voyager spacecrafts in the interstellar space,
a large collection of multi-channel and time-resolved Galactic cosmic ray (GCR)
data has recently become available. Here we present an improved
measured-validated model of the "solar modulation" effect, i.e., the temporal
evolution of the GCR flux inside the heliosphere caused by the 11-year
variability cycle of the Sun's magnetic activity. We present our improved
modeling of the structure of the heliosphere, the physical mechanisms of
diffusion, drift, and energy losses of GCR particles in the heliosphere. We
present our results for the temporal dependence of the key model parameters and
their relationship with solar activity proxies. We discuss implications for the
GCR transport in magnetic turbulence, and new insights on our understanding of
the solar modulation phenomenon.


  We show that in a superconductor where two or more bands cross the Fermi
level it is possible, in the framework of the conventional (s-wave) BCS theory,
that the sign of the superconducting gap is different on the different sheets
of the Fermi surface. At least one of two conditions has to be satisfied: (1)
The interband pairing interaction is weaker than the Coulomb pseudopotential,
while the intraband one is stronger, or (2) there is strong interband
scattering by magnetic impurities. In the case of YBa$_2$% Cu$_3$O$_7$ we shall
argue that the first condition is possibly satisfied, and the second one very
likely satisfied. In many aspects such a sign-reversal $s-$wave superconductor
is similar to a d-wave superconductor, and thus demands revising recent
experiments aimed to distinguish between the $s-$ and $d-$wave
superconductivity in this compound.


  In this paper we consider the NLS equation with power nonlinearity and a
point interaction (a "$\delta$-potential" in the physical literature) in
dimension two and three. We will show that for low power nonlinearities there
is failure of scattering to the free dynamics or to standing waves. In the
recent paper Murphy and Nakanishi consider the NLS equation with potentials and
measures, singular enough to include the $\delta$-potential in dimension one
and they show analogous properties. In this respect our contribution is an
extension to higher dimension and it needs a different treatment of the linear
part of the interaction, due the qualitatively different and stronger character
of the singularity involved.


  In earlier work, planar graphs of massless phi^3 theory were summed with the
help of the light cone world sheet picture and the mean field approximation. In
the present article, the same methods are applied to the problem of summing
planar bosonic open strings. We find that in the ground state of the system,
string boundaries form a condensate on the world sheet, and a new string
emerges from this summation. Its slope is always greater than the initial
slope, and it remains non-zero even when the initial slope is set equal to
zero. If we assume that the initial string tends to some field theory in the
zero slope limit, this result provides evidence for string formation in field
theory.


  It is proved that if $G$ is a compact Lie group, then an equivariant Serre
fibration of $G$-CW-complexes is an equivariant Hurewicz fibration in the class
of compactly generated $G$-spaces. In the nonequivariant setting, this result
is due to Steinberger, West and Cauty. The main theorem is proved using the
following key result: a $G$-CW-complex can be embedded as an equivariant
retract in a simplicial $G$-complex. It is also proved that an equivariant map
$p: E \to B$ of $G$-CW-complexes is a Hurewicz $G$-fibration if and only if the
$H$-fixed point map $p^H : E^H \to B^H$ is a Hurewicz fibration for any closed
subgroup $H$ of $G$. This gives a solution to the problem of James and Segal in
the case of $G$-CW-complexes.


  In this paper, we develop a new type of accelerated algorithms to solve some
classes of maximally monotone equations as well as monotone inclusions. Instead
of using Nesterov's accelerating approach, our methods rely on a so-called
Halpern-type fixed-point iteration in [32], and recently exploited by a number
of researchers, including [24, 70]. Firstly, we derive a new variant of the
anchored extra-gradient scheme in [70] based on Popov's past extra-gradient
method to solve a maximally monotone equation $G(x) = 0$. We show that our
method achieves the same $\mathcal{O}(1/k)$ convergence rate (up to a constant
factor) as in the anchored extra-gradient algorithm on the operator norm $\Vert
G(x_k)\Vert$, , but requires only one evaluation of $G$ at each iteration,
where $k$ is the iteration counter. Next, we develop two splitting algorithms
to approximate a zero point of the sum of two maximally monotone operators. The
first algorithm originates from the anchored extra-gradient method combining
with a splitting technique, while the second one is its Popov's variant which
can reduce the per-iteration complexity. Both algorithms appear to be new and
can be viewed as accelerated variants of the Douglas-Rachford (DR) splitting
method. They both achieve $\mathcal{O}(1/k)$ rates on the norm $\Vert
G_{\gamma}(x_k)\Vert$ of the forward-backward residual operator
$G_{\gamma}(\cdot)$ associated with the problem. We also propose a new
accelerated Douglas-Rachford splitting scheme for solving this problem which
achieves $\mathcal{O}(1/k)$ convergence rate on $\Vert G_{\gamma}(x_k)\Vert$
under only maximally monotone assumptions. Finally, we specify our first
algorithm to solve convex-concave minimax problems and apply our accelerated DR
scheme to derive a new variant of the alternating direction method of
multipliers (ADMM).


  We present a new 'piggybacking' framework for designing distributed storage
codes that are efficient in data-read and download required during node-repair.
We illustrate the power of this framework by constructing classes of explicit
codes that entail the smallest data-read and download for repair among all
existing solutions for three important settings: (a) codes meeting the
constraints of being Maximum-Distance-Separable (MDS), high-rate and having a
small number of substripes, arising out of practical considerations for
implementation in data centers, (b) binary MDS codes for all parameters where
binary MDS codes exist, (c) MDS codes with the smallest repair-locality. In
addition, we employ this framework to enable efficient repair of parity nodes
in existing codes that were originally constructed to address the repair of
only the systematic nodes. The basic idea behind our framework is to take
multiple instances of existing codes and add carefully designed functions of
the data of one instance to the other. Typical savings in data-read during
repair is 25% to 50% depending on the choice of the code parameters.


  Simulations with more than $10^{12}$ spins are used to study the motion of a
domain wall driven through a three-dimensional random-field Ising magnet (RFIM)
by an external field $H$. The interface advances in a series of avalanches
whose size diverges at a critical external field $H_c$. Finite-size scaling is
applied to determine critical exponents and test scaling relations. Growth is
intrinsically anisotropic with the height of an avalanche normal to the
interface $\ell_\perp$ scaling as the width along the interface $\ell_\|$ to a
power $\chi=0.85 \pm 0.01$. The total interface roughness is consistent with
self-affine scaling with a roughness exponent $\zeta \approx \chi$ that is much
larger than values found previously for the RFIM and related models that
explicitly break orientational symmetry by requiring the interface to be
single-valued. Because the RFIM maintains orientational symmetry, the interface
develops overhangs that may surround unfavorable regions to create uninvaded
bubbles. Overhangs complicate measures of the roughness exponent but decrease
in importance with increasing system size.


