  Training large deep learning models requires parallelization techniques to
scale. In existing methods such as Data Parallelism or ZeRO-DP, micro-batches
of data are processed in parallel, which creates two drawbacks: the total
memory required to store the model's activations peaks at the end of the
forward pass, and gradients must be simultaneously averaged at the end of the
backpropagation step. We propose Cyclic Data Parallelism, a novel paradigm
shifting the execution of the micro-batches from simultaneous to sequential,
with a uniform delay. At the cost of a slight gradient delay, the total memory
taken by activations is constant, and the gradient communications are balanced
during the training step. With Model Parallelism, our technique reduces the
number of GPUs needed, by sharing GPUs across micro-batches. Within the ZeRO-DP
framework, our technique allows communication of the model states with
point-to-point operations rather than a collective broadcast operation. We
illustrate the strength of our approach on the CIFAR-10 and ImageNet datasets.


  With advances in data collection technologies, tensor data is assuming
increasing prominence in many applications and the problem of supervised tensor
learning has emerged as a topic of critical significance in the data mining and
machine learning community. Conventional methods for supervised tensor learning
mainly focus on learning kernels by flattening the tensor into vectors or
matrices, however structural information within the tensors will be lost. In
this paper, we introduce a new scheme to design structure-preserving kernels
for supervised tensor learning. Specifically, we demonstrate how to leverage
the naturally available structure within the tensorial representation to encode
prior knowledge in the kernel. We proposed a tensor kernel that can preserve
tensor structures based upon dual-tensorial mapping. The dual-tensorial mapping
function can map each tensor instance in the input space to another tensor in
the feature space while preserving the tensorial structure. Theoretically, our
approach is an extension of the conventional kernels in the vector space to
tensor space. We applied our novel kernel in conjunction with SVM to real-world
tensor classification problems including brain fMRI classification for three
different diseases (i.e., Alzheimer's disease, ADHD and brain damage by HIV).
Extensive empirical studies demonstrate that our proposed approach can
effectively boost tensor classification performances, particularly with small
sample sizes.


  We study the performance of Empirical Risk Minimization in noisy phase
retrieval problems, indexed by subsets of $\R^n$ and relative to subgaussian
sampling; that is, when the given data is $y_i=\inr{a_i,x_0}^2+w_i$ for a
subgaussian random vector $a$, independent noise $w$ and a fixed but unknown
$x_0$ that belongs to a given subset of $\R^n$.
  We show that ERM produces $\hat{x}$ whose Euclidean distance to either $x_0$
or $-x_0$ depends on the gaussian mean-width of the indexing set and on the
signal-to-noise ratio of the problem. The bound coincides with the one for
linear regression when $\|x_0\|_2$ is of the order of a constant. In addition,
we obtain a minimax lower bound for the problem and identify sets for which ERM
is a minimax procedure. As examples, we study the class of $d$-sparse vectors
in $\R^n$ and the unit ball in $\ell_1^n$.


  Solar flare X-ray emission results from rapidly increasing temperatures and
emission measures in flaring active region loops. To date, observations from
the X-Ray Sensor (XRS) onboard the Geostationary Operational Environmental
Satellite (GOES) have been used to derive these properties, but have been
limited by a number of factors, including the lack of a consistent background
subtraction method capable of being automatically applied to large numbers of
flares. In this paper, we describe an automated temperature and emission
measure-based background subtraction method (TEBBS), which builds on the
methods of Bornmann (1990). Our algorithm ensures that the derived temperature
is always greater than the instrumental limit and the pre-flare background
temperature, and that the temperature and emission measure are increasing
during the flare rise phase. Additionally, TEBBS utilizes the improved
estimates of GOES temperatures and emission measures from White et al. (2005).
TEBBS was successfully applied to over 50,000 solar flares occurring over
nearly three solar cycles (1980-2007), and used to create an extensive catalog
of the solar flare thermal properties. We confirm that the peak emission
measure and total radiative losses scale with background subtracted GOES X-ray
flux as power-laws, while the peak temperature scales logarithmically. As
expected, the peak emission measure shows an increasing trend with peak
temperature, although the total radiative losses do not. While these results
are comparable to previous studies, we find that flares of a given GOES class
have lower peak temperatures and higher peak emission measures than previously
reported. The resulting TEBBS database of thermal flare plasma properties is
publicly available on Solar Monitor (www.solarmonitor.org/TEBBS/) and will be
available on Heliophysics Integrated Observatory (www.helio-vo.eu).


  We expose a double-copy structure in the scattering amplitudes of the generic
Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
theories in four and five dimensions. The Maxwell-Einstein supergravity
amplitudes are obtained through the color/kinematics duality as a product of
two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory
and the other from the dimensional reduction of a bosonic higher-dimensional
pure Yang-Mills theory. We identify a specific symplectic frame in four
dimensions for which the on-shell fields and amplitudes from the double-copy
construction can be identified with the ones obtained from the supergravity
Lagrangian and Feynman-rule computations. The Yang-Mills/Einstein supergravity
theories are obtained by gauging a compact subgroup of the isometry group of
their Maxwell-Einstein counterparts. For the generic Jordan family this process
is identified with the introduction of cubic scalar couplings on the bosonic
gauge-theory side, which through the double copy are responsible for the
non-abelian vector interactions in the supergravity theory. As a demonstration
of the power of this structure, we present explicit computations at tree-level
and one loop. The double-copy construction allows us to obtain compact
expressions for the supergravity superamplitudes which are naturally organized
as polynomials in the gauge coupling constant.


  In this paper, we study differentially private (DP) algorithms for computing
the geometric median (GM) of a dataset: Given $n$ points, $x_1,\dots,x_n$ in
$\mathbb{R}^d$, the goal is to find a point $\theta$ that minimizes the sum of
the Euclidean distances to these points, i.e., $\sum_{i=1}^{n} \|\theta -
x_i\|_2$. Off-the-shelf methods, such as DP-GD, require strong a priori
knowledge locating the data within a ball of radius $R$, and the excess risk of
the algorithm depends linearly on $R$. In this paper, we ask: can we design an
efficient and private algorithm with an excess error guarantee that scales with
the (unknown) radius containing the majority of the datapoints? Our main
contribution is a pair of polynomial-time DP algorithms for the task of private
GM with an excess error guarantee that scales with the effective diameter of
the datapoints. Additionally, we propose an inefficient algorithm based on the
inverse smooth sensitivity mechanism, which satisfies the more restrictive
notion of pure DP. We complement our results with a lower bound and demonstrate
the optimality of our polynomial-time algorithms in terms of sample complexity.


  Tiny deep learning on microcontroller units (MCUs) is challenging due to the
limited memory size. We find that the memory bottleneck is due to the
imbalanced memory distribution in convolutional neural network (CNN) designs:
the first several blocks have an order of magnitude larger memory usage than
the rest of the network. To alleviate this issue, we propose a generic
patch-by-patch inference scheduling, which operates only on a small spatial
region of the feature map and significantly cuts down the peak memory. However,
naive implementation brings overlapping patches and computation overhead. We
further propose network redistribution to shift the receptive field and FLOPs
to the later stage and reduce the computation overhead. Manually redistributing
the receptive field is difficult. We automate the process with neural
architecture search to jointly optimize the neural architecture and inference
scheduling, leading to MCUNetV2. Patch-based inference effectively reduces the
peak memory usage of existing networks by 4-8x. Co-designed with neural
networks, MCUNetV2 sets a record ImageNet accuracy on MCU (71.8%), and achieves
>90% accuracy on the visual wake words dataset under only 32kB SRAM. MCUNetV2
also unblocks object detection on tiny devices, achieving 16.9% higher mAP on
Pascal VOC compared to the state-of-the-art result. Our study largely addressed
the memory bottleneck in tinyML and paved the way for various vision
applications beyond image classification.


  An improved generator for continuous unitary transformations is introduced to
describe systems with unstable quasiparticles. Its general properties are
derived and discussed. To illustrate this approach we investigate the
asymmetric antiferromagnetic spin-1/2 Heisenberg ladder which allows for
spontaneous triplon decay. We present results for the low energy spectrum and
the momentum resolved spectral density of this system. In particular, we show
the resonance behavior of the decaying triplon explicitly.


  As an important research topic in computer vision, fine-grained
classification which aims to recognition subordinate-level categories has
attracted significant attention. We propose a novel region based ensemble
learning network for fine-grained classification. Our approach contains a
detection module and a module for classification. The detection module is based
on the faster R-CNN framework to locate the semantic regions of the object. The
classification module using an ensemble learning method, which trains a set of
sub-classifiers for different semantic regions and combines them together to
get a stronger classifier. In the evaluation, we implement experiments on the
CUB-2011 dataset and the result of experiments proves our method s efficient
for fine-grained classification. We also extend our approach to remote scene
recognition and evaluate it on the NWPU-RESISC45 dataset.


  In this paper, we study the energy conversion and spectra in a corona current
sheet by 2.5-dimensional MHD numerical simulations. Numerical results show that
many Petschek-like fine structures with slow-mode shocks mediated by plasmoid
instabilities develop during the magnetic reconnection process. The termination
shocks can also be formed above the primary magnetic island and at the head of
secondary islands. These shocks play important roles in generating thermal
energy in a corona current sheet. For a numerical simulation with initial
conditions close to the solar corona environment, the ratio of the generated
thermal energy to the total dissipated magnetic energy is around $1/5$ before
secondary islands appear. After secondary islands appear, the generated thermal
energy starts to increase sharply and this ratio can reach a value about $3/5$.
In an environment with a relatively lower plasma density and plasma $\beta$,
the plasma can be heated to a much higher temperature. After secondary islands
appear, the one dimensional energy spectra along the current sheet do not
behave as a simple power law and the spectrum index increases with the wave
number. The average spectrum index for the magnetic energy spectrum along the
current sheet is about $1.8$. The two dimensional spectra intuitively show that
part of the high energy is cascaded to large $kx$ and $ky$ space after
secondary islands appear. The plasmoid distribution function calculated from
numerical simulations behaves as a power law closer to $f(\psi) \sim \psi^{-1}$
in the intermediate $\psi$ regime. By using $\eta_{eff} = v_{inflow}\cdot L$,
the effective magnetic diffusivity is estimated about
$10^{11}\sim10^{12}$~m$^2$\,s$^{-1}$.


