  We study closed subspaces of $L^2(X)$, where $(X, \mu)$ is a $\sigma$-finite
measure space, that are invariant under the unitary representation associated
to a measurable action of a discrete countable LCA group $\Gamma$ on $X$. We
provide a complete description for these spaces in terms of range functions and
a suitable generalized Zak transform. As an application of our main result, we
prove a characterization of frames and Riesz sequences in $L^2(X)$ generated by
the action of the unitary representation under consideration on a countable set
of functions in $L^2(X)$. Finally, closed subspaces of $L^2(G)$, for $G$ being
an LCA group, that are invariant under translations by elements on a closed
subgroup $\Gamma$ of $G$ are studied and characterized.


  This article presents an overview of the idea that "information compression
by multiple alignment, unification and search" (ICMAUS) may serve as a unifying
principle in computing (including mathematics and logic) and in such aspects of
human cognition as the analysis and production of natural language, fuzzy
pattern recognition and best-match information retrieval, concept hierarchies
with inheritance of attributes, probabilistic reasoning, and unsupervised
inductive learning. The ICMAUS concepts are described together with an outline
of the SP61 software model in which the ICMAUS concepts are currently realised.
A range of examples is presented, illustrated with output from the SP61 model.


  This paper improves previously known bounds on the determinant of 0-1
matrices where each row has fixed support size. This uses a method based on
Scheinerman's, with new analyses to improve upon his conjectures.


  The primary issue in inverse halftoning is removing noisy dots on flat areas
and restoring image structures (e.g., lines, patterns) on textured areas.
Hence, a new structure-aware deep convolutional neural network that
incorporates two subnetworks is proposed in this paper. One subnetwork is for
image structure prediction while the other is for continuous-tone image
reconstruction. First, to predict image structures, patch pairs comprising
continuous-tone patches and the corresponding halftoned patches generated
through digital halftoning are trained. Subsequently, gradient patches are
generated by convolving gradient filters with the continuous-tone patches. The
subnetwork for the image structure prediction is trained using the mini-batch
gradient descent algorithm given the halftoned patches and gradient patches,
which are fed into the input and loss layers of the subnetwork, respectively.
Next, the predicted map including the image structures is stacked on the top of
the input halftoned image through a fusion layer and fed into the image
reconstruction subnetwork such that the entire network is trained adaptively to
the image structures. The experimental results confirm that the proposed
structure-aware network can remove noisy dot-patterns well on flat areas and
restore details clearly on textured areas. Furthermore, it is demonstrated that
the proposed method surpasses the conventional state-of-the-art methods based
on deep convolutional neural networks and locally learned dictionaries.


  Electroencephalography (EEG) signals' interpretation is based on waveform
analysis, where meaningful information should emerge from a plethora of data.
Nonetheless, the continuous increase in computational power and the development
of new data processing algorithms in the recent years have put into reach the
possibility of analysing raw EEG signals. Bearing that motivation, the authors
propose a new approach using raw data EEG signals and deep learning neural
networks, for the classification of motor activities (executed and imagery).
The hypothesis to be presented here is: each instantaneous measurement of the
raw signal of all EEG channels (superchord) is unique per motor activity
regardless the moment of measurement. This study has confirmed the hypothesis
(results with accuracy over 80%, mean for 109 subjects), reinforcing the need
of further research for the understanding of mental processes.


  Causal discovery (CD) from time-varying data is important in neuroscience,
medicine, and machine learning. Techniques for CD encompass randomized
experiments, which are generally unbiased but expensive, and algorithms such as
Granger causality, conditional-independence-based, structural-equation-based,
and score-based methods that are only accurate under strong assumptions made by
human designers. However, as demonstrated in other areas of machine learning,
human expertise is often not entirely accurate and tends to be outperformed in
domains with abundant data. In this study, we examine whether we can enhance
domain-specific causal discovery for time series using a data-driven approach.
Our findings indicate that this procedure significantly outperforms
human-designed, domain-agnostic causal discovery methods, such as Mutual
Information, VAR-LiNGAM, and Granger Causality on the MOS 6502 microprocessor,
the NetSim fMRI dataset, and the Dream3 gene dataset. We argue that, when
feasible, the causality field should consider a supervised approach in which
domain-specific CD procedures are learned from extensive datasets with known
causal relationships, rather than being designed by human specialists. Our
findings promise a new approach toward improving CD in neural and medical data
and for the broader machine learning community.


  We study the elastic response of rigid, wire frame particles in concentrated,
glassy suspensions to a step strain by applying the simple, geometric methods
developed in part I. The wire frame particles are comprised of thin, rigid rods
of length $L$ and their number density, $\rho$, is such that $\rho L^3 \gg 1$.
We specifically compare rigid rods to L-shapes made of two equal length rods
joined at right angles. The behaviour of wire frames is found to be strikingly
different from that of rods. The linear elasticity scales like $\rho^3 L^6$ for
L-shaped particles, whereas it scales proportional to $\rho$ for rods and the
non-linear response shows a transition from shear hardening to shear softening
at a critical density $\rho_c \sim \sqrt{K / k_B T L^6}$, where $K$ is the
bending modulus of the particles. For realistic particles made of double
stranded DNA, this transition occurs at densities of about $\rho L^3 \sim 10$.
The reason for these differences is that wire frames can be forced to bend by
the entanglements with their surroundings, whereas rods always remain straight.
This is found to be very important even for small strains, with most particles
being bent above a critical strain $\gamma_c \sim (\rho L^3)^{-1}$.


  The left-invariant sub-Riemannian problem on the group of motions of a plane
is considered. Sub-Riemannian geodesics are parametrized by Jacobi's functions.
Discrete symmetries of the problem generated by reflections of pendulum are
described. The corresponding Maxwell points are characterized, on this basis an
upper bound on the cut time is obtained.


  A model for the joint evolution of opinions and how much the agents trust
each other is presented. The model is built using the framework of the
Continuous Opinions and Discrete Actions (CODA) model. Instead of a fixed
probability that the other agents will decide in the favor of the best choice,
each agent considers that other agents might be one one of two types:
trustworthy or useless. Trustworthy agents are considered more likely to be
right than wrong, while the opposite holds for useless ones. Together with the
opinion about the discussed issue, each agent also updates that probability for
each one of the other agents it interacts withe probability each one it
interacts with is of one type or the other. The dynamics of opinions and the
evolution of the trust between the agents are studied. Clear evidences of the
existence of two phases, one where strong polarization is observed and the
other where a clear division is permanent and reinforced are observed. The
transition seems signs of being a first-order transition, with a location
dependent on both the parameters of the model and the initial conditions. This
happens despite the fact that the trust network evolves much slower than the
opinion on the central issue.


  Differential systems of pure Gaussian type are examples of D-modules on the
complex projective line with an irregular singularity at infinity, and as such
are subject to the Stokes phenomenon. We employ the theory of enhanced
ind-sheaves and the Riemann-Hilbert correspondence for holonomic D-modules of
A. D'Agnolo and M. Kashiwara to describe the Stokes phenomenon topologically.
Using this description, we perform a topological computation of the
Fourier-Laplace transform of a D-module of pure Gaussian type in this
framework, recovering and generalizing a result of C. Sabbah.


  When embedding models of noncommutative geometry inspired black holes into
the peridium of large extra dimensions, it is natural to relate the
noncommutativity scale to the higher-dimensional Planck scale. If the Planck
scale is of the order of a TeV, noncommutative geometry inspired black holes
could become accessible to experiments. In this paper, we present a detailed
phenomenological study of the production and decay of these black holes at the
Large Hadron Collider (LHC). Noncommutative inspired black holes are relatively
cold and can be well described by the microcanonical ensemble during their
entire decay. One of the main consequences of the model is the existence of a
black hole remnant. The mass of the black hole remnant increases with
decreasing mass scale associated with noncommutative and decreasing number of
dimensions. The experimental signatures could be quite different from previous
studies of black holes and remnants at the LHC since the mass of the remnant
could be well above the Planck scale. Although the black hole remnant can be
very heavy, and perhaps even charged, it could result in very little activity
in the central detectors of the LHC experiments, when compared to the usual
anticipated black hole signatures. If this type of noncommutative inspired
black hole can be produced and detected, it would result in an additional mass
threshold above the Planck scale at which new physics occurs.


  We analyze a class of distributed quantized consensus algorithms for
arbitrary static networks. In the initial setting, each node in the network has
an integer value. Nodes exchange their current estimate of the mean value in
the network, and then update their estimation by communicating with their
neighbors in a limited capacity channel in an asynchronous clock setting.
Eventually, all nodes reach consensus with quantized precision. We analyze the
expected convergence time for the general quantized consensus algorithm
proposed by Kashyap et al \cite{Kashyap}. We use the theory of electric
networks, random walks, and couplings of Markov chains to derive an $O(N^3\log
N)$ upper bound for the expected convergence time on an arbitrary graph of size
$N$, improving on the state of art bound of $O(N^5)$ for quantized consensus
algorithms. Our result is not dependent on graph topology. Example of complete
graphs is given to show how to extend the analysis to graphs of given topology.


  We study the interaction of meson-baryon coupled channels carrying quantum
numbers of $\Omega_{cc}$ , $\Omega_{bb}$ and $\Omega_{bc}$ presently under
investigation by the LHCb collaboration. The interaction is obtained from an
extension of the local hidden gauge approach to the heavy quark sector that has
proved to provide accurate results compared to experiment in the case of
$\Omega_{c}$ , $\Xi_{c}$ states and pentaquarks, $P_c$ and $P_{cs}$. We obtain
many bound states, with small decay widths within the space of the chosen
coupled channels. The spin-parity of the states are $J^P={\frac{1}{2}}^-$ for
coupled channels of pseudoscalar-baryon (${\frac{1}{2}}^+$),
$J^P={\frac{3}{2}}^-$ for the case of pseudoscalar-baryon (${\frac{3}{2}}^+$),
$J^P={\frac{1}{2}}^-,{\frac{3}{2}}^-$ for the case of vector-baryon
(${\frac{1}{2}}^+$) and $J^P={\frac{1}{2}}^-,{\frac{3}{2}}^-,{\frac{5}{2}}^-$
for the vector-baryon (${\frac{3}{2}}^+$) channels. We look for poles of the
states and evaluate the couplings to the different channels. The couplings
obtained for the open channels can serve as a guide to see in which reaction
the obtained states are more likely to be observed.


