  In this paper, we consider the cubic fourth-order nonlinear Schr\"odinger
equation (4NLS) under the periodic boundary condition. We prove two results.
One is the local well-posedness in $H^s$ with $-1/3 \le s < 0$ for the Cauchy
problem of the Wick ordered 4NLS. The other one is the non-squeezing property
for the flow map of 4NLS in the symplectic phase space $L^2(\mathbb{T})$. To
prove the former we used the ideas introduced in [Takaoka and Tsutsumi 2004]
and [Nakanish et al 2010], and to prove the latter we used the ideas in
[Colliander et al 2005].


  In this paper, we define a problem on lattices called the Maximum Distance
Sub-lattice Problem (MDSP). The decision version of this problem is shown to be
in NP. We prove that MDSP is isomorphic to a well-known problem called closest
vector problem (CVP). We give an exact and a heuristic algorithm for MDSP.
Using experimental results we show that the LLL algorithm can be accelerated
when it is combined with the heuristic algorithm for MDSP.


  Levitated diamond nanocrystals with nitrogen-vacancy (NV) centres in high
vacuum have been proposed as a unique system for experiments in fundamental
quantum mechanics, including the generation of large quantum superposition
states and tests of quantum gravity. This system promises extreme isolation
from its environment while providing quantum control and sensing through the NV
centre spin. While optical trapping has been the most explored method of
levitation, recent results indicate that excessive optical heating of the
nanodiamonds under vacuum may make the method impractical with currently
available materials. Here, we study an alternative magneto-gravitational trap
for diamagnetic particles, such as diamond nanocrystals, with stable levitation
from atmospheric pressure to high vacuum. Magnetic field gradients from
permanent magnets confine the particle in two dimensions, while confinement in
the third dimension is gravitational. We demonstrate that feedback cooling of
the centre-of-mass motion of a trapped nanodiamond cluster results in cooling
of one degree of freedom to less than 1 K.


  Majorana zero modes are quasiparticle excitations in condensed matter systems
that have been proposed as building blocks of fault-tolerant quantum computers
[1]. They are expected to exhibit non-Abelian particle statistics, in contrast
to the usual statistics of fermions and bosons, enabling quantum operations to
be performed by braiding isolated modes around one another. Quantum braiding
operations are topologically protected insofar as these modes are pinned near
zero energy, and the pinning is predicted to be exponential as the modes become
spatially separated. Following theoretical proposals, several experiments have
identified signatures of Majorana modes in proximitized nanowires and atomic
chains, with small mode-splitting potentially explained by hybridization of
Majoranas. Here, we use Coulomb-blockade spectroscopy in an InAs nanowire
segment with epitaxial aluminum, which forms a proximity-induced
superconducting Coulomb island (a Majorana island) that is isolated from
normal-metal leads by tunnel barriers, to measure the splitting of
near-zero-energy Majorana modes. We observe exponential suppression of energy
splitting with increasing wire length. For short devices of a few hundred
nanometers, sub-gap state energies oscillate as the magnetic field is varied,
as is expected for hybridized Majorana modes. Splitting decreases by a factor
of about ten for each half micrometer of increased wire length. For devices
longer than about one micrometer, transport in strong magnetic fields occurs
through a zero-energy state that is energetically isolated from a continuum,
yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with
teleportation via Majorana modes. Our results help explain the
trivial-to-topological transition in finite systems and to quantify the scaling
of topological protection with end-mode separation.


  We give an explicit formulation of the three-dimensional $SL(4,R)/SO(2,2)
\sigma$-model representing the five-dimensional Einstein gravity coupled to the
dilaton and the three-form field for spacetimes with two commuting Killing
vector fields. New matrix representation is obtained which is similar to one
found earlier in the four-dimensional Einstein-Maxwell-Dilaton-Axion (EMDA)
theory. The SL(4,R) symmetry joins a variety of 5D solutions of different
physical types including strings, 0-branes, KK monopoles etc. interpreting them
as duals to the four-dimensional Kerr metric translated along the fifth
coordinate. The symmetry transformations are used to construct new rotating
strings and composite 0-1-branes endowed with a NUT parameter.


  Linear discriminant analysis (LDA) is a fundamental method for feature
extraction and dimensionality reduction. Despite having many variants,
classical LDA has its own importance, as it is a keystone in human knowledge
about statistical pattern recognition. For a dataset containing C clusters, the
classical solution to LDA extracts at most C-1 features. Here, we introduce a
novel solution to classical LDA, called LDA++, that yields C features, each
interpretable as measuring similarity to one cluster. This novel solution
bridges dimensionality reduction and multiclass classification. Specifically,
we prove that, for homoscedastic Gaussian data and under some mild conditions,
the optimal weights of a linear multiclass classifier also make an optimal
solution to LDA. In addition, we show that LDA++ reveals some important new
facts about LDA that remarkably changes our understanding of classical
multiclass LDA after 75 years of its introduction. We provide a complete
numerical solution for LDA++ for the cases 1) when the scatter matrices can be
constructed explicitly, 2) when constructing the scatter matrices is
infeasible, and 3) the kernel extension.


  Present human languages display slightly asymmetric log-normal (Gauss)
distribution for size [1-3], whereas present cities follow power law
(Pareto-Zipf law)[4]. Our model considers the competition between languages and
that between cities in terms of growing (multiplicative noise process)[5] and
fragmentation [6]; where, relevant parameters are (naturally) different for
languages and cities. We consider lifetime distribution for old and living
languages and that for old and living cities. We study also the effect of
random elimination (punctuation) within time evolution of languages and cities.
Finally, we assume decreasing exponential distribution for cities over size
with independent random amplitude and random (negative) exponent; and show
that, this gives the Pareto-Zipf law.


  Using data taken with the CLEO-c detector at the Cornell Electron Storage
Ring, we have investigated the direct photon momentum spectrum in the decay
J/psi->gamma+gluon+gluon, via the 'tagged' process: e+e- -> psi(2S);
psi(2S)->J/psi pi+pi-; J/psi->photon + X. Including contributions from two-body
radiative decay processes, we find the ratio of the inclusive direct photon
branching fraction to that of the dominant three-gluon branching fraction to be
R=0.137+/-0.001+/-0.016+/-0.004, where the errors shown are statistical,
systematic, and the model-dependent uncertainty related to the extrapolation to
zero photon energy. The shape of the scaled photon energy spectrum in J/psi->gg
gamma is observed to be very similar to that of Upsilon(1S)->gg gamma. The R
value obtained is roughly consistent with that expected by a simple
quark-charge scaling of the value determined at the Upsilon(1S), but somewhat
higher than the value expected from the running of the strong coupling
constant.


  This paper presents a safe, efficient, and agile ground vehicle navigation
algorithm for 3D off-road terrain environments. Off-road navigation is subject
to uncertain vehicle-terrain interactions caused by different terrain
conditions on top of 3D terrain topology. The existing works are limited to
adopt overly simplified vehicle-terrain models. The proposed algorithm learns
the terrain-induced uncertainties from driving data and encodes the learned
uncertainty distribution into the traversability cost for path evaluation. The
navigation path is then designed to optimize the uncertainty-aware
traversability cost, resulting in a safe and agile vehicle maneuver. Assuring
real-time execution, the algorithm is further implemented within parallel
computation architecture running on Graphics Processing Units (GPU).


  Quantum computers can be used for supervised learning by treating
parametrised quantum circuits as models that map data inputs to predictions.
While a lot of work has been done to investigate practical implications of this
approach, many important theoretical properties of these models remain unknown.
Here we investigate how the strategy with which data is encoded into the model
influences the expressive power of parametrised quantum circuits as function
approximators. We show that one can naturally write a quantum model as a
partial Fourier series in the data, where the accessible frequencies are
determined by the nature of the data encoding gates in the circuit. By
repeating simple data encoding gates multiple times, quantum models can access
increasingly rich frequency spectra. We show that there exist quantum models
which can realise all possible sets of Fourier coefficients, and therefore, if
the accessible frequency spectrum is asymptotically rich enough, such models
are universal function approximators.


  Using Peebles' least action principle, we determine trajectories for the
galaxies in the Local Group and the more massive galaxies in the Local
Neighbourhood. We deduce the resulting angular momentum for the whole of the
Local Group and study the tidal force acting on the Local Group and its
galaxies. Although Andromeda and the Milky Way dominate the tidal force acting
on each other during the present epoch, we show that there is a transition time
at $z\approx 1$ before which the tidal force is dominated by galaxies outside
the Local Group in each case. This shows that the Local Group can not be
considered as an isolated system as far as the tidal forces are concerned. We
integrate the tidal torques acting on the Milky Way and Andromeda and derive
their spin angular momenta, obtaining results which are comparable with
observation.


  We investigate whether the recent ultra-high energy (UHE) neutrino events
detected at the IceCube neutrino observatory could come from the decay of
charmed mesons produced within the mildly relativistic jets of supernova-like
astrophysical sources. We demonstrate that the $5.7\sigma$ excess of neutrinos
observed by IceCube in the energy range 30 TeV--2 PeV can be explained by a
diffuse flux of neutrinos produced in such slow-jet supernovae, using the
values of astrophysical and QCD parameters within the theoretical uncertainties
associated with neutrino production from charmed meson decay in astrophysical
sources. We discuss the theoretical uncertainties inherent in the evaluation of
charm production in high energy hadronic collisions, as well as the
astrophysical uncertainties associated with slow-jet supernova sources. The
proton flux within the source, and therefore also the produced neutrino flux,
is cut off at around a few PeV, when proton cooling processes become dominant
over proton acceleration. This directly explains the sudden drop in event rates
at energies above a few PeV. We incorporate the effect of energy dependence in
the spectrum-weighted charm production cross-section and show that this has a
very significant effect on the shape, magnitude and cut-off energies for the
neutrino flux.


  It is shown that the diluted thermodynamical limit of a self-gravitating
system proposed by de Vega and Sanchez suffers from the same problems as the
usual thermodynamical limit and leads to divergent thermodynamical functions.
This question is also discussed from the point of view of mean field theory.