  The advent of Large Language Models (LLMs) has significantly transformed the
AI landscape, enhancing machine learning and AI capabilities. Factuality issue
is a critical concern for LLMs, as they may generate factually incorrect
responses. In this paper, we propose GraphEval to evaluate an LLM's performance
using a substantially large test dataset. Specifically, the test dataset is
retrieved from a large knowledge graph with more than 10 million facts without
expensive human efforts. Unlike conventional methods that evaluate LLMs based
on generated responses, GraphEval streamlines the evaluation process by
creating a judge model to estimate the correctness of the answers given by the
LLM. Our experiments demonstrate that the judge model's factuality assessment
aligns closely with the correctness of the LLM's generated outputs, while also
substantially reducing evaluation costs. Besides, our findings offer valuable
insights into LLM performance across different metrics and highlight the
potential for future improvements in ensuring the factual integrity of LLM
outputs. The code is publicly available at https://github.com/xz-liu/GraphEval.


  Over the past few decades, tremendous progress has been made in the
development of particle-based discrete simulation methods versus the
conventional continuum-based methods. In particular, the lattice Boltzmann (LB)
method has evolved from a theoretical novelty to a ubiquitous, versatile and
powerful computational methodology for both fundamental research and
engineering applications. It is a kinetic-based mesoscopic approach that
bridges the microscales and macroscales, which offers distinctive advantages in
simulation fidelity and computational efficiency. Applications of the LB method
have been found in a wide range of disciplines including physics, chemistry,
materials, biomedicine and various branches of engineering. The present work
provides a comprehensive review of the LB method for thermofluids and energy
applications, focusing on multiphase flows, thermal flows and thermal
multiphase flows with phase change. The review first covers the theoretical
framework of the LB method, revealing the existing inconsistencies and defects
as well as common features of multiphase and thermal LB models. Recent
developments in improving the thermodynamic and hydrodynamic consistency,
reducing the spurious currents, enhancing the numerical stability, etc., are
highlighted. These efforts have put the LB method on a firmer theoretical
foundation with enhanced LB models that can achieve larger liquid-gas density
ratio, higher Reynolds number and flexible surface tension. Examples of
applications are provided in fuel cells and batteries, droplet collision,
boiling heat transfer and evaporation, and energy storage. Finally, further
developments and future prospect of the LB method are outlined for thermofluids
and energy applications.


  This paper presents a systematic approach to exploit TV white space (TVWS)
for device-to-device (D2D) communications with the aid of the existing cellular
infrastructure. The goal is to build a location-specific TVWS database, which
provides a look-up table service for any D2D link to determine its maximum
permitted emission power (MPEP) in an unlicensed digital TV (DTV) band. To
achieve this goal, the idea of mobile crowd sensing is firstly introduced to
collect active spectrum measurements from massive personal mobile devices.
Considering the incompleteness of crowd measurements, we formulate the problem
of unknown measurements recovery as a matrix completion problem and apply a
powerful fixed point continuation algorithm to reconstruct the unknown elements
from the known elements. By joint exploitation of the big spectrum data in its
vicinity, each cellular base station further implements a nonlinear support
vector machine algorithm to perform irregular coverage boundary detection of a
licensed DTV transmitter. With the knowledge of the detected coverage boundary,
an opportunistic spatial reuse algorithm is developed for each D2D link to
determine its MPEP. Simulation results show that the proposed approach can
successfully enable D2D communications in TVWS while satisfying the
interference constraint from the licensed DTV services. In addition, to our
best knowledge, this is the first try to explore and exploit TVWS inside the
DTV protection region resulted from the shadowing effect. Potential application
scenarios include communications between internet of vehicles in the
underground parking, D2D communications in hotspots such as subway, game
stadiums, and airports, etc.


  The method of isolines (contours) is proposed to be used for deter- mination
of core location of extensive air shower on the array plane. As variable
z=f(x,y) are used flux densities of particles, registrated from ground
detectors. Obtained isolines are approximated with circles, which centers show
impact point of shower axis. The method was demostrated on experimental data
from Tien-Shan shower array in period 1974-82. The possibilities and
difficulties of the method are discussed.


  This paper presents an exhaustive how-to guide on measuring the total
vanadium concentration and state of charge of vanadium electrolytes using
UV-Visible spectroscopy. The study is provided with an open-access database
(https://github.com/AngeAM/SOC_Vanadium_Spectra_2023.git) that supports the
methods and procedures and facilitates access to the calibration data. The
study covers the three types of electrolyte solutions relevant to vanadium
redox flow batteries, namely the anolyte $V^{II}/V^{III}$, the catholyte
$V^{IV}V^V$, and the $V^{III}/V^{IV}$ commercial electrolyte, meant to be
preconditioned to either $V^{III}$ or $V^{IV}$ before battery operation.
Analytical expressions to calculate the concentration of different vanadium
species in the electrolyte solutions are provided based on either empirical
correlations or spectral deconvolution methods. The paper also examines the
limitations of the measurement technique and provides insightful
recommendations for future research. The open-access database provided by the
authors is expected to serve as a valuable repository for scholars and
scientists working in the field of vanadium redox flow batteries.


  Phenotypic heterogeneity in cancer cells is widely observed and is often
linked to drug resistance. In several cases, such heterogeneity in drug
sensitivity of tumors is driven by stochastic and reversible acquisition of a
drug tolerant phenotype by individual cells even in an isogenic population.
Accumulating evidence further suggests that cell-fate transitions such as the
epithelial to mesenchymal transition (EMT) are associated with drug resistance.
In this study, we analyze stochastic models of phenotypic switching to provide
a framework for analyzing cell-fate transitions such as EMT as a source of
phenotypic variability in drug sensitivity. Motivated by our cell-culture based
experimental observations connecting phenotypic switching in EMT and drug
resistance, we analyze a coarse-grained model of phenotypic switching between
two states in the presence of cytotoxic stress from chemotherapy. We derive
analytical results for time-dependent probability distributions that provide
insights into the rates of phenotypic switching and characterize initial
phenotypic heterogeneity of cancer cells. The results obtained can also shed
light on fundamental questions relating to adaptation and selection scenarios
in tumor response to cytotoxic therapy.


  Spatial-query-by-sketch is an intuitive tool to explore human spatial
knowledge about geographic environments and to support communication with scene
database queries. However, traditional sketch-based spatial search methods
perform insufficiently due to their inability to find hidden multi-scale map
features from mental sketches. In this research, we propose a deep
convolutional neural network, namely Deep Spatial Scene Network (DeepSSN), to
better assess the spatial scene similarity. In DeepSSN, a triplet loss function
is designed as a comprehensive distance metric to support the similarity
assessment. A positive and negative example mining strategy using qualitative
constraint networks in spatial reasoning is designed to ensure a consistently
increasing distinction of triplets during the training process. Moreover, we
develop a prototype spatial scene search system using the proposed DeepSSN, in
which the users input spatial query via sketch maps and the system can
automatically augment the sketch training data. The proposed model is validated
using multi-source conflated map data including 131,300 labeled scene samples
after data augmentation. The empirical results demonstrate that the DeepSSN
outperforms baseline methods including k-nearest-neighbors, multilayer
perceptron, AlexNet, DenseNet, and ResNet using mean reciprocal rank and
precision metrics. This research advances geographic information retrieval
studies by introducing a novel deep learning method tailored to spatial scene
queries.


  For spherically symmetric repulsive Hamiltonians we prove the Besov bound,
the radiation condition bounds and the limiting absorption principle. The
Sommerfeld uniqueness result also follows as a corollary of these. In
particular, the Hamiltonians considered in this paper cover the case of
inverted harmonic oscillator. In the proofs of our theorems, we mainly use a
commutator argument invented recently by Ito and Skibsted. This argument is
simple and elementary, and dose not employ energy cut-offs or the microlocal
analysis.


