  Consider an arbitrary set $S$ and an arbitrary function $f : \mathbb{R} \to
S$. We think of the domain of $f$ as representing time, and for each $x \in
\mathbb{R}$, we think of $f(x)$ as the state of some system at time $x$.
Imagine that, at each time $x$, there is an agent who can see $f
\upharpoonright (-\infty, x)$ and is trying to guess $f(x)$--in other words,
the agent is trying to guess the present state of the system from its past
history. In a 2008 paper, Christopher Hardin and Alan Taylor use the axiom of
choice to construct a strategy that the agents can use to guarantee that, for
every function $f$, all but countably many of them will guess correctly. In a
2013 monograph they introduce the idea of anonymous guessing strategies, in
which the agents can see the past but don't know where they are located in
time. In this paper we consider a number of variations on anonymity. For
instance, what if, in addition to not knowing where they are located in time,
agents also do not know the rate at which time is progressing? What if they
have no sense of how much time elapses between any two events? We show that in
some cases agents can still guess successfully, while in others they perform
very poorly.


  Quantum duality is a far reaching concept in contemporary theoretical
physics. In the present paper, we reveal the quantum dualities in quantum
anomalous Hall (QAH) phases through concrete two bands Hamiltonian models. Our
models can realize QAH phases with arbitrary large Chern numbers. In real
materials these models may be realized by stacked $n$ layer systems of $c_1=1$
QAH insulators. The topological phase transitions that can change the Chern
numbers are studied. And we investigate the gapless edge modes of our models in
details, and find a new mechanism for the bulk boundary correspondence.


  Anonymous database search protocols allow users to query a database
anonymously. This can be achieved by letting the users form a peer-to-peer
community and post queries on behalf of each other. In this article we discuss
an application of combinatorial configurations (also known as regular and
uniform partial linear spaces) to a protocol for anonymous database search, as
defining the key-distribution within the user community that implements the
protocol. The degree of anonymity that can be provided by the protocol is
determined by properties of the neighborhoods and the closed neighborhoods of
the points in the combinatorial configuration that is used. Combinatorial
configurations with unique neighborhoods or unique closed neighborhoods are
described and we show how to attack the protocol if such configurations are
used. We apply k-anonymity arguments and present the combinatorial
configurations with k-anonymous neighborhoods and with k-anonymous closed
neighborhoods. The transversal designs and the linear spaces are presented as
optimal configurations among the configurations with k-anonymous neighborhoods
and k-anonymous closed neighborhoods, respectively.


  The increased availability of data on real networks has favoured an explosion
of activity in the elaboration of models able to reproduce both qualitatively
and quantitatively the measured properties. What has been less explored is the
reliability of the data, and whether the measurement technique biases them.
Here we show that tree-like explorations (similar in principle to traceroute)
can indeed change the measured exponents of a scale-free network.


  The crystal structure, magnetic ordering, and electrical resistivity of
TlFe1.6Se2 were studied at high pressures. Below ~7 GPa, TlFe1.6Se2 is an
antiferromagnetically ordered semiconductor with a ThCr2Si2-type structure. The
insulator-to-metal transformation observed at a pressure of ~ 7 GPa is
accompanied by a loss of magnetic ordering and an isostructural phase
transition. In the pressure range ~ 7.5 - 11 GPa a remarkable downturn in
resistivity, which resembles a superconducting transition, is observed below 15
K. We discuss this feature as the possible onset of superconductivity
originating from a phase separation in a small fraction of the sample in the
vicinity of the magnetic transition.


  We prove that, the initial value problem associated to u_{t} + i\alphau_{xx}
+ \beta u_{xxx} + i\gamma |u|^{2}u = 0, x,t \in R, is locally well-posed in
Sobolev spaces H^{s} for s>-1/4.


  The properties of the entanglement entropy (EE) of two particle excited
states in a one-dimensional ring are studied. For a clean system we show
analytically that as long as the momenta of the two particles are not close,
the EE is twice the value of the EE of any single particle state. For almost
identical momenta the EE is lower than this value. The introduction of disorder
is numerically shown to lead to a decrease in the median EE of a two particle
excited state, while interactions (which have no effect for the clean case)
mitigate the decrease. For a ring which is of the same size as the localization
length, interaction increase the EE of a typical two particle excited state
above the clean system EE value.


  Let $R$ be a constant. Let $\mathcal{M}^R_\gamma$ be the space of smooth
metrics $g$ on a given compact manifold $\Omega^n$ ($n\ge 3$) with smooth
boundary $\Sigma $ such that $g$ has constant scalar curvature $R$ and
$g|_{\Sigma}$ is a fixed metric $\gamma$ on $\Sigma$. Let $V(g)$ be the volume
of $g\in\mathcal{M}^R_\gamma$. In this work, we classify all Einstein or
conformally flat metrics which are critical points of $V(\cdot)$ in
$\mathcal{M}^R_\gamma$.


  Naively, the LHC Higgs boson looks like a Standard Model Higgs boson, with no
guidance to physics beyond the Standard Model, as has often been remarked. The
data show that what was discovered is the true Higgs boson. If one includes the
full information available, experimental and theoretical, there are actually
four significant clues implied by data. They point toward a supersymmetric
two-doublet decoupling theory, and a hierarchy problem solution via TeV scale
supersymmetry. That in turn suggests an underlying compactified string/M theory
with a de Sitter vacuum, so we can be confident that the low scale model has an
ultraviolet completion.


  We show that the "puzzling" chemical composition observed in the extremely
metal poor star HE0107-5240 may be naturally explained by the concurrent
pollution of at least two supernovae. In the simplest possible model a
supernova of quite low mass (~15 Msun), underwent a "normal" explosion and
ejected ~0.06 Msun of 56Ni while a second one was massive enough (~35 Msun) to
experience a strong fall back that locked in a compact remnant all the
carbon-oxygen core. In a more general scenario, the pristine gas clouds were
polluted by one or more supernovae of relatively low mass (less than ~25 Msun).
The successive explosion of a quite massive star experiencing an extended fall
back would have largely raised the abundances of the light elements in its
close neighborhood.


  We report the comprehensive experimental results identifying the magnetic
spin ordering and the magnetization dynamics of a double perovskite Pr2CoFeO6
by employing the (dc and ac) magnetization, powder neutron diffraction (NPD)
and X-ray magnetic circular dichroism (XMCD) techniques. X-ray diffraction and
neutron diffraction studies revealed that Pr2CoFeO6 adopts a B-site disordered
orthorhombic structure with space group Pnma. Additionally, ab initio band
structure calculations performed on this system suggested an insulating
anti-ferromagnetic (Fe-Fe) ground state. Magnetometry study showed the system
to possess a spectrum of interesting magnetic phases including long range
antiferromagnetic (canted) spin ordering (TN ~269 K), Griffiths phase,
re-entrant cluster glass (RCG) (TG~ 34 K) and exchange bias. However, the NPD
study divulged the exhibition of a long range G-type (below TN ~269 K) of spin
ordering by Fe spins. Spin dynamics study by ac susceptibility technique
confirmed the system possessing long range ordering at higher
temperatureundergoes a RCG transition at ~34 K. Existence of Griffiths phase
was confirmed by non-analytic field variation of magnetization and Heisenberg
type temporal spin relaxation above long range ordering temperature TN ~269 K.
The anti-site disorder related to the B-sites (Co/Fe) is found to be the main
driving force forthe observed multiple magnetic phases. Furthermore, the
electronic structure probed by the X-ray absorption spectroscopy (XAS) study
suggested a nominal valance state of +3 for both of the B-site ions (Co/Fe)
which in turn triggered the anti-site disorder in the system. Magnetic, XRD,
NPD and XAS analysis yielded a low spin state (LS) for the Co3+ ions. The
random non-magnetic dilution of magnetic Fe3+ (HS) ions by Co3+ (LS) ions
essentially played a crucial role in manifesting the magnetic properties of the
system.


  Differential Higgs boson (H) production cross sections are sensitive probes
for physics beyond the standard model. New physics may contribute in the
gluon-gluon fusion loop, the dominant Higgs boson production mechanism at the
LHC, and manifest itself through deviations from the distributions predicted by
the standard model. Combined spectra for the H $\to$ $\gamma\gamma$, H $\to$
ZZ, and H $\to$ $\mathrm{b\overline{b}}$ decay channels and the inclusive Higgs
boson production cross section are presented, based on proton-proton collision
data recorded with the CMS detector at $\sqrt{s} =$ 13 TeV corresponding to an
integrated luminosity of 35.9 fb$^{-1}$. The transverse momentum spectrum is
used to place limits on the Higgs boson couplings to the top, bottom, and charm
quarks, as well as its direct coupling to the gluon field. No significant
deviations from the standard model are observed in any differential
distribution. The measured total cross section is 61.1 $\pm$ 6.0 (stat) $\pm$
3.7 (syst) pb, and the precision of the measurement of the differential cross
section of the Higgs boson transverse momentum is improved by about 15% with
respect to the H $\to$ $\gamma\gamma$ channel alone.


  Animal groups exhibit emergent properties that are a consequence of local
interactions. Linking individual-level behaviour to coarse-grained descriptions
of animal groups has been a question of fundamental interest. Here, we present
two complementary approaches to deriving coarse-grained descriptions of
collective behaviour at so-called mesoscopic scales, which account for the
stochasticity arising from the finite sizes of animal groups. We construct
stochastic differential equations (SDEs) for a coarse-grained variable that
describes the order/consensus within a group. The first method of construction
is based on van Kampen's system-size expansion of transition rates. The second
method employs Gillespie's chemical Langevin equations. We apply these two
methods to two microscopic models from the literature, in which organisms
stochastically interact and choose between two directions/choices of foraging.
These `binary-choice' models differ only in the types of interactions between
individuals, with one assuming simple pair-wise interactions, and the other
incorporating higher-order effects. In both cases, the derived mesoscopic SDEs
have multiplicative, or state-dependent, noise. However, the different models
demonstrate the contrasting effects of noise: increasing order in the pair-wise
interaction model, whilst reducing order in the higher-order interaction model.
Although both methods yield identical SDEs for such binary-choice, or
one-dimensional, systems, the relative tractability of the chemical Langevin
approach is beneficial in generalizations to higher-dimensions. In summary,
this book chapter provides a pedagogical review of two complementary methods to
construct mesoscopic descriptions from microscopic rules and demonstrates how
resultant multiplicative noise can have counter-intuitive effects on shaping
collective behaviour.