  In this paper, we propose a novel integrated communication and positioning
design for orthogonal frequency division multiplexing system aided by a
reconfigurable intelligent surface (RIS) in indoor circumstances. The channel
frequency responses on pilots (CFROPs) of places of interest are used for
online mapping with the offline CFROP database. We transform the objective of
minimizing the similarity of different CFROPs into creating a differentiated
database by optimizing the phase coefficients of RIS. Imperfect channel state
information is considered due to time-varying caused by the two-stage mapping.
We formulate a universal optimization problem for maximizing either the average
or the minimum virtual distance of CFROPs. The communication service
requirements are converted as constraints. A moderate case is discussed to
reduce computational complexity with minor accuracy loss. A special property
called correlation dispersion is analyzed. It is capable of eliminating the
spatial consistency that incurs inaccuracy to traditional positioning methods.
The property and the moderate case complement each other well with clear and
logical physical interpretation. The particular characteristic makes our design
outperform others especially in high-level-noise environments. It works even
better when the prior information of user's potential location is available.
The validity of our design is confirmed by numerical results.


  Let $H$ be an arbitrary family of hyper-planes in $d$-dimensions. We show
that the point-location problem for $H$ can be solved by a linear decision tree
that only uses a special type of queries called \emph{generalized comparison
queries}. These queries correspond to hyperplanes that can be written as a
linear combination of two hyperplanes from $H$; in particular, if all
hyperplanes in $H$ are $k$-sparse then generalized comparisons are $2k$-sparse.
The depth of the obtained linear decision tree is polynomial in $d$ and
logarithmic in $|H|$, which is comparable to previous results in the literature
that use general linear queries.
  This extends the study of comparison trees from a previous work by the
authors [Kane {et al.}, FOCS 2017]. The main benefit is that using generalized
comparison queries allows to overcome limitations that apply for the more
restricted type of comparison queries.
  Our analysis combines a seminal result of Forster regarding sets in isotropic
position [Forster, JCSS 2002], the margin-based inference dimension analysis
for comparison queries from [Kane {et al.}, FOCS 2017], and compactness
arguments.


  We report the results of two Chandra ACIS-S observations from February and
August 2003 of the highly X-ray variable Narrow-Line Seyfert 1 galaxy RX
J2217.9--5941. Observations spanning the time from the ROSAT All Sky Survey
(RASS) through an ASCA observation in 1998 indicate apparently monotonically
decreasing flux by a factor of 30. The Chandra observations reveal increased
emission over that seen in ASCA, supporting a persistent variability rather
than an X-ray outburst event. However, the cause of the strong X-ray
variability remains unclear. Our Chandra observations confirm the steep soft
X-ray spectrum in the 0.2-2.0 keV band found during the ROSAT All-Sky Survey
observation (\ax=2.7). The spectral shape of the source appears to be variable
with the spectrum becoming softer when the source becomes fainter. Best fitting
models to the data include an absorbed broken power law, a blackbody plus power
law, and a power law with partial covering absorption. The latter model
suggests a variable partial-covering absorber in the line of sight which can
explain in part the variability seen in RX J2217.9--5941. We suggest that there
might be a population of Narrow Line Seyfert 1 galaxies which are at least at
times highly absorbed.


  The exploration mechanism used by a Deep Reinforcement Learning (RL) agent
plays a key role in determining its sample efficiency. Thus, improving over
random exploration is crucial to solve long-horizon tasks with sparse rewards.
We propose to leverage an ensemble of partial solutions as teachers that guide
the agent's exploration with action suggestions throughout training. While the
setup of learning with teachers has been previously studied, our proposed
approach - Actor-Critic with Teacher Ensembles (AC-Teach) - is the first to
work with an ensemble of suboptimal teachers that may solve only part of the
problem or contradict other each other, forming a unified algorithmic solution
that is compatible with a broad range of teacher ensembles. AC-Teach leverages
a probabilistic representation of the expected outcome of the teachers' and
student's actions to direct exploration, reduce dithering, and adapt to the
dynamically changing quality of the learner. We evaluate a variant of AC-Teach
that guides the learning of a Bayesian DDPG agent on three tasks - path
following, robotic pick and place, and robotic cube sweeping using a hook - and
show that it improves largely on sampling efficiency over a set of baselines,
both for our target scenario of unconstrained suboptimal teachers and for
easier setups with optimal or single teachers. Additional results and videos at
https://sites.google.com/view/acteach/home.


  We present a novel supervised word alignment method based on cross-language
span prediction. We first formalize a word alignment problem as a collection of
independent predictions from a token in the source sentence to a span in the
target sentence. As this is equivalent to a SQuAD v2.0 style question answering
task, we then solve this problem by using multilingual BERT, which is
fine-tuned on a manually created gold word alignment data. We greatly improved
the word alignment accuracy by adding the context of the token to the question.
In the experiments using five word alignment datasets among Chinese, Japanese,
German, Romanian, French, and English, we show that the proposed method
significantly outperformed previous supervised and unsupervised word alignment
methods without using any bitexts for pretraining. For example, we achieved an
F1 score of 86.7 for the Chinese-English data, which is 13.3 points higher than
the previous state-of-the-art supervised methods.


  We determine the central simple algebras D over a functionfield K of
trancendence degree two which admit a model of smooth Cayley-Hamilton algebras.
This happens if and only if there is a smooth model S of K such that the
ramification divisor of a maximal S-order in D is a disjoint union of smooth
curves. Further, we prove that the Brauer-Severi fibration of smooth models
which are in addition maximal orders is a flat morphism and determine the
number of irreducible components of the fibers.


  Binary star systems containing a neutron star or a black hole with an
evolved, massive star are dynamically perturbed when the latter undergoes a
supernova explosion. It is possible that the natal kick received by the
newly-formed neutron star in the supernova may place the stellar remnants into
a bound, highly eccentric orbit. In this case, the two compact objects can
tidally interact and spiral into one another on a short timescale. The
interaction with an accretion disc of supernova debris is also considered. We
quantify the likelihood of such events and show that they would be expected to
produce a high-energy transient, possibly a short gamma-ray burst, typically
within a few days of the supernova.


  Studies of the Gaussian core model (GCM) have shown that it behaves like a
mean field model and the properties are quite different from standard glass
former. In this work we investigate the entropies, namely the excess entropy
($S_{ex}$) and the configurational entropy ($S_c$) and their different
components to address these anomalies. Our study corroborates most of the
earlier observations and also sheds new light on the high and low temperature
dynamics. We find that unlike in standard glass former where high temperature
dynamics is dominated by two body correlation and low temperature by many body
correlations, in GCM both high and low temperature dynamics are dominated by
many body correlations. We also find that the many body entropy which is
usually positive at low temperatures and is associated with activated dynamics
is negative in GCM suggesting suppression of activation. Interestingly despite
suppression of activation the Adam-Gibbs (AG) relation which describes
activated dynamics holds in GCM, thus suggesting a non-activated contribution
in AG relation. We also find an overlap between the AG and mode coupling power
law regime leading to a power law behaviour of $S_c$. From our analysis of this
power law behaviour we predict that in GCM the high temperature dynamics will
disappear at dynamical transition temperature and below that there will be a
transition to the activated regime. Our study further reveals that the
activated regime in GCM is quite narrow.


  The thermodyanmics of a metastable hadronic phase of QCD at large $N_C$ are
related to properties of an effective QCD string. In particular, it is shown
that in the large $N_c$ limit and near the maximum hadronic temperature, $T_H$,
the energy density and pressure of the metastable phase scale as ${\cal E} \sim
(T_H-T)^{-(D_\perp-6)/2}$ (for $D_\perp <6$) and $P \sim
(T_H-T)^{-(D_\perp-4)/2}$ (for $D_\perp <4$) where $D_\perp$ is the effective
number of transverse dimensions of the string theory. It is shown, however,
that for the thermodynamic quantities of interest the limits $T \to T_H$ and
$N_c \to \infty$ do not commute. The prospect of extracting $D_\perp$ via
lattice simulations of the metastable hadronic phase at moderately large $N_c$
is discussed.


  For a group G and positive interger m, Gm denotes the subgroup generated by
the elements gm where g runs through G. The subgroups not of the form Gm are
called nonpower subgroups. We extend the classification of groups with few
nonpower subgroups from groups with at most 9 nonpower subgroups to groups with
at most 13 nonpower subgroups.


  Detecting objects and estimating their viewpoints in images are key tasks of
3D scene understanding. Recent approaches have achieved excellent results on
very large benchmarks for object detection and viewpoint estimation. However,
performances are still lagging behind for novel object categories with few
samples. In this paper, we tackle the problems of few-shot object detection and
few-shot viewpoint estimation. We demonstrate on both tasks the benefits of
guiding the network prediction with class-representative features extracted
from data in different modalities: image patches for object detection, and
aligned 3D models for viewpoint estimation. Despite its simplicity, our method
outperforms state-of-the-art methods by a large margin on a range of datasets,
including PASCAL and COCO for few-shot object detection, and Pascal3D+ and
ObjectNet3D for few-shot viewpoint estimation. Furthermore, when the 3D model
is not available, we introduce a simple category-agnostic viewpoint estimation
method by exploiting geometrical similarities and consistent pose labelling
across different classes. While it moderately reduces performance, this
approach still obtains better results than previous methods in this setting.
Last, for the first time, we tackle the combination of both few-shot tasks, on
three challenging benchmarks for viewpoint estimation in the wild, ObjectNet3D,
Pascal3D+ and Pix3D, showing very promising results.


  Developing multithreaded software is an extremely challenging task, even for
experienced programmers. The challenge does not end after the code is written.
There are other tasks associated with a development process that become
exceptionally hard in a multithreaded environment. A good example of this is
creating unit tests for concurrent data structures. In addition to the desired
test logic, such a test contains plenty of synchronization code that makes it
hard to understand and maintain.
  In our work we propose a novel approach for specifying and executing
schedules for multithreaded tests. It allows explicit specification of desired
thread scheduling for some unit test and enforces it during the test execution,
giving the developer an ability to construct deterministic and repeatable unit
tests. This goal is achieved by combining a few basic tools available in every
modern runtime/IDE and does not require dedicated runtime environment, new
specification language or code under test modifications.


  Motivated by the famous Hadwiger's Conjecture, we study the properties of
$8$-contraction-critical graphs with no $K_7$ minor; we prove that every
$8$-contraction-critical graph with no $K_7$ minor has at most one vertex of
degree $8$, where a graph $G$ is $8$-contraction-critical if $G$ is not
$7$-colorable but every proper minor of $G$ is $7$-colorable. This is one step
in our effort to prove that every graph with no $K_7$ minor is $7$-colorable,
which remains open.


