  In recent years, Denoising Diffusion Probabilistic Models (DDPMs) have
demonstrated exceptional performance in various 2D generative tasks. Following
this success, DDPMs have been extended to 3D shape generation, surpassing
previous methodologies in this domain. While many of these models are
unconditional, some have explored the potential of using guidance from
different modalities. In particular, image guidance for 3D generation has been
explored through the utilization of CLIP embeddings. However, these embeddings
are designed to align images and text, and do not necessarily capture the
specific details needed for shape generation. To address this limitation and
enhance image-guided 3D DDPMs with augmented 3D understanding, we introduce
CISP (Contrastive Image-Shape Pre-training), obtaining a well-structured
image-shape joint embedding space. Building upon CISP, we then introduce IC3D,
a DDPM that harnesses CISP's guidance for 3D shape generation from single-view
images. This generative diffusion model outperforms existing benchmarks in both
quality and diversity of generated 3D shapes. Moreover, despite IC3D's
generative nature, its generated shapes are preferred by human evaluators over
a competitive single-view 3D reconstruction model. These properties contribute
to a coherent embedding space, enabling latent interpolation and conditioned
generation also from out-of-distribution images. We find IC3D able to generate
coherent and diverse completions also when presented with occluded views,
rendering it applicable in controlled real-world scenarios.


  This paper investigates reliable and covert transmission strategies in a
multiple-input multiple-output (MIMO) wiretap channel with a transmitter,
receiver and an adversarial wiretapper, each equipped with multiple antennas.
In a departure from existing work, the wiretapper possesses a novel capability
to act either as a passive eavesdropper or as an active jammer, under a
half-duplex constraint. The transmitter therefore faces a choice between
allocating all of its power for data, or broadcasting artificial interference
along with the information signal in an attempt to jam the eavesdropper
(assuming its instantaneous channel state is unknown). To examine the resulting
trade-offs for the legitimate transmitter and the adversary, we model their
interactions as a two-person zero-sum game with the ergodic MIMO secrecy rate
as the payoff function. We first examine conditions for the existence of
pure-strategy Nash equilibria (NE) and the structure of mixed-strategy NE for
the strategic form of the game.We then derive equilibrium strategies for the
extensive form of the game where players move sequentially under scenarios of
perfect and imperfect information. Finally, numerical simulations are presented
to examine the equilibrium outcomes of the various scenarios considered.


  In contrast to Part I of this treatise [1] that focuses on the optimization
problems associated with single matrix variables, in this paper, we investigate
the application of the matrix-monotonic optimization framework in the
optimization problems associated with multiple matrix variables. It is revealed
that matrix-monotonic optimization still works even for multiple matrix-variate
based optimization problems, provided that certain conditions are satisfied.
Using this framework, the optimal structures of the matrix variables can be
derived and the associated multiple matrix-variate optimization problems can be
substantially simplified. In this paper, several specific examples are given,
which are essentially open problems. Firstly, we investigate multi-user
multiple-input multiple-output (MU- MIMO) uplink communications under various
power constraints. Using the proposed framework, the optimal structures of the
precoding matrices at each user under various power constraints can be derived.
Secondly, we considered the optimization of the signal compression matrices at
each sensor under various power constraints in distributed sensor networks.
Finally, we investigate the transceiver optimization for multi-hop
amplify-and-forward (AF) MIMO relaying networks with imperfect channel state
information (CSI) under various power constraints. At the end of this paper,
several simulation results are given to demonstrate the accuracy of the
proposed theoretical results.


  The gauge-links connecting the parton field operators in the hadronic matrix
elements appearing in the transverse momentum dependent distribution functions
give rise to T-odd effects. Due to the process-dependence of the gauge-links
the T-odd distribution functions appear with different pre-factors. A
consequence is that in the description of single spin asymmetries the parton
distribution and fragmentation functions are convoluted with gluonic pole cross
sections rather than the basic partonic cross sections. In this paper we
calculate the gluonic pole cross sections encountered in single spin
asymmetries in hadron-hadron scattering. The case of back-to-back pion
production in polarized proton-proton scattering is worked out explicitly. It
is shown how T-odd gluon distribution functions originating from gluonic pole
matrix elements appear in twofold.


  Several approaches have been proposed in the literature that allow connected
and automated vehicles (CAVs) to coordinate in areas where there is a potential
conflict, for example, in intersections, merging at roadways and roundabouts.
In this paper, we consider the problem of coordinating CAVs in a corridor
consisting of several conflict areas where collision may occur. We derive a
solution that yields the optimal control input, in terms of fuel consumption,
for each CAV to cross the corridor under the hard safety constraints. We
validate the effectiveness of the solution through simulation, and we show that
both fuel consumption and travel time can be improved significantly.


  With the development of Internet technology and the expansion of social
networks, online platforms have become an important way for people to obtain
information. The introduction of tags facilitates information categorization
and retrieval. Meanwhile, the development of tag recommendation systems not
only enables users to input tags more efficiently, but also improves the
quality of tags. However, current tag recommendation methods only consider the
content of the current post and do not take into account the influence of user
preferences. Since the main body of tag recommendation is the user, it is very
necessary to obtain the user's tagging habits. Therefore, this paper proposes a
tag recommendation algorithm (MLP4STR) based on the dynamic preference of
user's behavioral sequence, which models the user's historical post information
and historical tag information to obtain the user's dynamic interest changes. A
pure MLP structure across feature dimensions is used in sequence modeling to
model the interaction between tag content and post content to fully extract the
user's interests. Finally tag recommendation is performed.


  Necessary optimality conditions in the form of the maximum principle for
control problems with infinite time horizon are considered. Both finite and
infinite values of objective functional are allowed since the concept of
overtaking or weakly overtaking optimality is used. New form of optimality
condition is obtained and compared with the transversality conditions usually
used in the literature. The examples, where these transversality conditions may
fail while the new condition holds are presented. For Ramsey problem of capital
accumulation a simple form of necessary optimality conditions is derived, which
is also valid in the case of zero discounting.


  We combine high resolution hydrodynamical simulations with an intermediate
resolution, dark matter only simulation and an analytical model for the growth
of ionized regions to estimate the large scale distribution and redshift
evolution of the visibility of Lyman-alpha emission in 6<=z<=8 galaxies. The
inhomogeneous distribution of neutral hydrogen during the reionization process
results in significant fluctuations in the Lyman-alpha transmissivity on large
scales. The transmissivity depends not only on the ionized fraction of the
intergalactic medium by volume and the amplitude of the local ionizing
background, but is also rather sensitive to the evolution of the relative
velocity shift of the Lyman-alpha emission line due to resonant scattering. We
reproduce a decline in the space density of Lyman-alpha emitting galaxies as
rapid as observed with a rather rapidly evolving neutral fraction between
z=6-8, and a typical Lyman-alpha line velocity offset of 100 km/s redward of
systemic at z=6 which decreases toward higher redshift. The new (02/2015)
Planck results indicate such a recent end to reionization is no longer
disfavoured by constraints from the cosmic microwave background.


  To describe the dynamics of a single peak of the Rosensweig instability a
model is proposed which approximates the peak by a half-ellipsoid atop a layer
of magnetic fluid. The resulting nonlinear equation for the height of the peak
leads to the correct subcritical character of the bifurcation for static
induction. For a time-dependent induction the effects of inertia and damping
are incorporated. The results of the model show qualitative agreement with the
experimental findings, as in the appearance of period doubling, trebling, and
higher multiples of the driving period. Furthermore a quantitative agreement is
also found for the parameter ranges of frequency and induction in which these
phenomena occur.


  In paper approach of double complex SUSY-transformations with not coincident
complex energies of transformation is developed, allowing to deform given real
potential $V_{1}$ with obtaining exact solutions. The explicit solutions of the
deformation of shape of the potential, its wave function at arbitrary energy,
not coincident with energies of transformation, wave functions at the energies
of transformation are obtained, condition of keeping of continuity of the
solutions and isospectral condition are determined. Using a rectangular well of
finite width with infinitely high walls as the starting $V_{1}$ with discrete
energy spectrum, by the proposed approach new types of deformation of this
potential with deformation of the energy spectrum as a whole have been
obtained. The new potential contains the rectangular well as own partial case
(with simultaneous transformation of the shape of this new potential, energy
spectrum, wave functions of all bound states, wave function at arbitrary energy
into corresponding characteristics of the rectangular well at needed choice of
parameters). Using null potential as the starting $V_{1}$ with continuous
energy spectrum, new form of reflectionless real potential has been
constructed. This potential generalizes well-known reflectionless potential of
the type $V_{\rm ref}(x) = A^{2}(1-2 {\rm sech}^{2}{Ax})$, allowing: to pull
down tails of the potential $V_{\rm ref}$ in the asymptotic regions up to zero
(with keeping of nonzero depth); to pull down continuously the depth of the
hole; to displace arbitrary along axis $x$ the hole with its passing through
zero; to create and to increase the second hole, transforming $V_{\rm ref}$
into double-well potential; to control continuously and simply the asymmetry of
the shape of such reflectionless potential.


  This work studies jet-like electromagnetic configurations surrounding a
slowly-spinning black-hole immersed in a uniformly magnetized force-free
plasma. In the first part of this work, we present a family of stationary
solutions that are jet-capable. While these solutions all satisfy the
force-free equations and the appropriate boundary conditions, our numerical
experiments show a unique relaxed state starting from different initial data,
and so one member of the family is likely preferred over the others. In the
second part of this work, we analyze the perturbations of this family of
jet-like solutions, and show that the perturbative modes exhibit a similar
split into the trapped and traveling categories previously found for perturbed
Blandford-Znajek solutions. In the eikonal limit, the trapped modes can be
identified with the fast magnetosonic waves in the force-free plasma and the
traveling waves are essentially the Alfven waves. Moreover, within the scope of
our analysis, we have not seen signs of unstable modes at the light-crossing
timescale of the system, within which the numerical relaxation process occurs.
This observation disfavors mode instability as the selection mechanism for
picking out a preferred solution. Consequently, our analytical study is unable
to definitively select a particular solution out of the family to serve as the
aforementioned preferred final state. This remains an interesting open problem.


