  While the use of artificial intelligence (AI) for medical image analysis is
gaining wide acceptance, the expertise, time and cost required to generate
annotated data in the medical field are significantly high, due to limited
availability of both data and expert annotation. Strongly supervised object
localization models require data that is exhaustively annotated, meaning all
objects of interest in an image are identified. This is difficult to achieve
and verify for medical images. We present a method for the transformation of
real data to train any Deep Neural Network to solve the above problems. We show
the efficacy of this approach on both a weakly supervised localization model
and a strongly supervised localization model. For the weakly supervised model,
we show that the localization accuracy increases significantly using the
generated data. For the strongly supervised model, this approach overcomes the
need for exhaustive annotation on real images. In the latter model, we show
that the accuracy, when trained with generated images, closely parallels the
accuracy when trained with exhaustively annotated real images. The results are
demonstrated on images of human urine samples obtained using microscopy.


  We have studied the influences of isospin symmetry breaking of
nucleon-nucleon interaction on the various properties of asymmetrical nuclear
matter and $\beta$-stable matter. For asymmetrical nuclear matter, it is found
that by including this isospin symmetry breaking, the changes of bulk
properties increase by increasing both density and asymmetry parameter.
However, these effects on the total energy and equation of state of
$\beta$-stable matter are ignorable. For asymmetrical nuclear matter, the
validity of the empirical parabolic law in the isospin symmetry breaking case
is shown. It is observed that the isospin symmetry breaking of nucleon-nucleon
interaction affects the $\beta$-equilibrium conditions in $\beta$-stable
matter.


  The success of Deep Learning and its potential use in many safety-critical
applications has motivated research on formal verification of Neural Network
(NN) models. In this context, verification involves proving or disproving that
an NN model satisfies certain input-output properties. Despite the reputation
of learned NN models as black boxes, and the theoretical hardness of proving
useful properties about them, researchers have been successful in verifying
some classes of models by exploiting their piecewise linear structure and
taking insights from formal methods such as Satisifiability Modulo Theory.
However, these methods are still far from scaling to realistic neural networks.
To facilitate progress on this crucial area, we exploit the Mixed Integer
Linear Programming (MIP) formulation of verification to propose a family of
algorithms based on Branch-and-Bound (BaB). We show that our family contains
previous verification methods as special cases. With the help of the BaB
framework, we make three key contributions. Firstly, we identify new methods
that combine the strengths of multiple existing approaches, accomplishing
significant performance improvements over previous state of the art. Secondly,
we introduce an effective branching strategy on ReLU non-linearities. This
branching strategy allows us to efficiently and successfully deal with high
input dimensional problems with convolutional network architecture, on which
previous methods fail frequently. Finally, we propose comprehensive test data
sets and benchmarks which includes a collection of previously released
testcases. We use the data sets to conduct a thorough experimental comparison
of existing and new algorithms and to provide an inclusive analysis of the
factors impacting the hardness of verification problems.


  Recently, the proliferation of highly realistic synthetic images, facilitated
through a variety of GANs and Diffusions, has significantly heightened the
susceptibility to misuse. While the primary focus of deepfake detection has
traditionally centered on the design of detection algorithms, an investigative
inquiry into the generator architectures has remained conspicuously absent in
recent years. This paper contributes to this lacuna by rethinking the
architectures of CNN-based generators, thereby establishing a generalized
representation of synthetic artifacts. Our findings illuminate that the
up-sampling operator can, beyond frequency-based artifacts, produce generalized
forgery artifacts. In particular, the local interdependence among image pixels
caused by upsampling operators is significantly demonstrated in synthetic
images generated by GAN or diffusion. Building upon this observation, we
introduce the concept of Neighboring Pixel Relationships(NPR) as a means to
capture and characterize the generalized structural artifacts stemming from
up-sampling operations. A comprehensive analysis is conducted on an open-world
dataset, comprising samples generated by \tft{28 distinct generative models}.
This analysis culminates in the establishment of a novel state-of-the-art
performance, showcasing a remarkable \tft{11.6\%} improvement over existing
methods. The code is available at
https://github.com/chuangchuangtan/NPR-DeepfakeDetection.


  Among transition metal dichalcogenides (TMDs), VSe$_2$ is considered to
develop a purely 3-dimensional (3D) charge-density wave (CDW) at T$_{CDW}$=110
K. Here, by means of high resolution inelastic x-ray scattering (IXS), we show
that the CDW transition is driven by the collapse of an acoustic mode at the
critical wavevector \textit{q}$_{CDW}$= (2.25 0 0.7) r.l.u. and critical
temperature T$_{CDW}$=110 K. The softening of this mode starts to be pronounced
for temperatures below 2$\times$ T$_{CDW}$ and expands over a rather wide
region of the Brillouin zone, suggesting a large contribution of the
electron-phonon interaction to the CDW formation. This interpretation is
supported by our first principles calculations that determine a large
momentum-dependence of the electron-phonon interaction, peaking at the CDW
wavevector, in the presence of nesting. Fully anharmonic {\it ab initio}
calculations confirm the softening of one acoustic branch at \textit{q}$_{CDW}$
as responsible for the CDW formation and show that van der Waals interactions
are crucial to melt the CDW. Our work also highlights the important role of
out-of-plane interactions to describe 3D CDWs in TMDs.


  We present the most recent results from the FASTSUM collaboration for hadron
properties at high temperature. This includes the temperature dependence of the
light and charmed meson and baryon spectrum, as well as properties of heavy
quarkonia. The results are obtained using anisotropic lattices with a fixed
scale approach. We also present the status of our next generation gauge
ensembles.


  Applications of Domain Wall fermions to various vector-like lattice theories
are reviewed with an emphasis on QCD thermodynamics. Methods for improving
their chiral properties at strong coupling are discussed and results from
implementing them are presented.


  We study the optical properties of highly anisotropic quantum dot structures
(quantum dashes) characterized by the presence of two trapping centers located
along the structure. Such a system can exhibit some of the properties
characteristic for double quantum dots. We show that sub- and super-radiant
states can form for certain quantum dash geometries, which is manifested by a
pronounced transfer of intensity between spectral lines, accompanied by the
appearance of strong electron-hole correlations. We also compare exciton
absorption spectra and polarization properties of a system with a single and
double trapping center and show how the geometry of multiple trapping centers
influences the optical properties of the system. We show that for a broad range
of trapping geometries the relative absorption intensity of the ground state is
larger than that of the lowest excited states, contrary to the quantum dash
systems characterized by a single trapping center. Thus, optical properties of
these structures are determined by fine details of their morphology.


  The realization of a paradigm chaotic system, namely the harmonically driven
oscillator, in the quantum domain using cold trapped ions driven by lasers is
theoretically investigated. The simplest characteristics of regular and chaotic
dynamics are calculated. The possibilities of experimental realization are
discussed.


  Ferroelectric domain walls hold great promise for innovative applications in
ferroelectric devices. However, the underlying mechanisms behind the observed
giant conductance of charged domain walls remain poorly understood. Using a
first-principles approach that incorporates Boltzmann transport theory and the
relaxation time approximation, we determine the carrier concentration,
mobility, and conductivity of domain walls with head-to-head and tail-to-tail
polarization orientations. Our systematic exploration reveals that the
accumulation of carriers, particularly their concentration, plays a dominant
role in the domain wall conductance mechanism. However, the observed
conductance differences between head-to-head and tail-to-tail domain walls are
primarily due to differences in carrier mobility. The width of the domain wall
is a key factor determining the device scale. Our calculated domain wall width
is significantly smaller than previously reported values. This method, not
limited to a certain ferroelectric material, can be used for the optimization
and application development of various domain wall materials and devices.


  Question answering based on retrieval augmented generation (RAG-QA) is an
important research topic in NLP and has a wide range of real-world
applications. However, most existing datasets for this task are either
constructed using a single source corpus or consist of short extractive
answers, which fall short of evaluating large language model (LLM) based RAG-QA
systems on cross-domain generalization. To address these limitations, we create
Long-form RobustQA (LFRQA), a new dataset comprising human-written long-form
answers that integrate short extractive answers from multiple documents into a
single, coherent narrative, covering 26K queries and large corpora across seven
different domains. We further propose RAG-QA Arena by directly comparing
model-generated answers against LFRQA's answers using LLMs as evaluators. We
show via extensive experiments that RAG-QA Arena and human judgments on answer
quality are highly correlated. Moreover, only 41.3% of the most competitive
LLM's answers are preferred to LFRQA's answers, demonstrating RAG-QA Arena as a
challenging evaluation platform for future research.


  The gravitational fields of vacuumless global and gauge strings have been
studied in Brans-Dicke theory under the weak field assumption of the field
equations. It has been shown that both global and gauge string can have
repulsive as well as attractive gravitational effect in Brans-Dicke theory
which is not so in General Relativity.


  The cosmological term, $\Lambda$, in Einstein's equations is an essential
ingredient of the `concordance' $\Lambda$CDM model of cosmology. In this
mini-review presentation, we assess the possibility that $\Lambda$ can be a
dynamical quantity, more specifically a `running quantity' in quantum field
theory in curved spacetime. A great deal of phenomenological works have shown
in the last few years that this option (sometimes accompanied with a running
gravitational coupling) may cure some of the tensions afflicting the
$\Lambda$CDM. The `running vacuum models' (RVM's) are characterized by the
vacuum energy density, $\rho_{\rm vac}$, being a series of (even) powers of the
Hubble rate and its time derivatives. Here we describe the technical quantum
field theoretical origin of the RVM structure in FLRW spacetime, which goes
well-beyond the original semi-qualitative renormalization group arguments. In
particular, we compute the renormalized energy-momentum tensor using the
adiabatic regularization procedure and show that it leads to the RVM form. In
other words, we find that the renormalized vacuum energy density,
$\rho_{vac}(H)$ evolves as a (constant) additive term plus a leading dynamical
components ${\cal O}(H^2)$. There are also ${\cal O}(H^4)$ contributions, which
can be relevant for the early universe. Remarkably enough, the renormalized
$\rho_{\rm vac}(H)$ does not exhibit dangerous terms proportional to the
quartic power of the masses ($\sim m^4$) of the fields. It is well-known that
these terms have been the main source of trouble since they are responsible for
the extreme fine tuning and ultimately for the cosmological constant problem.
In this context, the current $\rho_{vac}(H)$ is dominated by a constant term,
as it should be, but it acquires a mild dynamical component $\sim \nu H^2$
($|\nu|\ll1$) which makes the RVM to mimic quintessence.


