  We present local and nonlocal electrical transport measurements of the
correlated insulator FeSb$_2$. By employing wiring configurations that
delineate between bulk- and surface-dominated conduction, we reveal the
formation of a metallic surface state in FeSb$_2$ for temperatures $\lessapprox
5$~K. This result is corroborated by an angular rotation study of this
material's magnetotransport, which also shows signatures of the transition from
bulk- to surface-dominated conduction over the same temperature interval as the
local/nonlocal transport divergence. Notable similarities with the topological
Kondo insulator candidate SmB$_6$ are discussed.


  Upon its release in late 2022, ChatGPT has brought a seismic shift in the
entire landscape of AI, both in research and commerce. Through
instruction-tuning a large language model (LLM) with supervised fine-tuning and
reinforcement learning from human feedback, it showed that a model could answer
human questions and follow instructions on a broad panel of tasks. Following
this success, interests in LLMs have intensified, with new LLMs flourishing at
frequent interval across academia and industry, including many start-ups
focused on LLMs. While closed-source LLMs (e.g., OpenAI's GPT, Anthropic's
Claude) generally outperform their open-source counterparts, the progress on
the latter has been rapid with claims of achieving parity or even better on
certain tasks. This has crucial implications not only on research but also on
business. In this work, on the first anniversary of ChatGPT, we provide an
exhaustive overview of this success, surveying all tasks where an open-source
LLM has claimed to be on par or better than ChatGPT.


  Augmented reality have undergone considerable improvement in past years. Many
special techniques and hardware devices were developed, but the crucial
breakthrough came with the spread of intelligent mobile phones. This enabled
mass spread of augmented reality applications. However mobile devices have
limited hardware capabilities, which narrows down the methods usable for scene
analysis. In this article we propose an augmented reality application which is
using cloud computing to enable using of more complex computational methods
such as neural networks. Our goal is to create an affordable augmented reality
application suitable which will help car designers in by 'virtualizing' car
modifications.


  We analyze the gaps in the excitation spectrum of a Haldane chain with
single-ion anisotropy in a staggered field. We show that the gap along the
direction of the field increases at a faster rate than the others, while its
spectral weight decreases, being transferred to a two-magnon continuum.


  We consider the massive vector field propagating in the inhomogeneous
parity-breaking medium, such as the dense hot hadronic matter with chiral
imbalance. The transition between the regions with approximately constant
values of the parity-breaking parameter allows for the states localized on such
boundary to occur. The adiabatic change of the background introduces either
decay or the amplification of the localized states. We also discuss the
non-adiabatic destruction of these bound states.


  We present Unified Contrastive Arbitrary Style Transfer (UCAST), a novel
style representation learning and transfer framework, which can fit in most
existing arbitrary image style transfer models, e.g., CNN-based, ViT-based, and
flow-based methods. As the key component in image style transfer tasks, a
suitable style representation is essential to achieve satisfactory results.
Existing approaches based on deep neural network typically use second-order
statistics to generate the output. However, these hand-crafted features
computed from a single image cannot leverage style information sufficiently,
which leads to artifacts such as local distortions and style inconsistency. To
address these issues, we propose to learn style representation directly from a
large amount of images based on contrastive learning, by taking the
relationships between specific styles and the holistic style distribution into
account. Specifically, we present an adaptive contrastive learning scheme for
style transfer by introducing an input-dependent temperature. Our framework
consists of three key components, i.e., a parallel contrastive learning scheme
for style representation and style transfer, a domain enhancement module for
effective learning of style distribution, and a generative network for style
transfer. We carry out qualitative and quantitative evaluations to show that
our approach produces superior results than those obtained via state-of-the-art
methods.


  In Computer Vision, Zero-Shot Learning (ZSL) aims at classifying unseen
classes -- classes for which no matching training image exists. Most of ZSL
works learn a cross-modal mapping between images and class labels for seen
classes. However, the data distribution of seen and unseen classes might
differ, causing a domain shift problem. Following this observation,
transductive ZSL (T-ZSL) assumes that unseen classes and their associated
images are known during training, but not their correspondence. As current
T-ZSL approaches do not scale efficiently when the number of seen classes is
high, we tackle this problem with a new model for T-ZSL based upon CycleGAN.
Our model jointly (i) projects images on their seen class labels with a
supervised objective and (ii) aligns unseen class labels and visual exemplars
with adversarial and cycle-consistency objectives. We show the efficiency of
our Cross-Modal CycleGAN model (CM-GAN) on the ImageNet T-ZSL task where we
obtain state-of-the-art results. We further validate CM-GAN on a language
grounding task, and on a new task that we propose: zero-shot sentence-to-image
matching on MS COCO.


  We study conformal $Spin$-subgeometry of submanifolds in a semi-Riemannian
$Spin$-manifold, focusing on conformal $Spin$-manifolds $(M,[h])$ and their
Poincar\'e-Einstein metrics $(X,g_+)$. Our approach is based on the spectral
theory of Dirac operator in the ambient $Spin$-manifold, and associated spinor
valued meromorphic family of distributions with residues given by the residue
family operators $\slashed{D}_N^{res}(h;\lambda)$ on spinors. We develop basic
aspects and properties of $\slashed{D}_N^{res}(h;\lambda)$ including conformal
covariance, factorization properties by conformally covariant operators for
both flat and curved semi-Riemannian $Spin$-manifolds, and Poisson
transformation.


  Jim Hannan is a professor who has lived an interesting life and one whose
fundamental research in repeated games was not fully appreciated until late in
his career. During his service as a meteorologist in the Army in World War II,
Jim played poker and made weather forecasts. It is curious that his later
research included strategies for repeated play that apply to selecting the best
forecaster. James Hannan was born in Holyoke, Massachusetts on September 14,
1922. He attended St. Jerome's High School and in January 1943 received the
Ph.B. from St. Michael's College in Colchester, Vermont. Jim enlisted in the US
Army Air Force to train and serve as a meteorologist. This took him to army
airbases in China by the close of the war. Following discharge from the army,
Jim studied mathematics at Harvard and graduated with the M.S. in June 1947. To
prepare for doctoral work in statistics at the University of North Carolina
that fall, Jim went to the University of Michigan in the summer of 1947. The
routine admissions' physical revealed a spot on the lung and the possibility of
tuberculosis. This caused Jim to stay at Ann Arbor through the fall of 1947 and
then at a Veterans Administration Hospital in Framingham, Massachusetts to have
his condition followed more closely. He was discharged from the hospital in the
spring and started his study at Chapel Hill in the fall of 1948. There he began
research in compound decision theory under Herbert Robbins. Feeling the need
for teaching experience, Jim left Chapel Hill after two years and short of
thesis to take a three year appointment as an instructor at Catholic University
in Washington, DC. When told that renewal was not coming, Jim felt pressure to
finish his degree.


  We describe how bi-maximal neutrino mixing can be realized in realistic
models based on MSSM and SUSY GUTs such as SU(5) and SO(10). A crucial role is
played by an anomalous ${\cal U}(1)$ flavor symmetry, which also helps
understand the observed charged fermion mass hierarchies and the magnitudes of
the CKM matrix elements. While in MSSM a variety of solutions for the solar
neutrino puzzle are possible, SUSY SU(5) and SO(10) only permit the large
mixing angle MSW solution. Models in which the ${\cal U}(1)$ symmetry also
mediates SUSY breaking allow both the large mixing angle and the low MSW
solutions.
  We also present renormalization group studies for the neutrino mass matrix,
generated through the ${\cal U}(1)$ flavor symmetry. Our analysis shows that
renormalization does not change the desirable picture of bi-maximal mixing.


  This paper introduces two new closely related betweenness centrality measures
based on the Randomized Shortest Paths (RSP) framework, which fill a gap
between traditional network centrality measures based on shortest paths and
more recent methods considering random walks or current flows. The framework
defines Boltzmann probability distributions over paths of the network which
focus on the shortest paths, but also take into account longer paths depending
on an inverse temperature parameter. RSP's have previously proven to be useful
in defining distance measures on networks. In this work we study their utility
in quantifying the importance of the nodes of a network. The proposed RSP
betweenness centralities combine, in an optimal way, the ideas of using the
shortest and purely random paths for analysing the roles of network nodes,
avoiding issues involving these two paradigms. We present the derivations of
these measures and how they can be computed in an efficient way. In addition,
we show with real world examples the potential of the RSP betweenness
centralities in identifying interesting nodes of a network that more
traditional methods might fail to notice.


  We propose a CPT-even and Lorentz-violating dimension-five nonminimal
coupling between fermionic and gauge fields, involving the CPT-even and
Lorentz-violating gauge tensor of the Standard-Model Extension. This nonminimal
coupling modifies the nonrelativistic regime of Dirac particles, inducing new
effects such as an electric-Zeeman-like spectrum splitting and an
anomalous-like contribution to the electron magnetic moment. These new effects
allow to constrain the magnitude of this nonminimal coupling in 1 part in
$10^{16}.$


  Methods for extracting Higgs boson signals at a 1 TeV center-of-mass energy
e+e- linear collider are described. In addition, estimates are given for the
accuracy with which branching fractions can be measured for Higgs boson decays
to bb, WW, gluon-gluon, and gamma-gamma.


  The main contribution of this thesis is the development of a new algorithm
for solving convex quadratic programs. It consists in combining the method of
multipliers with an infeasible active-set method. Our approach is iterative. In
each step we calculate an augmented Lagrange function. Then we minimize this
function using an infeasible active-set method that was already successfully
applied to similar problems. After this we update the Lagrange multiplier for
the equality constraints. Finally we try to solve convex quadratic program
directly, again with the infeasible active-set method, starting from the
optimal solution of the actual Lagrange function. Computational experience with
our method indicates that typically only few (most of the time only one) outer
iterations (multiplier-updates) and also only few (most of the time less than
ten) inner iterations (minimization of the Lagrange function) are required to
reach the optimal solution.
  The diploma thesis is organized as follows. We close this chapter with some
nota- tion used throughout. In Chapter 2 we show the equivalence of different
QP problem formulations and present some important so-called direct methods for
solving equality-constrained QPs. We cover the most important aspects for
practically successful interior point methods for linear and convex quadratic
programming in Chapter 3. Chapter 4 deals with ingredients for practically
efficient feasible active set methods. Finally Chapter 5 provides a close
description of our Lagrangian infeasible active set method and further gives a
convergence analysis of the subalgorithms involved.


