title:
Practical Challenges in Differentially-Private Federated Survival
  Analysis of Medical Data

abstract:
  Survival analysis or time-to-event analysis aims to model and predict the
time it takes for an event of interest to happen in a population or an
individual. In the medical context this event might be the time of dying,
metastasis, recurrence of cancer, etc. Recently, the use of neural networks
that are specifically designed for survival analysis has become more popular
and an attractive alternative to more traditional methods. In this paper, we
take advantage of the inherent properties of neural networks to federate the
process of training of these models. This is crucial in the medical domain
since data is scarce and collaboration of multiple health centers is essential
to make a conclusive decision about the properties of a treatment or a disease.
To ensure the privacy of the datasets, it is common to utilize differential
privacy on top of federated learning. Differential privacy acts by introducing
random noise to different stages of training, thus making it harder for an
adversary to extract details about the data. However, in the realistic setting
of small medical datasets and only a few data centers, this noise makes it
harder for the models to converge. To address this problem, we propose
DPFed-post which adds a post-processing stage to the private federated learning
scheme. This extra step helps to regulate the magnitude of the noisy average
parameter update and easier convergence of the model. For our experiments, we
choose 3 real-world datasets in the realistic setting when each health center
has only a few hundred records, and we show that DPFed-post successfully
increases the performance of the models by an average of up to $17\%$ compared
to the standard differentially private federated learning scheme.


title:
Time to Focus: A Comprehensive Benchmark Using Time Series Attribution
  Methods

abstract:
  In the last decade neural network have made huge impact both in industry and
research due to their ability to extract meaningful features from imprecise or
complex data, and by achieving super human performance in several domains.
However, due to the lack of transparency the use of these networks is hampered
in the areas with safety critical areas. In safety-critical areas, this is
necessary by law. Recently several methods have been proposed to uncover this
black box by providing interpreation of predictions made by these models. The
paper focuses on time series analysis and benchmark several state-of-the-art
attribution methods which compute explanations for convolutional classifiers.
The presented experiments involve gradient-based and perturbation-based
attribution methods. A detailed analysis shows that perturbation-based
approaches are superior concerning the Sensitivity and occlusion game. These
methods tend to produce explanations with higher continuity. Contrarily, the
gradient-based techniques are superb in runtime and Infidelity. In addition, a
validation the dependence of the methods on the trained model, feasible
application domains, and individual characteristics is attached. The findings
accentuate that choosing the best-suited attribution method is strongly
correlated with the desired use case. Neither category of attribution methods
nor a single approach has shown outstanding performance across all aspects.


title: Modeling Structure with Undirected Neural Networks

abstract:
  Neural networks are powerful function estimators, leading to their status as
a paradigm of choice for modeling structured data. However, unlike other
structured representations that emphasize the modularity of the problem --
e.g., factor graphs -- neural networks are usually monolithic mappings from
inputs to outputs, with a fixed computation order. This limitation prevents
them from capturing different directions of computation and interaction between
the modeled variables.
  In this paper, we combine the representational strengths of factor graphs and
of neural networks, proposing undirected neural networks (UNNs): a flexible
framework for specifying computations that can be performed in any order. For
particular choices, our proposed models subsume and extend many existing
architectures: feed-forward, recurrent, self-attention networks, auto-encoders,
and networks with implicit layers. We demonstrate the effectiveness of
undirected neural architectures, both unstructured and structured, on a range
of tasks: tree-constrained dependency parsing, convolutional image
classification, and sequence completion with attention. By varying the
computation order, we show how a single UNN can be used both as a classifier
and a prototype generator, and how it can fill in missing parts of an input
sequence, making them a promising field for further research.


title: Meshless Methods for Magnetohydrodynamics with Vector Potential

abstract:
  We present a meshless method for magnetohydrodynamics by evolving the vector
potential of magnetic fields. A novel scheme and numerical techniques are
developed to restrict the divergence of magnetic field, based on the Meshless
Finite Mass/Volume with HLLD Riemann solver for conservative flux calculation.
We found the magnetic field could be stabilized by a proper smoothing process
and so the long-term evolution becomes available. To verify the new scheme, we
perform the Brio-Wu shock tube, 2D and 3D Orszag-Tang vortex test problems. Our
results suggest that our method is robust and has better precision on central
offset, amplitude and detailed pattern than an existing meshless code$-$GIZMO.