  The so-called generalized Wigner distribution has earlier been shown to be an
excellent approximation for the terrace width distribution (TWD) of vicinal
surfaces characterized by step-step interactions that are perpendicular to the
average step direction and fall off as the inverse square of the step spacing.
In this paper we show that the generalized Wigner distribution corresponds to a
mean-field treatment of a single step, discuss generalizations to more general
step-step interactions, and show that the mean-field predictions are in good
agreement with TWDs derived from numerical transfer-matrix calculations and
Monte Carlo simulations. We also show that this mean-field treatment allows the
step-step interaction to be extracted from experimental TWDs.


  A review of theoretical and experimental studies of the electronic structure,
electronic and magnetic properties of various systems of Heusler alloys in the
states of a half-metallic ferromagnet, a spin gapless semiconductor, and a
topological semimetal is presented. These substances have unusual, highly
sensitive to external influences, magnetic and electronic characteristics,
which is associated with the presence of energy gaps and exotic excitations in
them. The features of the behavior and evolution of the electronic structure
and properties in each of these states, as well as during the transition
between them, are considered. The possibility to purposefully control the
properties of such materials is prospective for their practical application.


  Let G be a semi-simple algebraic group over a finitely generated field K of
characteristic zero, and let \Gamma < G(K) be a finitely generated
Zariski-dense subgroup. In this note we prove that the set of K-generic
elements of \Gamma (whose existence was established earlier in [9]) is open in
the profinite topology of \Gamma. We then extend this result to the fields of
positive characteristic, and also prove the existence of generic elements in
this case.


  Water autoionization plays a critical role in determining pH and properties
of various chemical and biological processes occurring in the water mediated
environment. The strikingly unsymmetrical potential energy surface of the
dissociation process poses a great challenge to the mechanistic study. Here, we
demonstrate that reliable sampling of the ionization path is accessible through
nanosecond timescale metadynamics simulation enhanced by machine learning of
the neural network potentials with ab initio precision, which is proved by
quantitatively reproduced water equilibrium constant (p$K_\mathrm{w}$=14.14)
and ionization rate constant (1.566$\times10^{-3}$ s$^{-1}$). Statistical
analysis unveils the asynchronous character of the concerted triple proton
transfer process. Based on conditional ensemble average calculations, we
propose a dual-presolvation mechanism, which suggests that a pair of
hypercoordinated and undercoordinated waters bridged by one \ce{H2O}
cooperatively constitutes the initiation environment for autoionization, and
contributes majorly to the local electric field fluctuation to promote water
dissociation.


  In the realm of autonomous agents, ensuring safety and reliability in complex
and dynamic environments remains a paramount challenge. Safe reinforcement
learning addresses these concerns by introducing safety constraints, but still
faces challenges in navigating intricate environments such as complex driving
situations. To overcome these challenges, we present the safe constraint reward
(Safe CoR) framework, a novel method that utilizes two types of expert
demonstrations$\unicode{x2013}$reward expert demonstrations focusing on
performance optimization and safe expert demonstrations prioritizing safety. By
exploiting a constraint reward (CoR), our framework guides the agent to balance
performance goals of reward sum with safety constraints. We test the proposed
framework in diverse environments, including the safety gym, metadrive, and the
real$\unicode{x2013}$world Jackal platform. Our proposed framework enhances the
performance of algorithms by $39\%$ and reduces constraint violations by $88\%$
on the real-world Jackal platform, demonstrating the framework's efficacy.
Through this innovative approach, we expect significant advancements in
real-world performance, leading to transformative effects in the realm of safe
and reliable autonomous agents.


  We present a convex approach to probabilistic segmentation and modeling of
time series data. Our approach builds upon recent advances in multivariate
total variation regularization, and seeks to learn a separate set of parameters
for the distribution over the observations at each time point, but with an
additional penalty that encourages the parameters to remain constant over time.
We propose efficient optimization methods for solving the resulting (large)
optimization problems, and a two-stage procedure for estimating recurring
clusters under such models, based upon kernel density estimation. Finally, we
show on a number of real-world segmentation tasks, the resulting methods often
perform as well or better than existing latent variable models, while being
substantially easier to train.


  Since the Turing test was first proposed by Alan Turing in 1950, the primary
goal of artificial intelligence has been predicated on the ability for
computers to imitate human behavior. However, the majority of uses for the
computer can be said to fall outside the domain of human abilities and it is
exactly outside of this domain where computers have demonstrated their greatest
contribution to intelligence. Another goal for artificial intelligence is one
that is not predicated on human mimicry, but instead, on human amplification.
This article surveys various systems that contribute to the advancement of
human and social intelligence.


  The gauge covariance of the wave function phase factor in noncommutative
quantum mechanics (NCQM) is discussed. We show that the naive path integral
formulation and an approach where one shifts the coordinates of NCQM in the
presence of a background vector potential leads to the gauge non-covariance of
the phase factor. Due to this fact, the Aharonov-Bohm phase in NCQM which is
evaluated through the path-integral or by shifting the coordinates is neither
gauge invariant nor gauge covariant. We show that the gauge covariant
Aharonov-Bohm effect should be described by using the noncommutative Wilson
lines, what is consistent with the noncommutative Schr\"odinger equation. This
approach can ultimately be used for deriving an analogue of the Dirac
quantization condition for the magnetic monopole.


  The in-memory graph layout or organization has a considerable impact on the
time and energy efficiency of distributed memory graph computations. It affects
memory locality, inter-task load balance, communication time, and overall
memory utilization. Graph layout could refer to partitioning or replication of
vertex and edge arrays, selective replication of data structures that hold
meta-data, and reordering vertex and edge identifiers. In this work, we present
DGL, a fast, parallel, and memory-efficient distributed graph layout strategy
that is specifically designed for small-world networks (low-diameter graphs
with skewed vertex degree distributions). Label propagation-based partitioning
and a scalable BFS-based ordering are the main steps in the layout strategy. We
show that the DGL layout can significantly improve end-to-end performance of
five challenging graph analytics workloads: PageRank, a parallel subgraph
enumeration program, tuned implementations of breadth-first search and
single-source shortest paths, and RDF3X-MPI, a distributed SPARQL query
processing engine. Using these benchmarks, we additionally offer a
comprehensive analysis on how graph layout affects the performance of graph
analytics with variable computation and communication characteristics.


  The discrete prolate spheroidal sequences (DPSSs) are a set of orthonormal
sequences in $\ell_2(\mathbb{Z})$ which are strictly bandlimited to a frequency
band $[-W,W]$ and maximally concentrated in a time interval $\{0,\ldots,N-1\}$.
The timelimited DPSSs (sometimes referred to as the Slepian basis) are an
orthonormal set of vectors in $\mathbb{C}^N$ whose discrete time Fourier
transform (DTFT) is maximally concentrated in a frequency band $[-W,W]$. Due to
these properties, DPSSs have a wide variety of signal processing applications.
The DPSSs are the eigensequences of a timelimit-then-bandlimit operator and the
Slepian basis vectors are the eigenvectors of the so-called prolate matrix. The
eigenvalues in both cases are the same, and they exhibit a particular
clustering behavior -- slightly fewer than $2NW$ eigenvalues are very close to
$1$, slightly fewer than $N-2NW$ eigenvalues are very close to $0$, and very
few eigenvalues are not near $1$ or $0$. This eigenvalue behavior is critical
in many of the applications in which DPSSs are used. There are many asymptotic
characterizations of the number of eigenvalues not near $0$ or $1$. In
contrast, there are very few non-asymptotic results, and these don't fully
characterize the clustering behavior of the DPSS eigenvalues. In this work, we
establish two novel non-asymptotic bounds on the number of DPSS eigenvalues
between $\epsilon$ and $1-\epsilon$. Also, we obtain bounds detailing how close
the first $\approx 2NW$ eigenvalues are to $1$ and how close the last $\approx
N-2NW$ eigenvalues are to $0$. Furthermore, we extend these results to the
eigenvalues of the prolate spheroidal wave functions (PSWFs), which are the
continuous-time version of the DPSSs. Finally, we present numerical experiments
demonstrating the quality of our non-asymptotic bounds on the number of DPSS
eigenvalues between $\epsilon$ and $1-\epsilon$.


  Using the semiclassical two-step model for strong-field ionization we
investigate the interference structures emerging in strong-field photoelectron
holography, taking into account the Coulomb potential of the atomic core. For
every kind of the interference pattern predicted by the three-step model, we
calculate the corresponding structure in the presence of the Coulomb field,
showing that the Coulomb potential modifies the interference patterns
significantly.


  We calculate the Debye and Meissner masses and investigate chromomagnetic
instability associated with the gapless color superconducting phase changing
the strange quark mass $M_s$ and the temperature $T$. Based on the analytical
study, we develop a computational procedure to derive the screening masses
numerically from curvatures of the thermodynamic potential. When the
temperature is zero, from our numerical results for the Meissner masses, we
find that instability occurs for $A_1$ and $A_2$ gluons entirely in the gapless
color-flavor locked (gCFL) phase, while the Meissner masses are real for $A_4$,
$A_5$, $A_6$, and $A_7$ until $M_s$ exceeds a certain value that is larger than
the gCFL onset. We then handle mixing between color-diagonal gluons $A_3$,
$A_8$, and photon $A_\gamma$, and clarify that, among three eigenvalues of the
mass squared matrix, one remains positive, one is always zero because of an
unbroken $U(1)_\tilde{Q}$ symmetry, and one exhibits chromomagnetic instability
in the gCFL region. We also examine the temperature effects that bring
modifications into the Meissner masses. The instability found at large $M_s$
for $A_4$, $A_5$, $A_6$, and $A_7$ persists at finite $T$ into the $u$-quark
color superconducting (uSC) phase which has $u$-$d$ and $s$-$u$ but no $d$-$s$
quark pairing and also into the two-flavor color superconducting (2SC) phase
characterized by $u$-$d$ quark pairing only. The $A_1$ and $A_2$ instability
also goes into the uSC phase, but the 2SC phase has no instability for $A_1$,
$A_2$, and $A_3$. We map the unstable region for each gluon onto the phase
diagram as a function of $M_s$ and $T$.