  As the prices of magnetic storage continue to decrease, the cost of replacing
failed disks becomes increasingly dominated by the cost of the service call
itself. We propose to eliminate these calls by building disk arrays that
contain enough spare disks to operate without any human intervention during
their whole lifetime. To evaluate the feasibility of this approach, we have
simulated the behavior of two-dimensional disk arrays with n parity disks and
n(n-1)/2 data disks under realistic failure and repair assumptions. Our
conclusion is that having n(n+1)/2 spare disks is more than enough to achieve a
99.999 percent probability of not losing data over four years. We observe that
the same objectives cannot be reached with RAID level 6 organizations and would
require RAID stripes that could tolerate triple disk failures.


  Polarimetric experiments driven by the strong field of a circularly polarized
laser wave can become a powerful tool to limit the parameter space of not yet
detected hidden-photons and minicharged particles associated with extra U(1)
gauge symmetries. We show how the absorption and dispersion of probe
electromagnetic waves in the vacuum polarized by such a background are modified
due to the coupling between the visible U(1)-gauge sector and these
hypothetical degrees of freedom. The results of this analysis reveal that the
regime close to the two-photon reaction threshold can be a sensititive probe of
these hidden particles. Parameters of modern laser systems are used to estimate
the constraints on the corresponding coupling constants in regions where
experiments driven by dipole magnets are less constricted. The role played by a
paraphoton field is analyzed via a comparison with a model in which the
existence of minicharges is assumed only. For both scenarios is found that the
most stringent exclusion limit occurs at the lowest threshold mass; this one
being determined by a certain combination of the field frequencies and dictated
by energy momentum balance of the photo-production of a pair of minicharged
particles. The dependencies of the observables on the laser attributes as well
as on the unknown particle parameters are also analyzed.


  Within the Standard Model (SM) one predicts both direct and indirect CP
violation in D^0 \to \pi^+\pi^-, K^+K^- transitions, although the effects are
tiny: Indirect CP asymmetry cannot exceed O(10^{-4}), probably even O(10^{-5});
direct effects are estimated at not larger than 10^{-4}. At B factories direct
and indirect asymmetries have been studied with <t>/\tau_{D^0} ~ 1; no CP
asymmetry was found with an upper bound of about 1%. CDF has shown intriguing
data on CP violation in D^0 \to \pi^+\pi^- [K^+K^-] with <t>/\tau_{D^0} ~ 2.4
[2.65]. Also, CDF has not seen any CP violation. For direct CP asymmetry, CDF
has a sensitivity similar to the combination of the B factories, yet for
indirect CP violation it yields a significantly smaller sensitivity of
a_{cp}^{ind}=(-0.01 +- 0.06_{stat} +- 0.05_{syst})% due to it being based on
longer decay times. New Physics models (NP) like Little Higgs Models with
T-Parity (LHT) can produce an indirect CP asymmetry up to 1%; CDF's findings
thus cover the upper range of realistic NP predictions ~ 0.1 - 1%. One hopes
that LHCb and a Super-Flavour Factory will probe the lower range down to
~0.01%. Such non-ad-hoc NP like LHT cannot enhance direct CP violation
significantly over the SM level in D^0 \to \pi^+\pi^-, K^+K^- and D^{\pm} \to
\pi^{\pm}K^+K^- transitions, but others might well do so.


  A low-pressure double-inductively coupled plasma device is used to study the
fundamental plasma parameters, plasma chemistry, and UV photon emission from
the first excited state of nitric oxide, NO(A), in gas mixtures of nitrogen and
oxygen. In addition to the gas mixture, rf power and gas pressure are varied,
and the E-H mode transition of the inductively coupled plasma is studied
specifically. The gas temperature and UV photon emission are measured by
optical emission spectroscopy (OES), the absolute density of the nitric oxide
electronic ground state by laser-induced fluorescence (LIF), as well as
electron density and electron temperature by a multipole resonance probe (MRP).
A simple collisional-radiative model for UV emission from NO(A) is developed,
which takes the measured densities of ground state nitric oxide and electrons,
as well as the electron temperature and neutral gas temperature, as input
parameters. The results reveal the links between the absolute densities of
ground state nitric oxide, the excitation of this species driven by electron
impact and collisions with nitrogen metastables, quenching of the nitrogen
metastables, and the resulting UV photon emission rate. The density of ground
state nitric oxide is shown to increase with power, while the discharge remains
in E-mode, and to decrease significantly with the transition into H-mode, when
sufficient rf power is deposited in the discharge. Despite the lower densities
of ground state nitric oxide in H-mode, the UV photon emission intensity
increases continuously with higher rf powers and over the E-H transition. This
effect is shown to be caused by increased excitation of NO(A) by nitrogen
metastables in H-mode, which is sufficient to overcompensate the decrease in
ground state nitric oxide density.


  We study the evolution of the orbit of a planetary companion as the primary
star evolves during the red giant branch phase. Our aim is to determine a
prescription for the capture radius and capture timescales for companions in a
wide range of masses, from planet to star, including the effect of a non
constant f parameter. Our initial results reproduce past findings. According to
our study the mass-loss during the red giant branch does not significantly
affect the semi major axis of the planet and for a 1.5 M star the capture
radius is approximately 300 R or 1.4 AU.


  For a family of varieties, we prove that the alternating sum of the traces of
"local" monodromy acting on the $\ell$-adic \'etale cohomology groups of the
generic fiber is an integer which is independent of $\ell$.


  Network functions virtualization provides opportunities to design, deploy,
and manage networking services. It utilizes cloud computing virtualization
services that run on high-volume servers, switches, and storage hardware to
virtualize network functions. Virtualization techniques can be used in IP
multimedia subsystem (IMS) cloud computing to develop different networking
functions (e.g., load balancing and call admission control). IMS network
signaling happens through session initiation protocol (SIP). An open issue is
the control of overload that occurs when an SIP server lacks sufficient CPU and
memory resources to process all messages. This paper proposes a virtual load
balanced call admission controller (VLB-CAC) for the cloud-hosted SIP servers.
VLB-CAC determines the optimal call admission rates and signaling paths for
admitted calls along with the optimal allocation of CPU and memory resources of
the SIP servers. This optimal solution is derived through a new linear
programming model. This model requires some critical information of SIP servers
as input. Further, VLB-CAC is equipped with an autoscaler to overcome resource
limitations. The proposed scheme is implemented in smart applications on
virtual infrastructure (SAVI) which serves as a virtual testbed. An assessment
of the numerical and experimental results demonstrates the efficiency of the
proposed work.


  Chain-of-Thought (CoT) prompting has marked a significant advancement in
enhancing the reasoning capabilities of large language models (LLMs). Previous
studies have developed various extensions of CoT, which focus primarily on
enhancing end-task performance. In addition, there has been research on
assessing the quality of reasoning chains in CoT. This raises an intriguing
question: Is it possible to predict the accuracy of LLM outputs by scrutinizing
the reasoning chains they generate? To answer this research question, we
introduce a benchmark, R2PE, designed specifically to explore the relationship
between reasoning chains and performance in various reasoning tasks spanning
five different domains. This benchmark aims to measure the falsehood of the
final output of LLMs based on the reasoning steps. To make full use of
information in multiple reasoning chains, we propose the process discernibility
score (PDS) framework that beats the answer-checking baseline by a large
margin. Concretely, this resulted in an average of $5.1\%$ increase in the F1
score and $2.97\%$ improvement in AUC-PR across all 45 subsets within R2PE. We
further demonstrate our PDS's efficacy in advancing open-domain QA accuracy.
Data and code are available at https://github.com/XinXU-USTC/R2PE.


  Data streams are a sequence of data flowing between source and destination
processes. Streaming is widely used for signal, image and video processing for
its efficiency in pipelining and effectiveness in reducing demand for memory.
The goal of this work is to extend the use of data streams to support both
conventional scientific applications and emerging data analytic applications
running on HPC platforms. We introduce an extension called MPIStream to the
de-facto programming standard on HPC, MPI. MPIStream supports data streams
either within a single application or among multiple applications. We present
three use cases using MPI streams in HPC applications together with their
parallel performance. We show the convenience of using MPI streams to support
the needs from both traditional HPC and emerging data analytics applications
running on supercomputers.


  In this work, we consider inflection point inflation in the framework of
running kinetic term inflation in supergravity. We study the inflationary
dynamics and show that the predicted value of the scalar spectral index and
tensor-to-scalar ratio can lie within the $1\sigma$ confidence region allowed
by the result of Planck 2015.


  Multipion production in high energy nucleus-nucleus collisions is considered
in the model of the pion radiation by classical current. Strong coherent
effects of narrowing of pion longitudinal and transverse momenta distributions
are predicted at the RHIC energy. The coherence enhances the large
pseudorapidities producing the bump in the distribution. The growth of the
average pion multiplicity and the oscillation effect in the multiplicity
distribution are caused by the coherence as well.


  In this note we study, for a random lattice L of large dimension n, the
supremum of the real parts of the zeros of the Epstein zeta function E_n(L,s)
and prove that this random variable has a limit distribution, which we give
explicitly. This limit distribution is studied in some detail; in particular we
give an explicit formula for its distribution function.


  We study correlation functions of parafermionic currents and disorder fields
in the Z(N) symmetric conformal field theory perturbed by the first thermal
operator. Following the ideas of Al. Zamolodchikov, we develop for the
correlation functions the conformal perturbation theory at small scales and the
form factors spectral decomposition at large ones. For all N there is an
agreement between the data at the intermediate distances. We consider the
problems arising in the description of the space of scaling fields in perturbed
models, such as null vector relations, equations of motion and a consistent
treatment of fields related by a resonance condition.


