  We present the first results of our survey of asteroid polarization-phase
curves in the near-infrared J and H bands using the WIRC+Pol instrument on the
Palomar 200-inch telescope. We confirm through observations of standard stars
that WIRC+Pol can reach the 0.1% precision needed for asteroid phase curve
characterization, and show that C-complex asteroids could act as an alternate
calibration source as they show less wavelength variation than stellar
polarized standards. Initial polarization-phase curve results for S-complex
asteroids show a shift in behavior as a function of wavelength from visible to
near-infrared bands, extending previously observed trends. Full near-infrared
polarization-phase curve characterization of individual asteroids will provide
a unique constraint on surface composition of these objects by probing the
wavelength dependence of albedo and index of refraction of the surface
material.


  We address the expressions for the rates of the Keplerian orbital elements
within a two-body problem perturbed by the tides in both partners. The formulae
for these rates have appeared in the literature in various forms, at times with
errors. We reconsider, from scratch, the derivation of these rates and arrive
at the Lagrange-type equations which, in some details, differ from the
corresponding equations obtained previously by Kaula (1964).
  We also write down detailed expressions for $da/dt$, $de/dt$ and $di/dt$, to
order $e^4$. They differ from Kaula's expressions which contain a redundant
factor of $M/(M+M^{\prime}),$ with $M$ and $M^{\prime}$ being the masses of the
primary and the secondary. As Kaula was interested in the Earth-Moon system,
this redundant factor was close to unity and was unimportant in his
developments. This factor, however, must be reinstated when Kaula's theory is
applied to a binary composed of partners of comparable masses.
  We have found that, while it is legitimate to simply sum the primary's and
secondary's inputs in $da/dt$ or $de/dt$, this is not the case for $di/dt$. So
our expression for $di/dt$ differs from that of Kaula in two regards. First,
the contribution due to the dissipation in the secondary averages out when the
apsidal precession is uniform. Second, we have obtained an additional term
which emerges owing to the conservation of the angular momentum: a change in
the inclination of the orbit causes a change of the primary's plane of equator.


  We consider asymptotic behavior of the following fourth order equation \[
\Delta^2 u= \rho \frac{e^{u}}{\int_\Om e^{u} dx} {in} \Om, u= \partial_\nu u=0
{on} \partial \Omega \] where $\Om$ is a smooth oriented bounded domain in
$\R^4$. Assuming that $0<\rho \leq C$, we completely characterize the
asymptotic behavior of the unbounded solutions.


  We perform a comprehensive study of the time evolution of heavy-quarkonium
states in an expanding hot QCD medium by implementing effective field theory
techniques in the framework of open quantum systems. The formalism incorporates
quarkonium production and its subsequent evolution in the fireball including
quarkonium dissociation and recombination. We consider a fireball with a local
temperature that is much smaller than the inverse size of the quarkonium and
much larger than its binding energy. The calculation is performed at an
accuracy that is leading-order in the heavy-quark density expansion and
next-to-leading order in the multipole expansion. Within this accuracy, for a
smooth variation of the temperature and large times, the evolution equation can
be written as a Lindblad equation. We solve the Lindblad equation numerically
both for a weakly-coupled quark-gluon plasma and a strongly-coupled medium. As
an application, we compute the nuclear modification factor for the
$\Upsilon(1S)$ and $\Upsilon(2S)$ states. We also consider the case of static
quarks, which can be solved analytically. Our study fulfils three essential
conditions: it conserves the total number of heavy quarks, it accounts for the
non-Abelian nature of QCD and it avoids classical approximations.


  We prove an abstract result giving a $\langle t\rangle^{\epsilon}$ upper
bound on the growth of the Sobolev norms of a time dependent Schr\"odinger
equation of the form $i \dot \psi = H_0 \psi + V(t) \psi $. $H_0$ is assumed to
be the Hamiltonian of a steep quantum integrable system and to be a
pseudodifferential operator of order ${\tt d}>1$; $V(t)$ is a time dependent
family of pseudodifferential operators, unbounded, but of order ${\tt b}<{\tt
d}$. The abstract theorem is then applied to perturbations of the quantum
anharmonic oscillators in dimension 2 and to perturbations of the Laplacian on
a manifold with integrable geodesic flow, and in particular Zoll manifolds,
rotation invariant surfaces and Lie groups. We also cover the case of several
particles on a Zoll manifold or on a Lie group, possibly obeying some
restrictions due to the Fermionic or Bosonic nature of the particles. The proof
is based a on quantum version of the proof of the classical Nekhoroshev
theorem.


  In this paper, we study the generalization properties of neural networks
under input perturbations and show that minimal training data corruption by a
few pixel modifications can cause drastic overfitting. We propose an
evolutionary algorithm to search for optimal pixel perturbations using novel
cost function inspired from literature in domain adaptation that explicitly
maximizes the generalization gap and domain divergence between clean and
corrupted images. Our method outperforms previous pixel-based data distribution
shift methods on state-of-the-art Convolutional Neural Networks (CNNs)
architectures. Interestingly, we find that the choice of optimization plays an
important role in generalization robustness due to the empirical observation
that SGD is resilient to such training data corruption unlike adaptive
optimization techniques (ADAM). Our source code is available at
https://github.com/subhajitchaudhury/evo-shift.


  Even though many objects and phenomena of importance in geophysics have been
shown to have fractal character, there are still many of them which show
self-similar character and yet to be studied. The objective of the present work
is to demonstrate that the fractal dimension of the boundary of a natural water
body can be used to shed light on irregularity as well as other properties of a
region. Owing to easy availability of satellite images and image processing
softwares this turns out to be a handy tool. In this study, we have analyzed
several lakes in India mostly around the Western Ghats region. We find that the
fractal dimension of their boundaries for the length scales between around 40
meters to 2 kilometers, in general, has broad variation from 1.2 to 1.6. But
when they are grouped into three categories, viz., lakes along the ridge of
Western Ghats, lakes in the planes and lakes in the mountain region, we find
the first two groups to have a narrower distribution of dimensions.


  Security metrics are not standardized, but inter-national proposals such as
the Common Vulnerability ScoringSystem (CVSS) for quantifying the severity of
known vulnerabil-ities are widely used. Many CVSS aggregation mechanisms
havebeen proposed in the literature. Nevertheless, factors related tothe
context of the System Under Test (SUT) are not taken intoaccount in the
aggregation process; vulnerabilities that in theoryaffect the SUT, but are not
exploitable in reality. We propose aCVSS aggregation algorithm that integrates
information aboutthe functionality disruption of the SUT, exploitation
difficulty,existence of exploits, and the context where the SUT operates.The
aggregation algorithm was applied to OpenPLC V3, showingthat it is capable of
filtering out vulnerabilities that cannot beexploited in the real conditions of
deployment of the particularsystem. Finally, because of the nature of the
proposed algorithm,the result can be interpreted in the same way as a normal
CVSS.


  We propose a beyond mean field approach to evaluate Yang-Mills thermodynamics
from the partition function with n-body gluon contribution, in the presence of
a uniform background Polyakov field. Using a path integral based formalism, we
obtain, unlike the previous mean field studies within this model framework,
physically consistent results with good agreement to the lattice data
throughout the temperature range.


  Xgrid is the first distributed computing architecture built into a desktop
operating system. It allows you to run a single job across multiple computers
at once. All you need is at least one Macintosh computer running Mac OS X v10.4
or later. (Mac OS X Server is not required.) We provide explicit instructions
and example code to get you started, including examples of how to distribute
your computing jobs, even if your initial cluster consists of just two old
laptops in your basement.


  The aim of this paper is to study quasitriangular structures on a class of
semisimple Hopf algebras constructed through abelian extensions of $Z_2$ for an
abelian group $G$. We prove that there are only two forms of them. Using such
description together with some other techniques, we get a complete list of all
universal $\mathcal{R}$-matrices on some Hopf algebras.


  The rapid advancement of artificial intelligence (AI) has been marked by the
large language models exhibiting human-like intelligence. However, these models
also present unprecedented challenges to energy consumption and environmental
sustainability. One promising solution is to revisit analogue computing, a
technique that predates digital computing and exploits emerging analogue
electronic devices, such as resistive memory, which features in-memory
computing, high scalability, and nonvolatility. However, analogue computing
still faces the same challenges as before: programming nonidealities and
expensive programming due to the underlying devices physics. Here, we report a
universal solution, software-hardware co-design using structural
plasticity-inspired edge pruning to optimize the topology of a randomly
weighted analogue resistive memory neural network. Software-wise, the topology
of a randomly weighted neural network is optimized by pruning connections
rather than precisely tuning resistive memory weights. Hardware-wise, we reveal
the physical origin of the programming stochasticity using transmission
electron microscopy, which is leveraged for large-scale and low-cost
implementation of an overparameterized random neural network containing
high-performance sub-networks. We implemented the co-design on a 40nm 256K
resistive memory macro, observing 17.3% and 19.9% accuracy improvements in
image and audio classification on FashionMNIST and Spoken digits datasets, as
well as 9.8% (2%) improvement in PR (ROC) in image segmentation on DRIVE
datasets, respectively. This is accompanied by 82.1%, 51.2%, and 99.8%
improvement in energy efficiency thanks to analogue in-memory computing. By
embracing the intrinsic stochasticity and in-memory computing, this work may
solve the biggest obstacle of analogue computing systems and thus unleash their
immense potential for next-generation AI hardware.


  In this paper we revisit Noether's theorem on the constants of motion for
Lagrangian mechanical systems in the ODE case, with some new perspectives on
both the theoretical and the applied side. We make full use of invariance up to
a divergence, or, as we call it here, Bessel-Hagen (BH) invariance. By
recognizing that the Bessel-Hagen (BH) function need not be a total time
derivative, we can easily deduce nonlocal constants of motion. We prove that we
can always trivialize either the time change or the BH-function, so that, in
particular, BH-invariance turns out not to be more general than Noether's
original invariance. We also propose a version of time change that simplifies
some key formulas. Applications include Lane-Emden equation, dissipative
systems, homogeneous potentials and superintegrable systems. Most notably, we
give two derivations of the Laplace-Runge-Lenz vector for Kepler's problem that
require space and time change only, without BH invariance, one with and one
without use of the Lagrange equation.