  Spiking Neural Networks (SNNs) are a biologically plausible neural network
model with significant advantages in both event-driven processing and
spatio-temporal information processing, rendering SNNs an appealing choice for
energyefficient object detection. However, the non-differentiability of the
biological neuronal dynamics model presents a challenge during the training of
SNNs. Furthermore, a suitable decoding strategy for object detection in SNNs is
currently lacking. In this study, we introduce the Current Mean Decoding (CMD)
method, which solves the regression problem to facilitate the training of deep
SNNs for object detection tasks. Based on the gradient surrogate and CMD, we
propose the SNN-YOLOv3 model for object detection. Our experiments demonstrate
that SNN-YOLOv3 achieves a remarkable performance with an mAP of 61.87% on the
PASCAL VOC dataset, requiring only 6 time steps. Compared to SpikingYOLO, we
have managed to increase mAP by nearly 10% while reducing energy consumption by
two orders of magnitude.


  We discuss the physics of interacting tensor fields and particles living in
$M=\mathrm{S0}(1,4)/\mathrm{S0} (1,3)\simeq\mathbb{R}\times S^{3}$ a
submanifold of $\mathring{M}=(\mathbb{R}^{5},\boldsymbol{\mathring{g}})$, where
$\boldsymbol{\mathring {g}}$ has signature $(1,4)$. Structure
$(M,\boldsymbol{g})$ where $(\boldsymbol{g=i}^{\ast}\boldsymbol{\mathring{g}})$
is a Lorentzian manifold. Structure
$(M,\boldsymbol{g,}\tau_{\boldsymbol{g}},\uparrow)$ is primely used to study
the energy-momentum conservation law (for a system of physical fields (and
particles) living in $M$ and to get the respective equations of motion. We
construct two different de Sitter spacetime structures
$M^{dSL}=(M,\boldsymbol{g,D},\tau_{\boldsymbol{g}},\uparrow)$ and
$M^{dSTP}=(M,\boldsymbol{g,\nabla},\tau_{\boldsymbol{g} },\uparrow)$. Both
(metrical compatible) connections are used only as mathematical devices. In
particular $M^{dSL}$ is not supposed to be the model of any gravitational field
in the(\textbf{GRT}). We clarify some misconceptions appearing in the
literature. We use the Clifford and spin-Clifford bundles formalism and gives a
thoughtful presentation of the concept of a Komar current $\mathcal{J}_{A}$ (in
GRT}) associated to any vector field $\mathbf{A}$. A formula for the Komar
current and its physical meaning are given. We show also how $F=dA$ satisfy in
the Clifford bundle a Maxwell like equation encoding the contents of Einstein
equation. We show that in GRT there are infinitely many conserved
currents,independently of the fact that the Lorentzian spacetime possess or not
Killing vector fields and that even when the appropriate Killing vector fields
exist there does not exist a conserved energy-momentum covector (not a covector
field) as in SRT.


  We prove that a real-valued function (that is not assumed to be continuous)
on a real analytic manifold is analytic whenever all its restrictions to
analytic submanifolds homeomorphic to the 2-sphere are analytic. This is a real
analog for the classical theorem of Hartogs that a function on a complex
manifold is complex analytic iff it is complex analytic when restricted to any
complex curve.


  Protein structure prediction is a fundamental problem in computational
molecular biology. Classical algorithms such as ab-initio or threading as well
as many learning methods have been proposed to solve this challenging problem.
However, most reinforcement learning methods tend to model the state-action
pairs as discrete objects. In this paper, we develop a reinforcement learning
(RL) framework in a continuous setting and based on a stochastic parametrized
Hamiltonian version of the Pontryagin maximum principle (PMP) to solve the
side-chain packing and protein-folding problem. For special cases our
formulation can be reduced to previous work where the optimal folding
trajectories are trained using an explicit use of Langevin dynamics. Optimal
continuous stochastic Hamiltonian dynamics folding pathways can be derived with
use of different models of molecular energetics and force fields. In our RL
implementation we adopt a soft actor-critic methodology however we can replace
this other RL training based on A2C, A3C or PPO.


  The Ablowitz-Ladik equation is a very important model in the nonlinear
mathematical physics. In this paper, the hyperbolic function solitary wave
solutions, the trigonometric function periodic wave solutions and the rational
wave solutions with more arbitrary parameters of 2-dimensional Ablowitz-Ladik
equation are derived by using the GG-expansion method, and the effect of the
parameters (including the coupling constant and other parameters) on the linear
stability of the exact solutions is analysed and numerically simulated.


  Stochastic Gradient Descent (SGD) is arguably the most important single
algorithm in modern machine learning. Although SGD with unbiased gradient
estimators has been studied extensively over at least half a century, SGD
variants relying on biased estimators are rare. Nevertheless, there has been an
increased interest in this topic in recent years. However, existing literature
on SGD with biased estimators (BiasedSGD) lacks coherence since each new paper
relies on a different set of assumptions, without any clear understanding of
how they are connected, which may lead to confusion. We address this gap by
establishing connections among the existing assumptions, and presenting a
comprehensive map of the underlying relationships. Additionally, we introduce a
new set of assumptions that is provably weaker than all previous assumptions,
and use it to present a thorough analysis of BiasedSGD in both convex and
non-convex settings, offering advantages over previous results. We also provide
examples where biased estimators outperform their unbiased counterparts or
where unbiased versions are simply not available. Finally, we demonstrate the
effectiveness of our framework through experimental results that validate our
theoretical findings.


  New quantum degrees of freedom of space-time, originating at the Planck
scale, could create a coherent indeterminacy and noise in the transverse
position of massive bodies on macroscopic scales. An experiment is under
development at Fermilab designed to detect or rule out a transverse position
noise with Planck spectral density, using correlated signals from an adjacent
pair of Michelson interferometers. A detection would open an experimental
window on quantum space-time.


  We explore the ultimate fate of the Universe by using a divergence-free
parametrization for dark energy $w(z)=w_0+w_a({\ln (2+z)\over 1+z}-\ln2)$.
Unlike the CPL parametrization, this parametrization has well behaved, bounded
behavior for both high redshifts and negative redshifts, and thus can genuinely
cover many theoretical dark energy models. After constraining the parameter
space of this parametrization by using the current cosmological observations,
we find that, at the 95.4% confidence level, our Universe can still exist at
least 16.7 Gyr before it ends in a big rip. Moreover, for the phantom energy
dominated Universe, we find that a gravitationally bound system will be
destroyed at a time $t \simeq P\sqrt{2|1+3w(-1)|}/[6\pi |1+w(-1)|]$, where $P$
is the period of a circular orbit around this system, before the big rip.


  Motivation: Genome rearrangement plays an important role in evolutionary
biology and has profound impacts on phenotype in organisms ranging from
microbes to humans. The mechanisms for genome rearrangement events remain
unclear. Lots of comparisons have been conducted among different species. To
reveal the mechanisms for rearrangement events, comparison of different
individuals/strains within the same species or genus (pan-genomes) is more
helpful since they are much closer to each other. Results: We study the
mechanism for inversion events via core-genome scaffold comparison of different
strains within the same species. We focus on two kinds of bacteria, Pseudomonas
aeruginosa and Escherichia coli, and investigate the inversion events among
different strains of the same specie. We find an interesting phenomenon that
long (larger than 10,000 bp) inversion regions are flanked by a pair of
Inverted Repeats (IRs) (with lengths ranging from 385 bp to 27476 bp) which are
often Insertion Sequences (ISs).This mechanism can also explain why the
breakpoint reuses for inversion events happen. We study the prevalence of the
phenomenon and find that it is a major mechanism for inversions. The other
observation is that for different rearrangement events such as transposition
and inverted block interchange, the two ends of the swapped regions are also
associated with repeats so that after the rearrangement operations the two ends
of the swapped regions remain unchanged. To our knowledge, this is the first
time such a phenomenon is reported for transposition event.


  Chemically peculiar stars define a class of stars that show unusual elemental
abundances due to stellar photospheric effects and not due to natal variations.
In this paper, we compare the elemental abundance patterns of the ultra
metal-poor stars with metallicities [Fe/H] $\sim -5 $ to those of a subclass of
chemically peculiar stars. These include post-AGB stars, RV Tauri variable
stars, and the Lambda Bootis stars, which range in mass, age, binarity, and
evolutionary status, yet can have iron abundance determinations as low as
[Fe/H] $\sim -5$. These chemical peculiarities are interpreted as due to the
separation of gas and dust beyond the stellar surface, followed by the
accretion of dust depleted-gas. Contrary to this, the elemental abundances in
the ultra metal-poor stars are thought to represent yields of the most
metal-poor supernova and, therefore, observationally constrain the earliest
stages of chemical evolution in the Universe. The abundance of the elements in
the photospheres of the ultra metal-poor stars appear to be related to the
condensation temperature of that element; if so, then their CNO abundances
suggest true metallicities of [X/H]~ -2 to -4, rather than their present
metallicities of [Fe/H] < -5.


  Follow-up observations of short gamma-ray bursts (sGRBs) have continuously
unveiled late extended/plateau emissions, attributed to jet launch due to late
engine activity, the nature of which remains enigmatic. Observations of
GW170817 confirmed that sGRBs are linked to neutron star (NS) mergers, and
discovered a kilonova (KN) transient. Nevertheless, the origin of the early
"blue" KN in GW170817 remains unclear. Here, we investigate the propagation of
late jets in the merger ejecta. By analytically modeling jet dynamics, we
determine the properties of the jet heated cocoon, and estimate its cooling
emission. Our results reveal that late jets generate significantly brighter
cocoons compared to prompt jets, primarily due to reduced energy loss by
adiabatic cooling. Notably, with typical late jets, emission from the cocoon
trapped inside the ejecta can reproduce the blue KN emission. We estimate that
the forthcoming Einstein Probe mission will detect the early cocoon emission
with a rate of $\sim 2.1_{-1.6}^{+3.2}$ yr$^{-1}$, and that optical/UV
follow-ups in the LIGO-VIRGO-KAGRA O5 run will be able to detect $\sim
1.0_{-0.7}^{+1.5}$ cocoon emission events. As an electromagnetic counterpart,
this emission provides an independent tool to probe NS mergers in the Universe,
complementing insights from sGRBs and gravitational waves.


  We present a systematic comparison of various iterative methods to obtain the
fermion propagator with both overlap and twisted mass fermions at fixed pion
mass in the quenched approximation. Taking the best available algorithm in each
case we find that calculations with the overlap operator are by a factor of
20-40 more expensive than with the twisted mass operator at the parameter
values considered here. For the overlap operator we also compare the efficiency
of various methods for calculating the topological index.