  Suppose an oracle knows a string $S$ that is unknown to us and that we want
to determine. The oracle can answer queries of the form "Is $s$ a substring of
$S$?". In 1995, Skiena and Sundaram showed that, in the worst case, any
algorithm needs to ask the oracle $\sigma n/4 -O(n)$ queries in order to be
able to reconstruct the hidden string, where $\sigma$ is the size of the
alphabet of $S$ and $n$ its length, and gave an algorithm that spends
$(\sigma-1)n+O(\sigma \sqrt{n})$ queries to reconstruct $S$. The main
contribution of our paper is to improve the above upper-bound in the context
where the string is compressible. We first present a universal algorithm that,
given a (computable) compressor that compresses the string to $\tau$ bits,
performs $q=O(\tau)$ substring queries; this algorithm, however, runs in
exponential time. For this reason, the second part of the paper focuses on more
time-efficient algorithms whose number of queries is bounded by specific
compressibility measures. We first show that any string of length $n$ over an
integer alphabet of size $\sigma$ with $rle$ runs can be reconstructed with
$q=O(rle (\sigma + \log \frac{n}{rle}))$ substring queries in linear time and
space. We then present an algorithm that spends $q \in O(\sigma g\log n)$
substring queries and runs in $O(n(\log n + \log \sigma)+ q)$ time using linear
space, where $g$ is the size of a smallest straight-line program generating the
string.


  We study the ground-state phase transitions of quasi-one-dimensional quantum
Heisenberg antiferromagnets by the quantum Monte Carlo method with the
continuous-time loop algorithm and finite-size scaling. For a model which
consists of S=1 chains with bond alternation coupled on a square lattice, we
determine the ground state phase diagram and the universality class of the
quantum phase transitions.


  This paper is devoted to the prescribed scalar curvature under minimal
boundary mean curvature on the standard four dimensional half sphere. Using
topological methods from the theory of critical points at infinity, we prove
some existence results. These methods were first introduced by A. Bahri.


  We present a technique to treat systems with very many levels, like
molecules, in non-LTE. This method is based on a superlevel formalism coupled
with rate operator splitting. Superlevels consist of many individual levels
that are assumed to be in LTE relative to each other. The usage of superlevels
reduces the dimensionality of the rate equations dramatically and, thereby,
makes the problem computationally more easily treatable. Our superlevel
formalism retains maximum accuracy by using direct opacity sampling (dOS) when
calculating the radiative transitions and the opacities. We developed this
method in order to treat molecules in cool dwarf model calculations in non-LTE.
Cool dwarfs have low electron densities and a radiation field that is far from
a black body radiation field, both properties may invalidate the conditions for
the common LTE approximation. Therefore, the most important opacity sources,
the molecules, need to be treated in non-LTE. As a case study we applied our
method to carbon monoxide. We find that our method gives accurate results since
the conditions for the superlevel method are very well met for molecules. Due
to very high collisional cross sections with hydrogen, and the high densities
of H_2 the population of CO itself shows no significant deviation from LTE.


  We show that the so called $\lambda$ deformed $\sigma$-model as well as the
$\eta$ deformed one belong to a class of the ${\cal E}$-models introduced in
the context of the Poisson-Lie-T-duality. The $\lambda$ and $\eta$ theories
differ solely by the choice of the Drinfeld double; for the $\lambda$ model the
double is the direct product $G\times G$ while for the $\eta$ model it is the
complexified group $G^{\mathbb{C}}$. As a consequence of this picture, we prove
for any $G$ that the target space geometries of the $\lambda$-model and of the
Poisson-Lie T-dual of the $\eta$-model are related by a simple analytic
continuation.


  The extension of the classical Bayesian penalized spline method to inference
on vector-valued functions is considered, with an emphasis on characterizing
the suitability of the method for general application.We show that the standard
quadratic penalty is exactly analogous to the energy of a stretched string,
with the penalty parameter corresponding to its tension. This physical analogy
motivates a discussion of resolution independence, which we define as the
convergence of a computational function estimate to arbitrary accuracy with
increasing resolution.The multidimensional context makes direct application of
standard procedures for choosing the penalty parameter difficult, and a new
method is proposed and compared to the established generalized cross-validation
(GCV) and Akaike information criterion (AIC) functions.Our Bayesian method for
choosing this parameter is derived by introducing a scal e independence
criterion to ensure that simultaneously scaling the function samples and their
variances does not significantly change the posterior parameter distribution.
Due to the possibility of an exact polynomial fit, numerical issues prevent the
use of this prior, and a solution is presented based on adding a st ring
zero-point energy. This makes more complicated approaches recently propose d in
the literature unnecessary, and eliminates the requirement for sensitivity
analysis when the function deviates from the above mentioned polynomial. An
important class of problems which can be analyzed by this method are stochastic
numerical integrators, which are considered as an example problem. This work
represents the first extension of penalized spline methods to inference on
multidimensional numerical integrators reported in the literature. Several
numerical calculations illustrate the above points and address practical
application issues.


  We explore the use of symmetry-adapted perturbation theory (SAPT) as a simple
and efficient means to compute interaction energies between large molecular
systems with a hybrid method combing NISQ-era quantum and classical computers.
From the one- and two-particle reduced density matrices of the monomer
wavefunctions obtained by the variational quantum eigensolver (VQE), we compute
SAPT contributions to the interaction energy [SAPT(VQE)]. At first order, this
energy yields the electrostatic and exchange contributions for non-covalently
bound systems. We empirically find from ideal statevector simulations that the
SAPT(VQE) interaction energy components display orders of magnitude lower
absolute errors than the corresponding VQE total energies. Therefore, even with
coarsely optimized low-depth VQE wavefunctions, we still obtain sub kcal/mol
accuracy in the SAPT interaction energies. In SAPT(VQE), the quantum
requirements, such as qubit count and circuit depth, are lowered by performing
computations on the separate molecular systems. Furthermore, active spaces
allow for large systems containing thousands of orbitals to be reduced to a
small enough orbital set to perform the quantum portions of the computations.
We benchmark SAPT(VQE) (with the VQE component simulated by ideal state-vector
simulators) against a handful of small multi-reference dimer systems and the
iron center containing human cancer-relevant protein lysine-specific
demethylase 5 (KDM5A).


  The general theory of N=1 supergravity with supermatter is applied to a
Bianchi type IX diagonal model. The supermatter is constituted by a complex
scalar field and its spin-$1\over 2$ fermionic partners. The K\"ahler geometry
is chosen to be a two-dimensional flat one. The Lorentz invariant Ansatz for
the wave function of the universe is taken to be as simple as possible in order
to obtain {\it new} solutions. The set of differential equations derived from
the quantum constraints are analysed in two different cases: if the supermatter
terms include an analytical potential or not. In the latter the wave function
is found to have a simple form.


  We introduce an improved solution to the neural image-based rendering problem
in computer vision. Given a set of images taken from a freely moving camera at
train time, the proposed approach could synthesize a realistic image of the
scene from a novel viewpoint at test time. The key ideas presented in this
paper are (i) Recovering accurate camera parameters via a robust pipeline from
unposed day-to-day images is equally crucial in neural novel view synthesis
problem; (ii) It is rather more practical to model object's content at
different resolutions since dramatic camera motion is highly likely in
day-to-day unposed images. To incorporate the key ideas, we leverage the
fundamentals of scene rigidity, multi-scale neural scene representation, and
single-image depth prediction. Concretely, the proposed approach makes the
camera parameters as learnable in a neural fields-based modeling framework. By
assuming per view depth prediction is given up to scale, we constrain the
relative pose between successive frames. From the relative poses, absolute
camera pose estimation is modeled via a graph-neural network-based multiple
motion averaging within the multi-scale neural-fields network, leading to a
single loss function. Optimizing the introduced loss function provides camera
intrinsic, extrinsic, and image rendering from unposed images. We demonstrate,
with examples, that for a unified framework to accurately model multiscale
neural scene representation from day-to-day acquired unposed multi-view images,
it is equally essential to have precise camera-pose estimates within the scene
representation framework. Without considering robustness measures in the camera
pose estimation pipeline, modeling for multi-scale aliasing artifacts can be
counterproductive. We present extensive experiments on several benchmark
datasets to demonstrate the suitability of our approach.


  We propose to use eigenvalue densities of unitary random matrix ensembles as
mass distributions in gravitational lensing. The corresponding lens equations
reduce to algebraic equations in the complex plane which can be treated
analytically. We prove that these models can be applied to describe lensing by
systems of edge-on galaxies. We illustrate our analysis with the Gaussian and
the quartic unitary matrix ensembles.


  We define formal orbifolds over an algebraically closed field of arbitrary
characteristic as curves together with some branch data. Their \'etale
coverings and their fundamental groups are also defined. These fundamental
group approximates the fundamental group of an appropriate affine curve. We
also define vector bundles on these objects and the category of orbifold
bundles on any smooth projective curve. Analogues of various statement about
vector bundles which are true in characteristic zero are proved. Some of these
are positive characteristic avatar of notions which appear in the second
author's work ([Par]) in characteristic zero.


  Tensor decomposition methods have proven effective in various applications,
including compression and acceleration of neural networks. At the same time,
the problem of determining optimal decomposition ranks, which present the
crucial parameter controlling the compression-accuracy trade-off, is still
acute. In this paper, we introduce MARS -- a new efficient method for the
automatic selection of ranks in general tensor decompositions. During training,
the procedure learns binary masks over decomposition cores that "select" the
optimal tensor structure. The learning is performed via relaxed maximum a
posteriori (MAP) estimation in a specific Bayesian model and can be naturally
embedded into the standard neural network training routine. Diverse experiments
demonstrate that MARS achieves better results compared to previous works in
various tasks.


  We develop a linear response theory of solvation of ionic and dipolar solutes
in anisotropic, axially symmetric polar solvents. The theory is applied to
solvation in polar nematic liquid crystals. The formal theory constructs the
solvation response function from projections of the solvent dipolar
susceptibility on rotational invariants. These projections are obtained from
Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist
both in the isotropic and nematic phase. Based on the properties of the solvent
susceptibility from simulations and the formal solution, we have obtained a
formula for the solvation free energy which incorporates experimentally
available properties of nematics and the length of correlation between the
dipoles in the liquid crystal. Illustrative calculations are presented for the
Stokes shift and Stokes shift correlation function of coumarin-153 in
4-n-pentyl-4'-cyanobiphenyl (5CB) and 4,4-n-heptyl-cyanopiphenyl (7CB) solvents
as a function of temperature in both the nematic and isotropic phase.