  Assuming the Riemann Hypothesis we obtain asymptotic estimates for the mean
value of the number of representations of an integer as a sum of two primes. By
proving a corresponding Omega-term, we prove that our result is essentially the
best possible.


  Millions of people are affected by acute and chronic wounds yearly across the
world. Continuous wound monitoring is important for wound specialists to allow
more accurate diagnosis and optimization of management protocols. Machine
Learning-based classification approaches provide optimal care strategies
resulting in more reliable outcomes, cost savings, healing time reduction, and
improved patient satisfaction. In this study, we use a deep learning-based
method to classify burn wound images into two or three different categories
based on the wound conditions. A pre-trained deep convolutional neural network,
AlexNet, is fine-tuned using a burn wound image dataset and utilized as the
classifier. The classifier's performance is evaluated using classification
metrics such as accuracy, precision, and recall as well as confusion matrix. A
comparison with previous works that used the same dataset showed that our
designed classifier improved the classification accuracy by more than 8%.


  We study the magneto-rotational instability (MRI) driven dynamo in a
geometrically thin disc ($H/R\ll 1$) using stratified zero net flux (ZNF)
shearing box simulations. We find that mean fields and EMFs oscillate with a
primary frequency $f_{\rm dyn} = 0.017$ ($\approx 9$ orbital period), but also
have higher harmonics at $3f_{\rm dyn}$. Correspondingly, the current helicity,
has two frequencies $2f_{\rm dyn}$ and $4f_{\rm dyn}$ respectively, which
appear to be the beat frequencies of mean fields and EMFs as expected from the
magnetic helicity density evolution equation. Further, we adopt a novel
inversion algorithm called the `Iterative Removal Of Sources' (IROS), to
extract the turbulent dynamo coefficients in the mean-field closure using the
mean magnetic fields and EMFs obtained from the shearing box simulation. We
show that an $\alpha-$effect ($\alpha_{yy}$) is predominantly responsible for
the creation of the poloidal field from the toroidal field, while shear
generates back a toroidal field from the poloidal field; indicating that an
$\alpha-\Omega$-type dynamo is operative in MRI-driven accretion discs. We also
find that both strong outflow ($\bar{v}_z$) and turbulent pumping ($\gamma_z$ )
transport mean fields away from the mid-plane. Instead of turbulent
diffusivity, they are the principal sink terms in the mean magnetic energy
evolution equation. We find encouraging evidence that a generative helicity
flux is responsible for the effective $\alpha$-effect. Finally, we point out
potential limitations of horizontal ($x-y$) averaging in defining the `mean' on
the extraction of dynamo coefficients and their physical interpretations.


  We study how to utilize (possibly machine-learned) predictions in a model for
computing under uncertainty in which an algorithm can query unknown data. The
goal is to minimize the number of queries needed to solve the problem. We
consider fundamental problems such as finding the minima of intersecting sets
of elements or sorting them (these problems can also be phrased as (hyper)graph
orientation problems), as well as the minimum spanning tree problem. We discuss
different measures for the prediction accuracy and design algorithms with
performance guarantees that improve with the accuracy of predictions and that
are robust with respect to very poor prediction quality. These measures are
intuitive and might be of general interest for inputs involving uncertainty
intervals. We show that our predictions are PAC learnable. We also provide new
structural insights for the minimum spanning tree problem that might be useful
in the context of explorable uncertainty regardless of predictions. Our results
prove that untrusted predictions can circumvent known lower bounds in the model
of explorable uncertainty. We complement our results by experiments that
empirically confirm the performance of our algorithms.


  In the search for phase change materials (PCM) that may rival traditional
random access memory, a complete understanding of the amorphous to crystalline
phase transition is required. For the well-known Ge2Sb2Te5 (GST) and GeTe (GT)
chalcogenides, which display nucleation and growth dominated crystallization
kinetics, respectively, this work explores the nanomechanical morphology of
amorphous and crystalline phases in 50 nm thin films. Subjecting these PCM
specimens to a lateral thermal gradient spanning the crystallization
temperature allows for a detailed morphological investigation. Surface and
depth-dependent analyses of the resulting amorphous, transition and crystalline
regions are achieved with shallow angle cross-sections, uniquely implemented
with beam exit Ar ion polishing. To resolve the distinct phases, ultrasonic
force microscopy (UFM) with simultaneous topography is implemented revealing a
relative stiffness contrast between the amorphous and crystalline phases of 14%
for the free film surface and 20% for the cross-sectioned surface. Nucleation
is observed to occur preferentially at the PCM-substrate and free film
interface for both GST and GT, while fine subsurface structures are found to be
sputtering direction dependent. Combining surface and cross-section
nanomechanical mapping in this manner allows 3D analysis of microstructure and
defects with nanoscale lateral and depth resolution, applicable to a wide range
of materials characterization studies where the detection of subtle variations
in elastic modulus or stiffness are required.


  Quillen et al.(2007) presented an imaging survey with the {\it Spitzer Space
Telescope} of 62 brightest cluster galaxies with optical line emission located
in the cores of X-ray luminous clusters. They found that at least half of these
sources have signs of excess infrared emission. Here we discuss the nature of
the IR emission and its implications for cool core clusters. The strength of
the mid-IR excess emission correlates with the luminosity of the optical
emission lines. Excluding the four systems dominated by an AGN, the excess
mid-infrared emission in the remaining brightest cluster galaxies is likely
related to star formation. The mass of molecular gas (estimated from CO
observations) is correlated with the IR luminosity as found for normal star
forming galaxies. The gas depletion time scale is about 1 Gyr. The physical
extent of the infrared excess is consistent with that of the optical emission
line nebulae. This supports the hypothesis that the star formation occurs in
molecular gas associated with the emission line nebulae and with evidence that
the emission line nebulae are mainly powered by ongoing star formation. We find
a correlation between mass deposition rates (${\dot M}_X$) estimated from the
X-ray emission and the star formation rate estimated from the infrared
luminosity. The star formation rates are 1/10 to 1/100 of the mass deposition
rates suggesting that the re-heating of the ICM is generally very effective in
reducing the amount of mass cooling from the hot phase but not eliminating it
completely.


  Recently, the increasing availability of repeated measurements in biomedical
studies has motivated the development of several statistical methods for the
dynamic prediction of survival in settings where a large (potentially
high-dimensional) number of longitudinal covariates is available. These methods
differ in both how they model the longitudinal covariates trajectories, and how
they specify the relationship between the longitudinal covariates and the
survival outcome. Because these methods are still quite new, little is known
about their applicability, limitations and performance when applied to
real-world data.
  To investigate these questions, we present a comparison of the predictive
performance of the aforementioned methods and two simpler prediction approaches
to three datasets that differ in terms of outcome type, sample size, number of
longitudinal covariates and length of follow-up. We discuss how different
modelling choices can have an impact on the possibility to accommodate
unbalanced study designs and on computing time, and compare the predictive
performance of the different approaches using a range of performance measures
and landmark times.


  Signatures of collective behavior have been measured in highly relativistic
p+p collisions, as well as in p+A, d+A, and 3He+A collisions. Numerous particle
correlation measurements in these systems have been successfully described by
calculations based on viscous hydrodynamic and transport models. These
observations raise the question of the minimum necessary conditions for a
system to exhibit collectivity. Recently, numerous scientists have raised the
question of whether the quarks and gluons generated in e+e- collisions may
satisfy these minimum conditions. In this paper we explore possible signatures
of collectivity, or lack thereof, in e+e- collisions utilizing A Multi-Phase
Transport (AMPT) framework which comprises melted color strings, parton
scattering, hadronization, and hadron re-scattering.


  The need for modern data analytics to combine relational, procedural, and
map-reduce-style functional processing is widely recognized. State-of-the-art
systems like Spark have added SQL front-ends and relational query optimization,
which promise an increase in expressiveness and performance. But how good are
these extensions at extracting high performance from modern hardware platforms?
  While Spark has made impressive progress, we show that for relational
workloads, there is still a significant gap compared with best-of-breed query
engines. And when stepping outside of the relational world, query optimization
techniques are ineffective if large parts of a computation have to be treated
as user-defined functions (UDFs).
  We present Flare: a new back-end for Spark that brings performance closer to
the best SQL engines, without giving up the added expressiveness of Spark. We
demonstrate order of magnitude speedups both for relational workloads such as
TPC-H, as well as for a range of machine learning kernels that combine
relational and iterative functional processing.
  Flare achieves these results through (1) compilation to native code, (2)
replacing parts of the Spark runtime system, and (3) extending the scope of
optimization and code generation to large classes of UDFs.


  Planar functions over finite fields give rise to finite projective planes and
other combinatorial objects. They exist only in odd characteristic, but
recently Zhou introduced an even characteristic analogue which has similar
applications. In this paper we determine all planar functions on F_q of the
form c-->uc^t, where q is a power of 2, t is an integer with 0<t<=q^{1/4}, and
u is a nonzero element of F_q. This settles and sharpens a conjecture of
Schmidt and Zhou.


  By using AKNS scheme and soliton connection taking values in N=1
superconformal algebra we obtain new coupled super Nonlinear Schrodinger
equations.


  he starting process with countable number of types \mu(t) generates a stopped
branching process \xi(t). The starting process stops, by falling into the
nonempty set S. It is assumed, that the starting process is subcritical,
indecomposable and noncyclic. It is proved, that the extinction probability
converges to the cyclic function with period 1.


  The flavor changing top quark decays t -> cV (V=Z,photon,gluon) induced by
R-parity-violating couplings in the minimal supersymmetric standard model
(MSSM) are evaluated. We find that the decays t -> cV can be significantly
enhanced relative to those in the R-parity conserving SUSY model. Our results
show that the top quark FCNC decay can be as large as Br(t->cg)=10^-3,
Br(t->cZ)=10^-4 and Br(t-> c\gamma)= 10^-5, which may be observable at the
upgraded Tevatron and/or the LHC.


  The cohomology theory TMF of topological modular forms is a derived
algebro-geometric interpretation of the classical ring of complex modular forms
from number theory. In this article, we refine the classical Adams operations,
Hecke operators, and Atkin--Lehner involutions from endomorphisms of classical
modular forms to stable operators on TMF. Our algebro-geometric formulation of
these operators leads to simple proofs of their many remarkable properties and
computations. From these properties, we use techniques from homotopy theory to
make simple number-theoretic deductions, including a rederivation of some
classical congruences of Ramanujan and providing new infinite families of
classical Hecke operators which satisfy Maeda's conjecture.