  3D Gaussian Splatting has emerged as an alternative 3D representation for
novel view synthesis, benefiting from its high-quality rendering results and
real-time rendering speed. However, the 3D Gaussians learned by 3D-GS have
ambiguous structures without any geometry constraints. This inherent issue in
3D-GS leads to a rough boundary when segmenting individual objects. To remedy
these problems, we propose SAGD, a conceptually simple yet effective
boundary-enhanced segmentation pipeline for 3D-GS to improve segmentation
accuracy while preserving segmentation speed. Specifically, we introduce a
Gaussian Decomposition scheme, which ingeniously utilizes the special structure
of 3D Gaussian, finds out, and then decomposes the boundary Gaussians.
Moreover, to achieve fast interactive 3D segmentation, we introduce a novel
training-free pipeline by lifting a 2D foundation model to 3D-GS. Extensive
experiments demonstrate that our approach achieves high-quality 3D segmentation
without rough boundary issues, which can be easily applied to other scene
editing tasks.


  Time-dependent thermal effects should accompany standard non-thermal
afterglows of GRB when gamma-rays pass through inhomogeneous surroundings of
the GRB site. Thermal relaxation of an optically thin plasma is calculated
using time-dependent collisional ionization of the plasma ion species. X-ray
emission lines are similar to those found in the fading X-ray afterglow of GRB
011211. Thermal relaxation of clouds or shells around the GRB site could also
contribute to the varying late optical GRB afterglows, such as in GRB021004 and
GRB030329.


  Reliable positioning services are extremely important for users and devices
in mountainous environments as it enables a variety of location-based
applications. However, in such environments, the service reliability of
conventional wireless positioning technologies is often disappointing. Frequent
non-line-of-sight (NLoS) propagation and poor geometry of available anchor
nodes are two significant challenges. Due to the high maneuverability and
flexible deployment of unmanned aerial vehicles (UAVs), UAV-enabled positioning
could be a promising solution to these challenges. Compared with satellites and
terrestrial base stations, UAVs are capable of flying to places where both the
propagation conditions and geometry are favorable for positioning. The eventual
aim of this research project is to design a novel UAV-enabled positioning
system that uses a low-altitude UAV platform to provide highly reliable
services for ground users in mountainous environments. In this article, we
introduce the recent progress made in the first phase of our project, including
the following. First, the structure of the proposed system and the positioning
method used are determined after comprehensive consideration of various
factors. Utilizing the digital elevation model of the realistic terrain, we
then establish a geometry-based NLoS probability model so that the NLoS
propagation can be treated as a type of fault during the reliability analysis.
Most importantly, a reliability prediction method and the corresponding metric
are developed to evaluate the system's ability to provide reliable positioning
services. At the end of this article, we also propose a voting-based method for
improving the service reliability. Numerical results demonstrate the tremendous
potential of the proposed system in reliable positioning.


  The explanation of the nature of superconducting gap in high temperature
superconductors (HTSC) is a fundamental task which solution can lead to the
understanding of superconducting mechanism. However, it has not been fully
solved yet. From the mid of the twentieth century when Bardeen, Cooper and
Schrieffer constructed their theory it has been believed that a superconducting
gap is a collective phenomenon of electron excitations. In this work it is
demonstrated that according to translation-invariant bipolaron theory of HTSC
the different types of experiments measure for the gap different values. Thus
tunneling experiments determine the bipolaron energy for a superconducting gap.
On the other hand, the angle - resolved photoemission spectroscopy method
measures the phonon frequency for which the electron-phonon interaction is
maximum. Such effects as kinks in spectral measurements of gap, its angular
dependence, existence of pseudogap and others have got natural explanations.


  We first give two new proofs of an old result that the reduced Euler
characteristic of a matroid complex is equal to the M\"obius number of the
lattice of cycles of the matroid up to the sign. The purpose has been to find a
model to establish an analogous result for the case of $q$-matroids and we find
a relation between the Euler characteristic of the simplicial chain complex
associated to a $q$-matroid complex and the lattice of $q$-cycles of the
$q$-matroid. We use this formula to find the complete homology over
$\mathbb{Z}$ of this shellable simplicial complex. We give a characterization
of nonzero Euler characteristic for such order complexes. Finally, based on
these results we remark why singular homology of a $q$-matroid equipped with
order topology may not be effective to describe the $q$-cycles unlike the
classical case of matroids.


  Public models offer predictions to a variety of downstream tasks and have
played a crucial role in various AI applications, showcasing their proficiency
in accurate predictions. However, the exclusive emphasis on prediction accuracy
may not align with the diverse end objectives of downstream agents. Recognizing
the public model's predictions as a service, we advocate for integrating the
objectives of downstream agents into the optimization process. Concretely, to
address performance disparities and foster fairness among heterogeneous agents
in training, we propose a novel Equitable Objective. This objective, coupled
with a policy gradient algorithm, is crafted to train the public model to
produce a more equitable/uniform performance distribution across downstream
agents, each with their unique concerns. Both theoretical analysis and
empirical case studies have proven the effectiveness of our method in advancing
performance equity across diverse downstream agents utilizing the public model
for their decision-making. Codes and datasets are released at
https://github.com/Ren-Research/Socially-Equitable-Public-Models.


  We study deformation of Courant pairs with a commutative algebra base. We
consider the deformation cohomology bi-complex and describe a universal
infinitesimal deformation. In a sequel, we formulate an extension of a given
deformation of a Courant pair to another with extended base. This leads to
describe the obstruction in extending a given deformation. We also discuss
about the construction of versal deformation of Courant pairs. As an
application, we explicitly compute universal infinitesimal deformation of
Poisson algebra structures


  We investigate the consequences of one extra compactified dimension for the
energy spectrum of the non-relativistic hydrogen atom with a potential defined
by Gauss' law, i.e. proportional to $1/|x|^2$ in non-compactified 4d space. The
calculations were performed numerically by diagonalizing the Hamiltonian in two
different sets of basis vectors. The energy levels and electron probability
density are plotted as a function of the compactification radius. The
occurrence of several physical effects is discussed and interpreted.


  Superfluid 3He-A displays the largest variety in vortex structure among the
presently known coherent quantum systems. The experimentally verified
information comes mostly from NMR measurements on the rotating fluid, from
which the order-parameter texture can often be worked out. The various vortex
structures differ in the topology of their order-parameter field, in energy,
critical velocity, and in their response to temporal variations in the
externally applied flow. They require different experimental conditions for
their creation. When the flow is applied in the superfluid state, the structure
with the lowest critical velocity is formed. In 3He-A this leads to the various
forms of continuous (or singularity-free) vorticity. Which particular structure
is created depends on the externally applied conditions and on the global
order-parameter texture.


  In this paper, applied strictly monotonic increasing scaled maps, a kind of
well-conditioned linear barycentric rational interpolations are proposed to
approximate functions of singularities at the origin, such as $x^\alpha$ for
$\alpha \in (0,1)$ and $\log(x)$. It just takes $O(N)$ flops and can achieve
fast convergence rates with the choice the scaled parameter, where $N$ is the
maximum degree of the denominator and numerator. The construction of the
rational interpolant couples rational polynomials in the barycentric form of
second kind with the transformed Jacobi-Gauss-Lobatto points. Numerical
experiments are considered which illustrate the accuracy and efficiency of the
algorithms. The convergence of the rational interpolation is also considered.


  The mapping of time-dependent densities on potentials in quantum mechanics is
critically examined. The issue is of significance ever since Runge and Gross
(Phys. Rev. Lett. 52, 997 (1984)) established the uniqueness of the mapping,
forming a theoretical basis for time-dependent density functional theory. We
argue that besides existence (so called v-representability) and uniqueness
there is an important question of stability and chaos. Studying a 2-level
system we find innocent, almost constant densities that cannot be constructed
from any potential (non-existence). We further show via a Lyapunov analysis
that the mapping of densities on potentials has chaotic regions in this case.
In real space the situation is more subtle. V-representability is formally
assured but the mapping is often chaotic making the actual construction of the
potential almost impossible. The chaotic nature of the mapping, studied for the
first time here, has serious consequences regarding the possibility of using
TDDFT in real-time settings.


  Unsupervised neural machine translation (UNMT) has recently achieved
remarkable results for several language pairs. However, it can only translate
between a single language pair and cannot produce translation results for
multiple language pairs at the same time. That is, research on multilingual
UNMT has been limited. In this paper, we empirically introduce a simple method
to translate between thirteen languages using a single encoder and a single
decoder, making use of multilingual data to improve UNMT for all language
pairs. On the basis of the empirical findings, we propose two knowledge
distillation methods to further enhance multilingual UNMT performance. Our
experiments on a dataset with English translated to and from twelve other
languages (including three language families and six language branches) show
remarkable results, surpassing strong unsupervised individual baselines while
achieving promising performance between non-English language pairs in zero-shot
translation scenarios and alleviating poor performance in low-resource language
pairs.


  We obtain a universal energy estimate up to the boundary for stable solutions
of semilinear equations with variable coefficients. Namely, we consider
solutions to $- L u = f(u)$, where $L$ is a linear uniformly elliptic operator
and $f$ is $C^1$, such that the linearized equation $-L - f'(u)$ has
nonnegative principal eigenvalue. Our main result is an estimate for the
$L^{2+\gamma}$ norm of the gradient of stable solutions vanishing on the flat
part of a half-ball, for any nonnegative and nondecreasing $f$. This bound only
requires the elliptic coefficients to be Lipschitz. As a consequence, our
estimate continues to hold in general $C^{1,1}$ domains if we further assume
the nonlinearity $f$ to be convex. This result is new even for the Laplacian,
for which a $C^3$ regularity assumption on the domain was needed.


  Intensities in high-resolution phase-contrast images from electron
microscopes build up discretely in time by detecting single electrons. A wave
description of pulse-like coherent-inelastic interaction of an electron with
matter is detailed and verified. In perspective, the interaction time of any
matter wave compares with the lifetime of a virtual particle of any elemental
interaction, suggesting the present concept of coherent-inelastic interactions
of matter waves might be generalizable.


  We investigated long range correlations in two literary texts, Moby Dick by
H. Melville and Grimm's tales. The analysis is based on the calculation of
entropy like quantities as the mutual information for pairs of letters and the
entropy, the mean uncertainty, per letter. We further estimate the number of
different subwords of a given length n. Filtering out the contributions due to
the effects of the finite length of the texts, we find correlations ranging to
a few hundred letters. Scaling laws for the mutual information (decay with a
power law), for the entropy per letter (decay with the inverse square root of
n) and for the word numbers (stretched exponential growth with n and with a
power law of the text length) were found.