  The single-particle density is the most basic quantity that can be calculated
from a given many-body wave function. It provides the probability to find a
particle at a given position when the average over many realizations of an
experiment is taken. However, the outcome of single experimental shots of
ultracold atom experiments is determined by the $N$-particle probability
density. This difference can lead to surprising results. For example,
independent Bose-Einstein condensates (BECs) with definite particle numbers
form interference fringes even though no fringes would be expected based on the
single-particle density [1-4]. By drawing random deviates from the $N$-particle
probability density single experimental shots can be simulated from first
principles [1, 3, 5]. However, obtaining expressions for the $N$-particle
probability density of realistic time-dependent many-body systems has so far
been elusive. Here, we show how single experimental shots of general ultracold
bosonic systems can be simulated based on numerical solutions of the many-body
Schr\"odinger equation. We show how full counting distributions of observables
involving any number of particles can be obtained and how correlation functions
of any order can be evaluated. As examples we show the appearance of
interference fringes in interacting independent BECs, fluctuations in the
collisions of strongly attractive BECs, the appearance of randomly fluctuating
vortices in rotating systems and the center of mass fluctuations of attractive
BECs in a harmonic trap. The method described is broadly applicable to bosonic
many-body systems whose phenomenology is driven by information beyond what is
typically available in low-order correlation functions.


  In this article we construct a new family of semifields, containing and
extending two well-known families, namely Albert's generalised twisted fields
and Petit's cyclic semifields (also known as Johnson-Jha semifields). The
construction also gives examples of semifields with parameters for which no
examples were previously known. In the case of semifields two dimensions over a
nucleus and four-dimensional over their centre, the construction gives all
possible examples.
  Furthermore we embed these semifields in a new family of maximum
rank-distance codes, encompassing most known current constructions, including
the (twisted) Delsarte-Gabidulin codes, and containing new examples for most
parameters.


  We prove several new formulas for the visual angle metric of the unit disk in
terms of the hyperbolic metric and apply these to prove a sharp Schwarz lemma
for the visual angle metric under quasiregular mappings.


  We present a self-supervised speech restoration method without paired speech
corpora. Because the previous general speech restoration method uses artificial
paired data created by applying various distortions to high-quality speech
corpora, it cannot sufficiently represent acoustic distortions of real data,
limiting the applicability. Our model consists of analysis, synthesis, and
channel modules that simulate the recording process of degraded speech and is
trained with real degraded speech data in a self-supervised manner. The
analysis module extracts distortionless speech features and distortion features
from degraded speech, while the synthesis module synthesizes the restored
speech waveform, and the channel module adds distortions to the speech
waveform. Our model also enables audio effect transfer, in which only acoustic
distortions are extracted from degraded speech and added to arbitrary
high-quality audio. Experimental evaluations with both simulated and real data
show that our method achieves significantly higher-quality speech restoration
than the previous supervised method, suggesting its applicability to real
degraded speech materials.


  We present the results from e+e- coincidence measurements in 238U + 206Pb
collisions at a beam energy of 5.93 MeV/u, using an improved experimental setup
at the double-Orange spectrometer of GSI. The capability of our device to
detect Internal-Pair-Conversion (IPC) e+e- pairs from discrete nuclear
transitions of a moving emitter is demonstrated by investigating the known
1.844 MeV (E1) transition in 206Pb and the 1.770 MeV (M1) transition in 207Pb,
excited via Coulomb excitation and a neutron transfer reaction, respectively.
The Doppler-shift corrected e+- sum-energy spectra show weak lines at the
expected energies with cross sections being consistent with the measured
excitation cross sections of the corresponding $\gamma$ lines and the
theoretically predicted IPC coefficients. No other e+e- sum-energy lines were
found in the measured spectra. The observed transfer cross sections show a
strong dependence on the distance of closest approach (R_min), thus signaling
also a strong dependence on the bombarding energy close to the Coulomb barrier.


  We analyse backward Euler time stepping schemes for the primal DPG
formulation of a class of parabolic problems. Optimal error estimates are shown
in the natural norm and in the $L^2$ norm of the field variable. For the heat
equation the solution of our primal DPG formulation equals the solution of a
standard Galerkin scheme and, thus, optimal error bounds are found in the
literature. In the presence of advection and reaction terms, however, the
latter identity is not valid anymore and the analysis of optimal error bounds
requires to resort to elliptic projection operators. It is essential that these
operators be projections with respect to the spatial part of the PDE, as in
standard Galerkin schemes, and not with respect to the full PDE at a time step,
as done previously.


  Disordered systems submitted to a slowly increasing external stress often
reacts with a jerky dynamics characterized by bursts of activity, called
avalanches, which are the manifestation of an out-of-equilibrium phase
transition. This thesis focuses on the dynamics of elastic interfaces near the
depinning transition, and more specially on the effect of long-range
interactions. I derive the universal scaling form of the correlation functions
of the local velocity field. It allows to test the universality class of the
transition as well as the range of the interactions. I also study the
statistics of the clusters that form in presence of long-range interactions and
show how it relates to the statistics of the global avalanches. Finally I
present analytical advances towards the understanding of the spatial structure
of avalanches within a mean-field model, the Brownian force model.


  In this paper, we propose SceNDD: a scenario-based naturalistic driving
dataset that is built upon data collected from an instrumented vehicle in
downtown Indianapolis. The data collection was completed in 68 driving sessions
with different drivers, where each session lasted about 20--40 minutes. The
main goal of creating this dataset is to provide the research community with
real driving scenarios that have diverse trajectories and driving behaviors.
The dataset contains ego-vehicle's waypoints, velocity, yaw angle, as well as
non-ego actor's waypoints, velocity, yaw angle, entry-time, and exit-time.
Certain flexibility is provided to users so that actors, sensors, lanes, roads,
and obstacles can be added to the existing scenarios. We used a Joint
Probabilistic Data Association (JPDA) tracker to detect non-ego vehicles on the
road. We present some preliminary results of the proposed dataset and a few
applications associated with it. The complete dataset is expected to be
released by early 2023.


  We study Phragm\'en-Lindel\"of properties for viscosity solutions to a class
of nonlinear parabolic equations of the type $H(Du, D^2u+Z(u)Du\otimes
Du)+\chi(t)|Du|^\sigma-u_t=0$ under a certain boundedness condition on $H$. We
also state results for positive solutions to a class of doubly nonlinear
equation $H(Du, D^2u)-f(u)u_t=0$.


  We address the standard quantum error correction using the three-qubit
bit-flip code, yet in continuous-time. This entails rendering a target manifold
of quantum states globally attractive. Previous feedback designs could feature
spurious equilibria, or resort to discrete kicks pushing the system away from
these equilibria to ensure global asymptotic stability. We present a new
approach that consists of introducing controls driven by Brownian motions.
Unlike the previous methods, the resulting closed-loop dynamics can be shown to
stabilize the target manifold exponentially. We further present a reduced-order
filter formulation with classical probabilities. The exponential property is
important to quantify the protection induced by the closed-loop
error-correction dynamics against disturbances. We study numerically the
performance of this control law and of the reduced filter.


  A new effective field theory has been developed to describe shallow $P$-wave
resonances using nonlocal, momentum-dependent two-body potentials. This
approach is expected to facilitate many-body calculations and has been
demonstrated to converge and to be renormalizable in perturbative calculations
at subleading orders. The theory has been applied to the neutron-alpha system,
with good agreement found between its predictions and a phase-shift analysis of
neutron-alpha elastic scattering. In the three-body system consisting of two
neutrons and an alpha particle, the nonlocal potential in this framework has
been found to recover the same qualitative features as previously shown with
energy-dependent formulations.


  Due to their very nature, Spin Waves (SWs) created in the same waveguide, but
with different frequencies, can coexist while selectively interacting with
their own species only. The absence of inter-frequency interferences isolates
input data sets encoded in SWs with different frequencies and creates the
premises for simultaneous data parallel SW based processing without hardware
replication or delay overhead. In this paper we leverage this SW property by
introducing a novel computation paradigm, which allows for the parallel
processing of n-bit input data vectors on the same basic SW based logic gate.
Subsequently, to demonstrate the proposed concept, we present 8-bit parallel
3-input Majority gate implementation and validate it by means of Object
Oriented MicroMagnetic Framework (OOMMF) simulations. To evaluate the potential
benefit of our proposal we compare the 8-bit data parallel gate with equivalent
scalar SW gate based implementation. Our evaluation indicates that 8-bit data
3-input Majority gate implementation requires 4.16x less area than the scalar
SW gate based equivalent counterpart while preserving the same delay and energy
consumption figures.


  In this article we study the geodesic motion of test particles and light in
the Einstein-Maxwell-Dilaton-Axion black hole spacetime. We derive the
equations of motion and present their solutions in terms of the Weierstra{\ss}
$\wp$-, $\sigma$- and $\zeta$-functions. With the help of parametric diagrams
and effective potentials we analyze the geodesic motion and give a list of all
possible orbit types.


  We combine two popular optimization approaches to derive learning algorithms
for generative models: variational optimization and evolutionary algorithms.
The combination is realized for generative models with discrete latents by
using truncated posteriors as the family of variational distributions. The
variational parameters of truncated posteriors are sets of latent states. By
interpreting these states as genomes of individuals and by using the
variational lower bound to define a fitness, we can apply evolutionary
algorithms to realize the variational loop. The used variational distributions
are very flexible and we show that evolutionary algorithms can effectively and
efficiently optimize the variational bound. Furthermore, the variational loop
is generally applicable ("black box") with no analytical derivations required.
To show general applicability, we apply the approach to three generative models
(we use noisy-OR Bayes Nets, Binary Sparse Coding, and Spike-and-Slab Sparse
Coding). To demonstrate effectiveness and efficiency of the novel variational
approach, we use the standard competitive benchmarks of image denoising and
inpainting. The benchmarks allow quantitative comparisons to a wide range of
methods including probabilistic approaches, deep deterministic and generative
networks, and non-local image processing methods. In the category of
"zero-shot" learning (when only the corrupted image is used for training), we
observed the evolutionary variational algorithm to significantly improve the
state-of-the-art in many benchmark settings. For one well-known inpainting
benchmark, we also observed state-of-the-art performance across all categories
of algorithms although we only train on the corrupted image. In general, our
investigations highlight the importance of research on optimization methods for
generative models to achieve performance improvements.


