  We propose a new model which can naturally explain origins of fermion
generations, quark mass hierarchy, and Cabibbo-Kobayashi-Maskawa matrix
simultaneously from geometry of an extra dimension. We take the extra dimension
to be an interval with point interactions, which are additional boundary points
in the bulk space of the interval. Because of the Dirichlet boundary condition
for fermion at the positions of point interactions, profiles of chiral fermion
zero modes are split and localized, and then we can realize three generations
from each five-dimensional Dirac fermion. Our model allows fermion flavor
mixing but the form of non-diagonal elements of fermion mass matrices is found
to be severely restricted due to geometry of the extra dimension. The Robin
boundary condition for a scalar leads to an extra coordinate-dependent vacuum
expectation value, which can naturally explain the fermion mass hierarchy.


  Prior work demonstrated the ability of machine learning to automatically
recognize surgical workflow steps from videos. However, these studies focused
on only a single type of procedure. In this work, we analyze, for the first
time, surgical step recognition on four different laparoscopic surgeries:
Cholecystectomy, Right Hemicolectomy, Sleeve Gastrectomy, and Appendectomy.
Inspired by the traditional apprenticeship model, in which surgical training is
based on the Halstedian method, we paraphrase the "see one, do one, teach one"
approach for the surgical intelligence domain as "train one, classify one,
teach one". In machine learning, this approach is often referred to as transfer
learning. To analyze the impact of transfer learning across different
laparoscopic procedures, we explore various time-series architectures and
examine their performance on each target domain. We introduce a new
architecture, the Time-Series Adaptation Network (TSAN), an architecture
optimized for transfer learning of surgical step recognition, and we show how
TSAN can be pre-trained using self-supervised learning on a Sequence Sorting
task. Such pre-training enables TSAN to learn workflow steps of a new
laparoscopic procedure type from only a small number of labeled samples from
the target procedure. Our proposed architecture leads to better performance
compared to other possible architectures, reaching over 90% accuracy when
transferring from laparoscopic Cholecystectomy to the other three procedure
types.


  In this paper we investigate relations between solutions to the minimal
surface equation in Euclidean $3$-space $\mathbb{E}^3$, the zero mean curvature
equation in Lorentz-Minkowski $3$-space $\mathbb{L}^3$ and the Born-Infeld
equation under Wick rotations. We prove that the existence conditions of real
solutions and imaginary solutions after Wick rotations are written by
symmetries of solutions, and reveal how real and imaginary solutions are
transformed under Wick rotations. We also give a transformation theory for zero
mean curvature surfaces containing lightlike lines with some symmetries. As an
application, we give new correspondences among some solutions to the above
equations by using the non-commutativity between Wick rotations and isometries
in the ambient space.


  The geometric phase of a bi-particle model is discussed. For different
initial states, especially when the initial state is pure or mixed, the
geometric phase will show different properties. The relationship between the
geometric phase and the entanglement or mixedness of the initial state is
considered.


  Many microorganisms are capable of swimming through viscous fluids such as
water in order to search for nutrients, swim toward oxygen or light, or to
escape from predators. To navigate their environment they often perform large
nonreciprocal periodic deformations of their shape, by waving appendages such
as cilia or flagella, or by deforming their entire body. Even unicellular
organisms are fundamentally made of parts, which need to be cooperatively
utilized to allow these creatures to navigate their environment, without using
a centralized control mechanism. Here, we investigate the physical implications
of decentralized decision-making of the actuators of a generalized N-bead
Najafi Golestanian microswimmer, self-propelling via coordinated non-reciprocal
swimming strokes. We treat each bead as an artificial neural network-based
agent that perceives information about its neighbors and whose actions induce
strokes of its adjacent arms. With neuroevolution techniques, we evolve optimal
policies for the single-bead decision centers such that the N-bead collective
efficiently self-propels as an individual, allowing us to investigate optimal
locomotion policies for increasingly large microswimmer bodies. We demonstrate
that such decentralized policies are robust and tolerant concerning
morphological changes or defects and facilitate cargo transport or drug
delivery applications "out of the box", without further optimization. Our
approach allows us to train large swimmers ($N=100$ and more), and we show that
long-wavelength solutions lead to surprisingly efficient swimming gaits. Our
work is of relevance to understand robust locomotion of biological
microswimmers, to develop robust artificial microswimmer navigation strategies,
and, in a broader conceptional context, for Artificial Life< and in general
emergent levels of individuality.


  We investigate the implications for fermion mass models in heterotic
orbifolds of the modular symmetry mixing twisted states localized at different
fixed points. We show that, unlike in the case of continuous gauge symmetries,
the mass eigenstates do not mix under the symmetry; thus coupling constants in
the low-energy theory are invariant functions of the moduli.


  A theoretical model for polydisperse systems of hard spheres is said to be
truncatable when the excess free energy depends on the size distribution
through a finite number $K$ of moments. This Note proves an exact scaling
relation for truncatable free energies, which allows to reduce the effective
degrees of freedom to $K-2$ independent combinations of the moments.


  We introduce a method to analyze the effect of hybridization by shifting
corresponding atomic levels using external potentials. Based on this approach,
we study perovskite ruthenates,\ and unambiguously identify that the covalency
between the \textit{A}-site cation and O ion will modify the Ru-O hybridization
and change the density of state at Fermi level, consequently affect the
magnetic properties significantly. We also study the effect of pressure and
reveal that hydrostatic pressure has a small effect on the Ru-O-Ru bond angle
of SrRuO$_{3}$, while it will decrease the Ru-O length and increase the band
width significantly. Therefore, the magnetic ordering temperature will decrease
monotonically with pressure.


  Astronomers usually need the highest angular resolution possible, but the
blurring effect of diffraction imposes a fundamental limit on the image quality
from any single telescope. Interferometry allows light collected at
widely-separated telescopes to be combined in order to synthesize an aperture
much larger than an individual telescope thereby improving angular resolution
by orders of magnitude. Radio and millimeter wave astronomers depend on
interferometry to achieve image quality on par with conventional visible and
infrared telescopes. Interferometers at visible and infrared wavelengths extend
angular resolution below the milli-arcsecond level to open up unique research
areas in imaging stellar surfaces and circumstellar environments.
  In this chapter the basic principles of interferometry are reviewed with an
emphasis on the common features for radio and optical observing. While many
techniques are common to interferometers of all wavelengths, crucial
differences are identified that will help new practitioners avoid unnecessary
confusion and common pitfalls. Concepts essential for writing observing
proposals and for planning observations are described, depending on the science
wavelength, angular resolution, and field of view required. Atmospheric and
ionospheric turbulence degrades the longest-baseline observations by
significantly reducing the stability of interference fringes. Such
instabilities represent a persistent challenge, and the basic techniques of
phase-referencing and phase closure have been developed to deal with them.
Synthesis imaging with large observing datasets has become a routine and
straightforward process at radio observatories, but remains challenging for
optical facilities. In this context the commonly-used image reconstruction
algorithms CLEAN and MEM are presented. Lastly, a concise overview of current
facilities is included as an appendix.


  The recovery and resilience of the cultural and creative sectors after the
COVID-19 pandemic is a current topic with priority for the European Commission.
Cultural gems is a crowdsourced web platform managed by the Joint Research
Centre of the European Commission aimed at creating community-led maps as well
as a common repository for cultural and creative places across European cities
and towns. More than 130,000 physical locations and online cultural activities
in more than 300 European cities and towns are currently tracked by the
application. The main objective of Cultural gems consists in raising a holistic
vision of European culture, reinforcing a sense of belonging to a common
European cultural space. This data article describes the ontology developed for
Cultural gems, adopted to represent the domain of knowledge of the application
by means of FAIR (Findable, Accessible, Interoperable, Reusable) principles and
following the paradigms of Linked Open Data (LOD). We provide an overview of
this dataset, and describe the ontology model, along with the services used to
access and consume the data.


  We propose to induce topological defects in particle-hole symmetric
superfluids, with the prime example of the BCS state of ultracold atoms and
detect their time evolution and decay. We demonstrate that the time evolution
is qualitatively distinct for particle-hole symmetric superfluids, and point
out that the dynamics of topological defects is strongly modified in
particle-hole symmetric fluids. We obtain results for different charges and
compare them with the standard Gross-Pitaevskii prediction for Bose-Einstein
condensates. We highlight the observable signatures of the particle-hole
symmetry in the dynamics of decaying solitons and subsequent vortices.


  The problem of simultaneous decomposition of binary forms as sums of powers
of linear forms is studied. For generic forms the minimal number of linear
forms needed is found and the space parametrizing all the possible
decompositions is described. These results are applied to the study of rational
curves.


  We study the impurity pinning of the Quantum Hall (QH) smectic state arising
in two dimensional electron systems in high Landau levels. We use replicas and
a Gaussian Variational method to deal with the disorder. The pinned quantum
smectic exhibits very anisotropic behaviour, with density correlations along
the direction of the stripes manifesting a Bragg-Glass type behaviour i.e.,
quasi long range order whereas those in the transverse direction are infra red
divergent. We calculate the dynamical conductivity along the stripe direction
and find a wavelength dependent pinning peak.


  We prove that the weakly singular, non-linear convolution integral equation
$\int_{\mathbb{R}^n}|x-y|^{-\lambda}f(y)dy=f(x)^{p-1}$, where $0<\lambda<n$,
and $p=2n/(2n-\lambda)$ has at least two non-equivalent solutions. This answers
a problem of Elliott Lieb. We also prove certain orthogonality relations among
linear differential forms with constant coefficients related to the
corresponding type of convolution operators. Finally, we discuss the regularity
of the solutions of such non-linear integral equations over not necessarily
bounded open subsets of $\mathbb{R}^n$.


  We study a nonlocal 4th order degenerate equation deriving from the epitaxial
growth on crystalline materials. We first prove the global existence of
evolution variational inequality solution with a general initial data using the
gradient flow structure. Then with a monotone initial data, we prove the
subdifferential of the associated convex functional is indeed single-valued,
which gives higher regularities of the global solution. Particularly, higher
regularites imply that the strict monotonicity maintains for all time, which
provides rigorous justification for global-in time monotone solution to
epitaxial growth model with nonlocal elastic effects on vicinal surface.