  We discuss consequences of an entropic view of gravity, which differs in
details from the original proposals of Jacobson and Verlinde. We assume the
entropy is localized in the degrees of freedom of the systems interacting
gravitationally. We then find there is a density-dependent minimum length for
Newtonian gravity. This makes renormalizability issues irrelevant. It also
follows that at nanometer scales Newton's universal law fails, black holes with
mass $M_{BH} \lesssim 10^{-13} M_{\odot}$ do not exist and all Hawking
radiation is at unobservably low temperature.


  Let p > 2 be a prime number and let N be any rational integer. We consider
the p-class groups Cl(L), Cl(M) of the fields $L:=Q(N^{1/p})$ and
$M:=Q(N^{1/p},\mu_p)$, by comparison with the p-torsion groups T(L) and T(M) of
the abelian p-ramification theory, in the framework of the reflection theorem,
and obtain relations between the ranks of the isotypic components (Theorem
2.6). For p=3, we characterize the integers N such that L is 3-rational (i.e.,
T(L)=1), giving the following values: $N=3$; $N=3^d \ell$, $\ell = -1+ 3u$;
$N=3^d \ell$, $\ell=(1+3a)^2+27b^2$, with $\ell$ prime and $uab$ prime to 3
(Theorem 2.18). We show that the 3-class group Cl(L) is trivial if and only
Cl(M) is trivial (Theorem 2.19). We give various tables with PARI/GP programs
computing the structure of Cl(L), Cl(M), T(L), T(M), and of the logarithmic
class groups (Appendix A, B, C).


  We study the behaviour, in the simultaneous limits \hbar going to 0, t going
to \infty, of the Husimi and Wigner distributions of initial coherent states
and position eigenstates, evolved under the quantized hyperbolic toral
automorphisms and the quantized baker map. We show how the exponential mixing
of the underlying dynamics manifests itself in those quantities on time scales
logarithmic in \hbar. The phase space distributions of the coherent states,
evolved under either of those dynamics, are shown to equidistribute on the
torus in the limit \hbar going to 0, for times t between |\log\hbar|/(2\gamma)
and |\log|\hbar|/\gamma, where \gamma is the Lyapounov exponent of the
classical system. For times shorter than |\log\hbar|/(2\gamma), they remain
concentrated on the classical trajectory of the center of the coherent state.
The behaviour of the phase space distributions of evolved position eigenstates,
on the other hand, is not the same for the quantized automorphisms as for the
baker map. In the first case, they equidistribute provided t goes to \infty as
\hbar goes to 0, and as long as t is shorter than |\log\hbar|/\gamma. In the
second case, they remain localized on the evolved initial position at all such
times.


  We consider an asymptotic 1D (in space) rotation-Camassa-Holm (R-CH) model,
which could be used to describe the propagation of long-crested shallow-water
waves in the equatorial ocean regions with allowance for the weak Coriolis
effect due to the Earth's rotation. This model equation has similar
wave-breaking phenomena as the Camassa-Holm equation. It is analogous to the
rotation-Green-Naghdi (R-GN) equations with the weak Earth's rotation effect,
modeling the propagation of wave allowing large amplitude in shallow water. We
provide here a rigorous justification showing that solutions of the R-GN
equations tend to associated solution of the R-CH model equation in the
Camassa-Holm regime with the small amplitude and the larger wavelength.
Furthermore, we demonstrate that the R-GN model equations are locally
well-posed in a Sobolev space by the refined energy estimates.


  The goodness of fit methods for classification problems relies traditionally
on confusion matrices. This paper aims to enrich these methods with a risk
evaluation and stability analysis tools. For this purpose, we present a
parametric PDF framework.


  Stickers are increasingly used in social media to express sentiment and
intent. When finding typing troublesome, people often use a sticker instead.
Despite the significant impact of stickers on sentiment analysis and intent
recognition, little research has been conducted. To address this gap, we
propose a new task: Multimodal chat Sentiment Analysis and Intent Recognition
involving Stickers (MSAIRS). Additionally, we introduce a novel multimodal
dataset containing Chinese chat records and stickers excerpted from several
mainstream social media platforms. Our dataset includes paired data with the
same text but different stickers, and various stickers consisting of the same
images with different texts, allowing us to better understand the impact of
stickers on chat sentiment and intent. We also propose an effective multimodal
joint model, MMSAIR, for our task, which is validated on our datasets and
indicates that visual information of stickers counts. Our dataset and code will
be publicly available.


  In this study, we investigate the geodesic motion of a test particle around
the Schwarzchild black hole in a $\kappa$-deformed space-time. We compute a
modified Lagrangian to obtain the $\kappa$-deformed effective potential and
find the particle trajectories based on the constants of motion. For the same
value of angular momentum, we obtain a significant deformation in the orbits of
the particles due to the non-commutativity of the $\kappa$-deformed space-time.
The deformation parameter becomes more significant for higher values of the
angular momentum. The radius of the individual trajectories become smaller and
their velocities decrease compared to the commutative case. The radius of the
innermost stable circular orbit ($r_{ISCO}$) is also found using the modified
effective potential. Though the equations get modified due to the
non-commutativity of the $\kappa$-deformed space-time, the $r_{ISCO}$ remains
the same. We then study a large number of freely streaming particles moving in
this $\kappa$-deformed space-time and analyze the movement of these particles
around the black hole due to the non-commutativity of the space-time. We
concentrate on particles with different angular momentum moving around the
black hole. We find that the motion of the particles are modified due to the
non-commutativity of the space-time. The particles move slower along their
respective trajectories in the deformed space-time. So, they remain closer to
the black hole for a longer period of time, indicating that the accretion of
freely streaming particles around the black hole would be modified by the
non-commutativity of the space-time.


  We investigate the solvent mediated interactions between nanoparticles
adsorbed at a liquid-vapor interface in comparison to the solvent mediated
interactions in the bulk liquid and vapor phases of a Lennard-Jones solvent.
Molecular dynamics simulation data for the latter are in good agreement with
results from integral equations in the reference functional approximation and a
simple geometric approximation. Simulation results for the solvent mediated
interactions at the interface differ markedly from the interactions of the
particles in the corresponding bulk phases. We find that at short interparticle
distances the interactions are considerably more repulsive than those in either
bulk phase. At long interparticle distances we find evidence for a long-ranged
attraction. We discuss these observations in terms of interfacial interactions,
namely, the three-phase line tension that would operate at short distances, and
capillary wave interactions for longer interparticle distances.


  The interpretation of the most recent solar neutrinos experiments requires a
good knowledge of the cross section of the reaction 7Be(p,gamma)8B at very
small energy (Ecm=18 keV). We have recently measured this cross section for
Ecm=0.35-1.4 MeV and for Ecm=0.112-0.190 MeV. We report here on the description
of the preparation of the radioactive targets of 7Be used in these experiments.


  Uncertain recognition success, unfavorable scaling of connection complexity
or dependence on complex external input impair the usefulness of current
oscillatory neural networks for pattern recognition or restrict technical
realizations to small networks. We propose a new network architecture of
coupled oscillators for pattern recognition which shows none of the mentioned
aws. Furthermore we illustrate the recognition process with simulation results
and analyze the new dynamics analytically: Possible output patterns are
isolated attractors of the system. Additionally, simple criteria for
recognition success are derived from a lower bound on the basins of attraction.


  Large language models (LLMs) have demonstrated impressive performance on a
number of natural language processing tasks, such as question answering and
text summarization. However, their performance on sequence labeling tasks such
as intent classification and slot filling (IC-SF), which is a central component
in personal assistant systems, lags significantly behind discriminative models.
Furthermore, there is a lack of substantive research on the robustness of LLMs
to various perturbations in the input prompts. The contributions of this paper
are three-fold. First, we show that fine-tuning sufficiently large LLMs can
produce IC-SF performance comparable to discriminative models. Next, we
systematically analyze the performance deterioration of those fine-tuned models
due to three distinct yet relevant types of input perturbations - oronyms,
synonyms, and paraphrasing. Finally, we propose an efficient mitigation
approach, Prompt Perturbation Consistency Learning (PPCL), which works by
regularizing the divergence between losses from clean and perturbed samples.
Our experiments demonstrate that PPCL can recover on average 59% and 69% of the
performance drop for IC and SF tasks, respectively. Furthermore, PPCL beats the
data augmentation approach while using ten times fewer augmented data samples.


  Vacua of two dimensional incompressible system, such as Fractional Quantum
Hall system, are characterized by rational conformal field theory. We develop a
method to express the wavefunctions of those systems in terms of chiral
vertices. We formulate quantum mechanics on those expressions, which reveals
the underlying simple structure of the conformal field theory discription of
FQH systems. Also we argue the recent conjecture of Nayak and Wilczek on the
spinor statistics of 2n quasihole state in paired quantum hall system.


  The isoscalar giant monopole resonance (ISGMR) in even-A Cd isotopes has been
studied by inelastic ${\alpha}$-scattering at 100 MeV/u and at extremely
forward angles, including 0deg. The asymmetry term in the nuclear
incompressibility extracted from the ISGMR in Cd isotopes is found to be
$K_{\tau} = -555 \pm 75$ MeV, confirming the value previously obtained from the
Sn isotopes. ISGMR strength has been computed in relativistic RPA using NL3 and
FSUGold effective interactions. Both models significantly overestimate the
centroids of the ISGMR strength in the Cd isotopes. Combined with other recent
theoretical effort, the question of the "softness" of the open-shell nuclei in
the tin region remains open still.


  Symmetry and non-Hermiticity play pivotal roles in photonic lattices. While
symmetries such as parity-time ($\mathcal{PT}$) symmetry have attracted ample
attention, more intricate crystalline symmetries have been neglected in
comparison.
  Here, we investigate the impact of the 17 wallpaper space groups of
two-dimensional crystals on non-Hermitian band structures. We show that the
non-trivial space group representations enforce degeneracies at high symmetry
points and dictate their dispersion away from these points. In combination with
either $\mathcal{T}$ or $\mathcal{PT}$, the symmorphic p4mm symmetry, as well
as the non-symmorphic p2mg, p2gg, and p4gm symmetries, protect novel
exceptional chains intersecting at the pertinent high symmetry points.