  Algorithmic recourse emerges as a prominent technique to promote the
explainability, transparency and hence ethics of machine learning models.
Existing algorithmic recourse approaches often assume an invariant predictive
model; however, the predictive model is usually updated upon the arrival of new
data. Thus, a recourse that is valid respective to the present model may become
invalid for the future model. To resolve this issue, we propose a novel
framework to generate a model-agnostic recourse that exhibits robustness to
model shifts. Our framework first builds a coverage-validity-aware linear
surrogate of the nonlinear (black-box) model; then, the recourse is generated
with respect to the linear surrogate. We establish a theoretical connection
between our coverage-validity-aware linear surrogate and the minimax
probability machines (MPM). We then prove that by prescribing different
covariance robustness, the proposed framework recovers popular regularizations
for MPM, including the $\ell_2$-regularization and class-reweighting.
Furthermore, we show that our surrogate pushes the approximate hyperplane
intuitively, facilitating not only robust but also interpretable recourses. The
numerical results demonstrate the usefulness and robustness of our framework.


  The proton emission induced by polarized photons is studied in the energy
range above the giant resonance region and below the pion emission threshold.
Results for the 12C, 16O and 40Ca nuclei are presented. The sensitivity of
various observables to final state interaction, meson exchange currents and
short range correlations is analyzed. We found relevant effects due to the
virtual excitation of the $\Delta$ resonance.


  We give an infinitary extension of the Ne\v{s}et\v{r}il-R\"{o}dl theorem for
category of relational structures with special type-respecting embeddings.


  We present a generalization of the Nambu mechanics on the base of Liouville's
theorem. We prove that the Poisson structure of an n-dimensional
multisymplectic phase space is induced by (n-1)-Hamiltonian k-vector field
seach of which requires introduction of k-Hamiltonians.


  Excited nuclear fragments are emitted during nuclear fission. The
de-excitation of these fission fragments takes place as sequential emission of
neutrons followed by photons. A correlation between neutron and photon
multiplicities accompanying fission is thus expected. Fission event generators
based on established statistical nuclear physics models predict a negative
event-by-event correlation in neutron-photon multiplicity. A survey of
published experimental results of an event-by-event covariance between the
neutron and photon multiplicities emitted following the spontaneous fission of
$^{252}$Cf is presented. Analytic unfolding expressions are developed in this
work to determine the bias introduced by background sources, particle
misclassification, pulse pileup, and inelastic photon production. The published
experimental data are re-analyzed using these unfolding techniques and are
found to be in qualitative agreement with the predictions of model-based
calculations. In particular, we have concluded that there exists a significant
event-by-event neutron-photon emission competition following the spontaneous
fission of $^{252}$Cf.


  We explore the possibility of a consistent cosmology based on the
gauge-fixing independent running of the gravitational and cosmological
constants ($G$ and $\Lambda$) in the framework of effective quantum gravity. In
particular, their running in this framework was found to satisfy $G \propto
\Lambda^4$. In the cosmological setting, the covariance of the theory provides
energy conservation relations, which are impossible to satisfy with the unique
scale parameter. However, by introducing the second sub-dominant scale
corresponding to the higher-loop corrections and higher-derivative terms, one
can close the system of equations for the running of parameters and arrive at
the consistent cosmological solutions. This approach yields a change in the
cosmological expansion history that affects the ratio of the Hubble parameter
today to the Hubble parameter at high redshift.


  If a function $f:\mathbb{R}\to\mathbb{R}$ can be represented as the sum of
$n$ periodic functions as $f=f_1+\dots+f_n$ with $f(x+\alpha_j)=f(x)$
($j=1,\dots,n$), then it also satisfies a corresponding $n$-order difference
equation $\Delta_{\alpha_1}\dots\Delta_{\alpha_n} f=0$. The periodic
decomposition problem asks for the converse implication, which may hold or fail
depending on the context (on the system of periods, on the function class in
which the problem is considered, etc.). The problem has natural extensions and
ramifications in various directions, and is related to several other problems
in real analysis, Fourier and functional analysis. We give a survey about the
available methods and results, and present a number of intriguing open
problems.


  Texture segmentation is the process of partitioning an image into regions
with different textures containing a similar group of pixels. Detecting the
discontinuity of the filter's output and their statistical properties help in
segmenting and classifying a given image with different texture regions. In
this proposed paper, chili x-ray image texture segmentation is performed by
using Gabor filter. The texture segmented result obtained from Gabor filter fed
into three texture filters, namely Entropy, Standard Deviation and Range
filter. After performing texture analysis, features can be extracted by using
Statistical methods. In this paper Gray Level Co-occurrence Matrices and First
order statistics are used as feature extraction methods. Features extracted
from statistical methods are given to Support Vector Machine (SVM) classifier.
Using this methodology, it is found that texture segmentation is followed by
the Gray Level Co-occurrence Matrix feature extraction method gives a higher
accuracy rate of 84% when compared with First order feature extraction method.
  Key Words: Texture segmentation, Texture filter, Gabor filter, Feature
extraction methods, SVM classifier.


  We introduce and develop the notion of hyper-ideals of multilinear operators
between Banach spaces. While the well studied notion of ideals of multilinear
operators (multi-ideals) relies on the composition with linear operators, the
notion we propose, by considering the composition with multilinear operators,
explores more deeply the nonlinear feature of the subject. The results we prove
show that, although more restrictive a priori, hyper-ideals enjoy nice general
properties and its theory is rich enough to provide distinguished examples in
every situation where the corresponding multi-ideal fails to be a hyper-ideal.


  The transient 500 s X-ray pulsar MAXI J1409-619 was discovered by the slit
cameras aboard MAXI on October 17, 2010, and soon after accurately localized by
Swift. We found that the source position was serendipitously observed in 2000
during BeppoSAX observations of the Galactic plane. Two sources are clearly
detected in the MECS: one is consistent with the position of IGR J14043-6148
and the other one with that of MAXI J1409-619. We report on the analysis of
this archival BeppoSAX/MECS observation integrated with newly analyzed
observation from ASCA and a set of high-energy observations obtained from the
offset fields of the BeppoSAX/PDS instrument. For the ON-source observation,
the 1.8-100 keV spectrum is fit by an absorbed power law with a photon index
Gamma = 0.87_{-0.19}^{+0.29}, corresponding to 2-10 and 15-100 keV unabsorbed
fluxes of 2.7E-12 and 4E-11 erg/cm2/s, respectively, and a 2-10 keV luminosity
of 7E+34 erg/s for a 15 kpc distance. For a PDS offset field observation,
performed about one year later and showing a 15-100 keV flux of 7E-11
erg/cm2/s, we clearly pinpoint three spectral absorption features at 44, 73,
and 128 keV, resolved both in the spectral fit and in the Crab ratio. We
interpret these not harmonically spaced features as due to cyclotron
resonances. The fundamental energy of 44 +/- 3 keV corresponds to a magnetic
field strength at the neutron star surface of 3.8E12 (1+z) G, where z is the
gravitational redshift. We discuss the nature of the source in the light of its
possible counterpart.


  We show that in the dual version of the generalized Dick model
monopole-anti-monopole pairs have finite energy. It is possible to use the
potential between monopole and anti-monopole to find the mass spectrum of the
glueballs. The results are discussed in connection with the Faddeev-Niemi model
and toroidal soliton solutions. Some others finite energy configurations are
found, both in the magnetic and electric sector.


  This paper gives a summary of selected highlights discussed in the working
group on "Structure Functions and Parton Densities" (WG1) at the DIS 2017
conference. From the many talks presented we extract some general themes
discussed with respect to global PDF fits, new PDF-sensitive measurements from
the LHC experiments and elsewhere, exploitation of new ideas, tools to perform
PDF fits, PDFs of heavy nuclei, and finally progress in basic theory
calculations.


  It is shown that high energy features of the cosmic ray spectrum, in
particular the kink around 4 PeV and the corresponding change in spectral
index, may be explained from interactions between highly energetic protons and
relic Big Bang antineutrinos, if the latter have a rest mass of about 0.4
eV/$c^2$. This explanation is supported by experimental data from extensive
air-shower experiments.


  In embedded control systems, the potential risks of software defects have
been increasing because of software complexity which leads to, for example,
timing related problems. These defects are rarely found by tests or
simulations. To detect such defects, we propose a modeling method which can
generate software models for model checking with a program slicing technique
based on a variable dependence graph. We have applied the proposed method to
one case in automotive control software and demonstrated the effectiveness of
the method. Furthermore, we developed a software tool to automate model
generation and achieved a 35% decrease in total verification time on model
checking.


  This paper examines the problem of learning with a finite and possibly large
set of p base kernels. It presents a theoretical and empirical analysis of an
approach addressing this problem based on ensembles of kernel predictors. This
includes novel theoretical guarantees based on the Rademacher complexity of the
corresponding hypothesis sets, the introduction and analysis of a learning
algorithm based on these hypothesis sets, and a series of experiments using
ensembles of kernel predictors with several data sets. Both convex combinations
of kernel-based hypotheses and more general Lq-regularized nonnegative
combinations are analyzed. These theoretical, algorithmic, and empirical
results are compared with those achieved by using learning kernel techniques,
which can be viewed as another approach for solving the same problem.


  Antibody design is valuable for therapeutic usage and biological research.
Existing deep-learning-based methods encounter several key issues: 1)
incomplete context for Complementarity-Determining Regions (CDRs) generation;
2) incapability of capturing the entire 3D geometry of the input structure; 3)
inefficient prediction of the CDR sequences in an autoregressive manner. In
this paper, we propose Multi-channel Equivariant Attention Network (MEAN) to
co-design 1D sequences and 3D structures of CDRs. To be specific, MEAN
formulates antibody design as a conditional graph translation problem by
importing extra components including the target antigen and the light chain of
the antibody. Then, MEAN resorts to E(3)-equivariant message passing along with
a proposed attention mechanism to better capture the geometrical correlation
between different components. Finally, it outputs both the 1D sequences and 3D
structure via a multi-round progressive full-shot scheme, which enjoys more
efficiency and precision against previous autoregressive approaches. Our method
significantly surpasses state-of-the-art models in sequence and structure
modeling, antigen-binding CDR design, and binding affinity optimization.
Specifically, the relative improvement to baselines is about 23% in
antigen-binding CDR design and 34% for affinity optimization.