  We give an elementary proof of a theorem that characterizes quasisymmetric
maps of the unit circle in terms of shear coordinates on the Farey tesselation.
The proof only uses the normal family argument for quasisymmetric maps and some
elementary hyperbolic geometry.


  The tempered spectrum of the similitude groups of non-degenerate symplectic,
hermitian, or split orthogonal forms defined over $p$\snug-adic groups of
characteristic zero is studied. The components of representations induced from
discrete series of proper parabolic subgroups are classified in terms of
$R$\snug-groups. Multiplicity one is proved. The tempered elliptic spectrum is
identified, and the relation between elliptic characters appearing in a given
induced representation is determined. Those irreducible tempered
representations which are not elliptic and not fully induced from elliptic
tempered representations are described.


  In this paper, we construct a comparison map from the topological fundamental
group to the pro-\'etale fundamental group for a complex variety.


  The dynamics of many systems from physics, economics, chemistry, and biology
can be modelled through polynomial functions. In this paper, we provide a
computational means to find positively invariant sets of polynomial dynamical
systems by using semidefinite programming to solve sum-of-squares (SOS)
programmes. With the emergence of SOS programmes, it is possible to efficiently
search for Lyapunov functions that guarantee stability of polynomial systems.
Yet, SOS computations often fail to find functions, such that the conditions
hold in the entire state space. We show here that restricting the SOS
optimisation to specific domains enables us to obtain positively invariant
sets, thus facilitating the analysis of the dynamics by considering separately
each positively invariant set. In addition, we go beyond classical Lyapunov
stability analysis and use SOS decompositions to computationally implement
sufficient positivity conditions that guarantee existence, uniqueness, and
exponential stability of a limit cycle. Importantly, this approach is
applicable to systems of any dimension and, thus, goes beyond classical methods
that are restricted to two-dimensional phase space. We illustrate our different
results with applications to classical systems, such as the van der Pol
oscillator, the Fitzhugh-Nagumo neuronal equation, and the Lorenz system.


  During migration, amoeboid cells perform a cycle of quasi-periodic repetitive
events (motility cycle). the cell length and the strain energy exchanged with
the substrate oscillate in time with an average frequency, f, on top of which
are imposed smaller random fluctuations. the fact that a considerable portion
of the changes in cell shape are due to periodic repetitive events enables the
use of conditional statistics methods to analyze the network of biochemical
processes involved in cell motility. taking advan- tage of this cyclic nature,
we apply Principal Component analysis (PCa) and phase- average statistics to
analyze the dominant modes of shape change and their association to the
activity and localization of molecular motors. We analyze time-lapse measure-
ments of cell shape, traction forces and fluorescence from green fluorescent
protein (GfP) reporters for f-actin in Dictyostelium cells undergoing guided
chemotactic migration. using wild-type cells (wt) as reference, we investigated
the contractile and actin crosslinking functions of myosin II by studying
myosin II heavy chain null mutant cells (mhcA-) and myosin II essential light
chain null cells (mlcE-).


  Terahertz (THz) chirality pursues customizable manipulation from narrowband
to broadband. While conventional THz chirality is restricted by non-negligible
linewidth and unable to handle narrowband well. Recently, the concept "quasi
bound states in continuum" (quasi-BIC) is introduced to optics resonance system
whose the quality factor can be extremely high with the ultra-low radiative
loss, thus providing a conceptual feasibility for wave control with
ultra-narrow linewidth. Herein, we construct quasi-BIC in a planar all-silicon
THz metasurface with in-plane C2 and mirror symmetries breaking. Such system
not only exposes the symmetry-protected BIC, but also exposes the
parameter-tuned BIC assigned to single resonance type. An extremely narrow
linewidth (below 0.06 GHz) with high quality factor (104 level) is obtained at
quasi-BIC frequency, which achieves the ultra-narrowband THz chirality.


  Addressing the issue of hallucinations in large language models (LLMs) is a
critical challenge. As the cognitive mechanisms of hallucination have been
related to memory, here we explore hallucination for LLM that is enabled with
explicit memory mechanisms. We empirically demonstrate that by simply scaling
the readout vector that constrains generation in a memory-augmented LLM
decoder, hallucination mitigation can be achieved in a training-free manner.
Our method is geometry-inspired and outperforms a state-of-the-art LLM editing
method on the task of generation of Wikipedia-like biography entries both in
terms of generation quality and runtime complexity.


  We show that the fundamental groups of any two closed irreducible
non-geometric graph-manifolds are quasi-isometric. This answers a question of
Kapovich and Leeb. We also classify the quasi-isometry types of fundamental
groups of graph-manifolds with boundary in terms of certain finite two-colored
graphs. A corollary is the quasi-isometry classification of Artin groups whose
presentation graphs are trees. In particular any two right-angled Artin groups
whose presentation graphs are trees of diameter at least 3 are quasi-isometric,
answering a question of Bestvina; further, this quasi-isometry class does not
include any other right-angled Artin groups.


  We present a formalism for analysing redshift distortions based on a
spherical harmonic expansion of the density field. We use a maximum likelihood
estimator for the combination of density and bias parameters, $\Omega^0.6/b$.
We test the method with $N$-body simulations and apply it to the 1.2 Jy IRAS
redshift survey.


  Determining the relevant spatial covariates is one of the most important
problems in the analysis of point patterns. Parametric methods may lead to
incorrect conclusions, especially when the model of interactions between points
is wrong. Therefore, we propose a fully nonparametric approach to testing
significance of a covariate, taking into account the possible effects of
nuisance covariates. Our tests match the nominal significance level, and their
powers are comparable with the powers of parametric tests in cases where both
the model for intensity function and the model for interactions are correct.
When the parametric model for the intensity function is wrong, our tests
achieve higher powers. The proposed methods rely on Monte Carlo testing and
take advantage of the newly introduced covariate-weighted residual measure. We
also define a correlation coefficient between a point process and a covariate
and a partial correlation coefficient quantifying the dependence between a
point process and a covariate of interest while removing the influence of
nuisance covariates.


  The collapse of non-collisional dark matter and the formation of pancake
structures in the Universe are investigated approximately. Collapse is
described by a system of ordinary differential equations, in the model of a
uniformly rotating, three-axis, uniform density ellipsoid. Violent relaxation,
mass and angular momentum losses are taken into account phenomenologically. The
formation of the equilibrium configuration, secular instability and the
transition from a spheroid to a three-axis ellipsoid are investigated
numerically and analytically in this dynamical model.


  This paper presents a brand new nonparametric density estimation strategy
named the best-scored random forest density estimation whose effectiveness is
supported by both solid theoretical analysis and significant experimental
performance. The terminology best-scored stands for selecting one density tree
with the best estimation performance out of a certain number of purely random
density tree candidates and we then name the selected one the best-scored
random density tree. In this manner, the ensemble of these selected trees that
is the best-scored random density forest can achieve even better estimation
results than simply integrating trees without selection. From the theoretical
perspective, by decomposing the error term into two, we are able to carry out
the following analysis: First of all, we establish the consistency of the
best-scored random density trees under $L_1$-norm. Secondly, we provide the
convergence rates of them under $L_1$-norm concerning with three different tail
assumptions, respectively. Thirdly, the convergence rates under
$L_{\infty}$-norm is presented. Last but not least, we also achieve the above
convergence rates analysis for the best-scored random density forest. When
conducting comparative experiments with other state-of-the-art density
estimation approaches on both synthetic and real data sets, it turns out that
our algorithm has not only significant advantages in terms of estimation
accuracy over other methods, but also stronger resistance to the curse of
dimensionality.


  Neural Network Language Models (NNLMs) for Virtual Assistants (VAs) are
generally language-, region-, and in some cases, device-dependent, which
increases the effort to scale and maintain them. Combining NNLMs for one or
more of the categories is one way to improve scalability. In this work, we
combine regional variants of English to build a ``World English'' NNLM for
on-device VAs. In particular, we investigate the application of adapter
bottlenecks to model dialect-specific characteristics in our existing
production NNLMs {and enhance the multi-dialect baselines}. We find that
adapter modules are more effective in modeling dialects than specializing
entire sub-networks. Based on this insight and leveraging the design of our
production models, we introduce a new architecture for World English NNLM that
meets the accuracy, latency, and memory constraints of our single-dialect
models.


  This paper proposes a plane wave activation based neural network (PWNN) for
solving Helmholtz equation, the basic partial differential equation to
represent wave propagation, e.g. acoustic wave, electromagnetic wave, and
seismic wave. Unlike using traditional activation based neural network (TANN)
or $sin$ activation based neural network (SIREN) for solving general partial
differential equations, we instead introduce a complex activation function
$e^{\mathbf{i}{x}}$, the plane wave which is the basic component of the
solution of Helmholtz equation. By a simple derivation, we further find that
PWNN is actually a generalization of the plane wave partition of unity method
(PWPUM) by additionally imposing a learned basis with both amplitude and
direction to better characterize the potential solution. We firstly investigate
our performance on a problem with the solution is an integral of the plane
waves with all known directions. The experiments demonstrate that: PWNN works
much better than TANN and SIREN on varying architectures or the number of
training samples, that means the plane wave activation indeed helps to enhance
the representation ability of neural network toward the solution of Helmholtz
equation; PWNN has competitive performance than PWPUM, e.g. the same
convergence order but less relative error. Furthermore, we focus a more
practical problem, the solution of which only integrate the plane waves with
some unknown directions. We find that PWNN works much better than PWPUM at this
case. Unlike using the plane wave basis with fixed directions in PWPUM, PWNN
can learn a group of optimized plane wave basis which can better predict the
unknown directions of the solution. The proposed approach may provide some new
insights in the aspect of applying deep learning in Helmholtz equation.