  We propose a random matrix theory describing the influence of a time
dependent external field on the average magnetoresistance of open quantum dots.
The effect is taken into account in all orders of perturbation theory, and the
result is applicable to both weak and strong external fields.


  We present a numerical method for computing the \textit{Fermi} and
\textit{observational coordinates} of a distant test particle with respect to
an observer. We apply this method for computing some previously introduced
concepts of relative velocity: \textit{kinematic}, \textit{Fermi},
\textit{spectroscopic} and \textit{astrometric} relative velocities. We also
extend these concepts to non-convex normal neighborhoods and we make some
convergence tests, studying some fundamental examples in Schwarzschild and Kerr
spacetimes. Finally, we show an alternative method for computing the Fermi and
astrometric relative velocities.


  We study a class of combinatorial scheduling problems characterized by a
particular type of constraint often associated with electrical power or gas
energy. This constraint appears in several practical applications and is
expressed as a sum of squares of linear functions. Its nonlinear nature adds
complexity to the scheduling problem, rendering it notably challenging, even in
the case of a linear objective. In fact, exact polynomial time algorithms are
unlikely to exist, and thus, prior works have focused on designing
approximation algorithms with polynomial running time and provable guarantees
on the solution quality. In an effort to advance this line of research, we
present novel approximation algorithms yielding significant improvements over
the existing state-of-the-art results for these problems.


  In this paper, we present the Bag-of-Attributes (BoA) model for video
representation aiming at video event retrieval. The BoA model is based on a
semantic feature space for representing videos, resulting in high-level video
feature vectors. For creating a semantic space, i.e., the attribute space, we
can train a classifier using a labeled image dataset, obtaining a
classification model that can be understood as a high-level codebook. This
model is used to map low-level frame vectors into high-level vectors (e.g.,
classifier probability scores). Then, we apply pooling operations to the frame
vectors to create the final bag of attributes for the video. In the BoA
representation, each dimension corresponds to one category (or attribute) of
the semantic space. Other interesting properties are: compactness, flexibility
regarding the classifier, and ability to encode multiple semantic concepts in a
single video representation. Our experiments considered the semantic space
created by state-of-the-art convolutional neural networks pre-trained on 1000
object categories of ImageNet. Such deep neural networks were used to classify
each video frame and then different coding strategies were used to encode the
probability distribution from the softmax layer into a frame vector. Next,
different pooling strategies were used to combine frame vectors in the BoA
representation for a video. Results using BoA were comparable or superior to
the baselines in the task of video event retrieval using the EVVE dataset, with
the advantage of providing a much more compact representation.


  $ \newcommand{\R}{\ensuremath{\mathbb{R}}} \newcommand{\lat}{\mathcal{L}}
\newcommand{\ensuremath}[1]{#1} $We show that for any lattice $\lat \subseteq
\R^n$ and vectors $\vec{x}, \vec{y} \in \R^n$, \[ \rho(\lat + \vec{x})^2
\rho(\lat + \vec{y})^2 \leq \rho(\lat)^2 \rho(\lat + \vec{x} + \vec{y})
\rho(\lat + \vec{x} - \vec{y}) \; , \] where $\rho$ is the Gaussian measure
$\rho(A) := \sum_{\vec{w} \in A} \exp(-\pi \| \vec{w} \|^2)$. We show a number
of applications, including bounds on the moments of the discrete Gaussian
distribution, various monotonicity properties of the heat kernel on flat tori,
and a positive correlation inequality for Gaussian measures on lattices.


  In this work a method is proposed for computing step free energies for
faceted solid-liquid interfaces based on atomistic simulations. The method is
demonstrated in an application to (111) interfaces in elemental Si, modeled
with the classical Stillinger-Weber potential. The approach makes use of an
adiabatic trapping procedure, and involves simulations of systems with
coexisting solid and liquid phases separated by faceted interfaces containing
islands with different sizes, for which the corresponding equilibrium
temperatures are computed. We demonstrate that the calculated coexistence
temperature is strongly affected by the geometry of the interface. We find that
island radius is inversely proportional to superheating, allowing us to compute
the step free energy by fitting simulation data within the formalism of
classical nucleation theory. The approach outlined in this work paves the way
to the calculation of step free energies relevant to the solidification of
faceted crystals from liquid mixtures, as encountered in nanowire growth by the
vapor-liquid-solid mechanism and in alloy casting. The present work also shows
that at low undercoolings the Stillinger-Weber interatomic potential for Si
tends to crystallize in the wurtzite, rather than the diamond-cubic structure.


  We study dynamically coupled one-dimensional Bose-Hubbard models and solve
for the wave functions and energies of two-particle eigenstates. Even though
the wave functions do not directly follow the form of a Bethe Ansatz, we
describe an intuitive construction to express them as combinations of
Choy-Haldane states for models with intra- and inter-species interaction. We
find that the two-particle spectrum of the system with generic interactions
comprises in general four different continua and three doublon dispersions. The
existence of doublons depends on the coupling strength $\Omega$ between two
species of bosons, and their energies vary with $\Omega$ and interaction
strengths. We give details on one specific limit, i.e., with infinite
interaction, and derive the spectrum for all types of two-particle states and
their spatial and entanglement properties. We demonstrate the difference in
time evolution under different coupling strengths, and examine the relation
between the long-time behavior of the system and the doublon dispersion. These
dynamics can in principle be observed in cold atoms and might also be simulated
by digital quantum computers.


  We provide a nonasymptotic analysis of convergence to stationarity for a
collection of Markov chains on multivariate state spaces, from arbitrary
starting points, thereby generalizing results in [Khare and Zhou Ann. Appl.
Probab. 19 (2009) 737-777]. Our examples include the multi-allele Moran model
in population genetics and its variants in community ecology, a generalized
Ehrenfest urn model and variants of the Polya urn model. It is shown that all
these Markov chains are stochastically monotone with respect to an appropriate
partial ordering. Then, using a generalization of the results in [Diaconis,
Khare and Saloff-Coste Sankhya 72 (2010) 45-76] and [Wilson Ann. Appl. Probab.
14 (2004) 274-325] (for univariate totally ordered spaces) to multivariate
partially ordered spaces, we obtain explicit nonasymptotic bounds for the
distance to stationarity from arbitrary starting points. In previous
literature, bounds, if any, were available only from special starting points.
The analysis also works for nonreversible Markov chains, and allows us to
analyze cases of the multi-allele Moran model not considered in [Khare and Zhou
Ann. Appl. Probab. 19 (2009) 737-777].


  It is common practice to represent spoken languages at their phonetic level.
However, for sign languages, this implies breaking motion into its constituent
motion primitives. Avatar based Sign Language Production (SLP) has
traditionally done just this, building up animation from sequences of hand
motions, shapes and facial expressions. However, more recent deep learning
based solutions to SLP have tackled the problem using a single network that
estimates the full skeletal structure.
  We propose splitting the SLP task into two distinct jointly-trained
sub-tasks. The first translation sub-task translates from spoken language to a
latent sign language representation, with gloss supervision. Subsequently, the
animation sub-task aims to produce expressive sign language sequences that
closely resemble the learnt spatio-temporal representation. Using a progressive
transformer for the translation sub-task, we propose a novel Mixture of Motion
Primitives (MoMP) architecture for sign language animation. A set of distinct
motion primitives are learnt during training, that can be temporally combined
at inference to animate continuous sign language sequences.
  We evaluate on the challenging RWTH-PHOENIX-Weather-2014T(PHOENIX14T)
dataset, presenting extensive ablation studies and showing that MoMP
outperforms baselines in user evaluations. We achieve state-of-the-art back
translation performance with an 11% improvement over competing results.
Importantly, and for the first time, we showcase stronger performance for a
full translation pipeline going from spoken language to sign, than from gloss
to sign.


  A new negative result for nonparametric estimation of binary ergodic
processes is shown. I The problem of estimation of distribution with any degree
of accuracy is studied. Then it is shown that for any countable class of
estimators there is a zero-entropy binary ergodic process that is inconsistent
with the class of estimators. Our result is different from other negative
results for universal forecasting scheme of ergodic processes.


  Maximum Likelihood Estimation (MLE) and Likelihood Ratio Test (LRT) are
widely used methods for estimating the transition probability matrix in Markov
chains and identifying significant relationships between transitions, such as
equality. However, the estimated transition probability matrix derived from MLE
lacks accuracy compared to the real one, and LRT is inefficient in
high-dimensional Markov chains. In this study, we extended the adaptive Lasso
technique from linear models to Markov chains and proposed a novel model by
applying penalized maximum likelihood estimation to optimize the estimation of
the transition probability matrix. Meanwhile, we demonstrated that the new
model enjoys oracle properties, which means the estimated transition
probability matrix has the same performance as the real one when given.
Simulations show that our new method behave very well overall in comparison
with various competitors. Real data analysis further convince the value of our
proposed method.


  We prove the existence of global solutions to the Cauchy problem for
noncommutative nonlinear wave equations in arbitrary even spatial dimensions
where the noncommutativity is only in the spatial directions. We find that for
existence there are no conditions on the degree of the nonlinearity provided
the potential is positive. We furthermore prove that nonlinear noncommutative
waves have infinite propagation speed, i.e., if the initial conditions at time
0 have a compact support then for any positive time the support of the solution
can be arbitrarily large.


  In many real-world applications, from robotics to pedestrian trajectory
prediction, there is a need to predict multiple real-valued outputs to
represent several potential scenarios. Current deep learning techniques to
address multiple-output problems are based on two main methodologies: (1)
mixture density networks, which suffer from poor stability at high dimensions,
or (2) multiple choice learning (MCL), an approach that uses $M$ single-output
functions, each only producing a point estimate hypothesis. This paper presents
a Mixture of Multiple-Output functions (MoM) approach using a novel variant of
dropout, Multiple Hypothesis Dropout. Unlike traditional MCL-based approaches,
each multiple-output function not only estimates the mean but also the variance
for its hypothesis. This is achieved through a novel stochastic winner-take-all
loss which allows each multiple-output function to estimate variance through
the spread of its subnetwork predictions. Experiments on supervised learning
problems illustrate that our approach outperforms existing solutions for
reconstructing multimodal output distributions. Additional studies on
unsupervised learning problems show that estimating the parameters of latent
posterior distributions within a discrete autoencoder significantly improves
codebook efficiency, sample quality, precision and recall.