  We investigate the effect of the quadratic correction $\alpha R^2$ and
non-minimal coupling $\xi \phi^2 R$ on a quintessence model with an exponential
potential $V(\phi) = M^4\exp(-\lambda\phi)$ in the Palatini formulation of
gravity. We use dynamical system techniques to analyze the attractor structure
of the model and uncover the possible trajectories of the system. We find that
the quadratic correction cannot play a role in the late time dynamics, except
for unacceptably large values of the parameter $\alpha$; although it can play a
role at early times. We find viable evolutions, from a matter-dominated phase
to an accelerated expansion phase, with the dynamics driven by the non-minimal
coupling. These evolutions correspond to trajectories where the field ends up
frozen, thus acting as a cosmological constant.


  There is broad consensus in the worldwide physics community as to the need
for a new reactor-neutrino experiment to measure or limit the neutrino mixing
angle $\theta_{13}$. The Double Chooz Experiment, planned for operation in the
years 2008-2011, will search for values of $\sin^2{2\theta_{13}}$ down to
$\approx$0.03. This will be the first new information on $\theta_{13}$ in over
a decade and will cover most of the remaining parameter space. A quick and
relatively inexpensive project is made possible by the existing neutrino
laboratory at the Chooz site.


  The elliptic flow in heavy ion collisions at RHIC is studied in a multiphase
transport model. By converting the strings in the high energy density regions
into partons, we find that the final elliptic flow is sensitive to the parton
scattering cross section. To reproduce the large elliptic flow observed in
Au+Au collisions at $\sqrt s=130A$ GeV requires a parton scattering cross
section of about 6 mb. We also study the dependence of the elliptic flow on the
particle multiplicity, transverse momentum, and particle mass.


  We confirm an eighth gravitational lens system in the CASSOWARY catalogue.
Exploratory observations with the X-shooter spectrograph on the VLT show the
system CSWA5 to consist of at least three images of a blue star-forming galaxy
at z = 1.0686, lensed by an apparent foreground group of red galaxies one of
which is at z = 0.3877. The lensed galaxy exhibits a rich spectrum with broad
interstellar absorption lines and a wealth of nebular emission lines.
Preliminary analysis of these features shows the galaxy to be young, with an
age of 25-50 Myr. With a star-formation rate of approximately 20 solar
masses/yr, the galaxy has already assembled a stellar mass of 3 x 10^9 solar
masses and reached half-solar metallicity. Its blue spectral energy
distribution and Balmer line ratios suggest negligible internal dust
extinction. A more in-depth analysis of the properties of this system is
currently hampered by the lack of a viable lensing model. However, it is
already clear that CSWA5 shares many of its physical characteristics with the
general population of UV-selected galaxies at redshifts z = 1-3, motivating
further study of both the source and the foreground mass concentration
responsible for the gravitational lensing.


  In this letter, new exact explicit solutions are obtained for the Li\'enard
equation, and the applications of the results to the generalized
Pochhammer-Chree equation, the Kundu equation and the generalized long-short
wave resonance equations are presented.


  The condensates of cold atoms at zero temperature in the tunable binary
Bose-Einstein condensate system are studied with the Rabi transition between
atomic hyperfine states where the system can be represented by a coupled
two-field model of gapless excitations and gapped excitations. We set up the
configuration of the supersonic and subsonic regimes with the acoustic horizon
between them in the elongated two-component Bose-Einstein condensates, trying
to mimic Hawking radiations, in particular due to the gapped excitations. The
simplified step-like sound speed change is adopted for the subsonic-supersonic
transition so that the model can be analytically treatable. The effective
energy gap term in the dispersion relation of the gapped excitations introduces
the threshold frequency $\omega_\text{min}$ in the subsonic regime, below which
the propagating modes do not exist. Thus, the particle spectrum of the Hawking
modes significantly deviates from that of the gapless cases near the threshold
frequency due to the modified grey-body factor, which vanishes as the mode
frequency is below $\omega_\text{min}$. The influence from the gapped
excitations to the quantum entanglement of the Hawking mode and its partner of
the gapless excitations is also studied according to the Peres-Horodecki-Simon
(PHS) criterion. It is found that the presence of the gapped excitations will
deteriorate the quantumness of the pair modes of the gapless excitations when
the frequency of the pair modes in particular is around $\omega \sim
\omega_\text{min}$. On top of that, when the coupling constant between the
gapless and gapped excitations becomes large enough, the huge particle density
of the gapped excitations in the small $\omega$ regime will significantly
disentangle the pair modes of the gapless excitations. The detailed
time-dependent PHS criterion will be discussed.


  Explicit expressions for the non-singlet and singlet structure functions g_1
at the small $x$-region are obtained. They include the total resummation of
double-logarithmic contributions and accounting for the running QCD coupling
effects. We predict that both the non-singlet and singlet g_1 asymptotically ~
x^{- \Delta}, with the singlet intercept
  = 0.86 and being more than twice larger than the non-singlet intercept = 0.4.
The impact of the initial quark and gluon densities on the sign of g_1 at x <<
1 is discussed.


  We develop an efficient parallel multiscale method that bridges the atomistic
and mesoscale regimes, from nanometer to micron and beyond, via concurrent
coupling of atomistic simulation and mesoscopic dynamics. In particular, we
combine an all-atom molecular dynamics (MD) description for specific atomistic
details in the vicinity of the functional surface, with a dissipative particle
dynamics (DPD) approach that captures mesoscopic hydrodynamics in the domain
away from the functional surface. In order to achieve a seamless transition in
dynamic properties we endow the MD simulation with a DPD thermostat, which is
validated against experimental results by modeling water at different
temperatures. We then validate the MD-DPD coupling method for transient Couette
and Poiseuille flows, demonstrating that the concurrent MD-DPD coupling can
resolve accurately the continuum-based analytical solutions. Subsequently, we
simulate shear flows over polydimethylsiloxane (PDMS)-grafted surfaces (polymer
brushes) for various grafting densities, and investigate the slip flow as a
function of the shear stress. We verify that a "universal" power law exists for
the sliplength, in agreement with published results. Having validated the
MD-DPD coupling method, we simulate time-dependent flows past an endothelial
glycocalyx layer (EGL) in a microchannel. Coupled simulation results elucidate
the dynamics of EGL changing from an equilibrium state to a compressed state
under shear by aligning the molecular structures along the shear direction.
MD-DPD simulation results agree well with results of a single MD simulation,
but with the former more than two orders of magnitude faster than the latter
for system sizes above one micron.


  In this paper, we prove that a set of $N$ points in ${\bf R}^2$ has at least
$c{N \over \log N}$ distinct distances, thus obtaining the sharp exponent in a
problem of Erd\"os. We follow the set-up of Elekes and Sharir which, in the
spirit of the Erlangen program, allows us to study the problem in the group of
rigid motions of the plane. This converts the problem to one of point-line
incidences in space. We introduce two new ideas in our proof. In order to
control points where many lines are incident, we create a cell decompostion
using the polynomial ham sandwich theorem. This creates a dichotomy: either
most of the points are in the interiors of the cells, in which case we
immediately get sharp results, or alternatively the points lie on the walls of
the cells, in which case they are in the zero set of a polynomial of
suprisingly low degree, and we may apply the algebraic method. In order to
control points where only two lines are incident, we use the flecnode
polynomial of the Rev. George Salmon to conclude that most of the lines lie on
a ruled surface. Then we use the geometry of ruled surfaces to complete the
proof.