  We investigate Fourier multipliers with smooth symbols defined over locally
compact Hausdorff groups. Our main results in this paper establish new
H\"ormander-Mikhlin criteria for spectral and non-spectral multipliers. The key
novelties which shape our approach are three. First, we control a broad class
of Fourier multipliers by certain maximal operators in noncommutative $L_p$
spaces. This general principle ---exploited in Euclidean harmonic analysis
during the last 40 years--- is of independent interest and might admit further
applications. Second, we replace the formerly used cocycle dimension by the
Sobolev dimension. This is based on a noncommutative form of the Sobolev
embedding theory for Markov semigroups initiated by Varopoulos, and yields more
flexibility to measure the smoothness of the symbol. Third, we introduce a dual
notion of polynomial growth to further exploit our maximal principle for
non-spectral Fourier multipliers. The combination of these ingredients yields
new $L_p$ estimates for smooth Fourier multipliers in group algebras.


  The processes of ecological interactions, dispersal and mutations shape the
dynamics of biological communities, and analogous eco-evolutionary processes
acting upon economic entities have been proposed to explain economic change.
This hypothesis is compelling because it explains economic change through
endogenous mechanisms, but it has not been quantitatively tested at the global
economy level. Here, we use an inverse modelling technique and 59 years of
economic data covering 77 countries to test whether the collective dynamics of
national economic activities can be characterised by eco-evolutionary
processes. We estimate the statistical support of dynamic community models in
which the dynamics of economic activities are coupled with positive and
negative interactions between the activities, the spatial dispersal of the
activities, and their transformations into other economic activities. We find
strong support for the models capturing positive interactions between economic
activities and spatial dispersal of the activities across countries. These
results suggest that processes akin to those occurring in ecosystems play a
significant role in the dynamics of economic systems. The strength-of-evidence
obtained for each model varies across countries and may be caused by
differences in the distance between countries, specific institutional contexts,
and historical contingencies. Overall, our study provides a new quantitative,
biologically inspired framework to study the forces shaping economic change.


  The phonon dispersion and the electron-phonon interaction for the $\beta$-Po
and the bcc high pressure phases of tellurium are computed with
density-functional perturbation theory. Our calculations reproduce and explain
the experimentally observed pressure dependence of the superconducting critical
temperature (T$_{\rm c}$) and confirm the connection between the jump in
T$_{\rm c}$ and the structural phase transition. The phonon contribution to the
free energy is shown to be responsible for the difference in the structural
transition pressure observed in low and room temperature experiments.


  We present a novel p-GaN gate HEMT structure with reduced hole concentration
near the Schottky interface by doping engineering in MOCVD, which aims at
lowering the electric field across the gate. By employing an additional
unintentionally doped GaN layer, the gate leakage current is suppressed and the
gate breakdown voltage is boosted from 10.6 to 14.6 V with negligible influence
on the threshold voltage and on-resistance. Time-dependent gate breakdown
measurements reveal that the maximum gate drive voltage increases from 6.2 to
10.6 V for a 10-year lifetime with a 1% gate failure rate. This method
effectively expands the operating voltage margin of the p-GaN gate HEMTs
without any other additional process steps.


  We give a formula for the Carath\'eodory distance on the Neil parabola, the
variety ${z^2=w^3}$ restricted to the bidisk; thus making it the first variety
with a singularity to have its Carath\'eodory distance explicitly computed. In
addition, we relate this to a mixed Carath\'eodory-Pick interpolation problem
for which known interpolation theorems do not apply. Finally, we prove a
bounded holomorphic function extension result from the Neil parabola to the
bidisk.


  In this paper, we consider large-scale linearly constrained composite convex
optimization problem, whose objective is a sum of a smooth function and a
possibly nonsmooth function. We propose a scalable
\textbf{F}rank-\textbf{W}olfe based \textbf{A}ugmented \textbf{L}agrangian
(FW-AL) method for solving this problem. At each iteration, the proposed FW-AL
method employs the FW method (or its variants) to approximately solve the AL
subproblem {(with fixed Lagrange multiplier)} within a preselected tolerance
and then updates the Lagrange multiplier. The proposed FW-AL method is well
suitable for solving large-scale problems, because its computational cost per
step scales (essentially) linearly with the size of the input. We analyze the
non-ergodic convergence rate of the proposed FW-AL method.


  A consistent variational derivation of the Majorana 4-spinor field equations
coupled to Einstein's theory of gravitation is given. The equivalence of the
first and the second order variational field equations is explicitly
demonstrated. The Lagrange multiplier 2-forms we use turn out to be precisely
the Belinfante-Rosenfeld 2-forms that are needed to symmetrize the canonical
energy-momentum tensor of the Majorana spinor.


  We point out that if neutron--antineutron oscillation is observed in a free
neutron oscillation experiment, it will put an upper limit on the strengths of
Lorentz invariance violating (LIV) mass operators for neutrons at the level of
$10^{-23}$ GeV or so, which would be the most stringent LIV limit for neutrons.
We also study constraints on $\Delta B=2$ LIV operators and find that for one
particular operator degaussing is not necessary to obtain a visible signal. We
also note that observation of $n-\bar{n}$ oscillation signal in the nucleon
decay search experiment involving nuclei does not lead to any limit on LIV
operators since the nuclear potential difference between neutron and
antineutrons will mask any Lorentz violating effect.


  The superconductor to insulator or metal transition in two dimensions (2D)
provides a valuable platform for studying continuous quantum phase transitions
(QPTs) and critical phenomena. Distinct theoretical models, including both
fermionic and bosonic localization scenarios, have been developed, but many
questions remain unsettled despite decades of research. Extending Nernst
experiments down to millikelvin temperatures, we uncover anomalous quantum
fluctuations and identify an unconventional superconducting quantum critical
point (QCP) in a gate-tuned excitonic quantum spin Hall insulator (QSHI), the
monolayer tungsten ditelluride (WTe2). The observed vortex Nernst effect
reveals singular superconducting fluctuations in the resistive normal state
induced by magnetic fields or temperature, even well above the transition. Near
the doping-induced QCP, the Nernst signal driven by quantum fluctuations is
exceptionally large in the millikelvin regime, with a coefficient of ~ 4,100
uV/KT at zero magnetic field, an indication of the proliferation of vortices.
Surprisingly, the Nernst signal abruptly disappears when the doping falls below
the critical value, in striking conflict with conventional expectations. This
series of phenomena, which have no prior analogue, call for careful
examinations of the mechanism of the QCP, including the possibility of a
continuous QPT between two distinct ordered phases in the monolayer. Our
experiments open a new avenue for studying unconventional QPTs and quantum
critical matter.


  We study sequences of oriented Riemannian manifolds with boundary and, more
generally, integral current spaces and metric spaces with boundary.
{\color{blue}For a metric space, we define its boundary to be the completion of
the space minus the space. We impose conditions on these spaces in order to get
Gromov-Hausdorff (GH) subconvergence. By adding some other conditions} we prove
theorems demonstrating that the Gromov-Hausdorff (GH) and Sormani-Wenger
Intrinsic Flat (SWIF) limits of sequences of such metric spaces agree. Thus in
particular the limit spaces we get are countably $\mathcal{H}^n$ rectifiable
spaces. From these we derive GH compactness theorems for sequences of
Riemannian manifolds with boundary where both the GH and SWIF limits agree.
  For sequences of Riemannian manifolds with boundary we only require
nonnegative Ricci curvature, upper bounds on volume, noncollapsing conditions
on the interior of the manifold and diameter controls on the level sets near
the boundary.


  Video scene parsing incorporates temporal information, which can enhance the
consistency and accuracy of predictions compared to image scene parsing. The
added temporal dimension enables a more comprehensive understanding of the
scene, leading to more reliable results. This paper presents the winning
solution of the CVPR2023 workshop for video semantic segmentation, focusing on
enhancing Spatial-Temporal correlations with contrastive loss. We also explore
the influence of multi-dataset training by utilizing a label-mapping technique.
And the final result is aggregating the output of the above two models. Our
approach achieves 65.95% mIoU performance on the VSPW dataset, ranked 1st place
on the VSPW challenge at CVPR 2023.


  We present a PyTorch-powered implementation of the emulator-based component
analysis used for ill-posed numerical non-linear inverse problems, where an
approximate emulator for the forward problem is known. This emulator may be a
numerical model, an interpolating function, or a fitting function such as a
neural network. With the help of the emulator and a data set, the method seeks
dimensionality reduction by projection in the variable space so that maximal
variance of the target (response) values of the data is covered. The obtained
basis set for projection in the variable space defines a subspace of the
greatest response for the outcome of the forward problem. The method allows for
the reconstruction of the coordinates in this subspace for an approximate
solution to the inverse problem. We present an example of using the code
provided as a Python class.


  We investigate the effects of the presence of a non-vanishing net baryon
number density and its diffusion on dilepton production, within a
hydrodynamical description of the medium created at $\sqrt{s_{NN}}=7.7$ GeV
collision energy. This energy value is explored within the Beam Energy Scan
(BES) program at Relativistic Heavy Ion Collider (RHIC) at Brookhaven National
Laboratory. Particular attention is devoted to a new dissipative degree of
freedom: the net baryon number diffusion ($V^\mu$), and to the net baryon
number conductivity ($\kappa$) | a transport coefficients governing the overall
magnitude of $V^\mu$. The effects of $\kappa$ on dilepton production are
assessed, with an outlook on how future experimental dilepton data can be used
to learn more about $\kappa$.


  We propose a new model for the extended Ly alpha blobs found recently at high
redshift z ~ 3. The observational properties of these blobs are; 1) the
observed Ly alpha luminosities are ~ 10^{43} h^{-2} ergs s^{-1}, 2) they appear
elongated morphologically, 3) their sizes amount to ~ 100 kpc, 4) the observed
line widths amount to ~ 1000 km s^{-1}, and 5) they are not associated with
strong radio-continuum sources. All these observational properties seem to be
explained in terms of galactic winds driven by successive supernova explosions
shortly after the initial burst of massive star formation in the galactic
centers. The observed number density of Ly alpha blobs (~ 3.4 x 10^{-5} h^3
Mpc^{-3}) may be explained if their present-day counterparts are elliptical
galaxies with a luminosity above ~ 1 L^*.


  We use intersection theory techniques to define an invariant of closed
3-manifolds counting the characters of irreducible representations of the
fundamental group in PSL(2,C). We note several properties of the invariant and
compute the invariant for certain Seifert fibered spaces and for some Dehn
surgeries on twist knots. We discuss the relationship between this invariant
and the SL(2,C)-invariant.