  We conceptualized three-array scalable metasurfaces comprising only three
thin strip grids and numerically demonstrated their characteristics in the
mid-infrared spectral regime for switchable polarization manipulation and
related asymmetric diodelike transmission (AT). A few or all of the grids were
taken to be made of VO$_2$, a phase-change material. For each proposed
metasurface, two effective structures and, therefore, two different
functionalities exist, corresponding to the metallic and insulating phases of
VO$_2$. The achieved scenarios of functionality switching that depend on the
VO$_2$ phase are shown to significantly depend in the way in which VO$_2$ is
incorporated to the metasurface. Switchable bands of polarization manipulation
are up to 40 THz wide. The AT band can be modulated when Fabry--Perot
(anti-)resonances come into play.


  We compute the Lyapunov exponents and the Kolmogorov-Sinai (KS) entropy for a
self-bound N-body system that is realized as a convex billiard. This system
exhibits truly high-dimensional chaos, and 2N-4 Lyapunov exponents are found to
be positive. The KS entropy increases linearly with the numbers of particles.
We examine the chaos generating defocusing mechanism and investigate how
high-dimensional chaos develops in this system with no dispersing elements.


  Threshold enhanced perturbative QCD corrections to rapidity distributions of
$Z$ and $W^\pm$ bosons at hadron colliders are presented using the Sudakov
resummed cross sections at N${}^3$LO level. We have used renormalisation group
invariance and the mass factorisation theorem that these hard scattering cross
sections satisfy to construct the QCD amplitudes. We show that these higher
order threshold QCD corrections stabilise the theoretical predictions for
vector boson production at the LHC under variations of both renormalisation and
factorisation scales.


  As Underwater Vehicle Manipulator Systems (UVMSs) have gotten smaller and
lighter over the past years, it is becoming increasingly important to consider
the coupling forces between the manipulator and the vehicle when planning and
controlling the system. A number of different models have been proposed, each
using different rigid body dynamics or hydrodynamics algorithms, or purporting
to consider different dynamic effects on the system, but most go without
experimental validation of the full model, and in particular, of the coupling
effect between the two systems. In this work, we return to a model combining
Featherstone's rigid body dynamics algorithms with Fossen's equations for
underwater dynamics by using the Julia package RigidBodyDynamics.jl. We compare
the simulation's output with experimental results from pool trials with a ten
degree of freedom UVMS that integrates a Reach Alpha manipulator with a
BlueROV2. We validate the model's usefulness and identify its strengths and
weaknesses in studying the dynamic coupling effect.


  In a single quantum dot (QD), the electrons were driven out of thermal
equilibrium by the back-action from a nearby quantum point contact (QPC). We
found the driving to energy excited states can be probed with the random
telegraph signal (RTS) statistics, when the excited states relax slowly
compared with RTS tunneling rate. We studied the last few electrons, and found
back-action driven spin singlet-triplet (S-T) excitation for and only for all
the even number of electrons. We developed a phenomenological model to
quantitatively characterize the spin S-T excitation rate, which enabled us to
evaluate the influence of back-action on spin S-T based qubit operations.


  The aim of this paper is to introduce a certain number of tools and results
suitable for the study of valuations of higher rank on function fields of
algebraic varieties. This will be based on a study of higher rank
quasi-monomial valuations taking values in the lexicographically ordered group
R^k.
  We prove a duality theorem that gives a geometric realization of higher rank
quasi-monomial valuations as tangent cones of dual cone complexes. Using this
duality, we provide an analytic description of quasi-monomial valuations as
multi-directional derivative operators on tropical functions.
  We consider moreover a refined notion of tropicalization in which we remember
the initial terms of power series on each cone of a dual complex, and prove a
tropical analogue of the weak approximation theorem in number theory by showing
that any compatible collection of initial terms on cones of a dual cone complex
is the refined tropicalization of a rational function in the function field of
the variety.
  Endowing the value group R^k with its Euclidean topology, we study then a
natural topology on spaces of higher rank valuations that we call the tropical
topology. By using the approximation theorem we provide an explicit description
of the tropical topology on tangent cones of dual cone complexes.
  Finally, we show that tangent cones of dual complexes provide a notion of
skeleton in higher rank non-archimedean geometry. That is, generalizing the
picture in rank one to higher rank, we construct retraction maps to tangent
cones of dual cone complexes, and use them to obtain limit formulae in which we
reconstruct higher rank non-archimedian spaces with their tropical topology as
the projective limit of their higher rank skeleta.
  We conjecture that these higher rank skeleta provide appropriate bases for
the study of variations of Newton-Okounkov bodies.


  In this article, we investigate the quantum circuit complexity and
entanglement entropy in the recently studied black hole gas framework using the
two-mode squeezed states formalism written in arbitrary dimensional spatially
flat cosmological Friedmann-Lema$\hat{i}$tre-Robertson-Walker (FLRW) background
space-time. We compute the various complexity measures and study the evolution
of these complexities by following two different prescriptions viz. Covariant
matrix method and Nielsen's method. Independently, using the two-mode squeezed
states formalism we also compute the R\'enyi and Von-Neumann entanglement
entropy, which show an inherent connection between the entanglement entropy and
quantum circuit complexity. We study the behaviour of the complexity measures
and entanglement entropy separately for three different spatial dimensions and
observe various significant different features in three spatial dimensions on
the evolution of these quantities with respect to the scale factor.
Furthermore, we also study the underlying behaviour of the equilibrium
temperature with two of the most essential quantities i.e. rate of change of
complexity with scale factor and the entanglement entropy. We observe that
irrespective of the spatial dimension, the equilibrium temperature depends
quartically on entanglement entropy.


  The goal of open-world compositional zero-shot learning (OW-CZSL) is to
recognize compositions of state and objects in images, given only a subset of
them during training and no prior on the unseen compositions. In this setting,
models operate on a huge output space, containing all possible state-object
compositions. While previous works tackle the problem by learning embeddings
for the compositions jointly, here we revisit a simple CZSL baseline and
predict the primitives, i.e. states and objects, independently. To ensure that
the model develops primitive-specific features, we equip the state and object
classifiers with separate, non-linear feature extractors. Moreover, we estimate
the feasibility of each composition through external knowledge, using this
prior to remove unfeasible compositions from the output space. Finally, we
propose a new setting, i.e. CZSL under partial supervision (pCZSL), where
either only objects or state labels are available during training, and we can
use our prior to estimate the missing labels. Our model, Knowledge-Guided
Simple Primitives (KG-SP), achieves state of the art in both OW-CZSL and pCZSL,
surpassing most recent competitors even when coupled with semi-supervised
learning techniques. Code available at: https://github.com/ExplainableML/KG-SP.


  We investigated the dependence of the optical depth $\tau$ of the
microlensing events on model parameters of the Galactic halo. We only consider
Galactic mass models in which the rotation curve inside the Sun is compatible
with the observation and LMC is bound to the Galaxy. It is found that $\tau$
varies up to a factor 2.5 from the standard spherical and flat rotation halo
model. This implies that only the most centrally concentrated halo model can be
consistent with the observation if the halo consists of only MACHOs. We also
calculate the power $x$ of IMF of MACHO consistent with Tyson's CCD survey as
well as Bahcall \etal's observation by {\em HST}. It is found that $x$ is
greater than 5.


  Nanoscale materials display enhanced strength and toughness but also larger
fluctuations and more pronounced size effects with respect to their macroscopic
counterparts. Here we study the system size-dependence of the failure strength
distribution of a monolayer graphene sheet with a small concentration of
vacancies by molecular dynamics simulations. We simulate sheets of varying size
encompassing more than three decades and systematically study their deformation
as a function of disorder, temperature and loading rate. We generalize the
weakest-link theory of fracture size effects to rate and temperature dependent
failure and find quantitative agreement with the simulations. Our numerical and
theoretical results explain the crossover of the fracture strength distribution
between a thermal and rate-dependent regime and a disorder-dominated regime
described by extreme value theory.


  A facile route for the fabrication of surface-attached hydrogel thin films
with well-controlled chemistry and tailored architecture on wide range of
thickness from nanometers to micrometers is reported. The synthesis, which
consists in cross-linking and grafting the preformed and ene-reactive polymer
chains through thiol--ene click chemistry, has the main advantage of being
well-controlled without the addition of initiators. As thiol--ene click
reaction can be selectively activated by UV-irradiation (in addition to thermal
heating), micropatterned hydrogel films are easily synthesized. The versatility
of our approach is illustrated by the possibility to fabricate various chemical
polymer networks, like stimuli-responsive hydrogels, on various solid
substrates, such as silicon wafers, glass, and gold surfaces. Another
attractive feature is the development of new complex hydrogel films with
targeted architecture. The fabrication of various architectures for polymer
films is demonstrated: multilayer hydrogel films in which single-networks are
stacked one onto the other, interpenetrating networks films with mixture of two
networks in the same layer, and nanocomposite hydrogel films where
nanoparticles are stably trapped inside the mesh of the network. Thanks to its
simplicity and its versatility this novel approach to surface-attached hydrogel
films should have a strong impact in the area of polymer coatings


  Quasiparticle states in Dirac systems with complex impurity potentials are
investigated. It is shown that an impurity site with loss leads to a nontrivial
distribution of the local density of states (LDOS). While the real part of
defect potential induces a well-pronounced peak in the density of states (DOS),
the DOS is either weakly enhanced at small frequencies or even forms a peak at
the zero frequency for a lattice in the case of non-Hermitian impurity. As for
the spatial distribution of the LDOS, it is enhanced in the vicinity of
impurity but shows a dip at a defect itself when the potential is sufficiently
strong. The results for a two-dimensional hexagonal lattice demonstrate the
characteristic trigonal-shaped profile for the LDOS. The latter acquires a
double-trigonal pattern in the case of two defects placed at neighboring sites.
The effects of non-Hermitian impurities could be tested both in photonic
lattices and certain condensed matter setups.


  We consider global topological defects in symmetry breaking models with a
non-canonical kinetic term. Apart from a mass parameter entering the potential,
one additional dimensional parameter arises in such models -- a ``kinetic''
mass. The properties of defects in these models are quite different from
``standard'' global domain walls, vortices and monopoles, if their kinetic mass
scale is smaller than their symmetry breaking scale. In particular, depending
on the concrete form of the kinetic term, the typical size of such a defect can
be either much larger or much smaller than the size of a standard defect with
the same potential term. The characteristic mass of a non-standard defect,
which might have been formed during a phase transition in the early universe,
depends on both the temperature of a phase transition and the kinetic mass.