  The isotope ratio, 85Rb/87Rb, places constraints on models of the
nucleosynthesis of heavy elements, but there is no precise determination of the
ratio for material beyond the Solar System. We report the first measurement of
the interstellar Rb isotope ratio. Our measurement of the Rb I line at 7800 A
for the diffuse gas toward rho Oph A yields a value of 1.21 +/- 0.30 (1-sigma)
that differs significantly from the meteoritic value of 2.59. The Rb/K
elemental abundance ratio for the cloud also is lower than that seen in
meteorites. Comparison of the 85Rb/K and 87Rb/K ratios with meteoritic values
indicates that the interstellar 85Rb abundance in this direction is lower than
the Solar System abundance. We attribute the lower abundance to a reduced
contribution from the r-process. Interstellar abundances for Kr, Cd, and Sn are
consistent with much less r-process synthesis for the solar neighborhood
compared to the amount inferred for the Solar System.


  In the conventional information theoretic analysis of multiterminal
communication scenarios, it is often assumed that all of the distributed
terminals use the communication channel simultaneously. However, in practical
wireless communication systems - due to restricted computation complexity at
network terminals - a limited number of users can be activated either in uplink
or downlink simultaneously. This necessitates the design of a scheduler which
determines the set of active users at each time-slot. A well designed scheduler
maximizes the average system utility subject to a set of fairness criteria,
which must be met in a limited window-length to avoid long starvation periods.
In this work, scheduling under short-term temporal fairness constraints is
considered. The objective is to maximize the average system utility such that
the fraction of the time-slots that each user is activated is within desired
upper and lower bounds in the fairness window-length. The set of feasible
window-lengths is characterized as a function of system parameters. It is shown
that the optimal system utility is non-monotonic and super-additive in
window-length. Furthermore, a scheduling strategy is proposed which satisfies
short-term fairness constraints for arbitrary window-lengths, and achieves
optimal average system utility as the window-length is increased
asymptotically. Numerical simulations are provided to verify the results.


  We consider the family of irreducible crystalline representations of
dimension $2$ of ${\rm Gal}(\overline{\bf Q}_p/{\bf Q}_p)$ given by the
$V_{k,a_p}$ for a fixed weight integer $k\geq 2$. We study the locus of the
parameter $a_p$ where these representations have a given reduction modulo $p$.
We give qualitative results on this locus and show that for a fixed $p$ and $k$
it can be computed by determining the reduction modulo $p$ of $V_{k,a_p}$ for a
finite number of values of the parameter $a_p$. We also generalize these
results to other Galois types.


  Berenstein and Kirillov have studied the action of Bender-Knuth moves on
semistandard tableaux. Losev has studied a cactus group action in
Kazhdan-Lusztig theory; in type $A$ this action can also be identified in the
work of Henriques and Kamnitzer. We establish the relationship between the two
actions. We show that the Berenstein-Kirillov group is a quotient of the cactus
group. We use this to derive previously unknown relations in the
Berenstein-Kirillov group. We also determine precise implications between
subsets of relations in the two groups, which yields a presentation for cactus
groups in terms of Bender-Knuth generators.


  We study the K\"ahler geometry of stage n Bott manifolds, which can be viewed
as $n$-dimensional generalizations of Hirzebruch surfaces. We show, using a
simple induction argument and the generalized Calabi construction from
[ACGT04,ACGT11], that any stage n Bott manifold $M_n$ admits an extremal
K\"ahler metric. We also give necessary conditions for $M_n$ to admit a
constant scalar curvature K\"ahler metric. We obtain more precise results for
stage 3 Bott manifolds, including in particular some interesting relations with
c-projective geometry and some explicit examples of almost K\"ahler structures.
  To place these results in context, we review and develop the topology,
complex geometry and symplectic geometry of Bott manifolds. In particular, we
study the K\"ahler cone, the automorphism group and the Fano condition. We also
relate the number of conjugacy classes of maximal tori in the symplectomorphism
group to the number of biholomorphism classes compatible with the symplectic
structure.


  Multi-access edge computing (MEC) is a key enabler to reduce the latency of
vehicular network. Due to the vehicles mobility, their requested services
(e.g., infotainment services) should frequently be migrated across different
MEC servers to guarantee their stringent quality of service requirements. In
this paper, we study the problem of service migration in a MEC-enabled
vehicular network in order to minimize the total service latency and migration
cost. This problem is formulated as a nonlinear integer program and is
linearized to help obtaining the optimal solution using off-the-shelf solvers.
Then, to obtain an efficient solution, it is modeled as a multi-agent Markov
decision process and solved by leveraging deep Q learning (DQL) algorithm. The
proposed DQL scheme performs a proactive services migration while ensuring
their continuity under high mobility constraints. Finally, simulations results
show that the proposed DQL scheme achieves close-to-optimal performance.


  When solving renormalisation group equations in a quantum field theory, one
often specifies the boundary conditions at multiple renormalisation scales,
such as the weak and grand-unified scales in a theory beyond the standard
model. A point in the parameter space of such a model is usually specified by
the values of couplings at these boundaries of the renormalisation group flow,
but there is no theorem guaranteeing that such a point has a unique solution to
the associated differential equations, and so there may exist multiple,
phenomenologically distinct solutions, all corresponding to the same point in
parameter space. We show that this is indeed the case in the constrained
minimal supersymmetric standard model (CMSSM), and we exhibit such solutions,
which cannot be obtained using out-of-the-box computer programs in the public
domain. Some of the multiple solutions we exhibit have CP-even lightest Higgs
mass predictions between 124 and 126 GeV. Without an exhaustive 11-dimensional
MSSM parameter scan per CMSSM parameter point to capture all of the multiple
solutions, CMSSM phenomenological analyses are incomplete.


  This paper proposes a hybrid approach for co-channel speech segregation. HMM
(hidden Markov model) is used to track the pitches of 2 talkers. The resulting
pitch tracks are then enriched with the prominent pitch. The enriched tracks
are correctly grouped using pitch continuity. Medium frame harmonics are used
to extract the second pitch for frames with only one pitch deduced using the
previous steps. Finally, the pitch tracks are input to CASA (computational
auditory scene analysis) to segregate the mixed speech. The center frequency
range of the gamma tone filter banks is maximized to reduce the overlap between
the channels filtered for better segregation. Experiments were conducted using
this hybrid approach on the speech separation challenge database and compared
to the single (non-hybrid) approaches, i.e. signal processing and CASA. Results
show that using the hybrid approach outperforms the single approaches.


  We summarize recent progress in next-to-leading order QCD calculations made
using the Monte Carlo MCFM. In particular, we focus on the calculations of p
anti-p -> W b-bbar, Z b-bbar and highlight the significant corrections to
background estimates for Higgs searches in the channels WH and ZH at the
Tevatron. We also report on the current progress of, and strategies for, the
calculation of the process p anti-p -> W/Z + 2 jets.