  Efforts to detect ultrahigh energy neutrinos are driven by several
objectives: What is the origin of astrophysical neutrinos detected with
IceCube? What are the sources of ultrahigh energy cosmic rays? Do the ANITA
detected events point to new physics? Shedding light on these questions
requires instruments that can detect neutrinos above $10^7$ GeV with sufficient
sensitivity - a daunting task. While most ultrahigh energy neutrino experiments
are based on the detection of a radio signature from shower particles following
a neutrino interaction, we believe that the detection of Cherenkov and
fluorescence light from shower particles is an attractive alternative. Imaging
air showers with Cherenkov and fluorescence light is a technique that is
successfully used in several ultrahigh energy cosmic ray and very-high energy
gamma-ray experiments. We performed a case study of an air-shower imaging
system for the detection of earth-skimming tau neutrinos. The detector
configuration we consider consists of an imaging system that is located on top
of a mountain and is pointed at the horizon. From the results of this study we
conclude that a sensitivity of $3\cdot10^{-9}$ GeV cm$^{-2}$s$^{-1}$sr$^{-1}$
can be achieved at $2\cdot10^8$ GeV with a relatively small and modular system
after three years of observation. In this presentation we discuss key findings
of our study and how they translate into design requirements for an imaging
system we dub Trinity.


  The interplay between the ground state energy of the generalized Bernasconi
model to multi-phase, and the minimal value of the maximal autocorrelation
function, $C_{max}=\max_K{|C_K|}$, $K=1,..N-1$, is examined analytically and
the main results are: (a) The minimal value of $\min_N{C_{max}}$ is
$0.435\sqrt{N}$ significantly smaller than the typical value for random
sequences $O(\sqrt{\log{N}}\sqrt{N})$. (b) $\min_N{C_{max}}$ over all sequences
of length N is obtained in an energy which is about 30% above the ground-state
energy of the generalized Bernasconi model, independent of the number of phases
m. (c) The maximal merit factor $F_{max}$ grows linearly with m. (d) For a
given N, $\min_N{C_{max}}\sim\sqrt{N/m}$ indicating that for m=N,
$\min_N{C_{max}}=1$, i.e. a Barker code exits. The analytical results are
confirmed by simulations.


  Kagome magnets provide a fascinating platform for the realization of
correlated topological quantum phases under various magnetic ground states.
However, the intricate effect of the magnetic spin configurations on the
characteristic electronic structure directly from the kagome lattice layer
remains still elusive. Here, utilizing angle-resolved photoemission
spectroscopy and density functional theory calculations, we report the
spectroscopic evidence for the spin-reorientation effect of a kagome
ferromagnet Fe$_3$Ge, which is composed only of the kagome planes. There are
two kinds of kagome-derived Dirac fermions due to the structural
three-dimensionality -- one is less dispersive ($k_z$ $\sim$ 0) and the other
disperses linearly ($k_z$ $\sim$ $\pi$). As the Fe moments cant from the $c$
axis into the $ab$ plane upon cooling, the Dirac fermion in $k_z$ $\sim$ 0
plane with a mixture of the Fe-$3d_{xy}$ and Fe-$3d_{x^2-y^2}$ components
evolves from gapped into nearly gapless, while the Dirac cone in $k_z$ $\sim$
$\pi$ plane mainly of the Fe-$3d_{x^2-y^2}$ orbital character remains intact,
suggesting that the effect of spin reorientation on the Dirac fermions has an
orbital selectivity. Our unambiguous observations provide a feasible route to
design and manipulate the mass of Dirac fermions for realizing the novel
quantum phases. We also perform comparative studies between the
non-charge-ordered Fe$_3$Ge and its sibling compound FeGe, a newly established
charge-density-wave kagome magnet, the results suggest that the
orbital-selective van Hove singularities near the Fermi level play an
indispensable part in driving the charge order on a magnetic kagome lattice.


  Using the self-consistent Born approximation to the Dirac fermions under
finite-range impurity scatterings, we show that the current-current correlation
function is determined by four-coupled integral equations. This is very
different from the case for impurities with short-range potentials. As a test
of the present approach, we calculate the electric conductivity in graphene for
charged impurities with screened Coulomb potentials. The obtained conductivity
at zero temperature varies linearly with the carrier concentration, and the
minimum conductivity at zero doping is larger than the existing theoretical
predictions, but still smaller than that of the experimental measurement. The
overall behavior of the conductivity obtained by the present calculation at
room temperature is similar to that at zero temperature except the minimum
conductivity is slightly larger.


  The required amount of labeled data is one of the biggest issues in deep
learning. Semi-Supervised Learning can potentially solve this issue by using
additional unlabeled data. However, many datasets suffer from variability in
the annotations. The aggregated labels from these annotation are not consistent
between different annotators and thus are considered fuzzy. These fuzzy labels
are often not considered by Semi-Supervised Learning. This leads either to an
inferior performance or to higher initial annotation costs in the complete
machine learning development cycle. We envision the incorporation of fuzzy
labels into Semi-Supervised Learning and give a proof-of-concept of the
potential lower costs and higher consistency in the complete development cycle.
As part of our concept, we discuss current limitations, futures research
opportunities and potential broad impacts.


  The chaotic transport of charged particles in a turbulent electrostatic
potential sets the conditions of a severe limitation to the plasma confinement
in devices such as tokamaks. In this chapter, we consider the motion of
impurities driven by the ExB velocity where a strong magnetic field B (which
allows for the guiding center approximation) is uniform and constant, and a
turbulent electric field is obtained from models or from numerical fluid codes.
Hamiltonian dynamics rule the transport properties of these impurities.
Therefore a technique to reduce chaotic diffusion in Hamiltonian systems is
able to address the issue of reducing the radial transport of impurities under
some approximations. The general idea is to build barriers in phase space by a
small and apt modification of the Hamiltonian. We show numerically that such
perturbations are able to drastically reduce the diffusion of test-particles,
and we discuss the robustness of such additional modifications.


  In this paper, a novel theoretical scheme is presented to investigate
resonant levels in weakly bound nuclear systems by the use of isospectral
potentials. In this scheme, a new potential is constructed which is strictly
isospectral with the original shallow-well potential and has properties that
are desirable to calculate resonances more accurately and easier. Effectiveness
of the method has been had been demonstrated in terms of its application to the
first $0^+$ resonances in the neutron-rich isotopes $^A$C ($\equiv
^{A-2}$C+n+n) in the three-body cluster model for A=18, 20.


  For cosmic neutrinos we study the conditions and the effects of the coherence
loss as well as coherent broadening of the spectrum. We evaluate the width of
the neutrino wavepacket produced by charged particles under various
circumstances: in an interaction-free environment, in a radiation-dominated
medium (typical of the sources of the gamma ray bursts) and in the presence of
a magnetic field. The effect of the magnetic field on the wavepacket size
appears to be more important than the scattering. If the magnetic field at the
source is larger than $\sim$10 Gauss, the coherence of neutrinos will be lost
while traveling over cosmological distances. Various applications of these
results have been considered. We find that for large magnetic fields ($B> 10^9$
Gauss) and high energies ($E_\nu>{\rm PeV}$), "coherent broadening" can modify
the energy spectrum of neutrinos. In the coherent case, averaging out the
oscillatory terms of the probabilities does not induce any statistical
uncertainty beyond what expected in the absence of these terms. A deviation
from the standard quantum mechanics that preserves average energy and unitarity
cannot alter the picture.


  We investigate the Teukolsky equation in horizon-penetrating coordinates to
study the behavior of perturbation waves crossing the outer horizon. For this
purpose, we use the null ingoing/outgoing Eddington-Finkelstein coordinates.
The first derivative of the radial equation is a Fuchsian differential equation
with an additional regular singularity to the ones the radial one has. The
radial functions satisfy the physical boundary conditions without imposing any
regularity conditions. We also observe that the Hertz-Weyl scalar equations
preserve their angular and radial signatures in these coordinates. Using the
angular equation, we construct the metric perturbation for a circularly
orbiting perturber around a black hole in Kerr spacetime in a
horizon-penetrating setting. Furthermore, we completed the missing metric
pieces due to the mass M and angular momentum J perturbations. We also provide
an explicit formula for the metric perturbation as a function of the radial
part, its derivative, and the angular part of the solution to the Teukolsky
equation. Finally, we discuss the importance of the extra singularity in the
radial derivative for the convergence of the metric expansion.


  Most ML-like functional languages provide records and overloading as
unrelated features. Records not only represent data structures, but are also
used to implement dictionary passing, whereas overloading produces type
constraints that are basically dictionaries subject to compiler-driven
dispatching. In this paper we explore how records and overloading constraints
can be converted one into the other, allowing the programmer to switch between
the two at a very reasonable cost in terms of syntactic overhead. To achieve
this we introduce two language constructs, namely inject and eject, performing
a type-driven syntactic transformation. The former literally injects
constraints into the type and produces a function adding an extra record
argument. The latter does the opposite, ejecting a record argument from a
function and turning fields into type constraints. The conversion is reversible
and can be restricted to a subset of symbols, granting additional control to
the programmer. Although what we call inject has already been proposed in
literature, making it a language operator and coupling it with its reverse
counterpart represent a novel design. The goal is to allow the programmer to
switch from a dictionary-passing style to compiler-assisted constraint
resolution, and vice versa, enabling reuse between libraries that otherwise
would not interoperate.


  We obtain exact dynamics of a two-qubit central spin model (CSM) consisting
of two interacting qubits homogeneously coupled to a spin bath via the
$XXZ$-type coupling, with the bath initially prepared in linear superpositions
of the symmetric Dicke states. Using the interaction picture Hamiltonian with
respect to the non-spin-flipping part of the model, we derive a sequence of
equations of motion within each magnetization sector satisfied by the
probability amplitudes of the time-evolved state. These equations of motion
admit analytical solutions for the single-qubit CSM in which one of the two
central qubits decouples from the rest of the system. Based on this, we provide
a quantitative interpretation to the observed collapse-revival phenomena in the
single-qubit Rabi oscillations when the bath is prepared in the spin coherent
state. We then study the disentanglement and coherence dynamics of two
initially entangled noninteracting qubits when the two qubits interact with
individual baths or with a common bath. For individual baths the coherent
dynamics is found to positively correlated to the single-qubit purity dynamics,
and entanglement sudden disappearance and revivals are observed in both cases.
The entanglement creation of two initially separable qubits coupled to a common
bath is also studied and collapse and revival behaviors in the entanglement
dynamics are observed. Choosing the equally weighted state and the $W$-class
states as the bath initial states, we finally study the dynamics of
entanglement between two individual bath spins and demonstrate the entanglement
sharing mechanism in such a system.


