  We study the proximity effect in SF'(AF)F'S and SF'(F)F'S planar junctions,
where S is a clean conventional (s-wave) superconductor, while F' and middle
layers are clean or moderately diffusive ferromagnets. Middle layers consist of
two equal ferromagnets with antiparallel (AF) or parallel (F) magnetizations
that are not collinear with magnetizations in the neighboring F' layers. We use
fully self-consistent numerical solutions of the Eilenberger equations to
calculate the superconducting pair amplitudes and the Josephson current for
arbitrary thickness of ferromagnetic layers and the angle between in-plane
magnetisations. For moderate disorder in ferromagnets the triplet proximity
effect is practically the same for AF and F structures, like in the dirty
limit. Triplet Josephson current is dominant for $d'\approx\hbar v_F/2h'$,
where $d'$ is the F' layer thickness and $h'$ is the exchange energy. Our
results are in a qualitative agreement with the recent experimental
observations [T. S. Khaire, M. A. Khasawneh, W. P. Pratt, and N. O. Birge,
Phys. Rev. Lett. \textbf{104}, 137002 (2010)].


  In cell-free massive MIMO networks, an efficient distributed detection
algorithm is of significant importance. In this paper, we propose a distributed
expectation propagation (EP) detector for cell-free massive MIMO. The detector
is composed of two modules, a nonlinear module at the central processing unit
(CPU) and a linear module at the access point (AP). The turbo principle in
iterative decoding is utilized to compute and pass the extrinsic information
between modules. An analytical framework is then provided to characterize the
asymptotic performance of the proposed EP detector with a large number of
antennas. Simulation results will show that the proposed method outperforms the
distributed detectors in terms of bit-error-rate.


  We study formal and non-formal deformation quantizations of a family of
manifolds that can be obtained by phase space reduction from $\mathbb{C}^{1+n}$
with the Wick star product in arbitrary signature. Two special cases of such
manifolds are the complex projective space $\mathbb{CP}^n$ and the complex
hyperbolic disc $\mathbb{D}^n$. We generalize several older results to this
setting: The construction of formal star products and their explicit
description by bidifferential operators, the existence of a convergent
subalgebra of "polynomial" functions, and its completion to an algebra of
certain analytic functions that allow an easy characterization via their
holomorphic extensions. Moreover, we find an isomorphism between the non-formal
deformation quantizations for different signatures, linking e.g. the star
products on $\mathbb{CP}^n$ and $\mathbb{D}^n$. More precisely, we describe an
isomorphism between the (polynomial or analytic) function algebras that is
compatible with Poisson brackets and the convergent star products. This
isomorphism is essentially given by Wick rotation, i.e. holomorphic extension
of analytic functions and restriction to a new domain. It is not compatible
with the *-involution of pointwise complex conjugation.


  We investigate the dynamics of a scalar field governed by the Lifshitz-type
action which should appear naturally in Horava-Lifshitz gravity. The wave of
the scalar field may propagate with any speed without an upper bound. To
preserve the causality, the action cannot have a generic form. Due to the
superluminal propagation, a formation of a singularity may cause the breakdown
of the predictability of the theory. To check whether such a catastrophe could
occur in Horava-Lifshitz gravity, we investigate the dynamics of a dust. It
turns out that the dust does not collapse completely to form a singularity in a
generic situation, but expands again after it attains a maximum energy density.


  Recent advances in generative compression methods have demonstrated
remarkable progress in enhancing the perceptual quality of compressed data,
especially in scenarios with low bitrates. However, their efficacy and
applicability to achieve extreme compression ratios ($<0.05$ bpp) remain
constrained. In this work, we propose a simple yet effective coding framework
by introducing vector quantization (VQ)--based generative models into the image
compression domain. The main insight is that the codebook learned by the VQGAN
model yields a strong expressive capacity, facilitating efficient compression
of continuous information in the latent space while maintaining reconstruction
quality. Specifically, an image can be represented as VQ-indices by finding the
nearest codeword, which can be encoded using lossless compression methods into
bitstreams. We propose clustering a pre-trained large-scale codebook into
smaller codebooks through the K-means algorithm, yielding variable bitrates and
different levels of reconstruction quality within the coding framework.
Furthermore, we introduce a transformer to predict lost indices and restore
images in unstable environments. Extensive qualitative and quantitative
experiments on various benchmark datasets demonstrate that the proposed
framework outperforms state-of-the-art codecs in terms of perceptual
quality-oriented metrics and human perception at extremely low bitrates ($\le
0.04$ bpp). Remarkably, even with the loss of up to $20\%$ of indices, the
images can be effectively restored with minimal perceptual loss.


  By using generalized fractional derivative, the parametric generalized
fractional Nikiforov-Uvarov (NU) method is introduced. The second-order
parametric generalized differential equation is exactly solved in the
fractional form. The obtained results are applied on the extended Cornell
potential, the pesudoharmonic potential, the Mie potential, the Kratzer-Fues
potential, the harmonic oscillator potential, the Morse potential, the
Woods-Saxon potential, the Hulthen potential, the deformed Rosen-Morse
potential and the Poschl-Teller potential which play an important role in the
fields of molecular and hadron physics. The special classical cases are
obtained from the fractional cases at ELFA = BETA =1 which are agreements with
recent works.


  Recently, neutron scattering data on powder samples of Zn-paratacamite,
Zn$_x$Cu$_{4-x}$(OH)$_6$Cl$_{2}$, with small Zn concentration has been
interpreted as evidence for valence bond solid and N\'eel ordering [1]. We
study the classical and quantum Heisenberg models on the distorted kagome
lattice appropriate for Zn-paratacamite at low Zn doping. Our theory naturally
leads to the emergence of the valence bond solid and collinear magnetic order
at zero temperature. Implications of our results to the existing experiments
are discussed. We also suggest future inelastic neutron and X-ray scattering
experiments that can test our predictions.


  Brizolis asked for which primes p greater than 3 does there exist a pair (g,
h) such that h is a fixed point of the discrete exponential map with base g, or
equivalently h is a fixed point of the discrete logarithm with base g. Zhang
(1995) and Cobeli and Zaharescu (1999) answered with a "yes" for sufficiently
large primes and gave estimates for the number of such pairs when g and h are
primitive roots modulo p. In 2000, Campbell showed that the answer to Brizolis
was "yes" for all primes. The first author has extended this question to
questions about counting fixed points, two-cycles, and collisions of the
discrete exponential map. In this paper, we use p-adic methods, primarily
Hensel's lemma and p-adic interpolation, to count fixed points, two cycles,
collisions, and solutions to related equations modulo powers of a prime p.


  The electric dipole moments of closed-shell atoms are sensitive to the parity
and time-reversal violating phenomena in the nucleus. The nuclear Schiff moment
is one such property, it arises from the parity and time reversal violating
quark-quark interactions and the quark-chromo electric dipole moments. We
calculate the electric dipole moment of atomic $^{199}{\rm Hg}$ arising from
the nuclear Schiff moment using the relativistic coupled-cluster theory. This
is the most accurate calculation of the quantity to date. Our calculations in
combination with the experiment data provide important insights to the P and T
violating coupling constants at the elementary particle level. In addition, a
new limit on the tensor-pseudo tensor induced atomic EDM, calculated using the
relativistic coupled-cluster theory is also presented.


  Photometry with the transit method has arguably been the most successful
exoplanet discovery method to date. A short overview about the rise of that
method to its present status is given. The method's strength is the rich set of
parameters that can be obtained from transiting planets, in particular in
combination with radial velocity observations; the basic principles of these
parameters are given, with explicit formulations for the transit detection
probability and the times of transit epochs in comparison to radial velocity
epochs. The transit method has however also drawbacks, which are the low
probability of properly aligned planet systems and the presence of
astrophysical phenomena that may mimic transits and give rise to false
detection positives. In the second part, we outline the main factors that
determine the design of transit surveys, such as the size of the survey sample,
the temporal coverage, the photometric precision, the sample brightness and the
methods to extract transit events from observed light curves. Lastly, an
overview over past, current, and future transit surveys is given. For these
surveys we indicate their basic instrument configuration and their planet
catch, including the ranges of planet sizes and stellar magnitudes that were
encountered. Current and future transit detection experiments concentrate
primarily on bright or special targets, and we expect that the transit method
remains a principal driver of exoplanet science, through new discoveries to be
made and through the development of new generations of instruments.


  We present a detailed study of the spatial resolution of our time-resolved
neutron imaging detector utilizing a new neutron position reconstruction method
that improves both spatial resolution and event reconstruction efficiency. Our
prototype detector system, employing a micro-pattern gaseous detector known as
the micro-pixel chamber ({\mu}PIC) coupled with a
field-programmable-gate-array-based data acquisition system, combines
100{\mu}m-level spatial and sub-{\mu}s time resolutions with excellent gamma
rejection and high data rates, making it well suited for applications in
neutron radiography at high-intensity, pulsed neutron sources. From data taken
at the Materials and Life Science Experimental Facility within the Japan Proton
Accelerator Research Complex (J-PARC), the spatial resolution was found to be
approximately Gaussian with a sigma of 103.48 +/- 0.77 {\mu}m (after correcting
for beam divergence). This is a significant improvement over that achievable
with our previous reconstruction method (334 +/- 13 {\mu}m), and compares well
with conventional neutron imaging detectors and with other high-rate detectors
currently under development. Further, a detector simulation indicates that a
spatial resolution of less than 60 {\mu}m may be possible with optimization of
the gas characteristics and {\mu}PIC structure. We also present an example of
imaging combined with neutron resonance absorption spectroscopy.


  We study the interband transport in a superconducting device composed of
graphene with EuO-induced exchange interaction. We show that pure crossed
Andreev reflection can be generated exclusively without the parasitic local
Andreev reflection and elastic cotunnelling over a wide range of bias and Fermi
levels in an EuO-graphene/superconductor/EuO-graphene device. The pure
non-local conductance exhibits rapid on/off switching and oscillatory behavior
when the Fermi levels in the normal and the superconducting leads are varied.
The oscillation reflects the quasiparticle propagation in the superconducting
lead and can be used as a tool to probe the subgap quasiparticle mode in
superconducting graphene, which is inaccessible from the current-voltage
characteristics. Our results suggest that the device can be used as a highly
tunable transistor that operates purely in the non-local and spin-polarized
transport regime.