  We present the open-source $\texttt{C++}$ library $\texttt{FireFly}$ for the
reconstruction of multivariate rational functions over finite fields. We
discuss the involved algorithms and their implementation. As an application, we
use $\texttt{FireFly}$ in the context of integration-by-parts reductions and
compare runtime and memory consumption to a fully algebraic approach with the
program $\texttt{Kira}$.


  A new detailed mathematical model for dynamics of immune response to
hepatitis B is proposed, which takes into account contributions from innate and
adaptive immune responses, as well as cytokines. Stability analysis of
different steady states is performed to identify parameter regions where the
model exhibits clearance of infection, maintenance of a chronic infection, or
periodic oscillations. Effects of nucleoside analogues and interferon
treatments are analysed, and the critical drug efficiency is determined.


  Non-topological defects such as grain boundaries abound in pattern forming
systems, arising from local variations of pattern properties such as amplitude,
wavelength, orientation, etc. We introduce the idea of treating such
non-topological defects as spatially localised structures that are embedded in
a background pattern, instead of treating them in an amplitude-phase
decomposition. Using the two-dimensional quadratic-cubic Swift--Hohenberg
equation as an example we obtain fully nonlinear equilibria that contain grain
boundaries which are closed curves containing multiple penta-hepta defects
separating regions of hexagons with different orientations. These states arise
from local orientation mismatch between two stable hexagon patterns, one of
which forms the localised grain and the other its background, and do not
require a subcritical bifurcation connecting them. Multiple robust isolas that
span a wide range of parameters are obtained even in the absence of a unique
Maxwell point, underlining the importance of retaining pinning when analysing
patterns with defects, an effect omitted from the amplitude-phase description.


  We define a class of amenable Weyl group elements in the Lie types B, C, and
D, which we propose as the analogues of vexillary permutations in these Lie
types. Our amenable signed permutations index flagged theta and eta
polynomials, which generalize the double theta and eta polynomials of Wilson
and the author. In geometry, we obtain corresponding formulas for the
cohomology classes of symplectic and orthogonal degeneracy loci.


  We present a novel geometric deep learning method to compute the acoustic
scattering properties of geometric objects. Our learning algorithm uses a point
cloud representation of objects to compute the scattering properties and
integrates them with ray tracing for interactive sound propagation in dynamic
scenes. We use discrete Laplacian-based surface encoders and approximate the
neighborhood of each point using a shared multi-layer perceptron. We show that
our formulation is permutation invariant and present a neural network that
computes the scattering function using spherical harmonics. Our approach can
handle objects with arbitrary topologies and deforming models, and takes less
than 1ms per object on a commodity GPU. We have analyzed the accuracy and
perform validation on thousands of unseen 3D objects and highlight the benefits
over other point-based geometric deep learning methods. To the best of our
knowledge, this is the first real-time learning algorithm that can approximate
the acoustic scattering properties of arbitrary objects with high accuracy.


  In overparametrized models, the noise in stochastic gradient descent (SGD)
implicitly regularizes the optimization trajectory and determines which local
minimum SGD converges to. Motivated by empirical studies that demonstrate that
training with noisy labels improves generalization, we study the implicit
regularization effect of SGD with label noise. We show that SGD with label
noise converges to a stationary point of a regularized loss $L(\theta) +\lambda
R(\theta)$, where $L(\theta)$ is the training loss, $\lambda$ is an effective
regularization parameter depending on the step size, strength of the label
noise, and the batch size, and $R(\theta)$ is an explicit regularizer that
penalizes sharp minimizers. Our analysis uncovers an additional regularization
effect of large learning rates beyond the linear scaling rule that penalizes
large eigenvalues of the Hessian more than small ones. We also prove extensions
to classification with general loss functions, SGD with momentum, and SGD with
general noise covariance, significantly strengthening the prior work of Blanc
et al. to global convergence and large learning rates and of HaoChen et al. to
general models.


  We consider the categorical equivalence between crossed modules over
groupoids and double groupoids with thin structures; and by this equivalence,
we prove how normality and quotient concepts are related in these two
categories and give some examples of these objects.


  Sequential tabular data is one of the most commonly used data types in
real-world applications. Different from conventional tabular data, where rows
in a table are independent, sequential tabular data contains rich contextual
and sequential information, where some fields are dynamically changing over
time and others are static. Existing transformer-based approaches analyzing
sequential tabular data overlook the differences between dynamic and static
fields by replicating and filling static fields into each transformer, and
ignore temporal information between rows, which leads to three major
disadvantages: (1) computational overhead, (2) artificially simplified data for
masked language modeling pre-training task that may yield less meaningful
representations, and (3) disregarding the temporal behavioral patterns implied
by time intervals. In this work, we propose FATA-Trans, a model with two field
transformers for modeling sequential tabular data, where each processes static
and dynamic field information separately. FATA-Trans is field- and time-aware
for sequential tabular data. The field-type embedding in the method enables
FATA-Trans to capture differences between static and dynamic fields. The
time-aware position embedding exploits both order and time interval information
between rows, which helps the model detect underlying temporal behavior in a
sequence. Our experiments on three benchmark datasets demonstrate that the
learned representations from FATA-Trans consistently outperform
state-of-the-art solutions in the downstream tasks. We also present
visualization studies to highlight the insights captured by the learned
representations, enhancing our understanding of the underlying data. Our codes
are available at https://github.com/zdy93/FATA-Trans.


  Age of Information (AoI) has gained importance as a Key Performance Indicator
(KPI) for characterizing the freshness of information in information-update
systems and time-critical applications. Recent theoretical research on the
topic has generated significant understanding of how various algorithms perform
in terms of this metric on various system models and networking scenarios. In
this paper, by the help of the theoretical results, we analyzed the AoI
behavior on real-life networks, using our two test-beds, addressing IoT
networks and regular computers. Excessive number of AoI measurements are
provided for variations of transport protocols such as TCP, UDP and web-socket,
on wired and wireless links. Practical issues such as synchronization and
selection of hardware along with transport protocol, and their effects on AoI
are discussed. The results provide insight toward application and transport
layer mechanisms for optimizing AoI in real-life networks.


  This work is concerned with a simple model for a polar fluid, a Gaussian
field model based on the excess density and on the polarization. It is a
convenient framework to implement the dielectric properties of correlated
liquids that stem from nanometric correlations between molecules. It allows to
study the effects of coupling terms between density and polarization on the
structure of the fluid. Despite the simplicity of such a model, it can capture
some interesting features of the response functions of water such as the
quasi-resonant longitudinal dielectric susceptibility or the presence of two
maxima in the structure factor. Explicit models of water generate extremely
high computational cost and implicit models sometimes fail to treat properly
the electrostatic interactions. A Gaussian field theory could therefore be an
interesting alternative to describe water.


  Surface-electrode (SE) rf traps are a promising approach to manufacturing
complex ion-trap networks suitable for large-scale quantum information
processing. In this paper we present analytical methods for modeling SE traps
in the gapless plane approximation, and apply these methods to two particular
classes of SE traps. For the SE ring trap we derive analytical expressions for
the trap geometry and strength, and also calculate the depth in the absence of
control fields. For translationally symmetric multipole configurations (analogs
of the linear Paul trap), we derive analytical expressions for electrode
geometry and strength. Further, we provide arbitrarily good approximations of
the trap depth in the absence of static fields and identify the requirements
for obtaining maximal depth. Lastly, we show that the depth of SE multipoles
can be greatly influenced by control fields.


  Growth mixture models are an important tool for detecting group structure in
repeated measures data. Unlike traditional clustering methods, they explicitly
model the repeat measurements on observations, and the statistical framework
they are based on allows for model selection methods to be used to select the
number of clusters. However, the basic growth mixture model makes the
assumption that all of the measurements in the data have grouping
information/separate the clusters. In other clustering contexts, it has been
shown that including non-clustering variables in clustering procedures can lead
to poor estimation of the group structure both in terms of the number of
clusters and cluster membership/parameters. In this paper, we present an
extension of the growth mixture model that allows for incorporation of stepwise
variable selection based on the work done by Maugis et al. (2009) and Raftery
and Dean (2006). Results presented on a simulation study suggest that the
method performs well in correctly selecting the clustering variables and
improves on recovery of the cluster structure compared with the basic growth
mixture model. The paper also presents an application of the model to a
clinical study dataset and concludes with a discussion and suggestions for
directions of future work in this area.


  While the longitudinal field that dominates photospheric network regions has
been studied extensively, small scale transverse fields have recently been
found to be ubiquitous in the quiet internetwork photosphere. Few observations
have captured how this field evolves. We aim to statistically characterise the
magnetic properties and observe the temporal evolution of small scale magnetic
features. We present two high spatial/temporal resolution observations that
reveal the dynamics of two disk centre internetwork regions taken by the new
GRIS/IFU (GREGOR Infrared Spectrograph Integral Field Unit) with the highly
magnetically sensitive Fe I line pair at 15648.52 {\AA} and 15652.87 {\AA}.
With the SIR code, we consider two inversion schemes: scheme 1 (S1), where a
magnetic atmosphere is embedded in a field free medium, and scheme 2 (S2), with
two magnetic models and a fixed stray light component. S1 inversions returned a
median magnetic field strength of 200 and 240 G for the two datasets,
respectively. We consider the median transverse (horizontal) component, among
pixels with Stokes Q or U, and the median unsigned longitudinal (vertical)
component, among pixels with Stokes V, above a noise threshold. We determined
the former to be 263 G and 267 G, and the latter to be 131 G and 145 G, for the
two datasets, respectively. We present three regions of interest (ROIs),
tracking the dynamics of small scale magnetic features. We apply S1 and S2
inversions to specific profiles, and find S2 produces better approximations
when there is evidence of mixed polarities. We find patches of linear
polarization with magnetic flux density between 130 and 150 G, appearing
preferentially at granule/intergranular lane (IGL) boundaries. The weak hG
magnetic field appears to be organised in terms of complex loop structures,
with transverse fields often flanked by opposite polarity longitudinal fields.