  Many natural patterns, such as the distributions of blood particles in a
blood sample, proteins on cell surfaces, biological populations in their
habitat, galaxies in the universe, the sequence of human genes, and the fitness
in evolutionary computing, have been found to follow power law. Taylor's power
law (Taylor 1961: Nature, 189:732-) is well recognized as one of the
fundamental models in population ecology. A fundamental property of biological
populations, which Taylor's power law reveals, is the near universal
heterogeneity of population abundance distribution in habitat. Obviously, the
heterogeneity also exists at the community level, where not only the
distributions of population abundances but also the proportions of the species
composition in the community are often heterogeneous. Nevertheless, existing
community diversity indexes such as Shannon index and Simpson index can only
measure "local" or "static" diversity in the sense that they are computed for
each habitat at a specific time point, and the indexes alone do not reflect the
diversity changes. In this note, I propose to extend the application scope of
Taylor's power law to the studies of human microbial communities, specifically,
the community heterogeneity at both population and community levels. I further
suggested that population dispersion models such as Taylor (1980: Nature, 286,
53-), which is known to generate population distribution patterns consistent
with the power law, should also be very useful for analyzing the distribution
patterns of human microbes within the human body. Overall, I hope that the
approach to human microbial community with the power law offers an example that
ecological theories can play an important role in the emerging medical ecology,
which aims at studying the ecology of human microbiome and its implications to
human diseases and health, as well as in personalized medicine.


  Owing to the success of transformer models, recent works study their
applicability in 3D medical segmentation tasks. Within the transformer models,
the self-attention mechanism is one of the main building blocks that strives to
capture long-range dependencies. However, the self-attention operation has
quadratic complexity which proves to be a computational bottleneck, especially
in volumetric medical imaging, where the inputs are 3D with numerous slices. In
this paper, we propose a 3D medical image segmentation approach, named UNETR++,
that offers both high-quality segmentation masks as well as efficiency in terms
of parameters, compute cost, and inference speed. The core of our design is the
introduction of a novel efficient paired attention (EPA) block that efficiently
learns spatial and channel-wise discriminative features using a pair of
inter-dependent branches based on spatial and channel attention. Our spatial
attention formulation is efficient having linear complexity with respect to the
input sequence length. To enable communication between spatial and
channel-focused branches, we share the weights of query and key mapping
functions that provide a complimentary benefit (paired attention), while also
reducing the overall network parameters. Our extensive evaluations on five
benchmarks, Synapse, BTCV, ACDC, BRaTs, and Decathlon-Lung, reveal the
effectiveness of our contributions in terms of both efficiency and accuracy. On
Synapse, our UNETR++ sets a new state-of-the-art with a Dice Score of 87.2%,
while being significantly efficient with a reduction of over 71% in terms of
both parameters and FLOPs, compared to the best method in the literature. Code:
https://github.com/Amshaker/unetr_plus_plus.


  In Einstein-Maxwell theory black holes are uniquely determined by their mass,
their charge and their angular momentum. This is no longer true in
Einstein-Yang-Mills theory. We discuss sequences of neutral and charged SU(N)
Einstein-Yang-Mills black holes, which are static spherically symmetric and
asymptotically flat, and which carry Yang-Mills hair. Furthermore, in
Einstein-Maxwell theory static black holes are spherically symmetric. We
demonstrate that, in contrast, SU(2) Einstein-Yang-Mills theory possesses a
sequence of black holes, which are static and only axially symmetric.


  The ResNet architecture has been widely adopted in deep learning due to its
significant boost to performance through the use of simple skip connections,
yet the underlying mechanisms leading to its success remain largely unknown. In
this paper, we conduct a thorough empirical study of the ResNet architecture in
classification tasks by linearizing its constituent residual blocks using
Residual Jacobians and measuring their singular value decompositions. Our
measurements reveal a process called Residual Alignment (RA) characterized by
four properties:
  (RA1) intermediate representations of a given input are equispaced on a line,
embedded in high dimensional space, as observed by Gai and Zhang [2021];
  (RA2) top left and right singular vectors of Residual Jacobians align with
each other and across different depths;
  (RA3) Residual Jacobians are at most rank C for fully-connected ResNets,
where C is the number of classes; and
  (RA4) top singular values of Residual Jacobians scale inversely with depth.
  RA consistently occurs in models that generalize well, in both
fully-connected and convolutional architectures, across various depths and
widths, for varying numbers of classes, on all tested benchmark datasets, but
ceases to occur once the skip connections are removed. It also provably occurs
in a novel mathematical model we propose. This phenomenon reveals a strong
alignment between residual branches of a ResNet (RA2+4), imparting a highly
rigid geometric structure to the intermediate representations as they progress
linearly through the network (RA1) up to the final layer, where they undergo
Neural Collapse.


  A novel prediction is derived by the Two-State-Vector-Formalism (TSVF) for a
particle superposed over three boxes. Under appropriate pre- and
postselections, and with tunneling enabled between two of the boxes, it is
possible to derive not only one, but three predictions for three different
times within the intermediate interval. These predictions are moreover
contradictory. The particle (when looked for using a projective measurement)
seems to disappear from the first box where it would have been previously found
with certainty, appearing instead within the third box, to which no tunneling
is possible, and later re-appearing within the second. It turns out that local
measurement (i.e. opening one of the boxes) fails to indicate the particle's
presence, but subtler measurements performed on the two boxes together reveal
the particle's nonlocal modular momentum spatially separated from its mass.
Another advance of this setting is that, unlike other predictions of the TSVF
that rely on weak and/or counterfactual measurements, the present one uses
actual projective measurements. This outcome is then corroborated by adding
weak measurements and the Aharonov-Bohm effect. The results strengthen the
recently suggested time-symmetric Heisenberg ontology based on nonlocal
deterministic operators. They can be also tested using the newly developed
quantum router.


  We study a link between complete non-ambiguous trees (CNATs) and permutations
exhibited by Daniel Chen and Sebastian Ohlig in recent work. In this, they
associate a certain permutation to the leaves of a CNAT, and show that the
number of $n$-permutations that are associated with exactly one CNAT is
$2^{n-2}$. We connect this to work by the first author and co-authors linking
complete non-ambiguous trees and the Tutte polynomial of the associated
permutation graph. This allows us to prove a number of conjectures by Chen and
Ohlig on the number of $n$-permutations that are associated with exactly $k$
CNATs for various $k > 1$, via various bijective correspondences between such
permutations. We also exhibit a new bijection between $(n-1)$-permutations and
CNATs whose permutation is the decreasing permutation $n(n-1)\cdots1$. This
bijection maps the left-to-right minima of the permutation to dots on the top
row of the corresponding CNAT, and descents of the permutation to empty rows of
the CNAT.


  An extension $B\subset A$ of finite dimensional algebras is bounded if the
$B$-$B$-bimodule $A/B$ is $B$-tensor nilpotent, its projective dimension is
finite and $\mathrm{Tor}_i^B(A/B, (A/B)^{\otimes_B j})=0$ for all $i, j\geq 1$.
We show that for a bounded extension $B\subset A$, the algebras $A$ and $B$ are
singularly equivalent of Morita type with level. Additionally, under mild
conditions, their stable categories of Gorenstein projective modules and
Gorenstein defect categories are equivalent, respectively. Some homological
conjectures are also investigated for bounded extensions, including
Auslander-Reiten conjecture, finististic dimension conjecture, Fg condition,
Han's conjecture, and Keller's conjecture. Applications to trivial extensions
and triangular matrix algebras are given.
  In course of proof, we give some handy criteria for a functor between module
categories to induce triangle functors between stable categories of Gorenstein
projective modules and Gorenstein defect categories, which generalise some
known criteria, and hence might be of independent interest.


  Relativistic magnetized jets from active galaxies are among the most powerful
cosmic accelerators, but their particle acceleration mechanisms remain a
mystery. We present a new acceleration mechanism associated with the
development of the helical kink instability in relativistic jets, which leads
to the efficient conversion of the jet's magnetic energy into nonthermal
particles. Large-scale three-dimensional ab initio simulations reveal that the
formation of highly tangled magnetic fields and a large-scale inductive
electric field throughout the kink-unstable region promotes rapid energization
of the particles. The energy distribution of the accelerated particles develops
a well-defined power-law tail extending to the radiation-reaction limited
energy in the case of leptons, and to the confinement energy of the jet in the
case of ions. When applied to the conditions of well-studied bright knots in
jets from active galaxies, this mechanism can account for the spectrum of
synchrotron and inverse Compton radiating particles, and offers a viable means
of accelerating ultra-high-energy cosmic rays to $10^{20}$ eV.


  Correlated equilibria are sometimes more efficient than the Nash equilibria
of a game without signals. We investigate whether the availability of quantum
signals in the context of a classical strategic game may allow the players to
achieve even better efficiency than in any correlated equilibrium with
classical signals, and find the answer to be positive.


  Background
  Clinical studies using real-world data may benefit from exploiting clinical
reports, a particularly rich albeit unstructured medium. To that end, natural
language processing can extract relevant information. Methods based on transfer
learning using pre-trained language models have achieved state-of-the-art
results in most NLP applications; however, publicly available models lack
exposure to speciality-languages, especially in the medical field.
  Objective
  We aimed to evaluate the impact of adapting a language model to French
clinical reports on downstream medical NLP tasks.
  Methods
  We leveraged a corpus of 21M clinical reports collected from August 2017 to
July 2021 at the Greater Paris University Hospitals (APHP) to produce two
CamemBERT architectures on speciality language: one retrained from scratch and
the other using CamemBERT as its initialisation. We used two French annotated
medical datasets to compare our language models to the original CamemBERT
network, evaluating the statistical significance of improvement with the
Wilcoxon test.
  Results
  Our models pretrained on clinical reports increased the average F1-score on
APMed (an APHP-specific task) by 3 percentage points to 91%, a statistically
significant improvement. They also achieved performance comparable to the
original CamemBERT on QUAERO. These results hold true for the fine-tuned and
from-scratch versions alike, starting from very few pre-training samples.
  Conclusions
  We confirm previous literature showing that adapting generalist pre-train
language models such as CamenBERT on speciality corpora improves their
performance for downstream clinical NLP tasks. Our results suggest that
retraining from scratch does not induce a statistically significant performance
gain compared to fine-tuning.