  We report here the status of different gauge conditions in the canonical
formulation of quantum electrodynamics on light-front surfaces. We start with
the massive vector fields as pedagogical models where all basic concepts and
possible problems manifestly appear. Several gauge choices are considered for
both the infinite and the finite volume formulation of massless gauge field
electrodynamics. We obtain the perturbative Feynman rules in the first approach
and the quantum Hamiltonian for all sectors in the second approach. Different
space-time dimensions are discussed in all models where they crucially change
the physical meaning. Generally, fermions are considered as the charged matter
fields but also one simple 1+1 dimensional model is discussed for scalar
fields. Finally the perspectives for further research projects are discussed.


  We report the first observation of $B^{\pm}\to\psi(2S)\pi^{\pm}$, a Cabibbo-
and color-suppressed decay. This analysis is based on $657\times10^{6}$
$B\overline B$ events collected at the $\Upsilon(4S)$ resonance with the Belle
detector at the KEKB energy-asymmetric $e^+e^-$ collider. The measured
branching fraction is ($2.44 \pm 0.22 \pm 0.20$)$\times 10^{-5}$ and the charge
asymmetry is $\mathcal{A}=0.022 \pm 0.085 \pm 0.016$. The ratio of the
branching fractions $\mathcal {B}(B^{\pm} \to \psi(2S) \pi^{\pm})$$/ \mathcal
{B}(B^{\pm} \to \psi(2S) K^{\pm})$ $ = (3.99 \pm 0.36\pm 0.17)%$ is also
determined.


  Adversarial training has shown impressive success in learning bilingual
dictionary without any parallel data by mapping monolingual embeddings to a
shared space. However, recent work has shown superior performance for
non-adversarial methods in more challenging language pairs. In this work, we
revisit adversarial autoencoder for unsupervised word translation and propose
two novel extensions to it that yield more stable training and improved
results. Our method includes regularization terms to enforce cycle consistency
and input reconstruction, and puts the target encoders as an adversary against
the corresponding discriminator. Extensive experimentations with European,
non-European and low-resource languages show that our method is more robust and
achieves better performance than recently proposed adversarial and
non-adversarial approaches.


  We consider the set of affine alcoves associated with a root system R as a
topological space and consider a certain category S of sheaves of Z-modules on
this space. Here Z is the structure algebra of the root system over a field k.
To any wall reflection we associate a wall crossing functor on S. In the
companion article "Sheaves on the alcoves and modular representations II" we
prove that S encodes the simple rational characters of the connected, simply
connected algebraic group with root system R over k, in the case that k is
algebraically closed with characteristic above the Coxeter number.


  We present the number counts of Ks-band selected high redshift galaxy
populations such as extremely red objects (EROs), B, z & K -band selected
galaxies (BzKs) and distant red galaxies (DRGs) in the AKARI NEP field. The
final catalogue contains 308 EROs (Ks<19.0 ; 54 percent are dusty star-forming
EROs and the rest are passive old EROs), 137 star-forming BzKs and 38 passive
old BzKs (Ks<19.0) and 64 DRGs (Ks<18.6). We also produce individual component
source counts for both the dusty star-forming and passive populations. We
compare the observed number counts of the high redshift passively evolving
galaxy population with a backward pure luminosity evolution (PLE) model
allowing different degrees of number density evolution. We find that the PLE
model without density evolution fails to explain the observed counts at faint
magnitudes, while the model incorporating negative density evolution is
consistent with the observed counts of the passively evolving population. We
also compare our observed counts of dusty star-forming EROs with a
phenomenological evolutionary model postulating that the near-infrared EROs can
be explained by the source densities of the far-infrared - submillimetre
populations. Our model predicts that the dusty ERO source counts can be
explained assuming a 25 percent contribution of submillimetre star-forming
galaxies with the majority of brighter Ks -band detected dusty EROs having
luminous (rather than HR10 type ultra-luminous) submillimetre counterparts. We
propose that the fainter Ks>19.5 population is dominated by the sub-millijansky
submillimetre population. We also predict a turnover in in dusty ERO counts
around 19<Ks<20.


  The evolution of asymptotic giant branch stars from the spherical symmetry
into the diverse shapes of planetary nebulae (PNe) is a topic of intensive
research. Young PNe provide a unique opportunity to characterize the onset of
this transitional phase. In particular, OH maser-emitting PNe (OHPNe) are
considered nascent PNe. In fact, only 6 OHPNe have been confirmed to date. In
order to identify and characterize more OHPNe, we processed the unpublished
continuum data of the interferometric follow-up of the Southern Parkes
Large-Area Survey in Hydroxyl (SPLASH). We then matched the interferometric
positions of OH maser and radio continuum emission, considering the latter as a
possible tracer of free-free emission from photoionized gas, characteristic of
PNe. We report 8 objects with a positive coincidence, 4 of which are classified
as candidate OHPNe here for the first time (IRAS 16372-4808, IRAS 17494-2645,
IRAS 18019-2216 and OH 341.6811+00.2634). Available evidence strongly indicates
that they are evolved stars, while the comparison with confirmed OHPNe
indicates that they are likely to be PNe. Their final confirmation as bona fide
PNe, however, requires optical/infrared spectroscopy. The obtained spectral
indices of the radio continuum emission (between $\simeq$ 0.4 - 1.3) are
consistent with partially optically thick free-free emission from photoionized
gas. Also, they cluster in the same region of a WISE colour-colour diagram as
that of the confirmed OHPNe ($9.5 \lesssim [3.4]-[22] \lesssim 13.5$, and $4.0
\lesssim [4.6]-[12] \lesssim 7.0$), thus this diagram could help to identify
more OHPNe candidates in the future.


  We introduce a novel approach to measure the behavior of a geometric operator
before and after coarsening. By comparing eigenvectors of the input operator
and its coarsened counterpart, we can quantitatively and visually analyze how
well the spectral properties of the operator are maintained. Using this
measure, we show that standard mesh simplification and algebraic coarsening
techniques fail to maintain spectral properties. In response, we introduce a
novel approach for spectral coarsening. We show that it is possible to
significantly reduce the sampling density of an operator derived from a 3D
shape without affecting the low-frequency eigenvectors. By marrying techniques
developed within the algebraic multigrid and the functional maps literatures,
we successfully coarsen a variety of isotropic and anisotropic operators while
maintaining sparsity and positive semi-definiteness. We demonstrate the utility
of this approach for applications including operator-sensitive sampling, shape
matching, and graph pooling for convolutional neural networks.


  Seismic waves sensitive to the outermost part of the Earth's liquid core seem
to be affected by a stably stratified layer at the core-mantle boundary. Such a
layer could have an observable signature in both long-term and short-term
variations of the magnetic field of the Earth, which are used to probe the flow
at the top of the core. Indeed, with the recent SWARM mission, it seems
reasonable to be able to identify waves propagating in the core with period of
several months, which may play an important role in the large-scale dynamics.
In this paper, we characterize the influence of a stratified layer at the top
of the core on deep quasi-geostrophic (Rossby) waves. We compute numerically
the quasi-geostrophic eigenmodes of a rapidly rotating spherical shell, with a
stably stratified layer near the outer boundary. Two simple models of
stratification are taken into account, which are scaled with commonly adopted
values of the Brunt-V{\"a}is{\"a}l{\"a} frequency in the Earth's core. In the
absence of magnetic field, we find that both azimuthal wavelength and frequency
of the eigenmodes control their penetration into the stratified layer: the
higher the phase speed, the higher the permeability of the stratified layer to
the wave motion. We also show that the theory developed by Takehiro and Lister
[2001] for thermal convection extends to the whole family of Rossby waves in
the core. Adding a magnetic field, the penetrative behaviour of the
quasi-geostrophic modes (the so-called fast branch) is insensitive to the
imposed magnetic field and only weakly sensitive to the precise shape of the
stratification. Based on these results, the large-scale and high frequency
modes (1 to 2 month periods) may be detectable in the geomagnetic data measured
at the Earth's surface, especially in the equatorial area where the modes can
be trapped.


  Dense matter as it can be found in core-collapse supernovae and neutron stars
is expected to exhibit different phase transitions which impact the matter
composition and the equation of state, with important consequences on the
dynamics of core-collapse supernova explosion and on the structure of neutron
stars. In this paper we will address the specific phenomenology of two of such
transitions, namely the crust-core solid-liquid transition at sub-saturation
density, and the possible strange transition at super-saturation density in the
presence of hyperonic degrees of freedom. Concerning the neutron star
crust-core phase transition at zero and finite temperature, it will be shown
that, as a consequence of the presence of long-range Coulomb interactions, a
clusterized phase is expected which is not accessible in the grand-canonical
ensemble. A specific quasi-particle model will be introduced and some
quantitative results relevant for the supernova dynamics will be shown. The
opening of hyperonic degrees of freedom at higher densities corresponding to
the neutron stars core also modifies the equation of state. The general
characteristics and order of phase transitions in this regime will be analyzed
in the framework of a self-consistent mean-field approach.


  Human mathematicians are often good at recognizing modular and reusable
theorems that make complex mathematical results within reach. In this paper, we
propose a novel method called theoREm-from-prooF extrACTOR (REFACTOR) for
training neural networks to mimic this ability in formal mathematical theorem
proving. We show on a set of unseen proofs, REFACTOR is able to extract 19.6%
of the theorems that humans would use to write the proofs. When applying the
model to the existing Metamath library, REFACTOR extracted 16 new theorems.
With newly extracted theorems, we show that the existing proofs in the MetaMath
database can be refactored. The new theorems are used very frequently after
refactoring, with an average usage of 733.5 times, and help shorten the proof
lengths. Lastly, we demonstrate that the prover trained on the new-theorem
refactored dataset proves more test theorems and outperforms state-of-the-art
baselines by frequently leveraging a diverse set of newly extracted theorems.
Code can be found at https://github.com/jinpz/refactor.


  Collective excitations of N = 1 supersymmetric electromagnetic plasma are
studied. Since the Keldysh-Schwinger approach is used, not only equilibrium but
also non-equilibrium plasma, which is assumed to be ultrarelativistic, is under
consideration. The dispersion equations of photon, photino, electron and
selectron modes are written down and the self-energies, which enter the
equations, are computed in the Hard Loop Approximation. The self-energies are
discussed in the context of effective action which is also given. The photon
modes and electron ones appear to be the same as in the usual ultrarelativistic
plasma of electrons, positrons and photons. The photino modes coincide with the
electron ones and the selectron modes are as of free relativistic massive
particle.