  Pure states in quantum field theory can be represented by many-fingered
block-time wave functions, which treat time on an equal footing with space and
make the notions of "time evolution" and "state at a given time" fundamentally
irrelevant. Instead of information destruction resulting from an attempt to use
a "state at a given time" to describe semi-classical black-hole evaporation,
the full many-fingered block-time wave function of the universe conserves
information by describing the correlations of outgoing Hawking particles in the
future with ingoing Hawking particles in the past.


  Usually, the study of city population distribution has been reduced to power
laws. In such analysis, a common practice is to consider cities with more than
one hundred thousand inhabitants. Here, we argue that the distribution of
cities for all ranges of populations can be well described by using a
$q$-exponential distribution. This function, which reproduces the
Zipf-Mandelbrot law, is related to the generalized nonextensive statistical
mechanics and satisfies an anomalous decay equation.


  The number of known variable stars has increased by several magnitudes over
the last decade, and automated classification routines are becoming
increasingly important to cope with this development. Here we show that the
"upside-down CBH variables", which were proposed as a potentially new class of
variable stars by Heinze et al. (2018) in the ATLAS First Catalogue of Variable
Stars, are, at least to a high percentage, made up of alpha2 Canum Venaticorum
(ACV) variables - that is, photometrically variable magnetic chemically
peculiar (CP2/He-peculiar) stars - with distinct double-wave light curves.
Using suitable selection criteria, we identified 264 candidate ACV variables in
the ATLAS variable star catalogue. 62 of these objects were spectroscopically
confirmed with spectra from the Large Sky Area Multi-Object Fiber Spectroscopic
Telescope (all new discoveries except for nine stars) and classified on the MK
system. The other 202 stars are here presented as ACV star candidates that
require spectroscopic confirmation. The vast majority of our sample of stars
are main-sequence objects. Derived masses range from 1.4M(Sun) to 5M(Sun), with
half our sample stars being situated in the range from 2 M(Sun) to 2.4 M(Sun),
in good agreement with the spectral classifications. Most stars belong to the
thin or thick disk; four objects, however, classify as members of the halo
population. With a peak magnitude distribution at around 14th magnitude, the
here presented stars are situated at the faint end of the known Galactic mCP
star population. Our study highlights the need to consider rare variability
classes, like ACV variables, in automated classification routines.


  In this research, we are interested in constraining the nonlinear interacting
and noninteracting Tsallis holographic dark energy (THDE) with Ricci horizon
cutoff by employing three observational datasets. To this aim, the THDE with
Ricci horizon considering the noninteraction and nonlinear interaction terms
will be fitted by the SNe Ia, SNe Ia+H(z), and SNe Ia+H(z)+GRB samples to
investigate the Hubble ($H(z)$), dark energy equation of state ($\omega_{DE}$),
effective equation of state ($\omega_{eff}$), and deceleration ($q$)
parameters. Investigating the $H(z)$ parameter illustrates that our models are
in good consistent with respect to observation. Also, it can reveal the turning
point for both noninteracting and nonlinear interacting THDE with Ricci cutoff
in the late time era. Next, the analysis of the $\omega_{DE}$ for our models
displays that the dark energy can experience the phantom state at the current
time. However, it lies in the quintessence regime in the early era and
approaches the cosmological constant in the late-time epoch. Similar results
will be for the $\omega_{eff}$ parameter with this difference that the
$\omega_{eff}$ will experience the quintessence region at the current redshift.
Next to the mentioned parameters, the study of the $q$ parameter indicates that
the models satisfy an acceptable transition phase from the matter to the dark
energy-dominated era. After that, the classical stability ($v_{s}^{2}$) will be
analyzed for our models. The $v_{s}^{2}$ shows that the noninteracting and
nonlinear interacting THDE with Ricci cutoff will be stable in the past era,
unstable in the present, and progressive epochs. Then, we will employ the
$Jerk$ ($J$) and $OM$ parameters to distinguish between our models and the
$\Lambda CDM$ model. Finally, we will calculate the age of the Universe for the
THDE and nonlinear interacting THDE with Ricci as the IR cutoff.


  We adapt a general method to solve both the full and reduced Salpeter
equations and systematically explore the conditions under which these two
equations give equivalent results in meson dynamics. The effects of constituent
mass, angular momentum state, type of interaction, and the nature of
confinement are all considered in an effort to clearly delineate the range of
validity of the reduced Salpeter approximations. We find that for
$J\not{\hspace*{-1.0mm}=}0$ the solutions are strikingly similar for all
constituent masses. For zero angular momentum states the full and reduced
Salpeter equations give different results for small quark mass especially with
a large additive constant coordinate space potential. We also show that
$\frac{1}{m}$ corrections to heavy-light energy levels can be accurately
computed with the reduced equation.


  I show that by assuming a standard Blandford-Konigl jet, it is possible to
determine the bulk Lorentz factor and angle to the line of sight of
self-similar parsec-scale blazar jets by using five measured quantities:
redshift, core radio flux, extended radio flux, the magnitude of the core shift
between two frequencies, and apparent jet opening angle. From the bulk Lorentz
factor and angle computed with this method, one can compute other jet
properties such as the Doppler factor, magnetic field strength, and intrinsic
jet opening angle. I use data taken from the literature and marginalize over
nuisance parameters associated with the electron distribution and equipartition
to compute these quantities, although the errors are large. Results are
generally consistent with constraints from other methods. Primary sources of
uncertainty are the errors on the core shift measurements and the uncertainty
in the electron spectral index.


  Let X be a simply connected compact Riemannian symmetric space, let U be the
universal covering group of the identity component of the isometry group of X,
and let \g denote the complexification of the Lie algebra of U, \g=\u^\C. Each
\u-compatible triangular decomposition \g=\n_- + \h + \n_+ determines a Poisson
Lie group structure \pi_U on U. The Evens-Lu construction produces a
(U,\pi_U)-homogeneous Poisson structure on X. By choosing the basepoint in X
appropriately, X is presented as U/K where K is the fixed point set of an
involution which stabilizes the triangular decomposition of \g. With this
presentation, a connection is established between the symplectic foliation of
the Evens-Lu Poisson structure and the Birkhoff decomposition of U/K. This is
done through reinterpretation of results of Pickrell. Each symplectic leaf
admits a natural torus action. It is shown that the action is Hamiltonian and
the momentum map is computed using triangular factorization. Finally, local
formulas for the Evens-Lu Poisson structure are displayed in several examples.


  We present a genetic algorithm (GA) for structural search that combines the
speed of structure exploration by classical potentials with the accuracy of
density functional theory (DFT) calculations in an adaptive and iterative way.
This strategy increases the efficiency of the DFT-based GA by several orders of
magnitude. This gain allows considerable increase in size and complexity of
systems that can be studied by first principles. The method's performance is
illustrated by successful structure identifications of complex binary and
ternary inter-metallic compounds with 36 and 54 atoms per cell, respectively.
The discovery of a multi-TPa Mg-silicate phase with unit cell containing up to
56 atoms is also reported. Such phase is likely to be an essential component of
terrestrial exoplanetary mantles.


  Using the language of operated algebras, we construct and investigate a class
of operator rings and enriched modules induced by a derivation or Rota-Baxter
operator. In applying the general framework to univariate polynomials, one is
led to the integro-differential analogs of the classical Weyl algebra. These
are analyzed in terms of skew polynomial rings and noncommutative Groebner
bases.


  We consider an incompressible kinetic Fokker Planck equation in the flat
torus, which is a simplified version of the Lagrangian stochastic models for
turbulent flows introduced by S.B. Pope in the context of computational fluid
dynamics. The main difficulties in its treatment arise from a pressure type
force that couples the Fokker Planck equation with a Poisson equation which
strongly depends on the second order moments of the fluid velocity. In this
paper we prove short time existence of analytic solutions in the
one-dimensional case, for which we are able to use techniques and functional
norms that have been recently introduced in the study of a related singular
model.


  Interactive search can provide a better experience by incorporating
interaction feedback from the users. This can significantly improve search
accuracy as it helps avoid irrelevant information and captures the users'
search intents. Existing state-of-the-art (SOTA) systems use reinforcement
learning (RL) models to incorporate the interactions but focus on item-level
feedback, ignoring the fine-grained information found in sentence-level
feedback. Yet such feedback requires extensive RL action space exploration and
large amounts of annotated data. This work addresses these challenges by
proposing a new deep Q-learning (DQ) approach, DQrank. DQrank adapts BERT-based
models, the SOTA in natural language processing, to select crucial sentences
based on users' engagement and rank the items to obtain more satisfactory
responses. We also propose two mechanisms to better explore optimal actions.
DQrank further utilizes the experience replay mechanism in DQ to store the
feedback sentences to obtain a better initial ranking performance. We validate
the effectiveness of DQrank on three search datasets. The results show that
DQRank performs at least 12% better than the previous SOTA RL approaches. We
also conduct detailed ablation studies. The ablation results demonstrate that
each model component can efficiently extract and accumulate long-term
engagement effects from the users' sentence-level feedback. This structure
offers new technologies with promised performance to construct a search system
with sentence-level interaction.


  We present the results of our analysis on $b \to s \gamma$ in the minimal
supersymmetric standard model with a general flavor mixing in the squark
sector. We identify the next--to--leading order focusing effect, which
considerably reduces the gluino contribution to $b \to s \gamma$ relative to
the leading order calculation. We illustrate that $BR(B \to X_s \gamma)$ is
still very sensitive to the flavor mixing parameters, $\delta^d_{ll}$ and
$\delta^d_{lr}$ so that the lower bound for $m_{1/2}$ obtained in the minimal
flavor violation can be easily removed even at $\mu<0$, while it is rather
stable against $\delta^d_{rr}$ and $\delta^d_{rl}$.


  We present direct numerical simulations of turbulent channel flow with
passive Lagrangian polymers. To understand the polymer behavior we investigate
the behavior of infinitesimal line elements and calculate the probability
distribution function (PDF) of finite-time Lyapunov exponents and from them the
corresponding Cramer's function for the channel flow. We study the statistics
of polymer elongation for both the Oldroyd-B model (for Weissenberg number $\Wi
<1$) and the FENE model. We use the location of the minima of the Cramer's
function to define the Weissenberg number precisely such that we observe
coil-stretch transition at $\Wi\approx1$. We find agreement with earlier
analytical predictions for PDF of polymer extensions made by Balkovsky, Fouxon
and Lebedev [Phys. Rev. Lett., 84, 4765 (2000).] for linear polymers (Oldroyd-B
model) with $\Wi<1$ and by Chertkov [Phys. Rev. Lett., 84, 4761 (2000).] for
nonlinear FENE-P model of polymers. For $\Wi>1$ (FENE model) the polymer are
significantly more stretched near the wall than at the center of the channel
where the flow is closer to homogenous isotropic turbulence. Furthermore near
the wall the polymers show a strong tendency to orient along the stream-wise
direction of the flow but near the centerline the statistics of orientation of
the polymers is consistent with analogous results obtained recently in
homogeneous and isotropic flows.