  Truss was proposed to study social network data represented by graphs. A
k-truss of a graph is a cohesive subgraph, in which each edge is contained in
at least k-2 triangles within the subgraph. While truss has been demonstrated
as superior to model the close relationship in social networks and efficient
algorithms for finding trusses have been extensively studied, very little
attention has been paid to truss maintenance. However, most social networks are
evolving networks. It may be infeasible to recompute trusses from scratch from
time to time in order to find the up-to-date $k$-trusses in the evolving
networks. In this paper, we discuss how to maintain trusses in a graph with
dynamic updates. We first discuss a set of properties on maintaining trusses,
then propose algorithms on maintaining trusses on edge deletions and
insertions, finally, we discuss truss index maintenance. We test the proposed
techniques on real datasets. The experiment results show the promise of our
work.


  The growing sample of LIGO--Virgo black holes (BHs) opens new perspectives
for the study of massive binary evolution. Here, we study the impact of mass
accretion efficiency and common envelope on the properties of binary BH (BBH)
mergers, by means of population synthesis simulations. We model mass accretion
efficiency with the parameter $f_{\rm MT}\in[0.05,1]$, which represents the
fraction of mass lost from the donor which is effectively accreted by the
companion. Lower values of $f_{\rm MT}$ result in lower BBH merger rate
densities and produce mass spectra skewed towards lower BH masses. Our
hierarchical Bayesian analysis, applied to BBH mergers in the first and second
gravitational wave transient catalogue, yields zero support for values of
$f_{\rm MT}\lesssim{}0.6$, with a lower boundary of the 99\% credible intervals
equal to $f_{\rm MT}= 0.59$. This result holds for all the values of the
common-envelope efficiency parameter we considered in this study $\alpha_{\rm
CE} \in [1,10]$. This confirms that gravitational-wave data can be used to put
constraints on several uncertain binary evolution processes.


  According to a popular scenario supported by numerical models, the mass
assembly and growth of massive galaxies, in particular the Early-Type Galaxies
(ETGs), is, below a redshift of 1, mainly due to the accretion of multiple
gas--poor satellites. In order to get observational evidence of the role played
by minor dry mergers, we are obtaining extremely deep optical images of a
complete volume limited sample of nearby ETGs.
  These observations, done with the CFHT as part of the \AD, NGVS and MATLAS
projects, reach a stunning 28.5)29 mag.arcsec-2 surface brightness limit in the
g' band. They allow us to detect the relics of past collisions such as faint
stellar tidal tails as well as the very extended stellar halos which keep the
memory of the last episodes of galactic accretion.
  Images and preliminary results from this on-going survey are presented, in
particular a possible correlation between the fine structure index (which
parametrizes the amount of tidal perturbation) of the ETGs, their stellar mass,
effective radius and gas content.


  We propose the first general framework to automatically correct different
types of geometric distortion in a single input image. Our proposed method
employs convolutional neural networks (CNNs) trained by using a large synthetic
distortion dataset to predict the displacement field between distorted images
and corrected images. A model fitting method uses the CNN output to estimate
the distortion parameters, achieving a more accurate prediction. The final
corrected image is generated based on the predicted flow using an efficient,
high-quality resampling method. Experimental results demonstrate that our
algorithm outperforms traditional correction methods, and allows for
interesting applications such as distortion transfer, distortion exaggeration,
and co-occurring distortion correction.


  In this paper we prove strong unique continuation for the following
degenerate elliptic equation \begin{equation}\label{e0} \Delta_zu
+|z|^2\partial_t^2u = Vu,\quad (z,t) \in \mathbb{R}^N \times \mathbb{R}
\end{equation} where the potential $V$ satisfies either of the following growth
assumptions \begin{align} & |V(z,t)| \leq \frac{f(\rho(z,t))}{\rho(z,t)^2},\
\text{where $f$ satisfies the Dini integrability condition as in (1.3)} \\ &
\text{or when } \notag \\ & |V(z,t)| \leq
C\frac{\psi(z,t)^{\epsilon}}{\rho(z,t)^2},\ \text{for some $\epsilon>0$ with
$\psi$ as in (2.6) and $N$ even.} \notag \end{align} This extends some of the
previous results obtained in [G] for this subfamily of Baouendi-Grushin
operators. As corollaries, we obtain new unique continuation properties for
solutions $u$ to \[ \Delta_{\mathbb{H}} u = Vu \] with certain symmetries as
expressed in (1.6) where $\Delta_{\mathbb{H}}$ corresponds to the sub-Laplacian
on the Heisenberg group $\mathbb{H}^n$.


  We present evidence for the presence of a transition in the accretion
properties of radio-loud sources. For a sample of radio galaxies and radio-loud
quasars, selected based on their extended radio properties, the accretion rate
is estimated from the black hole mass and nuclear luminosity. The inferred
distribution is bimodal, with paucity of sources at accretion rates, in
Eddington units, of order ~ 10^{-2} - assuming a radiative efficiency of 10 per
cent - and possibly spanning one-two orders of magnitude. Selection biases are
unlikely to be responsible for such behavior; we discuss possible physical
explanations, including a fast transition to low accretion rates, a change in
the accretion mode/actual accretion rate/radiative efficiency, the lack of
stable disc solutions at intermediate accretion rates or the inefficiency of
the jet formation processes in geometrically thin flows. This transition might
be analogous to spectral states (and jet) transitions in black hole binary
systems.


  In latent variable models the parameter estimation can be implemented by
using the joint or the marginal likelihood, based on independence or
conditional independence assumptions. The same dilemma occurs within the
Bayesian framework with respect to the estimation of the Bayesian marginal (or
integrated) likelihood, which is the main tool for model comparison and
averaging. In most cases, the Bayesian marginal likelihood is a high
dimensional integral that cannot be computed analytically and a plethora of
methods based on Monte Carlo integration (MCI) are used for its estimation. In
this work, it is shown that the joint MCI approach makes subtle use of the
properties of the adopted model, leading to increased error and bias in finite
settings. The sources and the components of the error associated with
estimators under the two approaches are identified here and provided in exact
forms. Additionally, the effect of the sample covariation on the Monte Carlo
estimators is examined. In particular, even under independence assumptions the
sample covariance will be close to (but not exactly) zero which surprisingly
has a severe effect on the estimated values and their variability. To address
this problem, an index of the sample's divergence from independence is
introduced as a multivariate extension of covariance. The implications
addressed here are important in the majority of practical problems appearing in
Bayesian inference of multi-parameter models with analogous structures.


  This paper presents InterMPL, a semi-supervised learning method of end-to-end
automatic speech recognition (ASR) that performs pseudo-labeling (PL) with
intermediate supervision. Momentum PL (MPL) trains a connectionist temporal
classification (CTC)-based model on unlabeled data by continuously generating
pseudo-labels on the fly and improving their quality. In contrast to
autoregressive formulations, such as the attention-based encoder-decoder and
transducer, CTC is well suited for MPL, or PL-based semi-supervised ASR in
general, owing to its simple/fast inference algorithm and robustness against
generating collapsed labels. However, CTC generally yields inferior performance
than the autoregressive models due to the conditional independence assumption,
thereby limiting the performance of MPL. We propose to enhance MPL by
introducing intermediate loss, inspired by the recent advances in CTC-based
modeling. Specifically, we focus on self-conditional and hierarchical
conditional CTC, that apply auxiliary CTC losses to intermediate layers such
that the conditional independence assumption is explicitly relaxed. We also
explore how pseudo-labels should be generated and used as supervision for
intermediate losses. Experimental results in different semi-supervised settings
demonstrate that the proposed approach outperforms MPL and improves an ASR
model by up to a 12.1% absolute performance gain. In addition, our detailed
analysis validates the importance of the intermediate loss.


  The concept of a Point Cloud has played an increasingly important role in
many areas of Engineering, Science, and Mathematics. Examples are: LIDAR,
3D-Printing, Data Analysis, Computer Graphics, Machine Learning, Mathematical
Visualization, Numerical Analysis, and Monte Carlo Methods. Entering point
cloud into Google returns nearly 3.5 million results! A point cloud for a
finite volume manifold M is a finite subset or a sequence in M, with the
essential feature that it is a representative sample of M. The definition of a
point cloud varies with its use, particularly what constitutes being
representative. Point clouds arise in many different ways: in LIDAR they are
just 3D data captured by a scanning device, while in Monte Carlo applications
they are constructed using highly complex algorithms developed over many years.
In this article we outline a rigorous mathematical theory of point clouds,
based on the classic Cauchy Crofton formula of Integral Geometry and its
generalizations. We begin with point clouds on surfaces in R^3, which
simplifies the exposition and makes our constructions easily visualizable. We
proceed to hyper-surfaces and then sub-manifolds of arbitrary co-dimension in
R^n, and finally, using an elegant result of Jurgen Moser to arbitrary smooth
manifolds with a volume element.


  We extract the phase coherence of a qubit defined by singlet and triplet
electronic states in a gated GaAs triple quantum dot, measuring on timescales
much shorter than the decorrelation time of the environmental noise. In this
non-ergodic regime, we observe that the coherence is boosted and several
dephasing times emerge, depending on how the phase stability is extracted. We
elucidate their mutual relations, and demonstrate that they reflect the noise
short-time dynamics.


  The main result of the present paper is that the projective line over a ring
$R$ is connected with respect to the relation "distant" if, and only if, $R$ is
a $GE_2$-ring.


  Short-term forecasts of infectious disease spread are a critical component in
risk evaluation and public health decision making. While different models for
short-term forecasting have been developed, open questions about their relative
performance remain. Here, we compare short-term probabilistic forecasts of
popular mechanistic models based on the renewal equation with forecasts of
statistical time series models. Our empirical comparison is based on data of
the daily incidence of COVID-19 across six large US states over the first
pandemic year. We find that, on average, probabilistic forecasts from
statistical time series models are overall at least as accurate as forecasts
from mechanistic models. Moreover, statistical time series models better
capture volatility. Our findings suggest that domain knowledge, which is
integrated into mechanistic models by making assumptions about disease
dynamics, does not improve short-term forecasts of disease incidence. We note,
however, that forecasting is often only one of many objectives and thus
mechanistic models remain important, for example, to model the impact of
vaccines or the emergence of new variants.