  The possibility of obtaining robust edge state of light by mimicking the
topological properties of solid state system, have brought a profound impact on
optical sciences. With the advent of high-brilliance, accelerator-driven light
sources such as storage rings or X-ray lasers, it has become attractive to
extend the concept of optical topological manipulation to the X-ray regime. In
this paper, we theoretically proposed and experimentally demonstrated the
topological edge state at the interface of two photonic crystals having
different band-gap topological characteristics for X-ray. Remarkably, this
topologically protected edge state is immune to the weak disorder in form of
the thickness disorder and strong disorder in form of the positional disorder
of layers in the structure, as long as the zero-average-effective-mass
condition is satisfied. Our investigation therefore brings the topological
characteristics to the X-ray regime, provides new theoretical tools to study
X-ray optics and may pave way to exploit some important potential applications,
such as the high efficiency band filter in X-ray band.


  In order to coordinate multiple different scheduling objectives from the
perspectives of economy, environment and users, a practical multi-objective
dynamic optimal dispatch model incorporating energy storage and user experience
is proposed for isolated microgrids. In this model, besides Microturbine units,
energy storage is employed to provide spinning reserve services for microgirds;
and furthermore, from the perspective of demand side management, a consumer
satisfaction indicator is developed to measure the quality of user experience.
A two-step solution methodology incorporating multi-objective optimization
(MOO) and decision analysis is put forward to address this model. First, a
powerful heuristic optimization algorithm, called the {\theta}-dominance based
evolutionary algorithm, is used to find a well-distributed set of
Pareto-optimal solutions of the problem. And thereby, the best compromise
solutions (BCSs) are identified from the entire solutions with the use of
decision analysis by integrating fuzzy C-means clustering and grey relation
projection. The simulation results on the modified Oak Ridge National
Laboratory Distributed Energy Control and Communication lab microgrid test
system demonstrate the effectiveness of the proposed approach.


  The current approach for testing the robustness of object detectors suffers
from serious deficiencies such as improper methods of performing
out-of-distribution detection and using calibration metrics which do not
consider both localisation and classification quality. In this work, we address
these issues, and introduce the Self-Aware Object Detection (SAOD) task, a
unified testing framework which respects and adheres to the challenges that
object detectors face in safety-critical environments such as autonomous
driving. Specifically, the SAOD task requires an object detector to be: robust
to domain shift; obtain reliable uncertainty estimates for the entire scene;
and provide calibrated confidence scores for the detections. We extensively use
our framework, which introduces novel metrics and large scale test datasets, to
test numerous object detectors in two different use-cases, allowing us to
highlight critical insights into their robustness performance. Finally, we
introduce a simple baseline for the SAOD task, enabling researchers to
benchmark future proposed methods and move towards robust object detectors
which are fit for purpose. Code is available at https://github.com/fiveai/saod


  We demonstrate on the basis of first-principles calculations that the
formation of carbonate-like moiety in SiO$_2$ could be the intrinsic origin of
negative fixed charge in SiC thermal oxidation. We find that two possible
origins for the negative fixed charges are O-lone-pair state and a negatively
charged CO$_3$ ion in SiO$_2$. Such CO$_3$ ion is able to be formed as a result
of the existence of residual C atoms in SiO$_2$, which are expected to be
emitted from the interface between SiC and SiO$_2$, and the incorporation of H
atoms during wet oxidation.


  We prove that the reciprocal of Fisher information of a log-concave
probability density $X$ in ${\bf{R}}^n$ is concave in $t$ with respect to the
addition of a Gaussian noise $Z_t = N(0, tI_n)$. As a byproduct of this result
we show that the third derivative of the entropy power of a log-concave
probability density $X$ in ${\bf{R}}^n$ is nonnegative in $t$ with respect to
the addition of a Gaussian noise $Z_t$. For log-concave densities this improves
the well-known Costa's concavity property of the entropy power.


  The diffusion of a fractional Brownian particle passing over the saddle point
is studied in the field of the metastable potential. The barrier escaping
probability is found to be greatly related to the fractional exponent $\alpha$.
Properties are revealed to move reversely in the opposite direction of
diffusion when $\alpha$ is relatively large despite of the zero-approximating
effective friction of the system. This is very anomalous to the standard
Brownian motion.


  We introduce a synthetic dataset called Sentences Involving Complex
Compositional Knowledge (SICCK) and a novel analysis that investigates the
performance of Natural Language Inference (NLI) models to understand
compositionality in logic. We produce 1,304 sentence pairs by modifying 15
examples from the SICK dataset (Marelli et al., 2014). To this end, we modify
the original texts using a set of phrases - modifiers that correspond to
universal quantifiers, existential quantifiers, negation, and other concept
modifiers in Natural Logic (NL) (MacCartney, 2009). We use these phrases to
modify the subject, verb, and object parts of the premise and hypothesis.
Lastly, we annotate these modified texts with the corresponding entailment
labels following NL rules. We conduct a preliminary verification of how well
the change in the structural and semantic composition is captured by neural NLI
models, in both zero-shot and fine-tuned scenarios. We found that the
performance of NLI models under the zero-shot setting is poor, especially for
modified sentences with negation and existential quantifiers. After fine-tuning
this dataset, we observe that models continue to perform poorly over negation,
existential and universal modifiers.


  Based upon mesoscale simulations of binary mixtures with very low surface
tension and positive disjoining pressure (frustration), we measure the
correlation length of the stress field within the flowing mixture, as a
function of the frequency of the applied load. Two scaling regimes are clearly
identified, with a sharp crossover between the liquid and solid regions, with
exponent -1/2 and -1, respectively. The crossover correlation length is shown
to be closely connected to the typical scale of the coherent excitations of the
density field, whose collective dynamics is shown to be responsible for
non-trivial rheological effects including the emergence of yield stress.


  We report on a novel stochastic analysis of seismic time series for the
Earth's vertical velocity, by using methods originally developed for complex
hierarchical systems, and in particular for turbulent flows. Analysis of the
fluctuations of the detrended increments of the series reveals a pronounced
change of the shapes of the probability density functions (PDF) of the series'
increments. Before and close to an earthquake the shape of the PDF and the
long-range correlation in the increments both manifest significant changes. For
a moderate or large-size earthquake the typical time at which the PDF undergoes
the transition from a Gaussian to a non-Gaussian is about 5-10 hours. Thus, the
transition represents a new precursor for detecting such earthquakes.


  Current implementations of the Variational Quantum Eigensolver (VQE)
technique for solving the electronic structure problem involve splitting the
system qubit Hamiltonian into parts whose elements commute within their single
qubit subspaces. The number of such parts rapidly grows with the size of the
molecule, this increases the uncertainty in the measurement of the energy
expectation value because elements from different parts need to be measured
independently. To address this problem we introduce a more efficient
partitioning of the qubit Hamiltonian using fewer parts that need to be
measured separately. The new partitioning scheme is based on two ideas: 1)
grouping terms into parts whose eigenstates have a single-qubit product
structure, and 2) devising multi-qubit unitary transformations for the
Hamiltonian or its parts to produce less entangled operators. The first
condition allows the new parts to be measured in the number of involved qubit
consequential one-particle measurements. Advantages of the new partitioning
scheme resulting in several-fold reduction of separately measured terms are
illustrated on the H2 and LiH problems.


  Well characterized sequences of dynamical states play an important role for
motor control and associative neural computation in the brain. Autonomous
dynamics involving sequences of transiently stable states have been termed
associative latching in the context of grammar generation. We propose that
generating functionals allow for a systematic construction of dynamical
networks with well characterized dynamical behavior, such as regular or
intermittent bursting latching dynamics.
  Coupling local, slowly adapting variables to an attractor network allows to
destabilize all attractors, turning them into attractor ruins. The resulting
attractor relict network may show ongoing autonomous latching dynamics. We
propose to use two generating functionals for the construction of attractor
relict networks. The first functional is a simple Hopfield energy functional,
known to generate a neural attractor network. The second generating functional,
which we denote polyhomeostatic optimization, is based on
information-theoretical principles, encoding the information content of the
neural firing statistics. Polyhomeostatic optimization destabilizes the
attractors of the Hopfield network inducing latching dynamics.
  We investigate the influence of stress, in terms of conflicting optimization
targets, on the resulting dynamics. Objective function stress is absent when
the target level for the mean of neural activities is identical for the two
generating functionals and the resulting latching dynamics is then found to be
regular. Objective function stress is present when the respective target
activity levels differ, inducing intermittent bursting latching dynamics. We
propose that generating functionals may be useful quite generally for the
controlled construction of complex dynamical systems.


  Our lives are surrounded by a rich assortment of disordered materials. In
particular, glasses are well known as dense, amorphous materials, whereas gels
exist in low-density, disordered states. Recent progress has provided a
significant step forward in understanding the material properties of glasses,
such as mechanical, vibrational, and transport properties. In contrast, our
understanding of particulate physical gels is still highly limited. Here, using
molecular dynamics simulations, we study a simple model of particulate physical
gels, the Lennard-Jones (LJ) gels, and provide a comprehensive understanding of
their structural, mechanical, and vibrational properties, all of which are
markedly different from those of glasses. First, the LJ gels show sparse,
heterogeneous structures, and the length scale $\xi_s$ of the structures grows
as the density is lowered. Second, the gels are extremely soft, with both shear
$G$ and bulk $K$ moduli being orders of magnitude smaller than those of
glasses. Third, many low-frequency vibrational modes are excited, which form a
characteristic plateau with the onset frequency $\omega_\ast$ in the
vibrational density of states. Structural, mechanical, and vibrational
properties, characterized by $\xi_s$, $G$, $K$, and $\omega_\ast$,
respectively, show power-law scaling behaviors with the density, which
establishes a close relationship between them. Throughout the present work, we
reveal that gels are multiscale, solid-state materials: (i) homogeneous elastic
bodies at long lengths, (ii) heterogeneous elastic bodies with fractal
structures at intermediate lengths, and (iii) amorphous structural bodies at
short lengths.