  In this paper, SER_AMPEL, a multi-source dataset for speech emotion
recognition (SER) is presented. The peculiarity of the dataset is that it is
collected with the aim of providing a reference for speech emotion recognition
in case of Italian older adults. The dataset is collected following different
protocols, in particular considering acted conversations, extracted from movies
and TV series, and recording natural conversations where the emotions are
elicited by proper questions. The evidence of the need for such a dataset
emerges from the analysis of the state of the art. Preliminary considerations
on the critical issues of SER are reported analyzing the classification results
on a subset of the proposed dataset.


  This paper presents a Bayesian model for unsupervised learning of verb
selectional preferences. For each verb the model creates a Bayesian network
whose architecture is determined by the lexical hierarchy of Wordnet and whose
parameters are estimated from a list of verb-object pairs found from a corpus.
``Explaining away'', a well-known property of Bayesian networks, helps the
model deal in a natural fashion with word sense ambiguity in the training data.
On a word sense disambiguation test our model performed better than other state
of the art systems for unsupervised learning of selectional preferences.
Computational complexity problems, ways of improving this approach and methods
for implementing ``explaining away'' in other graphical frameworks are
discussed.


  In this brief review, I discuss recent developments in the study of
pulsar-powered nebulae ("plerions"). The large volume of data which has been
acquired in recent years reveals a diverse range of observational properties,
demonstrating how differing environmental and pulsar properties manifest
themselves in the resulting nebulae.


  We consider the XXZ spin-1/2 Heisenberg chain with antiperiodic boundary
conditions. The inhomogeneous version of this model can be solved by Separation
of Variables (SoV), and the eigenstates can be constructed in terms of
Q-functions, solution of a Baxter TQ-equation, which have double periodicity
compared to the periodic case. We compute in this framework the scalar products
of a particular class of separate states which notably includes the eigenstates
of the transfer matrix. We also compute the form factors of local spin
operators, i.e. their matrix elements between two eigenstates of the transfer
matrix. We show that these quantities admit determinant representations with
rows and columns labelled by the roots of the Q-functions of the corresponding
separate states, as in the periodic case, although the form of the determinant
are here slightly different. We also propose alternative types of determinant
representations written directly in terms of the transfer matrix eigenvalues.


  Unsupervised pre-training methods utilizing large and diverse datasets have
achieved tremendous success across a range of domains. Recent work has
investigated such unsupervised pre-training methods for model-based
reinforcement learning (MBRL) but is limited to domain-specific or simulated
data. In this paper, we study the problem of pre-training world models with
abundant in-the-wild videos for efficient learning of downstream visual control
tasks. However, in-the-wild videos are complicated with various contextual
factors, such as intricate backgrounds and textured appearance, which precludes
a world model from extracting shared world knowledge to generalize better. To
tackle this issue, we introduce Contextualized World Models (ContextWM) that
explicitly separate context and dynamics modeling to overcome the complexity
and diversity of in-the-wild videos and facilitate knowledge transfer between
distinct scenes. Specifically, a contextualized extension of the latent
dynamics model is elaborately realized by incorporating a context encoder to
retain contextual information and empower the image decoder, which encourages
the latent dynamics model to concentrate on essential temporal variations. Our
experiments show that in-the-wild video pre-training equipped with ContextWM
can significantly improve the sample efficiency of MBRL in various domains,
including robotic manipulation, locomotion, and autonomous driving. Code is
available at this repository: https://github.com/thuml/ContextWM.


  Single-snapshot direction-of-arrival (DOA) estimation using sparse linear
arrays (SLAs) has gained significant attention in the field of automotive MIMO
radars. This is due to the dynamic nature of automotive settings, where
multiple snapshots aren't accessible, and the importance of minimizing hardware
costs. Low-rank Hankel matrix completion has been proposed to interpolate the
missing elements in SLAs. However, the solvers of matrix completion, such as
iterative hard thresholding (IHT), heavily rely on expert knowledge of
hyperparameter tuning and lack task-specificity. Besides, IHT involves
truncated-singular value decomposition (t-SVD), which has high computational
cost in each iteration. In this paper, we propose an IHT-inspired neural
network for single-snapshot DOA estimation with SLAs, termed IHT-Net. We
utilize a recurrent neural network structure to parameterize the IHT algorithm.
Additionally, we integrate shallow-layer autoencoders to replace t-SVD,
reducing computational overhead while generating a novel optimizer through
supervised learning. IHT-Net maintains strong interpretability as its network
layer operations align with the iterations of the IHT algorithm. The learned
optimizer exhibits fast convergence and higher accuracy in the full array
signal reconstruction followed by single-snapshot DOA estimation. Numerical
results validate the effectiveness of the proposed method.


  Recent efforts to produce single photons via heralding have relied on
creating spectrally factorable two-photon states in order to achieve both high
purity and high production rate. Through a careful multimode analysis, we find,
however, that spectral factorability is not necessary. Utilizing single-mode
detection, a similar or better performance can be achieved with non-factorable
states. This conclusion rides on the fact that even when using a broadband
filter, a single-mode measurement can still be realized, as long as the
coherence time of the triggering photons exceeds the measurement window of the
on/off detector.


  In person re-identification (re-ID), the key task is feature representation,
which is used to compute distance or similarity in prediction. Person re-ID
achieves great improvement when deep learning methods are introduced to tackle
this problem. The features extracted by convolutional neural networks (CNN) are
more effective and discriminative than the hand-crafted features. However, deep
feature extracted by a single CNN network is not robust enough in testing
stage. To improve the ability of feature representation, we propose a new
ensemble network (EnsembleNet) by dividing a single network into multiple
end-to-end branches. The ensemble feature is obtained by concatenating each of
the branch features to represent a person. EnsembleNet is designed based on
ResNet-50 and its backbone shares most of the parameters for saving computation
and memory cost. Experimental results show that our EnsembleNet achieves the
state-of-the-art performance on the public Market1501, DukeMTMC-reID and CUHK03
person re-ID benchmarks.


  We propose a differentiable vertex fitting algorithm that can be used for
secondary vertex fitting, and that can be seamlessly integrated into neural
networks for jet flavour tagging. Vertex fitting is formulated as an
optimization problem where gradients of the optimized solution vertex are
defined through implicit differentiation and can be passed to upstream or
downstream neural network components for network training. More broadly, this
is an application of differentiable programming to integrate physics knowledge
into neural network models in high energy physics. We demonstrate how
differentiable secondary vertex fitting can be integrated into larger
transformer-based models for flavour tagging and improve heavy flavour jet
classification.


  The standard self-similar model of galaxy cluster formation predicts that the
X-ray luminosity-temperature ($L_X$-$T_X$) relation of galaxy clusters should
have been $L_X\propto T_X^2$ in absence of the baryonic physics, such as
radiative cooling and feedback from stars and black holes. However, this
baseline relation is predicted without considering the fact that the halo
concentration and the characteristic density of clusters increases as their
mass decreases, which is a consequence of hierarchical structure formation of
the universe. Here, we show that the actual baseline relation should be
$L_X\propto T_X^\alpha$, where $\alpha\sim 1.7$, instead of $\alpha=2$, given
the mass dependence of the concentration and the fundamental plane relation of
galaxy clusters. Numerical simulations show that $\alpha\sim 1.6$, which is
consistent with the prediction. We also show that the baseline luminosity-mass
($L_X$-$M_\Delta$) relation should have been $L_X\propto M_\Delta^\beta$, where
$\beta\sim 1.1$-1.2, in contrast with the conventional prediction
($\beta=4/3$). In addition, some of the scatter in the $L_X$-$M_\Delta$
relation can be attributed to the scatter in the concentration-mass ($c$-$M$)
relation. The confirmation of the shallow slope could be a proof of
hierarchical clustering. As an example, we show that the new baseline relations
could be checked by studying the temperature or mass dependence of gas mass
fraction of clusters. Moreover, the highest-temperature clusters would follow
the shallow baseline relations if the influences of cool cores and cluster
mergers are properly removed.


  In this paper, we consider a stochastic differential equation driven by a
fractional Brownian motion (fBm) and a Wiener process and having jumps. We
prove that this equation has a unique solution and show that all its moments
are finite.


  We describe a novel approach to statistical learning from particles tracked
while moving in a random environment. The problem consists in inferring
properties of the environment from recorded snapshots. We consider here the
case of a fluid seeded with identical passive particles that diffuse and are
advected by a flow. Our approach rests on efficient algorithms to estimate the
weighted number of possible matchings among particles in two consecutive
snapshots, the partition function of the underlying graphical model. The
partition function is then maximized over the model parameters, namely
diffusivity and velocity gradient. A Belief Propagation (BP) scheme is the
backbone of our algorithm, providing accurate results for the flow parameters
we want to learn. The BP estimate is additionally improved by incorporating
Loop Series (LS) contributions. For the weighted matching problem, LS is
compactly expressed as a Cauchy integral, accurately estimated by a saddle
point approximation. Numerical experiments show that the quality of our
improved BP algorithm is comparable to the one of a fully polynomial randomized
approximation scheme, based on the Markov Chain Monte Carlo (MCMC) method,
while the BP-based scheme is substantially faster than the MCMC scheme.


  Point clouds obtained from photogrammetry are noisy and incomplete models of
reality. We propose an evolutionary optimization methodology that is able to
approximate the underlying object geometry on such point clouds. This approach
assumes a priori knowledge on the 3D structure modeled and enables the
identification of a collection of primitive shapes approximating the scene.
Built-in mechanisms that enforce high shape diversity and adaptive population
size make this method suitable to modeling both simple and complex scenes. We
focus here on the case of cylinder approximations and we describe, test, and
compare a set of mutation operators designed for optimal exploration of their
search space. We assess the robustness and limitations of this algorithm
through a series of synthetic examples, and we finally demonstrate its general
applicability on two real-life cases in vegetation and industrial settings.


  The dynamic disorder model for charge carrier transport in organic
semiconductors has been extensively studied in recent years. Although it is
successful on determining the value of bandlike mobility in the organic
crystalline materials, the incoherent hopping, the typical transport
characteristic in organic semiconductors, cannot be described. In this work,
the decoherence process is taken into account via a phenomenological parameter,
say decoherence time, and the projective and Monte Carlo method is applied for
this model to determine the waiting time and thus the diffusion coefficient. We
find the type of transport changes from bandlike to incoherent hopping with a
sufficiently short decoherence time, which indicates the essential role of
decoherence time in determining the type of transport in organics. We have also
discussed the spatial extent of carriers for different decoherence time, and
the transition from delocalization (carrier resides in about 10 molecules) to
localization is observed. Based on the experimental results of spatial extent,
we estimate the decoherence time in pentacene has the order of 1ps.
Furthermore, the dependence of diffusion coefficient on decoherence time is
also investigated, and corresponding experiments are discussed.