  This work is devoted to the study of processes generated by random
substitutions over a finite alphabet. We prove, under mild conditions on the
substitution's rule, the existence of a unique process which remains invariant
under the substitution, and exhibiting polynomial decay of correlations. For
constant-length substitutions, we go further by proving that the invariant
state is precisely a Gibbs measure which can be obtained as the projective
limit of its natural Markovian approximations. We close the paper with a class
of substitutions whose invariant state is the unique Gibbs measure for a
hierarchical two-body interaction.


  Rossi X-ray Timing Explorer (RXTE)/Proportional Counter Array (PCA)
observations of IGR J19294+1816 covering two outburst episodes are reported.
The first outburst happened during MJD 54921-54925 (2009 C.E.) and the second
one happened during MJD 55499-55507 (2010 C.E.). In both the cases the PCA
observations were made during the decay phase of the outburst, with the source
exhibiting temporal and spectral evolution with the change in flux. At the
bright flux level an absorption feature at 35.5 keV is detected in the spectra
which may be attributed to Cyclotron Resonance Scattering Feature corresponding
to a magnetic field of B = 4.13*10^12 Gauss. This is also detected at a lower
significance in two other observations. In addition an Fe line emission at 6.4
keV is prominently detected during the highest flux. X-ray pulsations are
detected in 9 out of 10 observations; no pulsations were found in the
observation with the lowest flux level. During this observation with the lowest
flux the pulsation phenomenon becomes detectable only at the soft X-ray bands.


  We argue about a possible scenario of physical reality based on the
parallelism between Poincare group and the sunyata philosophy of Nagarjuna. The
notion of "relational" is the common denominator of two views. We have
approached the relational concept in third-person perspective (ontic level). It
is possible to deduce different physical consequence and interpretation through
first-person perspective approach. This relational interpretation leave open
the questions: i)we must abandon the idea for a physical system the possibility
to extract completeness information? ii)we must abandon the idea to infer a
possible structure of physical reality?


  Highly entangled graph states of photons have applications in universal
quantum computing and in quantum communications. In the latter context, they
have been proposed as the key ingredient in the establishment of long-distance
entanglement across quantum repeater networks. Recently, a general
deterministic approach to generate repeater graph states from quantum emitters
was given. However, a detailed protocol for the generation of such states from
realistic systems is still needed in order to guide experiments. Here, we
provide such explicit protocols for the generation of repeater graph states
from two types of quantum emitters: NV centers in diamond and self-assembled
quantum dots. A crucial element of our designs is an efficient controlled-Z
gate between the emitter and a nuclear spin, used as an ancilla qubit.
Additionally, a fast protocol for using pairs of exchange-coupled quantum dots
to produce repeater graph states is described. Our focus is on near-term
experiments feasible with existing experimental capabilities.


  We give a criterion of integrality of an one-dimensional formal group law in
terms of congruences satisfied by the coefficients of the canonical invariant
differential. For an integral formal group law a p-adic analytic formula for
the local characteristic polynomial at p is given. We demonstrate applications
of our results to formal group laws attached to L-functions, Artin--Mazur
formal groups of algebraic varieties and hypergeometric formal group laws.
(This is the final version submitted to a journal; new parts are added in the
section on hypergeometric formal group laws.)


  Vacuum energy in quantum field theory, being the sum of zero-point energies
of all field modes, is formally infinite but yet, after regularization or
renormalization, can give rise to finite observable effects. One way of
understanding how these effects arise is to compute the vacuum energy in an
idealized system such as a large cavity divided into disjoint regions by
pistons. In this paper, this type of calculation is carried out for situations
where the potential affecting a field is not the same in all regions of the
cavity. It is shown that the observable parts of the vacuum energy in such
potentials do not fall off to zero as the region where the potential is
nontrivial becomes large. This unusual behavior might be interesting for tests
involving quantum vacuum effects and for studies on the relation between vacuum
energy in quantum field theory and geometry.


  We numerically investigate the quantum crystallographic phases of a
Rydberg-dressed Bose gas loaded on a square lattice by using the mean-field
Gross--Pitaevskii model. For a relatively weak lattice confinement, the phases
of ground state undergo amorphism, polycrystal, and polymorphism following the
increase of the blockade radius, and if the confinement is stronger, a single
crystal with a specific filling factor will be formed. In order to
distinctively characterize these phases, the structure function is also
studied. In such an anisotropic system, we report that the first diagonal
element of the superfluid-fraction tensor should be a measurable quantity, and
an anisotropy parameter can be defined. In addition, for such crystallographic
phases, the interaction potential can manifest where the grain boundaries
appear.


  We propose a $D$-dimensional generalization of $4D$ bi-scalar conformal
quantum field theory recently introduced by G\"{u}rdogan and one of the authors
as a strong-twist double scaling limit of $\gamma$-deformed $\mathcal{N}=4$ SYM
theory. Similarly to the $4D$ case, this D-dimensional CFT is also dominated by
"fishnet" Feynman graphs and is integrable in the planar limit. The dynamics of
these graphs is described by the integrable conformal $SO(D+1,1)$ spin chain.
In $2D$ it is the analogue of L. Lipatov's $SL(2,\mathbb{C})$ spin chain for
the Regge limit of $QCD$, but with the spins $s=1/4$ instead of $s=0$.
Generalizing recent $4D$ results of Grabner, Gromov, Korchemsky and one of the
authors to any $D$ we compute exactly, at any coupling, a four point
correlation function, dominated by the simplest fishnet graphs of cylindric
topology, and extract from it exact dimensions of R-charge 2 operators with any
spin and some of their OPE structure constants.


  A long-term decrease in downward surface solar radiation from the 1950s to
the 1980s ("global dimming") followed by a multi-decadal increase up to the
present ("brightening") have been detected in many regions worldwide. In
addition, some researchers have suggested the existence of an "early
brightening" period in the first half of 20th century. However, this latter
phenomenon is an open issue due to the opposite results found in literature and
the scarcity of solar radiation data during this period. This paper contributes
to this relevant discussion analyzing, for the first time in Southern Europe,
the atmospheric column transparency derived from pyrheliometer measurements in
Madrid (Spain) for the period 1911-1928. This time series is one of the three
longest dataset during the first quarter of the 20th century in Europe. The
results showed the great effects of the Katmai eruption (June 1912, Alaska) on
transparency values during 1912-1913 with maximum relative anomalies around 8%.
Outside the period affected by this volcano, the atmospheric transparency
exhibited a stable behavior with a slight negative trend without any
statistical significance on an annual and seasonal basis. Overall, there is no
evidence of a possible early brightening period in direct solar radiation in
Madrid. This phenomenon is currently an open issue and further research is
needed using the few sites with available experimental records during the first
half of the 20th century.


  We report a correlative microscopy study of a sample containing three stacks
of InGaN/GaN quantum dots (QDs) grown at different substrate temperature, each
stack consisting of 3 layers of QDs. Decreasing the substrate temperature along
the growth axis leads to the proliferation of structural defects. However, the
luminescence intensity increases towards the surface, in spite of the higher
density of threading dislocations, revealing that the QD layers closer to the
substrate behave as traps for non-radiative point defects. During atom probe
tomography experiments combined with in-situ micro-photoluminescence, it was
possible to isolate the optical emission of a single QD located in the topmost
QD stack, closer to the sample surface. The single QD emission line displayed a
spectral shift during the experiment confirming the relaxation of elastic
strain due to material evaporation during atom probe tomography.


  A new energy and enstrophy conserving scheme is evaluated using a suite of
test cases over the global spherical domain or bounded domains. The evaluation
is organized around a set of pre-defined properties: accuracy of individual
opeartors, accuracy of the whole scheme, conservation, control of the
divergence variable, representation of the energy and enstrophy spectra, and
simulation of nonlinear dynamics. The results confirm that the scheme is
between the first and second order accurate, and conserves the total energy and
potential enstrophy up to the time truncation errors. The scheme is capable of
producing more physically realistic energy and enstrophy spectra, indicating
that the new scheme can help prevent the unphysical energy cascade towards the
finest resolvable scales. With an optimal representation of the dispersive wave
relations, the scheme is able to keep the flow close to being non-divergent,
maintain the geostrophically balanced structures with large-scale geophysical
flows over long-term simulations.


  We present a non-demolition quantum information processing task of probing
the information of a class of quantum state. In this task, the information is
extracted by some unitary evolution with the introduced probing qubit assisted,
but the probed quantum state (density matrix) is undisturbed at any time and
independent of the choice of the initial probing state. We give a sufficient
and necessary condition on the Hamiltonian that can lead to the successful
realization of such a task. We prove that, for any feasible scheme, the probed
plus probing system will always stay at a disentangled state with one side
quantum discord absent and the other side one inevitably produced in the
probing process. An explicit example is given for the demonstration, whilst the
example shows that the ratio of quantum discord to the total correlation will
have to reduce to zero for the maximal accessible information. In this sense,
we say that quantum discord plays the dual roles in this case.


  We prove short-time existence of \phi-regular solutions to the planar
anisotropic curvature flow, including the crystalline case, with an additional
forcing term possibly unbounded and discontinuous in time, such as for instance
a white noise. We also prove uniqueness of such solutions when the anisotropy
is smooth and elliptic. The main tools are the use of an implicit variational
scheme in order to define the evolution, and the approximation with flows
corresponding to regular anisotropies.


  We introduce the chemical potential in a system of two-dimensional massless
fermions, confined to a finite region, by imposing twisted boundary conditions
in the Euclidean time direction. We explore in this simple model the
application of functional techniques which could be used in more complicated
situations.


  In this paper, we construct an infinite families of group $G$ of order $4p^m$
which can be an automorphism group of some regular polytope with type $\{p,
2p\}$, where $m \geq 3$ and $p$ is an odd prime. For $p=3$, our polytopes are
the regular toroidal maps $\{3, 6\}$.


  We propose an efficient and robust iterative solution to the multi-object
matching problem. We first clarify serious limitations of current methods as
well as the inappropriateness of the standard iteratively reweighted least
squares procedure. In view of these limitations, we suggest a novel and more
reliable iterative reweighting strategy that incorporates information from
higher-order neighborhoods by exploiting the graph connection Laplacian. We
demonstrate the superior performance of our procedure over state-of-the-art
methods using both synthetic and real datasets.