  We study extensions of the mappings arising in usual Channel-State duality to
the case of Hilbert spaces with a direct sum structure. This setting arises in
representations of algebras with centers, which are commonly associated with
constraints, and it has many physical applications from quantum many-body
theory to holography and quantum gravity. We establish that there is a general
relationship between non-separability of the state and the isometric properties
of the induced channel. We also provide a generalisation of our approach to
algebras of trace-class operators on infinite dimensional Hilbert spaces.


  In this paper, we justify the low Mach number limit of the steady
irrotational Euler flows for the airfoil problem, which is the first result for
the low Mach number limit of the steady Euler flows in an exterior domain. The
uniform estimates on the compressibility parameter $\varepsilon$, which is
singular for the flows, are established via a variational approach based on the
compressible-incompressible difference functions. The limit is on the
H\"{o}lder space and is unique. Moreover, the convergence rate is of order
$\varepsilon^2$. It is noticeable that, due to the feature of the airfoil
problem, the extra force dominates the asymptotic decay rate of the
compressible flow to the infinity. And the effect of extra force vanishes in
the limiting process from compressible flows to the incompressible ones, as the
Mach number goes to zero.


  The Australian, Chinese, European, Indian, and North American pulsar timing
array (PTA) collaborations recently reported, at varying levels, evidence for
the presence of a nanohertz gravitational wave background (GWB). Given that
each PTA made different choices in modeling their data, we perform a comparison
of the GWB and individual pulsar noise parameters across the results reported
from the PTAs that constitute the International Pulsar Timing Array (IPTA). We
show that despite making different modeling choices, there is no significant
difference in the GWB parameters that are measured by the different PTAs,
agreeing within $1\sigma$. The pulsar noise parameters are also consistent
between different PTAs for the majority of the pulsars included in these
analyses. We bridge the differences in modeling choices by adopting a
standardized noise model for all pulsars and PTAs, finding that under this
model there is a reduction in the tension in the pulsar noise parameters. As
part of this reanalysis, we "extended" each PTA's data set by adding extra
pulsars that were not timed by that PTA. Under these extensions, we find better
constraints on the GWB amplitude and a higher signal-to-noise ratio for the
Hellings and Downs correlations. These extensions serve as a prelude to the
benefits offered by a full combination of data across all pulsars in the IPTA,
i.e., the IPTA's Data Release 3, which will involve not just adding in
additional pulsars, but also including data from all three PTAs where any given
pulsar is timed by more than as single PTA.


  Let $X$ be a separable nonquasireflexive Banach space. Let $Y$ be a Banach
space isomorphic to a subspace of $X^*$. The paper is devoted to the following
questions: 1. Under what conditions does there exist an isomorphic embedding
$T:Y\to X^*$ such that subspace $T(Y)\subset X^*$ is total? 2. If such
embeddings exist, what are the possible orders of $T(Y)$?
  Here we need to recall some definitions. For a subset $M\subset X^*$ we
denote the set of all limits of weak$^*$ convergent sequences in $M$ by
$M_{(1)}$. Inductively, for ordinal number $\alpha$ we let
$$M_{(\alpha)}=\cup_{\beta<\alpha}(M_{(\beta)})_{(1)}.$$
  The least ordinal $\alpha$ for which $M_{(\alpha)}= M_{(\alpha+1)}$ is called
the {\it order} of $M$.


  Deep learning techniques have shown promising results in the automatic
classification of respiratory sounds. However, accurately distinguishing these
sounds in real-world noisy conditions poses challenges for clinical deployment.
Additionally, predicting signals with only background noise could undermine
user trust in the system. In this study, we propose an audio enhancement (AE)
pipeline as a pre-processing step before respiratory sound classification,
aiming to improve performance in noisy environments. Multiple experiments were
conducted using different audio enhancement model structures, demonstrating
improved classification performance compared to the baseline method of noise
injection data augmentation. Specifically, the integration of the AE pipeline
resulted in a 2.59% increase in the ICBHI classification score on the ICBHI
respiratory sound dataset and a 2.51% improvement on our recently collected
Formosa Archive of Breath Sounds (FABS) in multi-class noisy scenarios.
Furthermore, a physician validation study assessed the clinical utility of our
system. Quantitative analysis revealed enhancements in efficiency, diagnostic
confidence, and trust during model-assisted diagnosis with our system compared
to raw noisy recordings. Workflows integrating enhanced audio led to an 11.61%
increase in diagnostic sensitivity and facilitated high-confidence diagnoses.
Our findings demonstrate that incorporating an audio enhancement algorithm
significantly enhances robustness and clinical utility.


  We consider the stochastic volatility model obtained by adding a compound
Hawkes process to the volatility of the well-known Heston model. A Hawkes
process is a self-exciting counting process with many applications in
mathematical finance, insurance, epidemiology, seismology and other fields. We
prove a general result on the existence of a family of equivalent (local)
martingale measures. We apply this result to a particular example where the
sizes of the jumps are exponentially distributed.


  Gromov and Lawson conjectured that a closed spin manifold M of dimension n
with fundamental group pi admits a metric with positive scalar curvature if and
only if an associated element in KO_n(B pi) vanishes. In this note we present
counter examples to the `if' part of this conjecture for groups pi which are
torsion free and whose classifying space is a manifold with negative curvature
(in the Alexandrov sense).


  For a low-mobile Poisson bipolar network and under
line-of-sight/non-line-of-sight (LOS/NLOS) path-loss model, we study repetitive
retransmissions (RR) and blocked incremental redundancy (B-IR). We consider
spatially-coded multiple-input multiple-output (MIMO) zero-forcing beamforming
(ZFBF) multiplexing system, whereby the packet success reception is determined
based on the aggregate data rate across spatial dimensions of the MIMO system.
Characterization of retransmission performance in this low-mobile configuration
is practically important, but inherently complex due to a substantial rate
correlation across retransmissions and intractability of evaluating the
probability density function (pdf) of aggregate data rate. Adopting tools of
stochastic geometry, we firstly characterize the rate correlation coefficient
(RCC) for both schemes. Our results show that, compared to RR scheme, B-IR
scheme has higher RCC while its coverage probability is substantially larger.
We demonstrate that the spotted contention between coverage probability and RCC
causes the mean transmission delay (MTD) of B-IR to become either smaller or
larger than the MTD of RR scheme. Finally, we develop a numerical approximation
of MTD, and evaluate the effective spatial throughput (EST), which is
reciprocal to MTD, of RR and B-IR schemes. Our numerical results highlight
fundamental tradeoffs between densification, multiplexing gain, block length,
and activity factor of nodes. We further observe that for dense networks 1) LOS
component is considerably instrumental to enhance EST; 2) EST of B-IR scheme
can be much higher than that of RR scheme; 3) When Doppler spread exists, it
can improve MTD of B-IR while it does not cast any meaningful effect on the MTD
of RR.


  The recent confirmation by FNAL of the $(g-2)_\mu$ muon anomaly gives strong
evidence for the possible existence of new physics beyond the Standard Model in
the muon sector. Thus it is worthy to revisit the existing experimental
constraints on models suggesting theoretically consistent explanations of the
anomaly. In this work, we point out that accounting for the loss of coherence
between the wave packets(mass states) of solar neutrinos is important for
setting limits on any model with new flavor-sensitive couplings in the neutrino
sector. By taking into account this effect and considering more accurately the
experimental constraints from the BOREXINO measurement of the $^7$Be solar
neutrino interaction rate we corrected the limits previously placed on the
coupling of the light $Z'$ to $L_\mu$-$L_\tau$ current in the parameter space
relevant to the muon $(g-2)_\mu$.


  We revisit model calculations of the anomalous Hall effect (AHE) and show
that, in isotropic Rashba-coupled two-dimensional electron gas (2DEG) with
pointlike potential impurities, the full solution of the semiclassical
Boltzmann equation (SBE) may differ from the widely-used $1/\tau^{||}$ &
$1/\tau^{\perp}$ solution [Phys. Rev. B 68, 165311 (2003)]. Our approach to AHE
is analogous to the SBE-based analysis of the anisotropic magnetoresistance
leading to an integral equation for the distribution function [Phys. Rev. B 79,
045427 (2009)] but in the present case, we reduce the description to
band-index-dependent transport relaxation times. When both Rashba bands are
partially occupied, these are determined by solving a system of linear
equations. Detailed calculations show that, for intrinsic and hybrid skew
scatterings the difference between $1/\tau^{||}$ & $1/\tau^{\perp}$ and the
full solution of SBE is notable for large Fermi energies. For coordinate-shift
effects, the side-jump velocity acquired in the inter-band elastic scattering
process is shown to be more important for larger Rashba coupling and may even
exceed the intra-band one for the outer Rashba band. The coordinate-shift
contribution to AHE in the considered case notably differs from that in the
limit of smooth disorder potential analyzed before.


  Statistical phylogenetic inference methods use tree rearrangement operations
to perform either hill-climbing local search or Markov chain Monte Carlo across
tree topologies. The canonical class of such moves are the
subtree-prune-regraft (SPR) moves that remove a subtree and reattach it
somewhere else via the cut edge of the subtree. Phylogenetic trees and such
moves naturally form the vertices and edges of a graph, such that tree search
algorithms perform a (potentially stochastic) traversal of this SPR graph.
Despite the centrality of such graphs in phylogenetic inference, rather little
is known about their large-scale properties. In this paper we learn about the
rooted-tree version of the graph, known as the rSPR graph, by calculating the
Ricci-Ollivier curvature for pairs of vertices in the rSPR graph with respect
to two simple random walks on the rSPR graph. By proving theorems and direct
calculation with novel algorithms, we find a remarkable diversity of different
curvatures on the rSPR graph for pairs of vertices separated by the same
distance. We confirm using simulation that degree and curvature have the
expected impact on mean access time distributions, demonstrating relevance of
these curvature results to stochastic tree search. This indicates significant
structure of the rSPR graph beyond that which was previously understood in
terms of pairwise distances and vertex degrees; a greater understanding of
curvature could ultimately lead to improved strategies for tree search.