  We present a class of graviton-dilaton models in which a homogeneous
isotropic universe, such as our observed one, evolves with no singularity at
any time. Such models may stand on their own as interesting models for
singularity free cosmology, and may be studied further accordingly. They may
also arise from string theory. We discuss critically a few such possibilities.


  Public speaking is an important aspect of human communication and
interaction. The majority of computational work on public speaking concentrates
on analyzing the spoken content, and the verbal behavior of the speakers. While
the success of public speaking largely depends on the content of the talk, and
the verbal behavior, non-verbal (visual) cues, such as gestures and physical
appearance also play a significant role. This paper investigates the importance
of visual cues by estimating their contribution towards predicting the
popularity of a public lecture. For this purpose, we constructed a large
database of more than $1800$ TED talk videos. As a measure of popularity of the
TED talks, we leverage the corresponding (online) viewers' ratings from
YouTube. Visual cues related to facial and physical appearance, facial
expressions, and pose variations are extracted from the video frames using
convolutional neural network (CNN) models. Thereafter, an attention-based long
short-term memory (LSTM) network is proposed to predict the video popularity
from the sequence of visual features. The proposed network achieves
state-of-the-art prediction accuracy indicating that visual cues alone contain
highly predictive information about the popularity of a talk. Furthermore, our
network learns a human-like attention mechanism, which is particularly useful
for interpretability, i.e. how attention varies with time, and across different
visual cues by indicating their relative importance.


  The effect of correlated hopping on the charge and heat transport of strongly
correlated particles is studied for the Falicov-Kimball model on the Bethe
lattice. Exact solutions for the one particle density of states (DOS) and two
particle transport function (the "quasiparticle" scattering time) are derived
using dynamical mean field theory. For a wide range of the correlated hopping,
the transport function exhibits singularities due to the resonant two-particle
contribution, whereas the one particle DOS does not show any anomalous
features. By tuning the number of itinerant electrons, so as to bring the Fermi
level close to the resonant frequency, we get a large increase of the
electrical and thermal conductivities, and the thermoelectric power. When the
hopping amplitude between the occupied sites is reduced sufficiently, the
itinerant electrons localize in the clusters of sites occupied by $f$
electrons. This gives rise to an additional narrow band in the DOS between the
lower and upper Hubbard bands, but has only a minor effect on the
thermoelectric properties.


  We study the problem of maximizing a monotone submodular set function subject
to linear packing constraints. An instance of this problem consists of a matrix
$A \in [0,1]^{m \times n}$, a vector $b \in [1,\infty)^m$, and a monotone
submodular set function $f: 2^{[n]} \rightarrow \bbR_+$. The objective is to
find a set $S$ that maximizes $f(S)$ subject to $A x_{S} \leq b$, where $x_S$
stands for the characteristic vector of the set $S$. A well-studied special
case of this problem is when $f$ is linear. This special case captures the
class of packing integer programs.
  Our main contribution is an efficient combinatorial algorithm that achieves
an approximation ratio of $\Omega(1 / m^{1/W})$, where $W = \min\{b_i / A_{ij}
: A_{ij} > 0\}$ is the width of the packing constraints. This result matches
the best known performance guarantee for the linear case. One immediate
corollary of this result is that the algorithm under consideration achieves
constant factor approximation when the number of constraints is constant or
when the width of the constraints is sufficiently large. This motivates us to
study the large width setting, trying to determine its exact approximability.
We develop an algorithm that has an approximation ratio of $(1 - \epsilon)(1 -
1/e)$ when $W = \Omega(\ln m / \epsilon^2)$. This result essentially matches
the theoretical lower bound of $1 - 1/e$. We also study the special setting in
which the matrix $A$ is binary and $k$-column sparse. A $k$-column sparse
matrix has at most $k$ non-zero entries in each of its column. We design a fast
combinatorial algorithm that achieves an approximation ratio of $\Omega(1 /
(Wk^{1/W}))$, that is, its performance guarantee only depends on the sparsity
and width parameters.


  Complex networks have gained more attention from the last few years. The size
of real-world complex networks, such as online social networks, WWW network,
collaboration networks, is increasing exponentially with time. It is not
feasible to collect the complete data and store and process it. In the present
work, we propose a method to estimate the degree centrality rank of a node
without having the complete structure of the graph. The proposed algorithm uses
the degree of a node and power-law exponent of the degree distribution to
calculate the ranking. Simulation results on the Barabasi-Albert networks show
that the average error in the estimated ranking is approximately $5\%$ of the
total number of nodes.


  We consider theoretically a Josephson junction with a superconducting
critical current density which has a random sign along the junction's surface.
We show that the ground state of the junction corresponds to the phase
difference equal to \pi/2. Such a situation can take place in superconductor-
ferromagnet junction.


  In this work, we analyze the properties of the solution to the covariance
steering problem for discrete time Gaussian linear systems with a squared
Wasserstein distance terminal cost. In our previous work, we have shown that by
utilizing the state feedback control policy parametrization, this stochastic
optimal control problem can be associated with a difference of convex functions
program. Here, we revisit the same covariance control problem but this time we
focus on the analysis of the problem. Specifically, we establish the existence
of solutions to the optimization problem and derive the first and second order
conditions for optimality. We provide analytic expressions for the gradient and
the Hessian of the performance index by utilizing specialized tools from matrix
calculus. Subsequently, we prove that the optimization problem always admits a
global minimizer, and finally, we provide a sufficient condition for the
performance index to be a strictly convex function (under the latter condition,
the problem admits a unique global minimizer). In particular, we show that when
the terminal state covariance is upper bounded, with respect to the L\"{o}wner
partial order, by the covariance matrix of the desired terminal normal
distribution, then our problem admits a unique global minimizing state feedback
gain. The results of this paper set the stage for the development of
specialized control design tools that exploit the structure of the solution to
the covariance steering problem with a squared Wasserstein distance terminal
cost.


  The Rosse Solar-Terrestrial Observatory (RSTO; www.rosseobservatory.ie) was
established at Birr Castle, Co. Offaly, Ireland (53 05'38.9", 7 55'12.7") in
2010 to study solar radio bursts and the response of the Earth's ionosphere and
geomagnetic field. To date, three Compound Astronomical Low-cost Low-frequency
Instrument for Spectroscopy and Transportable Observatory (CALLISTO)
spectrometers have been installed, with the capability of observing in the
frequency range 10-870 MHz. The receivers are fed simultaneously by biconical
and log-periodic antennas. Nominally, frequency spectra in the range 10-400 MHz
are obtained with 4 sweeps per second over 600 channels. Here, we describe the
RSTO solar radio spectrometer set-up, and present dynamic spectra of a sample
of Type II, III and IV radio bursts. In particular, we describe fine-scale
structure observed in Type II bursts, including band splitting and rapidly
varying herringbone features.


  A semiclassical, four-level model of a nanosecond, chirped pulse interacting
with all optically accessible hyperfine states in the ultracold Rb atom is
analyzed aiming at population inversion within $5S_{1/2}$ electronic state. The
nature of two-photon adiabatic passage performed by such a single pulse having
a bandwidth smaller than the hyperfine splitting of $5S_{1/2}$ state is
investigated in the framework of the dressed state picture. It is shown that
two dressed states are involved in the adiabatic dynamics of population
inversion. The excited state manifold appeared to play an important mediating
role in the mechanism of population transfer.


  Fuels dispersed with engineered nanoparticle additives, or nanofuels, are
desirable for the vastly different combustion properties such as combustion
rate and ignition delay they exhibit compared to base fuels. The stability of
such nanofuels over time and under different particle loadings is a very
important parameter to consider before they can be put into practical use. Many
techniques exist today to analyze suspension stability, which have been
developed to analyze water-based nanofluids. Sometimes these techniques can be
expensive, and/or require specialized equipment, and/or require a method that
is invasive and disturbs the suspension. Present research uses a non-contact,
non-invasive, low-cost experimental setup to analyze suspension stability over
long periods of time. Nanofuels made from carbon-based nanomaterials (acetylene
black, multiwalled carbon nanotubes) and metal oxide nanomaterials (copper
oxide, aluminum oxide) with hydrocarbon fuels (canola biodiesel, petrodiesel)
have been prepared and their settling rates have been analyzed over the period
of three days. It is found that metal oxides go through several metastable
states as they settle. The effect of initial concentration and liquid column
height is shown. It is hoped that present research showcases the positive
traits of the presented technique and will spark further interest in nanofuel
stability.


  We study the heavy-dense limit of QCD on the lattice with heavy quarks at
high density. The effective three dimensional theory has a sign problem which
is alleviated by sign optimization where the path integration domain is
deformed in complex space in a way that minimizes the phase oscillations. We
simulate the theory via a Hybrid-Monte-Carlo, for different volumes, both to
leading order and next-to-next-to leading order in the hopping expansion, and
show that sign optimization successfully mitigates the sign problem at large
enough volumes where usual re-weighting methods fail. Finally we show that
there is a significant overlap between the complex manifold generated by sign
optimization and the Lefschetz thimbles associated with the theory.


  Consider two elliptic curves $E,E'$ defined over the finite field
$\mathbb{F}_q$, and suppose that there exists an isogeny $\psi$ between $E$ and
$E'$. We propose an algorithm that determines $\psi$ from the knowledge of $E$,
$E'$ and of its degree $r$, by using the structure of the $\ell$-torsion of the
curves (where $\ell$ is a prime different from the characteristic $p$ of the
base field). Our approach is inspired by a previous algorithm due to
Couveignes, that involved computations using the $p$-torsion on the curves. The
most refined version of that algorithm, due to De Feo, has a complexity of
$\tilde{O}(r^2) p^{O(1)}$ base field operations. On the other hand, the cost of
our algorithm is $\tilde{O}(r^2 + \sqrt{r} \log(q))$; this makes it an
interesting alternative for the medium- and large-characteristic cases.