  We argue that the cosmic ray positron excess observed in ATIC-2, Fermi LAT,
PAMELA, HESS and recently in the precision AMS-02 experiment can be attributed
to the production in a local, middle-aged supernova remnant (SNR). Using the
prediction of our model of cosmic ray acceleration in SNR we estimate that the
SNR responsible for the observed positron excess is located between 250 and
320pc from the Sun and is 170-380 kyear old. The most probable candidate for
such a source is the SNR which gave birth to the well-known Geminga pulsar, but
is no longer visible. Other contenders are also discussed.


  We use the grid of hydrodynamic accretion disc calculations of Stehle (1999)
to construct orbital phase dependent emission line profiles of thin discs
carrying spiral density waves. The observational signatures of spiral waves are
explored to establish the feasibility of detecting spiral waves in cataclysmic
variable discs using prominent emission lines in the visible range of the
spectrum. For high Mach number accretion discs (M = 15-30), we find that the
spiral shock arms are so tightly wound that they leave few obvious fingerprints
in the emission lines. Only a minor variation of the double peak separation in
the line profile at a level of 8% is produced. For accretion discs in outburst
(M = 5-20) however, the lines are dominated by the emission from an m=2 spiral
pattern in the disc. We show that reliable Doppler tomograms of spiral shock
patterns can be reconstructed provided that a signal to noise of at least 15, a
wavelength resolution of 80 km/s and a time resolution of 50 spectra per binary
orbit is achieved. We confirm that the observed spiral pattern in the disc of
IP Pegasi can be reproduced by tidal density waves in the accretion disc and
demands the presence of a large, hot disc, at least in the early outburst
stages.


  We show that a quantum field theoretic model of anyons cannot be ``free'' in
the (restrictive) sense that the basic fields create only one-particle states
out of the vacuum.


  We give the construction of twisted quantum Lax equations associated with
quantum groups. We solve these equations using factorization properties of the
corresponding quantum groups. Our construction generalizes in many respects the
Adler-Kostant-Symes construction for Lie groups and the construction of M. A.
Semenov Tian-Shansky for the Lie-Poisson case.


  In this paper, we investigate a fluid antenna system (FAS)-assisted downlink
non-orthogonal multiple access (NOMA) for short-packet communications. The base
station (BS) adopts a single fixed antenna, while both the central user (CU)
and the cell-edge user (CEU) are equipped with a FAS. Each FAS comprises $N$
flexible positions (also known as ports), linked to $N$ arbitrarily correlated
Rayleigh fading channels. We derive expressions for the average block error
rate (BLER) of the FAS-assisted NOMA system and provide asymptotic BLER
expressions. We determine that the diversity order for CU and CEU is $N$,
indicating that the system performance can be considerably improved by
increasing $N$. Simulation results validate the great performance of FAS.


  We propose a 3D color point cloud processing pipeline to count apples on
individual apple trees in trellis structured orchards. Fruit counting at the
tree level requires separating trees, which is challenging in dense orchards.
We employ point clouds acquired from the leaf-off orchard in winter period,
where the branch structure is visible, to delineate tree crowns. We localize
apples in point clouds acquired in harvest period. Alignment of the two point
clouds enables mapping apple locations to the delineated winter cloud and
assigning each apple to its bearing tree. Our apple assignment method achieves
an accuracy rate higher than 95%. In addition to presenting a first proof of
feasibility, we also provide suggestions for further improvement on our apple
assignment pipeline.


  What happens when scientists are, at certain points in a field's development,
playing a game? I present a framework for such an analysis that draws on the
theory of games provided by the historian Johan Huizinga. Huizinga gives five
conditions for a social practice to become a game: free engagement,
disconnection, boundedness in time and arena, the order-creation of rules, and
the presence of tension. Application of this theory to scientific practice
predicts patterns of behavior that can be tested by quantitative analysis: the
emergence of hard boundaries between disciplines, the closure of loopholes in
theory creation, resistance to certain innovations in journal publication, and
the ways in which scientists fail to prosecute colleagues who engage in
questionable research practices.


  The area law-like scaling of local quantum entropies is the central
characteristic of the entanglement inherent in quantum fields, many-body
systems, and spacetime. Whilst the area law is primarily associated with the
entanglement structure of the underlying quantum state, we here show that it
equally manifests in classical entropies over measurement distributions when
vacuum contributions dictated by the uncertainty principle are subtracted.
Using the examples of the Gaussian ground and thermal states, but also the
non-Gaussian particle state of a relativistic scalar field, we present
analytical and numerical area laws for the entropies of various distributions
and unveil how quantities of widespread interest such as the central charge and
the (local) temperature are encoded in classical observables. With our
approach, quantum entropies are no longer necessary to probe quantum phenomena,
thereby rendering area laws and other quantum features directly accessible to
theoretical models of high complexity as well as state-of-the-art experiments.


  We search for galaxy counterparts to damped Lyman-alpha absorbers (DLAs) at
z>2 towards nine quasars, which have 14 DLAs and 8 sub-DLAs in their spectra.
We use integral field spectroscopy to search for Ly-alpha emission line objects
at the redshifts of the absorption systems. Besides recovering two previously
confirmed objects, we find six statistically significant candidate Ly-alpha
emission line objects. The candidates are identified as having wavelengths
close to the DLA line where the background quasar emission is absorbed. In
comparison with the six currently known Ly-alpha emitting DLA galaxies the
candidates have similar line fluxes and line widths, while velocity offsets
between the emission lines and systemic DLA redshifts are larger. The impact
parameters are larger than 10 kpc, and lower column density systems are found
at larger impact parameters. Assuming that a single gas cloud extends from the
QSO line of sight to the location of the candidate emission line, we find that
the average candidate DLA galaxy is surrounded by neutral gas with an
exponential scale length of ~5 kpc.


  A novel phase-field for ductile fracture model is presented. The model is
developed within a consistent variational framework in the context of
finite-deformation kinematics. A novel coalescence dissipation introduces a new
coupling mechanism between plasticity and fracture by degrading the fracture
toughness as the equivalent plastic strain increases. The proposed model is
compared with a recent alternative where plasticity and fracture are strongly
coupled. Several representative numerical examples motivate specific modeling
choices. In particular, a linear crack geometric function provides an
"unperturbed" ductile response prior to crack initiation, and Lorentz-type
degradation functions ensure that the critical fracture strength remains
independent of the phase-field regularization length. In addition, the response
of the model is demonstrated to converge with a vanishing phase-field
regularization length. The model is then applied to calibrate and simulate a
three-point bending experiment of an aluminum specimen with a complex geometry.
The effect of the proposed coalescence dissipation coupling on simulations of
the experiment is first investigated in a two-dimensional plane strain setting.
The calibrated model is then applied to a three-dimensional calculation, where
the calculated load-deflection curves and the crack trajectory show excellent
agreement with experimental observations. Finally, the model is applied to
simulate crack nucleation and growth in a specimen from a recent Sandia
Fracture Challenge.


  We demonstrate the feasibility of ballistic electron spectroscopy as a new
tool for mesoscopic physics. A quantum dot is utilised as an energy-selective
detector of non-equilibrium ballistic electrons injected into a two-dimensional
electron system. In this paper we use a second quantum dot as the electron
injector to evaluate the scheme. We propose an application in the study of
interacting 1D and 0D systems.


  We derive a relationship between network representation in energy-efficient
neuromorphic architectures and block Toplitz convolutional matrices. Inspired
by this connection, we develop deep convolutional networks using a family of
structured convolutional matrices and achieve state-of-the-art trade-off
between energy efficiency and classification accuracy for well-known image
recognition tasks. We also put forward a novel method to train binary
convolutional networks by utilising an existing connection between
noisy-rectified linear units and binary activations.


  While pre-trained language models (PLMs) are the go-to solution to tackle
many natural language processing problems, they are still very limited in their
ability to capture and to use common-sense knowledge. In fact, even if
information is available in the form of approximate (soft) logical rules, it is
not clear how to transfer it to a PLM in order to improve its performance for
deductive reasoning tasks. Here, we aim to bridge this gap by teaching PLMs how
to reason with soft Horn rules. We introduce a classification task where, given
facts and soft rules, the PLM should return a prediction with a probability for
a given hypothesis. We release the first dataset for this task, and we propose
a revised loss function that enables the PLM to learn how to predict precise
probabilities for the task. Our evaluation results show that the resulting
fine-tuned models achieve very high performance, even on logical rules that
were unseen at training. Moreover, we demonstrate that logical notions
expressed by the rules are transferred to the fine-tuned model, yielding
state-of-the-art results on external datasets.


  The linear marginal instability of an axisymmetric MHD Taylor-Couette flow of
infinite vertical extension is considered. The dependence of the flow stability
on magnetic Prandtl number, Pm, and gap-width between rotating cylinders is
investigated. There is an unstability for flows with resting outer cylinder
even without a magnetic field. Nevertheless, there are solutions with smaller
critical Reynolds numbers for certain (weak) magnetic fields. These solutions,
however, exist for not too small Pm or large enough gap. For hydrodynamically
stable flow, we found that a magnetic field amplitude always exsits where the
critical Reynolds number is minimal. In all calculated cases the minimal
critical Reynolds numbers are running with 1/Pm for small Pm and the critical
Reynolds numbers exceed value of 10^6 for Pm of sodium (10^{-5}) or gallium
(10^{-6}).


  We report photometric observations of the eclipsing close binary CSS21055
(SDSS J141126+200911) that strongly suggest that the companion to the
carbon-oxygen white dwarf is a brown dwarf with a mass between 0.030 and 0.074
Msun. The measured orbital period is 121.73min and the totality of the eclipse
lasts 125s. If confirmed, CSS21055 would be the first detached eclipsing WD+BD
binary. Spectroscopy in the eclipse could provide information about the
companion's evolutionary state and atmospheric structure.