  Existing state-of-the-art human pose estimation methods require heavy
computational resources for accurate predictions. One promising technique to
obtain an accurate yet lightweight pose estimator is knowledge distillation,
which distills the pose knowledge from a powerful teacher model to a
less-parameterized student model. However, existing pose distillation works
rely on a heavy pre-trained estimator to perform knowledge transfer and require
a complex two-stage learning procedure. In this work, we investigate a novel
Online Knowledge Distillation framework by distilling Human Pose structure
knowledge in a one-stage manner to guarantee the distillation efficiency,
termed OKDHP. Specifically, OKDHP trains a single multi-branch network and
acquires the predicted heatmaps from each, which are then assembled by a
Feature Aggregation Unit (FAU) as the target heatmaps to teach each branch in
reverse. Instead of simply averaging the heatmaps, FAU which consists of
multiple parallel transformations with different receptive fields, leverages
the multi-scale information, thus obtains target heatmaps with higher-quality.
Specifically, the pixel-wise Kullback-Leibler (KL) divergence is utilized to
minimize the discrepancy between the target heatmaps and the predicted ones,
which enables the student network to learn the implicit keypoint relationship.
Besides, an unbalanced OKDHP scheme is introduced to customize the student
networks with different compression rates. The effectiveness of our approach is
demonstrated by extensive experiments on two common benchmark datasets, MPII
and COCO.


  This study addresses the challenge of detecting semantic column types in
relational tables, a key task in many real-world applications. While language
models like BERT have improved prediction accuracy, their token input
constraints limit the simultaneous processing of intra-table and inter-table
information. We propose a novel approach using Graph Neural Networks (GNNs) to
model intra-table dependencies, allowing language models to focus on
inter-table information. Our proposed method not only outperforms existing
state-of-the-art algorithms but also offers novel insights into the utility and
functionality of various GNN types for semantic type detection. The code is
available at https://github.com/hoseinzadeehsan/GAIT


  Aims: Detect tertiary components of close binaries from spectroscopy and
light curve modelling; investigate light-travel time effect and the possibility
of magnetic activity cycles; measure mass-ratios for unstudied systems and
derive absolute parameters.
  Methods: We carried out new photometric and spectroscopic observations of
five bright (V<10.5 mag) close eclipsing binaries, predominantly in the
southern skies. We obtained full Johnson BV light curves, which were modelled
with the Wilson-Devinney code. Radial velocities were measured with the
cross-correlation method using IAU radial velocity standards as spectral
templates. Period changes were studied with the O-C method, utilising published
epochs of minimum light (XY Leo) and ASAS photometry (VZ Lib).
  Results: For three objects (DX Tuc, QY Hya, V870 Ara), absolute parameters
have been determined for the first time. We detect spectroscopically the
tertiary components in XY Leo, VZ Lib and discover one in QY Hya. For XY Leo we
update the light-time effect parameters and detect a secondary periodicity of
about 5100 d in the O$-$C diagram that may hint about the existence of
short-period magnetic cycles. A combination of recent photometric data shows
that the orbital period of the tertiary star in VZ Lib is likely to be over
1500 d. QY Hya is a semi-detached X-ray active binary in a triple system with K
and M-type components, while V870 Ara is a contact binary with the third
smallest spectroscopic mass-ratio for a W UMa star to date (q=0.082+/-0.030).
This small mass-ratio, being close to the theoretical minimum for contact
binaries, suggests that V870 Ara has the potential of constraining evolutionary
scenarios of binary mergers. The inferred distances to these systems are
compatible with the Hipparcos parallaxes.


  Few-body $\Lambda$ hypernuclei provide valuable information towards
understanding strange matter. Recent experimental progress by the STAR
Collaboration at the RHIC facility and by the ALICE Collaboration at the LHC
has been matched by theoretical progress reviewed here: (i) lifetimes of the
hypertriton $_{\Lambda}^3$H, $_{\Lambda}^3$n if particle-stable,
$_{\Lambda}^4$H and $_{\Lambda}^4$He and their charge symmetry breaking, and
(ii) the onset of $\Lambda\Lambda$ hypernuclear binding.


  State machines play a pivotal role in augmenting the efficacy of protocol
analyzing to unveil more vulnerabilities. However, the task of inferring state
machines from network protocol implementations presents significant challenges.
Traditional methods based on dynamic analysis often overlook crucial state
transitions due to limited coverage, while static analysis faces difficulties
with complex code structures and behaviors. To address these limitations, we
propose an innovative state machine inference approach powered by Large
Language Models (LLMs). Utilizing text-embedding technology, this method allows
LLMs to dissect and analyze the intricacies of protocol implementation code.
Through targeted prompt engineering, we systematically identify and infer the
underlying state machines. Our evaluation across six protocol implementations
demonstrates the method's high efficacy, achieving an accuracy rate exceeding
90% and successfully delineating differences on state machines among various
implementations of the same protocol. Importantly, integrating this approach
with protocol fuzzing has notably enhanced AFLNet's code coverage by 10% over
RFCNLP, showcasing the considerable potential of LLMs in advancing network
protocol security analysis. Our proposed method not only marks a significant
step forward in accurate state machine inference but also opens new avenues for
improving the security and reliability of protocol implementations.


  Counting the frequency of small subgraphs is a fundamental technique in
network analysis across various domains, most notably in bioinformatics and
social networks. The special case of triangle counting has received much
attention. Getting results for 4-vertex or 5-vertex patterns is highly
challenging, and there are few practical results known that can scale to
massive sizes.
  We introduce an algorithmic framework that can be adopted to count any small
pattern in a graph and apply this framework to compute exact counts for
\emph{all} 5-vertex subgraphs. Our framework is built on cutting a pattern into
smaller ones, and using counts of smaller patterns to get larger counts.
Furthermore, we exploit degree orientations of the graph to reduce runtimes
even further. These methods avoid the combinatorial explosion that typical
subgraph counting algorithms face. We prove that it suffices to enumerate only
four specific subgraphs (three of them have less than 5 vertices) to exactly
count all 5-vertex patterns.
  We perform extensive empirical experiments on a variety of real-world graphs.
We are able to compute counts of graphs with tens of millions of edges in
minutes on a commodity machine. To the best of our knowledge, this is the first
practical algorithm for $5$-vertex pattern counting that runs at this scale. A
stepping stone to our main algorithm is a fast method for counting all
$4$-vertex patterns. This algorithm is typically ten times faster than the
state of the art $4$-vertex counters.


  Source localization and radio cartography using multi-way representation of
spectrum is the subject of study in this paper. A joint matrix factorization
and tensor decomposition problem is proposed and solved using an iterative
algorithm. The multi-way measured spectrum is organized in a tensor and it is
modeled by multiplication of a propagation tensor and a channel gain matrix.
The tensor indicates the propagating power from each location and each
frequency over time and the channel matrix links the propagating tensor to the
sensed spectrum. We utilize sparsity and other intrinsic characteristics of
spectrum to identify the solution of the proposed problem. Moreover, The online
implementation of the proposed framework results in online radio cartography
which is a powerful tool for efficient spectrum awareness and utilization. The
simulation results show that our algorithm is a promising technique for dynamic
primary user localization and online radio cartography.


  The Basal Ganglia is a central structure involved in multiple cortical and
subcortical loops. Some of these loops are believed to be responsible for
saccade target selection. We study here how the very specific structural
relationships of these saccadic loops can affect the ability of learning
spatial and feature-based tasks.
  We propose a model of saccade generation with reinforcement learning
capabilities based on our previous basal ganglia and superior colliculus
models. It is structured around the interactions of two parallel cortico-basal
loops and one tecto-basal loop. The two cortical loops separately deal with
spatial and non-spatial information to select targets in a concurrent way. The
subcortical loop is used to make the final target selection leading to the
production of the saccade. These different loops may work in concert or disturb
each other regarding reward maximization. Interactions between these loops and
their learning capabilities are tested on different saccade tasks.
  The results show the ability of this model to correctly learn basic target
selection based on different criteria (spatial or not). Moreover the model
reproduces and explains training dependent express saccades toward targets
based on a spatial criterion.
  Finally, the model predicts that in absence of prefrontal control, the
spatial loop should dominate.


  Quantifying the directionality of information flow is instrumental in
understanding, and possibly controlling, the operation of many complex systems,
such as transportation, social, neural, or gene-regulatory networks. The
standard Transfer Entropy (TE) metric follows Granger's causality principle by
measuring the Mutual Information (MI) between the past states of a source
signal $X$ and the future state of a target signal $Y$ while conditioning on
past states of $Y$. Hence, the TE quantifies the improvement, as measured by
the log-loss, in the prediction of the target sequence $Y$ that can be accrued
when, in addition to the past of $Y$, one also has available past samples from
$X$. However, by conditioning on the past of $Y$, the TE also measures
information that can be synergistically extracted by observing both the past of
$X$ and $Y$, and not solely the past of $X$. Building on a private key
agreement formulation, the Intrinsic TE (ITE) aims to discount such synergistic
information to quantify the degree to which $X$ is \emph{individually}
predictive of $Y$, independent of $Y$'s past. In this paper, an estimator of
the ITE is proposed that is inspired by the recently proposed Mutual
Information Neural Estimation (MINE). The estimator is based on variational
bound on the KL divergence, two-sample neural network classifiers, and the
pathwise estimator of Monte Carlo gradients.


  We consider an unbounded lattice and at each point of this lattice an
anharmonic oscillator, that interacts with its first neighborhoods via a pair
potential $V$ and is subjected to a restoring force of potential $U$. We assume
that $U$ and $V$ are even nonnegative polynomials of degree $2\sigma_1$ and
$2\sigma_2$. We study the time evolution of this system, with a control of the
growth in time of the local energy, and we give a nontrivial bound on the
velocity of propagation of a perturbation. This is an extension to the case
$\sigma_1 < 2\sigma_2-1$ of some already known results obtained for $\sigma_1
\geq 2\sigma_2-1$.


  We consider the scalar sector of a general renormalizable theory and evaluate
the effective potential through three loops analytically. We encounter
three-loop vacuum bubble diagrams with up to two masses and six lines, which we
solve using differential equations transformed into the favorable $\epsilon$
form of dimensional regularization. The master integrals of the canonical basis
thus obtained are expressed in terms of cyclotomic polylogarithms up to weight
four. We also introduce an algorithm for the numerical evaluation of cyclotomic
polylogarithms with multiple-precision arithmetic, which is implemented in the
Mathematica package cyclogpl.m supplied here.