  It is shown that the Lagrangian of Quantum Chromodynamics can be modified by
the adding gluon masses. On mass-shell renormalizability of the resulting
theory is discussed.


  Gardner conjectured that if two bounded measurable sets $A,B \subset
\mathbb{R}^n$ are equidecomposable by a set of isometries $\Gamma$ generating
an amenable group then $A$ and $B$ admit a measurable equidecomposition by all
isometries. Cie\'sla and Sabok asked if there is a measurable equidecomposition
using isometries only in the group generated by $\Gamma$. We answer this
question negatively.


  We propose an image resolution improvement method for optical coherence
tomography (OCT) based on sparse continuous deconvolution. Traditional
deconvolution techniques such as Lucy-Richardson deconvolution suffers from the
artifact convergence problem after a small number of iterations, which brings
limitation to practical applications. In this work, we take advantage of the
prior knowledge about the sample sparsity and continuity to constrain the
deconvolution iteration. Sparsity is used to achieve the resolution improvement
through the resolution preserving regularization term. And the continuity based
on the correlation of the grayscale values in different directions is
introduced to mitigate excessive image sparsity and noise reduction through the
continuity regularization term. The Bregman splitting technique is then used to
solve the resulting optimization problem. Both the numerical simulation study
and experimental study on phantoms and biological samples show that our method
can suppress artefacts of traditional deconvolution techniques effectively.
Meanwhile, clear resolution improvement is demonstrated. It achieved nearly
twofold resolution improvement for phantom beads image that can be
quantitatively evaluated


  Federated learning is becoming increasingly relevant and popular as we
witness a surge in data collection and storage of personally identifiable
information. Alongside these developments there have been many proposals from
governments around the world to provide more protections for individuals' data
and a heightened interest in data privacy measures. As deep learning continues
to become more relevant in new and existing domains, it is vital to develop
strategies like federated learning that can effectively train data from
different sources, such as edge devices, without compromising security and
privacy. Recently, the Flower (\texttt{Flwr}) Python package was introduced to
provide a scalable, flexible, and easy-to-use framework for implementing
federated learning. However, to date, Flower is only able to run synchronous
federated learning which can be costly and time-consuming to run because the
process is bottlenecked by client-side training jobs that are slow or fragile.
Here, we introduce \texttt{flwr-serverless}, a wrapper around the Flower
package that extends its functionality to allow for both synchronous and
asynchronous federated learning with minimal modification to Flower's design
paradigm. Furthermore, our approach to federated learning allows the process to
run without a central server, which increases the domains of application and
accessibility of its use. This paper presents the design details and usage of
this approach through a series of experiments that were conducted using public
datasets. Overall, we believe that our approach decreases the time and cost to
run federated training and provides an easier way to implement and experiment
with federated learning systems.


  We show analytically that the apparent non-analyticity discovered recently in
the inverse participation ratio (IPR) of the eigenstates in Anderson's model of
localization is also present in a simple two-site model, along with a
concurrent non-analyticity in the density of states (DOS) at the same energy.
We demonstrate its evolution from two sites to the thermodynamic limit by
numerical methods. For the two site model, non-analyticity in higher
derivatives of the DOS and IPR is also proven to exist for all bounded
distributions of disorder.


  In this paper, we describe an experimental investigation into the effect of
passivation layer thickness on heat dissipation between a quartz substrate and
liquid helium. We have observed that by depositing SiN from 0 to 240 nm, the
Kapitza resistance increases by 0.0365 m^2.K/W per nanometer more than for an
unpassivated semiconductor. We hypothesize that this increase in Kapitza
resistance represents an additional barrier to the cooling of semiconductor
devices in liquid helium.


  Existence of convex body with prescribed generalized curvature measures is
discussed, this result is obtained by making use of Guan-Li-Li's innovative
techniques. In surprise, that methods has also brought us to promote
Ivochkina's $C^2$ estimates for prescribed curvature equation in \cite{I1, I}.


  Some mutually quasi-unbiased weighing matrices are constructed from binary
codes satisfying certain conditions. Motivated by this, in this note, we study
binary codes satisfying the conditions. The weight distributions of binary
codes satisfying the conditions are determined. We also give a classification
of binary codes of lengths $8,16$ and binary maximal codes of length $32$
satisfying the conditions. As an application, sets of $8$ mutually
quasi-unbiased weighing matrices for parameters $(16,16,4,64)$ and $4$ mutually
quasi-unbiased weighing matrices for parameters $(32,32,4,256)$ are constructed
for the first time.


  We present a unified framework for low-rank matrix estimation with nonconvex
penalties. We first prove that the proposed estimator attains a faster
statistical rate than the traditional low-rank matrix estimator with nuclear
norm penalty. Moreover, we rigorously show that under a certain condition on
the magnitude of the nonzero singular values, the proposed estimator enjoys
oracle property (i.e., exactly recovers the true rank of the matrix), besides
attaining a faster rate. As far as we know, this is the first work that
establishes the theory of low-rank matrix estimation with nonconvex penalties,
confirming the advantages of nonconvex penalties for matrix completion.
Numerical experiments on both synthetic and real world datasets corroborate our
theory.


  On Archimedean lattices, the Ising model exhibits spontaneous ordering. Three
examples of these lattices of the majority-vote model with noise are considered
and studied through extensive Monte Carlo simulations. The order/disorder phase
transition is observed in this system. The calculated values of the critical
noise parameter are q_c=0.089(5), q_c=0.078(3), and q_c=0.114(2) for honeycomb,
Kagome and triangular lattices, respectively. The critical exponents beta/nu,
gamma/nu and 1/nu for this model are 0.15(5), 1.64(5), and 0.87(5); 0.14(3),
1.64(3), and 0.86(6); 0.12(4), 1.59(5), and 1.08(6) for honeycomb, Kagome and
triangular lattices, respectively. These results differs from the usual Ising
model results and the majority-vote model on so-far studied regular lattices or
complex networks. The effective dimensionalities of the system D_{eff}= 1.96(5)
(honeycomb), D_{eff} =1.92(4) (Kagome), and D_{eff}= 1.83(5) (triangular) for
these networks are just compatible to the embedding dimension two.


  We report an investigation of the low-lying excited states of the YbF
molecule--a candidate molecule for experimental measurements of the electron
electric dipole moment--with 2-component based multi-reference configuration
interaction (MRCI), equation of motion coupled cluster (EOM-CCSD) and the
extrapolated intermediate Hamiltonian Fock-space coupled cluster (XIHFS-CCSD).
Specifically, we address the question of the nature of these low-lying states
in terms of configurations containing filled or partially-filled Yb $4f$
shells. We show that while it does not appear possible to carry out
calculations with both kinds of configurations contained in the same active
space, reliable information can be extracted from different sectors of Fock
space--that is, by performing electron attachment and detachment IHFS-CCSD and
EOM-CCSD calculation on the closed-shell YbF$^+$ and YbF$^-$ species,
respectively. From these we observe $\Omega = 1/2, 3/2$ states that arise from
the $4f^{13}\sigma_{6s}^2$, $4f^{14}5d$/$6p$, and $4f^{13}5d\sigma_{6s}$
configurations appear in the same energy range around the ground-state
equilibrium geometry and they are therefore able to interact. As these states
are generated from different sectors of Fock space, they are almost orthogonal
and provide complementary descriptions of parts of the excited state manifold.
To obtain a comprehensive picture, we introduce a simple adiabatization model
to extract energies of interacting $\Omega = 1/2, 3/2$ states that can be
compared to experimental observations.


  It is shown that there exists a possibility of amplification of amplitudes of
quantum pion modes with low momenta in the late time of chiral phase transition
by using the Gaussian wave functional approximation in the O(4) linear sigma
model. It is also shown that the amplification occurs in the mechanism of the
resonance by forced oscillation as well as the parametric resonance induced by
the small oscillation of the chiral condensate. These mechanisms are
investigated in both the case of spatially homogeneous system and the spatially
expanded system described by the Bjorken coordinate.


  We give a constructive and exhaustive definition of Kochen-Specker (KS)
vectors in a Hilbert space of any dimension as well as of all the remaining
vectors of the space. KS vectors are elements of any set of orthonormal states,
i.e., vectors in n-dim Hilbert space, H^n, n>3 to which it is impossible to
assign 1s and 0s in such a way that no two mutually orthogonal vectors from the
set are both assigned 1 and that not all mutually orthogonal vectors are
assigned 0. Our constructive definition of such KS vectors is based on
algorithms that generate MMP diagrams corresponding to blocks of orthogonal
vectors in R^n, on algorithms that single out those diagrams on which algebraic
0-1 states cannot be defined, and on algorithms that solve nonlinear equations
describing the orthogonalities of the vectors by means of statistically
polynomially complex interval analysis and self-teaching programs. The
algorithms are limited neither by the number of dimensions nor by the number of
vectors. To demonstrate the power of the algorithms, all 4-dim KS vector
systems containing up to 24 vectors were generated and described, all 3-dim
vector systems containing up to 30 vectors were scanned, and several general
properties of KS vectors were found.


  (abridged version) Identifying the processes that determine the initial mass
function of stars (IMF) is a fundamental problem in star formation theory. One
of the major uncertainties is the exact chemical state of the star forming gas
and its influence on the dynamical evolution. Most simulations of star forming
clusters use an isothermal equation of state (EOS). We address these issues and
study the effect of a piecewise polytropic EOS on the formation of stellar
clusters in turbulent, self-gravitating molecular clouds. We increase the
polytropic exponent gamma from 0.7 to 1.1 at some chosen density n_c, which we
vary from from 4.3x10^4 cm^-3 to 4.3x10^7 cm^-3. The change of thermodynamic
state at n_c selects a characteristic mass scale for fragmentation M_ch, which
we relate to the peak of the observed IMF. We find a relation M_ch ~ n_c^-0.5,
supporting the idea that the distribution of stellar masses largely depends on
the thermodynamic state of the star-forming gas.


  Rapid injection of spin polarization into an ensemble of nuclear spins is a
problem of broad interest, spanning dynamic nuclear polarization (DNP) to
quantum information science. We report on a strategy to boost the spin
injection rate by exploiting electrons that can be rapidly polarized via
high-power optical pumping. We demonstrate this in a model system of Nitrogen
Vacancy center electrons injecting polarization into a bath of 13C nuclei in
diamond. We deliver >20W of continuous, nearly isotropic, optical power to the
sample, constituting a substantially higher power than in previous experiments.
Through a spin-ratchet polarization transfer mechanism, we show boosts in spin
injection rates by over two orders of magnitude. Our experiments elucidate
bottlenecks in the DNP process caused by rates of electron polarization,
polarization transfer to proximal nuclei, and spin diffusion. This work
demonstrates opportunities for rapid spin injection employing non-thermally
generated electron polarization, and has relevance to a broad class of
experimental systems including in DNP, quantum sensing, and spin-based MASERs.