  Classically, theorems of Fatou and Julia describe the boundary regularity of
functions in one complex variable. The former says that a complex analytic
function on the disk has non-tangential boundary values almost everywhere, and
the latter describes when a function takes an extreme value at a boundary point
and is differentiable there non-tangentially. We describe a class of
intermediate theorems in terms of averaged Julia-Fatou quotients. Boundary
regularity is related to integrability of certain quantities against a special
measure, the so-called Nevanlinna measure. Applications are given to spectral
theory.


  We can define a module to be an exact functor on a small abelian category.
This is explained and shown to be equivalent to the usual definition but it
does offer a different perspective, inspired by the notions from model theory
of imaginary sort and interpretation. A number of examples are worked through.


  We investigate a three-dimensional gravitational theory on a noncommutative
space which has a cosmological constant term only. We found various kinds of
nontrivial solutions, by applying a similar technique which was used to seek
noncommutative solitons in noncommutative scalar field theories. Some of those
solutions correspond to bubbles of spacetimes, or represent dimensional
reduction. The solution which interpolates $G_{\mu\nu}=0$ and Minkowski metric
is also found. All solutions we obtained are non-perturbative in the
noncommutative parameter $\theta$, therefore they are different from solutions
found in other contexts of noncommutative theory of gravity and would have a
close relation to quantum gravity.


  We utilize the weak convergence method to establish the Freidlin--Wentzell
large deviations principle (LDP) for stochastic delay differential equations
(SDDEs) with super-linearly growing coefficients, which covers a large class of
cases with non-globally Lipschitz coefficients. The key ingredient in our proof
is the uniform moment estimate of the controlled equation, where we handle the
super-linear growth of the coefficients by an iterative argument. Our results
allow both the drift and diffusion coefficients of the considered equations to
super-linearly grow not only with respect to the delay variable but also to the
state variable. This work extends the existing results which develop the LDPs
for SDDEs with super-linearly growing coefficients only with respect to the
delay variable.


  Deep generative models have shown success in automatically synthesizing
missing image regions using surrounding context. However, users cannot directly
decide what content to synthesize with such approaches. We propose an
end-to-end network for image inpainting that uses a different image to guide
the synthesis of new content to fill the hole. A key challenge addressed by our
approach is synthesizing new content in regions where the guidance image and
the context of the original image are inconsistent. We conduct four studies
that demonstrate our results yield more realistic image inpainting results over
seven baselines.


  We introduce a numerical method specifically designed for investigating
generic multifield models of inflation where a number of scalar fields $\phi^K$
are minimally coupled to gravity and live in a field space with a non-trivial
metric $G_{IJ}(\phi^K)$. Our algorithm consists of three main parts. Firstly,
we solve the field equations through the entire inflationary period, deriving
predictions for observable quantities such as the spectrum of scalar
perturbations, primordial gravitational waves, and isocurvature modes. We also
incorporate the transfer matrix formalism to track the behavior of adiabatic
and isocurvature modes on super-horizon scales and the transfer of entropy to
scalar modes after the horizon crossing. Secondly, we interface our algorithm
with Boltzmann integrator codes to compute the subsequent full cosmology,
including the cosmic microwave background anisotropies and polarization angular
power spectra. Finally, we develop a novel sampling algorithm able to
efficiently explore a large volume of the parameter space and identify a
sub-region where theoretical predictions agree with observations. In this way,
sampling over the initial conditions of the fields and the free parameters of
the models, we enable Monte Carlo analysis of multifield scenarios. We test all
the features of our approach by analyzing a specific model and deriving
constraints on its free parameters. Our methodology provides a robust framework
for studying multifield inflation, opening new avenues for future research in
the field.


  New two- and three-dimensional calculations are presented of relativistic jet
propagation and break out in massive Wolf-Rayet stars. Such jets are thought
responsible for gamma-ray bursts. As it erupts, the jet is surrounded by a
cocoon of less energetic, but still highly relativistic ejecta that expands and
becomes visible at much larger polar angles. These less energetic ejecta may be
the origin of X-ray flashes and other high-energy transients which will be
visible to a larger fraction of the sky, albeit to a shorter distance than
common gamma-ray bursts. Jet stability is also examined in three-dimensional
calculations. If the jet changes angle by more than three degrees in several
seconds, it will dissipate, producing a broad beam with inadequate Lorentz
factor to make a common gamma-ray burst.


  The heterobimetallic metallacrown (MC),
(TMA)$_2${Mn(OAc)$_2$[12-MC$_{Mn(III)Cu(II)N(shi)}$-4](CH$_3$OH)}$\cdot$2.90CH$_3$OH,
1, where TMA$^+$ is tetramethylammonium, $^-$OAc is acetate, and shi$^{3-}$ is
salicylhydroximate, consists of a Mn$^{II}$ ion captured in the central cavity
and alternating unambiguous and ordered manganese(III) and copper(II) sites
about the MC ring, a first for the archetypal MC structure design.
DC-magnetometry characterization and subsequent simulation with the Spin
Hamiltonian $$H =
-J_1(\mathbf{s}_1+\mathbf{s}_3)\cdot\mathbf{s}_5-J_2(\mathbf{s}_2+\mathbf{s}_4)\cdot\mathbf{s}_5-J_3\sum_{i=1}^{4}\mathbf{s}_i\cdot\mathbf{s}_{i+1}
+ d(s_{z,1}^2 + s_{z,3}^2) + \mu_B\sum_{j=1}^5 g_j\mathbf{s}_j\cdot\mathbf{B}$$
indicates an S = 5/2 ground state and a sizable axial zero-field splitting on
Mn$^{III}$. AC-susceptibility measurements reveal that 1 displays slow
magnetization relaxation akin to single-molecule magnet (SMM) behavior.


  We give a streamlined proof of the limit theorems for the free additive
convolution of infinitesimal triangular arrays of probability measures on the
real line. The result was first proved by Chistyakov and G\"otze using analytic
subordination.


  This work is a generalization of \cite{baldiotti2021} to Grassmann algebras
of arbitrary dimensions. Here we present a covariant quantization scheme for
pseudoclassical theories focused on non-hermitian quantum mechanics. The
quantization maps canonically related pseudoclassical theories to equivalent
quantum realizations in arbitrary dimensions. We apply the formalism to the
problem of two coupled spins with Heisenberg interaction.


  We prove in most cases that a general smooth complete intersection in
projective space has no non-trivial automorphism.


  Recent advances in unsupervised domain adaptation (UDA) techniques have
witnessed great success in cross-domain computer vision tasks, enhancing the
generalization ability of data-driven deep learning architectures by bridging
the domain distribution gaps. For the UDA-based cross-domain object detection
methods, the majority of them alleviate the domain bias by inducing the
domain-invariant feature generation via adversarial learning strategy. However,
their domain discriminators have limited classification ability due to the
unstable adversarial training process. Therefore, the extracted features
induced by them cannot be perfectly domain-invariant and still contain
domain-private factors, bringing obstacles to further alleviate the
cross-domain discrepancy. To tackle this issue, we design a Domain
Disentanglement Faster-RCNN (DDF) to eliminate the source-specific information
in the features for detection task learning. Our DDF method facilitates the
feature disentanglement at the global and local stages, with a Global Triplet
Disentanglement (GTD) module and an Instance Similarity Disentanglement (ISD)
module, respectively. By outperforming state-of-the-art methods on four
benchmark UDA object detection tasks, our DDF method is demonstrated to be
effective with wide applicability.


  Starobinsky inflation is an attractive, fundamental model to explain the
Planck measurements, and its higher-order extension may allow us to probe
quantum gravity effects. We show that future CMB data combined with the 21cm
intensity map from SKA will meaningfully probe such an extended Starobinsky
model. A combined analysis will provide a precise measurement and intriguing
insight into inflationary dynamics, even accounting for correlations with
astrophysical parameters.


  We consider a class of multi-type particle systems having similar structure
to the contact process and show that additivity is equivalent to the existence
of a dual process, extending a result of Harris. We give two additional
characterizations of these systems, in spacetime as percolation models, and
biologically as population models in which the interactions are due to
crowding. We prove a necessary and sufficient condition for the model to
preserve positive correlations. We then show that complete convergence on
$\mathbb{Z}^d$ holds for a large subclass of models including the two-stage
contact process and a household model, and give examples.


  We analyze, in perturbation theory, a theory of weakly interacting fractons
and non-relativistic fermions in a 2+1 dimensional Quantum Field Theory. In
particular we compute the 1-loop corrections to the self energies and
interaction vertex, and calculate the associated 1-loop Renormalization Group
flows of the coupling constants. Surprisingly, we find that the fracton-fermion
coupling does not flow due to an emergent coordinate-dependent symmetry of the
effective Lagrangian, making this model a well-defined quantum field theory. We
provide additional discussions on the regularization and renormalization of
interacting fractonic theories, as well as both qualitative and quantitative
remarks regarding the theory at finite temperature and finite chemical
potential.


  We in this paper consider a further generalization of the (optical) holonomic
quantum computation proposed by Zanardi and Rasetti (quant-ph/9904011), and
reinforced by Fujii (quant-ph/9910069) and Pachos and Chountasis
(quant-ph/9912093). We construct a quantum computational bundle on some
parameter space, and calculate non-abelian Berry connections and curvatures
explicitly in the special cases. Our main tool is unitary coherent operators
based on Lie algebras su(n+1) and su(n,1), where the case of n = 1 is the
previous one.


  We introduce a topological quantum number -- coined dynamical topological
order parameter (DTOP) -- that is dynamically defined in the real-time
evolution of a quantum many-body system and represented by a momentum space
winding number of the Pancharatnam geometric phase. Our construction goes
conceptually beyond the standard notion of topological invariants
characterizing the wave-function of a system, which are constants of motion
under coherent time evolution. In particular, we show that the DTOP can change
its integer value at discrete times where so called dynamical quantum phase
transitions occur, thus serving as a dynamical analog of an order parameter.
Interestingly, studying quantum quenches in one-dimensional two-banded
Bogoliubov de Gennes models, we find that the DTOP is capable of resolving if
the topology of the system Hamiltonian has changed over the quench.
Furthermore, we investigate the relation of the DTOP to the dynamics of the
string order parameter that characterizes the topology of such systems in
thermal equilibrium.