  If the inverse of a nonsingular polynomial matrix $L$ has a polynomial part
then one can associate with $L$ a module over the ring of proper rational
functions, which is related to the structure of $L$ at infinity. In this paper
we characterize homomorphisms of such modules.


  We study blocks with an abelian defect group and a cyclic inertial quotient
acting freely but not transitively. We prove that when p=2, such blocks are
inertial, i.e. basic Morita equivalent to their Brauer correspondent. Together
with a result of the second author on Singer cycle actions on homocyclic defect
groups, this completes the classification of 2-blocks with a cyclic inertial
quotient acting freely on an abelian defect group.


  Geotagging on social media has become an important proxy for understanding
people's mobility and social events. Research that uses geotags to infer public
opinions relies on several key assumptions about the behavior of geotagged and
non-geotagged users. However, these assumptions have not been fully validated.
Lack of understanding the geotagging behavior prohibits people further
utilizing it. In this paper, we present an empirical study of geotagging
behavior on Twitter based on more than 40 billion tweets collected from 20
million users. There are three main findings that may challenge these common
assumptions. Firstly, different groups of users have different geotagging
preferences. For example, less than 3% of users speaking in Korean are
geotagged, while more than 40% of users speaking in Indonesian use geotags.
Secondly, users who report their locations in profiles are more likely to use
geotags, which may affects the generability of those location prediction
systems on non-geotagged users. Thirdly, strong homophily effect exists in
users' geotagging behavior, that users tend to connect to friends with similar
geotagging preferences.


  A perturbative analysis of a massive Chern-Simons is presented. The mass term
is introduced in a BRST invariant way. With these method we prove that the
number of independent renormalisation of massive Chern-Simons is equal to
topologically massive Yang-Mills and different from pure Chern-Simons.


  We give a definition and study the basic properties of the irregular Hodge
filtration on the exponentially twisted de Rham cohomology of a smooth
quasi-projective complex variety.


  Current study on next POI recommendation mainly explores user sequential
transitions with the fine-grained individual-user POI check-in trajectories
only, which suffers from the severe check-in data sparsity issue. In fact,
coarse-grained signals (i.e., region- and global-level check-ins) in such
sparse check-ins would also benefit to augment user preference learning.
Specifically, our data analysis unveils that user movement exhibits noticeable
patterns w.r.t. the regions of visited POIs. Meanwhile, the global all-user
check-ins can help reflect sequential regularities shared by the crowd. We are,
therefore, inspired to propose the MCMG: a Multi-Channel next POI
recommendation framework with Multi-Granularity signals categorized from two
orthogonal perspectives, i.e., fine-coarse grained check-ins at either
POI/region level or local/global level. Being equipped with three modules
(i.e., global user behavior encoder, local multi-channel encoder, and
region-aware weighting strategy), MCMG is capable of capturing both fine- and
coarse-grained sequential regularities as well as exploring the dynamic impact
of multi-channel by differentiating the region check-in patterns. Extensive
experiments on four real-world datasets show that our MCMG significantly
outperforms state-of-the-art next POI recommendation approaches.


  In this work we construct a general class of exactly solvable
non-relativistic bi-dimensional quantum systems with position-dependent masses
(PDM). These systems are isospectral to a given system with constant mass. The
case of a charged particle with a PDM interacting with an external magnetic
field is included in the present investigation. We apply the approach in order
to construct the SU(2) coherent states in some examples which are isospectral
to the two-dimensional anisotropic harmonic oscillator, and discuss the impact
of the introduction of special non-homogeneous external magnetic fields.


  We introduce a variational Monte Carlo algorithm for approximating
finite-temperature quantum many-body systems, based on the minimization of a
modified free energy. We employ a variety of trial states -- both tensor
networks as well as neural networks -- as variational ans\"atze for our
numerical optimization. We benchmark and compare different constructions in the
above classes, both for one- and two-dimensional problems, with systems made of
up to \(N=100\) spins. Despite excellent results in one dimension, our results
suggest that the numerical ans\"atze employed have certain expressive
limitations for tackling more challenging two-dimensional systems.


  In the warm dense regime, where the electron temperature is increased to the
same order of the Fermi temperature, the dynamical stability of elemental
metals depends on its electronic band structure as well as its crystal
structure. It has been known that phonon hardening occurs due to an enhanced
internal pressure caused by electron excitations as in close-packed simple
metals, whereas phonon softening occurs at a specific point in the Brillouin
zone as in body-centered cubic metals. Here, we investigate the dynamical
stability of binary ordered alloys (Au and Cu) in the L1$_0$ and L1$_2$
structures. By performing first principles calculations on phonon dispersions,
we demonstrate that warm dense Au-Cu systems show phonon hardening behavior
except the lowest frequency phonon mode at point R of AuCu in the L1$_0$
structure. We show that when a phonon mode is stabilized by long-range
interatomic interactions at ambient condition, such a phonon will be
destabilized by the short-range nature of the warm dense matters.


  We perform coupled-cluster calculations of the energies and lifetimes of
single-particle states around the doubly magic nucleus 16O based on chiral
nucleon-nucleon interactions at next-to-next- to-next-to-leading order. To
incorporate effects from the scattering continuum, we solve the coupled-
cluster equations with a Gamow-Hartree-Fock basis. Our calculations for the
1/2+ proton-halo state in 17F and the 1/2+ state in 17O agree well with
experiment, while the calculated spin-orbit splitting between d5/2 and d3/2
states is too small due to the lack of three-nucleon forces. We find that
continuum effects yield a significant amount of additional binding energy for
the 1/2+ and 3/2+ states in 17O and 17F.


  We measure the stress state in and around a deformation nanotwin in a
twinning-induced plasticity (TWIP) steel. Using four-dimensional scanning
transmission electron microscopy (4D-STEM), we measure the elastic strain field
in a 68.2-by-83.1 nm area of interest with a scan step of 0.36 nm and a
diffraction limit resolution of 0.73 nm. The stress field in and surrounding
the twin matches the form expected from analytical theory and is on the order
of 15 GPa, close to the theoretical strength of the material. We infer that the
measured back-stress limits twin thickening, providing a rationale for why TWIP
steel twins remain thin during deformation, continuously dividing grains to
give substantial work hardening. Our results support modern mechanistic
understanding of the influence of twinning on crack propagation and
embrittlement in TWIP steels.


  We construct a theory in which the solution to the strong CP problem is an
emergent property of the background of the dark matter in the Universe. The
role of the axion degree of freedom is played by multi-body collective
excitations similar to spin-waves in the medium of the dark matter of the
Galactic halo. The dark matter is a vector particle whose low energy
interactions with the Standard Model take the form of its spin density coupled
to $G \widetilde{G}$, which induces a potential on the average spin density
inducing it to compensate $\overline{\theta}$, effectively removing CP
violation in the strong sector in regions of the Universe with sufficient dark
matter density. We discuss the viable parameter space, finding that light dark
matter masses within a few orders of magnitude of the fuzzy limit are
preferred, and discuss the associated signals with this type of solution to the
strong CP problem.


  Measurements of normalized differential cross sections for top quark pair
production are performed in the dilepton decay channels in proton-proton
collisions at a center-of-mass energy of 13 TeV. The differential cross
sections are measured with data corresponding to an integrated luminosity of
2.1 fb$^{-1}$ recorded by the CMS experiment at the LHC. We have measured the
cross sections differentially as a function of the kinematic properties of the
leptons (electron or muon), jets from bottom quark hadronization, top quarks,
and top quark pairs at the particle and parton levels. The $t\bar{t}$
differential cross section measurements are compared to several Monte Carlo
generators that implement calculations up to next-to-leading order in
perturbative quantum chromodynamics interfaced with parton showering, and also
to fixed-order theoretical calculations of top quark pair production beyond
next-to-leading order accuracy.


  Binary black hole simulations become increasingly more computationally
expensive with smaller mass ratios, partly because of the longer evolution
time, and partly because the lengthscale disparity dictates smaller time steps.
The program initiated by Dhesi et al. (arXiv:2109.03531) explores a method for
alleviating the scale disparity in simulations with mass ratios in the
intermediate astrophysical range ($10^{-4} \lesssim q \lesssim 10^{-2}$), where
purely perturbative methods may not be adequate. A region ("worldtube") much
larger than the small black hole is excised from the numerical domain, and
replaced with an analytical model approximating a tidally deformed black hole.
Here we apply this idea to a toy model of a scalar charge in a fixed circular
geodesic orbit around a Schwarzschild black hole, solving for the massless
Klein-Gordon field. This is a first implementation of the worldtube excision
method in full 3+1 dimensions. We demonstrate the accuracy and efficiency of
the method, and discuss the steps towards applying it for evolving orbits and,
ultimately, in the binary black-hole scenario. Our implementation is publicly
accessible in the SpECTRE numerical relativity code.


  The future of high-performance computing is aligning itself towards the
efficient use of highly parallel computing environments. One application where
the use of massive parallelism comes instinctively is Monte Carlo simulations,
where a large number of independent events have to be simulated. At the core of
the Monte Carlo simulation lies the Random Number Generator (RNG). In this
paper, the massively parallel implementation of a collection of pseudo-random
number generators on a graphics processing unit (GPU) is presented. The results
of the GPU implementation, in terms of samples/s, effective bandwidth and
operations per second, are presented. A comparison with other implementations
on different hardware platforms, in terms of samples/s, power efficiency and
cost-benefit, is also presented. Random numbers generation throughput of up to
~18MSamples/s have been achieved on the graphics hardware used. Efficient
hardware utilization, in terms of operations per second, has reached ~98% of
the possible integer operation throughput.


  Fix an integer $k \ge 3$. A $k$-uniform hypergraph is simple if every two
edges share at most one vertex. We prove that there is a constant $c$ depending
only on $k$ such that every simple $k$-uniform hypergraph $H$ with maximum
degree $\D$ has chromatic number satisfying $$\chi(H) <c (\frac{\D}{\log
\D})^{\frac{1}{k-1}}.$$ This implies a classical result of
Ajtai-Koml\'os-Pintz-Spencer-Szemer\'edi and its strengthening due to
Duke-Lefmann-R\"odl. The result is sharp apart from the constant $c$.