  We have performed a numerical solution for band structure of an Abrikosov
vortex lattice in type-II superconductors forming a periodic array in two
dimensions for applications of incorporating the photonic crystals concept into
superconducting materials with possibilities for optical electronics. The
implemented numerical method is based on the extensive numerical solution of
the Ginzburg-Landau equation for calculating the parameters of the two-fluid
model and obtaining the band structure from the permittivity, which depends on
the above parameters and the frequency. This is while the characteristics of
such crystals highly vary with an externally applied static normal magnetic
field, leading to nonlinear behavior of the band structure, which also has
nonlinear dependence on the temperature. The similar analysis for every
arbitrary lattice structure is also possible to be developed by this approach
as presented in this work. We also present some examples and discuss the
results.


  A complete parton level analysis of lv + four jets production at the LHC is
presented, including all processes at order O(alpha^6), O(alpha^4*alpha_s^2)
and O(alpha^2*alpha_s^4). The infinite Higgs mass scenario, which is considered
as a benchmark for strong scattering theories and is the limiting case for
composite Higgs models, is confronted with the Standard Model light Higgs
predictions in order to determine whether a composite Higgs signal can be
detected as an excess of events in boson--boson scattering.


  Traversable wormholes have traditionally been viewed as intrinsically
topological entities in some multiply connected spacetime. Here, we show that
topology is too limited a tool to accurately characterize a generic traversable
wormhole: in general one needs geometric information to detect the presence of
a wormhole, or more precisely to locate the wormhole throat. For an arbitrary
static spacetime we shall define the wormhole throat in terms of a
2-dimensional constant-time hypersurface of minimal area. (Zero trace for the
extrinsic curvature plus a "flare-out" condition.) This enables us to severely
constrain the geometry of spacetime at the wormhole throat and to derive
generalized theorems regarding violations of the energy conditions-theorems
that do not involve geodesic averaging but nevertheless apply to situations
much more general than the spherically symmetric Morris-Thorne traversable
wormhole. [For example: the null energy condition (NEC), when suitably weighted
and integrated over the wormhole throat, must be violated.] The major technical
limitation of the current approach is that we work in a static spacetime-this
is already a quite rich and complicated system.


  Solutions to the hierarchy problem usually require top partners. In standard
SUSY or composite Higgs theories, the partners carry SM color and are becoming
increasingly constrained by LHC searches. However, theories like Folded SUSY
(FS), Twin Higgs (TH) and Quirky Little Higgs (QLH) introduce uncolored top
partners, which can be SM singlets or carry electroweak charge. Their small
production cross section left doubt as to whether the LHC can effectively probe
such scenarios. Typically, these partners are charged under their own mirror
color gauge group. In FS and QLH, the absence of light mirror matter allows
glueballs to form at the bottom of the mirror spectrum. This is also the case
in some TH realizations. The Higgs can decay to these mirror glueballs, with
the glueballs decaying into SM particles with potentially observable lifetimes.
We undertake the first detailed study of this glueball signature and
quantitatively demonstrate the discovery potential of uncolored naturalness via
exotic Higgs decays at the LHC and a potential future 100 TeV collider. Our
findings indicate that mirror glueballs are the smoking gun signature of
natural FS and QLH type theories, in analogy to tree-level Higgs coupling
shifts for the TH. We show that glueball masses in the $\sim$ 10-60 GeV mass
range are theoretically preferred. Careful treatment of lifetime,
mirror-hadronization and nonperturbative uncertainties is required to perform
meaningful collider studies. We outline several new search strategies for
exotic Higgs decays of the form $h\to XX \to 4f$ at the LHC, with $X$ having
lifetimes in the $10 \mu m$ to $km$ range. We find that FS stops can be probed
with masses up to 600 (1100) GeV at the LHC with 300 (3000) /fb of data, and TH
top partners could be accessible with masses up to 900 (1500) GeV. This makes
exotic Higgs decays the prime discovery channel for uncolored naturalness at
the LHC.


  To solve a machine learning problem, one typically needs to perform data
preprocessing, modeling, and hyperparameter tuning, which is known as model
selection and hyperparameter optimization.The goal of automated machine
learning (AutoML) is to design methods that can automatically perform model
selection and hyperparameter optimization without human interventions for a
given dataset. In this paper, we propose a meta-learning method that can search
for a high-performance machine learning pipeline from the predefined set of
candidate pipelines for supervised classification datasets in an efficient way
by leveraging meta-data collected from previous experiments. More specifically,
our method combines an adaptive Bayesian regression model with a neural network
basis function and the acquisition function from Bayesian optimization. The
adaptive Bayesian regression model is able to capture knowledge from previous
meta-data and thus make predictions of the performances of machine learning
pipelines on a new dataset. The acquisition function is then used to guide the
search of possible pipelines based on the predictions.The experiments
demonstrate that our approach can quickly identify high-performance pipelines
for a range of test datasets and outperforms the baseline methods.


  We present the results from studying 140 radio sources in the GLEAM (GaLactic
and Extragalactic All-sky MWA [Murchison Widefield Array]) 4-Jy (G4Jy) Sample.
These sources were followed-up with MeerKAT to assess their radio morphology
and enable host-galaxy identification, as existing radio images of 25 to
45-arcsec resolution do not provide sufficient information. We refer to these
sources as the MeerKAT-2019 subset. The aim is to identify the host galaxy of
these sources by visually inspecting the overlays comprising radio data from
four surveys (at 150, 200, 843/1400, and 1300 MHz). Our morphological
classification and host-galaxy identification relies upon the ~7-arcsec
resolution images from MeerKAT (1300 MHz). Through the visual inspection of the
overlays, 14 radio sources in the MeerKAT-2019 subset have wide-angle tail
(WAT) morphology, 10 are head-tail, and 5 have X-, S-/Z-shaped morphology. Most
of the remaining sources have the radio morphology of typical symmetric lobes.
Of 140 sources, we find host galaxies for 98 sources, leaving 42 with no
identified host galaxy. These 42 sources still have ambiguous identification
even with higher resolution images from MeerKAT.


  The state-of-the-art physics consists of two irreconcilable branches, i.e.,
the quantum theory and the general relativity, which work well in their own
territories, independently. However, what are quantum and spacetime after all?
The key question was never addressed, satisfactorily. In this work, we describe
a possibility to reformulate the quantum theory in the Minkowski spacetime from
the viewpoint of classic physics in the Euclidean spacetime, i.e., classic
mechanics and stochastic process theory. We show that quantum theory and
Minkowski spacetime may connect with each other and emerge from a single
fundamental entity.


  We outline an approach to calculate the transverse-momentum-dependent
distribution of linearly polarized gluons inside an unpolarized hadron on the
lattice with the help of large momentum effective theory. To achieve this
purpose, we propose calculating a Euclidean version of the degree of
polarization for a fast-moving hadron on the lattice, which is ultraviolet
finite, and no soft function subtraction is needed. It indicates a practical
way to explore the distribution of the linearly polarized gluons in a proton
and the linearly polarized gluon effects in hadron collisions on the lattice.


  We show a transfer principle for the property that all types realised in a
given elementary extension are definable. It can be written as follows: a
Henselian valued fields is stably embedded in an elementary extension if and
only if its value group is stably embedded in its corresponding extension, its
residue field is stably embedded in its corresponding extension, and the
extension of valued fields satisfies a certain algebraic condition. We show for
instance that all types over the Hahn field $\mathbb{R}((\mathbb{Z}))$ are
definable. Similarly, all types over the quotient field of the Witt ring
$W(\mathbb{F}_p^{\text{alg}})$ are definable. This extends a work of Cubides
and Delon and of Cubides and Ye.


  Circular domains frequently appear in the fields of ecology, biology and
chemistry. In this paper, we investigate the equivariant Hopf bifurcation of
partial functional differential equations with Neumann boundary condition on a
two-dimensional disk. The properties of these bifurcations around equilibriums
are analyzed rigorously by studying the equivariant normal forms. Two
reaction-diffusion systems with discrete time delays are selected as numerical
examples to verify the theoretical results, in which spatially inhomogeneous
periodic solutions including standing waves and rotating waves, and spatially
homogeneous periodic solutions are found near the bifurcation points.


  In this contribution, we aim at presenting a gas-to-power benchmark problem
that can be used for the simulation of electricity and gas networks in a
time-dependent environment. Based on realistic data from the IEEE database and
the GasLib suite, we describe the full set up of the underlying equations and
motivate the choice of parameters. The simulation results demonstrate the
applicability of the proposed approach and also allow for a clear visualization
of gas-power conversion.


  Schwinger-Dyson equations are used to study spontaneous chiral and parity
symmetry breaking of three dimensional quantum electrodynamics with
two-component fermions. This theory admits a topological photon mass that
explicitly breaks parity symmetry and generates a fermion mass. We show that
the pattern of symmetry breaking maintains parity but breaks chiral symmetry.
We also find that chiral symmetry is restored at a critical number of fermion
flavours in our truncation scheme. The Coleman-Hill theorem is used to
demonstrate that the results are reasonably accurate.


  The rational map ansatz for light nuclei in the Skyrme model is shown to
imply the existence of an \eta-^4He bound state, with a binding energy of ~ 30
KeV.


  Choice models for populations of agents on graphs are studied in terms of
statistical thermodynamics. Equations of state are derived and discussed for
different connectivity schemes, utility approximations, and temperature and
volume regimes. Analogies to ideal classical and quantum gases are found and
features specific for network systems are discussed.


  I report about the unification of relativistic jets from compact objects. The
mass range is between 1.4 and 10 billion solar masses (i.e. from neutron stars
to supermassive black holes in galaxies).