  We present the calibration of the \textit{Nuclear Spectroscopic Telescope
Array} (\nustar) X-ray satellite. We used the Crab as the primary effective
area calibrator and constructed a piece-wise linear spline function to modify
the vignetting response. The achieved residuals for all off-axis angles and
energies, compared to the assumed spectrum, are typically better than $\pm 2$\%
up to 40\,keV and 5--10\,\% above due to limited counting statistics. An
empirical adjustment to the theoretical 2D point spread function (PSF) was
found using several strong point sources, and no increase of the PSF half power
diameter (HPD) has been observed since the beginning of the mission. We report
on the detector gain calibration, good to 60\,eV for all grades, and discuss
the timing capabilities of the observatory, which has an absolute timing of
$\pm$ 3\,ms. Finally we present cross-calibration results from two campaigns
between all the major concurrent X-ray observatories (\textit{Chandra},
\textit{Swift}, \textit{Suzaku} and \textit{XMM-Newton}), conducted in 2012 and
2013 on the sources 3C\,273 and PKS\,2155-304, and show that the differences in
measured flux is within $\sim$10\% for all instruments with respect to \nustar.


  Removing audio effects from electric guitar recordings makes it easier for
post-production and sound editing. An audio distortion recovery model not only
improves the clarity of the guitar sounds but also opens up new opportunities
for creative adjustments in mixing and mastering. While progress have been made
in creating such models, previous efforts have largely focused on synthetic
distortions that may be too simplistic to accurately capture the complexities
seen in real-world recordings.
  In this paper, we tackle the task by using a dataset of guitar recordings
rendered with commercial-grade audio effect VST plugins. Moreover, we introduce
a novel two-stage methodology for audio distortion recovery. The idea is to
firstly process the audio signal in the Mel-spectrogram domain in the first
stage, and then use a neural vocoder to generate the pristine original guitar
sound from the processed Mel-spectrogram in the second stage. We report a set
of experiments demonstrating the effectiveness of our approach over existing
methods, through both subjective and objective evaluation metrics.


  We analyze a numerical method to solve the time-dependent linear Pauli
equation in three space dimensions. The Pauli equation is a semi-relativistic
generalization of the Schr\"odinger equation for 2-spinors which accounts both
for magnetic fields and for spin, with the latter missing in preceding
numerical work on the linear magnetic Schr\"odinger equation. We use a four
operator splitting in time, prove stability and convergence of the method and
derive error estimates as well as meshing strategies for the case of given
time-independent electromagnetic potentials, thus providing a generalization of
previous results for the magnetic Schr\"odinger equation.


  This work introduces the Cleanformer, a streaming multichannel neural based
enhancement frontend for automatic speech recognition (ASR). This model has a
conformer-based architecture which takes as inputs a single channel each of raw
and enhanced signals, and uses self-attention to derive a time-frequency mask.
The enhanced input is generated by a multichannel adaptive noise cancellation
algorithm known as Speech Cleaner, which makes use of noise context to derive
its filter taps. The time-frequency mask is applied to the noisy input to
produce enhanced output features for ASR. Detailed evaluations are presented
with simulated and re-recorded datasets in speech-based and non-speech-based
noise that show significant reduction in word error rate (WER) when using a
large-scale state-of-the-art ASR model. It also will be shown to significantly
outperform enhancement using a beamformer with ideal steering. The enhancement
model is agnostic of the number of microphones and array configuration and,
therefore, can be used with different microphone arrays without the need for
retraining. It is demonstrated that performance improves with more microphones,
up to 4, with each additional microphone providing a smaller marginal benefit.
Specifically, for an SNR of -6dB, relative WER improvements of about 80\% are
shown in both noise conditions.


  We consider the problem of jointly optimum modulation and estimation of a
real-valued random parameter, conveyed over an additive white Gaussian noise
(AWGN) channel, where the performance metric is the large deviations behavior
of the estimator, namely, the exponential decay rate (as a function of the
observation time) of the probability that the estimation error would exceed a
certain threshold. Our basic result is in providing an exact characterization
of the fastest achievable exponential decay rate, among all possible
modulator-estimator (transmitter-receiver) pairs, where the modulator is
limited only in the signal power, but not in bandwidth. This exponential rate
turns out to be given by the reliability function of the AWGN channel. We also
discuss several ways to achieve this optimum performance, and one of them is
based on quantization of the parameter, followed by optimum channel coding and
modulation, which gives rise to a separation-based transmitter, if one views
this setting from the perspective of joint source-channel coding. This is in
spite of the fact that, in general, when error exponents are considered, the
source-channel separation theorem does not hold true. We also discuss several
observations, modifications and extensions of this result in several
directions, including other channels, and the case of multidimensional
parameter vectors. One of our findings concerning the latter, is that there is
an abrupt threshold effect in the dimensionality of the parameter vector: below
a certain critical dimension, the probability of excess estimation error may
still decay exponentially, but beyond this value, it must converge to unity.


  We investigate the intrinsic reason for spin statistics connection. It is
found that if a free field theory is rotationally (SU(2)) invariant, and has
time reversal ($T$) and charge conjugation ($C$) symmetries, it obeys the spin
statistics connection, except for a special case. Shr{\"o}dinger equation
belongs to this special case, and does not obey spin statistics connection.
Further we show that if the energy spectrum of a particle $E(p)$ takes the form
of a square root, namely contains branch points in the complex $p$ plane, the
particle cannot belong to this special case, and must obey the spin statistics
connection. This conclusion includes the relativistic particles as a particular
example.


  We study magnetic properties of spin glass SG systems under a random field
(RF), beased on the suggestion that RFs can be induced by a weak transverse
field in the compound LiHo$_x$Y$_{1-x}$F$_4$. We consider a cluster spin model
that allows long-range disordered interactions among clusters and short-range
interactions inside the clusters, besides a local RF for each spin following a
Gaussian distribution with standard deviation $\Delta$. We adopt the one-step
replica symmetry breaking (RSB) approach to get an exactly solvable
single-cluster problem. We discuss the behavior of order parameters, specific
heat $C_{m}$, nonlinear susceptibility $\chi_3$ and phase diagrams for
different disorder configurations. In the absence of RF, the $\chi_3$ exhibits
a divergence at $T_f$, while the $C_{m}$ shows a broad maximum at a temperature
$T^{**}$ around 30$\%$ above $T_f$, as expected for conventional SG systems.
The presence of RF changes this scenario. The $C_{m}$ still shows the maximum
at $T^{**}$ that is weakly dependent on $\Delta$. However, the $T_f$ is
displaced to lower temperatures, enhancing considerable the ration
$T^{**}/T_f$. Furthermore, the divergence in $\chi_3$ is replaced by a rounded
maximum at a temperature $T^{*}$, which becomes increasingly higher than $T_f$
as $\Delta$ enhances. As a consequence, the paramagnetic phase is unfolded in
three regions: (i) a conventional paramagnetism ($T>T^{**}$; (ii) a region with
formation of short-range order with frozen spins ($T^{*}<T<T^{**}$); (iii) a
region with slow growth of free-energy barriers slowing down the spin dynamics
before the SG transition ($T_f<T<T^{*}$) suggesting an intermediate Griffiths
phase before the SG state. Our results reproduce qualitatively some findings of
LiHo$_x$Y$_{1-x}$F$_4$ as the rounded maximum of $\chi_3$ behavior triggered by
RF.


  We investigate the effects of the symmetry energy on nuclear pasta phases and
the crust-core transition in neutron stars. We employ the relativistic
mean-field approach and the coexisting phases method to study the properties of
pasta phases presented in the inner crust of neutron stars. It is found that
the slope of the nuclear symmetry energy at saturation density plays an
important role in the crust-core transition and pasta phase properties. The
correlation between the symmetry energy slope and the crust-core transition
density obtained in this study is consistent with those obtained by other
methods.


  We study the electronic properties of AA-stacked bilayer graphene in a
transverse electric field. The strong on-site Coulomb repulsion stabilizes the
antiferromagnetic order in such a system. The antiferromagnetic order is
suppressed by the transverse bias voltage, at least partially. The inter-plane
Coulomb repulsion and non-zero voltage stabilize an exciton order parameter.
The exciton order parameter coexists with the antiferromagnetism and can be as
large as several tens of meV for realistic values of the bias voltage and
interaction constants. The application of a transverse bias voltage can be used
to control the transport properties of the bilayer.


  The information technology and security stakeholders like CIOs, CISOs and
CTOs in financial services organization are often asked to identify the risks
with mobile computing channel for financial services that they support. They
are also asked to come up with approaches for handling risks, define risk
acceptance level and mitigate them. This requires them to articulate strategy
for supporting a huge variety of mobile devices from various vendors with
different operating systems and hardware platforms and at the same time stay
within the accepted risk level. These articulations should be captured in
information security policy document or other suitable document of financial
services organization like banks, payment service provider, etc. While risks
and mitigation approaches are available from multiple sources, the senior
stakeholders may find it challenging to articulate the issues in a
comprehensive manner for sharing with business owners and other technology
stakeholders. This paper reviews the current research that addresses the issues
mentioned above and articulates a strategy that the senior stakeholders may use
in their organization. It is assumed that this type of comprehensive strategy
guide for senior stakeholders is not readily available and CIOs, CISOs and CTOs
would find this paper to be very useful.


  These notes are an extension of the rough notes provided for my four lecture
graduate level course on "Quadratic Forms and Automorphic Forms" at the March
2009 Arizona Winter School on Quadratic Forms. They are meant to give a survey
of some aspects of the classical theory of quadratic forms over number fields
and their rings of integers (e.g. over Q and Z), and their connection with
modular and automorphic forms.


  We study variations of the standard leptogenesis scenario that can arise if
an additional mass scale related to the breaking of some new symmetry (as for
example a flavor or the B-L symmetry) is present below the mass $M_{N_1}$ of
the lightest right-handed Majorana neutrino. Our scheme is inspired by U(1)
models of flavor \`a la Froggatt-Nielsen, and involves new vectorlike heavy
fields $F$. We show that depending on the specific hierarchy between $M_{N_1}$
and the mass scale of the fields $F$, qualitatively different realizations of
leptogenesis can emerge. We compute the CP asymmetries in $N_1$ decays in all
the relevant cases, and we conclude that in most situations leptogenesis could
be viable at scales much lower than in the standard scenario.