  Hyperbolic phonon polaritons (HPhPs) in orthorhombic-phase molybdenum
trioxide ($\alpha$-MoO3) show in-plane hyperbolicity, great wavelength
compression and ultra-long lifetime, therefore holding great potential in
nanophotonic applications. However, its polaritonic response in the
far-infrared (FIR) range has long remained unexplored due to challenges in
experimental characterization. Here, using monochromated electron energy loss
spectroscopy (EELS) in a scanning transmission electron microscope (STEM), we
probe HPhPs in $\alpha$-MoO3 in both mid-infrared (MIR) and FIR frequencies and
correlate their behaviors with microstructures and orientations. We find that
low-structural symmetry leads to various phonon modes and multiple Reststrahlen
bands (RBs) over a broad spectral range (over 70 meV) and in different
directions (55-63 meV and 119-125 meV along b axis, 68-106 meV along c axis,
101-121 meV along a axis). These HPhPs can be selectively excited by
controlling the direction of swift electrons. These findings provide new
opportunities in nanophotonic and optoelectronic applications such as directed
light propagation, hyperlenses and heat transfer.


  In many prediction problems, spurious correlations are induced by a changing
relationship between the label and a nuisance variable that is also correlated
with the covariates. For example, in classifying animals in natural images, the
background, which is a nuisance, can predict the type of animal. This
nuisance-label relationship does not always hold, and the performance of a
model trained under one such relationship may be poor on data with a different
nuisance-label relationship. To build predictive models that perform well
regardless of the nuisance-label relationship, we develop Nuisance-Randomized
Distillation (NURD). We introduce the nuisance-randomized distribution, a
distribution where the nuisance and the label are independent. Under this
distribution, we define the set of representations such that conditioning on
any member, the nuisance and the label remain independent. We prove that the
representations in this set always perform better than chance, while
representations outside of this set may not. NURD finds a representation from
this set that is most informative of the label under the nuisance-randomized
distribution, and we prove that this representation achieves the highest
performance regardless of the nuisance-label relationship. We evaluate NURD on
several tasks including chest X-ray classification where, using non-lung
patches as the nuisance, NURD produces models that predict pneumonia under
strong spurious correlations.


  Multi-view clustering integrates multiple feature sets, which reveal distinct
aspects of the data and provide complementary information to each other, to
improve the clustering performance. It remains challenging to effectively
exploit complementary information across multiple views since the original data
often contain noise and are highly redundant. Moreover, most existing
multi-view clustering methods only aim to explore the consistency of all views
while ignoring the local structure of each view. However, it is necessary to
take the local structure of each view into consideration, because different
views would present different geometric structures while admitting the same
cluster structure. To address the above issues, we propose a novel multi-view
subspace clustering method via simultaneously assigning weights for different
features and capturing local information of data in view-specific
self-representation feature spaces. Especially, a common cluster structure
regularization is adopted to guarantee consistency among different views. An
efficient algorithm based on an augmented Lagrangian multiplier is also
developed to solve the associated optimization problem. Experiments conducted
on several benchmark datasets demonstrate that the proposed method achieves
state-of-the-art performance. We provide the Matlab code on
https://github.com/Ekin102003/JFLMSC.


  Charged particle transport is an important energy transport mode in the
combustion process of inertial confinement fusion plasma. On the one hand,
charged particles inside the hot spot have a strong non-equilibrium effect, so
it is necessary to solve the Boltzmann transport equation to simulate the
energy transport process of charged particles accurately. On the other hand,
charged particle transport has the characteristics of high collision frequency
and complex blocking power, so the calculation amount of the traditional Monte
Carlo algorithm is difficult to bear under the existing calculation conditions.
Aiming at the computational bottleneck caused by the large Coulomb potential
collision cross-section, we developed a hybrid collision model which greatly
reduced the computational cost while maintaining the second-order accuracy of
the collision process. In order to solve the computational bottleneck caused by
the complex blocking power model, we developed a neural network model based on
machine learning to achieve formal unity and efficient calculation of different
blocking power. Based on the calculation method, we developed the charged
particle transport MC function modules of the RDMG program and LARED-S program
and applied them to the study of critical target performance of inertial
confinement fusion, which showed good computational efficiency and accuracy.


  In this work we use the framework of the Dyson-Schwinger and Bethe-Salpeter
equations to compute Light-Cone Distribution Amplitudes of heavy-light mesons
and quarkonia. In studying the meson properties, we introduce a flavor
dependence in the heavy-quark sector of the Bethe-Salpeter ladder kernel which
yields improved numerical results for masses and leptonic decay constants of
the pseudoscalar $D$, $D_s$, $B$ and $B_s$ mesons. Finally, the corresponding
heavy-light Bethe-Salpeter amplitudes are projected onto the light front and we
reconstruct the distribution amplitudes of the mesons in the full theory.


  In complex environments with high dimension, training a reinforcement
learning (RL) model from scratch often suffers from lengthy and tedious
collection of agent-environment interactions. Instead, leveraging expert
demonstration to guide RL agent can boost sample efficiency and improve final
convergence. In order to better integrate expert prior with on-policy RL
models, we propose a generic framework for Learning from Demonstration (LfD)
based on actor-critic algorithms. Technically, we first employ K-Means
clustering to evaluate the similarity of sampled exploration with demonstration
data. Then we increase the likelihood of actions in similar frames by modifying
the gradient update strategy to leverage demonstration. We conduct experiments
on 4 standard benchmark environments in Mujoco and 2 self-designed robotic
environments. Results show that, under certain condition, our algorithm can
improve sample efficiency by 20% ~ 40%. By combining our framework with
on-policy algorithms, RL models can accelerate convergence and obtain better
final mean episode rewards especially in complex robotic context where
interactions are expensive.


  We study the complexity of some algorithmic problems on directed hypergraphs
and their strongly connected components (SCCs). The main contribution is an
almost linear time algorithm computing the terminal strongly connected
components (i.e. SCCs which do not reach any components but themselves).
"Almost linear" here means that the complexity of the algorithm is linear in
the size of the hypergraph up to a factor alpha(n), where alpha is the inverse
of Ackermann function, and n is the number of vertices. Our motivation to study
this problem arises from a recent application of directed hypergraphs to
computational tropical geometry.
  We also discuss the problem of computing all SCCs. We establish a superlinear
lower bound on the size of the transitive reduction of the reachability
relation in directed hypergraphs, showing that it is combinatorially more
complex than in directed graphs. Besides, we prove a linear time reduction from
the well-studied problem of finding all minimal sets among a given family to
the problem of computing the SCCs. Only subquadratic time algorithms are known
for the former problem. These results strongly suggest that the problem of
computing the SCCs is harder in directed hypergraphs than in directed graphs.


  We prove new identities between the values of Rogers dilogarithm function and
describe a connection between these identities and spectra in conformal field
theory.


  When collapse of the iron core in a massive red or yellow supergiant does not
lead to an energetic supernova, a significant fraction of the convective
hydrogen envelope will fall in towards the black hole formed from the
collapsing core. The random velocity field in the convective envelope results
in finite specific angular momentum in each infalling shell. Using 3D
hydrodynamical simulations, we follow the infall of this material to small
radii, resolving the circularization radii of the flow. We show that infall of
the convective envelope leads to nearly complete envelope ejection in a
$\gtrsim$ 10$^{48}$ erg explosion with outflow speeds of $\gtrsim$ 200 km/s.
The light curve of such an explosion would show a characteristic, red plateau
as the ejecta cools and a hydrogen recombination front recedes through the
expanding ejecta. Adopting supernova IIp scalings, the event would have a
plateau luminosity of $\gtrsim$ 10$^{40}$ erg/s and a duration of several
hundreds of days. These events would appear quite similar to luminous red novae
with red or yellow supergiant progenitors; some luminous red novae may, in
fact, be signposts of black hole formation. The mechanism studied here produces
more energetic explosions than the weak shock generated from the radiation of
neutrino energy during the proto-neutron star phase. Because we cannot simulate
all the way to the horizon, our results are likely lower limits on the energy
and luminosity of transients produced during the collapse of a red or yellow
supergiant to form a black hole.


  In this work a method to regularize Cox frailty models is proposed that
accommodates time-varying covariates and time-varying coefficients and is based
on the full instead of the partial likelihood. A particular advantage in this
framework is that the baseline hazard can be explicitly modeled in a smooth,
semi-parametric way, e.g. via P-splines. Regularization for variable selection
is performed via a lasso penalty and via group lasso for categorical variables
while a second penalty regularizes wiggliness of smooth estimates of
time-varying coefficients and the baseline hazard. Additionally, adaptive
weights are included to stabilize the estimation. The method is implemented in
R as coxlasso and will be compared to other packages for regularized Cox
regression. Existing packages, however, do not allow for the combination of
different effects that are accommodated in coxlasso.


  We show that joinings of higher rank torus actions on S-arithmetic quotients
of semi-simple or perfect algebraic groups must be algebraic.


  We present an all-sky formalism for the Cosmic Microwave Background (CMB)
bispectrum induced by the primordial non-Gaussianities not only in scalar but
also in vector and tensor fluctuations. We find that the bispectrum can be
formed in an explicitly rationally invariant way by taking into account the
angular and polarization dependences of the vector and tensor modes. To
demonstrate this and present how to use our formalism, we consider a specific
example of the correlation between two scalars and a graviton as the source of
non-Gaussianity. As a result, we show that the CMB reduced bispectrum of the
intensity anisotropies is evaluated as a function of the multipole and the
coupling constant between two scalars and a graviton denoted by $g_{tss}$;
$|b_{\ell \ell \ell}| \sim \ell^{-4} \times 8 \times 10^{-18} |g_{tss}|$. By
estimating the signal-to-noise ratio, we find that the constraint as $|g_{tss}|
< 6$ will be expected from the PLANCK experiment.