  We discuss recently published results of two-dimensional measurements of the
cosmic ray anisotropy in the energy range 1-100 TeV. It is demonstrated that,
in spite of pretence of the authors to measure the anisotropy in more detail
than it was done in one-dimensional measurements of the first harmonic of CR
intensity in sidereal time, new measurements give nothing essentially new.
Moreover, two-dimensional picture is misleading creating an illusion that the
true direction of the anisotropy is observed, while, as before, only the
projection of the anisotropy onto the equatorial plane is measured and the
phase of the anisotropy remains to be the only directly measured parameter. The
sophisticated interpretations of the results of 2D measurements made by their
authors are invalid, since they are based on the false assumption that the
equatorial excess and deficit of CR intensity seen on the difference maps
represent the real anisotropy.


  We study the inverse problem for determining the time-dependent matrix
potential appearing in the wave equation. We prove the unique determination of
potential from the knowledge of solution measured on a part of the boundary.


  We apply recent bounds of the author (math.PR/0609224) for generalized
Smirnov statistics to the distribution of integers whose prime factors satisfy
certain systems of inequalities.


  We study the effects of the long-range disorder potential and warping on the
conductivity and mobility of graphene ribbons using the Landauer formalism and
the tight-binding p-orbital Hamiltonian. We demonstrate that as the length of
the structure increases the system undergoes a transition from the ballistic to
the diffusive regime. This is reflected in the calculated electron density
dependencies of the conductivity and the mobility. In particular, we show that
the mobility of graphene ribbons varies as mu(n) n^(-lambda), with
0<lambda<0.5. The exponent lambda depends on the length of the system with
lambda=0.5 corresponding to short structures in the ballistic regime, whereas
the diffusive regime lambda=0 (when the mobility is independent on the electron
density) is reached for sufficiently long structures. Our results can be used
for the interpretation of experimental data when the value of lambda can be
used to distinguish the transport regime of the system (i.e. ballistic,
quasi-ballistic or diffusive). Based on our findings we discuss available
experimental results.


  We study the effect of a perpendicular magnetic fieldBon a multinode Weyl
semimetal (mWSM)of arbitrary integer monopole chargen, with the two Weyl
multinodes separated ink-space. Besides type-I mWSMs, there exist type-II mWSMs
which are characterized by the tilted minimal dispersion for low-energy
excitations; the Weyl points in type-II mWSMs are still protected crossings but
appear at the contact of the electron and hole pockets, after the Lifshitz
transition. We find that the presence of a perpendicular magnetic field
quantizes the occupation pockets due to the presence of Fermi tubes. In this
theory, the Hilbert space is spanned by a set of $n$ chiral degenerate
groundstates, and a countably infinite number of particle-hole symmetric Landau
levels. We calculate the Hall conductivity for the tilt-symmetric case of
type-I mWSM using the Kubo formula, in the zero-frequency (DC) limit, and
recover the well-known vacuum contribution. We compute the Fermi surface
corrections and show that the expression generalizes from the formula for
elementary ($n=1$) type-I WSMs. We derive an expression for the type-II mWSM
Hall conductivity, which is bounded by a Landau level cutoff introduced on
physical grounds. Interestingly, we find that the anomalous vacuum Hall
conductivity is vanishing in the type-II phase at all temperatures. The
corresponding thermal Hall and Nernst conductivities are evaluated and
characterized for both phases. The qualitative and quantitative observations
presented here may serve in the characterization of generic mWSMs of both
types.


  Low-Rank Tensor Completion, a method which exploits the inherent structure of
tensors, has been studied extensively as an effective approach to tensor
completion. Whilst such methods attained great success, none have
systematically considered exploiting the numerical priors of tensor elements.
Ignoring numerical priors causes loss of important information regarding the
data, and therefore prevents the algorithms from reaching optimal accuracy.
Despite the existence of some individual works which consider ad hoc numerical
priors for specific tasks, no generalizable frameworks for incorporating
numerical priors have appeared. We present the Generalized CP Decomposition
Tensor Completion (GCDTC) framework, the first generalizable framework for
low-rank tensor completion that takes numerical priors of the data into
account. We test GCDTC by further proposing the Smooth Poisson Tensor
Completion (SPTC) algorithm, an instantiation of the GCDTC framework, whose
performance exceeds current state-of-the-arts by considerable margins in the
task of non-negative tensor completion, exemplifying GCDTC's effectiveness. Our
code is open-source.


  In this paper, we study binary triorthogonal codes and their relation to
CSS-T quantum codes. We characterize the binary triorthogonal codes that are
minimal or maximal with respect to the CSS-T poset, and we also study how to
derive new triorthogonal matrices from existing ones. Given a binary
triorthogonal matrix, we characterize which of its equivalent matrices are also
triorthogonal. As a consequence, we show that a binary triorthogonal matrix
uniquely determines the parameters of the corresponding triorthogonal quantum
code, meaning that any other equivalent matrix that is also triorthogonal gives
rise to a triorthogonal quantum code with the same parameters.


  Biaxially textured FeSe1-xTex films have been realized on Fe-buffered MgO
substrates by pulsed laser deposition. Similar to the Fe/BaFe2As2 bilayers, the
crystalline quality of FeSe1-xTex films exhibit a sharp out-of-plane and
in-plane texture less than 0.9{\deg}. The Fe/FeSe1-xTex bilayers showed high
superconducting transition temperatures of over 17 K. The angular-dependent
critical current densities exhibit peaks positioned at H // ab similar to other
pnictide thin films. The volume pinning force of FeSe1-xTex in this direction
is very strong compared with that of Co-doped BaFe2As2, due to a good matching
between the interlayer distance in the c direction and the out-of-plane
coherence length.


  A novel dynamic Bayesian nonparametric topic model for anomaly detection in
video is proposed in this paper. Batch and online Gibbs samplers are developed
for inference. The paper introduces a new abnormality measure for decision
making. The proposed method is evaluated on both synthetic and real data. The
comparison with a non-dynamic model shows the superiority of the proposed
dynamic one in terms of the classification performance for anomaly detection.


  Amorphous solids lack long-range order. Therefore identifying structural
defects -- akin to dislocations in crystalline solids -- that carry plastic
flow in these systems remains a daunting challenge. By comparing many different
structural indicators in computational models of glasses, under a variety of
conditions we carefully assess which of these indicators are able to robustly
identify the structural defects responsible for plastic flow in amorphous
solids. We further demonstrate that the density of defects changes as a
function of material preparation and strain in a manner that is highly
correlated with the macroscopic material response. Our work represents an
important step towards predicting how and when an amorphous solid will fail
from its microscopic structure.


  The first eclipsing binary pulsar, PSR B1957+20, was discovered in 1987.
Since then, 13 other eclipsing low-mass binary pulsars have been found, 12 of
these are in globular clusters. In this paper we list the known eclipsing
binary pulsars and their properties, with special attention to the eclipsing
systems in 47 Tuc. We find that there are two fundamentally different groups of
eclipsing binary pulsars; separated by their companion masses.
  The less massive systems (M_c ~ 0.02 M_sun) are a product of predictable
stellar evolution in binary pulsars. The systems with more massive companions
(M_c ~ 0.2 M_sun) were formed by exchange encounters in globular clusters, and
for that reason are exclusive to those environments. This class of systems can
be used to learn about the neutron star recycling fraction in the globular
clusters actively forming pulsars. We suggest that most of these binary systems
are undetectable at radio wavelengths.


  Peaking consistently in June for nearly eleven years, the annual modulation
signal reported by DAMA/NaI and DAMA/LIBRA offers strong evidence for the
identity of dark matter. DAMA's signal strongly suggest that dark matter
inelastically scatters into an excited state split by O(100 keV). We propose
that DAMA is observing hyperfine transitions of a composite dark matter
particle. As an example, we consider a meson of a QCD-like sector, built out of
constituent fermions whose spin-spin interactions break the degeneracy of the
ground state. An axially coupled U(1) gauge boson that mixes kinetically with
hypercharge induces inelastic hyperfine transitions of the meson dark matter
that can explain the DAMA signal.


  We discuss the relationship between the m-th homotopy group of the one-point
union of r copies of the two-dimensional sphere and the m-th homotopy group of
the one-point union of r+1 copies of the Thom space of the oriented
two-dimensional universal vector bundle. Using a suitably choosen isomorphism
between them a forgetful homomorphism is computed by evaluating on factors of
the Hilton splitting.


  We consider the scenario of electroweak baryogenesis mediated by cosmological
defect in models of supersymmetry breaking. When the effective electroweak
breaking scale is raised in the defect configuration, the mechanism of
electroweak baryogenesis works at a higher energy scale. The baryon charge
produced by the mechanism is captured in the defect, protected from sphalerons
and then released when the defect decay.


  We produce a flat $\Lambda$-module of $\Lambda$-adic critical slope
overconvergent modular forms, producing a Hida-type theory that interpolates
such forms over $p$-adically varying integer weights. This provides a
Hida-theoretic explanation for an observation of Coleman that the rank of such
forms is locally constant in the weight. The key to the interpolation is to use
Coleman's presentation of de Rham cohomology in terms of overconvergent forms
to link critical slope overconvergent modular forms with the ordinary part of
1st coherent cohomology of modular curves interpolated by Boxer--Pilloni's
higher Hida theory. We also set up a Galois deformation theory designed to
conform to these critical overconvergent forms and prove "$R = T$" for it. As
applications, we (1) produce a "formal" $\Lambda$-adic interpolation of the
ordinary part of de Rham cohomology, (2) produce a bi-ordinary complex whose
Hecke algebra $T$ is a natural candidate for an "$R = T$" theorem where $R$ is
a deformation ring for 2-dimensional $p$-adic representations of ${\rm
Gal}(\bar{\bf Q}/{\bf Q})$ that become reducible and decomposable upon
restriction to a decomposition group at $p$, (3) produce a degree-shifting
Hecke action on the cohomology of the bi-ordinary complex, and (4) specialize
this degree-shifting action to weight 1 and apply the critical "$R = T$"
theorem to find, under a supplemental assumption, an action of a Stark unit on
the part of weight 1 coherent cohomology over ${\bf Z}_p$ that is isotypic for
an ordinary eigenform with complex multiplication.