  In this talk I address some aspects in the recent developments for N=2 black
holes in 4 dimensions. I restrict myself on axion-free solutions that can
classically be related to intersections of isotropic $D$- or $M$-branes. After
reviewing of some classical properties I include corrections coming from a
general cubic prepotential. On the heterotic side these are quantum corrections
for these black hole solutions. Finally, I discuss a microscopic interpretation
of the entropy for the extremal as well as near-extremal black hole.


  We discuss the relation between the graded stable derived category of a
hypersurface and that of its hyperplane section. The motivation comes from the
compatibility between homological mirror symmetry for the Calabi-Yau manifold
defined by an invertible polynomial and that for the singularity defined by the
same polynomial.


  The notes contain a streamlined account on stability of univariate
polynomials and related problems


  We review the use of Cepheids as distance indicators with particular emphasis
on the methods which have been applied to HST observations of Cepheids. The
calibration of the period-luminosity relations is examined in detail and we
identify possible problems with the existing calibrations. New V- and I-band
period luminosity relations are presented based on a sample of 53 Cepheids in
the LMC with photometry drawn from the literature. These revised PL relations
result in a systematic decrease of approx 0.1 magnitudes in distance moduli
derived using the standard method of extinction correction. Hence estimates of
the Hubble constant based on such distances should be increased by $\sim5%$.
Other aspects of Cepheid distance determination, specifically incompleteness
bias, metallicity dependence, the effects of crowding and contamination of
samples by non-Cepheids are also discussed. We conclude that current HST
distance estimates to individual galaxies are probably good to about 10%, but
that much of this error is systematic. Efforts to reduce the systematics,
therefore, for example by improving the photometric calibration, refining the
distance to the LMC, and reobserving the Cepheid galaxies in the infrared with
NICMOS, will give large returns.


  What is the difference of a prediction that is made with a causal model and a
non-causal model? Suppose we intervene on the predictor variables or change the
whole environment. The predictions from a causal model will in general work as
well under interventions as for observational data. In contrast, predictions
from a non-causal model can potentially be very wrong if we actively intervene
on variables. Here, we propose to exploit this invariance of a prediction under
a causal model for causal inference: given different experimental settings (for
example various interventions) we collect all models that do show invariance in
their predictive accuracy across settings and interventions. The causal model
will be a member of this set of models with high probability. This approach
yields valid confidence intervals for the causal relationships in quite general
scenarios. We examine the example of structural equation models in more detail
and provide sufficient assumptions under which the set of causal predictors
becomes identifiable. We further investigate robustness properties of our
approach under model misspecification and discuss possible extensions. The
empirical properties are studied for various data sets, including large-scale
gene perturbation experiments.


  In this paper, we show $C^{2,\alpha}$ interior estimates for viscosity
solutions of fully non-linear, uniformly elliptic equations, which are close to
linear equations and we also compute an explicit bound for the closeness.


  The Mukhin-Tarasov-Varchenko Theorem, conjectured by B. and M. Shapiro, has a
number of interesting consequences. Among them is a well-behaved correspondence
between certain points on a Grassmannian - those sent by the Wronski map to
polynomials with only real roots - and (dual equivalence classes of) Young
tableaux.
  In this paper, we restrict this correspondence to the orthogonal Grassmannian
OG(n,2n+1) inside Gr(n,2n+1). We prove that a point lies on OG(n,2n+1) if and
only if the corresponding tableau has a certain type of symmetry. From this we
recover much of the theory of shifted tableaux for Schubert calculus on
OG(n,2n+1), including a new, geometric proof of the Littlewood-Richardson rule
for OG(n,2n+1).


  We describe a method for the extraction of spectra from high dispersion
objective prism plates. Our method is a catalogue driven plate solution
approach, making use of the Right Ascension and Declination coordinates for the
target objects. In contrast to existing methods of photographic plate
reduction, we digitize the entire plate and extract spectra off-line. This
approach has the advantages that it can be applied to CCD objective prism
images, and spectra can be re-extracted (or additional spectra extracted)
without having to re-scan the plate. After a brief initial interactive period,
the subsequent reduction procedure is completely automatic, resulting in
fully-reduced, wavelength justified spectra. We also discuss a method of
removing stellar continua using a combination of non-linear filtering
algorithms.
  The method described is used to extract over 12,000 spectra from a set of 92
objective prism plates. These spectra are used in an associated project to
develop automated spectral classifiers based on neural networks.


  We point out that the {\em spacetime void} inferred by Castro[J. Math. Phys.
49, 042501, (2008)] results from his choice of a discontinuous radial gauge.
Further since the integration constant $\alpha_0 = 2M_0$ ($G=c=1$) occurring in
the vacuum Hilbert/Schwarzschild solution of a neutral "point mass" is zero
[Arnowitt et al., in Gravitation: An Introduction to Current Research, ed. L.
Witten, Wiley, Chap. 7, p.227; also Phys. Rev. Lett., 4, 375, (1960)]; A.
Mitra, Adv. Sp. Res., 38, 2917 (2006)] Castro's gauge reduces to the well
behaved and physical Hilbert gauge. Physically this means that true
Hilbert/Schwarzschild black holes have unique gravitational mass M=0.
Accordingly, the unphysical {\em spacetime viod} inferred by Castro is actually
non-existent.


  Link prediction is an important way to complete knowledge graphs (KGs), while
embedding-based methods, effective for link prediction in KGs, perform poorly
on relations that only have a few associative triples. In this work, we propose
a Meta Relational Learning (MetaR) framework to do the common but challenging
few-shot link prediction in KGs, namely predicting new triples about a relation
by only observing a few associative triples. We solve few-shot link prediction
by focusing on transferring relation-specific meta information to make model
learn the most important knowledge and learn faster, corresponding to relation
meta and gradient meta respectively in MetaR. Empirically, our model achieves
state-of-the-art results on few-shot link prediction KG benchmarks.


  We simulate several magnetic reconnection processes in the low solar
chromosphere/photosphere, the radiation cooling, heat conduction and ambipolar
diffusion are all included. Our numerical results indicate that both the high
temperature($ \gtrsim 8\times10^4$~K) and low temperature($\sim 10^4$~K)
magnetic reconnection events can happen in the low solar atmosphere
($100\sim600$~km above the solar surface). The plasma $\beta$ controlled by
plasma density and magnetic fields is one important factor to decide how much
the plasma can be heated up. The low temperature event is formed in a high
$\beta$ magnetic reconnection process, Joule heating is the main mechanism to
heat plasma and the maximum temperature increase is only several thousand
Kelvin. The high temperature explosions can be generated in a low $\beta$
magnetic reconnection process, slow and fast-mode shocks attached at the edges
of the well developed plasmoids are the main physical mechanisms to heat the
plasma from several thousand Kelvin to over $8\times10^4$~K. Gravity in the low
chromosphere can strongly hinder the plasmoind instability and the formation of
slow-mode shocks in a vertical current sheet. Only small secondary islands are
formed; these islands, however, are not well developed as those in the
horizontal current sheets. This work can be applied for understanding the
heating mechanism in the low solar atmosphere and could possibly be extended to
explain the formation of common low temperature EBs ($\sim10^4$~K) and the high
tenperature IRIS bombs ($\gtrsim 8\times10^4$) in the future.


  I describe the recent progress in resolving two problems of nonperturbative
bosonic string inherited from 1980's. Both the lattice and KPZ-DDK no-go
theorems can be bypassed thanks to specific features of the theory with
diffeomorphism invariance.


  Analytic expressions that describe Casimir interactions over the entire range
of separations have been limited to planar surfaces. Here we derive analytic
expressions for the classical or high-temperature limit of Casimir interactions
between two spheres (interior and exterior configurations), including the
sphere-plane geometry as a special case, using bispherical coordinates. We
consider both Dirichlet boundary conditions and metallic boundary conditions
described by the Drude model. At short distances, closed-form expansions are
derived from the exact result, displaying an intricate structure of deviations
from the commonly employed proximity force approximation.


  In this paper, we consider the problem of multi-objective optimal control of
a dynamical system with additive and multiplicative noises with given second
moments and arbitrary probability distributions. The objectives are given by
quadratic constraints in the state and controller, where the quadratic forms
maybe indefinite and thus not necessarily convex. We show that the problem can
be transformed to a semidefinite program and hence convex. The optimization
problem is to be optimized with respect to a certain variable serving as the
covariance matrix of the state and the controller. We show that affine
controllers are optimal and depend on the optimal covariance matrix.
Furthermore, we show that optimal controllers are linear if all the quadratic
forms are convex in the control variable. The solutions are presented for both
the finite and infinite horizon cases. We give a necessary and sufficient
condition for mean square stabilizability of the dynamical system with additive
and multiplicative noises. The condition is a Lyapunov-like condition whose
solution is again given by the covariance matrix of the state and the control
variable. The results are illustrated with an example.


  A vigorous and growing set of technical debt analysis tools have been
developed in recent years -- both research tools and industrial products --
such as Structure 101, SonarQube, and DV8. Each of these tools identifies
problematic files using their own definitions and measures. But to what extent
do these tools agree with each other in terms of the files that they identify
as problematic? If the top-ranked files reported by these tools are largely
consistent, then we can be confident in using any of these tools. Otherwise, a
problem of accuracy arises. In this paper, we report the results of an
empirical study analyzing 10 projects using multiple tools. Our results show
that: 1) these tools report very different results even for the most common
measures, such as size, complexity, file cycles, and package cycles. 2) These
tools also differ dramatically in terms of the set of problematic files they
identify, since each implements its own definitions of "problematic". After
normalizing by size, the most problematic file sets that the tools identify
barely overlap. 3) Our results show that code-based measures, other than size
and complexity, do not even moderately correlate with a file's change-proneness
or error-proneness. In contrast, co-change-related measures performed better.
Our results suggest that, to identify files with true technical debt -- those
that experience excessive changes or bugs -- co-change information must be
considered. Code-based measures are largely ineffective at pinpointing true
debt. Finally, this study reveals the need for the community to create
benchmarks and data sets to assess the accuracy of software analysis tools in
terms of commonly used measures.