  Previously, Nova Puppis 1991 (V351 Pup) was measured to host one of the most
massive ejections claimed in the literature. Multi-frequency radio detections
from one epoch were published for this nova in the 1990's, and yet, the
remaining data collected by the Very Large Array (VLA) have remained
unpublished. In this paper, we analyze the remaining unpublished data sets for
V351 Pup at frequencies of 4.9, 8.4, 14.9, and 22.5 GHz. We fit the resulting
light curve to a model of expanding thermal ejecta, under the assumption that
the radio emission is dominated by free-free radiation and accounting for high
levels of clumping in the ejecta. Images of V351 Pup in both the radio (from
the VLA) and H$\alpha$+[N II] (from HST) exhibit no aspherical structure,
strengthening our assumption of spherical symmetry. From expansion parallax
methods, we estimate the distance to V351 Pup to be $5.0 \pm 1.5$ kpc. Our
light curve fit yields a value of $log_{10}(M_{ej})={-5.2} \pm {0.7}$
M$_{\odot}$ for the ejecta mass, implying that V351 Pup is on the low end of
expectations for ejecta mass from classical novae. A comparison between our
derived ejecta mass and theoretical models gives evidence for a very massive
(1.25 M$_{\odot}$) white dwarf, which is consistent with spectroscopic evidence
for an oxygen-neon white dwarf.


  Caustics are a generic feature of the nonlinear growth of structure in the
dark matter distribution. If the dark matter were absolutely cold, its mass
density would diverge at caustics, and the integrated annihilation probability
would also diverge for individual particles participating in them. For
realistic dark matter candidates, this behaviour is regularised by small but
non-zero initial thermal velocities. We present a mathematical treatment of
evolution from Hot, Warm or Cold Dark Matter initial conditions which can be
directly implemented in cosmological N-body codes. It allows the identification
of caustics and the estimation of their annihilation radiation in fully general
simulations of structure formation.


  The famous conjecture of V.Ya.Ivrii (1978) says that {\it in every billiard
with infinitely-smooth boundary in a Euclidean space the set of periodic orbits
has measure zero}. In the present paper we study the complex version of Ivrii's
conjecture for odd-periodic orbits in planar billiards, with reflections from
complex analytic curves. We prove positive answer in the following cases: 1)
triangular orbits; 2) odd-periodic orbits in the case, when the mirrors are
algebraic curves avoiding two special points at infinity, the so-called
isotropic points. We provide immediate applications to the real
piecewise-algebraic Ivrii's conjecture and to its analogue in the invisibility
theory.


  Let $N$ be a submodule of a finitely generated module $M$ over a Noetherian
ring. A method for the computation of the submodule generated by the envelope
of $N$ is given. The relations between weakly prime submodules and their
envelopes are investigated. Using these relations, a description of the weakly
radical of a submodule is obtained. The results are illustrated by examples.


  Assuming a standard Maxwellian velocity distribution for the WIMPs in the
halo of our Galaxy we use the null results of an exhaustive set of 9 direct
detection experiments to calculate the maximal variation of the exclusion plot
for each Wilson coefficient of the most general Galilean-invariant effective
Hamiltonian for a WIMP of spin one half due to interferences. We consider 56
Wilson coefficients $c_i^{p,n}$ and $\alpha_i^{n,p}$ for WIMP-proton and
WIMP-neutron contact interactions ${\cal O}_i^{p,n}$ and the corresponding long
range interaction ${\cal O}_i^{p,n}/q^2$, parameterized by a massless
propagator $1/q^2$. For each coupling we provide a different exclusion plot
when the following set of operators is allowed to interfere: proton-neutron,
i.e. $c_i^{p}$-$c_i^{n}$ or $\alpha_i^{p}$-$\alpha_i^{n}$; contact-contact or
long range-long range, i.e. $c_i^{p,n}$-$c_j^{p,n}$ or
$\alpha_i^{p,n}$-$\alpha_j^{p,n}$; contact-long range, i.e.
$c_i^{p,n}$-$\alpha_j^{p,n}$. For each of the 56 Wilson coefficients
$c_i^{p,n}$ and $\alpha_j^{p,n}$ and for the largest number of interfering
operators the exclusion plot variation can reach 3 orders of magnitude and
reduces to a factor as small as a few for the Wilson coefficients of the
effective interactions where the WIMP couples to the nuclear spin, thanks to
the combination of experiments using proton-odd and neutron-odd targets. Some
of the conservative bounds require an extremely high level of cancellation,
putting into question the reliability of the result. We analyze this issue in a
systematic way, showing that it affects some of the couplings driven by the
operators ${\cal O}_{1}$, ${\cal O}_{3}$, ${\cal O}_{11}$, ${\cal O}_{12}$ and
${\cal O}_{15}$, especially when interferences among contact and long range
interactions are considered.


  Learning to drive faithfully in highly stochastic urban settings remains an
open problem. To that end, we propose a Multi-task Learning from Demonstration
(MT-LfD) framework which uses supervised auxiliary task prediction to guide the
main task of predicting the driving commands. Our framework involves an
end-to-end trainable network for imitating the expert demonstrator's driving
commands. The network intermediately predicts visual affordances and action
primitives through direct supervision which provide the aforementioned
auxiliary supervised guidance. We demonstrate that such joint learning and
supervised guidance facilitates hierarchical task decomposition, assisting the
agent to learn faster, achieve better driving performance and increases
transparency of the otherwise black-box end-to-end network. We run our
experiments to validate the MT-LfD framework in CARLA, an open-source urban
driving simulator. We introduce multiple non-player agents in CARLA and induce
temporal noise in them for realistic stochasticity.


  We investigate the low-lying eigenvalues of the improved Wilson-Dirac
operator in the Schroedinger functional with two dynamical quark flavors. At a
lattice spacing of approximately 0.1 fm we find more very small eigenvalues
than in the quenched case. These cause problems with HMC-type algorithms and in
the evaluation of fermionic correlation functions. Through a simulation at a
finer lattice spacing we are able to establish their nature as cutoff-effects


  We analyze the collective modes of high-temperature QCD in the case when
there is an anisotropy in the momentum-space distribution function for the
gluons. We perform a tensor decomposition of the gluon self-energy and solve
the dispersion relations for both stable and unstable modes. Results are
presented for a class of anisotropic distribution functions which can be
obtained by stretching or squeezing an isotropic distribution function along
one direction in momentum space. We find that there are three stable modes and
either one or two unstable modes depending on whether the distribution function
is stretched or squeezed. The presence of unstable modes which have exponential
growth can lead to a more rapid thermalization and isotropization of the soft
modes in a quark gluon plasma and therefore may play an important role in the
dynamical evolution.


  We calculate the two-magnon Raman scattering spectra in antiferromagnetic
phases of several frustrated spin models defined on the honeycomb lattice.
These include the N\'{e}el antiferromagnetic phase of a $J_1$-$J_2$-$J_3$ model
and the stripe phase of the Heisenberg-Kitaev model. We show that both the
magnetic frustration and the anisotropy of interactions may significantly
affect the Raman spectra. We further discuss the implications of our results to
the magnetic excitations of the iron-based compound BaFe$_2$Se$_2$O and show
how the magnetic interactions can be extracted from fit to the Raman spectrum.


  We describe the coherent manipulation of harmonic oscillator and qubit modes
using resonant trains of single flux quantum pulses in place of microwaves. We
show that coherent rotations are obtained for pulse-to-pulse spacing equal to
the period of the oscillator. We consider a protocol for preparing bright and
dark harmonic oscillator pointer states. Next we analyze rotations of a
two-state qubit system. We calculate gate errors due to timing jitter of the
single flux quantum pulses and due to weak anharmonicity of the qubit. We show
that gate fidelities in excess of 99.9% are achievable for sequence lengths of
order 20 ns.


  In this paper, we propose a new non-local population model of logistic type
equation on a bounded Lipschitz domain in the whole Euclidean space. This model
preserves the L^2 norm, which is called mass, of the solution on the domain. We
show that this model has the global existence, stability and asymptotic
behavior at time infinity.


  This paper introduces Jensen, an easily extensible and scalable toolkit for
production-level machine learning and convex optimization. Jensen implements a
framework of convex (or loss) functions, convex optimization algorithms
(including Gradient Descent, L-BFGS, Stochastic Gradient Descent, Conjugate
Gradient, etc.), and a family of machine learning classifiers and regressors
(Logistic Regression, SVMs, Least Square Regression, etc.). This framework
makes it possible to deploy and train models with a few lines of code, and also
extend and build upon this by integrating new loss functions and optimization
algorithms.


  This paper is dedicated to the presentation and the analysis of a numerical
scheme for forward-backward SDEs of the McKean-Vlasov type, or equivalently for
solutions to PDEs on the Wasserstein space. Because of the mean field structure
of the equation, earlier methods for classical forward-backward systems fail.
The scheme is based on a variation of the method of continuation. The principle
is to implement recursively local Picard iterations on small time intervals. We
establish a bound for the rate of convergence under the assumption that the
decoupling field of the forward-bakward SDE (or equivalently the solution of
the PDE) satisfies mild regularity conditions. We also provide numerical
illustrations.


  Variational Monte Carlo studies employing projected entangled-pair states
(PEPS) have recently shown that they can provide answers on long-standing
questions such as the nature of the phases in the two-dimensional $J_1 - J_2$
model. The sampling in these Monte Carlo algorithms is typically performed with
Markov Chain Monte Carlo algorithms employing local update rules, which often
suffer from long autocorrelation times and interdependent samples. We propose a
sampling algorithm that generates independent samples from a PEPS, bypassing
all problems related to finite autocorrelation times. This algorithm is a
generalization of an existing direct sampling algorithm for unitary tensor
networks. We introduce an auxiliary probability distribution from which
independent samples can be drawn, and combine it with importance sampling in
order to evaluate expectation values accurately. We benchmark our algorithm on
the classical Ising model and on variational optimization of two-dimensional
quantum spin models.