  Integrated sources of indistinguishable photons have attracted a lot of
attention because of their applications in quantum communication and optical
quantum computing. Here, we demonstrate an ultra-compact quantum splitter for
degenerate single photons based on a monolithic chip incorporating Sagnac loop
and a micro-ring resonator with a footprint of 0.011 mm2, generating and
deterministically splitting indistinguishable photon pairs using time-reversed
Hong-Ou-Mandel interference. The ring resonator provides enhanced photon
generation rate, and the Sagnac loop ensures the photons travel through equal
path lengths and interfere with the correct phase to enable the reversed HOM
effect to take place. In the experiment, we observed a HOM dip visibility of
94.5 +- 3.3 %, indicating the photons generated by the degenerate single photon
source are in a suitable state for further integration with other components
for quantum applications, such as controlled-NOT gates.


  To date, little attention has been given to multi-view 3D human mesh
estimation, despite real-life applicability (e.g., motion capture, sport
analysis) and robustness to single-view ambiguities. Existing solutions
typically suffer from poor generalization performance to new settings, largely
due to the limited diversity of image-mesh pairs in multi-view training data.
To address this shortcoming, people have explored the use of synthetic images.
But besides the usual impact of visual gap between rendered and target data,
synthetic-data-driven multi-view estimators also suffer from overfitting to the
camera viewpoint distribution sampled during training which usually differs
from real-world distributions. Tackling both challenges, we propose a novel
simulation-based training pipeline for multi-view human mesh recovery, which
(a) relies on intermediate 2D representations which are more robust to
synthetic-to-real domain gap; (b) leverages learnable calibration and
triangulation to adapt to more diversified camera setups; and (c) progressively
aggregates multi-view information in a canonical 3D space to remove ambiguities
in 2D representations. Through extensive benchmarking, we demonstrate the
superiority of the proposed solution especially for unseen in-the-wild
scenarios.


  In this paper we study the eigenvalues of the laplacian matrices of the
cyclic graphs with one edge of weight $\alpha$ and the others of weight $1$. We
denote by $n$ the order of the graph and suppose that $n$ tends to infinity. We
notice that the characteristic polynomial and the eigenvalues depend only on
$\operatorname{Re}(\alpha)$. After that, through the rest of the paper we
suppose that $0<\alpha<1$. It is easy to see that the eigenvalues belong to
$[0,4]$ and are asymptotically distributed as the function $g(x)=4\sin^2(x/2)$
on $[0,\pi]$. We obtain a series of results about the individual behavior of
the eigenvalues. First, we describe more precisely their localization in
subintervals of $[0,4]$. Second, we transform the characteristic equation to a
form convenient to solve by numerical methods. In particular, we prove that
Newton's method converges for every $n\ge3$. Third, we derive asymptotic
formulas for all eigenvalues, where the errors are uniformly bounded with
respect to the number of the eigenvalue.


  In the paper the linear force model used in car accident simulation programs
is discussed. A model of restitution is proposed and the possible
interpretation of CRASH coefficients is also discussed.


  Non-LTE calculations for Mg I in red supergiant stellar atmospheres are
presented to investigate the importance of non-LTE for the formation of Mg I
lines in the NIR J-band. Recent work using medium resolution spectroscopy of
atomic lines in the J-band of individual red supergiant stars has demonstrated
that technique is a very promising tool to investigate the chemical composition
of the young stellar population in star forming galaxies. As in previous work,
where non-LTE effects were studied for iron, titanium and silicon, substantial
effects are found resulting in significantly stronger Mg I absorption lines.
For the quantitative spectral analysis the non-LTE effects lead to magnesium
abundances significantly smaller than in LTE with the non-LTE abundance
corrections varying smoothly between -0.4 dex and -0.1 dex for effective
temperatures between 3400 K and 4400 K. We discuss the physical reasons of the
non-LTE effects and the consequences for extragalactic J-band abundance studies
using individual red supergiants in the young massive galactic double cluster h
and chi Persei.


  We relate structurally dynamic cellular networks, a class of models we
developed in fundamental space-time physics, to SDCA, introduced some time ago
by Ilachinski and Halpern. We emphasize the crucial property of a non-linear
interaction of network geometry with the matter degrees of freedom in order to
emulate the supposedly highly erratic and strongly fluctuating space-time
structure on the Planck scale. We then embark on a detailed numerical analysis
of various large scale characteristics of several classes of models in order to
understand what will happen if some sort of macroscopic or continuum limit is
performed. Of particular relevance in this context is a notion of network
dimension and its behavior in this limit. Furthermore, the possibility of phase
transitions is discussed.


  We discuss the regularity of solutions of 2D incompressible Navier-Stokes
equations forced by singular forces. The problem is motivated by the study of
complex fluids modeled by the Navier-Stokes equations coupled to a nonlinear
Fokker-Planck equation describing microscopic corpora embedded in the fluid.
This leads naturally to bounded added stress and hence to $W^{-1,\infty}$
forcing of the Navier-Stokes equations.


  Given a simply connected, closed four manifold, we associate to it a simply
connected, closed, spin five manifold. This leads to several consequences : the
stable and unstable homotopy groups of such a four manifold is determined by
its second Betti number, and the ranks of the homotopy groups can be explicitly
calculated. We show that for a generic metric on such a smooth four manifold
with second Betti number at least three, the number of geometrically distinct
periodic geodesics of length at most l grow exponentially as a function of l.
The number of closed Reeb orbits of length at most l on the spherization of the
cotangent bundle also grow exponentially for any Reeb flow.


  We propose a new paradigm to help Large Language Models (LLMs) generate more
accurate factual knowledge without retrieving from an external corpus, called
RECITation-augmented gEneration (RECITE). Different from retrieval-augmented
language models that retrieve relevant documents before generating the outputs,
given an input, RECITE first recites one or several relevant passages from
LLMs' own memory via sampling, and then produces the final answers. We show
that RECITE is a powerful paradigm for knowledge-intensive NLP tasks.
Specifically, we show that by utilizing recitation as the intermediate step, a
recite-and-answer scheme can achieve new state-of-the-art performance in
various closed-book question answering (CBQA) tasks. In experiments, we verify
the effectiveness of \method~on four pre-trained models (PaLM, UL2, OPT, and
Codex) and three CBQA tasks (Natural Questions, TriviaQA, and HotpotQA). Our
code is available at "https://github.com/Edward-Sun/RECITE".


  A rapid transformation of current electric power and natural gas (NG)
infrastructure is imperative to meet the mid-century goal of CO2 emissions
reduction requires. This necessitates a long-term planning of the joint
power-NG system under representative demand and supply patterns, operational
constraints, and policy considerations. Our work is motivated by the
computational and practical challenges associated with solving the generation
and transmission expansion problem (GTEP) for joint planning of power-NG
systems. Specifically, we focus on efficiently extracting a set of
representative days from power and NG data in respective networks and using
this set to reduce the computational burden required to solve the GTEP. We
propose a Graph Autoencoder for Multiple time resolution Energy Systems (GAMES)
to capture the spatio-temporal demand patterns in interdependent networks and
account for differences in the temporal resolution of available data. The
resulting embeddings are used in a clustering algorithm to select
representative days. We evaluate the effectiveness of our approach in solving a
GTEP formulation calibrated for the joint power-NG system in New England. This
formulation accounts for the physical interdependencies between power and NG
systems, including the joint emissions constraint. Our results show that the
set of representative days obtained from GAMES not only allows us to tractably
solve the GTEP formulation, but also achieves a lower cost of implementing the
joint planning decisions.


  Most of the presently identified exoplanets have masses similar to that of
Jupiter and therefore are assumed to be gaseous objects. With the
ever-increasing interest in discovering lower-mass planets, several of the
so-called super-Earths (1 M_earth<M<10 M_earth), which are predicted to be
rocky, have already been found. Here we report the possible discovery of a
planet around the M-type star GJ 436 with a minimum mass of 4.7+/-0.6 M_earth
and a true mass of ~5 M_earth, which would make it the least massive planet
around a main-sequence star found to date. The planet is identified from its
perturbations on an inner Neptune-mass transiting planet (GJ 436b), by pumping
eccentricity and producing variations in the orbital inclination. Analysis of
published radial velocity measurements indeed reveals a significant signal
corresponding to an orbital period that is very close to the 2:1 mean motion
resonance with the inner planet. The near-grazing nature of the transit makes
it extremely sensitive to small changes in the inclination.


  We cast the problem of illuminating an object in a noisy environment into a
communication protocol. A probe is sent into the environment, and the presence
or absence of the object constitutes a signal encoded on the probe. The probe
is then measured to decode the signal. We calculate the Holevo information and
bounds to the accessible information between the encoded and received signal
with two different Gaussian probes---an Einstein-Podolsky-Rosen (EPR) state and
a coherent state. We also evaluate the Gaussian discord consumed during the
encoding process with the EPR probe. We find that the Holevo quantum advantage,
defined as the difference between the Holevo information obtained from the EPR
and coherent state probes, is approximately equal to the discord consumed.
These quantities become exact in the typical illumination regime of low object
reflectivity and low probe energy. Hence we show that discord is the resource
responsible for the quantum advantage in Gaussian quantum illumination.


  We consider non-twisted meromorphic connections in
$\mathfrak{sl}_2(\mathbb{C})$ and the associated symplectic Hamiltonian
structure. In particular, we provide explicit expressions of the Lax pair in
the geometric gauge supplementing previous results where explicit formulas have
been obtained in the oper gauge. Expressing the geometric Lax matrices requires
the introduction of specific Darboux coordinates for which we provide the
explicit Hamiltonian evolutions. These expressions allow to build bridges
between the isomonodromic deformations and the isospectral ones. More
specifically, we propose an explicit change of Darboux coordinates to obtain
isospectral coordinates for which Hamiltonians match the spectral invariants.
This result solves the issue left opened in \cite{BertolaHarnadHurtubise2022}
in the case of $\mathfrak{sl}_2(\mathbb{C})$.


  We present a detailed description of the idea and procedure for the newly
proposed Monte Carlo algorithm of tuning the critical point automatically,
which is called the probability-changing cluster (PCC) algorithm [Y. Tomita and
Y. Okabe, Phys. Rev. Lett. {\bf 86} (2001) 572]. Using the PCC algorithm, we
investigate the three-dimensional Ising model and the bond percolation problem.
We employ a refined finite-size scaling analysis to make estimates of critical
point and exponents. With much less efforts, we obtain the results which are
consistent with the previous calculations. We argue several directions for the
application of the PCC algorithm.