  We study totally decomposable symplectic and unitary involutions on central
simple algebras of index 2 and on split central simple algebras respectively.
We show that for every field extension, these involutions are either
anisotropic or hyperbolic after extending scalars, and that the converse holds
if the algebras are of 2-power degree. These results are new in characteristic
2, otherwise were shown in [3] and [6] respectively.


  In this paper we adopt a category-theoretic approach to the conception of
automata classes enjoying minimization by design. The main instantiation of our
construction is a new class of automata that are hybrid between deterministic
automata and automata weighted over a field.


  Given a probability measure $\mu$ with infinite support on the unit circle
$\partial\mathbb{D}=\{z:|z|=1\}$, we consider a sequence of paraorthogonal
polynomials $\h_n(z,\lambda)$ vanishing at $z=\lambda$ where $\lambda \in \T$
is fixed. We prove that for any fixed $z_0 \not \in \supp(d\mu)$ distinct from
$\lambda$, we can find an explicit $\rho>0$ independent of $n$ such that either
$\h_n$ or $\h_{n+1}$ (or both) has no zero inside the disk $B(z_0, \rho)$, with
the possible exception of $\lambda$.
  Then we introduce paraorthogonal polynomials of the second kind, denoted
$\s_n(z,\lambda)$. We prove three results concerning $\s_n$ and $\h_n$. First,
we prove that zeros of $\s_n$ and $\h_n$ interlace. Second, for $z_0$ an
isolated point in $\supp(d\mu)$, we find an explicit radius $\rt$ such that
either $\s_n$ or $\s_{n+1}$ (or both) have no zeros inside $B(z_0,\rt)$.
Finally we prove that for such $z_0$ we can find an explicit radius such that
either $\h_n$ or $\h_{n+1}$ (or both) has at most one zero inside the ball
$B(z_0,\rt)$.


  Thin-film nanocomposites, consisting of silver nanoparticles embedded in a
dielectric Teflon\textregistered AF matrix, were synthesized using vapor phase
co-deposition. The electrical conductivity of these composites was measured
in-situ as a function of film thickness at various metal concentrations. At low
metal concentrations (<30%), dielectric behavior and very little change with
film thickness was observed. At moderate to high silver loadings (30-80%) a
large increase in electrical conductivity was observed as the films grew
thicker. As the thickness increased further, the conductivity flattened out. At
very high silver content (>90%), fragmented fractal nanoclusters were able to
further interconnect to achieve the percolation process and eventually evolve
into a metallic continuum with dielectric polymer inclusions.


  Using the BATSE survey data I find that quite small fraction of GRBs
numbering 37 sources seems to emit the radiation similar to thermal
bremsstrahlung in the range 20 to 300 keV. I suggest that these bursts may
perhaps occur from collision of stars with primordial black holes (PBH). These
objects are relic of a hot matter in the early Universe. PBH in the vicinity of
stars may be found in consequence of incorporation processes during the
formation of stars from interstellar clouds. At present they can form the
gravitationally captured haloes around stars like the family of solar comets.
The comet paradigm has been used to understand various aspects of PBH. Comet
collisions with the Sun and planets are ordinary events in solar system
history. On the analogy, one can support the view that PBH collisions with the
parent star may be quite frequent events in its history, too. PBHs are the
engines driving gamma-ray bursts when collide with the stars. Entering a
stellar atmosphere, PBH is supposed to produce the gamma-ray burst due to
accretion with duration from a few tenths of second to a few seconds. It can
exhibit the main qualitative features of some GRBs. Their masses are estimated
in the range from thousandths to hundredths of the solar mass. I found that
these burst sources are isotropically distributed on the sky and are seen from
a distance up to 50 ps. In this context one may expect that some short GRBs are
observable signatures of primordial black holes in the Universe.


  We investigate the scalar perturbations in an AdS soliton background coupled
to a Maxwell field via marginally stable modes. In the probe limit, we study
the magnetic field effect on the holographic insulator/superconductor phase
transition numerically and analytically. The condensate will be localized in a
finite circular region for any finite constant magnetic field. Near the
critical point, we find that there exists a simple relation among the critical
chemical potential, magnetic field, the charge and mass of the scalar field.
This relation indicates that the presence of the magnetic field causes the
phase transition hard.


  Recently, deep neural networks have significant progress and successful
application in various fields, but they are found vulnerable to attack
instances, e.g., adversarial examples. State-of-art attack methods can generate
attack images by adding small perturbation to the source image. These attack
images can fool the classifier but have little impact to human. Therefore, such
attack instances are difficult to generate by searching the feature space. How
to design an effective and robust generating method has become a spotlight.
Inspired by adversarial examples, we propose two novel generative models to
produce adaptive attack instances directly, in which conditional generative
adversarial network is adopted and distinctive strategy is designed for
training. Compared with the common method, such as Fast Gradient Sign Method,
our models can reduce the generating cost and improve robustness and has about
one fifth running time for producing attack instance.


  We show that, under some technical conditions, the Strong Slope Conjecture
proposed by Kalfagianni and Tran is closed under connect sums and cabling. As
an application, we establish the Strong Slope Conjecture for graph knots.


  Recent experiments have observed strongly correlated physics in twisted
bilayer graphene (TBG) at very small angles, along with nearly flat electron
bands at certain fillings. A good starting point in understanding the physics
is a continuum model (CM) proposed by Lopes dos Santos et al. [Phys. Rev. Lett.
99, 256802 (2007)] and Bistritzer et al. [PNAS 108, 12233 (2011)] for TBG at
small twist angles, which successfully predicts the bandwidth reduction of the
middle two bands of TBG near the first magic angle $\theta_0=1.05^\circ$. In
this paper, we analyze the symmetries of the CM and investigate the low energy
flat band structure in the entire moir\'e Brillouin zone near $\theta_0$.
Instead of observing flat bands at only one "magic" angle, we notice that the
bands remain almost flat within a small range around $\theta_0$, where multiple
topological transitions occur. The topological transitions are caused by the
creation and annihilation of Dirac nodes at either $\text{K}$,
$\text{K}^\prime$, or $\Gamma$ points, or along the high symmetry lines in the
moir\'e Brillouin zone. We trace the evolution of the nodes and find that there
are several processes transporting them from $\Gamma$ to $\text{K}$ and
$\text{K}^\prime$. At the $\Gamma$ point, the lowest energy levels of the CM
are doubly degenerate for some range of twisting angle around $\theta_0$,
suggesting that the physics is not described by any two band model. Based on
this observation, we propose an effective six-band model (up to second order in
quasi-momentum) near the $\Gamma$ point with the full symmetries of the CM,
which we argue is the minimal model that explains the motion of the Dirac nodes
around $\Gamma$ as the twist angle is varied. By fitting the coefficients from
the numerical results, we show that this six-band model captures the important
physics over a wide range of angles near the first "magic" angle.


  Ferroelectric domains in PbTiO$_3$/SrTiO$_3$ superlattices were studied using
synchrotron X-ray diffraction. Macroscopic measurements revealed a change in
the domain wall orientation from $\left\lbrace 100 \right\rbrace $ to
$\left\lbrace 110 \right\rbrace $ crystallographic planes with increasing
temperature. The temperature range of this reorientation depends on the
ferroelectric layer thickness and domain period. Using a nanofocused beam,
local changes in domain wall orientation within the buried ferroelectric layers
were imaged, both in structurally uniform regions of the sample and near defect
sites and argon ion etched patterns. Domain walls were found to exhibit
preferential alignment with the straight edges of the etched patterns as well
as with structural features associated with defect sites. The distribution of
out-of-plane lattice parameters was mapped around one such feature, showing
that it is accompanied by inhomogeneous strain and large strain gradients.


  Immersive 3D media is an emerging type of media that captures, encodes and
reconstructs the 3D appearance of people and objects, with applications in
tele-presence, teleconference, entertainment, gaming and other fields. In this
paper, we discuss a novel concept of live 3D immersive media streaming in a
serverless setting. In particular, we present a novel network-centric adaptive
streaming framework which deviates from a traditional client-based adaptive
streaming used in 2D video. In our framework, the decisions for the production
of the transcoding profiles are taken in a centralized manner, by considering
consumer metrics vs provisioning costs and inferring an expected consumer
quality of experience and behaviour based on them. In addition, we demonstrate
that a naive application of the serverless paradigm might be sub optimal under
some common immersive 3D media scenarios.


  In this paper, we present a new spatial discriminative KSVD dictionary
algorithm (STKSVD) for learning target appearance in online multi-target
tracking. Different from other classification/recognition tasks (e.g. face,
image recognition), learning target's appearance in online multi-target
tracking is impacted by factors such as posture/articulation changes, partial
occlusion by background scene or other targets, background changes (human
detection bounding box covers human parts and part of the scene), etc. However,
we observe that these variations occur gradually relative to spatial and
temporal dynamics. We characterize the spatial and temporal information between
target's samples through a new STKSVD appearance learning algorithm to better
discriminate sparse code, linear classifier parameters and minimize
reconstruction error in a single optimization system. Our appearance learning
algorithm and tracking framework employ two different methods of calculating
appearance similarity score in each stage of a two-stage association: a linear
classifier in the first stage, and minimum residual errors in the second stage.
The results tested using 2DMOT2015 dataset and its public Aggregated Channel
features (ACF) human detection for all comparisons show that our method
outperforms the existing related learning methods.


  Let $X$ be a del Pezzo surface of degree $5$ defined over a field $F$. A
theorem of Yu. I. Manin and P. Swinnerton-Dyer asserts that every Del Pezzo
surface of degree $5$ is rational. In this paper we generalize this result as
follows. Recall that del Pezzo surfaces of degree $5$ over a field $F$ are
precisely the twisted $F$-forms of the moduli space $\overline{M_{0, 5}}$ of
stable curves of genus $0$ with $5$ marked points. Suppose $n \geq 5$ is an
integer, and $F$ is an infinite field of characteristic $\neq 2$. It is easy to
see that every twisted $F$-form of $\overline{M_{0, n}}$ is unirational over
$F$. We show that
  (a) if $n$ is odd, then every twisted $F$-form of $\overline{M_{0, n}}$ is
rational over $F$.
  (b) If $n$ is even, there exists a field extension $F/k$ and a twisted
$F$-form $X$ of $\overline{M_{0, n}}$ such that $X$ is not retract rational
over $F$.