  Context: To date, more than 30 planets have been discovered around giant
stars, but only one of them has been found to be orbiting within 0.6 AU from
the host star, in direct contrast to what is observed for FGK dwarfs. This
result suggests that evolved stars destroy/engulf close-in planets during the
red giant phase.
  Aims: We are conducting a radial velocity survey of 164 bright G and K giant
stars in the southern hemisphere with the aim of studying the effect of the
host star evolution on the inner structure of planetary systems. In this paper
we present the spectroscopic atmospheric parameters (\Teff, \logg, $\xi$,
[Fe/H]) and the physical properties (mass, radius, evolutionary status) of the
program stars. In addition, rotational velocities for all of our targets were
derived.
  Methods: We used high resolution and high S/N spectra to measure the
equivalent widths of many Fe{\sc\,i} and Fe{\sc\,ii} lines, which were used to
derive the atmospheric parameters by imposing local thermodynamic and
ionization equilibrium. The effective temperatures and metallicities were used,
along with stellar evolutionary tracks to determine the physical properties and
evolutionary status of each star.
  Results: We found that our targets are on average metal rich and they have
masses between $\sim$\,1.0\,M$_\odot$ and 3.5\,M$_\odot$. In addition, we found
that 122 of our targets are ascending the RGB, while 42 of them are on the HB
phase.


  The high-throughput calculation predicts that the Fe-based cubic ferromagnet
Fe$_3$Si may exhibit a large anomalous Nernst effect (ANE). Here, we report our
experimental observation of the large Nernst coefficient $S_{yx}\sim$2 $\mu$V/K
and the transverse thermoelectric coefficient $-\alpha_{yx}$ $\sim$ 3
Am$^{-1}$K$^{-1}$ for Fe$_3$Si polycrystal at room temperature. The large
$-\alpha_{yx}$ indicates that the large ANE originates from the intrinsic Berry
curvature mechanism. The high Curie temperature of 840 K and the most abundant
raw elements of Fe and Si make Fe$_3$Si a competitive candidate for Nernst
thermoelectric generations.


  We discuss the nonlinear transformations of standard Poincar\'{e} symmetry in
the context of recently introduced Doubly Special Relativity (DSR) theories. We
introduce four classes of modified relativistic theories with three of them
describing various DSR frameworks. We consider four examples of modified
relativistic symmetries, which illustrate each of the considered class.


  This commentary tests a methodology proposed by Munk et al. (2022) for using
failed predictions in machine learning as a method to identify ambiguous and
rich cases for qualitative analysis. Using a dataset describing actions
performed by fictional characters interacting with machine vision technologies
in 500 artworks, movies, novels and videogames, I trained a simple machine
learning algorithm (using the kNN algorithm in R) to predict whether or not an
action was active or passive using only information about the fictional
characters. Predictable actions were generally unemotional and unambiguous
activities where machine vision technologies were treated as simple tools.
Unpredictable actions, that is, actions that the algorithm could not correctly
predict, were more ambivalent and emotionally loaded, with more complex power
relationships between characters and technologies. The results thus support
Munk et al.'s theory that failed predictions can be productively used to
identify rich cases for qualitative analysis. This test goes beyond simply
replicating Munk et al.'s results by demonstrating that the method can be
applied to a broader humanities domain, and that it does not require complex
neural networks but can also work with a simpler machine learning algorithm.
Further research is needed to develop an understanding of what kinds of data
the method is useful for and which kinds of machine learning are most
generative. To support this, the R code required to produce the results is
included so the test can be replicated. The code can also be reused or adapted
to test the method on other datasets.


  We introduce the latest progress of Qwen-Audio, a large-scale audio-language
model called Qwen2-Audio, which is capable of accepting various audio signal
inputs and performing audio analysis or direct textual responses with regard to
speech instructions. In contrast to complex hierarchical tags, we have
simplified the pre-training process by utilizing natural language prompts for
different data and tasks, and have further expanded the data volume. We have
boosted the instruction-following capability of Qwen2-Audio and implemented two
distinct audio interaction modes for voice chat and audio analysis. In the
voice chat mode, users can freely engage in voice interactions with Qwen2-Audio
without text input. In the audio analysis mode, users could provide audio and
text instructions for analysis during the interaction. Note that we do not use
any system prompts to switch between voice chat and audio analysis modes.
Qwen2-Audio is capable of intelligently comprehending the content within audio
and following voice commands to respond appropriately. For instance, in an
audio segment that simultaneously contains sounds, multi-speaker conversations,
and a voice command, Qwen2-Audio can directly understand the command and
provide an interpretation and response to the audio. Additionally, DPO has
optimized the model's performance in terms of factuality and adherence to
desired behavior. According to the evaluation results from AIR-Bench,
Qwen2-Audio outperformed previous SOTAs, such as Gemini-1.5-pro, in tests
focused on audio-centric instruction-following capabilities. Qwen2-Audio is
open-sourced with the aim of fostering the advancement of the multi-modal
language community.


  Deep neural networks come in many sizes and architectures. The choice of
architecture, in conjunction with the dataset and learning algorithm, is
commonly understood to affect the learned neural representations. Yet, recent
results have shown that different architectures learn representations with
striking qualitative similarities. Here we derive an effective theory of
representation learning under the assumption that the encoding map from input
to hidden representation and the decoding map from representation to output are
arbitrary smooth functions. This theory schematizes representation learning
dynamics in the regime of complex, large architectures, where hidden
representations are not strongly constrained by the parametrization. We show
through experiments that the effective theory describes aspects of
representation learning dynamics across a range of deep networks with different
activation functions and architectures, and exhibits phenomena similar to the
"rich" and "lazy" regime. While many network behaviors depend quantitatively on
architecture, our findings point to certain behaviors that are widely conserved
once models are sufficiently flexible.


  Dynamical systems are ubiquitous in science and engineering as models of
phenomena that evolve over time. Although complex dynamical systems tend to
have important modular structure, conventional modeling approaches suppress
this structure. Building on recent work in applied category theory, we show how
deterministic dynamical systems, discrete and continuous, can be composed in a
hierarchical style. In mathematical terms, we reformulate some existing operads
of wiring diagrams and introduce new ones, using the general formalism of
C-sets (copresheaves). We then establish dynamical systems as algebras of these
operads. In a computational vein, we show that Euler's method is functorial for
undirected systems, extending a previous result for directed systems. All of
the ideas in this paper are implemented as practical software using Catlab and
the AlgebraicJulia ecosystem, written in the Julia programming language for
scientific computing.


  We measure acceleration statistics of neutrally buoyant spherical particles
with diameter 0.4 < d/eta <27 in intense turbulence (400< R_lambda <815). High
speed cameras image polystyrene tracer particles in a flow between
counter-rotating disks. The measurements of acceleration variance, <a^2>,
clearly resolve the transition from the tracer like behavior of small particles
to the much smaller accelerations of large particles. For d>5 eta, <a^2>
decreases with diameter as d^{-2/3} in agreement with inertial range scaling
arguments. A model relating <a^2> to the pressure structure functions matches
the transition from small to large particle behavior if the particles respond
to pressure differences over (1.7 +- 0.3) d. A model relating <a^2> to the
fluid acceleration averaged over the particle diameter predicts the transition
with no free parameters, but does not show clean inertial range scaling in the
size range studied. Consistent with earlier work, we find that the scaled
acceleration probability density function shows very little dependence on
particle size.


  The canonical covering maps from Hurwitz varieties to configuration varieties
are important in algebraic geometry. The scheme-theoretic fiber above a
rational point is commonly connected, in which case it is the spectrum of a
Hurwitz number field. We study many examples of such maps and their fibers,
finding number fields whose existence contradicts standard mass heuristics.


  The study of Whittaker models for representations of reductive groups over
local and global fields has become a central tool in representation theory and
the theory of automorphic forms. However, only generic representations have
Whittaker models. In order to encompass other representations, one attaches a
degenerate (or a generalized) Whittaker model $W_{\mathcal{O}}$, or a Fourier
coefficient in the global case, to any nilpotent orbit $\mathcal{O}$. In this
note we survey some classical and some recent work in this direction - for
Archimedean, p-adic and global fields. The main results concern the existence
of models. For a representation $\pi$, call the set of maximal orbits
$\mathcal{O}$ with $W_{\mathcal{O}}$ that includes $\pi$ the Whittaker support
of $\pi$. The two main questions discussed in this note are: (1) What kind of
orbits can appear in the Whittaker support of a representation? (2) How does
the Whittaker support of a given representation $\pi$ relate to other
invariants of $\pi$, such as its wave-front set?


  We introduce and initiate the study of a natural class of repeated two-player
matrix games, called Repeated-Until-Collision (RUC) games. In each round, both
players simultaneously pick an action from a common action set $\{1, 2, \dots,
n\}$. Depending on their chosen actions, they derive payoffs given by $n \times
n$ matrices $A$ and $B$, respectively. If their actions collide (i.e., they
pick the same action), the game ends, otherwise, it proceeds to the next round.
Both players want to maximize their total payoff until the game ends. RUC games
can be interpreted as pursuit-evasion games or repeated hide-and-seek games.
They also generalize hand cricket, a popular game among children in India.
  We show that under mild assumptions on the payoff matrices, every RUC game
admits a Nash equilibrium (NE). Moreover, we show the existence of a stationary
NE, where each player chooses their action according to a probability
distribution over the action set that does not change across rounds.
Remarkably, we show that all NE are effectively the same as the stationary NE,
thus showing that RUC games admit an almost unique NE. Lastly, we also show how
to compute (approximate) NE for RUC games.


  We introduce a generalized Bartholdi zeta function for simple graphs with
bounded degree. This zeta function is a generalization of both the Bartholdi
zeta function which was introduced by L.~Bartholdi and the Ihara zeta function
which was introduced by G.~Chinta, J.~Jorgenson and A.~Karlsson. Furthermore,
we establish a Bartholdi type formula of this Bartholdi zeta function for
simple graphs with bounded degree. Moreover, for regular graphs, we give a new
expression of the heat kernel which is regarded as a one-parameter deformation
of the expression obtained by G.~Chinta, J.~Jorgenson and A.~Karlsson. By
applying this formula, we give an alternative proof of the Bartholdi zeta
function formula for regular graphs.