  Countries across the world have instituted unprecedented restrictions on
freedom of movement, privacy and individual rights to control the spread of
COVID-19. These measures tend to have been derived from communally orientated
East Asian cultures. The way that culturally relevant concepts of rights and
freedoms underpin COVID restrictions in democratic and individually orientated
countries remains unknown. This data memo addresses this issue through analysis
of pro- and anti-restriction discourse on social media in the US. It finds that
anti-social and economic restriction discourse more frequently articulates
rights and freedoms, based on ideas of inviolable rights to freedom of movement
or freedom of economic activity or a cost-benefit analysis that places economic
activity over public health. Pro-social and economic restriction discourse less
frequently mentions rights and freedoms, instead supporting restrictions as
following state and medical advice and out of deference and respect to medical
professionals. Discourse is highly polarised and divisive and articulated
largely through established political identity positions. It is suggested that
more attention is paid to discussions of balancing rights and freedoms in COVID
control restrictions. To convince opposers of restrictions, supporters of
restrictions should base arguments around communal rights and positive
freedoms. It is also important to critically evaluate whether and how these
perspectives need to be adapted to be appropriate and resonant in democratic
and individualistic countries.


  We prove a number of results to the effect that generic quantum graphs
(defined via operator systems as in the work of Duan-Severini-Winter / Weaver)
have few symmetries: for a Zariski-dense open set of tuples $(X_1,\cdots,X_d)$
of traceless self-adjoint operators in the $n\times n$ matrix algebra the
corresponding operator system has trivial automorphism group, in the largest
possible range for the parameters: $2\le d\le n^2-3$. Moreover, the
automorphism group is generically abelian in the larger parameter range $1\le
d\le n^2-2$. This then implies that for those respective parameters the
corresponding random-quantum-graph model built on the GUE ensembles of $X_i$'s
(mimicking the Erd\H{o}s-R\'{e}nyi $G(n,p)$ model) has trivial/abelian
automorphism group almost surely.


  The recent WMAP data have confirmed that exotic dark matter together with the
vacuum energy (cosmological constant) dominate in the flat Universe. Thus the
direct dark matter detection, consisting of detecting the recoiling nucleus, is
central to particle physics and cosmology. Supersymmetry provides a natural
dark matter candidate, the lightest supersymmetric particle (LSP). The relevant
cross sections arise out of two mechanisms: i) The coherent mode, due to the
scalar interaction and ii) The spin contribution arising from the axial
current. In this paper we will focus on the spin contribution, which is
expected to dominate for light targets.
  For both modes it is possible to obtain detectable rates, but in most models
the expected rates are much lower than the present experimental goals. So one
should exploit two characteristic signatures of the reaction, namely the
modulation effect and, in directional experiments, the correlation of the event
rates with the sun's motion.
  In standard non directional experiments the modulation is small, less than
two per cent. In the case of the directional event rates we like to suggest
that the experiments exploit two features, of the process, which are
essentially independent of the SUSY model employed, namely: 1) The
forward-backward asymmetry, with respect to the sun's direction of motion, is
very large and 2) The modulation is much larger, especially if the observation
is made in a plane perpendicular to the sun's velocity. In this case the
difference between maximum and minimum can be larger than 40 per cent and the
phase of the Earth at the maximum is direction dependent.


  In an interactive belief model, are the players "commonly meta-certain" of
the model itself? This paper formalizes such implicit "common meta-certainty"
assumption. To that end, the paper expands the objects of players' beliefs from
events to functions defined on the underlying states. Then, the paper defines a
player's belief-generating map: it associates, with each state, whether a
player believes each event at that state. The paper formalizes what it means
by: "a player is (meta-)certain of her own belief-generating map" or "the
players are (meta-)certain of the profile of belief-generating maps (i.e., the
model)." The paper shows: a player is (meta-)certain of her own
belief-generating map if and only if her beliefs are introspective. The players
are commonly (meta-)certain of the model if and only if, for any event which
some player i believes at some state, it is common belief at the state that
player i believes the event. This paper then asks whether the "common
meta-certainty" assumption is needed for an epistemic characterization of
game-theoretic solution concepts. The paper shows: if each player is logical
and (meta-)certain of her own strategy and belief-generating map, then each
player correctly believes her own rationality. Consequently, common belief in
rationality alone leads to actions that survive iterated elimination of
strictly dominated actions.


  We propose that the broad $1^{--}$ resonance structure recently discovered by
BES in $J/\psi\to K^{+}K^{-}\pi^{0}$ is the P-wave excitation of a
diquark-antidiquark bound state. This interpretation implies that there exists
a negative parity, vector nonet. A rough estimate of the mass spectrum of the
nonet is presented, and the prediction for the mass of X(1576) is consistent
with the experimental data. The OZI allowed strong decays are studied, it can
decay into two pseudoscalars or one pseudoscalar plus one vector meson. A
crucial prediction is that X(1576) should dominantly decay into $K^{+}K^{-}$,
$K_{L}K_{S}$, $\phi\pi^{0}$. Since the isospin of X(1576) is $\mathbf{1}$, the
observation of $I_3=1$ or $I_3=-1$ states which predominantly decays into
strange mesons could provide another important test to our proposal. To search
the charged $I_3=1$ isospin partner associated with X(1576) in $J/\psi\to
\eta\pi^{+}\pi^{-}$, $J/\psi\to K^{+}K_{L}\pi^{-}$, $J/\psi\to
K^{+}K_{S}\pi^{-}$, $J/\psi\to \phi\pi^{+}\pi^{-}$ is suggested.


  These are general notes on tensor calculus which can be used as a reference
for an introductory course on tensor algebra and calculus. A basic knowledge of
calculus and linear algebra with some commonly used mathematical terminology is
presumed.


  Multiplayer games have long been used as testbeds in artificial intelligence
research, aptly referred to as the Drosophila of artificial intelligence.
Traditionally, researchers have focused on using well-known games to build
strong agents. This progress, however, can be better informed by characterizing
games and their topological landscape. Tackling this latter question can
facilitate understanding of agents and help determine what game an agent should
target next as part of its training. Here, we show how network measures applied
to response graphs of large-scale games enable the creation of a landscape of
games, quantifying relationships between games of varying sizes and
characteristics. We illustrate our findings in domains ranging from canonical
games to complex empirical games capturing the performance of trained agents
pitted against one another. Our results culminate in a demonstration leveraging
this information to generate new and interesting games, including mixtures of
empirical games synthesized from real world games.


  The thermal conductivity, $\kappa$, of the heavy fermion superconductor
UPt$_3$ was measured down to T$_c$/10. The absence of a linear term in the
temperature dependence as T$\rightarrow$0 strongly suggests there are no zero
energy quasiparticle excitations, in contradiction with the gapless behaviour
often inferred from specific heat. A non-vanishing anisotropy ratio
$\kappa_c$/$\kappa_b$ as T$\rightarrow$0 establishes a new property of the gap
structure: the presence of nodes along the c-axis. Furthermore, recent
calculations by Fledderjohann and Hirschfeld show these cannot be point nodes
with a linear k-dependence.


  Renling Jin proved that if A and B are two subsets of the natural numbers
with positive Banach density, then A+B is piecewise syndetic. In this paper, we
prove that, under various assumptions on positive lower or upper densities of A
and B, there is a high density set of witnesses to the piecewise syndeticity of
A+B. Most of the result are shown to hold more generally for subsets of Z^d.
The key technical tool is a Lebesgue density theorem for measure spaces induced
by cuts in the nonstandard integers.


  The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been
mutating since it was first sequenced in early January 2020. The genetic
variants have developed into a few distinct clusters with different properties.
Since the United States (US) has the highest number of viral infected patients
globally, it is essential to understand the US SARS-CoV-2. Using genotyping,
sequence-alignment, time-evolution, $k$-means clustering, protein-folding
stability, algebraic topology, and network theory, we reveal that the US
SARS-CoV-2 has four substrains and five top US SARS-CoV-2 mutations were first
detected in China (2 cases), Singapore (2 cases), and the United Kingdom (1
case). The next three top US SARS-CoV-2 mutations were first detected in the
US. These eight top mutations belong to two disconnected groups. The first
group consisting of 5 concurrent mutations is prevailing, while the other group
with three concurrent mutations gradually fades out. Our analysis suggests that
female immune systems are more active than those of males in responding to
SARS-CoV-2 infections. We identify that one of the top mutations,
27964C$>$T-(S24L) on ORF8, has an unusually strong gender dependence. Based on
the analysis of all mutations on the spike protein, we further uncover that
three of four US SASR-CoV-2 substrains become more infectious. Our study calls
for effective viral control and containing strategies in the US.


  We develope a new scheme for the construction of explicit complex-valued
proper biharmonic functions on Riemannian Lie groups. We exploit this and
manufacture many infinite series of uncountable families of new solutions on
the special unitary group $SU(n)$. We then show that the special orthogonal
group $SO(n)$ and the quaternionic unitary group $Sp(n)$ fall into the scheme.
As a by-product we obtain new harmonic morphisms on these groups. All the
constructed maps are defined on open and dense subsets of the corresponding
spaces.


  The scarcity of free-hand sketch presents a challenging problem. Despite the
emergence of some large-scale sketch datasets, these datasets primarily consist
of sketches at the single-object level. There continues to be a lack of
large-scale paired datasets for scene sketches. In this paper, we propose a
self-supervised method for scene sketch generation that does not rely on any
existing scene sketch, enabling the transformation of single-object sketches
into scene sketches. To accomplish this, we introduce a method for vector
sketch captioning and sketch semantic expansion. Additionally, we design a
sketch generation network that incorporates a fusion of multi-modal perceptual
constraints, suitable for application in zero-shot image-to-sketch downstream
task, demonstrating state-of-the-art performance through experimental
validation. Finally, leveraging our proposed sketch-to-sketch generation
method, we contribute a large-scale dataset centered around scene sketches,
comprising highly semantically consistent "text-sketch-image" triplets. Our
research confirms that this dataset can significantly enhance the capabilities
of existing models in sketch-based image retrieval and sketch-controlled image
synthesis tasks. We will make our dataset and code publicly available.