  We demonstrate a new type of cancellation of contributions to the electron
and neutron electric dipole moments (EDMs) that occurs in three Higgs doublet
models (3HDMs) when CP violation appears in the charged Higgs sector. The
cancellation becomes exact when the two physical charged Higgs bosons in the
model are degenerate in mass. Depending on the model parameters, degeneracies
at the 10\% level are however sufficient to evade current bounds on the
electron and neutron EDMs. We demonstrate that viable parameter space remains
with both charged Higgs bosons lighter than 500 GeV and large CP-violating
phases while also satisfying theoretical constraints from perturbativity and
experimental ones from $\bar{B} \to X_s \gamma$ and direct searches.


  Gravitational drainage of vertical films supported on a wire frame of
superspreader SILWET L-77 and its cousin non-superspreader SILWET L-7607
revealed drastic differences. The superspreader films showed complicated
dynamic turbulent-like interferometric patterns in distinction from the ordered
color bands of the cousin non-superspreader which reminded those of the
ordinary surfactants. Nevertheless the superspreader films stabilized
themselves at the thickness below 50 nm and revealed an order of magnitude
longer life time before bursting compared to the cousin non-superspreader.
Notably, the superspreader revealed drastic differences from the
non-superspreader in aqueous solutions with no contact with any solid Teflon
surface. The theoretical part of the work attributed the self-stabilization of
the superspreader films to significant disjoining pressure associated with the
van der Waals repulsion of the fluffy surfaces of the film formed by long
superspreader bilayers hanging from the free surfaces. The non-superspreaders
do not possess any significant disjoining pressure in the film with thicknesses
even in the range 30-50 nm. The results show that gravitational drainage of
vertical films is a useful simple tool for measuring disjoining pressure.


  Let $C$ be a symmetrizable generalized Cartan matrix with symmetrizer $D$ and
orientation $\Omega$. In previous work we associated an algebra $H$ to this
data, such that the locally free $H$-modules behave in many aspects like
representations of a hereditary algebra $\tilde{H}$ of the corresponding type.
We define a Noetherian algebra $\hat{H}$ over a power series ring, which
provides a direct link between the representation theory of $H$ and of
$\tilde{H}$. We define and study a reduction and a localization functor
relating the module categories of these three types of algebras. These are used
to show that there are natural bijections between the sets of isoclasses of
tilting modules over $H$, $\hat{H}$ and $\tilde{H}$. We show that the
indecomposable rigid locally free modules over $H$ and $\hat{H}$ are
parametrized, via their rank vector, by the real Schur roots associated to
$(C,\Omega)$. Moreover, the left finite bricks of $H$, in the sense of Asai,
are parametrized, via their dimension vector, by the real Schur roots
associated to the dual datum $(C^T,\Omega)$.


  Pseudo-splines of integer order $(m,\ell)$ were introduced by Daubechies,
Han, Ron, and Shen as a family which allows interpolation between the classical
B-splines and the Daubechies' scaling functions. The purpose of this paper is
to generalize the pseudo-splines to fractional and complex orders $(z, \ell)$
with $\alpha:=\re z > 1$. This allows increased flexibility in regard to
smoothness: instead of working with a discrete family of functions from $C^m$,
$m\in \N_0$, one uses a \emph{continuous} family of functions belonging to the
H\"older spaces $C^{\alpha-1}$. The presence of the imaginary part of $z$
allows for direct utilization in complex transform techniques for signal and
image analyses. We also show that in analogue to the integer case, the
generalized pseudo-splines lead to constructions of Parseval wavelet frames via
the unitary extension principle.


  We prove near-optimal upper bounds for the odd moments of the distribution of
coprime residues in short intervals, confirming a conjecture of Montgomery and
Vaughan. As an application we prove near-optimal upper bounds for the average
of the refined singular series in the Hardy-Littlewood conjectures concerning
the number of prime $k$-tuples for $k$ odd. The main new ingredient is a
near-optimal upper bound for the number of solutions to $\sum_{1\leq i\leq
k}\frac{a_i}{q_i}\in \mathbb{Z}$ when $k$ is odd, with $(a_i,q_i)=1$ and
restrictions on the size of the numerators and denominators, that is of
independent interest.


  We discuss how continuous probing of a quantum system allows estimation of
unknown classical parameters embodied in the Hamiltonian of the system. We
generalize the stochastic master equation associated with continuous
observation processes to a Bayesian filter equation for the probability
distribution of the desired parameters, and we illustrate its application by
estimating the direction of a magnetic field. In our example, the field causes
a ground state spin precession in a two-level atom which is detected by the
polarization rotation of off-resonant optical probes, interacting with the
atomic spin components.


  By exploring possible physical sense of notions, structures, and logic in a
class of noncommutative geometries, we try to unify the four fundamental
interactions within an axiomatic quantum picture. We identify the objects and
algebraic operations which could properly encode the formation and structure of
sub-atomic particles, antimatter, annihilation, CP-symmetry violation, mass
endowment mechanism, three lepton-neutrino matchings, spin, helicity and
chirality, electric charge and electromagnetism, as well as the weak and strong
interaction between particles, admissible transition mechanisms (e.g., muon to
muon neutrino, electron, and electron antineutrino), and decays (e.g., neutron
to proton, electron, and electron antineutrino).


  Using tremendous photon statistics gained with the stray light aperture of
the NuSTAR telescope over 11 years of operation, we set strong limits on the
emission of close to monochromatic photons from the radiative decays of
putative dark matter sterile neutrinos in the Milky Way. In the energy range of
3-20 keV covered by the NuSTAR, the obtained limits reach the edge of
theoretical predictions of realistic models leaving only a small room left to
explore.


  We study the dynamics of parallel brane-brane and brane-antibrane scattering
in string theory in flat spacetime, focusing on the pair production of open
strings that stretch between the branes. We are particularly interested in the
case of scattering at small impact parameter $b < l_s$, where there is a
tachyon in the spectrum when a brane and an antibrane approach within a string
length. Our conclusion is that despite the tachyon, branes and antibranes can
pass through each other with only a very small probability of annihilating, so
long as $g_s$ is small and the relative velocity $v$ is neither too small nor
too close to 1. Our analysis is relevant also to the case of charged open
string production in world-volume electric fields, and we make use of this
T-dual scenario in our analysis. We briefly discuss the application of our
results to a stringy model of inflation involving moving branes.


  We model the remarkable thin-film Ba-Ti-O structures formed by heat treatment
of an initial perovskite BaTiO$_3$ thin film on a Pt(111) surface. All
structures contain a rumpled Ti-O network with all Ti threefold coordinated
with O, and with Ba occupying the larger. mainly Ti$_7$O$_7$, pores. The
quasicrystal structure is a simple decoration of three types of tiles: square,
triangle and 30 degree rhombus, with edge lengths 6.85 Angstroms, joined
edge-to-edge in a quasicrystalline pattern; observed crystalline Ba-Ti-O
structures are built from these and other tiles. Simulated STM images reproduce
the patterns seen experimentally, and identify the bright protrusions as Ba
atoms. The models are consistent with all experimental observations.


  We show that the edges of any $d$-regular graph can be almost decomposed into
paths of length roughly $d$, giving an approximate solution to a problem of
Kotzig from 1957. Along the way, we show that almost all of the vertices of a
$d$-regular graph can be partitioned into $n/(d+1)$ paths, asymptotically
confirming a conjecture of Magnant and Martin from 2009.


  Optical fiber tapers are used to collect photoluminescence emission at ~1.5
um from photonic crystal cavities fabricated in erbium doped silicon nitride on
silicon. Photoluminescence collection via fiber taper is enhanced 2.5 times
relative to free space, with a total taper collection efficiency of 53%. By
varying the fiber taper offset from the cavity, a broad tuning range of
coupling strength is obtained. This material system combined with fiber taper
collection is promising for building on-chip optical amplifiers.


  We present a manually-labeled Author Name Disambiguation(AND) Dataset called
WhoisWho, which consists of 399,255 documents and 45,187 distinct authors with
421 ambiguous author names. To label such a great amount of AND data of high
accuracy, we propose a novel annotation framework where the human and computer
collaborate efficiently and precisely. Within the framework, we also propose an
inductive disambiguation model to classify whether two documents belong to the
same author. We evaluate the proposed method and other state-of-the-art
disambiguation methods on WhoisWho. The experiment results show that: (1) Our
model outperforms other disambiguation algorithms on this challenging
benchmark. (2) The AND problem still remains largely unsolved and requires more
in-depth research. We believe that such a large-scale benchmark would bring
great value for the author name disambiguation task. We also conduct several
experiments to prove our annotation framework could assist annotators to make
accurate results efficiently and eliminate wrong label problems made by human
annotators effectively.


  End-to-end research evaluation needs to separate out the bibliometric part of
the chain from the econometric part. We first introduce the role of
size-dependent and size-independent indicators in the bibliometric part of the
evaluation chain. We show that performance can then be evaluated at various
levels, namely a zeroth-order, a first-order or even a second-order. To
complete the evaluation chain, we take up the econometric part where efficiency
of the research production process is represented in terms of output and
outcome productivities. Both size-dependent and size-independent terms play a
crucial role to combine quantity and quality (impact) in a meaningful way.
Output or outcome at the bibliometric level can be measured using zeroth, first
or second-order composite indicators, and the productivity terms follow
accordingly using the input to output or outcome factors.


  The Gottesman-Knill theorem asserts that quantum circuits composed solely of
Clifford gates can be efficiently simulated classically. This theorem hinges on
the fact that Clifford gates map Pauli strings to other Pauli strings, thereby
allowing for a structured simulation process using classical computations. In
this work, we break down the step-by-step procedure of the Gottesman-Knill
theorem in a beginner-friendly manner, leveraging concepts such as matrix
products, tensor products, commutation, anti-commutation, eigenvalues, and
eigenvectors of quantum mechanical operators. Through detailed examples
illustrating superposition and entanglement phenomena, we aim to provide a
clear understanding of the classical simulation of Clifford gate-based quantum
circuits. While we do not provide a formal proof of the theorem, we offer
intuitive physical insights at each stage where necessary, empowering readers
to grasp the fundamental principles underpinning this intriguing aspect of
quantum computation.