  In this note we construct a new class of superconformal field theories as
mass deformed N=4 super Yang-Mills theories. We will argue that these theories
correspond to the fixed points which were recently found by Khavaev, Pilch and
Warner studying the deformations of the dual IIB string theory on AdS_5\times
S^5.


  Variational dropout (VD) is a generalization of Gaussian dropout, which aims
at inferring the posterior of network weights based on a log-uniform prior on
them to learn these weights as well as dropout rate simultaneously. The
log-uniform prior not only interprets the regularization capacity of Gaussian
dropout in network training, but also underpins the inference of such
posterior. However, the log-uniform prior is an improper prior (i.e., its
integral is infinite) which causes the inference of posterior to be ill-posed,
thus restricting the regularization performance of VD. To address this problem,
we present a new generalization of Gaussian dropout, termed variational
Bayesian dropout (VBD), which turns to exploit a hierarchical prior on the
network weights and infer a new joint posterior. Specifically, we implement the
hierarchical prior as a zero-mean Gaussian distribution with variance sampled
from a uniform hyper-prior. Then, we incorporate such a prior into inferring
the joint posterior over network weights and the variance in the hierarchical
prior, with which both the network training and the dropout rate estimation can
be cast into a joint optimization problem. More importantly, the hierarchical
prior is a proper prior which enables the inference of posterior to be
well-posed. In addition, we further show that the proposed VBD can be
seamlessly applied to network compression. Experiments on both classification
and network compression tasks demonstrate the superior performance of the
proposed VBD in terms of regularizing network training.


  We describe wild embeddings of polyhedra into $\mathbb{R}^N$ which show that
the answer to the question of B.J. Baker--M. Laidacker (1989) concerning
uncountable families of pairwise disjoint compacta can be twofold. The central
idea of our construction is the use of specific wild Cantor sets, namely,
Antoine--Blankinship--Ivanov necklaces and Krushkal sticky sets. Our basic
tools are Antoine's methods and Shtan'ko demension theory.


  We discuss the criteria that must be satisfied by a well-posed variational
principle. We clarify the role of Gibbons-Hawking-York type boundary terms in
the actions of higher derivative models of gravity, such as F(R) gravity, and
argue that the correct boundary terms are the naive ones obtained though the
correspondence with scalar-tensor theory, despite the fact that variations of
normal derivatives of the metric must be fixed on the boundary. We show in the
case of F(R) gravity that these boundary terms reproduce the correct ADM energy
in the hamiltonian formalism, and the correct entropy for black holes in the
semi-classical approximation.


  Optimizing the total cost of power systems is a common tool for network
operation and planning. Besides valuable information about how to run and
possibly expand a power system, the optimization provides an optimal Locational
Marginal Price per node and time step. This price can be seen as the price of
electricity paid by consumers and purchased by suppliers, while maximizing
social welfare. Naturally, it is a direct result of the optimization problem,
and therefore does not give any information about its internal composition.
This paper shows that by applying Flow Tracing, an algorithm for tracking flows
in complex networks, it is possible to interlink Locational Marginal Prices in
a coherent mathematical way. This does not only lead to important insights into
the price structure, but also provides an intuitive decomposition and
allocation of all system costs. Then individual consumers see how much they
have to pay to individual generators and transmission lines in the power
system. This method, introduced as Price Tracing, outperforms similar
approaches provided by the literature, since the resulting cost allocations are
transparent, plausible, and consistent with the Locational Marginal Prices from
the optimization. The Price Tracing method is applied and discussed on behalf
of a power system model of Germany with a high share of renewable power. The
presented analysis and its implications can help in finding a more efficient
market design to promote renewable power supply.


  Macroscopic quantum superpositions of massive objects are deeply interesting
as they have a number of potential applications ranging from the exploration of
the interaction of gravity with quantum mechanics to quantum sensing, quantum
simulation, and computation. In this letter, we propose two related schemes to
prepare a spatial superposition of massive quantum oscillator systems with high
Q-factor via a superposition of magnetic forces. In the first method, we
propose a large spatial superposition of a levitated spherical magnet generated
via magnetic forces applied by adjacent flux qubits. We find that in this
method the spatial superposition extent ($\Delta z$) is independent of the size
of the particle. In the second method, we propose a large spatial superposition
of a magnetically levitated (using the Meissner effect) flux qubit, generated
via driving the levitated qubit inductively. In both schemes, we show that
ultra-large superpositions $\Delta z/\delta z_{\rm zpm}\sim 10^6$, are
possible, where $\delta z_{\rm zpm}$ is the zero point motional extent.


  We introduce additively-weighted straight skeletons as a new generalization
of straight skeletons. An additively-weighted straight skeleton is the result
of a wavefront-propagation process where, unlike in previous variants of
straight skeletons, wavefront edges do not necessarily start to move at the
begin of the propagation process but at later points in time. We analyze the
properties of additively-weighted straight skeletons and show how to compute
straight skeletons with both additive and multiplicative weights.
  We then show how to use additively-weighted and multiplicatively-weighted
straight skeletons to generate roofs and terrains for polygonal shapes such as
the footprints of buildings or river networks. As a result, we get an automated
generation of roofs and terrains where the individual facets have different
inclinations and may start at different heights.


  The coupling between time-dependent, multidimensional MHD numerical codes and
radiative line emission is of utmost importance in the studies of the interplay
between dynamical and radiative processes in many astrophysical environments,
with particular interest for problems involving radiative shocks. There is a
widespread consensus that line emitting knots observed in Herbig-Haro jets can
be interpreted as radiative shocks. In this paper we address two different
aspects relevant to the time-dependent calculations of the line intensity
ratios of forbidden transitions, resulting from the excitation by planar,
time-dependent radiative shocks traveling in a stratified medium. The first one
concerns the impact of the radiation and ionization processes included in the
cooling model, and the second one the effects of the numerical grid resolution.
In this paper we apply the AMR methodology to the treatment of radiating shocks
and show how this method is able to vastly reduce the integration time. The
technique is applied to the knots of the HH 30 jet to obtain the observed line
intensity ratios and derive the physical parameters, such as density,
temperature and ionization fraction. We consider the impact of two different
cooling functions and different grid resolutions on the results. We conclude
that the use of different cooling routines has effects on results whose weight
depends upon the line ratio considered. Moreover, we find the minimum numerical
resolution of the simulation grid behind the shock to achieve convergence in
the results. This is crucial for the forthcoming 2D calculations of radiative
shocks.


  I present four-frequency radio observations of the wide-angle tail radio
galaxy 3C130. By a technique of simulated observations, I assess the systematic
errors in the data due to the varying uv plane coverage in the different
observations used. Using spectral tomography I show that, at least in the
southern plume, the source can be represented by a two-component model
consisting of a flat-spectrum core and steep-spectrum sheath, as recently found
in other FRI sources. In addition, there is a strong difference in the
high-frequency spectra of the northern and southern plumes. I discuss the
implications of these observations for the source's jet dynamics and particle
acceleration, and discuss models of the class of WATs as a whole.


  We study the temperature dependence of the magnetic penetration depth in a 3D
topological superconductor (TSC), incorporating the paramagnetic current due to
the surface states. A TSC is predicted to host a gapless 2D surface Majorana
fluid. In addition to the bulk-dominated London response, we identify a $T^3$
power-law-in-temperature contribution from the surface, valid in the
low-temperature limit. Our system is fully gapped in the bulk, and should be
compared to bulk nodal superconductivity, which also exhibits power-law
behavior. Power-law temperature dependence of the penetration depth can be one
indicator of topological superconductivity.


  In this paper, we study sample size thresholds for maximum likelihood
estimation for tensor normal models. Given the model parameters and the number
of samples, we determine whether, almost surely, (1) the likelihood function is
bounded from above, (2) maximum likelihood estimates (MLEs) exist, and (3) MLEs
exist uniquely. We obtain a complete answer for both real and complex models.
One consequence of our results is that almost sure boundedness of the
log-likelihood function guarantees almost sure existence of an MLE. Our
techniques are based on invariant theory and castling transforms.


  Inelastic electron tunneling and surface-enhanced optical spectroscopies at
the molecular scale require cryogenic local temperatures even under
illumination - conditions that are challenging to achieve with plasmonically
resonant metallic nanostructures. We report a detailed study of the laser
heating of plasmonically active nanowires at substrate temperatures from 5 to
60 K. The increase of the local temperature of the nanowire is quantified by a
bolometric approach and could be as large as 100 K for a substrate temperature
of 5 K and typical values of laser intensity. We also demonstrate that a $\sim
3\times$ reduction of the local temperature increase is possible by switching
to a sapphire or quartz substrate. Finite element modeling of the heat
dissipation reveals that the local temperature increase of the nanowire at
temperatures below $\sim$50 K is determined largely by the thermal boundary
resistance of the metal-substrate interface. The model reproduces the striking
experimental trend that in this regime the temperature of the nanowire varies
nonlinearly with the incident optical power. The thermal boundary resistance is
demonstrated to be a major constraint on reaching low temperatures necessary to
perform simultaneous inelastic electron tunneling and surface enhanced Raman
spectroscopies.


  Searches for new physics often face unknown backgrounds, causing false
detections or weakened upper limits. This paper introduces the deficit hawk
technique, which mitigates unknown backgrounds by testing multiple options for
data cuts, such as fiducial volumes or energy thresholds. Combining the power
of likelihood ratios with the robustness of the interval-searching techniques,
deficit hawks could improve mean upper limits on new physics by a factor two
for experiments with partial or speculative background knowledge. Deficit hawks
are well-suited to analyses that use machine learning or other multidimensional
discrimination techniques, and can be extended to permit discoveries in regions
without unknown background.


  A Kerr nonlinear oscillator (KNO) supports a pair of steady eigenstates,
coherent states with opposite phases, that are good for the encoding of
continuous variable qubit basis states. Arbitrary control of the KNO confined
within the steady state subspace allows extraction of the Berry curvature
through the linear response of the physical observable to the quench velocity
of the system, providing an effective method for the characterization of
topology in the KNO. As an alternative, the control adopting the "shortcut to
adiabaticity" to the KNO enables the exploration of the topology through
accelerated adiabatic eigenstate evolution to measure all three physical
observables. Topological transitions are revealed by the jump of the first
Chern number, obtained respectively from the integral of the Berry curvature
and of the new polar angle relation, over the whole parameter space. Our
strategy paves the way for measuring topological transitions in continuous
variable systems.