  The thermoelectric properties and electronic band structures for Se-doped
Co3SnInS2 were examined. The parent compound of this material (Co3Sn2S2) has
two kinds of Sn sites (Sn1 and Sn2 sites). The density functional theory (DFT)
calculations show that the indium substitution at the Sn2 site induces a
metallic band structure, on the other hand, a semiconducting band structure is
obtained from substitution at the Sn1 site. However, according to the previous
reports, since the indium atom prefers to replace the tin atom at the Sn1 site
rather than the Sn2 site, the resistivity of Co3SnInS2 shows
semiconducting-like behavior. In this study we have demonstrated that metallic
behavior and a decrease in resistivity for Se-doped Co3SnInS2 occurs without
suppression of the Seebeck coefficient. From the DFT calculations, when the
selenium content is above 0.5, the total crystallographic energy shows that a
higher indium occupancy at Sn2 site is more stable. Therefore, it is suggested
that the selenium doping suppress the site preference for indium substitution.
This is one of the possible explanations for the metallic conductivity observed
in Se-doped Co3SnInS2


  Soibelman's theory of quantized function algebra A_q(SL_n) provides a
representation theoretical scheme to construct a solution of the Zamolodchikov
tetrahedron equation. We extend this idea originally due to Kapranov and
Voevodsky to A_q(Sp_{2n}) and obtain the intertwiner K corresponding to the
quartic Coxeter relation. Together with the previously known 3-dimensional (3D)
R matrix, the K yields the first ever solution to the 3D analogue of the
reflection equation proposed by Isaev and Kulish. It is shown that matrix
elements of R and K are polynomials in q and that there are combinatorial and
birational counterparts for R and K. The combinatorial ones arise either at q=0
or by tropicalization of the birational ones. A conjectural description for the
type B and F_4 cases is also given.


  Nature provides us with a restricted set of microscopic interactions. The
question is whether we can synthesize out of these fundamental interactions an
arbitrary unitary operator. In this paper we present a constructive algorithm
for realization of any unitary operator which acts on a (truncated) Hilbert
space of a single bosonic mode. In particular, we consider a physical
implementation of unitary transformations acting on 1-dimensional vibrational
states of a trapped ion. As an example we present an algorithm which realizes
the discrete Fourier transform.


  We review the recent experimental and theoretical progress in $K$-shell
detachment studies of atomic anions. On the experimental side, this field has
largely benefitted from technical advances at 3rd generation synchrotron
radiation sources. For multiple detachment of C$^-$, O$^-$, and F$^-$ ions,
recent results were obtained at the photon-ion merged-beams setup PIPE which is
a permanent end station at beamline P04 of the PETRA III synchrotron light
source in Hamburg. In addition to a much increased photon flux as compared to
what was available previously, the PIPE setup has an extraordinary detection
sensitivity for heavy charged reaction products that allows one to study
detachment processes with extremely low cross sections in the kilobarn range,
e.g., for processes involving the simultaneous creation of two core-holes by a
single photon. The experimental findings pose new challenges for
state-of-the-art atomic theory and require calculations combining
photoexcitation (ionization) with decay cascade processes that follow after
initial core-hole production.


  We show in prime dimension that for two non-commuting totally irreducible
toral automorphisms the set of points that equidistribute under the first map
but have non-dense orbit under the second has full Hausdorff dimension. In
non-prime dimension the argument fails only if the automorphisms have strong
algebraic relations.


  Neural embeddings have been used with great success in Natural Language
Processing (NLP). They provide compact representations that encapsulate word
similarity and attain state-of-the-art performance in a range of linguistic
tasks. The success of neural embeddings has prompted significant amounts of
research into applications in domains other than language. One such domain is
graph-structured data, where embeddings of vertices can be learned that
encapsulate vertex similarity and improve performance on tasks including edge
prediction and vertex labelling. For both NLP and graph based tasks, embeddings
have been learned in high-dimensional Euclidean spaces. However, recent work
has shown that the appropriate isometric space for embedding complex networks
is not the flat Euclidean space, but negatively curved, hyperbolic space. We
present a new concept that exploits these recent insights and propose learning
neural embeddings of graphs in hyperbolic space. We provide experimental
evidence that embedding graphs in their natural geometry significantly improves
performance on downstream tasks for several real-world public datasets.


  A free-energy functional for a crystal that contains both the symmetry
conserved and symmetry broken parts of the direct pair correlation function is
developed. The free-energy functional is used to investigate the
crystallization of fluids interacting via the inverse power potential ;
$u(r)=\epsilon {(\sigma/r)}^n$. In agreement with simulation results we find
that for $n=12$ the freezing is into close packed f.c.c structure while for
soft repulsions $(n\leq 6)$ b.c.c phase is more stable.


  This paper presents the formulation and results for a control-aware
optimization of the combined geometric and structural design of an
energy-harvesting underwater kite. Because kite-based energy-harvesting
systems, both airborne and underwater, possess strong coupling between
closed-loop flight control, geometric design, and structural design,
consideration of all three facets of the design within a single co-design
framework is highly desirable. However, while prior literature has addressed
one or two attributes of the design at a time, the present work constitutes the
first comprehensive effort aimed at addressing all three. In particular,
focusing on the goals of power maximization and mass minimization, we present a
co-design formulation that fuses a geometric optimization tool, structural
optimization tool, and closed-loop flight efficiency map. The resulting
integrated co-design tool is used to address two mathematical optimization
formulations that exhibit subtle differences: a Pareto optimal formulation and
a dual-objective formulation that focuses on a weighted power-to-mass ratio as
the techno-economic metric of merit. Based on the resulting geometric and
structural designs, using a medium-fidelity closed-loop simulation tool, the
proposed formulation is shown to achieve more than three times the
power-to-mass ratio of a previously published, un-optimized benchmark design.


  Planetary turbulence is observed to self-organize into large-scale structures
such as zonal jets and coherent vortices. One of the simplest models that
retains the relevant dynamics of turbulent self-organization is a barotropic
flow in a beta-plane channel with turbulence sustained by random stirring.
Non-linear integrations of this model show that as the energy input rate of the
forcing is increased, the homogeneity of the flow is first broken by the
emergence of non-zonal, coherent, westward propagating structures and at larger
energy input rates by the emergence of zonal jets. The emergence of both
non-zonal coherent structures and zonal jets is studied using a statistical
theory, Stochastic Structural Stability Theory (S3T). S3T directly models a
second-order approximation to the statistical mean turbulent state and allows
the identification of statistical turbulent equilibria and study of their
stability. Using S3T, the bifurcation properties of the homogeneous state in
barotropic beta-plane turbulence are determined. Analytic expressions for the
zonal and non-zonal large-scale coherent flows that emerge as a result of
structural instability are obtained and the equilibration of the incipient
instabilities is studied through numerical integrations of the S3T dynamical
system. The dynamics underlying the formation of zonal jets are also
investigated. It is shown that zonal jets form from the upgradient momentum
fluxes that result from the shearing of the eddies by the emerging
infinitesimal large-scale flow. Finally, numerical simulations of the nonlinear
equations confirm the characteristics (scale, amplitude and phase speed) of the
structures predicted by S3T, even in highly non-linear parameter regimes such
as the regime of zonostrophic turbulence.


  The rural-urban migration phenomenon is analyzed by using an agent-based
computational model. Agents are placed on lattices which dimensions varying
from d=2 up to d=7. The localization of the agents in the lattice define their
social neighborhood (rural or urban) not being related to their spatial
distribution. The effect of the dimension of lattice is studied by analyzing
the variation of the main parameters that characterizes the migratory process.
The dynamics displays strong effects even for around one million of sites, in
higher dimensions (d=6, 7).


  In this thesis, we explore three phenomenological alternatives to the current
paradigm of the standard inflationary big bang scenario. The three alternative
themes are spin torsion (or Einstein-Cartan-Kibble-Sciama) theories, extra
dimensions (braneworld cosmology) and changing global symmetry. In the spin
torsion theories, we found new cosmological solutions with a cosmological
constant as alternative to the standard scalar field driven inflationary
scenario and we conclude that these toy models do not exhibit an inflationary
phase. In the theme of extra dimensions, we discuss the dynamics of linearized
scalar and tensor perturbations in an almost Friedmann-Robertson-Walker
braneworld cosmology of Randall-Sundrum type II using the 1+3 covariant
approach. We derive a complete set of frame-independent equations for the total
matter variables, and a partial set of equations for the non-local variables,
which arise from the projection of the Weyl tensor in the bulk. The latter
equations are incomplete since there is no propagation equation for the
non-local anisotropic stress. In the simplest approximation, we show the
braneworld imprint as a correction to the power spectra for standard
temperature and polarization anisotropies and similarly show that the tensor
anisotropies are also insensitive to the high energy effects. Finally in the
theme of changing global symmetry, we constructed a bounded isothermal solution
embedded in an expanding Einstein de Sitter universe and showed that there is a
possible phase transition in the far future.


  We introduce a novel method for acquiring boundary representations (B-Reps)
of 3D CAD models which involves a two-step process: it first applies a spatial
partitioning, referred to as the ``split``, followed by a ``fit`` operation to
derive a single primitive within each partition. Specifically, our partitioning
aims to produce the classical Voronoi diagram of the set of ground-truth (GT)
B-Rep primitives. In contrast to prior B-Rep constructions which were
bottom-up, either via direct primitive fitting or point clustering, our
Split-and-Fit approach is top-down and structure-aware, since a Voronoi
partition explicitly reveals both the number of and the connections between the
primitives. We design a neural network to predict the Voronoi diagram from an
input point cloud or distance field via a binary classification. We show that
our network, coined NVD-Net for neural Voronoi diagrams, can effectively learn
Voronoi partitions for CAD models from training data and exhibits superior
generalization capabilities. Extensive experiments and evaluation demonstrate
that the resulting B-Reps, consisting of parametric surfaces, curves, and
vertices, are more plausible than those obtained by existing alternatives, with
significant improvements in reconstruction quality. Code will be released on
https://github.com/yilinliu77/NVDNet.


  Semi-supervised learning has proven to be a powerful paradigm for leveraging
unlabeled data to mitigate the reliance on large labeled datasets. In this
work, we unify the current dominant approaches for semi-supervised learning to
produce a new algorithm, MixMatch, that works by guessing low-entropy labels
for data-augmented unlabeled examples and mixing labeled and unlabeled data
using MixUp. We show that MixMatch obtains state-of-the-art results by a large
margin across many datasets and labeled data amounts. For example, on CIFAR-10
with 250 labels, we reduce error rate by a factor of 4 (from 38% to 11%) and by
a factor of 2 on STL-10. We also demonstrate how MixMatch can help achieve a
dramatically better accuracy-privacy trade-off for differential privacy.
Finally, we perform an ablation study to tease apart which components of
MixMatch are most important for its success.