  Bundling a large number of distributed energy resources through a load
aggregator has been advocated as an effective means to integrate such resources
into whole-sale energy markets. To ease market clearing, system operators allow
aggregators to submit bidding models of simple prespecified polytopic shapes.
Aggregators need to carefully design and commit to a polytope that best
captures their energy flexibility along a day-ahead scheduling horizon. This
work puts forth a model-informed data-based optimal flexibility design for
aggregators, which deals with the time-coupled, uncertain, and non-convex
models of individual loads. The proposed solution first generates efficiently a
labeled dataset of (non)-disaggregatable schedules. The feasible set of the
aggregator is then approximated by an ellipsoid upon training a convex
quadratic classifier using the labeled dataset. The ellipsoid is subsequently
inner approximated by a polytope. Using Farkas lemma, the obtained polytope is
finally inner approximated by the polytopic shape dictated by the market.
Numerical tests show the effectiveness of the proposed flexibility design
framework for designing the feasible sets of small- and large-sized aggregators
coordinating solar photovoltaics, thermostatically-controlled loads, batteries,
and electric vehicles. The tests further demonstrate that it is crucial for the
aggregator to consider time-coupling and uncertainties in optimal flexibility
design.


  Future mobile networks supporting Internet of Things are expected to provide
both high throughput and low latency to user-specific services. One way to
overcome this challenge is to adopt Network Function Virtualization (NFV) and
Multi-access Edge Computing (MEC). Besides latency constraints, these services
may have strict function chaining requirements. The distribution of network
functions over different hosts and more flexible routing caused by service
function chaining raise new challenges for end-to-end performance analysis. In
this paper, as a first step, we analyze an end-to-end communications system
that consists of both MEC servers and a server at the core network hosting
different types of virtual network functions. We develop a queueing model for
the performance analysis of the system consisting of both processing and
transmission flows. We propose a method in order to derive analytical
expressions of the performance metrics of interest. Then, we show how to apply
the similar method to an extended larger system and derive a stochastic model
for such systems. We observe that the simulation and analytical results
coincide. By evaluating the system under different scenarios, we provide
insights for the decision making on traffic flow control and its impact on
critical performance metrics.


  The two-dimensional motion of a charged particle in a random potential and a
transverse magnetic field is believed to be delocalized only at discrete
energies $E_N$. In strong fields there is a small positive deviation of $E_N$
from the center of the $N$th Landau level, which is referred to as the ``weak
levitation'' of the extended state. I calculate the size of the weak levitation
effect for the case of a smooth random potential re-deriving earlier results of
Haldane and Yang [PRL 78, 298 (1997)] and extending their approach to lower
magnetic fields. I find that as the magnetic field decreases, this effect
remains weak down to the lowest field $B_{min}$ where such a quasiclassical
approach is still justified. Moreover, in the immediate vicinity of $B_{min}$
the weak levitation becomes additionally suppressed. This indicates that the
``strong levitation'' expected at yet even lower magnetic fields must be of a
completely different origin.


  Electronic health records (EHR's) are only a first step in capturing and
utilizing health-related data - the problem is turning that data into useful
information. Models produced via data mining and predictive analysis profile
inherited risks and environmental/behavioral factors associated with patient
disorders, which can be utilized to generate predictions about treatment
outcomes. This can form the backbone of clinical decision support systems
driven by live data based on the actual population. The advantage of such an
approach based on the actual population is that it is "adaptive". Here, we
evaluate the predictive capacity of a clinical EHR of a large mental healthcare
provider (~75,000 distinct clients a year) to provide decision support
information in a real-world clinical setting. Initial research has achieved a
70% success rate in predicting treatment outcomes using these methods.


  The density of states is calculated for a SU(2) and a compact U(1) lattice
gauge theory using a modified version of the Wang-Landau algorithm. We find
that the density of states of the SU(2) gauge theory can be reliably calculated
over a range of 120,000 orders of magnitude for lattice sizes as big as 20^4.
We demonstrate the potential of the algorithm by reproducing the SU(2) average
action, its specific heat and the critical couplings of the weak first order
transition in U(1).


  The black hole X-ray transient, XTE J1118+480, has now twice been observed in
outburst - 2000 and 2005 - and on both occasions remained in the low/hard X-ray
spectral state. Here we present radio, infrared, optical, soft X-ray and hard
X-ray observations of the more recent outburst. We find that the lightcurves
have very different morphologies compared with the 2000 event and the optical
decay is delayed relative to the X-ray/radio. We attribute this lesser degree
of correlation to contributions of emission from multiple components, in
particular the jet and accretion disc. Whereas the jet seemed to dominate the
broadband spectrum in 2000, in 2005 the accretion disc seems to be more
prominent and we use an analysis of the lightcurves and spectra to distinguish
between the jet and disc emission. There also appears to be an optically thin
component to the radio emission in the 2005 data, possibly associated with
multiple ejection events and decaying as the outburst proceeds. These results
add to the discussion that the term "low/hard state'" covers a wider range of
properties than previously thought, if it is to account for XTE J1118+480
during these two outbursts.


  We review the notion of a linearity-generating (LG) process introduced by
Gabaix (2007) and relate LG processes to linear-rational (LR) models studied by
Filipovic, Larsson, and Trolle (2017). We show that every LR model can be
represented as an LG process and vice versa. We find that LR models have two
basic properties which make them an important representation of LG processes.
First, LR models can be easily specified and made consistent with nonnegative
interest rates. Second, LR models go naturally with the long-term risk
factorization due to Alvarez and Jermann (2005), Hansen and Scheinkman (2009),
and Qin and Linetsky (2017). Every LG process under the long forward measure
can be represented as a lower dimensional LR model.


  This paper study the evolution of the universe filled with a neutral mass
dimension one fermionic field, sometimes called Elko. The numerical analysis of
the coupled system of equations furnish a scale factor growth and energy
density evolution that correctly reproduces the inflationary phase of the
universe. After that, supposing a mechanism of energy transference to ordinary
matter, the initial conditions generated after inflation drives the radiation
dominated phase and also the subsequent dark matter evolution, since the Elko
field is a good dark matter candidate. The energy density of the field at the
end of inflation, at the end of radiation phase and for present time are in
agreement to the standard model estimates. The analysis was performed with a
potential containing a quadratic mass term plus a quartic self-interaction
term, which follows naturally from the theory of mass dimension one fermions.
It is interesting to notice that inflation occurs when the field makes a kind
of transition around the Planck mass scale. The number of e-foldings during
inflation was found to be strongly dependent on the initial conditions of the
Elko field, as occurs in chaotic inflationary models. An upper mass limit for
Elko field has been obtained as $m<10^9$GeV. A possible interpretation of both
inflationary phase and recent cosmic acceleration as a consequence of a kind of
Pauli exclusion principle is presented at the end.


  The maximal amount of information which is reliably transmitted over two uses
of general Pauli channels with memory is proven to be achieved by maximally
entangled states beyond some memory threshold. In particular, this proves a
conjecture on the depolarizing channel by Macchiavello and Palma [Phys. Rev. A
{\bf 65}, 050301(R) (2002)]. Below the memory threshold, for arbitrary Pauli
channels, the two-use classical capacity is only achieved by a particular type
of product states.


  This paper proves that a particle with mass different of zero cannot be its
own antiparticle. Hence, particles such as pi-zero,eta-zero, and Z-zero must
have their correspondent antiparticles.


  We study electron transport properties of a monoatomic graphite layer
(graphene) with different types of disorder at half filling. We show that the
transport properties of the system depend strongly on the symmetry of disorder.
We find that the localization is ineffective if the randomness preserves one of
the chiral symmetries of the clean Hamiltonian or does not mix valleys. We
obtain the exact value of minimal conductivity $4e^2/\pi h$ in the case of
chiral disorder. For long-range disorder (decoupled valleys), we derive the
effective field theory. In the case of smooth random potential, it is a
symplectic-class sigma model including a topological term with $\theta = \pi$.
As a consequence, the system is at a quantum critical point with a universal
value of the conductivity of the order of $e^2/h$. When the effective time
reversal symmetry is broken, the symmetry class becomes unitary, and the
conductivity acquires the value characteristic for the quantum Hall transition.


  Although local Hamiltonians exhibit local time dynamics, this locality is not
explicit in the Schr\"{o}dinger picture in the sense that the wavefunction
amplitudes do not obey a local equation of motion. We show that geometric
locality can be achieved explicitly in the equations of motion by "gauging" the
global unitary invariance of quantum mechanics into a local gauge invariance.
That is, expectation values $\langle \psi|A|\psi \rangle$ are invariant under a
global unitary transformation acting on the wavefunction $|\psi\rangle \to U
|\psi\rangle$ and operators $A \to U A U^\dagger$, and we show that it is
possible to gauge this global invariance into a local gauge invariance. To do
this, we replace the wavefunction with a collection of local wavefunctions
$|\psi_J\rangle$, one for each patch of space $J$. The collection of spatial
patches is chosen to cover the space; e.g. we could choose the patches to be
single qubits or nearest-neighbor sites on a lattice. Local wavefunctions
associated with neighboring pairs of spatial patches $I$ and $J$ are related to
each other by dynamical unitary transformations $U_{IJ}$. The local
wavefunctions are local in the sense that their dynamics are local. That is,
the equations of motion for the local wavefunctions $|\psi_J\rangle$ and
connections $U_{IJ}$ are explicitly local in space and only depend on nearby
Hamiltonian terms. (The local wavefunctions are many-body wavefunctions and
have the same Hilbert space dimension as the usual wavefunction.) We call this
picture of quantum dynamics the gauge picture since it exhibits a local gauge
invariance. The local dynamics of a single spatial patch is related to the
interaction picture, where the interaction Hamiltonian consists of only nearby
Hamiltonian terms. We can also generalize the explicit locality to include
locality in local charge and energy densities.


  In this paper we discuss classical elliptic current algebras and show that
there are two different choices of commutative test function algebras on a
complex torus leading to two different elliptic current algebras. Quantization
of these classical current algebras give rise to two classes of quantized
dynamical quasi-Hopf current algebras studied by Enriquez-Felder-Rubtsov and
Arnaudon-Buffenoir-Ragoucy-Roche-Jimbo-Konno-Odake-Shiraishi. Different
degenerations of the classical elliptic algebras are considered. They yield
different versions of rational and trigonometric current algebras. We also
review the averaging method of Faddeev-Reshetikhin, which allows to restore
elliptic algebras from the trigonometric ones.