This paper has been withdrawn and no version of it will ever be published.


  In non-linear incompatible elasticity, the configurations are maps from a
non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$.
We prove the $\Gamma$-convergence of elastic energies for configurations of a
converging sequence, $\mathcal{M}_n\to\mathcal{M}$, of body manifolds. This
convergence result has several implications: (i) It can be viewed as a general
structural stability property of the elastic model. (ii) It applies to certain
classes of bodies with defects, and in particular, to the limit of bodies with
increasingly dense edge-dislocations. (iii) It applies to approximation of
elastic bodies by piecewise-affine manifolds. In the context of
continuously-distributed dislocations, it reveals that the torsion field, which
has been used traditionally to quantify the density of dislocations, is
immaterial in the limiting elastic model.


  It is proved that each bounded injective bilateral weighted shift $W$
satisfying the equality $W^{*n}W^{n}=(W^{*}W)^{n}$ for some integer $n\geq 2$
is quasinormal. For any integer $n\geq 2$, an example of a bounded
non-quasinormal weighted shift $A$ on a rootless directed tree with one
branching vertex which satisfies the equality $A^{*n}A^{n}=(A^{*}A)^{n}$ is
constructed. It is also shown that such an example can be constructed in the
class of composition operators in $L^2$-spaces over $\sigma$-finite measure
spaces.


  In recent years, decentralized finance (DeFi) has experienced remarkable
growth, with various protocols such as lending protocols and automated market
makers (AMMs) emerging. Traditionally, these protocols employ off-chain
governance, where token holders vote to modify parameters. However, manual
parameter adjustment, often conducted by the protocol's core team, is
vulnerable to collusion, compromising the integrity and security of the system.
Furthermore, purely deterministic, algorithm-based approaches may expose the
protocol to novel exploits and attacks.
  In this paper, we present "Auto.gov", a learning-based on-chain governance
framework for DeFi that enhances security and reduces susceptibility to
attacks. Our model leverages a deep Q- network (DQN) reinforcement learning
approach to propose semi-automated, intuitive governance proposals with
quantitative justifications. This methodology enables the system to efficiently
adapt to and mitigate the negative impact of malicious behaviors, such as price
oracle attacks, more effectively than benchmark models. Our evaluation
demonstrates that Auto.gov offers a more reactive, objective, efficient, and
resilient solution compared to existing manual processes, thereby significantly
bolstering the security and, ultimately, enhancing the profitability of DeFi
protocols.


  This paper discusses a Decision Support System (DSS) for cases prediction,
allocation of resources, and lockdown management for managing COVID-19 at
different levels of a government authority. Algorithms incorporated in the DSS
are based on a data-driven modeling approach and independent of physical
parameters of the region, and hence the proposed DSS is applicable to any area.
Based on predicted active cases, the demand of lower-level units and total
availability, allocation, and lockdown decision is made. A MATLAB-based GUI is
developed based on the proposed DSS and could be implemented by the local
authority.


  Additive noise in Partial Differential equations, in particular those of
fluid mechanics, has relatively natural motivations. The aim of this work is
showing that suitable multiscale arguments lead rigorously, from a model of
fluid with additive noise, to transport type noise. The arguments apply both to
small-scale random perturbations of the fluid acting on a large-scale passive
scalar and to the action of the former on the large scales of the fluid itself.
Our approach consists in studying the (stochastic) characteristics associated
to small-scale random perturbations of the fluid, here modelled by stochastic
2D Euler equations with additive noise, and their convergence in the infinite
scale separation limit.


  We study resonant mode conversion in the PT-symmetric multimode waveguides,
where symmetry breaking manifests itself in sequential destabilization
(appearance of the complex eigenvalues) of the pairs of adjacent guided modes.
We show that the efficient mode conversion is possible even in the presence of
the resonant longitudinal modulation of the complex refractive index. The
distinguishing feature of the resonant mode conversion in the PT-symmetric
structure is a drastic growth of the width of the resonance curve when the
gain/losses coefficient approaches a critical value, at which symmetry breaking
occurs. We found that in the system with broken symmetry the resonant coupling
between exponentially growing mode with stable higher-order one effectively
stabilizes dynamically coupled pair of modes and remarkably diminishes the
average rate of the total power growth.


  We show that if the Lorentz transformation properties of diffraction are
other than scalar, the $x \rightarrow 0$ behaviour of $g_1(x,Q^2)$ can grow. We
compare with new data on $g_1^p$ from SMC, assess implications for sum rules
and for future studies of sea polarisation.


  We are interested in the question when a Banach space $X$ with an
unconditional basis is isomorphic (as a Banach space) to an order-continuous
nonatomic Banach lattice. We show that this is the case if and only if $X$ is
isomorphic as a Banach space with $X(\ell_2)$. This and results of J. Bourgain
are used to show that spaces $H_1(\bold T^n)$ are not isomorphic to nonatomic
Banach lattices. We also show that tent spaces introduced in \cite{4} are
isomorphic to Rad $H_1$.


  The correlation between increased Sahel rainfall and reduced Saharan surface
pressure is well established in observations and global climate models, and has
been used to imply that increased Sahel rainfall is caused by a stronger
shallow meridional circulation (SMC) over the Sahara. This study uses two
atmospheric reanalyses to examine interannual variability of Sahel rainfall and
the Saharan SMC, which consists of northward near-surface flow across the Sahel
into the Sahara and southward flow near 700 hPa out of the Sahara. During wet
Sahel years, the Saharan SMC shifts poleward, producing a drop in low-level
geopotential and surface pressure over the Sahara. Statistically removing the
effect of the poleward shift from the low-level geopotential eliminates
significant correlations between this geopotential and Sahel precipitation. As
the Saharan SMC shifts poleward, its mid-tropospheric divergent outflow
decreases, indicating a weakening of its overturning mass flux. The poleward
shift and weakening of the Saharan SMC during wet Sahel years is reproduced in
an idealized model of West Africa; a wide range of imposed sea surface
temperature and land surface albedo perturbations in this model produce a much
larger range of SMC variations that nevertheless have similar quantitative
associations with Sahel rainfall as in the reanalyses. These results disprove
the idea that enhanced Sahel rainfall is caused by strengthening of the Saharan
SMC. Instead, these results are consistent with the hypothesis that the a
stronger SMC inhibits Sahel rainfall, perhaps by advecting mid-tropospheric
warm and dry air into the precipitation maximum.


  Federated Learning, as a popular paradigm for collaborative training, is
vulnerable against privacy attacks. Different privacy levels regarding users'
attitudes need to be satisfied locally, while a strict privacy guarantee for
the global model is also required centrally. Personalized Local Differential
Privacy (PLDP) is suitable for preserving users' varying local privacy, yet
only provides a central privacy guarantee equivalent to the worst-case local
privacy level. Thus, achieving strong central privacy as well as personalized
local privacy with a utility-promising model is a challenging problem. In this
work, a general framework (APES) is built up to strengthen model privacy under
personalized local privacy by leveraging the privacy amplification effect of
the shuffle model. To tighten the privacy bound, we quantify the heterogeneous
contributions to the central privacy user by user. The contributions are
characterized by the ability of generating "echos" from the perturbation of
each user, which is carefully measured by proposed methods Neighbor Divergence
and Clip-Laplace Mechanism. Furthermore, we propose a refined framework
(S-APES) with the post-sparsification technique to reduce privacy loss in
high-dimension scenarios. To the best of our knowledge, the impact of shuffling
on personalized local privacy is considered for the first time. We provide a
strong privacy amplification effect, and the bound is tighter than the baseline
result based on existing methods for uniform local privacy. Experiments
demonstrate that our frameworks ensure comparable or higher accuracy for the
global model.


  In this paper, we propose a novel speech emotion recognition model called
Cross Attention Network (CAN) that uses aligned audio and text signals as
inputs. It is inspired by the fact that humans recognize speech as a
combination of simultaneously produced acoustic and textual signals. First, our
method segments the audio and the underlying text signals into equal number of
steps in an aligned way so that the same time steps of the sequential signals
cover the same time span in the signals. Together with this technique, we apply
the cross attention to aggregate the sequential information from the aligned
signals. In the cross attention, each modality is aggregated independently by
applying the global attention mechanism onto each modality. Then, the attention
weights of each modality are applied directly to the other modality in a
crossed way, so that the CAN gathers the audio and text information from the
same time steps based on each modality. In the experiments conducted on the
standard IEMOCAP dataset, our model outperforms the state-of-the-art systems by
2.66% and 3.18% relatively in terms of the weighted and unweighted accuracy.


  We re-examine recent determinations of power corrections from tau-decay and
confront the results with the existing ones from QCD spectral sum rules (QSSR).
We conclude that contrary to the QSSR analysis, which lead to <alpha_s
G^2>=(6.8+-1.3)10^{-2} GeV^4, tau-decay is not a good place for extracting the
gluon condensate due to its extra alpha_s^2 coefficient which suppresses its
contribution in this process. Results from e^+e^- sum rules and tau-decay: rho
alpha_s<uu>^2= (4.5+-0.3)10^{-4}GeV^6, where rho=3.0+-0.2 confirm the deviation
from the vacuum saturation estimate of the four-quark condensate."Non-standard"
power corrections (direct instantons, duality violation and tachyonic gluon
mass) beyond the SVZ-expansion, partially cancel out in the V+A hadronic
tau-decay channel, which gives at order alpha_s^4:
alpha_s(M_tau)=0.3249(29)_{ex}(75)_{th} leading to als(M_Z)|_tau=0.1192
(4)_{ex}(9)_{th},in remarkable agreement with (but more accurate than)
alpha_s(M_Z)|_Z=0.1191(27)obtained at the same alpha_s^4 order from the Z-width
and the global fit of electroweak data. Finally, the role of the tachyonic
gluon mass in the determinations of |V_{us}|from tau-decay and of m_s from
tau-decay, e^+e^- and (pseudo)scalar channels is emphasized.