  The past decade has seen a rapid penetration of electric vehicles (EV) in the
market, more and more logistics and transportation companies start to deploy
EVs for service provision. In order to model the operations of a commercial EV
fleet, we utilize the EV routing problem with time windows (EVRPTW). In this
research, we propose an end-to-end deep reinforcement learning framework to
solve the EVRPTW. In particular, we develop an attention model incorporating
the pointer network and a graph embedding technique to parameterize a
stochastic policy for solving the EVRPTW. The model is then trained using
policy gradient with rollout baseline. Our numerical studies show that the
proposed model is able to efficiently solve EVRPTW instances of large sizes
that are not solvable with any existing approaches.


  We perform a pilot study of the perturbative renormalization of a
Supersymmetric gauge theory with matter fields on the lattice. As a specific
example, we consider Supersymmetric ${\cal N}{=}1$ QCD (SQCD). We study the
self-energies of all particles which appear in this theory, as well as the
renormalization of the coupling constant. To this end we compute,
perturbatively to one-loop, the relevant two-point and three-point Green's
functions using both dimensional and lattice regularizations. Our lattice
formulation involves the Wilson discretization for the gluino and quark fields;
for gluons we employ the Wilson gauge action; for scalar fields (squarks) we
use na\"ive discretization. The gauge group that we consider is $SU(N_c)$,
while the number of colors, $N_c$, the number of flavors, $N_f$, and the gauge
parameter, $\alpha$, are left unspecified.
  We obtain analytic expressions for the renormalization factors of the
coupling constant ($Z_g$) and of the quark ($Z_\psi$), gluon ($Z_u$), gluino
($Z_\lambda$), squark ($Z_{A_\pm}$), and ghost ($Z_c$) fields on the lattice.
We also compute the critical values of the gluino, quark and squark masses.
Finally, we address the mixing which occurs among squark degrees of freedom
beyond tree level: we calculate the corresponding mixing matrix which is
necessary in order to disentangle the components of the squark field via an
additional finite renormalization.


  The coupled dynamics of quantum turbulence (QT) and normal-fluid turbulence
(NFT) have been a central challenge in quantum hydrodynamics, since it is
expected to cause the unsolved T2 state of QT. We numerically studied the
coupled dynamics of the two turbulences in thermal counterflow. NFT is driven
by external forces to control its turbulent intensity, and the fast multipole
method accelerates the calculation of QT. We show that NFT enhances QT via
mutual friction. The vortex line density $L$ of the QT satisfies the
statistical law $L^{1/2} \approx \gamma V_{ns}$ with the counterflow velocity
$V_{ns}$. The obtained $\gamma$ agrees with the experiment of T2 state,
validating the idea that the T2 state is caused by NFT. We propose a
theoretical insight into the relation between the two turbulences.


  We present new Hubble Space Telescope observations of three a priori known
starlight-scattering circumstellar debris systems (CDSs) viewed at intermediate
inclinations around nearby close-solar analog stars: HD 207129, HD 202628, and
HD 202917. Each of these CDSs possesses ring-like components that are
more-massive analogs of our solar system's Edgeworth- Kuiper belt. These
systems were chosen for follow-up observations to provide higher-fidelity and
better sensitivity imaging for the sparse sample of solar-analog CDSs that
range over two decades in systemic ages with HD 202628 and HD 202917 (both ~
2.3 Gyr) currently the oldest CDSs imaged in visible or near-IR light. These
deep (10 - 14 ksec) observations, with six-roll point-spread-function template
subtracted visible-light coronagraphy using the Space Telescope Imaging
Spectrograph, were designed to better reveal their angularly large, diffuse/low
surface brightness, debris rings, and for all targets probe their exo-ring
environments for starlight-scattering materials that present observational
challenges for current ground-based facilities and instruments.
Contemporaneously also observing with a narrower occulter position, these
observations additionally probe the CDS endo-ring environments seen to be
relatively devoid of scatterers. We discuss the morphological, geometrical, and
photometric properties of these CDSs also in the context of other FGK-star
hosted CDSs we have previously imaged as a homogeneously observed ensemble.
From this combined sample we report a general decay in quiescent disk
F_disk/F_star optical brightness ~ t^-0.8, similar to what is seen in at
thermal IR wavelengths, and CDSs with a significant diversity in scattering
phase asymmetries, and spatial distributions of their starlight-scattering
grains.


  We prove that the main theorem for absolutely monotonic functions from the
book Mitrinovi\'{c}~D.S., Pe\v{c}ari\'{c}~J.E., Fink~A.M. "Classical And New
Inequalities In Analysis", Kluwer Academic Publishers, 1993, is not valid
without additional restrictions.


  Emergent $U(1)$ gauge theories and artificial photons in frustrated magnets
are outstanding examples of many-body collective phenomena. The classical and
quantum regimes of these systems provide platforms for classical and quantum
spin liquids, and are the subject of current active theoretical and
experimental investigations. Recently, realizations of rank-2 $U(1)$ (R2-U1)
gauge theories in three-dimensional frustrated magnets have been proposed. Such
systems in the quantum regime may lead to the so-called fracton ordered phases
-- a new class of topological order that has been associated with quantum
stabilizer codes and holography. However, there exist few distinguishing
characteristics of these states for their detection in real materials. Here we
focus on the classical limit, and present the dynamical spin structure factor
for a R2-U1 spin liquid state on a breathing pyrochlore lattice. Remarkably, we
find unique signatures of the R2-U1 state, and we contrast them with the
results obtained from a more conventional $U(1)$ spin liquid. These results
provide a new path of investigation for future inelastic neutron scattering
experiments on candidate materials.


  In the past decade, digital technologies have started to profoundly influence
healthcare systems. Digital self-tracking has facilitated more precise
epidemiological studies, and in the field of nutritional epidemiology, mobile
apps have the potential to alleviate a significant part of the journaling
burden by, for example, allowing users to record their food intake via a simple
scan of packaged products barcodes. Such studies thus rely on databases of
commercialized products, their barcodes, ingredients, and nutritional values,
which are not yet openly available with sufficient geographical and product
coverage. In this paper, we present FoodRepo (https://www.foodrepo.org), an
open food repository of barcoded food items, whose database is programmatically
accessible through an application programming interface (API). Furthermore, an
open source license gives the appropriate rights to anyone to share and reuse
FoodRepo data, including for commercial purposes. With currently more than
21,000 items available on the Swiss market, our database represents a solid
starting point for large-scale studies in the field of digital nutrition, with
the aim to lead to a better understanding of the intricate connections between
diets and health in general, and metabolic disorders in particular.


  Provably safe and scalable multi-vehicle path planning is an important and
urgent problem due to the expected increase of automation in civilian airspace
in the near future. Hamilton-Jacobi (HJ) reachability is an ideal tool for
analyzing such safety-critical systems and has been successfully applied to
several small-scale problems. However, a direct application of HJ reachability
to large scale systems is often intractable because of its
exponentially-scaling computation complexity with respect to system dimension,
also known as the "curse of dimensionality". To overcome this problem, the
sequential path planning (SPP) method, which assigns strict priorities to
vehicles, was previously proposed; SPP allows multi-vehicle path planning to be
done with a linearly-scaling computation complexity. In this work, we
demonstrate the potential of SPP algorithm for large-scale systems. In
particular, we simulate large-scale multi-vehicle systems in two different
urban environments, a city environment and a multi-city environment, and use
the SPP algorithm for trajectory planning. SPP is able to efficiently design
collision-free trajectories in both environments despite the presence of
disturbances in vehicles' dynamics. To ensure a safe transition of vehicles to
their destinations, our method automatically allocates space-time reservations
to vehicles while accounting for the magnitude of disturbances such as wind in
a provably safe way. Our simulation results show an intuitive multi-lane
structure in airspace, where the number of lanes and the distance between the
lanes depend on the size of disturbances and other problem parameters.


  From data centers to IoT devices to Internet-based applications, overlay
networks have become an important part of modern computing. Many of these
overlay networks operate in fragile environments where processes are
susceptible to faults which may perturb a node's state and the network
topology. Self-stabilizing overlay networks have been proposed as one way to
manage these faults, promising to build or restore a particular topology from
any initial configuration or after the occurrence of any transient fault. To
date there have been several self-stabilizing protocols designed for overlay
networks. These protocols, however, are either focused on a single specific
topology, or provide very inefficient solutions for a general set of overlay
networks.
  In this paper, we analyze an existing algorithm and show it can be used as a
general framework for building many other self-stabilizing overlay networks.
Our analysis for time and space complexity depends upon several properties of
the target topology itself, providing insight into how topology selection
impacts the complexity of convergence. We then demonstrate the application of
this framework by analyzing the complexity for several existing topologies.
Next, using insights gained from our analysis, we present a new topology
designed to provide efficient performance during convergence with the general
framework. Our process demonstrates how the implications of our analysis help
isolate the factors of interest to allow a network designer to select an
appropriate topology for the problem requirements.


  Evidence of curvature effects on the interaction and binding of silver
clusters on folded graphitic surfaces has been shown from both experiment and
theory. Density Functional Theory (DFT) calculations within the local density
and generalized gradient approximations have been performed for the structural
relaxation of both Ag and Ag$_2$ on curved surfaces, showing a cross-over from
quantum to classical behaviour. Using Lennard-Jones potential to model the
interaction between a single cluster and the graphene surface, evidence is
found for the curvature effect on the binding of silver nano-particles to
folding graphitic surfaces. The theoretical results are compared to SEM and AFM
images of samples obtained from pre-formed silver cluster deposition on
carboneous substrates exhibiting anisotropic pleat structures.


  We show that for any $m\in\NN\cup\{\infty\}$ there exist $m$ disjoint FB
domains whose union is dense in $\CC^k$. In fact we show that any point not in
the union is a boundary point for all the domains. We construct FB domains that
contains arbitrary countable collections of subvarieties of $\CC^k$, and we
construct FB domains that intersect elements of countable collections of affine
subspaces of $\CC^k$ in connected proper subsets. Moreover, we show that any
Runge FB domain is the attracting basin for a sequence of automorphisms of
$\CC^k$, although not necessarily if you only allow iteration of one
automorphism. We also show that an increasing sequence of Runge $\CC^k$'s is a
$\CC^k$.