  The fidelity susceptibility measures sensitivity of eigenstates to a change
of an external parameter. It has been fruitfully used to pin down quantum phase
transitions when applied to ground states (with extensions to thermal states).
Here we propose to use the fidelity susceptibility as a useful dimensionless
measure for complex quantum systems. We find analytically the fidelity
susceptibility distributions for Gaussian orthogonal and unitary universality
classes for arbitrary system size. The results are verified by a comparison
with numerical data.


  We report the detection of the Zeeman effect in the 44 GHz Class I methanol
maser line toward the star forming region DR21(OH). In a 219 Jy/beam maser
centered at an LSR velocity of 0.83 km s$^{-1}$, we find a 20-$\sigma$
detection of $zB_{\text{los}} = 53.5 \pm 2.7$ Hz. If 44 GHz methanol masers are
excited at $n \sim 10^{7-8}$ cm$^{-3}$, then the $B~vs.~n^{1/2}$ relation would
imply from comparison with Zeeman effect detections in the CN($1-0$) line
toward DR21(OH) that magnetic fields traced by 44 GHz methanol masers in
DR21(OH) should be $\sim$10 mG. Together with our detected $zB_{\text{los}} =
53.5$ Hz, this would imply that the value of the 44 GHz methanol Zeeman
splitting factor $z$ is $\sim$5 Hz mG$^{-1}$. Such small values of $z$ would
not be a surprise, as the methanol molecule is non paramagnetic, like H$_2$O.
Empirical attempts to determine $z$, as demonstrated, are important because
currently there are no laboratory measurements or theoretically calculated
values of $z$ for the 44 GHz methanol transition. Data from observations of a
larger number of sources are needed to make such empirical determinations
robust.


  This paper proposes a relaxed control regularization with general exploration
rewards to design robust feedback controls for multi-dimensional
continuous-time stochastic exit time problems. We establish that the
regularized control problem admits a H\"{o}lder continuous feedback control,
and demonstrate that both the value function and the feedback control of the
regularized control problem are Lipschitz stable with respect to parameter
perturbations. Moreover, we show that a pre-computed feedback relaxed control
has a robust performance in a perturbed system, and derive a first-order
sensitivity equation for both the value function and optimal feedback relaxed
control. These stability results provide a theoretical justification for recent
reinforcement learning heuristics that including an exploration reward in the
optimization objective leads to more robust decision making. We finally prove
first-order monotone convergence of the value functions for relaxed control
problems with vanishing exploration parameters, which subsequently enables us
to construct the pure exploitation strategy of the original control problem
based on the feedback relaxed controls.


  We give simple conditions on an ambient manifold that are necessary and
sufficient for isoperimetric inequalities (for submanifolds) to hold.


  Following the recent work of Eriksen et al. [arXiv:2008.02678], we report the
performance of the \textit{Configuration Interaction using a Perturbative
Selection made Iteratively} (CIPSI) method on the non-relativistic frozen-core
correlation energy of the benzene molecule in the cc-pVDZ basis. Following our
usual protocol, we obtain a correlation energy of $-863.4$ m$E_h$ which agrees
with the theoretical estimate of $-863$ m$E_h$ proposed by Eriksen et al. using
an extensive array of highly-accurate new electronic structure methods.


  We present a graded-geometric approach to modular classes of Lie algebroids
and their generalizations, introducing in this setting an idea of relative
modular class of a Dirac structure for a certain type of Courant algebroids,
called projectable. This novel approach puts several concepts related to
Poisson geometry and its generalizations in a new light and simplifies proofs.
It gives, in particular, a nice geometric interpretation of modular classes of
twisted-Poisson structures on Lie algebroids.


  We theoretically study harmonically trapped one-dimensional Bose gases (e.g.,
Li, Na, K, Rb, etc.) with multibands occupied, focusing on effects of
higher-energy bands. Combining the Ginzburg-Landau theory with the bosonization
techniques, we predict that the repulsive interaction between higher-band
bosons and the quantum fluctuation can induce the ground state with a finite
angular momentum around the trapped axis. In this state, the Z_2 reflection
symmetry (clockwise or anticlockwise rotations) is spontaneously broken.


  Gridded data products, for example interpolated daily measurements of
precipitation from weather stations, are commonly used as a convenient
substitute for direct observations because these products provide a spatially
and temporally continuous and complete source of data. However, when the goal
is to characterize climatological features of extreme precipitation over a
spatial domain (e.g., a map of return values) at the native spatial scales of
these phenomena, then gridded products may lead to incorrect conclusions
because daily precipitation is a fractal field and hence any smoothing
technique will dampen local extremes. To address this issue, we create a new
"probabilistic" gridded product specifically designed to characterize the
climatological properties of extreme precipitation by applying spatial
statistical analyses to daily measurements of precipitation from the GHCN over
CONUS. The essence of our method is to first estimate the climatology of
extreme precipitation based on station data and then use a data-driven
statistical approach to interpolate these estimates to a fine grid. We argue
that our method yields an improved characterization of the climatology within a
grid cell because the probabilistic behavior of extreme precipitation is much
better behaved (i.e., smoother) than daily weather. Furthermore, the spatial
smoothing innate to our approach significantly increases the signal-to-noise
ratio in the estimated extreme statistics relative to an analysis without
smoothing. Finally, by deriving a data-driven approach for translating extreme
statistics to a spatially complete grid, the methodology outlined in this paper
resolves the issue of how to properly compare station data with output from
earth system models. We conclude the paper by comparing our probabilistic
gridded product with a standard extreme value analysis of the Livneh gridded
daily precipitation product.


  Self-supervised pre-trained features have consistently delivered state-of-art
results in the field of natural language processing (NLP); however, their
merits in the field of speech emotion recognition (SER) still need further
investigation. In this paper we introduce a modular End-to- End (E2E) SER
system based on an Upstream + Downstream architecture paradigm, which allows
easy use/integration of a large variety of self-supervised features. Several
SER experiments for predicting categorical emotion classes from the IEMOCAP
dataset are performed. These experiments investigate interactions among
fine-tuning of self-supervised feature models, aggregation of frame-level
features into utterance-level features and back-end classification networks.
The proposed monomodal speechonly based system not only achieves SOTA results,
but also brings light to the possibility of powerful and well finetuned
self-supervised acoustic features that reach results similar to the results
achieved by SOTA multimodal systems using both Speech and Text modalities.


  Word-representable graphs, which are the same as semi-transitively orientable
graphs, generalize several fundamental classes of graphs. In this paper we
propose a novel approach to study word-representability of graphs using a
technique of homomorphisms. As a proof of concept, we apply our method to show
word-representability of the simplified graph of overlapping permutations that
we introduce in this paper. For another application, we obtain results on
word-representability of certain subgraphs of simplified de Bruijn graphs that
were introduced recently by Petyuk and studied in the context of
word-representability.


  By means of the in situ electrokinetic assessment of aqueous particles in
conjunction with the addition of anionic adsorbates, we develop and examine a
new approach to the scalable characterization of the specific accessible
surface area of particles in water. For alumina powders of differing morphology
in mildly acidic aqueous suspensions, the effective surface charge was modified
by carboxylate anion adsorption through the incremental addition of oxalic and
citric acids. The observed zeta potential variation as a function of the
proportional reagent additive was found to exhibit inverse hyperbolic sine-type
behavior predicted to arise from monolayer adsorption following the
Grahame-Langmuir model. Through parameter optimization by inverse problem
solving, the zeta potential shift with relative adsorbate addition revealed a
nearly linear correlation of a defined surface-area-dependent parameter with
the conventionally measured surface area values of the powders, demonstrating
that the proposed analytical framework is applicable for the in situ surface
area characterization of aqueous particulate matter. The investigated methods
have advantages over some conventional surface analysis techniques owing to
their direct applicability in aqueous environments at ambient temperature and
the ability to modify analysis scales by variation of the adsorption cross
section.


  The fitting of radial velocity curves is a frequent procedure in binary stars
and exoplanet research. In the majority of cases the fitting routines need to
be fed with a set of initial parameter values and priors from which to begin
the computations and their results can be affected by local minima. We present
a new code, the rvfit code, for fitting radial velocities of stellar binaries
and exoplanets using an Adaptive Simulated Annealing (ASA) global minimization
method, which fastly converges to a global solution minimum without the need to
provide preliminary parameter values. We show the performance of the code using
both synthetic and real data sets: double-lined binaries, single-lined
binaries, and exoplanet systems. In all examples the keplerian orbital
parameters fitted by the rvfit code and their computed uncertainties are
compared with literature solutions. Finally, we provide the source code with a
working example and a detailed description on how to use it.


  Hyperscanning with functional near-infrared spectroscopy (fNIRS) is an
emerging neuroimaging application that measures the nuanced neural signatures
underlying social interactions. Researchers have assessed the effect of sex and
task type (e.g., cooperation versus competition) on inter-brain coherence
during human-to-human interactions. However, no work has yet used deep
learning-based approaches to extract insights into sex and task-based
differences in an fNIRS hyperscanning context. This work proposes a
convolutional neural network-based approach to dyadic sex composition and task
classification for an extensive hyperscanning dataset with $N = 222$
participants. Inter-brain signal similarity computed using dynamic time warping
is used as the input data. The proposed approach achieves a maximum
classification accuracy of greater than $80$ percent, thereby providing a new
avenue for exploring and understanding complex brain behavior.


  Currently, there is renewed interest in the problem, raised by Shafer in
1985, of updating probabilities when observations are incomplete. This is a
fundamental problem in general, and of particular interest for Bayesian
networks. Recently, Grunwald and Halpern have shown that commonly used updating
strategies fail in this case, except under very special assumptions. In this
paper we propose a new method for updating probabilities with incomplete
observations. Our approach is deliberately conservative: we make no assumptions
about the so-called incompleteness mechanism that associates complete with
incomplete observations. We model our ignorance about this mechanism by a
vacuous lower prevision, a tool from the theory of imprecise probabilities, and
we use only coherence arguments to turn prior into posterior probabilities. In
general, this new approach to updating produces lower and upper posterior
probabilities and expectations, as well as partially determinate decisions.
This is a logical consequence of the existing ignorance about the
incompleteness mechanism. We apply the new approach to the problem of
classification of new evidence in probabilistic expert systems, where it leads
to a new, so-called conservative updating rule. In the special case of Bayesian
networks constructed using expert knowledge, we provide an exact algorithm for
classification based on our updating rule, which has linear-time complexity for
a class of networks wider than polytrees. This result is then extended to the
more general framework of credal networks, where computations are often much
harder than with Bayesian nets. Using an example, we show that our rule appears
to provide a solid basis for reliable updating with incomplete observations,
when no strong assumptions about the incompleteness mechanism are justified.