  We discuss the possibilities for extracting information on the parton density
functions and the strong coupling constant from one- and two-jet events at the
Fermilab TEVATRON. First we study the inclusive two-jet triply differential
cross section $d^3\sigma/dE_Td\eta_1d\eta_2$. Different $\eta_1$ and $\eta_2$
pseudorapidity regions are directly related to the parton momentum fractions at
leading order and the shape of the triply differential distribution at fixed
transverse energy $E_T$ is a particularly powerful tool for constraining the
parton distributions at small to moderate $x$ values. Second, we consider the
one-jet inclusive transverse energy distribution where there is impressive
agreement between theory and experiment over a wide range of transverse energy.
By equating the next-to-leading order theoretical prediction for a given set of
input parton densities with the published CDF data, the evolution of the strong
coupling constant at scale $\mu$ can be studied between $\mu \sim 50~$GeV and
$\mu \sim 400~$GeV. This evolution is in agreement with QCD and corresponds to
$\alpha_s(M_Z)$ = 0.121 for the MRSA parameterisation.


  In this paper, firstly, inspired by Nat\'{a}rio's recent work \cite{Na}, we
use the isoperimetric inequality to derive some Alexandrov-Fenchel type
inequalities for closed convex hypersurfaces in the hyperbolic space $\H^{n+1}$
and in the sphere $\SS^{n+1}$. We also get the rigidity in the spherical case.
Secondly, we use the inverse mean curvature flow in sphere \cite{gerh,Mak-Sch}
to prove an optimal Sobolev type inequality for closed convex hypersurfaces in
the sphere.


We prove rationality of the moduli variety of curves of genus 3.


  We present a novel approach to any-to-one (A2O) voice conversion (VC) in a
sequence-to-sequence (seq2seq) framework. A2O VC aims to convert any speaker,
including those unseen during training, to a fixed target speaker. We utilize
vq-wav2vec (VQW2V), a discretized self-supervised speech representation that
was learned from massive unlabeled data, which is assumed to be
speaker-independent and well corresponds to underlying linguistic contents.
Given a training dataset of the target speaker, we extract VQW2V and acoustic
features to estimate a seq2seq mapping function from the former to the latter.
With the help of a pretraining method and a newly designed postprocessing
technique, our model can be generalized to only 5 min of data, even
outperforming the same model trained with parallel data.


  In this paper, we proposed the \textit{link injection}, a novel method that
helps any differentiable graph machine learning models to go beyond observed
connections from the input data in an end-to-end learning fashion. It finds out
(weak) connections in favor of the current task that is not present in the
input data via a parametric link injection layer. We evaluate our method on
both node classification and link prediction tasks using a series of
state-of-the-art graph convolution networks. Results show that the link
injection helps a variety of models to achieve better performances on both
applications. Further empirical analysis shows a great potential of this method
in efficiently exploiting unseen connections from the injected links.


  We introduce a notion of relative isospectrality for surfaces with boundary
having possibly non-compact ends either conformally compact or asymptotic to
cusps. We obtain a compactness result for such families via a conformal surgery
that allows us to reduce to the case of surfaces hyperbolic near infinity
recently studied by Borthwick and Perry, or to the closed case by Osgood,
Phillips and Sarnak if there are only cusps.


  The ternary relation $B(x,y,z)$ of betweenness states that an element $y$ is
between the elements $x$ and $z$, in some sense depending on the considered
structure. In a partially ordered set $(N,\leq)$, $B(x,y,z):\Longleftrightarrow
x<y<z\vee z<y<x$. The corresponding betweenness structure is $(N,B)$. The class
of betweenness structures of linear orders is first-order definable. That of
partial orders is monadic second-order definable. An order-theoretic tree is a
partial order such that the set of elements larger that any element is linearly
ordered and any two elements have an upper-bound. Finite or infinite rooted
trees ordered by the ancestor relation are order-theoretic trees. In an
order-theoretic tree, we define $B(x,y,z)$ to mean that $x<y<z$ or $z<y<x$ or
$x<y\leq x\sqcup z$ or $z<y\leq x\sqcup z$ provided the least upper-bound
$x\sqcup z$ of $x$ and $z$ is defined when $x$ and $z$ are incomparable. In a
previous article, we established that the corresponding class of betweenness
structures is monadic second-order definable.We prove here that the induced
substructures of the betweenness structures of the countable order-theoretic
trees form a monadic second-order definable class, denoted by IBO. The proof
uses a variant of cographs, the partitioned probe cographs, and their known six
finite minimal excluded induced subgraphs called the bounds of the class. This
proof links two apparently unrelated topics: cographs and order-theoretic
trees.However, the class IBO has finitely many bounds, i.e., minimal excluded
finite induced substructures. Hence it is first-order definable. The proof of
finiteness uses well-quasi-orders and does not provide the finite list of
bounds. Hence, the associated first-order defining sentence is not known.


  In a recent paper, Brakensiek, Gopi and Makam introduced higher order MDS
codes as a generalization of MDS codes. An order-$\ell$ MDS code, denoted by
$\operatorname{MDS}(\ell)$, has the property that any $\ell$ subspaces formed
from columns of its generator matrix intersect as minimally as possible. An
independent work by Roth defined a different notion of higher order MDS codes
as those achieving a generalized singleton bound for list-decoding. In this
work, we show that these two notions of higher order MDS codes are (nearly)
equivalent.
  We also show that generic Reed-Solomon codes are $\operatorname{MDS}(\ell)$
for all $\ell$, relying crucially on the GM-MDS theorem which shows that
generator matrices of generic Reed-Solomon codes achieve any possible zero
pattern. As a corollary, this implies that generic Reed-Solomon codes achieve
list decoding capacity. More concretely, we show that, with high probability, a
random Reed-Solomon code of rate $R$ over an exponentially large field is list
decodable from radius $1-R-\epsilon$ with list size at most
$\frac{1-R-\epsilon}{\epsilon}$, resolving a conjecture of Shangguan and Tamo.


  A simplified model has previously described the inductive charging of
colliding identical grains in the presence of an external electric field. Here
we extend that model by including heterogeneous surface charge distributions,
grain rotations and electrostatic interactions between grains. We find from
this more realistic model that strong heterogeneities in charging can occur in
agitated granular beds, and we predict that shielding due to these
heterogeneities can dramatically alter the charging rate in such beds.


  This work examines the deep disconnect between existing theoretical analyses
of gradient-based algorithms and the practice of training deep neural networks.
Specifically, we provide numerical evidence that in large-scale neural network
training (e.g., ImageNet + ResNet101, and WT103 + TransformerXL models), the
neural network's weights do not converge to stationary points where the
gradient of the loss is zero. Remarkably, however, we observe that even though
the weights do not converge to stationary points, the progress in minimizing
the loss function halts and training loss stabilizes. Inspired by this
observation, we propose a new perspective based on ergodic theory of dynamical
systems to explain it. Rather than studying the evolution of weights, we study
the evolution of the distribution of weights. We prove convergence of the
distribution of weights to an approximate invariant measure, thereby explaining
how the training loss can stabilize without weights necessarily converging to
stationary points. We further discuss how this perspective can better align
optimization theory with empirical observations in machine learning practice.