  The quest for optimal operation in environments with unknowns and
uncertainties is highly desirable but critically challenging across numerous
fields. This paper develops a dual control framework for exploration and
exploitation (DCEE) to solve an auto-optimisation problem in such complex
settings. In general, there is a fundamental conflict between tracking an
unknown optimal operational condition and parameter identification. The DCEE
framework stands out by eliminating the need for additional perturbation
signals, a common requirement in existing adaptive control methods. Instead, it
inherently incorporates an exploration mechanism, actively probing the
uncertain environment to diminish belief uncertainty. An ensemble based
multi-estimator approach is developed to learn the environmental parameters and
in the meanwhile quantify the estimation uncertainty in real time. The control
action is devised with dual effects, which not only minimises the tracking
error between the current state and the believed unknown optimal operational
condition but also reduces belief uncertainty by proactively exploring the
environment. Formal properties of the proposed DCEE framework like convergence
are established. A numerical example is used to validate the effectiveness of
the proposed DCEE. Simulation results for maximum power point tracking are
provided to further demonstrate the potential of this new framework in real
world applications.


  In this paper, we propose an autonomous information seeking visual question
answering framework, AVIS. Our method leverages a Large Language Model (LLM) to
dynamically strategize the utilization of external tools and to investigate
their outputs, thereby acquiring the indispensable knowledge needed to provide
answers to the posed questions. Responding to visual questions that necessitate
external knowledge, such as "What event is commemorated by the building
depicted in this image?", is a complex task. This task presents a combinatorial
search space that demands a sequence of actions, including invoking APIs,
analyzing their responses, and making informed decisions. We conduct a user
study to collect a variety of instances of human decision-making when faced
with this task. This data is then used to design a system comprised of three
components: an LLM-powered planner that dynamically determines which tool to
use next, an LLM-powered reasoner that analyzes and extracts key information
from the tool outputs, and a working memory component that retains the acquired
information throughout the process. The collected user behavior serves as a
guide for our system in two key ways. First, we create a transition graph by
analyzing the sequence of decisions made by users. This graph delineates
distinct states and confines the set of actions available at each state.
Second, we use examples of user decision-making to provide our LLM-powered
planner and reasoner with relevant contextual instances, enhancing their
capacity to make informed decisions. We show that AVIS achieves
state-of-the-art results on knowledge-intensive visual question answering
benchmarks such as Infoseek and OK-VQA.


  Various approaches to estimate turbulent transport coefficients from
numerical simulations of hydromagnetic turbulence are discussed. A quantitative
comparison between the averaged magnetic field obtained from a specific
three-dimensional simulation of a rotating turbulent shear flow in a slab and a
simple one-dimensional alpha-omega dynamo model is given. A direct
determination of transport coefficients is attempted by calculating the
correlation matrix of different components of the field and its derivatives.
The alpha-effect operating on the toroidal field is found to be negative and of
similar magnitude as the value obtained previously by correlating the
electromotive force with the mean magnetic field. The turbulent diffusion of
the toroidal field is comparable to the kinematic viscosity that was determined
earlier by comparing the stress with the shear. However, the turbulent
diffusion of the radial field component is smaller and can even be formally
negative. The method is then modified to obtain the spectral dependence of the
turbulent transport coefficients on the wavenumber. There is evidence for
nonlocal behavior in that most of the response comes from the smallest
wavenumbers corresponding to the largest scale possible in the simulation.


  Motivated by a low-energy effective description of gauge theory/string theory
duality, we conjecture that the dynamics of $SO(4)$-invariant states in a large
class of four-dimensional conformal gauge theories on $S^3$ with non-equal
central charges $c\ne a$ are universal on time scales $t_{\rm universal}\propto
({\cal E}-{\cal E}_{\rm vacuum})^{-1}$, in the limit where the energy ${\cal
E}\to {\cal E}_{\rm vacuum}$. We show that low-energy excitations in $c\ne a$
CFTs do not thermalize in this limit. The holographic universality conjecture
then implies that within the Einstein-scalar field system (dual to theories
with $c=a$), $AdS_5$ is stable to spherically symmetric perturbations against
formation of trapped surfaces within time scales $t_{\rm universal}$.


  We prove that every integral rig in Sets is (functorially) the rig of global
sections of a sheaf of really local integral rigs. We also show that this
representation result may be lifted to residuated integral rigs and then
restricted to varieties of these. In particular, as a corollary, we obtain a
representation theorem for pre-linear residuated join-semilattices in terms of
totally ordered fibers. The restriction of this result to the level of
MV-algebras coincides with the Dubuc-Poveda representation theorem.


  Semantic Textual Relatedness holds significant relevance in Natural Language
Processing, finding applications across various domains. Traditionally,
approaches to STR have relied on knowledge-based and statistical methods.
However, with the emergence of Large Language Models, there has been a paradigm
shift, ushering in new methodologies. In this paper, we delve into the
investigation of sentence-level STR within Track A (Supervised) by leveraging
fine-tuning techniques on the RoBERTa transformer. Our study focuses on
assessing the efficacy of this approach across different languages. Notably,
our findings indicate promising advancements in STR performance, particularly
in Latin languages. Specifically, our results demonstrate notable improvements
in English, achieving a correlation of 0.82 and securing a commendable 19th
rank. Similarly, in Spanish, we achieved a correlation of 0.67, securing the
15th position. However, our approach encounters challenges in languages like
Arabic, where we observed a correlation of only 0.38, resulting in a 20th rank.


  This paper introduces a randomized Householder QR factorization (RHQR). This
factorization can be used to obtain a well conditioned basis of a vector space
and thus can be employed in a variety of applications. The RHQR factorization
of the input matrix $W$ is equivalent to the standard Householder QR
factorization of matrix $\Psi W$, where $\Psi$ is a sketching matrix that can
be obtained from any subspace embedding technique. For this reason, the RHQR
factorization can also be reconstructed from the Householder QR factorization
of the sketched problem, yielding a single-synchronization randomized QR
factorization (recRHQR). In most contexts, left-looking RHQR requires a single
synchronization per iteration, with half the computational cost of Householder
QR, and a similar cost to Randomized Gram-Schmidt (RGS) overall. We discuss the
usage of RHQR factorization in the Arnoldi process and then in GMRES, showing
thus how it can be used in Krylov subspace methods to solve systems of linear
equations. Based on Charles Sheffield's connection between Householder QR and
Modified Gram-Schmidt (MGS), a BLAS2-RGS is also derived. A finite precision
analysis shows that, under mild probabilistic assumptions, the RHQR
factorization of the input matrix $W$ inherits the stability of the Householder
QR factorization, producing a well-conditioned basis and a columnwise backward
stable factorization, all independently of the condition number of the input
$W$, and with the accuracy of the sketching step. We study the subsampled
randomized Hadamard transform (SRHT) as a very stable sketching technique.
  Numerical experiments show that RHQR produces a well conditioned basis whose
sketch is numerically orthogonal and an accurate factorization, even for the
most difficult inputs and with high-dimensional operations made in
half-precision.


  It was proved in 2009 that any partial Steiner triple system of order $u$ has
an embedding of order $v$ for each admissible integer $v\geq 2u+1$. This result
is best-possible in the sense that, for each $u\geq 9$, there exists a partial
Steiner triple system of order $u$ that does not have an embedding of order $v$
for any $v<2u+1$. Many partial Steiner triple systems do have embeddings of
orders smaller than $2u+1$, but little has been proved about when these
embeddings exist. In this paper we construct embeddings of orders less than
$2u+1$ for partial Steiner triple systems with few triples. In particular, we
show that a partial Steiner triple system of order $u \geq 62$ with at most
$\frac{u^2}{50}-\frac{11u}{100}-\frac{116}{75}$ triples has an embedding of
order $v$ for each admissible integer $v \geq \frac{8u+17}{5}$.


  The production of forward jets of transverse energy E_T\simeq Q and large
momentum fraction x_jet >> x is calculated in next-to-leading order including
consistently direct and resolved virtual photon contributions. The predictions
are compared to recent ZEUS and H1 data. Good agreement with the data is found.


  We present a new optimization-theoretic approach to analyzing
Follow-the-Leader style algorithms, particularly in the setting where
perturbations are used as a tool for regularization. We show that adding a
strongly convex penalty function to the decision rule and adding stochastic
perturbations to data correspond to deterministic and stochastic smoothing
operations, respectively. We establish an equivalence between "Follow the
Regularized Leader" and "Follow the Perturbed Leader" up to the smoothness
properties. This intuition leads to a new generic analysis framework that
recovers and improves the previous known regret bounds of the class of
algorithms commonly known as Follow the Perturbed Leader.


  Job burnout is a type of work-related stress associated with a state of
physical or emotional exhaustion that also involves a sense of reduced
accomplishment and loss of personal identity. Burnt out can affect one's
physical and mental health and has become a leading industry concern and can
result in high workforce turnover. Through an empirical study at Globant, a
large multi-national company, we created a theoretical model to evaluate the
complex interplay among organizational culture, work satisfaction, and team
climate, and how they impact developer burnout. We conducted a survey of
developers in software delivery teams (n=3281) to test our model and analyzed
the data using structural equation modeling, moderation, and multi-group
analysis. Our results show that Organizational Culture, Climate for Learning,
Sense of Belonging, and Inclusiveness are positively associated with Work
Satisfaction, which in turn is associated with Reduced Burnout. Our model
generated through a large-scale survey can guide organizations in how to reduce
workforce burnout by creating a climate for learning, inclusiveness in teams,
and a generative organizational culture where new ideas are welcome,
information is actively sought and bad news can be shared without fear.


  Motivated by the deviation of the W boson mass reported by the CDF
collaboration, we study an extension of the Standard Model (SM) including a
vector dark matter (VDM) candidate and a scalar mediator. In the model, the
one-loop corrections induced by the new scalar, shift the W boson mass. We
identify the parameter space of the model consistent with dark matter (DM)
relic abundance, W mass boson anomaly, invisible Higgs decay at LHC, and direct
detection of DM. It is shown that the W-mass anomaly can be explained for the
large part of parameter space of VDM mass and scalar mediator mass between
$100-124~\rm GeV$ by the model. We also investigate the renormalization group
equations (RGE) at one-loop order for the model. We show that the contribution
of new scalar mediator to RGE, guarantees positivity and vacuum stability of SM
Higgs up to Planck scale.