  Optimal transport distances, otherwise known as Wasserstein distances, have
recently drawn ample attention in computer vision and machine learning as a
powerful discrepancy measure for probability distributions. The recent
developments on alternative formulations of the optimal transport have allowed
for faster solutions to the problem and has revamped its practical applications
in machine learning. In this paper, we exploit the widely used kernel methods
and provide a family of provably positive definite kernels based on the Sliced
Wasserstein distance and demonstrate the benefits of these kernels in a variety
of learning tasks. Our work provides a new perspective on the application of
optimal transport flavored distances through kernel methods in machine learning
tasks.


  We propose a method to realize a robust quantum random number generator based
on bosonic stimulation. A particular implementation that employs weak coherent
pulses and conventional avalanche photo-diode detectors (APDs) is discussed.


  We present Kepler light curves and optical spectroscopy of twenty X-ray
bright stars located in the Kepler field of view. The stars, spectral type FK,
show evidence for rapid rotation including chromospheric activity 100 times or
more above the Sun at maximum and flaring behavior in their light curves.
Eighteen of our objects appear to be (sub)giants and may belong to the class of
FK Com variables, that is evolved rapidly spinning single stars with no
excretion disk and high levels of chromospheric activity. Such stars are rare
and are likely the result of W UMa binary mergers, a process believed to
produce the FK Com class of variable and their descendants. The FK Com stage,
including the presence of an excretion disk, is short-lived but leads to
longer-lived stages consisting of single, rapidly rotating evolved (sub)giants
with high levels of stellar activity.


  Pre-trained language models in the past years have shown exponential growth
in model parameters and compute time. ELECTRA is a novel approach for improving
the compute efficiency of pre-trained language models (e.g. BERT) based on
masked language modeling (MLM) by addressing the sample inefficiency problem
with the replaced token detection (RTD) task. Our work proposes adaptive early
exit strategy to maximize the efficiency of the pre-training process by
relieving the model's subsequent layers of the need to process latent features
by leveraging earlier layer representations. Moreover, we evaluate an initial
approach to the problem that has not succeeded in maintaining the accuracy of
the model while showing a promising compute efficiency by thoroughly
investigating the necessity of the generator module of ELECTRA.


  The full potential all electron linearized augmented plane wave plus local
orbitals (FP-LAPW + lo) method, as implemented in the suite of software WIEN2K,
has been used to systematically investigate the structural, electronic, and
magnetic properties of the actinide compounds AnN (An = Ac, Th, Pa, U, Np, Pu,
Am). The theoretical formalism used is the generalized gradient approximation
to density functional theory (GGA-DFT) with the Perdew-Burke-Ernzerhof (PBE)
exchange-correlation functional. Each compound has been studied at six levels
of theory: non-magnetic (NM), non-magnetic with spin-orbit coupling (NM+SOC),
ferromagnetic (FM), ferromagnetic with spin-orbit coupling (FM+SOC),
anti-ferromagnetic (AFM), and anti-ferromagnetic with spin-orbit coupling
(AFM+SOC). The structural parameters, bulk moduli, densities of states, and
charge distributions have been computed and compared to available experimental
data and other theoretical calculations published in the literature. The total
energy calculations indicate that the lowest energy structures of AcN, ThN, and
PaN are degenerate at the NM+SOC, FM+SOC, and AFM+SOC levels of theory with
vanishing total magnetic moments in the FM+SOC and AFM+SOC cases, making the
ground states essentially non-magnetic with spin-orbit interaction. The ground
states of UN, NpN, PuN, and AmN are found to be FM+SOC at the level of theory
used in the present computations. The nature of the interactions between the
actinide metals and nitrogen atom, and the implications on 5f electron
delocalization and localization are discussed in detail.


  We calculate the two-loop vertex function for the crossed topology, and for
arbitrary masses and external momenta. We derive a double integral
representation, suitable for a numerical evaluation by a Gaussian quadrature.
Real and imaginary parts of the diagram can be calculated separately.


  In these proceedings we discuss the measurement of Bose-Einstein momentum
correlation function of pairs of charged hadrons in PbPb collisions at 5.02
TeV. We describe the measured correlations with correlation functions derived
from Levy type source distributions. Using a transverse momentum and centrality
binning, we extract the correlation strength parameter lambda, Levy index alpha
and Levy scale parameter R as a function of pair transverse mass mT, for
various centralities.


  We introduce a canonical method for transforming a discrete sequential data
set into an associated rough path made up of lead-lag increments. In
particular, by sampling a $d$-dimensional continuous semimartingale $X:[0,1]
\rightarrow \mathbb{R}^d$ at a set of times $D=(t_i)$, we construct a piecewise
linear, axis-directed process $X^D: [0,1] \rightarrow\mathbb{R}^{2d}$ comprised
of a past and future component. We call such an object the Hoff process
associated with the discrete data $\{X_{t}\}_{t_i\in D}$. The Hoff process can
be lifted to its natural rough path enhancement and we consider the question of
convergence as the sampling frequency increases. We prove that the It\^{o}
integral can be recovered from a sequence of random ODEs driven by the
components of $X^D$. This is in contrast to the usual Stratonovich integral
limit suggested by the classical Wong-Zakai Theorem. Such random ODEs have a
natural interpretation in the context of mathematical finance.


  Wavelength division multiplexing (WDM) and non-orthogonal multiple access
(NOMA) are employed in a visible light communication (VLC) system to increase
the capacity of the system. The system is evaluated using two different
scenarios focusing on power and data rate, where the first scenario is based on
fair power allocation while the second scenario provides equal power
allocation. Data rate variation is evaluated as a function of the users
positioning and mobility. In both scenarios the proposed NOMA-WDM system
achieved higher data rate NOMA system.


  Different scattering mechanisms in graphene are explored and conductivity is
calculated within the Boltzmann transport theory. We provide results for
short-range scattering using the Random Phase Approximation for electron
screening, as well as analytical expressions for the dependence of conductivity
on the dielectric constant of the substrate. We further examine the effect of
ripples on the transport using a surface roughness model developed for
semiconductor heterostructures. We find that close to the Dirac point, \sigma
\sim n^\beta, where \beta=1,0,-2 for Coulomb, short-range and surface roughness
respectively; implying that Coulomb scattering dominates over both short-range
and surface roughness scattering at low density.


  We present the current optical design for the IRIS Atmospheric Dispersion
Corrector (ADC). The ADC is designed for residual dispersions less than ~1 mas
across a given passband at elevations of 25 degrees. Since the last report, the
area of the IRIS Imager has increased by a factor of four, and the pupil size
has increased from 75 to 90mm, both of which contribute to challenges with the
design. Several considerations have led to the current design: residual
dispersion, amount of introduced distortion, glass transmission, glass
availability, and pupil displacement. In particular it was found that there are
significant distortions that appear (two different components) that can lead to
image blur over long exposures. Also, pupil displacement increases the
wavefront error at the imager focus. We discuss these considerations, discuss
the compromises, and present the final design choice and expected performance.


  We report new rogue wave patterns in the nonlinear Schr\"{o}dinger equation.
These patterns include heart-shaped structures, fan-shaped sectors, and many
others, that are formed by individual Peregrine waves. They appear when
multiple internal parameters in the rogue wave solutions get large.
Analytically, we show that these new patterns are described asymptotically by
root structures of Adler-Moser polynomials through a dilation. Since
Adler-Moser polynomials are generalizations of the Yablonskii-Vorob'ev
polynomial hierarchy and contain free complex parameters, these new rogue
patterns associated with Adler-Moser polynomials are much more diverse than
previous rogue patterns associated with the Yablonskii-Vorob'ev polynomial
hierarchy. We also compare analytical predictions of these patterns to true
solutions and demonstrate good agreement between them.


  By applying a variational principle on a magnetic system within the framework
of extended irreversible thermodynamics, we find that the presence of a
temperature gradient in a ferromagnet leads to a generalisation of the
Landau-Lifshitz equation with an additional magnetic induction field
proportional to the temperature gradient. This field modulates the damping of
the magnetic excitation. It can increase or decrease the damping, depending on
the orientation of the magnetisation wave-vector with respect to the
temperature gradient. This variational approach confirms the existence of the
Magnetic Seebeck effect which was derived from thermodynamics and provides a
quantitative estimate of the strength of this effect.


  It has been found that functions can oscillate locally much faster than their
Fourier transform would suggest is possible - a phenomenon called
superoscillation. Here, we consider the case of superoscillating wave functions
in quantum mechanics. We find that they possess rather unusual properties which
raise measurement theoretic, thermodynamic and information theoretic issues. We
explicitly determine the wave functions with the most pronounced
superoscillations, together with their scaling behavior. We also address the
question how superoscillating wave functions could be produced.


  Formal logic has often been seen as uniquely placed to analyze mathematical
argumentation. While formal logic is certainly necessary for a complete
understanding of mathematical practice, it is not sufficient. Important aspects
of mathematical reasoning closely resemble patterns of reasoning in
nonmathematical domains. Hence the tools developed to understand informal
reasoning, collectively known as argumentation theory, are also applicable to
much mathematical argumentation. This chapter investigates some of the details
of that application. Consideration is given to the many contrasting meanings of
the word ``argument''; to some of the specific argumentation-theoretic tools
that have been applied to mathematics, notably Toulmin layouts and
argumentation schemes; to some of the different ways that argumentation is
implicated in mathematical practices; and to the social aspects of mathematical
argumentation.


  Let $X$ be a normal algebraic variety over a finitely generated field $k$ of
characteristic zero, and let $\ell$ be a prime. Say that a continuous
$\ell$-adic representation $\rho$ of $\pi_1^{\text{\'et}}(X_{\bar k})$ is
arithmetic if there exists a representation $\tilde \rho$ of a finite index
subgroup of $\pi_1^{\text{\'et}}(X)$, with $\rho$ a subquotient of
$\tilde\rho|_{\pi_1(X_{\bar k})}$. We show that there exists an integer $N=N(X,
\ell)$ such that every nontrivial, semisimple arithmetic representation of
$\pi_1^{\text{\'et}}(X_{\bar k})$ is nontrivial mod $\ell^N$. As a corollary,
we prove that any nontrivial semisimple representation of
$\pi_1^{\text{\'et}}(X_{\bar k})$, which arises from geometry, is nontrivial
mod $\ell^N$.