  When measuring a time-varying phase, the standard quantum limit and
Heisenberg limit as usually defined, for a constant phase, do not apply. If the
phase has Gaussian statistics and a power-law spectrum $1/|\omega|^p$ with
$p>1$, then the generalized standard quantum limit and Heisenberg limit have
recently been found to have scalings of $1/{\cal N}^{(p-1)/p}$ and $1/{\cal
N}^{2(p-1)/(p+1)}$, respectively, where ${\cal N}$ is the mean photon flux. We
show that this Heisenberg scaling can be achieved via adaptive measurements on
squeezed states. We predict the experimental parameters analytically, and test
them with numerical simulations. Previous work had considered the special case
of $p=2$.


  The first half of the review dedicated to survey works on Be stars (Baade,
Martayan, and Rivinius, this vol.) put emphasis on what we can learn from
surveys about Be stars as a part of an environment, such as Be stars in
binaries, Be stars in different metalicities, or Be stars as part of a star
forming and then co-evolving group. This second half will rather concentrate on
the information that more focused surveys can give on a Be star, understood as
an individual object, and in this way attempts to bridge the gap between highly
detailed single star studies, and necessarily broad survey and catalog work.


  Odd viscosity can emerge in 3D hydrodynamics when the time reversal symmetry
is broken and anisotropy is introduced. Its ramifications on the stability of
the prototypical Taylor-Couette flow in curved geometries have remained
unexplored. Here, we investigate the effects of odd viscosity on the stability
of Taylor-Couette flow under axisymmetric perturbations both analytically and
numerically, deriving analytically the critical Taylor number for different odd
viscosities in the narrow gap case as well as fully numerically implementing
the wide gap case. We find that the odd viscosity modifies the vortex pattern
by creating secondary vortices, and exerts an intriguing ``lever'' effect in
the stability diagram, completely suppressing the instability of Taylor-Couette
flow under axisymmetric perturbations when the odd viscosity is large,
irrespective of its sign. Our findings highlight the role of odd viscosity for
the rich flow patterns of the Taylor-Couette geometry and provide guidance for
viscometer experiments when odd viscosity is present.


  Recent work of Acharya et al. (NeurIPS 2019) showed how to estimate the
entropy of a distribution $\mathcal D$ over an alphabet of size $k$ up to
$\pm\epsilon$ additive error by streaming over $(k/\epsilon^3) \cdot
\text{polylog}(1/\epsilon)$ i.i.d. samples and using only $O(1)$ words of
memory. In this work, we give a new constant memory scheme that reduces the
sample complexity to $(k/\epsilon^2)\cdot \text{polylog}(1/\epsilon)$. We
conjecture that this is optimal up to $\text{polylog}(1/\epsilon)$ factors.


  Medical image segmentation have drawn massive attention as it is important in
biomedical image analysis. Good segmentation results can assist doctors with
their judgement and further improve patients' experience. Among many available
pipelines in medical image analysis, Unet is one of the most popular neural
networks as it keeps raw features by adding concatenation between encoder and
decoder, which makes it still widely used in industrial field. In the mean
time, as a popular model which dominates natural language process tasks,
transformer is now introduced to computer vision tasks and have seen promising
results in object detection, image classification and semantic segmentation
tasks. Therefore, the combination of transformer and Unet is supposed to be
more efficient than both methods working individually. In this article, we
propose Transformer-Unet by adding transformer modules in raw images instead of
feature maps in Unet and test our network in CT82 datasets for Pancreas
segmentation accordingly. We form an end-to-end network and gain segmentation
results better than many previous Unet based algorithms in our experiment. We
demonstrate our network and show our experimental results in this paper
accordingly.


  We show that all fermions of one generation of the Standard Model (SM) can be
elegantly described by a single fixed parity (say even) inhomogeneous
real-valued differential form in seven dimensions. In this formalism the full
kinetic term of the SM fermionic Lagrangian is reproduced as the appropriate
dimensional reduction of (Psi, D Psi) where Psi is a general even degree
differential form in R^7, the inner product is as described in the main text,
and D is essentially an appropriately interpreted exterior derivative operator.
The new formalism is based on geometric constructions originating in the
subjects of generalised geometry and double field theory.


  We prove that various subgroups of the mapping class group $Mod(\Sigma)$ of a
surface $\Sigma$ are at least exponentially distorted. Examples include the
Torelli group (answering a question of Hamenstadt), the "point-pushing" and
surface braid subgroups, and the Lagrangian subgroup. Our techniques include a
method to compute lower bounds on distortion via representation theory and an
extension of Johnson theory to arbitrary subgroups of $H_1(\Sigma;\mathbb{Z})$.


  High Energy Nuclear Physics (HENP) collaborations' experience show that the
computing resources available at a single site are often neither sufficient nor
satisfy the need of remote collaborators. From latencies in the network
connectivity to the lack of interactivity, work at distant computing centers is
often inefficient. Having fully functional software stack on local resources is
a strong enabler of science opportunities for any local group who can afford
the time investment.
  Prague's heavy-ions group participating in STAR experiment at RHIC has been a
strong advocate of local computing as the most efficient means of data
processing and physics analyses. Tier 2 computing center was set up at a
Regional Computing Center for Particle Physics called "Golias".
  We report on our experience in setting up a fully functional Tier 2 center
and discuss the solutions chosen to address storage space and analysis issues
and the impact on the farms overall functionality. This includes a locally
built STAR analysis framework, integration with a local DPM system (a cost
effective storage solution), the influence of the availability and quality of
the network connection to Tier 0 via a dedicated CESNET/ESnet link and the
development of light-weight yet fully automated data transfer tools allowing
the movement of entire datasets from BNL (Tier 0) to Golias (Tier 2).


  In this paper, we address the controversy regarding the recent extended solar
minimum as seen in helioseismic low- and intermediate-degree mode frequencies:
studies from different instruments identify different epochs of seismic minima.
Here we use mode frequencies from a network of six identical instruments,
Global Oscillation Network Group, continuously collecting data for more than 15
years, to investigate the epoch of minimum in solar oscillation frequencies
prior to the beginning of solar cycle 24. We include both low- and
intermediate-degree modes in the $\ell$ range of 0 -- 120 and frequency range
of 2.0 -- 3.5 mHz. In this analysis, we demonstrate that there were indeed two
minima in oscillation frequencies, depending upon the degree of modes, or more
precisely the lower turning point radius of the propagating wave. We also
analyze frequencies as a function of latitude to identify the beginning of
solar cycle 24. We observe two minima at high latitudes and a single minimum at
mid/low latitudes. This scenario is in contrast to cycle 23 where the epoch of
seismic minimum did not change with latitude or depth. Our results also hint
towards a possible role of the relic magnetic field in modifying the
oscillation frequencies of modes sampling deeper layers.


  We present Charlotte, a framework for composable, authenticated distributed
data structures. Charlotte data is stored in blocks that reference each other
by hash. Together, all Charlotte blocks form a directed acyclic graph, the
blockweb; all observers and applications use subgraphs of the blockweb for
their own data structures. Unlike prior systems, Charlotte data structures are
composable: applications and data structures can operate fully independently
when possible, and share blocks when desired. To support this composability, we
define a language-independent format for Charlotte blocks and a network API for
Charlotte servers.
  An authenticated distributed data structure guarantees that data is immutable
and self-authenticating: data referenced will be unchanged when it is
retrieved. Charlotte extends these guarantees by allowing applications to plug
in their own mechanisms for ensuring availability and integrity of data
structures. Unlike most traditional distributed systems, including distributed
databases, blockchains, and distributed hash tables, Charlotte supports
heterogeneous trust: different observers may have their own beliefs about who
might fail, and how. Despite heterogeneity of trust, Charlotte presents each
observer with a consistent, available view of data.
  We demonstrate the flexibility of Charlotte by implementing a variety of
integrity mechanisms, including consensus and proof of work. We study the power
of disentangling availability and integrity mechanisms by building a variety of
applications. The results from these examples suggest that developers can use
Charlotte to build flexible, fast, composable applications with strong
guarantees.


  We consider the following variational problem: minimize the $(n+1)$st
polynomial conserved quantity of KdV over $H^n(\mathbb{R})$ with the first $n$
conserved quantities constrained. Maddocks and Sachs used that $n$-solitons are
local minimizers for this problem in order to prove that $n$-solitons are
orbitally stable in $H^n(\mathbb{R})$.
  Given $n$ constraints that are attainable by an $n$-soliton, we show that
there is a unique set of $n$ amplitude parameters so that the corresponding
multisolitons satisfy the constraints. Moreover, we prove that these
multisolitons are the unique global constrained minimizers. We then use this
variational characterization to provide a new proof of the orbital stability
result of Maddocks and Sachs via concentration compactness.
  In the case when the constraints can be attained by functions in
$H^n(\mathbb{R})$ but not by an $n$-soliton, we discover new behavior for
minimizing sequences.


  Ethics in AI becomes a global topic of interest for both policymakers and
academic researchers. In the last few years, various research organizations,
lawyers, think tankers and regulatory bodies get involved in developing AI
ethics guidelines and principles. However, there is still debate about the
implications of these principles. We conducted a systematic literature review
(SLR) study to investigate the agreement on the significance of AI principles
and identify the challenging factors that could negatively impact the adoption
of AI ethics principles. The results reveal that the global convergence set
consists of 22 ethical principles and 15 challenges. Transparency, privacy,
accountability and fairness are identified as the most common AI ethics
principles. Similarly, lack of ethical knowledge and vague principles are
reported as the significant challenges for considering ethics in AI. The
findings of this study are the preliminary inputs for proposing a maturity
model that assess the ethical capabilities of AI systems and provide best
practices for further improvements.


  In this paper, we study the amount of information contained in the Steklov
spectrum of some compact manifolds with connected boundary equipped with a
warped product metric. Examples of such manifolds can be thought of as deformed
balls in R^d. We first prove that the Steklov spectrum determines uniquely the
warping function of the metric. We show in fact that the approximate knowledge
(in a given precise sense) of the Steklov spectrum is enough to determine
uniquely the warping function in a neighbourhood of the boundary. Second, we
provide stability estimates of log-type on the warping function from the
Steklov spectrum. The key element of these stability results relies on a
formula that, roughly speaking, connects the inverse data (the Steklov
spectrum) to the Laplace transform of the difference of the two warping
factors.