This paper has been withdrawn by the author


  A forcing poset of size 2^{2^{aleph_1}} which adds no new reals is described
and shown to provide a Delta^2_2 definable well-order of the reals (in fact,
any given relation of the reals may be so encoded in some generic extension).
The encoding of this well-order is obtained by playing with products of
Aronszajn trees: Some products are special while other are Suslin trees. The
paper also deals with the Magidor-Malitz logic: it is consistent that this
logic is highly non compact.


  Mechanical issues of noncircular and asymmetrical tunnelling can be estimated
using complex variable method with suitable conformal mapping. Exsiting
solution schemes of conformal mapping for noncircular tunnel generally need
iteration or optimization strategy, and are thereby mathematically complicated.
This paper proposes a new bidirectional conformal mapping for deep and shallow
tunnels of noncircular and asymmetrical shapes by incorporating Charge
Simulation Method. The solution scheme of this new bidirectional conformal
mapping only involves a pair of linear systems, and is therefore logically
straight-forward, computationally efficient, and practically easy in coding.
New numerical strategies are developed to deal with possible sharp corners of
cavity by small arc simulation and densified collocation points. Several
numerical examples are presented to illustrate the geometrical usage of the new
bidirectional conformal mapping. Furthermore, the new bidirectional conformal
mapping is embedded into two complex variable solutions of noncircular and
asymmetrical shallow tunnelling in gravitational geomaterial with reasonable
far-field displacement. The respective result comparisons with finite element
solution and exsiting analytical solution show good agreements, indicating the
feasible mechanical usage of the new bidirectional conformal mapping.


  It has recently been shown that generalized connections of the (A)dS space
symmetry algebra provide an effective geometric and algebraic framework for all
types of gauge fields in (A)dS, both for massless and partially-massless. The
equations of motion are equipped with a nilpotent operator called $\sigma_-$
whose cohomology groups correspond to the dynamically relevant quantities like
differential gauge parameters, dynamical fields, gauge invariant field
equations, Bianchi identities etc. In the paper the $\sigma_-$-cohomology is
computed for all gauge theories of this type and the field-theoretical
interpretation is discussed. In the simplest cases the $\sigma_-$-cohomology is
equivalent to the ordinary Lie algebra cohomology.


  Information Technology applications are growing significantly fast for the
past decade. Many Business organizations with emphasize on IT applications are
trying to gain competitive advantages. Empirical studies also demonstrate that
IT increases competitive advantage when it acts with human resources. In this
paper we analyzed and review how various IT applications can be utilized to to
provide a company with strategic advantages over the global marketplace
competitive forces.


  The two-parametric quantum superalgebra $U_{p,q}[gl(2/2)]$ and its induced
representations are considered. A method for constructing all
finite-dimensional irreducible representations of this quantum superalgebra is
also described in detail. It turns out that finite-dimensional representations
of the two-parametric $U_{p,q}[gl(2/2)]$, even at generic deformation
parameters, are not simply trivial deformations from those of the classical
superalgebra $gl(2/2)$, unlike the one-parametric cases.


  The Picard-Lefschetz theory offers a promising tool to solve the sign problem
in QCD and other field theories with complex path-integral weight. In this
paper the Lefschetz-thimble approach is examined in simple fermionic models
which share some features with QCD. In zero-dimensional versions of the
Gross-Neveu model and the Nambu-Jona-Lasinio model, we study the structure of
Lefschetz thimbles and its variation across the chiral phase transition. We map
out a phase diagram in the complex four-fermion coupling plane using a thimble
decomposition of the path integral, and demonstrate an interesting link between
anti-Stokes lines and Lee-Yang zeros. In the case of nonzero mass, it is shown
that the approach to the chiral limit is singular because of intricate
cancellation between competing thimbles, which implies the necessity to sum up
multiple thimbles related by symmetry. We also consider a Chern-Simons theory
with fermions in $0+1$-dimension and show how Lefschetz thimbles solve the
complex phase problem caused by a topological term. These prototypical examples
would aid future application of this framework to bona fide QCD.


  We study some sorts of dimensionally-deconstructed models for supersymmetric
(Euclidean) quantum mechanics, or zero-dimensional field theory. In these
models, we assign bosonic and fermionic variables to vertices and edges of a
graph. We investigate a discrete version for the Gaussian model and the
Wess-Zumino-type model on a graph. The topological index as a multiple integral
is discussed on these models. In addition, we propose simple examples for
supersymmetric extensions of the Lee-Wick model and the Galileon model. A model
with two supersymmetries is also provided and generalization to `local'
supersymmtric models is examined.


  Artificial intelligence (AI) and machine learning (ML) are nowadays mature
technologies considered essential for driving the evolution of future
communications systems. Simultaneously, Wi-Fi technology has constantly evolved
over the past three decades and incorporated new features generation after
generation, thus gaining in complexity. As such, researchers have observed that
AI/ML functionalities may be required to address the upcoming Wi-Fi challenges
that will be otherwise difficult to solve with traditional approaches. This
paper discusses the role of AI/ML in current and future Wi-Fi networks and
depicts the ways forward. A roadmap towards AI/ML-native Wi-Fi, key challenges,
standardization efforts, and major enablers are also discussed. An exemplary
use case is provided to showcase the potential of AI/ML in Wi-Fi at different
adoption stages.


  Shear Alfven wave parametric decay instability (PDI) provides a potential
path toward significant wave dissipation and plasma heating. However,
fundamental questions regarding how PDI is excited in a realistic
three-dimensional (3D) open system and how critically the finite perpendicular
wave scale--as found in both laboratory and space plasmas--affects the
excitation remain poorly understood. Here, we present the first 3D,
open-boundary, hybrid kinetic-fluid simulations of kinetic Alfven wave PDI in
low-beta plasmas. Key findings are that the PDI excitation is strongly limited
by the wave damping present, including electron-ion collisional damping
(represented by a constant resistivity) and geometrical attenuation associated
with the finite-scale Alfven wave, and ion Landau damping of the child acoustic
wave. The perpendicular wave scale alone, however, plays no discernible role:
waves of different perpendicular scales exhibit similar instability growth as
long as the magnitude of the parallel ponderomotive force remains unchanged.
These findings are corroborated by theoretical analysis and estimates. The new
understanding of 3D kinetic Alfv\'en wave PDI physics is essential for
laboratory study of the basic plasma process and may also help evaluate the
relevance/role of PDI in low-beta space plasmas.


  Federated learning (FL) hyper-parameters significantly affect the training
overheads in terms of computation time, transmission time, computation load,
and transmission load. However, the current practice of manually selecting FL
hyper-parameters puts a high burden on FL practitioners since various
applications prefer different training preferences. In this paper, we propose
FedTune, an automatic FL hyper-parameter tuning algorithm tailored to
applications' diverse system requirements of FL training. FedTune is
lightweight and flexible, achieving 8.48%-26.75% improvement for different
datasets compared to fixed FL hyper-parameters.


  Shared control can help in teleoperated object manipulation by assisting with
the execution of the user's intention. To this end, robust and prompt intention
estimation is needed, which relies on behavioral observations. Here, an
intention estimation framework is presented, which uses natural gaze and motion
features to predict the current action and the target object. The system is
trained and tested in a simulated environment with pick and place sequences
produced in a relatively cluttered scene and with both hands, with possible
hand-over to the other hand. Validation is conducted across different users and
hands, achieving good accuracy and earliness of prediction. An analysis of the
predictive power of single features shows the predominance of the grasping
trigger and the gaze features in the early identification of the current
action. In the current framework, the same probabilistic model can be used for
the two hands working in parallel and independently, while a rule-based model
is proposed to identify the resulting bimanual action. Finally, limitations and
perspectives of this approach to more complex, full-bimanual manipulations are
discussed.


  The general relativity is the base for any exact evolutionary theory of large
scale structures. We calculate the universal 2+1-dimensional plane equations of
gravitational field in general relativity. Based on the equations, the
evolutions of disk nebula are discussed. A system of nebula can form binary
stars or single star for different conditions. While any simplified linear
theory forms only a single star system. It is proved that the nonlinear
interactions are very general, so the binary stars are also common.


  We present the first detection of the mass donor star in the prototype X-ray
binary Scorpius X-1. Phase resolved spectroscopy revealed narrow emission lines
components from the irradiated secondary star. Radial velocity fits to the
Bowen blend emission are used to establish an absolute orbital ephemeris and
derive an accurate value for the systemic velocity; gamma= -113.8 +/- 0.6 km/s.
Emission from the irradiated front side of the secondary leads to solid limits
to the radial velocity of the mass donor of 87 < K_2 < 148 km/s. In conjunction
with an upper limit to the velocity of the primary K_1 < 53 km/s, we derive a
firm limit on the mass ratio of Sco X-1 of q < 0.61. % A likely set of system
parameters satisfying the various constraints as well as the recent inclination
estimate by Fomalont et al. (2001) is K_1=40 km/s, K_2=133 km/s, q=0.30
corresponding to component masses of M_1=1.4M_sun, M_2=0.42 M_sun for an
orbital inclination of 38 degrees.


  In the field of van der Waals heterostructures, the twist angle between
stacked two-dimensional (2D) layers has been identified to be of utmost
importance for the properties of the heterostructures. In this context, we
previously reported the growth of a single layer of unconventionally oriented
epitaxial graphene that forms in a surfactant atmosphere [F. C. Bocquet, et
al., Phys. Rev. Lett. 125, 106102 (2020)]. The resulting G-R0$^\circ$ layer is
aligned with the SiC lattice, and hence represents an important milestone
towards high quality twisted bilayer graphene (tBLG), a frequently investigated
model system in this field. Here, we focus on the surface structures obtained
in the same surfactant atmosphere, but at lower preparation temperatures at
which a boron nitride template layer forms on SiC(0001). In a comprehensive
study based on complementary experimental and theoretical techniques, we find
-- in contrast to the literature -- that this template layer is a hexagonal
B$_x$N$_y$ layer, but not high-quality hBN. It is aligned with the SiC lattice
and gradually replaced by low-quality graphene in the 0$^\circ$ orientation of
the B$_x$N$_y$ template layer upon annealing.