  Shape abstraction is an important task for simplifying complex geometric
structures while retaining essential features. Sweep surfaces, commonly found
in human-made objects, aid in this process by effectively capturing and
representing object geometry, thereby facilitating abstraction. In this paper,
we introduce \papername, a novel approach to shape abstraction through sweep
surfaces. We propose an effective parameterization for sweep surfaces,
utilizing superellipses for profile representation and B-spline curves for the
axis. This compact representation, requiring as few as 14 float numbers,
facilitates intuitive and interactive editing while preserving shape details
effectively. Additionally, by introducing a differentiable neural sweeper and
an encoder-decoder architecture, we demonstrate the ability to predict sweep
surface representations without supervision. We show the superiority of our
model through several quantitative and qualitative experiments throughout the
paper. Our code is available at https://mingrui-zhao.github.io/SweepNet/


  Three-body $B$ decays not only significantly broaden the study of $B$ meson
decay mechanisms, but also provide information of resonant particles. Because
of complicate dynamics, it is very hard for us to study the whole phase space
in a specific approach. In this review, we take $B\to K({\cal R}\to) K^+K^-$
decays as examples and show the application of the perturbative QCD (PQCD)
approach in studying the quasi-two-body $B$ decays, where two particles move
collinearly with large energy and the bachelor one recoils back. To describe
the dynamics of two collinear particles, the ($S$, $P$ and $D$)-wave functions
of kaon-pair with different waves are introduced. By keeping the transverse
momenta, all possible diagrams including the hard spectator diagrams and
annihilation ones can be calculated in PQCD approach. Most results are well
consistent with the current measurements from BaBar, Belle and LHCb
experiments. Moreover, under the narrow-width approximation we can extract the
branching fractions of the two-body decays involving the resonant states, and
also predict the branching fractions of the corresponding quasi-two-body decays
$B\to K(\cal{R}\to )\pi^+\pi^-$. All prediction are expected to be tested in
the ongoing LHCb and Belle-II experiments.


  The variable two-step backward differentiation formula (BDF2) is revisited
via a new theoretical framework using the positive semi-definiteness of BDF2
convolution kernels and a class of orthogonal convolution kernels. We prove
that, if the adjacent time-step ratios
$r_k:=\tau_k/\tau_{k-1}\le(3+\sqrt{17})/2\approx3.561$, the adaptive BDF2
time-stepping scheme for linear reaction-diffusion equations is unconditionally
stable and (maybe, first-order) convergent in the $L^2$ norm. The second-order
temporal convergence can be recovered if almost all of time-step ratios $r_k\le
1+\sqrt{2}$ or some high-order starting scheme is used. Specially, for linear
dissipative diffusion problems, the stable BDF2 method preserves both the
energy dissipation law (in the $H^1$ seminorm) and the $L^2$ norm monotonicity
at the discrete levels. An example is included to support our analysis.


  In this study, an advanced CCA-based algorithn called hybrid template
canonical correlation analysis (HTCCA) was proposed to improve the performance
of brain-computer interface (BCI) based on steady state visual evoked potential
(SSVEP) uuder data-linited condition. The HTCCA method combines the training
data from several subjects to construct SSVEP templates. The experinental
results evaluated on two public benchmark datasets showed that the proposed
method outperforms the compared methods in both detection accuracy and
information transfer rate when the number of tuials is small.Considering that
user-friendly experience will become a key factor for BCI in practical
application, it is very necessary to develop effective methods based on limited
EEG samples. This study demonstrates that the proposed method has great
potential in the application of SSVEP-based brain-computer interfaces.


  The article discusses the quantitative assessment approach to the innovation
of engineering system components. The validity of the approach is based on the
expert appraisal of the university's electronic information educational
environment components and the measurement of engineering solution innovation
in engineering education. The implementation of batch processing of object
innovation assessments is justified and described.


  The contributions of direct knockout processes, in addition to the
diffractive production and one-pion-exchange processes associated with the
phi-rho-pi and phi-gamma-pi couplings, to the polarization observables of the
phi photoproduction from proton are calculated. We make use of Pomeron-photon
analogy and a relativistic harmonic oscillator quark model. We find that some
of the double polarization observables are very sensitive to a possible (s
s-bar) admixture in the proton. It arises from the difference in the spin
structures of the three different amplitudes. This suggests that such
measurements could be very useful to probe the strangeness content in the
proton.


  Self-consistent bars that form in galaxies embedded within cuspy halos are
unable to flatten the cusp. Short bars form in models with quasi-flat rotation
curves. They lose angular momentum to the halo through dynamical friction, but
the continuous concentration of mass within the disk as the bar grows actually
compresses the halo further, overwhelming any density reduction due to the
modest angular momentum transfer to the halo. Thus the Weinberg-Katz proposed
solution to the non-existence of the predicted cuspy halos from CDM simulations
would seem to be unworkable. I also find that the concerns over the performance
of N-body codes raised by these authors do not apply to the methods used here.


  Newton's root finding method applied to a (transcendental) entire function
f:C->C is the iteration of a meromorphic function N. It is well known that if
for some starting value z, Newton's method converges to a point x in C, then f
has a root at x. We show that in many cases, if an orbit converges to infinity
for Newton's method, then f has a `virtual root' at infinity. More precisely,
we show that if N has an invariant Baker domain that satisfies some mild
assumptions, then 0 is an asymptotic value for f.
  Conversely, we show that if f has an asymptotic value of logarithmic type at
0, then the singularity over 0 is contained in an invariant Baker domain of N,
which we call a virtual immediate basin. We show by way of counterexamples that
this is not true for more general types of singularities.


  We present a suite of Mathematica-based computer-algebra packages, termed
"Kranc", which comprise a toolbox to convert (tensorial) systems of partial
differential evolution equations to parallelized C or Fortran code. Kranc can
be used as a "rapid prototyping" system for physicists or mathematicians
handling very complicated systems of partial differential equations, but
through integration into the Cactus computational toolkit we can also produce
efficient parallelized production codes. Our work is motivated by the field of
numerical relativity, where Kranc is used as a research tool by the authors. In
this paper we describe the design and implementation of both the Mathematica
packages and the resulting code, we discuss some example applications, and
provide results on the performance of an example numerical code for the
Einstein equations.


  We present a mapping of correlated multi-impurity Anderson models to a
cluster model coupled to a number of effective conduction bands capturing its
essential low-energy physics. The major ingredient is the complex
single-particle self energy matrix of the uncorrelated problem that encodes the
influence to the host conduction band onto the dynamics of a set of correlated
orbitals. While the real part of the self-energy matrix generates an effective
hopping between the cluster orbitals, the imaginary part determines the
coupling to the effective conduction bands in the mapped model. The rank of the
imaginary part determines the number of independent screening channels of the
problem, and allows the replacement of the phenomenological exhaustion
criterion by a rigorous mathematical statement. This rank provides a
distinction between multi-impurity models of first kind and of second kind. For
the latter, there are insufficient screening channels available, so that a
singlet ground state must be driven by the inter-cluster spin correlations.
This classification provides a fundamental answer to the question of why
ferromagnetic correlations between local moments are irrelevant for the spin
compensated ground state in dilute impurity models, whereas they compete with
the Kondo-scale in dense impurity arrays, without evoking a spin density wave.
The low-temperature physics of three examples taken from the literature are
deduced from the analytic structure of the mapped model, demonstrating the
potential power of this approach. NRG calculations are presented for up to five
site cluster. We investigate the appearance of frustration induced non-Fermi
liquid fixed points in the trimer, and demonstrate the existence of several
critical points of KT type at which ferromagnetic correlations suppress the
screening of an additional effective spin-$1/2$ degree of freedom.


  We consider the s-channel scattering of massive fermion or vector-boson pairs
with equal helicities, mediated by a graviton in the linearized Einstein
theory. We show that, although in general both spin-2 and spin-0 components are
present in the exchanged graviton, there is a special set of reference frames
where the spin-0 graviton component vanishes. This is connected to the
dependence of the trace of the graviton propagator on the effective dimension
of the space-time spanned by the sources. On the other hand, one finds a
non-vanishing (Lorentz-invariant) interference of the graviton amplitude with
the scalar-exchange amplitude, that in principle could give measurable effects.


  Ab initio electronic structure calculations show that the recently identified
quasi-two-dimensional electride Y$_2$C is a weak itinerant ferromagnet or at
least close to a ferromagnetic instability. The ferromagnetism is induced by
the electride electrons, which are loosely bound around interstitial sites and
overlap with each other to form two-dimensional interlayer conduction bands.
The semimetallicity and two-dimensionality of the band structure are the key to
understanding this ferromagnetic instability.


  The definition of Rouquier for the families of characters of Weyl groups in
terms of blocks of the associated Iwahori-Hecke algebra has made possible the
generalization of this notion to the complex reflection groups. Here we give an
algorithm for the determination of the "Rouquier blocks" of the cyclotomic
Ariki-Koike algebras.


  We have investigated the effects of primeval starbursts on the galactic
structure, showing that the dynamical structure of young galaxies is changed by
relaxation of a stellar system formed by a starburst-driven outflowing gas
(superwind). When a superwind interacts with halo gas, an expanding dense
supershell of shocked gas is formed. Using a similarity solution for the
expanding shell and a condition for the gravitational instability of a gaseous
shell, we show that an expanding gaseous shell with a mass of several $10^{10}
M_\odot$ and a radius of several kpc becomes gravitationally unstable to form
stars. A stellar shell is thus formed, relaxes and will evolve into a fat
stellar system. \par In order to investigate the fate of the stellar shell and
its dynamical influence on the host galaxy, we performed three dimensional
$N$-body simulations of a stellar shell plus disk system. The evolution of the
stellar shell was computed under two types of environment: an external
flattened potential and a live stellar disk. We find that the relaxation
process and resultant structure are significantly affected by the external disk
potential, and also depend on the velocity dispersion of the initial shell
stars and the mass of the shell. The final galactic structure ranges from a
thick disk and a compact bulge with a high density core to a thin disk with a
diffuse bulge. Isodensity maps of the computed disk plus bulge system resemble
isophotes of S0 galaxies. We suggest that the effects of primeval starbursts
would explain some observational properties of S0 galaxies.