  Within Lloyds Banking Group the heritage HBOS Corporate division deals with
Corporate loans, and is required to assess these loans for risk in accordance
with the Basle Accord regulations. Statistical Risk Rating models are developed
by the risk analysts to assess the obligors credit worthiness. It is necessary
then to provide the bankers who originated the loan ('Relationship Managers' or
RMs) with an assessment tool to generate the loan rating upon which they base
their lending decisions. Heritage HBoS Corporate required a new model build
system for holding its Risk Rating models in 2006 as a result of more complex
models being created to comply with the Basle Accord. The use of Excel was
promoted by the IT department for a number of reasons; the Excel solution now
in use is reviewed in this paper.


  We consider the problem of offline reinforcement learning with model-based
control, whose goal is to learn a dynamics model from the experience replay and
obtain a pessimism-oriented agent under the learned model. Current model-based
constraint includes explicit uncertainty penalty and implicit conservative
regularization that pushes Q-values of out-of-distribution state-action pairs
down and the in-distribution up. While the uncertainty estimation, on which the
former relies on, can be loosely calibrated for complex dynamics, the latter
performs slightly better. To extend the basic idea of regularization without
uncertainty quantification, we propose distributionally robust offline
model-based policy optimization (DROMO), which leverages the ideas in
distributionally robust optimization to penalize a broader range of
out-of-distribution state-action pairs beyond the standard empirical
out-of-distribution Q-value minimization. We theoretically show that our method
optimizes a lower bound on the ground-truth policy evaluation, and it can be
incorporated into any existing policy gradient algorithms. We also analyze the
theoretical properties of DROMO's linear and non-linear instantiations.


  We present the first K'-band, long-baseline interferometric observations of
the northern Be stars gamma Cas, phi Per, zeta Tau, and kappa Dra. The
measurements were made with multiple telescope pairs of the CHARA Array
interferometer, and in every case the observations indicate that the
circumstellar disks of the targets are resolved. We fit the interferometric
visibilities with predictions from a simple disk model that assumes an
isothermal gas in Keplerian rotation. We derive fits of the four model
parameters (disk base density, radial density exponent, disk normal
inclination, and position angle) for each of the targets. The resulting
densities are in broad agreement with prior studies of the IR excess flux and
the resulting orientations generally agree with those from interferometric
H-alpha and continuum polarimetric observations. We find that the angular size
of the K' disk emission is smaller than that determined for the H-alpha
emission, and we argue that the difference is the result of a larger H-alpha
opacity and the relatively larger neutral hydrogen fraction with increasing
disk radius. All the targets are known binaries with faint companions, and we
find that companions appear to influence the interferometric visibilities in
the cases of phi Per and kappa Dra. We also present contemporaneous
observations of the H-alpha, H-gamma, and Br-gamma emission lines. Synthetic
model profiles of these lines that are based on the same disk inclination and
radial density exponent as derived from the CHARA Array observations match the
observed emission line strength if the disk base density is reduced by
approximately 1.7 dex.


  Long-tailed datasets are very frequently encountered in real-world use cases
where few classes or categories (known as majority or head classes) have higher
number of data samples compared to the other classes (known as minority or tail
classes). Training deep neural networks on such datasets gives results biased
towards the head classes. So far, researchers have come up with multiple
weighted loss and data re-sampling techniques in efforts to reduce the bias.
However, most of such techniques assume that the tail classes are always the
most difficult classes to learn and therefore need more weightage or attention.
Here, we argue that the assumption might not always hold true. Therefore, we
propose a novel approach to dynamically measure the instantaneous difficulty of
each class during the training phase of the model. Further, we use the
difficulty measures of each class to design a novel weighted loss technique
called `class-wise difficulty based weighted (CDB-W) loss' and a novel data
sampling technique called `class-wise difficulty based sampling (CDB-S)'. To
verify the wide-scale usability of our CDB methods, we conducted extensive
experiments on multiple tasks such as image classification, object detection,
instance segmentation and video-action classification. Results verified that
CDB-W loss and CDB-S could achieve state-of-the-art results on many
class-imbalanced datasets such as ImageNet-LT, LVIS and EGTEA, that resemble
real-world use cases.


  We present high signal-to-noise ratio Gemini and MMT spectroscopy of the
optical afterglow of the gamma-ray burst (GRB) 130606A at redshift z=5.913,
discovered by Swift. This is the first high-redshift GRB afterglow to have
spectra of comparable quality to those of z~6 quasars. The data exhibit a
smooth continuum at near-infrared wavelengths that is sharply cut off blueward
of 8410 Angs due to absorption from Ly-alpha at redshift z~5.91, with some flux
transmitted through the Ly-alpha forest between 7000-7800 Angs. We use column
densities inferred from metal absorption lines to constrain the metallicity of
the host galaxy between a lower limit of [Si/H]>-1.7 and an upper limit of
[S/H]<-0.5 set by the non-detection of S II absorption. We demonstrate
consistency between the dramatic evolution in the transmission fraction of
Ly-alpha seen in this spectrum over the redshift range z=4.9 to 5.85 with that
previously measured from observations of high-redshift quasars. There is an
extended redshift interval of Delta-z=0.12 in the Ly-alpha forest at z=5.77
with no detected transmission, leading to a 3-sigma upper limit on the mean
Ly-alpha transmission fraction of <0.2% (or tau_eff(Ly-alpha) > 6.4). This is
comparable to the lowest-redshift Gunn-Peterson troughs found in quasar
spectra. We set a 2-sigma upper limit of 0.11 on the neutral fraction of the
IGM at the redshift of the GRB from the lack of a Ly-alpha red damping wing,
assuming a model with a constant neutral density. Some Ly-beta and Ly-gamma
transmission is detected in this redshift window, indicating that it is not
completely opaque, and hence that the IGM is nonetheless mostly ionized at
these redshifts. GRB 130606A thus for the first time realizes the promise of
GRBs as probes of the first galaxies and cosmic reionization.


  Automatically understanding emotions from visual data is a fundamental task
for human behaviour understanding. While models devised for Facial Expression
Recognition (FER) have demonstrated excellent performances on many datasets,
they often suffer from severe performance degradation when trained and tested
on different datasets due to domain shift. In addition, as face images are
considered highly sensitive data, the accessibility to large-scale datasets for
model training is often denied. In this work, we tackle the above-mentioned
problems by proposing the first Source-Free Unsupervised Domain Adaptation
(SFUDA) method for FER. Our method exploits self-supervised pretraining to
learn good feature representations from the target data and proposes a novel
and robust cluster-level pseudo-labelling strategy that accounts for in-cluster
statistics. We validate the effectiveness of our method in four adaptation
setups, proving that it consistently outperforms existing SFUDA methods when
applied to FER, and is on par with methods addressing FER in the UDA setting.


  The number of constituent quark (NCQ) scaling behavior of elliptic flow has
been systematically studied at the LHC energy within the framework of a
multiphase transport model (AMPT) in this work. We find that the parameters
used to generate the initial states and the collision centrality are important
for the existence of NCQ scaling even when hadronic rescattering contribution
is off in Pb-Pb collisions of $\sqrt{s_{NN}}=2.76$ TeV. By turning on the
hadron rescattering process, the hadronic evolution impacts are also found to
be significant. Extending the analysis to Pb-Pb collsions of
$\sqrt{s_{NN}}=5.02$ TeV, one would observe similar qualitative features.


  We explore the question whether Lipschitz functions of random variables under
various forms of negative correlation satisfy concentration bounds similar to
McDiarmid's inequality for independent random variables. We prove such a
concentration bound for random variables satisfying the condition of negative
regression, correcting an earlier proof by Dubhashi and Ranjan.


  Many fundamental machine learning tasks can be formulated as a problem of
learning with vector-valued functions, where we learn multiple scalar-valued
functions together. Although there is some generalization analysis on different
specific algorithms under the empirical risk minimization principle, a unifying
analysis of vector-valued learning under a regularization framework is still
lacking. In this paper, we initiate the generalization analysis of regularized
vector-valued learning algorithms by presenting bounds with a mild dependency
on the output dimension and a fast rate on the sample size. Our discussions
relax the existing assumptions on the restrictive constraint of hypothesis
spaces, smoothness of loss functions and low-noise condition. To understand the
interaction between optimization and learning, we further use our results to
derive the first generalization bounds for stochastic gradient descent with
vector-valued functions. We apply our general results to multi-class
classification and multi-label classification, which yield the first bounds
with a logarithmic dependency on the output dimension for extreme multi-label
classification with the Frobenius regularization. As a byproduct, we derive a
Rademacher complexity bound for loss function classes defined in terms of a
general strongly convex function.


  In this article, we study the behaviour of discrete one-dimensional dynamical
systems associated to functions on finite sets. We formalise the global orbit
pattern formed by all the periodic orbits (gop) as the ordered set of periods
when the initial value thumbs the finite set in the increasing order. We are
able to predict, using closed formulas, the number of gop for the set
$\mathcal{F}_N$ of all the functions on $X$. We also explore by computer
experiments special subsets of $\mathcal{F}_N$ in which interesting patterns of
gop are found.


  Extreme events are an important theme in various areas of science because of
their typically devastating effects on society and their scientific
complexities. The latter is particularly true if the underlying dynamics does
not lead to independent extreme events as often observed in natural systems.
Here, we focus on this case and consider stationary stochastic processes that
are characterized by long-range memory and heavy-tailed distributions, often
called fractional L\'evy noise. While the size distribution of extreme events
is not affected by the long-range memory in the asymptotic limit and remains a
Fr\'echet distribution, there are strong finite-size effects if the memory
leads to persistence in the underlying dynamics. Moreover, we show that this
persistence is also present in the extreme events, which allows one to make a
time-dependent hazard assessment of future extreme events based on events
observed in the past. This has direct applications in the field of space
weather as we discuss specifically for the case of the solar power influx into
the magnetosphere. Finally, we show how the statistics of records, or
record-breaking extreme events, is affected by the presence of long-range
memory.