  We present a novel framework inspired by the Immersed Boundary Method for
predicting the fluid-structure interaction of complex structures immersed in
flows with moderate to high Reynolds numbers. The main novelties of the
proposed fluid-structure interaction framework are 1) the use of elastodynamics
equations for the structure, 2) the use of a high-order Navier-Stokes solver
for the flow, and 3) the variational transfer (L2-projection) for coupling the
solid and fluid subproblems. The dynamic behavior of a deformable structure is
simulated in a finite element framework by adopting a fully implicit scheme for
its temporal integration. It allows for mechanical constitutive laws including
nonhomogeneous and fiber-reinforced materials. The Navier-Stokes equations for
the incompressible flow are discretized with high-order finite differences
which allow for the direct numerical simulation of laminar, transitional and
turbulent flows. The structure and the flow solvers are coupled by using an
L2-projection method for the transfer of velocities and forces between the
fluid grid and the solid mesh. This strategy allows for the numerical solution
of coupled large scale problems based on nonconforming structured and
unstructured grids. The framework is validated with the Turek-Hron benchmark
and a newly proposed benchmark modelling the flow-induced oscillation of an
inert plate. A three-dimensional simulation of an elastic beam in transitional
flow is provided to show the solver's capability of coping with anisotropic
elastic structures immersed in complex fluid flow.


  Graph neural network (GNN) and label propagation algorithm (LPA) are both
message passing algorithms, which have achieved superior performance in
semi-supervised classification. GNN performs feature propagation by a neural
network to make predictions, while LPA uses label propagation across graph
adjacency matrix to get results. However, there is still no effective way to
directly combine these two kinds of algorithms. To address this issue, we
propose a novel Unified Message Passaging Model (UniMP) that can incorporate
feature and label propagation at both training and inference time. First, UniMP
adopts a Graph Transformer network, taking feature embedding and label
embedding as input information for propagation. Second, to train the network
without overfitting in self-loop input label information, UniMP introduces a
masked label prediction strategy, in which some percentage of input label
information are masked at random, and then predicted. UniMP conceptually
unifies feature propagation and label propagation and is empirically powerful.
It obtains new state-of-the-art semi-supervised classification results in Open
Graph Benchmark (OGB).


  This paper has investigated the growth pattern of traffic oscillations in the
NGSIM vehicle trajectories data, via measuring the standard deviation of
vehicle velocity involved in oscillations. We found that the standard deviation
of the velocity increases in a concave way along vehicles in the oscillations.
Moreover, all datasets collapse into a single concave curve, which indicates a
universal evolution law of oscillations. A comparison with traffic experiment
shows that the empirical and the experimental results are highly compatible and
can be fitted by a single concave curve, which demonstrates that qualitatively
the growth pattern of oscillations is not affected by type of bottleneck and
lane changing behavior. We have shown theoretically that small disturbances
increase in a convex way in the initial stage in the traditional models
presuming a unique relationship between speed and density, which obviously
deviates from our findings. Simulations show that stochastic models in which
the traffic state dynamically spans a 2D region in the speed-spacing plane can
qualitatively or even quantitatively reproduce the concave growth pattern of
traffic oscillations.


  The ROSAT Deep Cluster Survey (RDCS) has provided a new large deep sample of
X-ray selected galaxy clusters. Observables such as the flux number counts
n(S), the redshift distribution n(z) and the X-ray luminosity function (XLF)
over a large redshift baseline (z\lesssim 0.8) are used here in order to
constrain cosmological models. Our analysis is based on the Press-Schechter
approach, whose reliability is tested against N-body simulations. Following a
phenomenological approach, no assumption is made a priori on the relation
between cluster masses and observed X-ray luminosities. As a first step, we use
the local XLF from RDCS, along with the high-luminosity extension provided by
the XLF from the BCS, in order to constrain the amplitude of the power
spectrum, \sigma_8, and the shape of the local luminosity-temperature relation.
We obtain \sigma_8=0.58 +/- 0.06 for Omega_0=1 for open models at 90%
confidence level, almost independent of the L-T shape. The density parameter
\Omega_0 and the evolution of the L-T relation are constrained by the RDCS XLF
at z>0 and the EMSS XLF at z=0.33, and by the RDCS n(S) and n(z) distributions.
By modelling the evolution for the amplitude of the L-T relation as (1+z)^A, an
\Omega_0=1 model can be accommodated for the evolution of the XLF with 1<A<3 at
90% confidence level, while \Omega_0=0.4^{+0.3}_{-0.2} and \Omega_0<0.6 are
implied by a non--evolving L-T for open and flat models, respectively.


  We generalise the previously given E_11 half BPS solution generating group
element to general weights of A_10. We find that it leads to solutions of
M-theory but in signatures (1,10), (2,9), (5,6), (6,5), (9,2) and (10,1). The
signature transformations of the solution are naturally generated by the Weyl
reflections required to transform the lowest A_10 weight into a general weight
in the same representation. We also rediscover known S-brane solutions in
M-theory from the group element in different signatures.


  Nodes in ad hoc networks have limited battery power. Hence they require an
energy-efficient technique to improve average network performance. Maintaining
energy-efficiency in ad hoc networks is really challenging because highest
energy efficiency is achieved if all the nodes are always switched off and
energy-efficiency will be minimum if all the nodes are fully operational i.e.
always turned-on. Energy preservation requires redirection of data packets
through some other routes having good performance. This improves the data
packet delivery ratio and the number of alive nodes decreasing the cost of
messages.


  The Gaussian process (GP) is a popular way to specify dependencies between
random variables in a probabilistic model. In the Bayesian framework the
covariance structure can be specified using unknown hyperparameters.
Integrating over these hyperparameters considers different possible
explanations for the data when making predictions. This integration is often
performed using Markov chain Monte Carlo (MCMC) sampling. However, with
non-Gaussian observations standard hyperparameter sampling approaches require
careful tuning and may converge slowly. In this paper we present a slice
sampling approach that requires little tuning while mixing well in both strong-
and weak-data regimes.


  Detailed investigations on the notch technique are performed on the ideal
data generated by the optical model potential parameters extracted from the
16O+208Pb system at the laboratory energy of 129.5 MeV, to study the
sensitivities of this technique on the model parameters as well as the
experimental data. It is found that, for the perturbation parameters, a
sufficient large reduced fraction and an appropriate small perturbation width
are necessary to determine the accurate radial sensitivity; while for the
potential parameters, almost no dependence was observed. For the experimental
measurements, the number of data points has little influence for the heavy
target system, and the relative inner information of the nuclear potential can
be derived when the measurement extended to a lower cross section.


  We present a primal--dual memory efficient algorithm for solving a relaxed
version of the general transportation problem. Our approach approximates the
original cost function with a differentiable one that is solved as a sequence
of weighted quadratic transportation problems. The new formulation allows us to
solve differentiable, non-- convex transportation problems.


  This article aims to be a self-contained account of the history of the B. B.
Newman Spelling Theorem, including the historical context in which it arose.
First, an account of B. B. Newman and how he came to prove his Spelling Theorem
is given, together with a description of the author's efforts to track this
information down. Following this, a high-level description of combinatorial
group theory is given. This is then tied in with a description of the history
of the word problem, a fundamental problem in the area. After a description of
some of the theory of one-relator groups, an important part of combinatorial
group theory, the natural division line into the torsion and torsion-free case
for such groups is described. This culminates in a statement of and general
discussion about the B. B. Newman Spelling Theorem and its importance.


  We show that crystal-field calculations for $C_1$ point-group symmetry are
possible, and that such calculations can be performed with sufficient accuracy
to have substantial utility for rare-earth based quantum information
applications. In particular, we perform crystal-field fitting for a
C$_1$-symmetry site in $^{167}$Er$^{3+}$:Y$_2$SiO$_5$. The calculation
simultaneously includes site-selective spectroscopic data up to 20,000
cm$^{-1}$, rotational Zeeman data, and ground- and excited-state hyperfine
structure determined from high-resolution Raman-heterodyne spectroscopy on the
1.5 $\mu$m telecom transition. We achieve an agreement of better than 50 MHz
for assigned hyperfine transitions. The success of this analysis opens the
possibility of systematically evaluating the coherence properties, as well as
transition energies and intensities, of any rare-earth ion doped into
Y$_2$SiO$_5$ .


  We theoretically studied the effect of the perpendicular electric field on
the thermoelectric properties of the intrinsic, n-type and p-type bismuth
telluride nanowires with the growth direction [110]. The electronic structure
and the wave functions were calculated by solving self-consistently the system
of the Schrodinger and Poisson equations using the spectral method. The Poisson
equation was solved in terms of the Newton - Raphson method within the
predictor-corrector approach. The electron - electron exchange - correlation
interactions were taken into account in our analysis. In the temperature range
from 77 to 500 K, the dependences of the Seebeck coefficient, thermal
conductivity, electron (hole) concentration, and thermoelectric figure of merit
on the nanowire thickness, gate voltage, and excess hole (electron)
concentration were investigated in the constant relaxation-time approximation.
The results of our calculations indicate that the external perpendicular
electric field can increase the Seebeck coefficient of the bismuth telluride
nanowires with thicknesses of 7 - 15 nm by nearly a factor of 2 and enhance ZT
by an order of magnitude. At room temperature, ZT can reach a value as high as
3.4 under the action of the external perpendicular electric field for realistic
widths of the nanowires. The obtain results may open up a completely new way
for a drastic enhancement of the thermoelectric figure of merit in a wide
temperature range.


  The mass matrix forms of quarks and leptons are discussed in theory with
permutation flavor symmetry. The structure of scalar potential is analyzed in
case that electroweak doublet Higgs fields have non-trivial flavor symmetry
charges. We find that realistic forms of mass matrices are obtained dynamically
in the vacuum of the theory, where some of Higgs bosons have vanishing
expectation values which lead to vanishing elements in quark and lepton mass
matrices. An interesting point is that, due to the flavor group structure, the
up and down quark mass matrices are automatically made different in the vacuum,
which lead to non-vanishing generation mixing. It is also discussed that flavor
symmetry is needed to be broken in order not to have too light scalars.