  Facial expression recognition (FER) has always been a challenging issue in
computer vision. The different expressions of emotion and uncontrolled
environmental factors lead to inconsistencies in the complexity of FER and
variability of between expression categories, which is often overlooked in most
facial expression recognition systems. In order to solve this problem
effectively, we presented a simple and efficient CNN model to extract facial
features, and proposed a complexity perception classification (CPC) algorithm
for FER. The CPC algorithm divided the dataset into an easy classification
sample subspace and a complex classification sample subspace by evaluating the
complexity of facial features that are suitable for classification. The
experimental results of our proposed algorithm on Fer2013 and CK-plus datasets
demonstrated the algorithm's effectiveness and superiority over other
state-of-the-art approaches.


  We report on an XMM-Newton observation of the ultraluminous infrared galaxy
NGC 6240. The 0.3-10 keV spectrum can be successfully modelled with: (i) three
collisionally ionized plasma components with temperatures of about 0.7, 1.4,
and 5.5 keV; (ii) a highly absorbed direct power-law component; and (iii) a
neutral Fe K_alpha and K_beta line. We detect a significant neutral column
density gradient which is correlated with the temperature of the three plasma
components. Combining the XMM-Newton spectral model with the high spatial
resolution Chandra image we find that the temperatures and the column densities
increase towards the center.
  With high significance, the Fe K line complex is resolved into three distinct
narrow lines: (i) the neutral Fe K_alpha line at 6.4 keV; (ii) an ionized line
at about 6.7 keV; and (iii) a higher ionized line at 7.0 keV (a blend of the Fe
XXVI and the Fe K_beta line). While the neutral Fe K line is most probably due
to reflection from optically thick material, the Fe XXV and Fe XXVI emission
arises from the highest temperature ionized plasma component.
  We have compared the plasma parameters of the ultraluminous infrared galaxy
NGC 6240 with those found in the local starburst galaxy NGC 253. We find a
striking similarity in the plasma temperatures and column density gradients,
suggesting a similar underlying physical process at work in both galaxies.


  We report a new hot post-asymptotic giant branch (PAGB) star in the Galactic
globular cluster (GC) E3, which is one of the first of the identified PAGB
stars in a GC to show a binary signature. The star stands out as the brightest
source in E3 in the \mbox{{\em Astrosat}}/UVIT images. We confirmed its
membership with the cluster E3 using Gaia DR3 kinematics and parallax
measurements. We supplemented the photometric observations with radial
velocities (RVs) from high-resolution spectroscopic observations at two epochs
and with ground- and space-based photometric observations from 0.13 $\mu$m to
22 $\mu$m. We find that the RVs vary over $\sim$6 \kms\ between the two epochs.
This is an indication of the star being in a binary orbit. A simulation of
possible binary systems with the observed RVs suggests a binary period of
either 39.12 days or 17.83 days with mass ratio q$\geq$1.0. The [Fe/H] derived
using the high-resolution spectra is $\sim -$0.7 dex, which closely matches the
cluster metallicity. The spectroscopic and photometric measurements suggest
\Teff\ and $\log g$ of the star as 17\,500$\pm$1\,000~K and 2.37$\pm$0.20~dex,
respectively. Various PAGB evolutionary tracks on the Hertzsprung--Russell
(H-R) diagram suggest a current mass of the star in the range 0.51$-$0.55
\Msun. The star is enriched with C and O abundances, showing similar CNO
abundances compared to the other PAGB stars in GCs with the evidence of the
third dredge-up on the AGB phase.


  We present a novel analytical approach for the calculation of the mean
density of states in many-body systems made of confined indistinguishable and
non-interacting particles. Our method makes explicit the intrinsic geometry
inherent in the symmetrization postulate and, in the spirit of the usual Weyl
expansion for the smooth part of the density of states in single-particle
confined systems, our results take the form of a sum over clusters of particles
moving freely around manifolds in configuration space invariant under elements
of the group of permutations. Being asymptotic, our approximation gives
increasingly better results for large excitation energies and we formally
confirm that it coincides with the celebrated Bethe estimate in the appropriate
region. Moreover, our construction gives the correct high energy asymptotics
expected from general considerations, and shows that the emergence of the
fermionic ground state is actually a consequence of an extremely delicate large
cancellation effect. Remarkably, our expansion in cluster zones is naturally
incorporated for systems of interacting particles, opening the road to address
the fundamental problem about the interplay between confinement and
interactions in many-body systems of identical particles.


  In this paper we present many new families of identities for multiple
harmonic sums using binomial coefficients. Some of these generalize a few
recent results of Hessami Pilehrood et al. As applications we prove several
conjectures involving multiple zeta star values (MZSV): the Two-one formula
conjectured by Ohno and Zudilin, and a few conjectures of Imatomi et al.
involving 2-3-2-1 type MZSV, where 2 means some finite string of 2's


  For one parameter subgroup action on a finite volume homogeneous space, we
consider the set of points admitting divergent on average trajectories. We show
that the Hausdorff dimension of this set is strictly less than the manifold
dimension of the homogeneous space. As a corollary we know that the Hausdorff
dimension of the set of points admitting divergent trajectories is not full,
which proves a conjecture of Y. Cheung.


  Transformer-based networks applied to image patches have achieved
cutting-edge performance in many vision tasks. However, lacking the built-in
bias of convolutional neural networks (CNN) for local image statistics, they
require large datasets and modifications to capture relationships between
patches, especially in segmentation tasks. Images in the frequency domain might
be more suitable for the attention mechanism, as local features are represented
globally. By transforming images into the frequency domain, local features are
represented globally. Due to MRI data acquisition properties, these images are
particularly suitable. This work investigates how the image domain (spatial or
k-space) affects segmentation results of deep learning (DL) models, focusing on
attention-based networks and other non-convolutional models based on MLPs. We
also examine the necessity of additional positional encoding for
Transformer-based networks when input images are in the frequency domain. For
evaluation, we pose a skull stripping task and a brain tissue segmentation
task. The attention-based models used are PerceiverIO and a vanilla Transformer
encoder. To compare with non-attention-based models, an MLP and ResMLP are also
trained and tested. Results are compared with the Swin-Unet, the
state-of-the-art medical image segmentation model. Experimental results show
that using k-space for the input domain can significantly improve segmentation
results. Also, additional positional encoding does not seem beneficial for
attention-based networks if the input is in the frequency domain. Although none
of the models matched the Swin-Unet's performance, the less complex models
showed promising improvements with a different domain choice.


  We present a program tool, SimClust, designed for Monte-Carlo modeling of
star clusters. It populates the available stellar isochrones with stars
according to the initial mass function and distributes stars randomly following
the analytical surface number density profile. The tool is aimed at simulating
realistic images of extragalactic star clusters and can be used to: (i)
optimize object detection algorithms, (ii) perform artificial cluster tests for
the analysis of star cluster surveys, and (iii) assess the stochastic effects
introduced into photometric and structural parameters of clusters due to random
distribution of luminous stars and non-uniform interstellar extinction. By
applying SimClust, we have demonstrated a significant influence of stochastic
effects on the determined photometric and structural parameters of low-mass
star clusters in the M31 galaxy disk. The source code and examples are
available at the SimClust website: http://www.astro.ff.vu.lt/software/simclust/


  We study an acceleration phenomenon arising in monostable
integro-differential equations with a weak Allee effect. Previous works have
shown its occurrence and have given correct upper bounds on the rate of
expansion in some particular cases, but precise lower bounds were still
missing. In this paper, we provide a sharp lower bound for this acceleration
rate, valid for a large class of dispersion operators. Our results manage to
cover fractional Laplace operators and standard convolutions in a unified way,
which is new in the literature. A first very important result of the paper is a
general flattening estimate of independent interest: this phenomenon appears
regularly in acceleration situations, but getting quantitative estimates is
most of the time open. This estimate at hand, we construct a very subtle
sub-solution that captures the expected dynamics of the accelerating solution
(rates of expansion and flattening) and identifies several various regimes that
appear in the dynamics depending on the parameters of the problem.


  Spin-dependent transport processes in thin near-surface doping regions
created by low energy ion implantation of arsenic in silicon are detected by
two methods, spin-dependent recombination (SDR) using microwave
photoconductivity and electrically detected magnetic resonance (EDMR)
monitoring the DC current through the sample. The high sensitivity of these
techniques allows the observation of the magnetic resonance in particular of As
in weak magnetic fields and at low resonance frequencies (40-1200 MHz), where
high-field-forbidden transitions between the magnetic substates can be observed
due to the mixing of electron and nuclear spin states. Several
implantation-induced defects are present in the samples studied and act as spin
readout partner. We explicitly demonstrate this by electrically detected
electron double resonance experiments and identify a pair recombination of
close pairs formed by As donors and oxygen-vacancy centers in an excited
triplet state (SL1) as the dominant spin-dependent process in As-implanted
Czochralski-grown Si.


  Drawing a direct analogy with the well-studied vibration or elastic modes, we
introduce an object's fracture modes, which constitute its preferred or most
natural ways of breaking. We formulate a sparsified eigenvalue problem, which
we solve iteratively to obtain the n lowest-energy modes. These can be
precomputed for a given shape to obtain a prefracture pattern that can
substitute the state of the art for realtime applications at no runtime cost
but significantly greater realism. Furthermore, any realtime impact can be
projected onto our modes to obtain impact-dependent fracture patterns without
the need for any online crack propagation simulation. We not only introduce
this theoretically novel concept, but also show its fundamental and practical
superiority in a diverse set of examples and contexts.


  The future Quantum Internet is expected to be based on a hybrid architecture
with core quantum transport capabilities complemented by conventional
networking.Practical and foundational considerations indicate the need for
conventional control and data planes that (i) utilize extensive existing
telecommunications fiber infrastructure, and (ii) provide parallel conventional
data channels needed for quantum networking protocols. We propose a
quantum-conventional network (QCN) harness to implement a new architecture to
meet these requirements. The QCN control plane carries the control and
management traffic, whereas its data plane handles the conventional and quantum
data communications. We established a local area QCN connecting three quantum
laboratories over dedicated fiber and conventional network connections. We
describe considerations and tradeoffs for layering QCN functionalities,
informed by our recent quantum entanglement distribution experiments conducted
over this network.