  In prediction tasks, there exist features that are related to the label in
the same way across different settings for that task; these are semantic
features or semantics. Features with varying relationships to the label are
nuisances. For example, in detecting cows from natural images, the shape of the
head is semantic but because images of cows often have grass backgrounds but
not always, the background is a nuisance. Models that exploit nuisance-label
relationships face performance degradation when these relationships change.
Building models robust to such changes requires additional knowledge beyond
samples of the features and labels. For example, existing work uses annotations
of nuisances or assumes ERM-trained models depend on nuisances. Approaches to
integrate new kinds of additional knowledge enlarge the settings where robust
models can be built. We develop an approach to use knowledge about the
semantics by corrupting them in data, and then using the corrupted data to
produce models which identify correlations between nuisances and the label.
Once these correlations are identified, they can be used to adjust for where
nuisances drive predictions. We study semantic corruptions in powering
different spurious-correlation avoiding methods on multiple out-of-distribution
(OOD) tasks like classifying waterbirds, natural language inference (NLI), and
detecting cardiomegaly in chest X-rays.


  We prove several results concerning the theory of Toeplitz algebras over
$p$-Fock spaces using a correspondence theory of translation invariant symbol
and operator spaces. The most notable results are: The full Toeplitz algebra is
the norm closure of all Toeplitz operators with bounded uniformly continuous
symbols. This generalizes a result obtained by J. Xia (J. Funct. Anal.
269:781-814, 2015) in the case $p = 2$, which was proven by different methods.
Further, we prove that every Toeplitz algebra which has a translation invariant
$C^\ast$ subalgebra of the bounded uniformly continuous functions as its set of
symbols is linearly generated by Toeplitz operators with the same space of
symbols.


  Polycrystalline Sr0.6K0.4Fe2As2 samples with various Pb additions (0-20 wt%)
were prepared using a one-step solid state reaction. X-ray diffraction analysis
shows no evidence for chemical reaction between the Pb and the FeAs-based
superconductor. However, the presence of the Pb can affect the microstructure
and superconducting properties of the final products. The critical transition
temperature Tc indicates no degradation up to 20 wt% Pb addition, and dramatic
improvements of magnetic Jc and irreversibility field Hirr were observed for
appropriate Pb concentration. Transport critical current property of pure and
Pb-added Sr0.6K0.4Fe2As2 tapes was also measured by a four-probe technique, and
a remarkable enhancement of Jc at low fields was detected for the Pb added
tapes.


  We studied the anelastic aftereffect of a flexure being used in a Kibble
balance, where the flexure is subjected to a large excursion in velocity mode
after which a high-precision force comparison is performed. We investigated the
effect of a constant and a sinusoidal excursion on the force comparison. We
explored theoretically and experimentally a simple erasing procedure, i.e.,
bending the flexure in the opposite direction for a given amplitude and time.
We found that the erasing procedure reduced the time-dependent force by about
30%. The investigation was performed with an analytical model and verified
experimentally with our new Kibble balance at the National Institute of
Standards and Technology employing flexures made from precipitation-hardened
Copper Beryllium alloy C17200.
  Our experimental determination of the modulus defect of the flexure yields
1.2E-4. This result is about a factor of two higher than previously reported
from experiments. We additionally found a static shift of the flexure's
internal equilibrium after a change in the stress and strain state. These
static shifts, although measurable, are small and deemed uncritical for our
Kibble balance application at present.
  During this investigation, we discovered magic flexures that promise to have
very little anelastic relaxation. In these magic flexures, the mechanism
causing anelastic relaxation is compensated for by properly shaping and loading
a flexure with a non-constant cross-section in the region of bending.


  We study the proton-hydrogen collision in the energy range from 0 to 5 K
where the hyperfine structure of the hydrogen atom is important. The proper
multichannel treatment of the hyperfine structure is found to be crucial at
cold temperatures compared to the elastic approximation used for higher
temperatures. Both elastic and hyperfine-changing inelastic processes are
investigated using the newly developed multichannel quantum-defect theory
(MQDT) as well as the traditional coupled-channel numerical method. Cross
section results from the two methods coincide well throughout the energy range.
The MQDT with a few parameters provide an efficient and basically analytic
description of the proton-hydrogen interaction in this energy regime.


  These are partial lecture notes from the fifteen Ess\'en Lectures for
graduate students at Uppsala University given (in four days!) in June 2013.


  Our day-to-day life has always been influenced by what people think. Ideas
and opinions of others have always affected our own opinions. The explosion of
Web 2.0 has led to increased activity in Podcasting, Blogging, Tagging,
Contributing to RSS, Social Bookmarking, and Social Networking. As a result
there has been an eruption of interest in people to mine these vast resources
of data for opinions. Sentiment Analysis or Opinion Mining is the computational
treatment of opinions, sentiments and subjectivity of text. In this report, we
take a look at the various challenges and applications of Sentiment Analysis.
We will discuss in details various approaches to perform a computational
treatment of sentiments and opinions. Various supervised or data-driven
techniques to SA like Na\"ive Byes, Maximum Entropy, SVM, and Voted Perceptrons
will be discussed and their strengths and drawbacks will be touched upon. We
will also see a new dimension of analyzing sentiments by Cognitive Psychology
mainly through the work of Janyce Wiebe, where we will see ways to detect
subjectivity, perspective in narrative and understanding the discourse
structure. We will also study some specific topics in Sentiment Analysis and
the contemporary works in those areas.


  Fracture limits the structural stability of macroscopic and microscopic
materials, from beams and bones to microtubules and nanotubes. Despite recent
progress, fracture control continues to present profound practical and
theoretical challenges. A famous longstanding problem posed by Feynman asks why
brittle elastic rods appear almost always to fragment into at least three
pieces when placed under large bending stresses. Feynman's observation raises
fundamental questions about the existence of protocols that can robustly induce
binary fracture in brittle materials. Using experiments, simulations and
analytical scaling arguments, we demonstrate controlled binary fracture of
brittle elastic rods for two distinct protocols based on twisting and
nonadiabatic quenching. Our experimental data for twist-controlled fracture
agree quantitatively with a theoretically predicted phase diagram. Furthermore,
we establish novel asymptotic scaling relations for quenched fracture. Due to
their general character, these results are expected to apply to torsional and
kinetic fracture processes in a wide range of systems.


  Energy spectra of particles accelerated by the first-order Fermi mechanism
are investigated at ultrarelativistic shock waves, outside the range of Lorentz
factors considered previously. For particle transport near the shock a
numerical method involving small amplitude pitch-angle scattering is applied
for flows with Lorentz factors $\gamma$ from 3 to 243. For large $\gamma$
shocks a convergence of derived energy spectral indices up to the value
$\sigma_\infty \approx 2.2$ is observed for all considered turbulence
amplitudes and magnetic field configurations. Recently the same index was
derived for $\gamma$-ray bursts by Waxman [Astrophys. J. Lett. 485, L5 (1997)].


  The results on chaos in FRW cosmology with a massive scalar field are
extended to another scalar field potential. It is shown that for sufficiently
steep potentials the chaos disappears. A simple and rather accurate analytical
criterion for the chaos to disappear is given. On the contrary, for gently
sloping potentials the transition to a strong chaotic regime can occur. Two
examples, concerning asymptotically flat and Damour-Mukhanov potentials are
given.


  We have investigated crystalline magnetic anisotropy in the electric field
(EF) for the Fe-Pt surface which have a large perpendicular anisotropy, by
means of the first-principles approach. The anisotropy is reduced linearly with
respect to the inward EF, associated with the induced spin density around the
Fe layer. Although the magnetic anisotropy energy (MAE) density reveals the
large variation around the atoms, the intrinsic contribution to the MAE is
found to mainly come from the Fe layer.


  The interaction of charged particles, moving in a uniform magnetic field,
with a plane-polarized gravitational wave is considered using the
Fokker-Planck- Kolmogorov (FPK) approach. By using a stochasticity criterion,
we determine the exact locations in phase space, where resonance overlapping
occurs. We investigate the diffusion of orbits around each primary resonance of
order (m) by deriving general analytical expressions for an effective diffusion
coeficient. A solution to the corresponding diffusion equation (Fokker-Planck
equation) for the static case is found. Numerical integration of the full
equations of motion and subsequent calculation of the diffusion coefficient
verifies the analytical results.


  Is the geometry of space a macroscopic manifestation of an underlying
microscopic statistical structure? Is geometrodynamics - the theory of gravity
- derivable from general principles of inductive inference? Tentative answers
are suggested by a model of geometrodynamics based on the statistical concepts
of entropy, information geometry, and entropic dynamics. The model shows
remarkable similarities with the 3+1 formulation of general relativity. For
example, the dynamical degrees of freedom are those that specify the conformal
geometry of space; there is a gauge symmetry under 3d diffeomorphisms; there is
no reference to an external time; and the theory is time reversible. There is,
in adition, a gauge symmetry under scale transformations. I conjecture that
under a suitable choice of gauge one can recover the usual notion of a
relativistic space-time.


  We analyze the decay of classically chaotic quantum systems in the presence
of fast ballistic escape routes on the Ehrenfest time scale. For a continuous
excitation process, the form factor of the decay cross section deviates from
the universal random-matrix result on the Heisenberg time scale, i.e. for times
much larger than the time for ballistic escape. We derive an exact analytical
description and compare our results with numerical simulations for a dynamical
model.


  We collected marathon performance data from a systematic sample of elite and
sub-elite athletes over the period 2015 to 2019, then searched the internet for
publicly-available photographs of these performances, identifying whether the
Nike Vaporfly shoes were worn or not in each performance. Controlling for
athlete ability and race difficulty, we estimated the effect on marathon times
of wearing the Vaporfly shoes. Assuming that the effect of Vaporfly shoes is
additive, we estimate that the Vaporfly shoes improve men's times between 2.0
and 3.9 minutes, while they improve women's times between 0.8 and 3.5 minutes.
Assuming that the effect of Vaporfly shoes is multiplicative, we estimate that
they improve men's times between 1.4 and 2.8 percent and women's performances
between 0.6 and 2.2 percent. The improvements are in comparison to the shoe the
athlete was wearing before switching to Vaporfly shoes, and represents an
expected improvement rather than a guaranteed improvement.