  The rare-earth based ternary intermetallic compounds $R_2TX_3$ ($R$ =
rare-earth, $T$ = transition-metal, $X$ = Si, Ge, Ga, In) have attracted
considerable interest due to a wide range of interesting low temperature
properties. Here we investigate the magnetic state of Nd$_{2}$PdSi$_{3}$ using
neutron diffraction, muon spin relaxation ($\mu$SR) and inelastic neutron
scattering (INS). This compound appears anomalous among the $R_{2}$PdSi$_{3}$
series, since it was proposed to order ferromagnetically, whereas others in
this series are antiferromagnets. Although some members of the $R_2TX_3$ series
have been reported to form ordered superstructures, our data are well described
by Nd$_{2}$PdSi$_{3}$ adopting the AlB$_2$-type structure with a single Nd
site, and we do not find evidence for superlattice peaks in neutron
diffraction. Our results confirm the onset of long range magnetic order below
$T_0=17$~K, where the whole sample enters the ordered state. Neutron
diffraction measurements establish the presence of a ferromagnetic component in
this compound, as well as an antiferromagnetic one which has a propagation
vector $\mathbf{k_2}=(1/2,1/2,1/4-\delta)$ with a temperature dependent
$\delta\approx0.02-0.04$, and moments orientated exclusively along the
$c$-axis. $\mu$SR measurements suggest that these components coexist on a
microscopic level, and therefore the magnetic structure of Nd$_{2}$PdSi$_{3}$
is predominantly ferromagnetic, with a sinusoidally modulated antiferromagnetic
contribution which reaches a maximum amplitude at 11~K, and becomes smaller
upon further decreasing the temperature. INS results show the presence of
crystalline-electric field (CEF) excitations above $T_0$, and from our analysis
we propose a CEF level scheme.


  We search for persistent and quasi-periodic release events of streamer blobs
during 2007 with the Large Angle Spectrometric Coronagraph on the \textit{Solar
and Heliospheric Observatory} and assess the velocity of the slow solar wind
along the plasma sheet above the corresponding streamer by measuring the
dynamic parameters of blobs. We find 10 quasi-periodic release events of
streamer blobs lasting for three to four days. In each day of these events, we
observe three-five blobs. The results are in line with previous studies using
data observed near the last solar minimum. Using the measured blob velocity as
a proxy for that of the mean flow, we suggest that the velocity of the
background slow solar wind near the Sun can vary significantly within a few
hours. This provides an observational manifestation of the large velocity
variability of the slow solar wind near the Sun.


  The Emergence of Artificial Intelligence (AI) has significantly impacted our
engagement with violence, sparking ethical deliberations regarding the
algorithmic creation of violent imagery. This paper scrutinizes the "Gore
Diffusion LoRA Model," an innovative AI model proficient in generating
hyper-realistic visuals portraying intense violence and bloodshed. Our
exploration encompasses the model's technical intricacies, plausible
applications, and the ethical quandaries inherent in its utilization. We
contend that the creation and implementation of such models warrant a
meticulous discourse concerning the convergence of AI, art, and violence.
Furthermore, we advocate for a structured framework advocating responsible
development and ethical deployment of these potent technologies.


  Information processing networks are the result of local rewiring rules. In
many instances, such rules promote links where the activity at the two end
nodes is positively correlated. The conceptual problem we address is what
network architecture prevails under such rules and how does the resulting
network, in turn, constrain the dynamics. We focus on a simple toy model that
captures the interplay between link self-reinforcement and a Self-Organised
Critical dynamics in a simple way. Our main finding is that, under these
conditions, a core of densely connected nodes forms spontaneously. Moreover, we
show that the appearance of such clustered state can be dynamically regulated
by a fatigue mechanism, eventually giving rise to non-trivial avalanche
exponents.


  In this work we explore how fine-grained differences between the shapes of
common objects are expressed in language, grounded on images and 3D models of
the objects. We first build a large scale, carefully controlled dataset of
human utterances that each refers to a 2D rendering of a 3D CAD model so as to
distinguish it from a set of shape-wise similar alternatives. Using this
dataset, we develop neural language understanding (listening) and production
(speaking) models that vary in their grounding (pure 3D forms via point-clouds
vs. rendered 2D images), the degree of pragmatic reasoning captured (e.g.
speakers that reason about a listener or not), and the neural architecture
(e.g. with or without attention). We find models that perform well with both
synthetic and human partners, and with held out utterances and objects. We also
find that these models are amenable to zero-shot transfer learning to novel
object classes (e.g. transfer from training on chairs to testing on lamps), as
well as to real-world images drawn from furniture catalogs. Lesion studies
indicate that the neural listeners depend heavily on part-related words and
associate these words correctly with visual parts of objects (without any
explicit network training on object parts), and that transfer to novel classes
is most successful when known part-words are available. This work illustrates a
practical approach to language grounding, and provides a case study in the
relationship between object shape and linguistic structure when it comes to
object differentiation.


  We consider a non-Hermitian generalization of the Kitaev model and study the
existence of stable Majorana zero energy modes. We show that they exist in the
limit of zero chemical potential even if balanced gain and loss are randomly
distributed along the lattice. We show that Majorana zero modes also appear if
the chemical potential is different from zero provided that not the full
Hamiltonian but the non-Hermitian part of the Hamiltonian is PT symmetric.


  We apply the notion of asymptotic iteration method (AIM) to determine
eigenvalues of the bosonic Hamiltonians that include a wide class of quantum
optical models. We consider solutions of the Hamiltonians, which are even
polynomials of the fourth order with the respect to Boson operators. We also
demonstrate applicability of the method for obtaining eigenvalues of the simple
Lie algebraic structures. Eigenvalues of the multi-boson Hamiltonians have been
obtained by transforming in the form of the single boson Hamiltonian in the
framework of AIM.


  Deep neural networks (DNN) and Gaussian processes (GP) are two powerful
models with several theoretical connections relating them, but the relationship
between their training methods is not well understood. In this paper, we show
that certain Gaussian posterior approximations for Bayesian DNNs are equivalent
to GP posteriors. This enables us to relate solutions and iterations of a
deep-learning algorithm to GP inference. As a result, we can obtain a GP kernel
and a nonlinear feature map while training a DNN. Surprisingly, the resulting
kernel is the neural tangent kernel. We show kernels obtained on real datasets
and demonstrate the use of the GP marginal likelihood to tune hyperparameters
of DNNs. Our work aims to facilitate further research on combining DNNs and GPs
in practical settings.


  In Reinforcement Learning-based Recommender Systems (RLRS), the complexity
and dynamism of user interactions often result in high-dimensional and noisy
state spaces, making it challenging to discern which aspects of the state are
truly influential in driving the decision-making process. This issue is
exacerbated by the evolving nature of user preferences and behaviors, requiring
the recommender system to adaptively focus on the most relevant information for
decision-making while preserving generaliability. To tackle this problem, we
introduce an innovative causal approach for decomposing the state and
extracting \textbf{C}ausal-\textbf{I}n\textbf{D}ispensable \textbf{S}tate
Representations (CIDS) in RLRS. Our method concentrates on identifying the
\textbf{D}irectly \textbf{A}ction-\textbf{I}nfluenced \textbf{S}tate Variables
(DAIS) and \textbf{A}ction-\textbf{I}nfluence \textbf{A}ncestors (AIA), which
are essential for making effective recommendations. By leveraging conditional
mutual information, we develop a framework that not only discerns the causal
relationships within the generative process but also isolates critical state
variables from the typically dense and high-dimensional state representations.
We provide theoretical evidence for the identifiability of these variables.
Then, by making use of the identified causal relationship, we construct
causal-indispensable state representations, enabling the training of policies
over a more advantageous subset of the agent's state space. We demonstrate the
efficacy of our approach through extensive experiments, showcasing our method
outperforms state-of-the-art methods.


  The interplay of confinement and Coulomb interactions in quantum dots can
lead to strongly correlated phases differing qualitatively from the Fermi
liquid behavior. We explore how the presence of magnetic impurities in quantum
dots can provide additional opportunities to study correlation effects and the
resulting ordering in carrier and impurity spin. By employing exact
diagonalization we reveal that seemingly simple two-carrier quantum dots lead
to a rich phase diagram. We propose experiments to verify our predictions, in
particular we discuss interband optical transitions as a function of
temperature and magnetic field.


  Reconfigurable intelligent surface (RIS) has shown promise in providing
apparent benefits in wireless communication and positioning. Most of the
existing research focuses on the ability of RIS to adjust the direction of
propagation. In this paper, we present another application based on RIS, named
multipath labeling, which intends to inject a label on propagation paths
through the RISs. Each labeled path contains spatial knowledge between the RIS
and the receiver, thus opening the door for sensing the surrounding world by
RISs. The critical challenge is how the labeled paths can be extracted and
distinguish from other paths, especially with multipath effects. To address
this challenge, we present a complete labeling procedure consisting of channel
flipping, parameter extraction, and RIS association. Simulations under a
practice ray-tracing model reveal the feasibility of the proposed labeling
technique even under the sub 6GHz channels with severe multipath effect. We
also apply the multipath labeling technique to localization, which assists user
equipment in obtaining its precise location through only a single base station.


  In this paper, we consider group classification of local and quasi-local
symmetries for a general fourth-order evolution equations in one spatial
variable. Following the approach developed by Zhdanov and Lahno, we construct
all inequivalent evolution equations belonging to the class under study which
admit either semi-simple Lie groups or solvable Lie groups. The obtained lists
of invariant equations (up to a local change of variables) contain both the
well-known equations and a variety of new ones possessing rich symmetry. Based
on the results on the group classification for local symmetries, the group
classification for quasi-local symmetries of the equations is also given.


  In this article, the Curie-Weiss type behavior and the appearance of an
"interaction" or "ordering" temperature for a collection of magnetic
nanoparticles is explored theoretically. We show that some systems where an
interaction temperature is reported are too dilute for dipolar interactions to
play a role unless at least some of the particles are clumped together. We then
show using the most simple type of clumps (particle pairs) that positive and
negative interaction temperatures are possible due to dipolar interactions. The
clump orientation dramatically changes this result. Finally, we show that an
apparent interaction temperature can be measured in magnetic nanoparticle
systems that have no interactions between particles, due to some alignment of
anisotropy easy axes. These results show that nanoscale physical structures
affect the measured magnetic response of nanoparticles.