  The Palatini $f(|\hat{\Omega}|)$ gravity is a generalized theory of the
Eddington-inspired Born-Infeld gravity, where
$\Omega_{~N}^{K}\equiv\delta_{~N}^{K}+bg^{KL}R_{LN}(\Gamma)$ is an auxiliary
tensor constructed with the spacetime metric $g$ and independent connection
$\Gamma$. In this paper, we study $f(|\hat{\Omega}|)$ theory with
$f(|\hat{\Omega}|)=|\hat{\Omega}|^{\frac{1}{2}+n}$ in the thick brane scenario
and give some constraints on the brane model. We finally found an analytic
solution of the thick brane generated by a single scalar field. The behavior of
the negative energy density denotes the localization of the thick brane at the
origin of the extra dimension. In our braneworld, the warp factor is divergent
at the boundary of the extra dimension while the brane system is asymptotically
anti$-$de Sitter. It is shown that the tensor perturbation of the brane is
stable and the massless graviton is localized on the thick brane. Therefore,
the effective Einstein-Hilbert action on the brane can be rebuilt in the
low-energy approximation. According to the recent test of the gravitational
inverse-square law, we give some constraints on the $f(|\hat{\Omega}|)$ brane.


  We introduce the higher order spreading models associated to a Banach space
$X$. Their definition is based on $\ff$-sequences $(x_s)_{s\in\ff}$ with $\ff$
a regular thin family and the plegma families. We show that the higher order
spreading models of a Banach space $X$ form an increasing transfinite hierarchy
$(\mathcal{SM}_\xi(X))_{\xi<\omega_1}$. Each $\mathcal{SM}_\xi (X)$ contains
all spreading models generated by $\ff$-sequences $(x_s)_{s\in\ff}$ with order
of $\ff$ equal to $\xi$. We also provide a study of the fundamental properties
of the hierarchy.


  Building practitioners (architects, engineers, energy managers) are showing a
growing interest in the design of more energy efficient and livable buildings.
The best way to predict how a building will behave regarding energy consumption
and thermal comfort is to use a dynamic simulation tool. However, the use of
this kind of tools is difficult on a daily basis practice due to the heuristic
and exploratory nature of the architectural design process. To deal with this
difficulty, the University of Coimbra and three companies have been working on
the development of a prototype design aiding tool, specifically devoted to the
space planning phase of building design, under the project GerAPlanO (Automatic
Generation of Architecture Floor plans with Energy Optimization). This project
aims to combine the capabilities of design generation techniques, thermal
assessment programs, and design optimization methods to provide assistance to
decision makers. This paper presents the overall concept, as well as the
current status of development of this tool.


  In this paper, the results in [Singular Hessians, J. Algebra 282 (2004), no.
1, 195--204], for polynomial Hessians with determinant zero in small dimensions
$r+1$, are generalized to similar results in arbitrary dimension, for
polynomial Hessians with rank $r$. All of this is over a field $K$ of
characteristic zero. The results in [Singular Hessians, J. Algebra 282 (2004),
no. 1, 195--204] are also reproved in a different perspective.
  One of these results is the classification by Gordan and Noether of
homogeneous polynomials in $5$ variables, for which the Hessians determinant is
zero. This result is generalized to homogeneous polynomials in general, for
which the Hessian rank is 4. Up to a linear transformation, such a polynomial
is either contained in $K[x_1,x_2,x_3,x_4]$, or contained in $$
K[x_1,x_2,p_3(x_1,x_2)x_3+p_4(x_1,x_2)x_4+\cdots+p_n(x_1,x_2)x_n] $$ for
certain $p_3,p_4,\ldots,p_n \in K[x_1,x_2]$ which are homogeneous of the same
degree.
  Furthermore, a new result which is similar to those in [Singular Hessians, J.
Algebra 282 (2004), no. 1, 195--204], is added, namely about polynomials $h \in
K[x_1,x_2,x_3,x_4,x_5]$, for which the last four rows of the Hessian matrix of
$t h$ are dependent. Here, $t$ is a variable, which is not one of those with
respect to which the Hessian is taken. This result is generalized to arbitrary
dimension as well: the Hessian rank of $t h$ is $4$ and the first row of the
Hessian matrix of $t h$ is independent of the other rows.


  The quasinormal modes of metric perturbations in asymptotically flat black
hole spacetimes in the Lovelock model are calculated for different spacetime
dimensions and higher orders of curvature. It is analytically established that
in the asymptotic limit $l \rightarrow \infty$, the imaginary parts of the
quasi normal frequencies become constant for tensor, scalar as well as vector
perturbations. Numerical calculation shows that this indeed is the case. Also,
the real and imaginary parts of the quasinormal modes are seen to increase as
the order of the theory $k$ increases. The real part of the modes decreases as
the spacetime dimension $d$ increases, indicating the presence of lower
frequency modes in higher dimensions. Also, it is seen that the modes are
roughly isospectral at very high values of the spacetime dimension $d$.


  In chemical graph theory, caterpillar trees have been an appealing model to
represent the molecular structures of benzenoid hydrocarbon. Meanwhile,
topological index has been thought of as a powerful tool for modeling
quantitative structure-property relationship and quantitative
structure-activity between molecules in chemical compounds. In this article, we
consider a class of caterpillar trees that are incorporated with randomness,
called random caterpillars, and investigate several popular topological indices
of this random class, including Zagreb index, Randi\'{c} index and Wiener
index, etc. Especially, a central limit theorem is developed for the asymptotic
distribution of the Zagreb index of random caterpillars.


  We study the variability of the cataclysmic variable DO Dra, on time-scales
of between minutes and decades.
  The characteristic decay time dt/dm=0.902(3) days/mag was estimated from our
3 nights of CCD R observations. The quiescent data show a photometric wave with
a cycle about 303(15)d. We analyzed the profile of the composite (or mean)
outburst. We discovered however, that a variety of different outburst heights
and durations had occurred, contrary to theoretical predictions. With
increasing maximum brightness, we find that the decay time also increases; this
is in contrast to the model predictions, which indicate that outbursts should
have a constant shape. This is interpreted as representing the presence of
outburst-to-outburst variability of the magnetospheric radius. A presence of a
number of missed weak narrow outbursts is predicted from this statistical
relationship. A new type of variability is detected, during 3 subsequent nights
in 2007: periodic (during one nightly run) oscillations with rapidly-decreasing
frequency from 86 to 47 cycles/day and a semi-amplitude increasing from 0.06 to
0. 10, during a monotonic brightness increase from 14. 27 to 14. 13. This
phenomenon was observed only during an unusually prolonged event of about 1 mag
brightening in 2007 (lasting till autumn), during which no (expected) outburst
was detected. We refer to this behaviour as to the transient periodic
oscillations (TPO). To study this new and interesting phenomenon, new regular
photometric and spectral (in a target of opportunity mode) observations are
required.


  We conduct an investigation into the dispersive post-shock oscillations in
the entropic lattice-Boltzmann method (ELBM). To this end we use a root finding
algorithm to implement the ELBM which displays fast cubic convergence and
guaranties the proper sign of dissipation. The resulting simulation on the
one-dimensional shock tube shows no benefit in terms of regularization from
using the ELBM over the standard LBGK method. We also conduct an experiment
investigating of the LBGK method using median filtering at a single point per
time step. Here we observe that significant regularization can be achieved.


  We present a measurement of the charmless semileptonic decay
$B^0\to\pi^-\ell^+\nu$ using a data sample containing 657$\times 10^6$
$B\bar{B}$ events collected with the Belle detector at the KEKB
asymmetric-energy $e^+e^-$ collider operating near the $\Upsilon(4S)$
resonance. We determine the total branching fraction of the decay,
$\mathcal{B}(B^0\to\pi^-\ell^+\nu)=(1.49\pm 0.04{(\mathrm{stat})}\pm
0.07{(\mathrm{syst})})\times 10^{-4}$. We also report a new precise measurement
of the differential decay rate, and extract the Cabibbo-Kobayashi-Maskawa
matrix element $|V_{ub}|$ using model-independent and -dependent approaches.
From a simultaneous fit to the measured differential decay rate and lattice QCD
results, we obtain $|V_{ub}|=(3.43\pm 0.33)\times 10^{-3}$, where the error
includes both statistical and systematic uncertainties.


  Studies of the composition of the highest energy cosmic rays with the Pierre
Auger Observatory, including examination of hadronic physics effects on the
structure of extensive air showers. Submissions to the 31st ICRC, Lodz, Poland
(July 2009).


  This paper studies generalized inverse reinforcement learning (GIRL) in
Markov decision processes (MDPs), that is, the problem of learning the basic
components of an MDP given observed behavior (policy) that might not be
optimal. These components include not only the reward function and transition
probability matrices, but also the action space and state space that are not
exactly known but are known to belong to given uncertainty sets. We address two
key challenges in GIRL: first, the need to quantify the discrepancy between the
observed policy and the underlying optimal policy; second, the difficulty of
mathematically characterizing the underlying optimal policy when the basic
components of an MDP are unobservable or partially observable. Then, we propose
the mathematical formulation for GIRL and develop a fast heuristic algorithm.
Numerical results on both finite and infinite state problems show the merit of
our formulation and algorithm.


  We report the realization of a large scale gravity antenna based on
matter-wave interferometry, the MIGA project. This experiment consists in an
array of cold Rb sources correlated by a 150 m long optical cavity. MIGA is in
construction at the LSBB underground laboratory, a site that benefits from a
low background noise and is an ideal premise to carry out precision gravity
measurements. The MIGA facility will be a demonstrator for a new generation of
GW detector based on atom interferometry that could open the infrasound window
for the observation of GWs. We describe here the status of the instrument
construction, focusing on the infrastructure works at LSBB and the realization
of the vacuum vessel of the antenna.


  Internet-wide scanning is commonly used to understand the topology and
security of the Internet. However, IPv4 Internet scans have been limited to
scanning only a subset of services -- exhaustively scanning all IPv4 services
is too costly and no existing bandwidth-saving frameworks are designed to scan
IPv4 addresses across all ports. In this work we introduce GPS, a system that
efficiently discovers Internet services across all ports. GPS runs a predictive
framework that learns from extremely small sample sizes and is highly
parallelizable, allowing it to quickly find patterns between services across
all 65K ports and a myriad of features. GPS computes service predictions in 13
minutes (four orders of magnitude faster than prior work) and finds 92.5% of
services across all ports with 131x less bandwidth, and 204x more precision,
compared to exhaustive scanning. GPS is the first work to show that, given at
least two responsive IP addresses on a port to train from, predicting the
majority of services across all ports is possible and practical.