  We study the consequences of timelike and spaccelike conformal Ricci and
conformal matter collineations for anisotropic fluid in the context of General
Relativity. Necessary and sufficient conditions are derived for a spacetime
with anisotropic fluid to admit conformal Ricci and conformal matter
collineations parallel to u^a and x^a. These conditions for timelike and
spacelike conformal Ricci and conformal matter collineations for anisotropic
fluid reduce to the conditions of perfect fluid when the heat flux and the
traceless anisotropic stress tensor vanish. Further, for $\alpha=0$ (the
conformal factor), we recover the earlier results of Ricci collineations and
matter collineations in each case of timelike and spacelike conformal Ricci
collineations and conformal matter collineations for the perfect fluid. Thus
our results give the generalization of the results already available in the
literature. It is worth noticing that the conditions of conformal matter
collineations can be derived from the conditions of conformal Ricci
collineations or vice versa under certain constraints.


  Uncertainty sampling in active learning is heavily used in practice to reduce
the annotation cost. However, there has been no wide consensus on the function
to be used for uncertainty estimation in binary classification tasks and
convergence guarantees of the corresponding active learning algorithms are not
well understood. The situation is even more challenging for multi-category
classification. In this work, we propose an efficient uncertainty estimator for
binary classification which we also extend to multiple classes, and provide a
non-asymptotic rate of convergence for our uncertainty sampling-based active
learning algorithm in both cases under no-noise conditions (i.e., linearly
separable data). We also extend our analysis to the noisy case and provide
theoretical guarantees for our algorithm under the influence of noise in the
task of binary and multi-class classification.


  We show the strength of the Fourier modal method (FMM) for numerically
investigating the optical properties of vertical cavities including
subwavelength gratings. Three different techniques for determining the
resonance frequency and Q-factor of a cavity mode are compared. Based on that,
the Fabry-Perot approach has been chosen due to its numerical efficiency. The
computational uncertainty in determining the resonance frequency and Q-factor
is investigated, showing that the uncertainty in the Q-factor calculation can
be a few orders of magnitude larger than that in the resonance frequency
calculation. Moreover, a method for reducing 3D simulations to
lower-dimensional simulations is suggested, and is shown to enable approximate
and fast simulations of certain device parameters. Numerical calculation of the
cavity dispersion, which is an important characteristic of vertical cavities,
is illustrated. By employing the implemented FMM, it is shown that adiabatic
heterostructures designs are advantageous compared to abrupt heterostructures
for minimizing the cavity scattering loss.


  Corresponding to Fresnel transform there exists a unitary operator in quantum
optics theory, which could be named Fresnel operator (FO). We show that the
multiplication rule of FO naturally leads to the quantum optical ABCD law. The
canonical operator methods as mapping of ray-transfer ABCD matrix is explicitly
shown by FO's normally ordered expansion through the coherent state
representation and the technique of integration within an ordered product of
operators. We show that time evolution of the damping oscillator embodies the
quantum optical ABCD law.


  A possible explanation is given for the anomalous $T^{3/2}$ temperature
dependence of the electrical resistivity of MnSi, which is observed in the
high-pressure paramagnetic state. The unusual Fermi surface of MnSi includes
large open sheets that intersect along the faces of the cubic Brillouin zone.
Close to these intersections, long-wavelength interband magnetic spin
fluctuations can scatter electrons from one sheet to the other. The current
relaxation rate due to such interband scattering events is not reduced by
vertex corrections as is that for scattering from intraband ferromagnetic
fluctuations. Consequently, current relaxation proceeds in a manner similar to
that occurring in nearly antiferromagnetic metals, in which low-temperature
$T^{3/2}$ behavior is well known. It is argued that this type of
non-Fermi-liquid behavior can, for a metal with ferromagnetic fluctuations near
Fermi sheet intersections, persist over a much wider temperature range than it
does in nearly antiferromagnetic metals.


  A recent result of Zheng and Tse states that over a quasi-static channel,
there exists a fundamental tradeoff, referred to as the diversity-multiplexing
gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity
gain that can be simultaneously achieved by a space-time (ST) block code. This
tradeoff is precisely known in the case of i.i.d. Rayleigh-fading, for T>=
n_t+n_r-1 where T is the number of time slots over which coding takes place and
n_t,n_r are the number of transmit and receive antennas respectively. For T <
n_t+n_r-1, only upper and lower bounds on the D-MG tradeoff are available.
  In this paper, we present a complete solution to the problem of explicitly
constructing D-MG optimal ST codes, i.e., codes that achieve the D-MG tradeoff
for any number of receive antennas. We do this by showing that for the square
minimum-delay case when T=n_t=n, cyclic-division-algebra (CDA) based ST codes
having the non-vanishing determinant property are D-MG optimal. While
constructions of such codes were previously known for restricted values of n,
we provide here a construction for such codes that is valid for all n.
  For the rectangular, T > n_t case, we present two general techniques for
building D-MG-optimal rectangular ST codes from their square counterparts. A
byproduct of our results establishes that the D-MG tradeoff for all T>= n_t is
the same as that previously known to hold for T >= n_t + n_r -1.


  For any countable $CW$-complex $K$ and a cardinal number $\tau\geq\omega$ we
construct a completely metrizable space $X(K,\tau)$ of weight $\tau$ with the
following properties: $\e X(K,\tau)\leq K$, $X(K,\tau)$ is an absolute extensor
for all normal spaces $Y$ with $\e Y\leq K$, and for any completely metrizable
space $Z$ of weight $\leq\tau$ and $\e Z\leq K$ the set of closed embeddings
$Z\to X(K,\tau)$ is dense in the space $C(Z,X(K,\tau))$ of all continuous maps
from $Z$ into $X(K,\tau)$ endowed with the limitation topology. This result is
applied to prove the existence of universal spaces for all metrizable spaces of
given weight and with a given cohomological dimension.


  The effective classical/quantum dynamics of a particle constrained on a
closed line embedded in a higher dimensional configuration space is analyzed.
By considering explicit examples it is shown how different reduction mechanisms
produce unequivalent dynamical behaviors. The relation with a formal treatment
of the constraint is discussed. While classically it is always possible to
strictly enforce the constraint by setting to zero the energy stored in the
motion normal to the constraint surface, the quantum description is far more
sensitive to the reduction mechanism. Not only quantum dynamics is plagued by
the usual ambiguities inherent to the quantization procedure, but also in some
cases the constraint's equations do not contain all the necessary information
to reconstruct the effective motion.


  The computation of many correlation functions in lattice QCD is severely
hindered by a signal-to-noise problem. Recent developments in the factorization
of both the fermion propagator and determinant pave the way for the
implementation of multi-level Monte Carlo integration techniques for lattice
QCD. In these proceedings we introduce new strategies for the estimation of the
factorized contribution to the connected and disconnected diagrams for meson
two-point functions. An estimator for the factorized connected diagram is
constructed sequentially for a two-level integration scheme. For the
disconnected diagram, we introduce an improved estimator by performing a
frequency-splitting of traces, applicable with or without multi-level
integration. Preliminary results in the quenched theory with a two-level
integration scheme are presented.


  In this article we introduce Graph Generation, an enhanced Column Generation
(CG) algorithm for solving expanded linear programming relaxations of mixed
integer linear programs. To apply Graph Generation, we must be able to map any
given column to a small directed acyclic graph for which any path from source
to sink describes a feasible column. This structure is easily satisfied for
vehicle routing and crew scheduling problems; and other such problems where
pricing is a resource constrained shortest path problem. Such graphs are then
added to the restricted master problem (RMP) when the corresponding column is
generated during pricing. The use of Graph Generation does not weaken the
linear programming relaxation being solved. At any given iteration of CG
enhanced by Graph Generation; the technique permits the RMP to express a much
wider set of columns than those generated during pricing, leading to faster
convergence of CG. Graph Generation does not change the structure of the CG
pricing problem. We show how the method can be applied in a general way, and
then demonstrate the effectiveness of our approach on the classical Capacitated
Vehicle Routing Problem.


  A dedicated 4{\pi}{\beta} (LS)-{\gamma} (HPGe)digital coincidence system has
been developed in this work, which includes five acquisition channels. Three
analog-to-digital converter (ADC) acquisition channels with an acquisition
resolution of 8 bits and acquisition rate of 1GSPS (sample per second) are
utilized to collect the signals from three Photo multiplier tubes (PMTs) which
are adopted to detect {\beta} decay, and two acquisition channels with an
acquisition resolution of 16 bits and acquisition rate of 50MSPS are utilized
to collect the signals from high-purity germanium (HPGe) which are adopted to
detect {\gamma} decay. In order to increase the accuracy of the coincidence
system, all the five acquisition channels are synchronous within 500ps. The
data collected by the five acquisition channels will be transmitted to the host
PC through PCI bus and saved as a file. Off-line software is applied for the
4{\pi}{\beta} (LS)-{\gamma} (HPGe) coincidence and data analysis as needed in
practical application. With all the above preconditions, the flexibility of the
system is increased, and the structure and application of the system are
simplified. According to the test, the highest coincidence rate of the system
is 20K per second, which is sufficient for most applications. This paper mainly
introduces the design of the hardware, the synchronization method and the test
result of this system.


  While the field of 3D scene reconstruction is dominated by NeRFs due to their
photorealistic quality, 3D Gaussian Splatting (3DGS) has recently emerged,
offering similar quality with real-time rendering speeds. However, both methods
primarily excel with well-controlled 3D scenes, while in-the-wild data -
characterized by occlusions, dynamic objects, and varying illumination -
remains challenging. NeRFs can adapt to such conditions easily through
per-image embedding vectors, but 3DGS struggles due to its explicit
representation and lack of shared parameters. To address this, we introduce
WildGaussians, a novel approach to handle occlusions and appearance changes
with 3DGS. By leveraging robust DINO features and integrating an appearance
modeling module within 3DGS, our method achieves state-of-the-art results. We
demonstrate that WildGaussians matches the real-time rendering speed of 3DGS
while surpassing both 3DGS and NeRF baselines in handling in-the-wild data, all
within a simple architectural framework.