  As the parameter scale of large language models (LLMs) grows, jointly
training knowledge graph (KG) embeddings with model parameters to enhance LLM
capabilities becomes increasingly costly. Consequently, the community has shown
interest in developing prompt strategies that effectively integrate KG
information into LLMs. However, the format for incorporating KGs into LLMs
lacks standardization; for instance, KGs can be transformed into linearized
triples or natural language (NL) text. Current prompting methods often rely on
a trial-and-error approach, leaving researchers with an incomplete
understanding of which KG input format best facilitates LLM comprehension of KG
content. To elucidate this, we design a series of experiments to explore LLMs'
understanding of different KG input formats within the context of prompt
engineering. Our analysis examines both literal and attention distribution
levels. Through extensive experiments, we indicate a counter-intuitive
phenomenon: when addressing fact-related questions, unordered linearized
triples are more effective for LLMs' understanding of KGs compared to fluent NL
text. Furthermore, noisy, incomplete, or marginally relevant subgraphs can
still enhance LLM performance. Finally, different LLMs have distinct
preferences for different formats of organizing unordered triples.


  In this paper, we survey Text Summarization (TS) datasets in Indian Languages
(ILs), which are also low-resource languages (LRLs). We seek to answer one
primary question: is the pool of Indian Language Text Summarization (ILTS)
dataset growing or is there a resource poverty? To an-swer the primary
question, we pose two sub-questions that we seek about ILTS datasets: first,
what characteristics: format and domain do ILTS datasets have? Second, how
different are those characteristics of ILTS datasets from high-resource
languages (HRLs) particularly English. We focus on datasets reported in
published ILTS research works during 2012-2022. The survey of ILTS and English
datasets reveals two similarities and one contrast. The two similarities are:
first, the domain of dataset commonly is news (Hermann et al., 2015). The
second similarity is the format of the dataset which is both extractive and
abstractive. The contrast is in how the research in dataset development has
progressed. ILs face a slow speed of development and public release of datasets
as compared with English. We argue that the relatively lower number of ILTS
datasets is because of two reasons: first, absence of a dedicated forum for
developing TS tools and resources; and second, lack of shareable standard
datasets in the public domain.


  We derive Gaussian approximation bounds for random forest predictions based
on a set of training points given by a Poisson process, under fairly mild
regularity assumptions on the data generating process. Our approach is based on
the key observation that the random forest predictions satisfy a certain
geometric property called region-based stabilization. In the process of
developing our results for the random forest, we also establish a probabilistic
result, which might be of independent interest, on multivariate Gaussian
approximation bounds for general functionals of Poisson process that are
region-based stabilizing. This general result makes use of the Malliavin-Stein
method, and is potentially applicable to various related statistical problems.


  Based on the data-driven analysis, the mid-rapidity transverse momentum
spectra of charged hadrons produced in central and peripheral gold-gold (Au-Au)
collisions from the Beam Energy Scan (BES) program at the relativistic Heavy
Ion Collider (RHIC) are fitted by the blast-wave model with Boltzmann-Gibbs
statistics. The model result are in agreement with the experimental data
measured by the STAR Collaboration at the RHIC-BES energies. We observe that
the kinetic freeze-out temperature, transverse flow velocity, mean transverse
momentum, and initial temperature increase with the collision energy and with
the event centrality.


  This work introduces two new techniques for random number generation with any
prescribed nonlinear distribution based on the k-vector methodology. The first
approach is based on inverse transform sampling using the optimal k-vector to
generate the samples by inverting the cumulative distribution. The second
approach generates samples by performing random searches in a pre-generated
large database previously built by massive inversion of the prescribed
nonlinear distribution using the k-vector. Both methods are shown suitable for
massive generation of random samples. Examples are provided to clarify these
methodologies.


  We propose a method for constructing Yukawa terms for noncommutative SO(10)
and E6 GUTs, when these GUTs are formulated within the enveloping-algebra
formalism. The most general noncommutative Yukawa term that we propose
contains, at first order in thetamunu, the most general BRS invariant Yukawa
contribution whose only dimensionful parameter is the noncommutativity
parameter. This noncommutative Yukawa interaction is thus renormalisable at
first order in thetamunu.


  Continuing with previous research (Camperi et al. 2011),new heliocentric
radial velocity distributions are presented for the nearby galaxy NGC 253,
obtained from the ionized hydrogen recombination line H-alpha. These
distributions have been derived from long-slit spectroscopy for various
position angles. It is also shown the heliocentric radial velocity distribution
corresponding to part of the infrared data (ionized hydrogen recombination line
Br-gamma) observed with the Phoenix spectrograph of the Gemini South
Observatory. Sequential mapping with the long slit using this instrument will
enable to study in detail the kinematics of the galaxy's core, which is
strongly obscured by dust.


  We conducted a two-night photometric survey of small Kuiper Belt objects
(KBOs) near opposition using the wide-field Hyper Suprime-Cam instrument on the
8.2 m Subaru Telescope. The survey covered about 90 deg^2 of sky, with each
field imaged in the g and i bands. We detected 356 KBOs, ranging in absolute
magnitude from 6.5 to 10.4. Filtering for high-inclination objects within the
hot KBO population, we show that the g-i color distribution is strongly
bimodal, indicative of two color classes - the red and very red subpopulations.
After categorizing objects into the two subpopulations by color, we present the
first dedicated analysis of the magnitude distributions of the individual color
subpopulations and demonstrate that the two distributions are roughly identical
in shape throughout the entire size range covered by our survey. Comparing the
color distribution of small hot KBOs with that of Centaurs, we find that they
have similar bimodal shapes, thereby providing strong confirmation of previous
explanations for the attested bimodality of Centaurs. We also show that the
magnitude distributions of the two KBO color subpopulations and the two color
subpopulations observed in the Jupiter Trojans are statistically
indistinguishable. Finally, we discuss a hypothesis describing the origin of
the KBO color bimodality based on our survey results.


  Switching of the direction of the magnetic moment in a nanomagnet is studied
within a modified Slonczewski's model that permits torsional oscillations of
the magnet. We show that the latter may inhibit or assist the magnetization
switching, depending on parameters. Three regimes have been studied: the
switching by torsional oscillations alone, the switching by the spin-polarized
current with torsional oscillations permitted, and the magnetization switching
by the current combined with the mechanical twist. We show that switching of
the magnetic moment is possible in all three cases and that allowing torsional
oscillations of the magnet may have certain advantages for applications. Phase
diagrams are computed that show the range of parameters required for the
switching.


  This paper studies the resilience of an AWGR and server based PON DCN
architecture against link failure scenarios and proposes a modified design for
improved resilience. A MILP model is developed to evaluate the performance of
the modified design considering different failure scenarios. The results show a
limited increase in power consumption and a large increase in delay under
failure scenarios compared to the normal state.


  Recent work in the literature has studied a version of non-commutative
Schwarzschild black holes where the effects of non-commutativity are described
by a mass function depending on both the radial variable r and a
non-commutativity parameter theta. The present paper studies the asymptotic
behaviour of solutions of the zero-rest-mass scalar wave equation in such a
modified Schwarzschild space-time in a neighbourhood of spatial infinity. The
analysis is eventually reduced to finding solutions of an inhomogeneous
Euler--Poisson--Darboux equation, where the parameter theta affects explicitly
the functional form of the source term. Interestingly, for finite values of
theta, there is full qualitative agreement with general relativity: the
conformal singularity at spacelike infinity reduces in a considerable way the
differentiability class of scalar fields at future null infinity. In the
physical space-time, this means that the scalar field has an asymptotic
behaviour with a fall-off going on rather more slowly than in flat space-time.


  An inflationary stage dominated by a D-term avoids the slow-roll problem of
inflation in supergravity and can naturally emerge in theories with a
non-anomalous or anomalous U(1) gauge symmetry. In the latter case, however,
the scale of inflation as imposed by the COBE normalization is in contrast with
the value fixed by the Green-Schwarz mechanism of anomaly cancellation. In this
paper we discuss possible solutions to this problem and comment about the fact
that the string-loop generated Fayet-Iliopoulos D-term may trigger the presence
of global and local cosmic strings at the end of inflation.


  One of the tests of nucleosynthesis theory is the $^3$He abundance in the
Galaxy. $^3$He$^+$ is observed through its 3.46 cm hyperfine level in Hii
regions and the $^3$He/H ratio compares well with theory. Since $^3$He can be
created or destroyed in nuclear reactions, one would expect that its abundance
shows a trend with the amount of such reactions, so with distance to the Center
of the Galaxy and with metallicity. Such trends are lacking in observations.
This is explained by assuming that the Hii clouds are recently formed out of
the primordial micro brown dwarfs of earth mass predicted by gravitational
hydrodynamics. If indeed existing, they would preserve their primordial
$^3$He/H ratio and spread this when evaporating into Hii clouds, independent of
the location in the Galaxy.
  In the development of the argument, it is also explained that wide binaries
do not rule out the MACHO dark matter predicted by gravitational hydrodynamics,
but are rather immersed as visible partners in Jeans clusters of dark micro
brown dwarfs.


  We consider dynamics of scalar semilinear parabolic equations on bounded
intervals with periodic boundary conditions, and on the entire real line, with
a general nonlinearity $g(t,x,u,u_x)$ either not depending on $t$, or periodic
in $t$. While the topological and geometric structure of their attractors has
been investigated in depth, we focus here on ergodic-theoretical properties.
The main result is that the union of supports of all the invariant measures
projects one-to-one to $\mathbb{R}^2$. We rely on a novel application of the
zero-number techniques with respect to evolution of measures on the phase
space, and on properties of the flux of zeroes, and the dissipation of zeroes.
As an example of an application, we prove uniqueness of an invariant measure
for a large family of considered equations which conserve a certain quantity
("mass"), thus generalizing the results by Sinai for the scalar viscous Burgers
equation.