  Superconductivity is one of the most intriguing properties of matter
described by an attractive interaction that bounds electrons into Cooper pairs.
To date, the highest critical temperature at ambient conditions is achieved in
copper oxides. While layered nickel oxides were long proposed to be analogous
to cuprates, superconductivity was only demonstrated in 2019 albeit without
clarifying the pairing mechanism. Here we use Density Functional Theory (DFT)
to show that superconductivity in nickelates is driven by an electron-phonon
coupling originating from a charge ordering. Due to an intrinsic electronic
instability in half-doped compounds, Ni$^{1.5+}$ cations dismutate into more
stable Ni$^+$ and Ni$^{2+}$ cations, which is accompanied by a bond
disproportionation of NiO$_4$ complexes producing an insulating charge ordered
state. Once doping suppresses the instability, the bond disproportionation
vibration is sufficient to reproduce the key characteristic of nickelates
observed experimentally, notably the dome of T$_c$ as a function of doping
content. These phenomena are identified if relevant degrees of freedom as well
as an exchange correlation functional that sufficiently amends self-interaction
errors are involved in the simulations. Finally, despite the presence of
correlation effects inherent to $3d$ elements, nickelates superconductors
appear similar to non-magnetic bismuth oxide superconductors.


  In modern age, the increasing complexity of computation and communication
technology is leading us towards the necessity of new paradigm. As a result,
unconventional approach like DNA coding theory is gaining considerable
attention. The storage capacity, information processing and transmission
properties of DNA molecules stimulate the notion of DNA coding theory as well
as DNA cryptography. In this paper we generate DNA codeword using DNA linear
block codes which ensures the secure transmission of information. In the
proposed code design strategy DNA-based XOR operation (DNAX) is applied for
effective construction of DNA codewords which are quadruples generated over the
set of alphabets consisting of four DNA bases adenine, thymine, guanine, and
cytosine. By worked out examples we explain the use of generator matrix and
parity check matrix in encryption and decryption of coded data in the form of
short single stranded DNA sequences. The newly developed technique can detect
as well as correcting error in transmission of DNA codewords through biological
channels from sender to the intended receiver. Through DNA coding theory we are
expanding the paths towards data compression and error correction in the form
of DNA strands. This leads us towards a broader domain of DNA cryptography.


  Dissipative systems can be described in terms of non-hermitian hamiltonians
H, whose left eigenvectors f^j and right eigenvectors f_j form a bi-orthogonal
system. Bi-orthogonal systems could suffer from two difficulties. (a) If the
eigenvectors do not span the whole space, then H can only be diagonalized to
blocks (the Jordan-block problem). (b) Normalization would not be possible and
many familiar-looking formulas would fail if (f^j,f_j) = 0 for some j (the
orthonormalization problem). Waves in open systems provide a well-founded
realization of a bi-orthogonal system, and it is shown that these two problems
can indeed occur and are both related to higher-order poles in the
frequency-domain Green's function. The resolution is then given by introducing
a generalized duality transformation involving extra basis vectors, whose time
evolution is modified by polynomials in the time t. One thus obtains a
nontrivial extension of the bi-orthogonal formalism for dissipative systems.


  We exploit the reduced space of C. elegans postures to develop a novel
tracking algorithm which captures both simple shapes and also self-occluding
coils, an important, yet unexplored, component of worm behavior. We apply our
algorithm to show that visually complex, coiled sequences are a superposition
of two simpler patterns: the body wave dynamics and a head-curvature pulse. We
demonstrate the precise coiled dynamics of an escape response and uncover new
behaviors in spontaneous, large amplitude coils; deep reorientations occur
through classical Omega-shaped postures and also through larger, new postural
excitations which we label here as delta-turns. We find that omega and delta
turns occur independently, the serpentine analog of a random left-right step,
suggesting a distinct triggering mechanism. We also show that omega and delta
turns display approximately equal rates and adapt to food-free conditions on a
similar timescale, a simple strategy to avoid navigational bias.


  Contact resistances between organic semiconductors and metal electrodes have
been shown to play a dominant role in electronic charge injection properties of
organic field-effect transistors. These effects are more prevalent in short
channel length devices and therefore should not be ignored when examining
intrinsic properties such as the mobility and its dependence on temperature or
gate voltage. Here we outline a general procedure to extract contact
current-voltage characteristics and the true channel mobility from the
transport characteristics in bottom contact poly(3-hexylthiophene) field-effect
transistors, for both Ohmic and nonlinear charge injection, over a broad range
of temperatures and gate voltages. Distinguishing between contact and channel
contributions in bottom contact OFETs is an important step toward improved
understanding and modeling of these devices.


  We present a radial velocity (RV) analysis of TOI-1136, a bright TESS system
with six confirmed transiting planets, and a seventh single-transiting planet
candidate. All planets in the system are amenable to transmission spectroscopy,
making TOI-1136 one of the best targets for intra-system comparison of
exoplanet atmospheres. TOI-1136 is young ($\sim$ 700 Myr), and the system
exhibits transit timing variations (TTVs). The youth of the system contributes
to high stellar variability on the order of 50 m s$^{-1}$, much larger than the
likely RV amplitude of any of the transiting exoplanets. Utilizing 359 HIRES
and APF RVs collected as a part of the TESS-Keck Survey (TKS), and 51 HARPS-N
RVs, we experiment with a joint TTV-RV fit. With seven possible transiting
planets, TTVs, more than 400 RVs, and a stellar activity model, we posit that
we may be presenting the most complex mass recovery of an exoplanet system in
the literature to date. By combining TTVs and RVs, we minimized GP overfitting
and retrieved new masses for this system: (m$_{b-g}$ = 3.50$^{+0.8}_{-0.7}$,
6.32$^{+1.1}_{-1.3}$, 8.35$^{+1.8}_{-1.6}$, 6.07$^{+1.09}_{-1.01}$,
9.7$^{+3.9}_{-3.7}$, 5.6$^{+4.1}_{-3.2}$ M$_{\oplus}$). We are unable to
significantly detect the mass of the seventh planet candidate in the RVs, but
we are able to loosely constrain a possible orbital period near 80 days. Future
TESS observations might confirm the existence of a seventh planet in the
system, better constrain the masses and orbital properties of the known
exoplanets, and generally shine light on this scientifically interesting
system.


  We study the real, massive Klein-Gordon field on a $C^\infty$
globally-hyperbolic background space-time with compact Cauchy hypersurfaces. In
particular, the parametrization of this system as initiated by Dirac and
Kucha\v{r} is put on a rigorous basis. The discussion is focussed on the
structure of the set of spacelike embeddings of the Cauchy manifold into the
space-time, and on the associated $e$-tensor density bundles and their tangent
and cotangent bundles. The dynamics of the field is expressed as a set of
automorphisms of the space of initial data in which each pair of embeddings
defines one such automorphism. Using these results, the extended phase space of
the system is shown to be a weak-symplectic manifold, and the Kucha\v{r}
constraint is shown to define a smooth constraint submanifold which is foliated
smoothly by the constraint orbits. The pull-back of the symplectic form to the
constraint surface is a presymplectic form which is singular on the tangent
spaces to the constraint orbits. Thus, the geometric structure of this
infinite-dimensional system is analogous to that of a finite-dimensional,
first-class parametrized system, and hence many of the results for the latter
can be transferred to the infinite-dimensional case without difficulty.


  A method for representing the digest information of each dataset is proposed,
oriented to the aid of innovative thoughts and the communication of data users
who attempt to create valuable products, services, and business models using or
combining datasets. Compared with methods for connecting datasets via shared
attributes (i.e., variables), this method connects datasets via events,
situations, or actions in a scenario that is supposed to be active in the real
world. This method reflects the consideration of the fitness of each metadata
to the feature concept, which is an abstract of the information or knowledge
expected to be acquired from data; thus, the users of the data acquire
practical knowledge that fits the requirements of real businesses and real
life, as well as grounds for realistic application of AI technologies to data.


  Anti-solar differential rotation profiles have been found for decades in
numerical simulations of convective envelopes of solar-type stars. These
profiles are characterized by a slow equator and fast poles (i.e., reversed
with respect to the Sun) and have been found in simulations for high Rossby
numbers (slow rotators). Rotation profiles like this have been reported
observationally in evolved stars, but have never been unambiguously observed
for cool solar-type stars on the main sequence. In this context, detecting this
regime in main-sequence solar-type stars would improve our understanding of
their magnetorotational evolution. The goal of this study is to identify the
most promising cool main-sequence stellar candidates for anti-solar
differential rotation in the \textit{Kepler} sample. First, we introduce a new
theoretical formula to estimate fluid Rossby numbers, $Ro_{\rm f}$, of
main-sequence solar-type stars, from observational quantities, and taking the
influences of the internal structure and metallicity into account. We obtain a
list of the most promising stars that are likely to show anti-solar
differential rotation. We identify two samples: one at solar metallicity,
including 14 targets, and another for other metallicities, including 8 targets.
We find that the targets with the highest $Ro_{\rm f}$ are likely to be early-G
or late-F stars at about log$_{10}g=4.37$~dex. We conclude that cool
main-sequence stellar candidates for anti-solar differential rotation exist in
the \textit{Kepler} sample. The most promising candidate is KIC~10907436, and
two other particularly interesting candidates are the solar analog KIC~7189915
and the seismic target KIC~12117868. Future characterization of these 22 stars
is expected to help us understand how dynamics can impact magnetic and
rotational evolution of old solar-type stars at high Rossby number.


  An investigation of the two-dimensional Widom-Rowlinson lattice gas under an
applied drive uncovered a remarkable non-equilibrium steady state in which
uniform stripes (reminiscent of an equilibrium lamellar phase) form
perpendicular to the drive direction [R. Dickman and R. K. P. Zia, Phys. Rev. E
97, 062126 (2018)]. Here we study this model at low particle densities in two
and three dimensions, where we find a disordered phase with a characteristic
length scale (a "microemulsion") along the drive direction. We develop a
continuum theory of this disordered phase to derive a coarse-grained
field-theoretic action for the non-equilibrium dynamics. The action has the
form of two coupled driven diffusive systems with different characteristic
velocities, generated by an interplay between the particle repulsion and the
drive. We then show how fluctuation corrections in the field theory may
generate the characteristic features of the microemulsion phase, including a
peak in the static structure factor corresponding to the characteristic length
scale. This work lays the foundation for understanding the stripe phenomenon
more generally.