  Numerous machine learning (ML) models employed in protein function and
structure prediction depend on evolutionary information, which is captured
through multiple-sequence alignments (MSA) or position-specific scoring
matrices (PSSM) as generated by PSI-BLAST. Consequently, these predictive
methods are burdened by substantial computational demands and prolonged
computing time requirements. The principal challenge stems from the necessity
imposed on the PSI-BLAST software to load large sequence databases sequentially
in batches and then search for sequence alignments akin to a given query
sequence. In the case of batch queries, the runtime scales even linearly. The
predicament at hand is becoming more challenging as the size of bio-sequence
data repositories experiences exponential growth over time and as a
consequence, this upward trend exerts a proportional strain on the runtime of
PSI-BLAST. To address this issue, an eminent resolution lies in leveraging the
MMseqs2 method, capable of expediting the search process by a magnitude of 100.
However, MMseqs2 cannot be directly employed to generate the final output in
the desired format of PSI-BLAST alignments and PSSM profiles. In this research
work, I developed a comprehensive pipeline that synergistically integrates both
MMseqs2 and PSI-BLAST, resulting in the creation of a robust, optimized, and
highly efficient hybrid alignment pipeline. Notably, the hybrid tool exhibits a
significant speed improvement, surpassing the runtime performance of PSI-BLAST
in generating sequence alignment profiles by a factor of two orders of
magnitude. It is implemented in C++ and is freely available under the MIT
license at https://github.com/issararab/EPSAPG.


  Security of an information system is only as strong as its weakest element.
Popular elements of such system include hardware, software, network and people.
Current approaches to computer security problems usually exclude people in
their studies even though it is an integral part of these systems. To fill that
gap, this paper discusses crucial people-related problems in computer security
and proposes a method of improving security in such systems by integrating
people tightly into the whole system. The integration is implemented via
visualization to provide visual feedbacks and capture people's awareness of
their actions and consequent results. By doing it, we can improve system
usability, shorten user's learning curve, and hence enable user uses computer
systems more securely.


  Bulk materials possessing a relative electric permittivity $\varepsilon$
close to zero exhibit giant Kerr nonlinearities. However, harnessing this
response in guided-wave geometries is not straightforward, due to the extreme
and counter-intuitive properties of epsilon-near-zero materials. Here we
investigate, through rigorous calculations of the Kerr nonlinear coefficient,
how the remarkable nonlinear properties of such materials can be exploited in
several different types of structures, including bulk films, plasmonic
nanowires, and metal nanoapertures. We find the largest Kerr nonlinear response
when both the modal area and the group velocity are simultaneously minimized,
corresponding to omnidirectional field enhancement. The physical insights
developed will be key for understanding and engineering nonlinear nanophotonic
systems with extreme nonlinearities and point to new design paradigms.


  In this paper, a novel semi-quantum key distribution (SQKD) protocol is
designed based on single photons in both polarization and spatial-mode degrees
of freedom, which allows to establish a raw key between one quantum communicant
and one classical communicant. The proposed SQKD protocol only adopts one kind
of quantum state as the initial quantum resource. The detailed security
analysis shows that it can resist Eve's active attacks, such as the
intercept-resend attack, the measure-resend attack, the Trojan horse attack and
the entangle-measure attack. The proposed SQKD protocol only needs single
photons in both polarization and spatial-mode degrees of freedom as quantum
resource and employs single-photon measurements. Thus, it has excellent
feasibility, since the preparation and the measurement of a single photon in
both polarization and spatial-mode degrees of freedom can be easily acheived
with present quantum technologies.


  Among the critical challenges around the COVID-19 pandemic is dealing with
the potentially detrimental effects on people's mental health. Designing
appropriate interventions and identifying the concerns of those most at risk
requires methods that can extract worries, concerns and emotional responses
from text data. We examine gender differences and the effect of document length
on worries about the ongoing COVID-19 situation. Our findings suggest that i)
short texts do not offer as adequate insights into psychological processes as
longer texts. We further find ii) marked gender differences in topics
concerning emotional responses. Women worried more about their loved ones and
severe health concerns while men were more occupied with effects on the economy
and society. This paper adds to the understanding of general gender differences
in language found elsewhere, and shows that the current unique circumstances
likely amplified these effects. We close this paper with a call for more
high-quality datasets due to the limitations of Tweet-sized data.


  The synchronisation between rotating turbulent flows in periodic boxes is
investigated numerically. The flows are coupled via a master-slave coupling,
taking the Fourier modes with wavenumber below a given value $k_m$ as the
master modes. It is found that synchronisation happens when $k_m$ exceeds a
threshold value $k_c$, and $k_c$ depends strongly on the forcing scheme. In
rotating Kolmogorov flows, $k_c\eta$ does not change with rotation in the range
of rotation rates considered, $\eta$ being the Kolmogorov length scale. Even
though the energy spectrum has a steeper slope, the value of $k_c\eta$ is the
same as that found in isotropic turbulence. In flows driven by a forcing term
maintaining constant energy injection rate, synchronisation becomes easier when
rotation is stronger. $k_c\eta$ decreases with rotation, and it is reduced
significantly for strong rotations when the slope of the energy spectrum
approaches $-3$. It is shown that the conditional Lyapunov exponent for a given
$k_m$ is reduced by rotation in the flows driven by the second type of forcing,
but it increases mildly with rotation for the Kolmogorov flows. The local
conditional Lyapunov exponents fluctuate more strongly as rotation is
increased, although synchronisation occurs as long as the average conditional
Lyapunov exponents are negative. We also look for the relationship between
$k_c$ and the energy spectra of the Lyapunov vectors. We find that the spectra
always seem to peak around $k_c$, and synchronisation fails when the energy
spectra of the conditional Lyapunov vectors have a local maximum in the slaved
modes.


  In this paper we develop a Bayesian statistical inference approach to the
unified analysis of isobaric labelled MS/MS proteomic data across multiple
experiments. An explicit probabilistic model of the log-intensity of the
isobaric labels' reporter ions across multiple pre-defined groups and
experiments is developed. This is then used to develop a full Bayesian
statistical methodology for the identification of differentially expressed
proteins, with respect to a control group, across multiple groups and
experiments. This methodology is implemented and then evaluated on simulated
data and on two model experimental datasets (for which the differentially
expressed proteins are known) that use a TMT labelling protocol.


  The Cosmic Dark Ages represent the period in the early evolution of the
Universe, starting immediately after the decoupling of CMB photons from matter,
and ending with the formation of the first stars and galaxies. The HI signal
from the neutral hydrogen atoms is the only mechanism for us to understand this
crucial phase in the cosmological history of the Universe and answer
fundamental questions about the validity of the standard cosmological model,
dark matter physics, and inflation. Due to cosmological redshift, this signal
is now only observable in the 3-30~MHz frequency band, which is blocked from
reaching the surface of the Earth by the ionosphere. In this paper, we present
the design of the Lunar Crater Radio Telescope that intends to carry out
unprecedented measurements of this signal by deploying a kilometer-sized
parabolic reflector mesh inside a lunar crater on the far side of the Moon and
suspending a receiver at its focus.


  A new formalism is given for the renormalization of quantum field theories to
all orders of perturbation theory, in which there are manifestly no overlapping
divergences. We prove the BPH theorem in this formalism, and show how the local
subtractions add up to counterterms in the action. Applications include the
renormalization of lattice perturbation theory, the decoupling theorem,
Zimmermann oversubtraction, the renormalization of operator insertions, and the
operator product expansion.


  The limitations of Hall MHD as a model for turbulence in weakly collisional
plasmas are explored using quantitative comparisons to Vlasov-Maxwell kinetic
theory over a wide range of parameter space. The validity of Hall MHD in the
cold ion limit is shown, but spurious undamped wave modes exist in Hall MHD
when the ion temperature is finite. It is argued that turbulence in the
dissipation range of the solar wind must be one, or a mixture, of three
electromagnetic wave modes: the parallel whistler, oblique whistler, or kinetic
Alfven waves. These modes are generally well described by Hall MHD. Determining
the applicability of linear kinetic damping rates in turbulent plasmas requires
a suite of fluid and kinetic nonlinear numerical simulations. Contrasting fluid
and kinetic simulations will also shed light on whether the presence of
spurious wave modes alters the nonlinear couplings inherent in turbulence and
will illuminate the turbulent dynamics and energy transfer in the regime of the
characteristic ion kinetic scales.


  Let $LG_n$ denote the Lagrangian Grassmannian parametrizing maximal isotropic
(Lagrangian) subspaces of a fixed symplectic vector space of dimension $2n.$
For each strict partition $\lambda=(\lambda_1,...,\lambda_k)$ with
$\lambda_1\leq n$ there is a Schubert variety $X(\lambda).$ Let $T$ denote a
maximal torus of the symplectic group acting on $LG_n.$ Consider the
$T$-equivariant cohomology of $LG_n$ and the $T$-equivariant fundamental class
$\sigma(\lambda)$ of $X(\lambda).$ The main result of the present paper is an
explicit formula for the restriction of the class $\sigma(\lambda)$ to any
torus fixed point. The formula is written in terms of factorial analogue of the
Schur $Q$-function, introduced by Ivanov. As a corollary to the restriction
formula, we obtain an equivariant version of the Giambelli-type formula for
$LG_n.$ As another consequence of the main result, we obtained a presentation
of the ring $H_T^*(LG_n).$


  Boltzmann machines (BMs) are appealing candidates for powerful priors in
variational autoencoders (VAEs), as they are capable of capturing nontrivial
and multi-modal distributions over discrete variables. However,
non-differentiability of the discrete units prohibits using the
reparameterization trick, essential for low-noise back propagation. The Gumbel
trick resolves this problem in a consistent way by relaxing the variables and
distributions, but it is incompatible with BM priors. Here, we propose the
GumBolt, a model that extends the Gumbel trick to BM priors in VAEs. GumBolt is
significantly simpler than the recently proposed methods with BM prior and
outperforms them by a considerable margin. It achieves state-of-the-art
performance on permutation invariant MNIST and OMNIGLOT datasets in the scope
of models with only discrete latent variables. Moreover, the performance can be
further improved by allowing multi-sampled (importance-weighted) estimation of
log-likelihood in training, which was not possible with previous models.


  We consider the robust version of items selection problem, in which the goal
is to choose representatives from a family of sets, preserving constraints on
the allowed items' combinations. We prove NP-hardness of the deterministic
version, and establish polynomially solvable special cases. Next, we consider
the robust version in which we aim at minimizing the maximum regret of the
solution under interval parameter uncertainty. We show that this problem is
hard for the second level of polynomial-time hierarchy. We develop an exact
solution algorithm for the robust problem, based on cut generation, and present
the results of computational experiments.