  This paper describes the Seventh Data Release of the Sloan Digital Sky Survey
(SDSS), marking the completion of the original goals of the SDSS and the end of
the phase known as SDSS-II. It includes 11663 deg^2 of imaging data, with most
of the roughly 2000 deg^2 increment over the previous data release lying in
regions of low Galactic latitude. The catalog contains five-band photometry for
357 million distinct objects. The survey also includes repeat photometry over
250 deg^2 along the Celestial Equator in the Southern Galactic Cap. A
coaddition of these data goes roughly two magnitudes fainter than the main
survey. The spectroscopy is now complete over a contiguous area of 7500 deg^2
in the Northern Galactic Cap, closing the gap that was present in previous data
releases. There are over 1.6 million spectra in total, including 930,000
galaxies, 120,000 quasars, and 460,000 stars. The data release includes
improved stellar photometry at low Galactic latitude. The astrometry has all
been recalibrated with the second version of the USNO CCD Astrograph Catalog
(UCAC-2), reducing the rms statistical errors at the bright end to 45
milli-arcseconds per coordinate. A systematic error in bright galaxy photometr
is less severe than previously reported for the majority of galaxies. Finally,
we describe a series of improvements to the spectroscopic reductions, including
better flat-fielding and improved wavelength calibration at the blue end,
better processing of objects with extremely strong narrow emission lines, and
an improved determination of stellar metallicities. (Abridged)


  We study the stability of neutron stars with toroidal magnetic fields by
magnetohydrodynamic simulation in full general relativity under assumption of
axial symmetry. Nonrotating and rigidly rotating neutron stars are prepared for
a variety of magnetic field configuration. For modeling the neutron stars, the
polytropic equation of state with the adiabatic index $\Gamma=2$ is used for
simplicity. It is found that nonrotating neutron stars are dynamically unstable
for the case that toroidal magnetic field strength varies $\propto
\varpi^{2k-1}$ with $k\geq 2$ (here $\varpi$ is the cylindrical radius),
whereas for $k=1$ the neutron stars are stable. After the onset of the
instability, unstable modes grow approximately in the Alfv\'en time scale and,
as a result, a convective motion is excited to change the magnetic field
profile until a new state, which is stable against axisymmetric perturbation,
is reached. We also find that rotation plays a role in stabilization, although
the instability still sets in in the Alfv\'en time scale when the ratio of
magnetic energy to rotational kinetic energy is larger than a critical value
$\sim 0.2$. Implication for the evolution of magnetized protoneutron stars is
discussed.


  This article deals with the construction of surfaces that are suitable for
representing pentachords or 5-pitch segments that are in the same $T/I$ class.
It is a generalization of the well known \"Ottingen-Riemann torus for triads of
neo-Riemannian theories. Two pentachords are near if they differ by a
particular set of contextual inversions and the whole contextual group of
inversions produces a Tiling (Tessellation) by pentagons on the surfaces. A
description of the surfaces as coverings of a particular Tiling is given in the
twelve-tone enharmonic scale case.


  We report on the calculation of the next-lo-leading order QCD corrections to
Higgs boson production and decay in association with top quarks. We consider
leptonic decays of top quarks leading to the hadronic process $pp\to e^+\nu_e\,
\mu^-\bar{\nu}_\mu \, b\bar{b}\,H\, (H\to X)$ at the LHC with $\sqrt{s}=13$
TeV. All resonant as well as non-resonant Feynman diagrams, interferences and
off-shell effects are included for the top quark and $W$ gauge boson. Decays of
the Higgs boson, on the other hand, are included in the
narrow-width-approximation. Specifically, we consider Higgs boson decays into
$b\bar{b}$, $\tau^+\tau^-$, $\gamma\gamma$ and $e^+e^-e^+e^-$. Numerical
results are given at the integrated and differential fiducial level for various
factorisation and renormalisation scale choices and different PDF sets. We
study the main theoretical uncertainties that are associated with neglected
higher order terms in the perturbative expansion and with different
parametrisations of the PDFs. Furthermore, we examine the size of the off-shell
effects by an explicit comparison to the calculation in the full
narrow-width-approximation. Finally, the impact of the contributions induced by
the bottom-quark parton density is investigated.


  We investigate the role of the chiral anomaly in hydrodynamic and crossover
regimes of transport in a Weyl or Dirac semimetal film. We show that the
magnetic-field-dependent part of the electric conductivity in the direction of
the magnetic field develops an unusual nonmonotonic dependence on temperature
dubbed the anomalous Gurzhi effect. This effect is realized in sufficiently
clean semimetals subject to a classically weak magnetic field where the
electron-electron scattering dominates and the relaxation of the
valley-imbalance charge density happens at the boundaries. Moreover, the
conditions for the realization of the conventional Gurzhi effect in
hydrodynamic and crossover regimes of transport in three-dimensional Dirac and
Weyl semimetals are determined.


  We make explict a description in terms of convex geometry of the higher
Bruhat orders B(n,d) sketched by Kapranov and Voevodsky. We give an analogous
description of the higher Stasheff-Tamari poset S_1(n,d). We show that the map
f sketched by Kapranov and Voevodsky from B(n,d) to S([0,n+1],d+1) coincides
with the map constructed by Rambau, and is a surjection for d<=2. We construct
a map analogous to f from S_1(n,d) to B(n-1,d), and show that it is always a
poset embedding. We also give an explicit criterion to determine if an element
of B(n-1,d) is in the image of this map.


  Spectrum sensing plays a critical role in dynamic spectrum sharing, a
promising technology to address the radio spectrum shortage. In particular,
sensing of Orthogonal frequency division multiplexing (OFDM) signals, a widely
accepted multi-carrier transmission paradigm, has received paramount interest.
Despite various efforts, most conventional OFDM sensing methods suffer from
noise uncertainty, timing delay and carrier frequency offset (CFO) that
significantly degrade the sensing accuracy. To address these challenges, this
work develops two novel OFDM sensing frameworks drawing support from deep
learning networks. Specifically, we first propose a stacked autoencoder based
spectrum sensing method (SAE-SS), in which a stacked autoencoder network is
designed to extract the inherent features of OFDM signals. Using these features
to classify the OFDM user's activities, SAE-SS is much more robust to noise
uncertainty, timing delay, and CFO than the conventional OFDM sensing methods.
Moreover, SAE-SS doesn't require any prior information of signals (e.g., signal
structure, pilot tones, cyclic prefix) which are essential for the conventional
feature-based OFDM sensing methods. To further improve the sensing accuracy of
SAE-SS, especially under low SNR conditions, we propose a stacked autoencoder
based spectrum sensing method using time-frequency domain signals (SAE-TF).
SAE-TF achieves higher sensing accuracy than SAW-SS at the cost of higher
computational complexity. Extensive simulation results show that both SAE-SS
and SAE-TF can achieve significantly higher sensing accuracy, compared with
state of the art approaches that suffer from noise uncertainty, timing delay
and CFO.


  We investigate the phenomenon of second sound in various states of matter
from the perspective of non-equilibrium effective field theory (EFT). In
particular, for each state of matter considered, we find that at least two
(though sometimes multiple) qualitatively different EFTs exist at finite
temperature such that there is always at least one EFT with a propagating
second-sound wave and at least one with no such second-sound wave. To aid in
the construction of these EFTs, we use the method of cosets developed for
non-equilibrium systems. It turns out that the difference between the EFTs with
and without second-sound modes can be understood as arising from different
choices of a new kind of inverse Higgs constraint. Finally, we demonstrate that
it is possible to bypass the need for new inverse Higgs constraints by
formulating EFTs on a new kind of manifold that is like the usual fluid
worldvolume, but with reduced gauge symmetries.