  H. Weyl proved in \cite{Weyl} that integer evaluations of polynomials are
equidistributed mod 1 whenever at least one of the non-free coefficients is
irrational. We use Weyl's result to prove a higher dimensional analogue of this
fact. Namely, we prove that evaluations of polynomials on lattice points are
equidistributed mod 1 whenever at least one of the non-free coefficients is
irrational. This result strengths the main result of
Arhipov-Karacuba-\v{C}ubarikov in \cite{PolWeyl}. We prove this analogue as a
Corollary of a Theorem that guarantees equidistribution of lattice evaluations
mod 1 for all functions which satisfy some restrains on their derivatives.
Another Corollary we prove is that for $p\in(1,\infty)$ the $\ell^p$ norms of
integer vectors are equidistributed mod 1.


  In this paper we present the N-norms/N-conorms in neutrosophic logic and set
as extensions of T-norms/T-conorms in fuzzy logic and set. Also, as an
extension of the Intuitionistic Fuzzy Topology we present the Neutrosophic
Topologies.


  Supernovae are the dominant source of stellar feedback, which plays an
important role in regulating galaxy formation and evolution. While this
feedback process is still quite uncertain, it is probably not due to individual
supernova remnants as commonly observed. Most supernovae likely take place in
low-density, hot gaseous environments, such as superbubbles and galactic
bulges, and typically produce no long-lasting bright remnants. I review recent
observational and theoretical work on the impact of such supernovae on galaxy
ecosystems, particularly on hot gas in superbubbles and galactic spheroids.


  The complexity of a graph can be obtained as a derivative of a variation of
the zeta function or a partial derivative of its generalized characteristic
polynomial evaluated at a point [\textit{J. Combin. Theory Ser. B}, 74 (1998),
pp. 408--410]. A similar result for the weighted complexity of weighted graphs
was found using a determinant function [\textit{J. Combin. Theory Ser. B}, 89
(2003), pp. 17--26]. In this paper, we consider the determinant function of two
variables and discover a condition that the weighted complexity of a weighted
graph is a partial derivative of the determinant function evaluated at a point.
Consequently, we simply obtain the previous results and disclose a new formula
for the Bartholdi zeta function. We also consider a new weighted complexity,
for which the weights of spanning trees are taken as the sum of weights of
edges in the tree, and find a similar formula for this new weighted complexity.
As an application, we compute the weighted complexities of the product of the
complete graphs.


  Black holes play a fundamental role in modern physics. They have
characteristic oscillation modes, called quasinormal modes. Past studies have
shown that these modes are important to our understanding of the dynamics of
astrophysical black holes. Recent studies indicate that they are important as a
link between gravitation and quantum mechanics. Thus, the investigation of
these modes is a timeliness topic.
  Quasinormal modes dominate almost every process involving black holes, in
particular gravitational wave emission during, for example, the collision
between two black holes. It may be possible to create black holes at future
accelerators, according to recent theories advocating the existence of extra
dimensions in our universe. It is therefore important to study in depth the
gravitational radiation emitted in high energy collision between two black
holes in several dimensions, and also to make a theoretical study of
gravitational waves in higher dimensions.
  In this thesis we shall make a thorough study of the quasinormal modes of
black holes in several kinds of background spacetimes. We shall investigate the
gravitational radiation given away when highly energetic particles collide with
black holes, and also when two black holes collide with each other. Finally, we
shall study the properties of gravitational waves in higher dimensions, for
instance, we generalize Einstein's quadrupole formula.


  GWs from BNS associated with SGRBs have drawn considerable attention due to
their prospect in cosmology. For such events, the sky locations of sources can
be pinpointed with techniques such as identifying the host galaxies. However,
the cosmological applications of these events still suffer from the problem of
degeneracy between luminosity distance and inclination angle. To address this
issue, a technique was proposed in previous study, i.e., using the property of
SGRBs. Based on the observations, we assume that the cosine of inclination
follows a Gaussian distribution, which may act as a prior in the Bayes analysis
to break the degeneracy. This paper investigates the effects of different
Gaussian priors and detector configurations on distance measurement and
cosmological research. We first derive a simplified Fisher information matrix
for demonstration, and then conduct quantitative analyses via simulation. By
varying the number of third-generation detectors and the scale of prior, we
generate four catalogs of 1000 events. It is shown that, in the same detecting
period, a network of detectors can recognize more and farther events than a
single detector. Besides, adopting tighter prior and employing multiple
detectors both decrease the error of luminosity distance. Also considered is
the performance of a widely adopted formula in the error budget, which turns
out to be a conservative choice in each case. As for cosmological applications,
for LCDM model, 500, 200, 600, and 300 events are required for the four
configurations to achieve 1% H_0 accuracy. With all 1000 events in each
catalog, H_0 and Omega_m can be constrained to 0.66%, 0.37%, 0.76%, 0.49%, and
0.010, 0.006, 0.013, 0.010, respectively. The results of the Gaussian process
also show that the GW standard siren can serve as a probe of high-redshift
universe.


  Blends of polymer and C$_{60}$-derived molecules are in the spotlight in
recent years for application in organic photovoltaics, forming what is known as
bulk-heterojunction active layers. The character of the heterojunction is
determinant, with clear relevance of morphology and phase separation. To better
understand the morphology of the systems, we present a classical molecular
dynamics (CMD) simulation of polymer/fullerene (P3HT/C$_{60}$) blends, coming
from different starting points, using the specifically designed Nanomol Force
Field based on the Universal Force Field. We use not-so-short regioregular
polymers with 30 hexyl-thiophene units ($\sim$5kg$\cdot$mol$^{-1}$ molecular
weight) and, adopting a $\sim$ 1:1 mass proportion for the polymer:molecule
blend, we simulate cells of $\sim$ 40 thousand atoms, at room temperature and
normal pressure conditions. We find that, independently of the starting-point
spatial distribution of C$_{60}$ molecules relative to P3HT chains, segregated
or isotropic, the fullerene molecules show a tendency to segregate, and phase
separation is the dominating regime.


  Bohmian mechanics represents the universe as a set of paths with a
probability measure defined on it. The way in which a mathematical model of
this kind can explain the observed phenomena of the universe is examined in
general. It is shown that the explanation does not make use of the full
probability measure, but rather of a suitable set function deriving from it,
which defines relative typicality between single-time cylinder sets. Such a set
function can also be derived directly from the standard quantum formalism,
without the need of an underlying probability measure. The key concept for this
derivation is the {\it quantum typicality rule}, which can be considered as a
generalization of the Born rule. The result is a new formulation of quantum
mechanics, in which particles follow definite trajectories, but which is only
based on the standard formalism of quantum mechanics.


  In the framework of the classical Glauber approach the exact analytical
expression for the variance of the number of participants (wounded nucleons)
for given centrality AA interactions is presented. It's shown, that in the case
of nucleus-nucleus collisions along with the optical approximation term the
additional "contact" term appears. The numerical calculations for PbPb
collisions at SPS energies show that at intermediate values of the impact
parameter the "optical" and "contact" terms contributions to the variance of
the participants number are of the same order and their sum is in a good
agreement with the results of independent MC simulations of this process. The
correlation between the numbers of participants in colliding nuclei is taken
into account. In particular it's demonstrated that in PbPb collisions at SPS
energies the variance of the total number of participants approximately three
times exceeds the Poisson one in the impact parameter region 10-12 Fm. The
fluctuations of the number of collisions are also discussed.


  This article pertains to the classification of multiple Schramm-Loewner
evolutions (SLE). We construct the pure partition functions of multiple
SLE$(\kappa)$ with $\kappa \in (0,4]$ and relate them to certain extremal
multiple SLE measures, thus verifying a conjecture from [BBK05, KP16]. We prove
that the two approaches to construct multiple SLEs - the global,
configurational construction of [KL07, Law09a] and the local, growth process
construction of [BBK05, Dub07, Gra07, KP16] - agree. The pure partition
functions are closely related to crossing probabilities in critical statistical
mechanics models. With explicit formulas in the special case of $\kappa = 4$,
we show that these functions give the connection probabilities for the level
lines of the Gaussian free field (GFF) with alternating boundary data. We also
show that certain functions, known as conformal blocks, give rise to multiple
SLE(4) that can be naturally coupled with the GFF with appropriate boundary
data.


  In this article we have developed a formalism to obtain the solution of
Schroedinger equation in a non-inertial frame. The frame is moving relative to
an inertial frame with an acceleration. The formulation has been developed
using Lagrangian formalism as discussed in Classical Mechanics book by Landau
and Lifshitz [1]. Hence we have obtained the Hamiltonian of the nucleons. Then
using the standard form of canonical quantization rule, we have setup the
Schroedinger equation in non-inertial frame. In the present study we have
considered only the accelerated rectilinear motion of the non-inertial frame.
The rotation will be considered in some future work based on quantum field
theory [2] (see also [3, 4]). We therefore drop the rotation part of the
Hamiltonian in our calculation. The physically acceptable result on our work is
basically the solution obtained by Fowler and Nordheim for the emission of
electrons from cold metal surface induced by strong electric field [5] known as
cold field emission of electrons. However in the present formulation, it is the
gravity which acts on mass of the particle and causes emission. The centrifugal
force acts like gravity. Hence we have got some flavor of Hawking radiation [6]
and also Unruh effect [7] within the limited scope of our non-relativistic
approach. We have also shown that relative motion of a two body quantum
mechanical system does not depend on the nature of the frame of reference.


  In this paper we consider classical and quantum versions of the critical
long-range $O(N)$ model, for which we study finite-size and finite-temperature
effects, respectively, at large $N$. First, we consider the classical
(isotropic) model, which is conformally invariant at criticality, and we
introduce one compact spatial direction. We show that the finite size
dynamically induces an effective mass and we compute the one-point functions
for bilinear primary operators with arbitrary spin and twist. Second, we study
the quantum model, mapped to a Euclidean anisotropic field theory, local in
Euclidean time and long-range in space, which we dub \emph{fractional Lifshitz
field theory}. We show that this model admits a fixed point at zero
temperature, where it displays anisotropic Lifshitz scaling, and show that at
finite temperature a thermal mass is induced. We then compute the one-point
functions for an infinite family of bilinear scaling operators. In both the
classical and quantum model, we find that, as previously noted for the
short-range $O(N)$ model in [arXiv:1802.10266], the large-$N$ two-point
function contains information about the one-point functions, not only of the
bilinear operators, but also of operators that appear in the operator product
expansion of two fundamental fields only at subleading order in $1/N$, namely
powers of the Hubbard-Stratonovich intermediate field.