  Outlier detection (OD) is a key machine learning (ML) task for identifying
abnormal objects from general samples with numerous high-stake applications
including fraud detection and intrusion detection. Due to the lack of ground
truth labels, practitioners often have to build a large number of unsupervised,
heterogeneous models (i.e., different algorithms with varying hyperparameters)
for further combination and analysis, rather than relying on a single model.
How to accelerate the training and scoring on new-coming samples by
outlyingness (referred as prediction throughout the paper) with a large number
of unsupervised, heterogeneous OD models? In this study, we propose a modular
acceleration system, called SUOD, to address it. The proposed system focuses on
three complementary acceleration aspects (data reduction for high-dimensional
data, approximation for costly models, and taskload imbalance optimization for
distributed environment), while maintaining performance accuracy. Extensive
experiments on more than 20 benchmark datasets demonstrate SUOD's effectiveness
in heterogeneous OD acceleration, along with a real-world deployment case on
fraudulent claim analysis at IQVIA, a leading healthcare firm. We open-source
SUOD for reproducibility and accessibility.


  In this paper we study the fermion quasi-normal modes of a 4-dimensional
rotating black-hole using the WKB(J) (to third and sixth order) and the AIM
semi-analytic methods in the massless Dirac fermion sector. These semi-analytic
approximations are computed in a pedagogical manner with comparisons made to
the numerical values of the quasi-normal mode frequencies presented in the
literature. It was found that The WKB(J) method and AIM show good agreement
with direct numerical solutions for low values of the overtone number $n$ and
angular quantum number l.


  In this paper, we develop a new method to classify abelian automorphism
groups of hypersurfaces. We use this method to classify (Theorem 4.2) abelian
groups that admit a liftable action on a smooth cubic fourfold. A parallel
result (Theorem 5.1) is obtained for quartic surfaces.


  This paper has been withdrawn due to the use of some incorrect neutrino
parameter space ranges.


  The contributions to the electron-electron-photon vertex of two-loop
electroweak corrections are calculated. The relative correction to the
parity-violating asymmetry of M{\o}ller scattering for the case of 11 GeV
electron scattered off the electron at rest is found to be about -0.0034 and
should be taken into account at future experiment MOLLER at JLab.


  We determine the quantum phase diagram of the antiferromagnetic spin-1/2 XXZ
model on the triangular lattice as a function of magnetic field and anisotropic
coupling $J_z$. Using the density matrix renormalization group (DMRG) algorithm
in two dimensions we establish the locations of the phase boundaries between a
plateau phase with 1/3 N\'eel order and two distinct coplanar phases. The two
coplanar phases are characterized by a simultaneous breaking of both
translational and U(1) symmetries, which is reminiscent of supersolidity. A
translationally invariant umbrella phase is entered via a first order phase
transition at relatively small values of $J_z$ compared to the corresponding
case of ferromagnetic hopping and the classical model. The phase transition
lines meet at two tricritical points on the tip of the lobe of the plateau
state, so that the two coplanar states are completely disconnected.
Interestingly, the phase transition between the plateau state and the upper
coplanar state changes from second order to first order for large values of
$J_z > 2.5J$.


  The problem of dynamical heating of galactic discs by spiral density waves is
discussed using the shearing sheet model. The secular evolution of the disc is
described quantitatively by a diffusion equation for the distribution function
of stars in the space spanned by integrals of motion of the stars, in
particular the radial action integral and an integral related to the angular
momentum. Specifically, disc heating by a succession of transient, `swing
amplified' density waves is studied. It is shown that such density waves lead
predominantly to diffusion of stars in radial action space. The stochastical
changes of angular momenta of the stars and the corresponding stochastic
changes of the guiding centre radii of the stellar orbits induced by this
process are much smaller.


  This paper surveys the current state of the art in document automation (DA).
The objective of DA is to reduce the manual effort during the generation of
documents by automatically creating and integrating input from different
sources and assembling documents conforming to defined templates. There have
been reviews of commercial solutions of DA, particularly in the legal domain,
but to date there has been no comprehensive review of the academic research on
DA architectures and technologies. The current survey of DA reviews the
academic literature and provides a clearer definition and characterization of
DA and its features, identifies state-of-the-art DA architectures and
technologies in academic research, and provides ideas that can lead to new
research opportunities within the DA field in light of recent advances in
generative AI and large language models.


  We explore the impact of nonstandard interactions on neutrino propagation in
accretion disks around binary neutron star mergers remnants. We show flavor
evolution can be significantly modified even for values of the nonstandard
couplings well below current bounds. We demonstrate the occurrence of I
resonances as synchronized MSW phenomena and show that intricate conversion
patterns might appear depending on the nonstandard interaction parameters. We
discuss the possible implications for nucleosynthesis.


  The study of the charge asymmetry of produced particles allows to investigate
the interference of different production mechanisms and to determine new
features of the corresponding amplitudes. In the process $e^- e^+ \to e^- e^+
\pi^+ \pi^-$ the two-pion system is produced via two mechanisms: two-photon
(C-even state) and bremsstrahlung (C-odd state) production. We study the charge
asymmetry of pions in a differential in the pion momenta cross section
originating from an interference between these two mechanisms. At low effective
mass of dipions this asymmetry is directly related to the s- and p-phases of
elastic $\pi\pi$ scattering. At higher energies it can give new information
about the $f_0$ meson family, $f_2(1270)$ meson, etc. The asymmetry is
expressed via the pion form factor $F_\pi$ and helicity amplitudes $M_{ab}$ for
the subprocess $\gamma^*\gamma\to \pi^+\pi^-$ as $\sum G_{ab}{\rm
Re}(F_\pi^*M_{ab})$ where we have calculated analytically the coefficients
$G_{ab}$ for the region giving the main contribution to the effect. Several
distributions of pions are presented performing a numerical analysis in a model
with point-like pions. In the region near the dipion threshold the asymmetry is
of the order of 1%. We show that with suitable cuts the signal to background
ratio can be increased up to about 10%.


  Discrete event simulation specification (DEVS) is a formalism designed to
describe both discrete state and continuous state systems. It is a powerful
abstract mathematical notation. However, until recently it lacked proper
graphical representation, which made computer simulation of DEVS models a
challenging issue. Unified modeling language (UML) is a multipurpose graphical
modeling language, a de-facto industrial modeling standard. There exist several
commercial and open-source UML editors and code generators. Most of them can
save UML models in XML-based XMI files ready for further automated processing.
In this paper, we propose a mapping of DEVS models onto UML state and component
diagrams. This mapping may lead to an eventual unification of the two modeling
formalisms, combining the abstractness of DEVS and expressive power and
``computer friendliness'' of the UML.


  Protoplanetary disks are mainly heated by radiation from the central star.
Since the incident stellar flux at any radius is sensitive to the disk
structure near that location, an unstable feedback may be present. Previous
investigations show that the disk would be stable to finite-amplitude
temperature perturbations if the vertical height of optical surface is
everywhere directly proportional to the gas scale height and if the intercepted
fraction of stellar radiation is determined from the local grazing angle. We
show that these assumptions may not be generally applicable. Instead, we
calculate the quasi-static thermal evolution of irradiated disks by directly
integrating the global optical depths to determine the optical surface and the
total emitting area-filling factor of surface dust. We show that, in disks with
modest mass accretion rates, thermal waves are spontaneously and continually
excited in the outer disk, propagate inward through the planet-forming domains,
and dissipated at small radii where viscous dissipation is dominant. This state
is quasi-periodic over several thermal timescales and its pattern does not
depend on the details of the opacity law. The viscous dissipation resulting
from higher mass accretion stabilizes this instability such that an
approximately steady state is realized throughout the disk. In passive
protostellar disks, especially transitional disks, these waves induce
significant episodic changes in SEDs, on the time scales of years to decades,
because the midplane temperatures can vary by a factor of two between the
exposed and shadowed regions. The transitory peaks and troughs in the potential
vorticity distribution may also lead to baroclinic instability and excite
turbulence in theplanet-forming regions.


  We show that both, the Jordan curve theorem and the Schoenflies theorem
extend to non-metric manifolds (at least in the two-dimensional context), and
conclude by some dynamical applications \`a la Poincar\'e-Bendixson.


  This article addresses the propagation of constitutive uncertainties between
scales occurring in the multiscale modelling of fibre-reinforced composites.
The amplification of such uncertainties through upward or downward transitions
by a homogenisation model is emphasized and exemplified with the Mori-Tanaka
model. In particular, the sensitivity to data uncertainty in the inverse
determination of constituent parameters based on downward transitions is
stressed on an example. Then a database improvement method, which exploits
simultaneously the available information on constitutive uncertainties at all
scales instead of just propagating those associated with one scale, is
presented and shown to yield substantial reductions in uncertainty for both the
constitutive parameters and the response of structures. The latter finding is
demonstrated on two examples of structures, with significant gains in
confidence obtained on both.


  In this paper, we propose a novel quantum multiple access technique based on
optical coherent states. The information of several coherent state optical
qubits is combined into a single qudit, which is the superposition of almost
orthogonal coherent states. The original information is encoded into a new
Hilbert space with the help of a quantum multiplexer (QMUX) and then recovered
at the other end with a quantum demultiplexer (QDEMUX). We introduce the
optical tools that complete the coherence state quantum computation model and
give the desired circuits. The proposed system can admit a number of users
above the optimal limit at the cost of a degradation of the transmitted data.
In this and some other aspects, it can be regarded as a quantum analogue of
classical Code Division Multiple Access techniques.


  In 2008, Rogalski and Zhang showed that if R is a strongly noetherian
connected graded algebra over an algebraically closed field, then R has a
canonical birationally commutative factor. This factor is, up to finite
dimension, a twisted homogeneous coordinate ring B(X, L, s); here X is the
projective parameter scheme for point modules over R, as well as tails of
points in qgr-R. (As usual, s is an automorphism of X, and L is an s-ample
invertible sheaf on X.)
  We extend this result to a large class of noetherian (but not strongly
noetherian) algebras. Specifically, let R be a noetherian connected graded
k-algebra, where k is an uncountable algebraically closed field. Let Y denote
the parameter space (or stack or proscheme) parameterizing R-point modules, and
suppose there is a projective variety X that is a coarse moduli space for tails
of points. There is a canonical map p: Y -> X. If the indeterminacy locus of
p^{-1} is 0-dimensional and X satisfies a mild technical assumption, we show
that there is a homomorphism g: R -> B(X, L, s), and that g(R) is, up to finite
dimension, a naive blowup on X in the sense of Keeler, Rogalski, and Stafford,
and satisfies a universal property. We further show that the point space Y is
noetherian.