  In this paper, we extend our PrInDT method (Weihs & Buschfeld 2021a) towards
undersampling with different percentages of the smaller and the larger classes
(psmall and plarge), stratification of predictors, varying the prediction
threshold, and measuring variable importance in ensembles. An application of
these methods to a linguistic example suggests the following: 1. In
undersampling, a careful selection of the percentages plarge and psmall is
important for building models with high balanced accuracies; 2. Stratification
of predictors does not majorly enhance balanced accuracies; 3. Lowering the
prediction threshold for the smaller class turns out to be an alternative
method to undersampling because it increases the likelihood of the smaller
class being selected. Finally, we introduce a method for ranking predictor
importance that allows for a straightforward interpretation of the results.


  The electronic properties of as-prepared and purified unoriented
single-walled carbon nanotube films were studied by transmission measurements
over a broad frequency range (far-infrared up to visible) as a function of
temperature (15 K - 295 K) and external pressure (up to 8 GPa). Both the
as-prepared and the purified SWCNT films exhibit nearly temperature-independent
properties. With increasing pressure the low-energy absorbance decreases
suggesting an increasing carrier localization due to pressure-induced
deformations. The energy of the optical transitions in the SWCNTs decreases
with increasing pressure, which can be attributed to pressure-induced
hybridization and symmetry-breaking effects. We find an anomaly in the
pressure-induced shift of the optical transitions at $\sim$2 GPa due to a
structural phase transition.


  The article continues our study of the genus of a regular language $L$,
defined as the minimal genus among all genera of all finite deterministic
automata recognizing $L$. Here we define and study two closely related tools on
a directed graph: directed emulators and automatic relations. A directed
emulator morphism essentially encapsulates at the graph-theoretic level an
epimorphism onto the minimal deterministic automaton. An automatic relation is
the graph-theoretic version of the Myhill-Nerode relation. We show that an
automatic relation determines a directed emulator morphism and respectively, a
directed emulator morphism determines an automatic relation up to isomorphism.
Consider the set $S$ of all directed emulators of the underlying directed graph
of the minimal deterministic automaton for $L$. We prove that the genus of $L$
is $\underset{G \in S}{\min}\ g(G)$. We also consider the more restrictive
notion of directed cover and prove that the genus of $L$ is reached in the
class of directed covers of the underlying directed graph of the minimal
deterministic automaton for $L$. This stands in sharp contrast to undirected
emulators and undirected covers which we also consider. Finally we prove that
if the problem of determining the minimal genus of a directed emulator of a
directed graph has a solution then the problem of determining the minimal genus
of an undirected emulator of an undirected graph has a solution.


  Ultraluminous and luminous infrared galaxies (ULIRGs and LIRGs) are the most
extreme star-forming galaxies in the universe, and dominate the total star
formation rate density at z>1. In the local universe (z<0.3), the majority of
ULIRGs and a significant portion of LIRGs are triggered by interactions between
gas-rich spiral galaxies, yet it is unclear if this is still the case at
high-z. To investigate the relative importance of galaxy interactions in
infrared luminous galaxies, we carry out a comparison of optical morphological
properties between local (U)LIRGs and (U)LIRGs at z=0.5-1.5 based on the same
sample selection, morphology classification scheme, and optical morphology at
similar rest-frame wavelengths. In addition, we quantify the systematics in
comparing local and high-z datasets by constructing a redshifted dataset from
local (U)LIRGs, in which its data quality mimics the high-z dataset. Based on
the Gini-M20 classification scheme, we find that the fraction of interacting
systems decreases by ~8% from local to z<~1, and it is consistent with the
reduction between local and redshifted datasets (6(+14-6)%). Based on visual
classifications, the merger fraction of local ULIRGs is found to be ~20% lower
compared to published results, and the reduction due to redshifiting is
15(+10-8)%. Consequently, the differences of merger fractions between local and
z<~1 (U)LIRGs is only ~17%. These results demonstrate that there is no strong
evolution in the fraction of (U)LIRGs classified as mergers at least out to
z~1. At z>1, the morphology types of ~30% of (U)LIRGs can not be determined due
to their faintness in the F814W-band, and thus the merger fraction measured at
z>1 suffers from large uncertainties.


  Systems for symbolic event recognition accept as input a stream of
time-stamped events from sensors and other computational devices, and seek to
identify high-level composite events, collections of events that satisfy some
pattern. RTEC is an Event Calculus dialect with novel implementation and
'windowing' techniques that allow for efficient event recognition, scalable to
large data streams. RTEC can deal with applications where event data arrive
with a (variable) delay from, and are revised by, the underlying sources. RTEC
can update already recognised events and recognise new events when data arrive
with a delay or following data revision. Our evaluation shows that RTEC can
support real-time event recognition and is capable of meeting the performance
requirements identified in a recent survey of event processing use cases.


  Stationary fronts connecting the trivial state and a cellular (distorted)
hexagonal pattern in the Swift-Hohenberg equation with a quadratic-cubic
nonlinearity are known to undergo a process of infinitely many folds as a
parameter is varied, known as homoclinic snaking, where new hexagon cells are
added to the core, leading to a region of infinitely-many, co-existing
localized states. Outside the homoclinic snaking region, the hexagon fronts can
invade the trivial state in a bursting fashion. In this paper, we use a
far-field core decomposition to set up a numerical path-following routine to
trace out the bifurcation diagrams of hexagon fronts for the two main
orientations of cellular hexagon pattern with respect to the interface in the
bistable region. We find for one orientation that the hexagon fronts can
destabilize as the distorted hexagons are stretched in the transverse direction
leading to defects occurring in the deposited cellular pattern. We then plot
diagrams showing when the selected fronts for the two main orientations,
aligned perpendicular to each other, are compatible leading to a hexagon
wavenumber selection prediction for hexagon patches on the plane. Finally, we
verify the compatibility criterion for hexagon patches in the Swift-Hohenberg
equation with a quadratic-cubic nonlinearity and a large non-variational
perturbation. The numerical algorithms presented in this paper can be adapted
to general reaction-diffusion systems.


  Using a proposed numerical technique for calculating anomalous Green's
functions characteristic of superconductivity, we show that the low-lying
excitations in a wide parameter and doping region of the two-dimensional
$t$$-$$J$ model are well described by the picture of dressed Bogoliubov
quasiparticles in the BCS pairing theory. The pairing occurs predominantly in
$d_{x^2-y^2}$-wave channel and the energy gap has a size
$\Delta_d$$\simeq$$0.15J$$-0.27J$ between quarter and half fillings. Opening of
the superconducting gap in the photoemission and inverse-photoemission spectrum
is demonstrated.