  The experimental searches for diffuse supernova neutrino background and
proton decay in next-generation large liquid-scintillator (LS) detectors are
competitive with and complementary to those in the water-Cherenkov detectors.
In this paper, we carry out a systematic study of the dominant background
induced by atmospheric neutrinos via their neutral-current (NC) interactions
with the $^{12}{\rm C}$ nuclei in the LS detectors. The atmospheric neutrino
fluxes at the location of Jiangmen Underground Neutrino Observatory (JUNO) are
used, as the JUNO detector is obviously a suitable representative for future LS
detectors. Then, we implement the sophisticated generators \texttt{GENIE} and
\texttt{NuWro} to simulate the neutrino interactions with the carbon nuclei,
and the package \texttt{TALYS} to deal with the deexcitations of final-state
nuclei. Finally, the event rates for the production of additional nucleons,
$\gamma$'s, $\alpha$'s, pions and kaons are obtained and categorized, and the
systematic uncertainty of the NC background represented by a variety of
data-driven nuclear models is estimated. The implications of the NC background
from atmospheric neutrinos for the detection of diffuse supernova neutrino
background and proton decay are also discussed.


  Fomalhaut is a bright star 7.7 parsecs (25 light years) from Earth that
harbors a belt of cold dust with a structure consistent with gravitational
sculpting by an orbiting planet. Here, we present optical observations of an
exoplanet candidate, Fomalhaut b. In the plane of the belt, Fomalhaut b lies
approximately 119 astronomical units (AU) from the star and 18 AU from the
belt, matching predictions. We detect counterclockwise orbital motion using
Hubble Space Telescope observations separated by 1.73 years. Dynamical models
of the interaction between the planet and the belt indicate that the planet's
mass is at most three times that of Jupiter for the belt to avoid gravitational
disruption. The flux detected at 800 nm is also consistent with that of a
planet with mass no greater than a few times that of Jupiter. The brightness at
600 nm and the lack of detection at longer wavelengths suggest that the
detected flux may include starlight reflected off a circumplanetary disk, with
dimension comparable to the orbits of the Galilean satellites. We also observed
variability of unknown origin at 600 nm.


  This paper studies the action of symplectic homeomorphisms on smooth
submanifolds, with a main focus on the behaviour of symplectic homeomorphisms
with respect to numerical invariants like capacities. Our main result is that a
symplectic homeomorphism may preserve and squeeze codimension $4$ symplectic
submanifolds ($C^0$-flexibility), while this is impossible for codimension $2$
symplectic submanifolds ($C^0$-rigidity). We also discuss $C^0$-invariants of
coistropic and Lagrangian submanifolds, proving some rigidity results and
formulating some conjectures. We finally formulate an Eliashberg-Gromov
$C^0$-rigidity type question for submanifolds, which we solve in many cases.
Our main technical tool is a quantitative $h$-principle result in symplectic
geometry.


  We consider a porous media equation with balanced bistable reactions,
equipped with some general nonlinear boundary condition. When the coefficient
of the reaction term is much larger than that of the diffusion term, we see
that, besides the possible free boundary, sharp interfaces appear between two
stable steady states. By using the method of matched asymptotic expansions, we
derive the motion law of each interface, which is a mean curvature flow (may
depends on normal direction of the interface). In addition, the original
boundary condition reduces to Robin ones at the points where the interface
contacts the domain boundary.


  We propose a new adiabatic algorithm for the unsorted database search
problem. This algorithm saves two thirds of qubits than Grover's algorithm in
realizations. Meanwhile, we analyze the time complexity of the algorithm by
both perturbative method and numerical simulation. The results show it provides
a better speedup than the previous adiabatic search algorithm.


  Using a nonlinear version of the tautological bundle over Gra{\ss}mannians,
we construct a transgression map for differential characters from $M$ to the
nonlinear Gra{\ss}mannians $\mathrm{Gr}^S(M)$ of submanifolds of $M$ of a fixed
type $S$. In particular, we obtain prequantum circle bundles of the nonlinear
Gra\ss{}mannian endowed with the Marsden-Weinstein symplectic form. The
associated Kostant-Souriau prequantum extension yields central Lie group
extensions of a group of volume-preserving diffeomorphisms integrating
Lichnerowicz cocycles.


  A propagation method for the time dependent Schr\"odinger equation was
studied leading to a general scheme of solving ode type equations. Standard
space discretization of time-dependent pde's usually results in system of ode's
of the form u_t -Gu = s where G is a operator (matrix) and u is a
time-dependent solution vector. Highly accurate methods, based on polynomial
approximation of a modified exponential evolution operator, had been developed
already for this type of problems where G is a linear, time independent matrix
and s is a constant vector. In this paper we will describe a new algorithm for
the more general case where s is a time-dependent r.h.s vector. An iterative
version of the new algorithm can be applied to the general case where G depends
on t or u. Numerical results for Schr\"odinger equation with time-dependent
potential and to non-linear Schr\"odinger equation will be presented.


  Using a diagrammatic scheme, we study the acoustoelectric effects in
two-dimensional (2D) hexagonal Dirac materials due to the sound-induced
pseudo-gauge field. We analyze both uniform and {\em spatially dispersive}
currents in response to copropagating and counterpropagating sound waves,
respectively. In addition to the longitudinal acoustoelectric current, we
obtain an exotic {\em transverse} charge current flowing perpendicular to the
sound propagation direction owing to the interplay of transverse and
longitudinal gauge field components $j_T\propto A_L A^\ast_T$. In contrast to
the almost isotropic directional profile of the longitudinal uniform current, a
highly anisotropic transverse component $j_T\sim\sin(6\theta)$ is achieved that
stems from the inherited three-fold symmetry of the hexagonal lattice. However,
both longitudinal and transverse parts of the dispersive current are predicted
to be strongly anisotropic $\sim\sin^2(3\theta)$ or $\cos^2(3\theta)$. We
quantitatively estimate the pseudogauge field contribution to the
acoustoelectric current that can be probed in future experiments in graphene
and other 2D hexagonal Dirac materials.


  Performance metrics for medical image segmentation models are used to measure
the agreement between the reference annotation and the predicted segmentation.
Usually, overlap metrics, such as the Dice, are used as a metric to evaluate
the performance of these models in order for results to be comparable. However,
there is a mismatch between the distributions of cases and difficulty level of
segmentation tasks in public data sets compared to clinical practice. Common
metrics fail to measure the impact of this mismatch, especially for clinical
data sets that include low signal pathologies, a difficult segmentation task,
and uncertain, small, or empty reference annotations. This limitation may
result in ineffective research of machine learning practitioners in designing
and optimizing models. Dimensions of evaluating clinical value include
consideration of the uncertainty of reference annotations, independence from
reference annotation volume size, and evaluation of classification of empty
reference annotations. We study how uncertain, small, and empty reference
annotations influence the value of metrics for medical image segmentation on an
in-house data set regardless of the model. We examine metrics behavior on the
predictions of a standard deep learning framework in order to identify metrics
with clinical value. We compare to a public benchmark data set (BraTS 2019)
with a high-signal pathology and certain, larger, and no empty reference
annotations. We may show machine learning practitioners, how uncertain, small,
or empty reference annotations require a rethinking of the evaluation and
optimizing procedures. The evaluation code was released to encourage further
analysis of this topic.
https://github.com/SophieOstmeier/UncertainSmallEmpty.git


  Stemming is the process of extracting root word from the given inflection
word and also plays significant role in numerous application of Natural
Language Processing (NLP). Tamil Language raises several challenges to NLP,
since it has rich morphological patterns than other languages. The rule based
approach light-stemmer is proposed in this paper, to find stem word for given
inflection Tamil word. The performance of proposed approach is compared to a
rule based suffix removal stemmer based on correctly and incorrectly predicted.
The experimental result clearly show that the proposed approach light stemmer
for Tamil language perform better than suffix removal stemmer and also more
effective in Information Retrieval System (IRS).


  We study a family of Markov processes on $\mathcal{P}^{(k)}$, the space of
partitions of the natural numbers with at most $k$ blocks. The process can be
constructed from a Poisson point process on
$\mathbb{R}^+\times\prod_{i=1}^k\mathcal{P}^{(k)}$ with intensity
$dt\otimes\varrho_{\nu}^{(k)}$, where $\varrho_{\nu}$ is the distribution of
the paintbox based on the probability measure $\nu$ on $\masspartition$, the
set of ranked-mass partitions of 1, and $\varrho_{\nu}^{(k)}$ is the product
measure on $\prod_{i=1}^k\mathcal{P}^{(k)}$. We show that these processes
possess a unique stationary measure, and we discuss a particular set of
reversible processes for which transition probabilities can be written down
explicitly.


  In NLP, recent work has seen increased focus on spurious correlations between
various features and labels in training data, and how these influence model
behavior. However, the presence and effect of such correlations are typically
examined feature by feature. We investigate the cumulative impact on a model of
many such intersecting features. Using a new statistical method, we examine
whether such spurious patterns in data appear in models trained on the data. We
select two tasks -- natural language inference and duplicate-question detection
-- for which any unigram feature on its own should ideally be uninformative,
which gives us a large pool of automatically extracted features with which to
experiment. The large size of this pool allows us to investigate the
intersection of features spuriously associated with (potentially different)
labels. We then apply an optimization approach to *reweight* the training data,
reducing thousands of spurious correlations, and examine how doing so affects
models trained on the reweighted data. Surprisingly, though this method can
successfully reduce lexical biases in the training data, we still find strong
evidence of corresponding bias in the trained models, including worsened bias
for slightly more complex features (bigrams). We close with discussion about
the implications of our results on what it means to "debias" training data, and
how issues of data quality can affect model bias.


  We explore the dielectric properties of spinor condensates. Gases with vector
(nematic) order, such as spin-1 condensates with ferromagnetic
(antiferromagnetic) interactions, display optical activity (birefringence).
This optical activity/birefringence is respectively seen for light detuned from
resonance by a frequency which is not too large compared with the
fine/hyperfine structure. Careful tuning of the light frequency can isolate
either of these two effects. These features can be used to image spin textures
in clouds of spin 1 bosons, and to discern states showing different types of
spin order.


  The present work is devoted to massive gauge fields in special relativity
with two fundamental constants-the velocity of light, and the Planck length, so
called doubly special relativity (DSR). The two invariant scales are accounted
for by properly modified boost parameters. Within above framework we construct
the vector potential as the (1/2,0)x(0,1/2) direct product, build the
associated field strength tensor together with the Dirac spinors and use them
to calculate various observables as functions of the Planck length.