  Stimulated Brillouin scattering provides optical gain for efficient and
narrow-linewidth lasers in high-Q microresonator systems. However, the thermal
dependence of the Brillouin process, as well as the microresonator, impose
strict temperature control requirements for long-term frequency-stable
operation. Here, we study Brillouin back action and use it to both measure and
phase-sensitively lock modal temperature to a reference temperature defined by
the Brillouin phase-matching condition. At a specific lasing wavelength, the
reference temperature can be precisely set by adjusting resonator free spectral
range. This backaction control method is demonstrated in a chip-based Brillouin
laser, but can be applied in all Brillouin laser platforms. It offers a new
approach for frequency-stable operation of Brillouin lasers in atomic clock,
frequency metrology, and gyroscope applications.


  We demonstrate the ability to reduce the carrier concentration of thin films
of the topological insulator (TI) Bi2Se3 by utilizing a novel approach, namely
non-volatile electrostatic gating via corona charging of electret polymers.
Sufficient electric field can be imparted to a polymer-TI bilayer to result in
significant electron density depletion, even without the continuous connection
of a gate electrode or the chemical modification of the TI. We show that the
Fermi level of Bi2Se3 is shifted towards the Dirac point with this method.
Using THz spectroscopy, we find that the surface chemical potential is lowered
into the bulk band gap (~ 50 meV above the Dirac point and 170 meV below the
conduction band minimum) and it is stabilized in the intrinsic regime while
enhancing electron mobility. This represents the first use of a charged polymer
gate for modulating TI charge density. The mobility of surface state electrons
is enhanced to a value as high as ~1600 cm^2/Vs at 5K.


  Even if Weyl semimetals are characterized by quasiparticles with well-defined
chirality, exploiting this experimentally is severely hampered by Weyl
lattice-fermions coming in pairs with opposite chirality, typically causing the
net chirality picked up by experimental probes to vanish. Here we show this
issue can be circumvented in a controlled manner when both time-reversal- and
inversion- symmetry are broken. To this end, we investigate
chirality-disbalance in the carbide family RMC$_2$ (R a rare-earth and M a
transition metal), showing several members to be Weyl semimetals. Using the
noncentrosymmetric ferromagnet NdRhC$_2$ as an illustrating example, we show
that an odd number of Weyl nodes can be stabilized at its Fermi surface by
properly tilting its magnetization. The tilt direction determines the sign of
the resulting net chirality, opening up a simple route to control it.


  In quantum mechanics, systems can be described in phase space in terms of the
Wigner function and the star-product operation. Quantum characteristics, which
appear in the Heisenberg picture as the Weyl's symbols of operators of
canonical coordinates and momenta, can be used to solve the evolution equations
for symbols of other operators acting in the Hilbert space. To any fixed order
in the Planck's constant, many-body potential scattering problem simplifies to
a statistical-mechanical problem of computing an ensemble of quantum
characteristics and their derivatives with respect to the initial canonical
coordinates and momenta. The reduction to a system of ordinary differential
equations pertains rigorously at any fixed order in $\hbar$. We present
semiclassical expansion of quantum characteristics for many-body scattering
problem and provide tools for calculation of average values of time-dependent
physical observables and cross sections. The method of quantum characteristics
admits the consistent incorporation of specific quantum effects, such as
non-locality and coherence in propagation of particles, into the semiclassical
transport models. We formulate the principle of stationary action for quantum
Hamilton's equations and give quantum-mechanical extensions of the Liouville
theorem on the conservation of phase-space volume and the Poincar\'e theorem on
the conservation of $2p$ forms. The lowest order quantum corrections to the
Kepler periodic orbits are constructed. These corrections show the resonance
behavior.


  In this paper, the well-known forwarder's dilemma is generalized by
accounting for the presence of link quality fluctuations; the forwarder's
dilemma is a four-node interaction model with two source nodes and two
destination nodes. It is known to be very useful to study ad hoc networks. To
characterize the long-term utility region when the source nodes have to control
their power with partial channel state information (CSI), we resort to a recent
result in Shannon theory. It is shown how to exploit this theoretical result to
find the long-term utility region and determine good power control policies.
This region is of prime importance since it provides the best performance
possible for a given knowledge at the nodes. Numerical results provide several
new insights into the repeated forwarder's dilemma power control problem; for
instance, the knowledge of global CSI only brings a marginal performance
improvement with respect to the local CSI case.


  Painleve equations belong to the class y'' + a_1 {y'}^3 + 3 a_2 {y'}^2 + 3
a_3 y' + a_4 = 0, where a_i=a_i(x,y). This class of equations is invariant
under the general point transformation x=Phi(X,Y), y=Psi(X,Y) and it is
therefore very difficult to find out whether two equations in this class are
related. We describe R. Liouville's theory of invariants that can be used to
construct invariant characteristic expressions (syzygies), and in particular
present such a characterization for Painleve equations I-IV.


  Recently, transformers have shown promising performance in learning graph
representations. However, there are still some challenges when applying
transformers to real-world scenarios due to the fact that deep transformers are
hard to train from scratch and the quadratic memory consumption w.r.t. the
number of nodes. In this paper, we propose Graph Masked Autoencoders (GMAEs), a
self-supervised transformer-based model for learning graph representations. To
address the above two challenges, we adopt the masking mechanism and the
asymmetric encoder-decoder design. Specifically, GMAE takes partially masked
graphs as input, and reconstructs the features of the masked nodes. The encoder
and decoder are asymmetric, where the encoder is a deep transformer and the
decoder is a shallow transformer. The masking mechanism and the asymmetric
design make GMAE a memory-efficient model compared with conventional
transformers. We show that, when serving as a conventional self-supervised
graph representation model, GMAE achieves state-of-the-art performance on both
the graph classification task and the node classification task under common
downstream evaluation protocols. We also show that, compared with training in
an end-to-end manner from scratch, we can achieve comparable performance after
pre-training and fine-tuning using GMAE while simplifying the training process.


  (abridged) We report here a factor of 5.7 higher total CO flux in Arp~244
(the ``Antennae'' galaxies) than that previously accepted in the literature
(thus a total molecular gas mass of 1.5x10$^{10}$ Msun), based on our fully
sampled CO(1-0) observations at the NRAO 12m telescope. Our observations show
that the molecular gas peaks predominately in the disk-disk overlap region
between the nuclei, similar to the far-infrared (FIR) and mid-infrared (MIR)
emission. The bulk of the molecular gas is forming into stars with a normal
star formation efficiency (SFE) L_{IR}/M(H_2) \approx 4.2 Lsun/Msun, same as
that of giant molecular clouds in the Galactic disk. Additional supportive
evidence is the extremely low fraction of the dense molecular gas in Arp~244,
revealed by our detections of the HCN(1-0) emission.
  We estimate the local SFE indicated by the ratio map of the radio continuum
to CO(1-0) emission. Remarkably, the local SFE stays roughly same over the bulk
of the molecular gas distribution. Only some localized regions show the highest
radio-to-CO ratios that we have identified as the sites of the most intense
starbursts with SFE >~ 20 Lsun/Msun. These starburst regions are confined
exclusively in the dusty patches seen in the HST images near the CO and FIR
peaks where presumably the violent starbursts are heavily obscured.
Nevertheless, recent large-scale star formation is going on throughout the
system, yet the measured level is more suggestive of a moderate starburst (SFE
>~ 10 Lsun/Msun) or a weak to normal star formation (SFE ~ 4 Lsun/Msun). The
overall starburst from the bulk of the molecular gas is yet to be initiated as
most of the gas further condenses into kpc scale in the final coalescence.


  A Bose star passing through cold molecular clouds may capture atoms,
molecules and dust particles. The observational signature of such an event
would be a relatively small amount of matter that is gravitationally bound.
This binding may actually be provided by invisible dark matter forming the Bose
star. We may expect a relative excess of heavier atoms, molecules, and solid
dust compared to the content of giant cold molecular clouds since the velocity
of heavy particles at a given temperature is lower and it may be small compared
to the escape velocity, $v_\mathrm{rms} = \sqrt{3k_\mathrm{B} T/m_\mathrm{gas}}
\ll v_\mathrm{esc}=\sqrt{2GM/R}$. Finally, the velocity of this captured matter
cloud may correlate with the expected velocity of free dark matter particles
(e.g. expected axion wind velocity relative to Earth).


  We investigate the potential of the process $gg \to H \to WW$ to provide
bounds on the Higgs width. Recent studies using off-shell $H\rightarrow ZZ$
events have shown that Run 1 LHC data can constrain the Higgs width, $\Gamma_H
< (25-45) \Gamma_{H}^{\rm SM}$. Using 20 fb-1 of 8 TeV ATLAS data, we estimate
a bound on the Higgs boson width from the WW channel between $\Gamma_H <
(100-500) \Gamma_H^{SM}$. The large spread in limits is due to the range of
cuts applied in the existing experimental analysis. The stricter cuts designed
to search for the on-shell Higgs boson limit the potential number of off-shell
events, weakening the constraints. As some of the cuts are lifted the bounds
improve. We show that there is potential in the high transverse mass region to
produce upper bounds of the order of $(25-50) \Gamma_H^{SM}$, depending
strongly on the level of systematic uncertainty that can be obtained. Thus, if
these systematics can be controlled, a constraint on the Higgs boson width from
the $H \to WW$ decay mode can complement a corresponding limit from $H \to ZZ$.