  The scientific claim verification task requires an NLP system to label
scientific documents which Support or Refute an input claim, and to select
evidentiary sentences (or rationales) justifying each predicted label. In this
work, we present MultiVerS, which predicts a fact-checking label and identifies
rationales in a multitask fashion based on a shared encoding of the claim and
full document context. This approach accomplishes two key modeling goals.
First, it ensures that all relevant contextual information is incorporated into
each labeling decision. Second, it enables the model to learn from instances
annotated with a document-level fact-checking label, but lacking sentence-level
rationales. This allows MultiVerS to perform weakly-supervised domain
adaptation by training on scientific documents labeled using high-precision
heuristics. Our approach outperforms two competitive baselines on three
scientific claim verification datasets, with particularly strong performance in
zero / few-shot domain adaptation experiments. Our code and data are available
at https://github.com/dwadden/multivers.


  It has been shown in previous work that DARKexp, which is a theoretically
derived, maximum entropy, one shape parameter model for isotropic collisionless
systems, provides very good fits to simulated and observed dark-matter halos.
Specifically, it fits the energy distribution, N(E), and the density profiles,
including the central cusp. Here, we extend DARKexp N(E) to include the
distribution in angular momentum, L^2, for spherically symmetric systems.
First, we argue, based on theoretical, semi-analytical, and simulation results,
that while dark-matter halos are relaxed in energy, they are not nearly as
relaxed in angular momentum, which precludes using maximum entropy to uniquely
derive N(E,L^2). Instead, we require that when integrating N(E,L^2) over
squared angular momenta one retrieves the DARKexp N(E). Starting with a general
expression for N(E,L^2) we show how the distribution of particles in L^2 is
related to the shape of the velocity distribution function, VDF, and velocity
anisotropy profile, \beta(r). We then demonstrate that astrophysically
realistic halos, as judged by the VDF shape and \beta(r), must have linear or
convex distributions in L^2, for each separate energy bin. The distribution in
energy of the most bound particles must be nearly flat, and become more tilted
in favor of radial orbits for less bound particles. These results are
consistent with numerical simulations and represent an important step towards
deriving the full distribution function for spherically symmetric dark-matter
halos.


  We present a simplified exposition of some pieces of [Gily\'en, Su, Low, and
Wiebe, STOC'19, arXiv:1806.01838], which introduced a quantum singular value
transformation (QSVT) framework for applying polynomial functions to
block-encoded matrices. The QSVT framework has garnered substantial recent
interest from the quantum algorithms community, as it was demonstrated by
[GSLW19] to encapsulate many existing algorithms naturally phrased as an
application of a matrix function. First, we posit that the lifting of quantum
singular processing (QSP) to QSVT is better viewed not through Jordan's lemma
(as was suggested by [GSLW19]) but as an application of the cosine-sine
decomposition, which can be thought of as a more explicit and stronger version
of Jordan's lemma. Second, we demonstrate that the constructions of bounded
polynomial approximations given in [GSLW19], which use a variety of ad hoc
approaches drawing from Fourier analysis, Chebyshev series, and Taylor series,
can be unified under the framework of truncation of Chebyshev series, and
indeed, can in large part be matched via a bounded variant of a standard
meta-theorem from [Trefethen, 2013]. We hope this work finds use to the
community as a companion guide for understanding and applying the powerful
framework of [GSLW19].


  Since the introduction of optical coherence tomography (OCT), it has been
possible to study the complex 3D morphological changes of the optic nerve head
(ONH) tissues that occur along with the progression of glaucoma. Although
several deep learning (DL) techniques have been recently proposed for the
automated extraction (segmentation) and quantification of these morphological
changes, the device specific nature and the difficulty in preparing manual
segmentations (training data) limit their clinical adoption. With several new
manufacturers and next-generation OCT devices entering the market, the
complexity in deploying DL algorithms clinically is only increasing. To address
this, we propose a DL based 3D segmentation framework that is easily
translatable across OCT devices in a label-free manner (i.e. without the need
to manually re-segment data for each device). Specifically, we developed 2 sets
of DL networks. The first (referred to as the enhancer) was able to enhance OCT
image quality from 3 OCT devices, and harmonized image-characteristics across
these devices. The second performed 3D segmentation of 6 important ONH tissue
layers. We found that the use of the enhancer was critical for our segmentation
network to achieve device independency. In other words, our 3D segmentation
network trained on any of 3 devices successfully segmented ONH tissue layers
from the other two devices with high performance (Dice coefficients > 0.92).
With such an approach, we could automatically segment images from new OCT
devices without ever needing manual segmentation data from such devices.


  A linear mapping $\phi$ from an algebra $\mathcal{A}$ into its bimodule
$\mathcal M$ is called a centralizable mapping at $G\in\mathcal{A}$ if
$\phi(AB)=\phi(A)B=A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$.
In this paper, we prove that if $\mathcal M$ is a von Neumann algebra without
direct summands of type $\mathrm{I}_1$ and type $\mathrm{II}$, $\mathcal A$ is
a $*$-subalgebra with $\mathcal M\subseteq\mathcal A\subseteq LS(\mathcal{M})$
and $G$ is a fixed element in $\mathcal A$, then every continuous (with respect
to the local measure topology $t(\mathcal M)$) centralizable mapping at $G$
from $\mathcal A$ into $\mathcal M$ is a centralizer.


  Abnormal driver states, particularly have been major concerns for road
safety, emphasizing the importance of accurate drowsiness detection to prevent
accidents. Electroencephalogram (EEG) signals are recognized for their
effectiveness in monitoring a driver's mental state by monitoring brain
activities. However, the challenge lies in the requirement for prior
calibration due to the variation of EEG signals among and within individuals.
The necessity of calibration has made the brain-computer interface (BCI) less
accessible. We propose a practical generalized framework for classifying driver
drowsiness states to improve accessibility and convenience. We separate the
normalization process for each driver, treating them as individual domains. The
goal of developing a general model is similar to that of domain generalization.
The framework considers the statistics of each domain separately since they
vary among domains. We experimented with various normalization methods to
enhance the ability to generalize across subjects, i.e. the model's
generalization performance of unseen domains. The experiments showed that
applying individual domain-specific normalization yielded an outstanding
improvement in generalizability. Furthermore, our framework demonstrates the
potential and accessibility by removing the need for calibration in BCI
applications.


  We introduce a prime number generator in the form of a stochastic algorithm.
The character of such algorithm gives rise to a continuous phase transition
which distinguishes a phase where the algorithm is able to reduce the whole
system of numbers into primes and a phase where the system reaches a frozen
state with low prime density. In this paper we firstly pretend to give a broad
characterization of this phase transition, both in terms of analytical and
numerical analysis. Critical exponents are calculated, and data collapse is
provided. Further on we redefine the model as a search problem, fitting it in
the hallmark of computational complexity theory. We suggest that the system
belongs to the class NP. The computational cost is maximal around the
threshold, as common in many algorithmic phase transitions, revealing the
presence of an easy-hard-easy pattern. We finally relate the nature of the
phase transition to an average-case classification of the problem.


  The wave functions, the autocorrelation functions of which decay faster than
$t^{-2}$, for both the one-dimensional free particle system and the
repulsive-potential system are examined. It is then shown that such wave
functions constitute a dense subset of $L^2 ({\bf R}^1)$, under several
conditions that are particularly satisfied by the square barrier potential
system. It implies that the faster than $t^{-2}$-decay character of the
autocorrelation function persists against the perturbation of potential. It is
also seen that the denseness of the above subset is guaranteed by that of the
domain of the Aharonov-Bohm time operator.


  We investigate the baryon number susceptibilities up to fourth order along
different freeze-out lines in a holographic QCD model with the critical end
point (CEP), and we propose that the peaked baryon number susceptibilities
along the freeze-out line can be used as a clean signature to locate the CEP in
the QCD phase diagram. On the temperature and baryon chemical potential plane,
the ratio of the baryon number susceptibilities (up to fourth order) forms a
ridge along the phase boundary, and develops a sword shape mountain standing
upright around the CEP in a narrow and oblate region. This feature is model
independent and universal if the CEP exists. The measurement of the baryon
number susceptibilities from heavy-ion collision experiment is along the
freeze-out line. If the freeze-out line crosses the foot of the CEP mountain,
then one can observe the peaked baryon number susceptibilities along the
freeze-out line, and the kurtosis of the baryon number distributions has the
tallest magnitude. The data from the first phase of beam energy scan program at
the Relativistic Heavy Ion Collisions indicates that a peak of the kurtosis of
the baryon number distribution would show up at the collision energy around 5
GeV, which suggests that the freeze-out line crosses the foot of the CEP
mountain and the summit of the CEP would be located nearby around the collision
energy of 3 GeV.


  The point vortex system is a system of longstanding interest in nonlinear
dynamics, describing the motion of a two-dimensional inviscid fluid that is
irrotational except at a discrete set of moving point vortices, at which the
vorticity diverges. The leapfrogging orbit consists of two rotating pairs of
like-signed vortices which, taken as a quartet, propagate at constant velocity.
It is known that if the two pairs are initially widely separated, the motion is
stable, while if they are closer together it becomes unstable, with this
relation represented by a dimensionless parameter $\alpha$ defined in the text.
We here demonstrate analytically that the transition from stability to
instability happens at a critical value $\alpha = \phi^{-2}$, where $\phi$ is
the golden ratio. This value had been hypothesized based on careful numerics by
Toph{\o}j and Aref, and by the present authors using a semi-analytic argument
but not previously demonstrated through exact analysis.