  In this paper, we consider a two-dimensional sticky Brownian motion. Sticky
Brownian motions can be viewed as time-changed semimartingale reflecting
Brownian motions, which find applications in many areas including queueing
theory and mathematical finance. For example, a sticky Brownian motion can be
used to model a storage system.with exceptional services. In this paper, we
focus on stationary distributions for sticky Brownian motions. The main results
obtained here include tail asymptotic properties in boundary stationary
distributions, marginal distributions, and joint distributions. The kernel
method, copula concept and extreme value theory are main tools used in our
analysis.


  In this study, we explore building a two-stage framework for enabling users
to directly manipulate high-level attributes of a natural scene. The key to our
approach is a deep generative network which can hallucinate images of a scene
as if they were taken at a different season (e.g. during winter), weather
condition (e.g. in a cloudy day) or time of the day (e.g. at sunset). Once the
scene is hallucinated with the given attributes, the corresponding look is then
transferred to the input image while preserving the semantic details intact,
giving a photo-realistic manipulation result. As the proposed framework
hallucinates what the scene will look like, it does not require any reference
style image as commonly utilized in most of the appearance or style transfer
approaches. Moreover, it allows to simultaneously manipulate a given scene
according to a diverse set of transient attributes within a single model,
eliminating the need of training multiple networks per each translation task.
Our comprehensive set of qualitative and quantitative results demonstrate the
effectiveness of our approach against the competing methods.


  We analyze a thought neutrino oscillation experiment in which neutrinos are
produced by electrons colliding with atomic nuclei of a target. The neutrinos
are detected by observing charged leptons, which are produced by neutrinos
colliding with nuclei of the detector. We consider the case when both the
target and detector nuclei have finite masses. (The case of infinitely heavy
nuclei was considered in the literature earlier.)


  Gaussian aperture pupil masks (GAPMs) can in theory achieve the contrast
requisite for directly imaging an extrasolar planet around a nearby solar type
star. We outline the process of designing, fabricating, and testing a GAPM for
use on current telescopes and specifically the Penn State near-IR Imager and
Spectrograph (PIRIS) at the Mt. Wilson 100$^{\prime\prime}$ telescope. We find
that the initial prototype observations are quite successful, achieving a
contrast similar to a traditional Lyot coronagraph without blocking any light
from a central object and useful for finding faint companions to nearby young
solar analogues. In the lab we can reproduce the expected PSF reasonably well
and with a single aperture design which achieves $\sim4 \times 10^{-5}$
contrast at 10$\lambda/D$.
  We find that small inaccuracies in the mask fabrication process and
insufficient correction of the atmosphere contribute the most degradation to
contrast at these levels.


  Distributed compression is the task of compressing correlated data by several
parties, each one possessing one piece of data and acting separately. The
classical Slepian-Wolf theorem (D. Slepian, J. K. Wolf, IEEE Transactions on
Inf. Theory, 1973) shows that if data is generated by independent draws from a
joint distribution, that is by a memoryless stochastic process, then
distributed compression can achieve the same compression rates as centralized
compression when the parties act together. Recently, the author (M. Zimand,
STOC 2017) has obtained an analogue version of the Slepian-Wolf theorem in the
framework of Algorithmic Information Theory (also known as Kolmogorov
complexity). The advantage over the classical theorem, is that the AIT version
works for individual strings, without any assumption regarding the generative
process. The only requirement is that the parties know the complexity profile
of the input strings, which is a simple quantitative measure of the data
correlation. The goal of this paper is to present in an accessible form that
omits some technical details the main ideas from the reference (M. Zimand, STOC
2017).


  Interest in weak cubical n-categories arises in various contexts, in
particular in topological field theories. In this paper, we describe a concept
of double bicategory, namely a strict model of the theory of bicategories in
Bicat. We show that in a special case one can reduce this to what we call a
Verity double bicategory, after Domenic Verity. This is a weakened version of a
double category, in the sense that composition in both horizontal and vertical
directions satisfy associativity and unit laws only up to (coherent)
isomorphisms. We prove that there are examples in the form of double
bicategories of "double cospans" (or "double spans") in any category with
pushouts (pullbacks, respectively), and give a construction from this which
involves taking isomorphism classes of objects, and gives a Verity double
bicategory of double cospans. We describe cobordisms with corners as an example
of this construction.


  Free theorems are a popular tool in reasoning about parametrically
polymorphic code. They are also of instructive use in teaching. Their
derivation, though, can be tedious, as it involves unfolding a lot of
definitions, then hoping to be able to simplify the resulting logical formula
to something nice and short. Even in a mechanised generator it is not easy to
get the right heuristics in place to achieve good outcomes. Dinaturality is a
categorical abstraction that captures many instances of free theorems.
Arguably, its origins are more conceptually involved to explain, though, and
generating useful statements from it also has its pitfalls. We present a simple
approach for obtaining dinaturality-related free theorems from the standard
formulation of relational parametricity in a rather direct way. It is
conceptually appealing and easy to control and implement, as the provided
Haskell code shows.


  This text is dedicated to the development of the theory of
$(\infty,\omega)$-categories. We present generalizations of standard results
from category theory, such as the lax Grothendieck construction, the Yoneda
lemma, lax (co)limits and lax Kan extensions, among others.


  We present an approximation algorithm for Weighted Tree Augmentation with
approximation factor $1+\ln 2 + \varepsilon < 1.7$. This is the first algorithm
beating the longstanding factor of $2$, which can be achieved through many
standard techniques.


  Matrices satisfying the Restricted Isometry Property (RIP) play an important
role in the areas of compressed sensing and statistical learning. RIP matrices
with optimal parameters are mainly obtained via probabilistic arguments, as
explicit constructions seem hard. It is therefore interesting to ask whether a
fixed matrix can be incorporated into a construction of restricted isometries.
In this paper, we construct a new broad ensemble of random matrices with
dependent entries that satisfy the restricted isometry property. Our
construction starts with a fixed (deterministic) matrix $X$ satisfying some
simple stable rank condition, and we show that the matrix $XR$, where $R$ is a
random matrix drawn from various popular probabilistic models (including,
subgaussian, sparse, low-randomness, satisfying convex concentration property),
satisfies the RIP with high probability. These theorems have various
applications in signal recovery, random matrix theory, dimensionality
reduction, etc. Additionally, motivated by an application for understanding the
effectiveness of word vector embeddings popular in natural language processing
and machine learning applications, we investigate the RIP of the matrix
$XR^{(l)}$ where $R^{(l)}$ is formed by taking all possible (disregarding
order) $l$-way entrywise products of the columns of a random matrix $R$.


  Subject of this article is the relationship between modern cosmology and
fundamental physics, in particular general relativity as a theory of gravity on
one side, together with its unique application in cosmology, and the formation
of structures and their statistics on the other. It summarises arguments for
the formulation for a metric theory of gravity and the uniqueness of the
construction of general relativity. It discusses symmetry arguments in the
construction of Friedmann-Lema\^itre cosmologies as well as assumptions in
relation to the presence of dark matter, when adopting general relativity as
the gravitational theory. A large section is dedicated to $\Lambda$CDM as the
standard model for structure formation and the arguments that led to its
construction, and to the of role statistics and to the problem of scientific
inference in cosmology as an empirical science. The article concludes with an
outlook on current and future developments in cosmology.


  We report the electronic properties of the cubic laves phase superconductor
CaIr2 (Tc = 5.8 K), in which the Ir atoms have a Pyrochlore lattice. The
estimated superconducting parameters obtained from magnetization and specific
heat measurements indicate that CaIr2 is a weakly coupled BCS superconductor.
Electronic band structure calculations show that the Ir d-states are dominant
at the Fermi level, creating a complex Fermi surface that is impacted
substantially by spin orbit coupling.


  In this paper, we study orbital stability of peakons for the generalized
modified Camassa-Holm (gmCH) equation, which is a natural higher-order
generalization of the modified Camassa-Holm (mCH) equation, and admits
Hamiltonian form and single peakons. We first show that the single peakon is
the usual weak solution of the PDEs. Some sign invariant properties and
conserved densities are presented. Next, by constructing the corresponding
auxiliary function $h(t,\,x)$ and establishing a delicate polynomial inequality
relating to the two conserved densities with the maximal value of approximate
solutions, the orbital stability of single peakon of the gmCH equation is
verified. We introduce a new approach to prove the key inequality, which is
different from that used for the mCH equation. This extends the result on the
stability of peakons for the mCH equation (Comm. Math. Phys., 322:967-997,
2013) successfully to the higher-order case, and is helpful to understand how
higher-order nonlinearities affect the dispersion dynamics.


  We combine the coordinate method and Erlangen program in the framework of
noncommutative geometry through an investigation of symmetries of
noncommutative coordinate algebras. As the model we use the coherent states
construction and the wavelet transform in functional spaces. New examples are a
three dimensional spectrum of a non-normal matrix and a quantisation procedure
from symplectomorphisms. Keywords: Heisenberg group, special linear group,
symplectic group, Hardy space, Segal-Bargmann space, Clifford algebra,
Cauchy-Riemann-Dirac operator, M\"obius transformations, functional calculus,
Weyl calculus (quantization), quantum mechanics, Schr\"odinger representation,
metaplectic representation.


  The effects of Coherent excitation of a two level system with a linearly
chirped pulse are studied theoretically and experimentally (in Rb (5s - 5p)) in
the low field regime. The Coherent Transients are measured directly on the
excited state population on an ultrashort time scale. A sharp step corresponds
to the passage through resonance. It is followed by oscillations resulting from
interferences between off-resonant and resonant contributions. We finally show
the equivalence between this experiment and Fresnel diffraction by a sharp
edge.


  This paper is a revised version of a previously posted paper in arxiv. The
authors posted it as a new submission by mistake. The latest version of the
paper can be found at arXiv:math-ph/0512003v2


  We suppose: (1) that the ground-state eigenvalue E = F(v) of the Schroedinger
Hamiltonian H = -Delta + vf(x) in one dimension is known for all values of the
coupling v > 0; and (2) that the potential shape can be expressed in the form
f(x) = g(x^2), where g is monotone increasing and convex. The inversion
inequality f(x) <= fbar(1/(4x^2)) is established, in which the `kinetic
potential' fbar(s) is related to the energy function F(v) by the
transformation: fbar(s) = F'(v), s = F(v) - vF'(v) As an example f is
approximately reconstructed from the energy function F for the potential f(x) =
x^2 + 1/(1+x^2).