  Automated segmentation can assist radiotherapy treatment planning by saving
manual contouring efforts and reducing intra-observer and inter-observer
variations. The recent development of deep learning approaches has revoluted
medical data processing, including semantic segmentation, by dramatically
improving performance. However, training effective deep learning models usually
require a large amount of high-quality labeled data, which are often costly to
collect. We developed a novel semi-supervised adversarial deep learning
approach for 3D pelvic CT image semantic segmentation. Unlike supervised deep
learning methods, the new approach can utilize both annotated and un-annotated
data for training. It generates un-annotated synthetic data by a data
augmentation scheme using generative adversarial networks (GANs). We applied
the new approach to segmenting multiple organs in male pelvic CT images, where
CT images without annotations and GAN-synthesized un-annotated images were used
in semi-supervised learning. Experimental results, evaluated by three metrics
(Dice similarity coefficient, average Hausdorff distance, and average surface
Hausdorff distance), showed that the new method achieved either comparable
performance with substantially fewer annotated images or better performance
with the same amount of annotated data, outperforming the existing
state-of-the-art methods.


  This is the third in a series of papers extending Martin-L\"of's meaning
explanations of dependent type theory to a Cartesian cubical realizability
framework that accounts for higher-dimensional types. We extend this framework
to include a cumulative hierarchy of univalent Kan universes of Kan types,
exact equality and other pretypes lacking Kan structure, and a cumulative
hierarchy of pretype universes. As in Parts I and II, the main result is a
canonicity theorem stating that closed terms of boolean type evaluate to either
true or false. This establishes the computational interpretation of Cartesian
cubical higher type theory based on cubical programs equipped with a
deterministic operational semantics.


  We propose a novel hybrid loss for multiclass and structured prediction
problems that is a convex combination of a log loss for Conditional Random
Fields (CRFs) and a multiclass hinge loss for Support Vector Machines (SVMs).
We provide a sufficient condition for when the hybrid loss is Fisher consistent
for classification. This condition depends on a measure of dominance between
labels--specifically, the gap between the probabilities of the best label and
the second best label. We also prove Fisher consistency is necessary for
parametric consistency when learning models such as CRFs. We demonstrate
empirically that the hybrid loss typically performs least as well as--and often
better than--both of its constituent losses on a variety of tasks, such as
human action recognition. In doing so we also provide an empirical comparison
of the efficacy of probabilistic and margin based approaches to multiclass and
structured prediction.


  Using methods introduced by Scargle in 1978 we derive a cumulative version of
the Lomb periodogram that exhibits frequency independent statistics when
applied to cumulative noise. We show how this cumulative Lomb periodogram
allows us to estimate the significance of log-periodic signatures in the S&P
500 anti-bubble that started in August 2000.


  The letter presents new field-theoretical approach to 2D passive scalar
problem. The Gaussian form of the distribution for the Lyapunov exponent is
derived and its parameters are found explicitly.


  Spin-dependent transport through a multilevel quantum dot weakly coupled to
ferromagnetic leads is analyzed theoretically by means of the real-time
diagrammatic technique. Both the sequential and cotunneling processes are taken
into account, which makes the results on tunnel magnetoresistance (TMR) and
shot noise applicable in the whole range of relevant bias and gate voltages.
Suppression of the TMR due to inelastic cotunneling and super-Poissonian shot
noise have been found in some of the Coulomb blockade regions. Furthermore, in
the Coulomb blockade regime there is an additional contribution to the noise
due to bunching of cotunneling processes involving the spin-majority electrons.
On the other hand, in the sequential tunneling regime TMR oscillates with the
bias voltage, while the current noise is generally sub-Poissonian.


  We present results of using individual galaxies' probability distribution
over redshift as a method of identifying potential catastrophic outliers in
empirical photometric redshift estimation. In the course of developing this
approach we develop a method of modification of the redshift distribution of
training sets to improve both the baseline accuracy of high redshift (z>1.5)
estimation as well as catastrophic outlier mitigation. We demonstrate these
using two real test data sets and one simulated test data set spanning a wide
redshift range (0<z<4). Results presented here inform an example `prescription'
that can be applied as a realistic photometric redshift estimation scenario for
a hypothetical large-scale survey. We find that with appropriate optimization,
we can identify a significant percentage (>30%) of catastrophic outlier
galaxies while simultaneously incorrectly flagging only a small percentage (<7%
and in many cases <3%) of non-outlier galaxies as catastrophic outliers. We
find also that our training set redshift distribution modification results in a
significant (>10) percentage point decrease of outlier galaxies for z>1.5 with
only a small (<3) percentage point increase of outlier galaxies for z<1.5
compared to the unmodified training set. In addition, we find that this
modification can in some cases cause a significant (~20) percentage point
decrease of galaxies which are non-outliers but which have been incorrectly
identified as outliers, while in other cases cause only a small (<1) percentage
increase in this metric.


  In this paper, we explore the geometry and the arithmetic of a family of
polytopal sphere packings induced by regular polytopes in any dimension. We
prove that every integral polytope is crystallographic, and we show that there
are 11 crystallographic regular polytopes in any dimension. After introducing
the notion of Apollonian section, we determine which Platonic crystallographic
packings emerge as cross-sections of the Apollonian arrangements of the regular
4-polytopes. Additionally, we compute the M\"obius spectrum of every regular
polytope.


  The Continuous Spontaneous Localization (CSL) model strives to describe the
quantum-to-classical transition from the viewpoint of collapse models. However,
its original formulation suffers from a fundamental inconsistency in that it is
explicitly energy non-conserving. Fortunately, a dissipative extension to CSL
has been recently formulated that solves such energy-divergence problem. We
compare the predictions of the dissipative and non-dissipative CSL models when
various optomechanical settings are used, and contrast such predictions with
available experimental data, thus building the corresponding exclusion plots.


  Using the 100-m radio telescope at Effelsberg, we mapped a large area around
the Andromeda Galaxy in the 21-cm line emission of neutral hydrogen to search
for high-velocity clouds (HVCs) out to large projected distances in excess of
100 kpc. Our 3-sigma HI mass sensitivity for the warm neutral medium is 8x10^4
solar masses. We can confirm the existence of a population of HVCs with typical
HI masses of a few times 10^5 solar masses near the disc of M31. However, we
did not detect any HVCs beyond a projected distance of about 50 kpc from M31,
suggesting that HVCs are generally found in proximity of large spiral galaxies
at typical distances of a few 10 kpc. Comparison with CDM-based models and
simulations suggests that only a few of the detected HVCs could be associated
with primordial dark-matter satellites, whereas others are most likely the
result of tidal stripping. The lack of clouds beyond a projected distance of 50
kpc from M31 is also in conflict with the predictions of recent CDM structure
formation simulations. A possible solution to this problem could be ionisation
of the HVCs as a result of decreasing pressure of the ambient coronal gas at
larger distances from M31. A consequence of this scenario would be the presence
of hundreds of mainly ionised or pure dark-matter satellites around large
spiral galaxies like the Milky Way and M31.


  We present explicit Pieri formulas for Macdonald's spherical functions (or
generalized Hall-Littlewood polynomials associated with root systems) and their
$q$-deformation the Macdonald polynomials. For the root systems of type $A$,
our Pieri formulas recover the well-known Pieri formulas for the
Hall-Littlewood and Macdonald symmetric functions due to Morris and Macdonald
as special cases.


  We present the first calculation of the complete set of NNLO QED corrections
for muon-electron scattering. This includes leptonic, non-perturbative
hadronic, and photonic contributions. All fermionic corrections as well as the
photonic subset that only corrects the electron or the muon line are included
with full mass dependence. The genuine four-point two-loop topologies are
computed as an expansion in the small electron mass, taking into account both,
logarithmically enhanced as well as constant mass effects using massification.
A fast and stable implementation of the numerically delicate real-virtual
contribution is achieved by combining OpenLoops with next-to-soft
stabilisation. All matrix elements are implemented in the McMule framework,
which allows for the fully-differential calculation of any infrared-safe
observable. This calculation is to be viewed in the context of the MUonE
experiment requiring a background prediction at the level of 10 ppm. Our
results thus represent a major milestone towards this ambitious precision goal.


  Exciton optical transitions in transition-metal dichalcogenides offer unique
opportunities to study rich many-body physics. Recent experiments in monolayer
WSe$_2$ and WS$_2$ have shown that while the low-temperature photoluminescence
from neutral excitons and three-body complexes is suppressed in the presence of
elevated electron densities or strong photoexcitation, new dominant peaks
emerge in the low-energy side of the spectrum. I present a theory that
elucidates the nature of these optical transitions showing the role of the
intervalley Coulomb interaction. After deriving a compact dynamical form for
the Coulomb potential, I calculate the self-energy of electrons due to their
interaction with this potential. For electrons in the upper valleys of the
spin-split conduction band, the self energy includes a moderate redshift due to
exchange, and most importantly, a correlation-induced virtual state in the
band-gap. The latter sheds light on the origin of the luminescence in monolayer
WSe$_2$ and WS$_2$ in the presence of pronounced many-body interactions.


  With a simple transformation of the three exponents the generalized Fermat
equation can be put into the same form as the Fermat equation. When it is
rewritten into this new altered form any real solutions to the altered equation
equal a subset of real solutions to the Fermat equation. This result, along
with a paradigm previously established by G. Frey and Y. Hellegouarch, can be
used to show that the generalized Fermat equation has no solutions in coprime
integers. In fact we prove one can derive an elliptic curve over $\mathbb{Q}$
for primes (p \geq 3), from the assumption that (x_{0}^{k} + y_{0}^{l} =
z_{0}^{m}), (k, l, m \geq 3), has coprime solutions in integers. The curve then
can be used to show the unsolvability of this equation. Our aim is not to
arrive at very deep results. Rather the goal in this paper is to apply prior
results obtained by G. Frey, K. Ribet and A. Wiles, to show the lack of
solutions to the generalized Fermat equation.


  We extract the K+K- couplings of the isoscalar scalar mesons sigma/f_0(600)
and f_0(980) from pi pi to pi pi / K K scatterings and found: |g_{sigma K+K-}|/
|g_{sigma pi+pi-}|= 0.8 and |g_{f_0 K+K-}|/ |g_{f_0 pi+pi-}|= 1.7. These
results, together with the tiny "direct" gamma gamma width of the sigma and its
large hadronic width, are a strong indication for the gluonium/glueball nature
of the sigma-meson, as predicted by QCD spectral sum rules (QSSR) + some
low-energy theorems (LET), while some other assignements (pi pi molecule,
tetraquark state and ordinary qq meson) do not satisfy simultaneously these
requirements from the data. These properties suggest that the sigma can be a
scalar meson associated to the U(1)V conformal anomaly like is the eta'-meson
for the U(1)A anomaly.