  In this report, we provide a comparative analysis of different techniques for
user intent classification towards the task of app recommendation. We analyse
the performance of different models and architectures for multi-label
classification over a dataset with a relative large number of classes and only
a handful examples of each class. We focus, in particular, on memory network
architectures, and compare how well the different versions perform under the
task constraints. Since the classifier is meant to serve as a module in a
practical dialog system, it needs to be able to work with limited training data
and incorporate new data on the fly. We devise a 1-shot learning task to test
the models under the above constraint. We conclude that relatively simple
versions of memory networks perform better than other approaches. Although, for
tasks with very limited data, simple non-parametric methods perform comparably,
without needing the extra training data.


  Extreme scattering events (ESEs) are observed as dramatic ($>50\%$) drops in
flux density that occur over an extended period of weeks to months. Discrete
plasma lensing structures are theorized to scatter the radio waves produced by
distant sources such as pulsars, causing the signature decrease in flux density
and characteristic caustic spikes in ESE light curves. While plasma lens models
in the extant literature have reproduced key features of ESE light curves, they
have all faced the problem of being highly over-dense and over-pressured
relative to the surrounding interstellar medium (ISM) by orders of magnitude.
We model ESEs by numerically ray-tracing through analytic, volumetric plasma
lens models by solving the eikonal equation. Delaunay triangulation connecting
the rays approximates the wavefront, generating a mapping from the observer
plane to the source plane to account for multiple-imaging. This eikonal method
of ray-tracing is tested against known analytic solutions and is then applied
to a three-dimensional Gaussian-distributed electron volume density lens, and a
filament model inspired by Grafton et al. (2023). We find convergence of our
numerical results with established analytic solutions validating our numerical
method, and reproduce ESE-like light curves. Our numerical ray-tracing method
lends itself well to exploring the lensing effects of volumetric turbulence as
well as sheet-like lenses, which is currently in progress.


  We show that central zeros of $L$-functions in the Selberg class have a
probabilistic interpretation by stating an equivalence condition of the Riemann
hypothesis for the $L$-functions in terms of infinitely divisible
distributions.


  The increasing difficulties in financing the welfare state and in particular
public retirement pensions have been one of the outcomes both of the decrease
of fertility and birth rates combined with the increase of life expectancy. The
dynamics of retirement pensions are usually studied in Economics using
overlapping generation models. These models are based on simplifying
assumptions like the use of a representative agent to ease the problem of
tractability. Alternatively, we propose to use agent-based modelling (ABM),
relaxing the need for those assumptions and enabling the use of interacting and
heterogeneous agents assigning special importance to the study of
inter-generational relations. We treat pension dynamics both in economics and
political perspectives. The model we build, following the ODD protocol, will
try to understand the dynamics of choice of public versus private retirement
pensions resulting from the conflicting preferences of different agents but
also from the cooperation between them. The aggregation of these individual
preferences is done by voting. We combine a microsimulation approach following
the evolution of synthetic populations along time, with the ABM approach
studying the interactions between the different agent types. Our objective is
to depict the conditions for the survival of the public pensions system
emerging from the relation between egoistic and altruistic individual and
collective behaviours.


  While stripe phases with broken rotational symmetry of charge density appear
in many complex correlated systems, the heterogeneity of spatial ordering and
dynamics remains elusive. This missing info is at the heart of understanding
the structure and function relation in quantum complex materials. We focus here
on the spatial heterogeneity of the motion of charge density wave (CDW) at
nanoscale in the archetypal case of La$_{2-x}$Sr$_x$NiO$_{4+y}$ perovskite at
low temperature. We report compelling evidence that the unconventional
increasing motion of CDW at T < 50K is related with the decreasing of its
correlation length using resonant soft X-ray photon correlation spectroscopy
(XPCS). The key result of this work is the direct visualization of nanoscale
spatial inhomogeneity of CDW relaxation dynamics by scanning micro X-ray
diffraction (SmXRD) showing a nanoscale landscape of percolating short range
dynamic CDW puddles competing with large quasi-static CDW puddles giving rise
to a novel form of nanoscale phase separation of the incommensurate stripes
order landscape.


  The recent detection of delayed X-ray flares during the afterglow phase of
gamma-ray bursts (GRBs) suggests an inner-engine origin, at radii inside the
deceleration radius characterizing the beginning of the forward shock afterglow
emission. Given the observed temporal overlapping between the flares and
afterglows, there must be inverse Compton (IC) emission arising from such flare
photons scattered by forward shock afterglow electrons. We find that this IC
emission produces GeV-TeV flares, which may be detected by GLAST and
ground-based TeV telescopes. We speculate that this kind of emission may
already have been detected by EGRET from a very strong burst--GRB940217. The
enhanced cooling of the forward shock electrons by the X-ray flare photons may
suppress the synchrotron emission of the afterglows during the flare period.
The detection of GeV-TeV flares combined with low energy observations may help
to constrain the poorly known magnetic field in afterglow shocks. We also
consider the self-IC emission in the context of internal-shock and
external-shock models for X-ray flares. The emission above GeV from internal
shocks is low, while the external shock model can also produce GeV-TeV flares,
but with a different temporal behavior from that caused by IC scattering of
flare photons by afterglow electrons. This suggests a useful approach for
distinguishing whether X-ray flares originate from late central engine activity
or from external shocks.


  Our study aims to build a machine learning model for crime prediction using
geospatial features for different categories of crime. The reverse geocoding
technique is applied to retrieve open street map (OSM) spatial data. This study
also proposes finding hotpoints extracted from crime hotspots area found by
Hierarchical Density-Based Spatial Clustering of Applications with Noise
(HDBSCAN). A spatial distance feature is then computed based on the position of
different hotpoints for various types of crime and this value is used as a
feature for classifiers. We test the engineered features in crime data from
Royal Canadian Mounted Police of Halifax, NS. We observed a significant
performance improvement in crime prediction using the new generated spatial
features.


  A result of Corfield, Sati, and Schreiber asserts that
$\mathfrak{gl}_n$-weight systems associated to the defining representation are
quantum states. In this short note we extend this result to all
$\mathfrak{gl}_n$-weight systems corresponding to labeling by symmetric and
exterior powers of the defining representation.


  There exists a paradox in quantum field theory: substituting a field
configuration which solves a subset of the field equations into the action and
varying it is not necessarily equivalent to substituting that configuration
into the remaining field equations. We take the $S^4$ and Freund-Rubin-like
instantons as two examples to clarify the paradox. One must match the
specialized configuration field variables with the corresponding boundary
conditions by adding appropriate Legendre terms to the action. Some comments
are made regarding exceptional degenerate cases.


  Noncollinear antiferromagnets, such as Mn$_3$Sn and Mn$_3$Ir, were recently
shown to be analogous to ferromagnets in that they have a large anomalous Hall
effect. Here we show that these materials are similar to ferromagnets in
another aspect: the charge current in these materials is spin-polarized. In
addition, we show that the same mechanism that leads to the spin-polarized
current also leads to a transverse spin current, which has a distinct symmetry
and origin from the conventional spin Hall effect. We illustrate the existence
of the spin-polarized current and the transverse spin current by performing
\emph{ab initio} microscopic calculations and by analyzing the symmetry. We
discuss possible applications of these novel spin currents, such as an
antiferromagnetic metallic or tunneling junction.


  In analogy to the classical isomorphism between
$\mathcal{L}(\mathcal{S}(\mathbb{R}^{n}) ,\mathcal{S}^{\prime}(\mathbb{R}^{m})
) $ and $\mathcal{S}^{\prime}(\mathbb{R}^{n+m}) $, we show that a large class
of moderate linear mappings acting between the space
$\mathcal{G}\_{\mathcal{S}}(\mathbb{R}^{n}) $ of Colombeau rapidly decreasing
generalized functions and the space $\mathcal{G}\_{\tau}(\mathbb{R}^{n}) $ of
temperate ones admits generalized integral representations, with kernels
belonging to $\mathcal{G}\_{\tau}(\mathbb{R}^{n+m}) $. Furthermore, this result
contains the classical one in the sense of the generalized distribution
equality.


  High pressure torsion (HPT) is one of the ways to form nanostructured
materials with high strength properties. However, HPT hardening mechanisms vary
from material to material and are poorly understood for some BCC metals,
particularly niobium and vanadium. This work aims to identify strain hardening
stages for Nb and V metals during HPT. Two approaches have been used to
identify the deformation stages during high pressure torsion. The approaches
are based on the application of a "piecewise" model, taking into account the
different deformation mechanisms that determine the type of the forming
structure, and on the analysis of the hardness vs. true strain dependence
according to the $H$$-$${e}^{0.5}$ law. We compared the identified stages with
the results of the electron microscopic study of the structure. Both models
describe well the structural changes observed microscopically in HPT-deformed
niobium. However, we have shown that only the piecewise model gives an adequate
description of the stages of structure development in vanadium. We have
provided an explanation for the observed difference in the behavior of niobium
and vanadium upon HPT.


  Regularization by Denoising (RED) is a well-known method for solving image
restoration problems by using learned image denoisers as priors. Since the
regularization parameter in the traditional RED does not have any physical
interpretation, it does not provide an approach for automatic parameter
selection. This letter addresses this issue by introducing the Constrained
Regularization by Denoising (CRED) method that reformulates RED as a
constrained optimization problem where the regularization parameter corresponds
directly to the amount of noise in the measurements. The solution to the
constrained problem is solved by designing an efficient method based on
alternating direction method of multipliers (ADMM). Our experiments show that
CRED outperforms the competing methods in terms of stability and robustness,
while also achieving competitive performances in terms of image quality.


  In the present paper we study the low density Bose gas in the thermodynamic
limit interacting via two-body and three-body interaction potentials. We prove
that the leading order of the ground state energy is entirely characterised by
both the scattering length of the two-body potential and the scattering energy
of the three-body potential. The corresponding result for two-body interactions
was proven in seminal papers of Dyson (1957) and of Lieb-Yngvason (1998), and
the result for three-body interactions was proven by Nam-Ricaud-Triay. The
present result resolves a conjecture of Nam-Ricaud-Triay.