  Two aspects of high-energy \pp collisions share common phenomenological
elements: (a) A correlation between jet production and \pp centrality is
suggested by the transverse partonic structure of hadrons inferred from
deep-inelastic scattering data. (b) The {\em underlying event} (UE) is defined
as the final-state particles complementary to a triggered high-energy dijet. An
observable common to both topics is variation of so-called {\em transverse
multiplicity} $N_\perp$ with a $p_{t,trig}$ dijet trigger. We test assumptions
associated with \pp collision centrality and the UE. We determine the nature of
the UE and explore the relation between jet production and \pp centrality. We
use the {\em two-component model} (TCM) of spectra and correlations derived
from 200 GeV \pp collisions to construct a simulated particle distribution on
$(p_t,n_{ch})$ to predict the $N_\perp$ response to $p_{t,trig}$. The $p_t$
spectrum TCM combined in this analysis with measured minimum-bias \pp angular
correlations suggests that the UE includes a substantial contribution from the
triggered dijet in addition to the contribution from projectile fragmentation
(beam-beam remnants). The jet contribution to $N_\perp$ may represent a
universal large-angle base common to all dijets that extends across $2\pi$
azimuth. The analysis further suggests that \pp centrality is not controlled
significantly by $p_{t,trig}$ but may be correlated to some extent with an
imposed $n_{ch}$ condition, depending on the role of fluctuations. Future
correlation studies may better determine the role of \pp centrality. These
results may have implications for ongoing RHIC analysis and LHC searches for
physics beyond the standard model.


  In this paper we will show how to classify Legendrian and transverse knots in
the knot type of "sufficiently positive" cables of a knot in terms of the
classification of the underlying knot. We will also completely explain the
phenomena of "Legendrian large" cables. These are Legendrian representatives of
cables that have Thurston-Bennequin invariant larger that the framing coming
from the cabling torus. Such examples have only recently, and unexpectedly,
been found. We will also give criteria that determines the classification of
Legendrian and transverse knots the the knot type of negative cables.


  Graphene has extraordinary electronic and optical properties and holds great
promise for applications in photonics and optoelectronics. Demonstrations
including high-speed photodetectors, optical modulators, plasmonic devices, and
ultrafast lasers have now been reported. More advanced device concepts would
involve photonic elements such as cavities to control light-matter interaction
in graphene. Here we report the first monolithic integration of a graphene
transistor and a planar, optical microcavity. We find that the
microcavity-induced optical confinement controls the efficiency and spectral
selection of photocurrent generation in the integrated graphene device. A
twenty-fold enhancement of photocurrent is demonstrated. The optical cavity
also determines the spectral properties of the electrically excited thermal
radiation of graphene. Most interestingly, we find that the cavity confinement
modifies the electrical transport characteristics of the integrated graphene
transistor. Our experimental approach opens up a route towards cavity-quantum
electrodynamics on the nanometre scale with graphene as a current-carrying
intra-cavity medium of atomic thickness.


  In this paper the necessary and sufficient conditions for the product of
composition operators to be isometry are obtained on weighted Bergman space.
With the help of a counter example we also proved that unlike on
$\mathcal{H}^2(\mathbb{D})$ and $\mathcal{A}_{\alpha}^2(\mathbb{D}),$ the
composition operator on $\mathcal{S}^2(\mathbb{D})$ induced by an analytic self
map on $\mathbb{D}$ with fixed origin need not be of norm one. We have
generalized the Schwartz's well known result on
$\mathcal{A}_{\alpha}^2(\mathbb{D})$ which characterizes the almost
multiplicative operator on $\mathcal{H}^2(\mathbb{D}).$


  We show how to use information about the equations defining secant varieties
to smooth projective varieties in order to construct a natural collection of
birational transformations. These were first constructed as flips in the case
of curves by M. Thaddeus via Geometric Invariant Theory, and the first flip in
the sequence was constructed by the author for varieties of arbitrary dimension
in an earlier paper. We expose the finer structure of a second flip; again for
varieties of arbitrary dimension. We also prove a result on the cubic
generation of the secant variety and give some conjectures on the behavior of
equations defining the higher secant varieties.


  Forward marginal effects (FMEs) have recently been introduced as a versatile
and effective model-agnostic interpretation method. They provide comprehensible
and actionable model explanations in the form of: If we change $x$ by an amount
$h$, what is the change in predicted outcome $\widehat{y}$? We present the R
package fmeffects, the first software implementation of FMEs. The relevant
theoretical background, package functionality and handling, as well as the
software design and options for future extensions are discussed in this paper.


  We explore the signals of axion-like particles (ALPs) in flavor-changing
neutral current (FCNC) processes. The most general effective linear Lagrangian
for ALP couplings to the electroweak bosonic sector is considered, and its
contribution to FCNC decays is computed up to one-loop order. The interplay
between the different couplings opens new territory for experimental
exploration, as analyzed here in the ALP mass range $0<m_a \lesssim 5$ GeV.
When kinematically allowed, $K\to \pi \nu \bar{\nu}$ decays provide the most
stringent constraints for channels with invisible final states, while $B$-meson
decays are more constraining for visible decay channels, such as displaced
vertices in $B\to K^{(\ast)} \mu^+ \mu^-$ data. The complementarity with
collider constraints is discussed as well.


  We study the selfenergy of the $\Theta^+$ pentaquark in nuclei associated
with two types of interaction: the KN decay of the $\Theta^+$ and two meson
baryon decay channels of the $\Theta^+$. Whereas the potential related to the
first source is quite weak, the second kind of interaction produces a large and
attractive potential that could lead to the existence of $\Theta^+$ nuclear
bound states.


  In a recent paper, I defined the "standard multiparameter Bailey pair"
(SMPBP) and demonstrated that all of the classical Bailey pairs considered by
W.N. Bailey in his famous paper (\textit{Proc. London Math. Soc. (2)},
\textbf{50} (1948), 1--10) arose as special cases of the SMPBP. Additionally, I
was able to find a number of new Rogers-Ramanujan type identities. From a given
Bailey pair, normally only one or two Rogers-Ramanujan type identities follow
immediately. In this present work, I present the set of $q$-difference
equations associated with the SMPBP, and use these $q$-difference equations to
deduce the complete families of Rogers-Ramanujan type identities.


  Many blockchain-based cryptocurrencies provide users with online blockchain
explorers for viewing online transaction data. However, traditional blockchain
explorers mostly present transaction information in textual and tabular forms.
Such forms make understanding cryptocurrency transaction mechanisms difficult
for novice users (NUsers). They are also insufficiently informative for
experienced users (EUsers) to recognize advanced transaction information. This
study introduces a new online cryptocurrency transaction data viewing tool
called SilkViser. Guided by detailed scenario and requirement analyses, we
create a series of appreciating visualization designs, such as paper
ledger-inspired block and blockchain visualizations and ancient copper
coin-inspired transaction visualizations, to help users understand
cryptocurrency transaction mechanisms and recognize advanced transaction
information. We also provide a set of lightweight interactions to facilitate
easy and free data exploration. Moreover, a controlled user study is conducted
to quantitatively evaluate the usability and effectiveness of SilkViser.
Results indicate that SilkViser can satisfy the requirements of NUsers and
EUsers. Our visualization designs can compensate for the inexperience of NUsers
in data viewing and attract potential users to participate in cryptocurrency
transactions.


  We proposed an analytical expression for the amplitude defining the long
distance asymptotic of the correlation function <\sigma^z_k \sigma^z_{k+n}>.


  Geo-neutrino studies are based on theoretical estimates of geo-neutrino
spectra. We propose a method for a direct measurement of the energy
distribution of antineutrinos from decays of long-lived radioactive isotopes.