title: Eliminating Sandwich Attacks with the Help of Game Theory

abstract:
  Predatory trading bots lurking in Ethereum's mempool present invisible
taxation of traders on automated market makers (AMMs). AMM traders specify a
slippage tolerance to indicate the maximum price movement they are willing to
accept. This way, traders avoid automatic transaction failure in case of small
price movements before their trade request executes. However, while a too-small
slippage tolerance may lead to trade failures, a too-large slippage tolerance
allows predatory trading bots to profit from sandwich attacks. These bots can
extract the difference between the slippage tolerance and the actual price
movement as profit.
  In this work, we introduce the sandwich game to analyze sandwich attacks
analytically from both the attacker and victim perspectives. Moreover, we
provide a simple and highly effective algorithm that traders can use to set the
slippage tolerance. We unveil that most broadcasted transactions can avoid
sandwich attacks while simultaneously only experiencing a low risk of
transaction failure. Thereby, we demonstrate that a constant auto-slippage
cannot adjust to varying trade sizes and pool characteristics. Our algorithm
outperforms the constant auto-slippage suggested by the biggest AMM, Uniswap,
in all performed tests. Specifically, our algorithm repeatedly demonstrates a
cost reduction exceeding a factor of 100.


title: Geodesic motion in Euclidean Schwarzschild geometry

abstract:
  This paper performs a systematic investigation of geodesic motion in
Euclidean Schwarzschild geometry, which is studied in the equatorial plane.
Unlike the Lorentzian-signature case, it is not compelling to impose
normalization of a four-velocity. Radial geodesics are obtained by a careful
use of an algebraic equation of third degree. No elliptic-like orbits exist in
Euclidean Schwarzschild geometry, unlike the corresponding Lorentzian pattern.
Among unbound orbits, only unbound first-kind orbits are allowed, unlike
general relativity where unbound second-kind orbits are always allowed. The
lack of normalization condition mentioned before makes it necessary to choose
an unknown function, which is selected after a detailed analysis.


title:
Spectral asymptotics for the fourth-order operator with periodic
  coefficients

abstract:
  We consider the self-adjoint fourth-order operator with real $1$-periodic
coefficients on the unit interval. The spectrum of this operator is discrete.
We determine the high energy asymptotics for its eigenvalues.


title: Towards modified bimetric theories within non-product spectral geometry

abstract:
  We discuss class of doubled geometry models with diagonal metrics. Based on
the analysis of known examples we formulate a hypothesis that supports treating
them as modified bimetric gravity theories. Certain steps towards the generic
case are then performed.


title:
First passage in the presence of stochastic resetting and a potential
  barrier

abstract:
  Diffusion and first passage in the presence of stochastic resetting and
potential bias have been of recent interest. We study a few models,
systematically progressing in their complexity, to understand the usefulness of
resetting. In the parameter space of the models, there are multiple continuous
and discontinuous transitions where the advantage of resetting vanishes. We
show these results analytically exactly for a tent-potential, and numerically
accurately for a quartic-potential relevant to a magnetic system at low
temperatures. We find that the spatial asymmetry of the potential across the
barrier, and the number of absorbing boundaries, play a crucial role in
determining the type of transition.


title:
Unsupervised topological learning approach of crystal nucleation in pure
  Tantalum

abstract:
  Nucleation phenomena commonly observed in our every day life are of
fundamental, technological and societal importance in many areas, but some of
their most intimate mechanisms remain however to be unraveled. Crystal
nucleation, the early stages where the liquid-to-solid transition occurs upon
undercooling, initiates at the atomic level on nanometer length and
sub-picoseconds time scales and involves complex multidimensional mechanisms
with local symmetry breaking that can hardly be observed experimentally in the
very details. To reveal their structural features in simulations without a
priori, an unsupervised learning approach founded on topological descriptors
loaned from persistent homology concepts is proposed. Applied here to a
monatomic metal, namely Tantalum (Ta), it shows that both translational and
orientational ordering always come into play simultaneously when homogeneous
nucleation starts in regions with low five-fold symmetry.


title:
Dynamical anomalies and structural features of Active Brownian Particles
  characterised by two repulsive length scales

abstract:
  In this work we study a two-dimensional system composed by Active Brownian
Particles (ABPs) interacting via a repulsive potential with two-length-scales,
a soft shell and a hard-core. Depending on the ratio between the strength of
the soft shell barrier and the activity, we find two regimes: If this ratio is
much larger or smaller than 1, the observed behaviour is comparable with ABPs
interacting via a single length-scale potential. If this ratio is similar to 1,
the two length-scales are relevant for both structure and dynamical properties.
On the structural side, when the system exhibits a motility induced phase
separation, the dense phase is characterised by new and more complex structures
compared with the hexatic phase observed in single length-scale systems. On the
dynamical side, as far as we are aware, this is the first representation of an
anomalous dynamics in active particles.


title:
Stability estimates for the sharp spectral gap bound under a
  curvature-dimension condition

abstract:
  We study stability of the sharp spectral gap bounds for metric-measure spaces
satisfying a curvature bound. Our main result, new even in the smooth setting,
is a sharp quantitative estimate showing that if the spectral gap of an
RCD$(N-1, N)$ space is almost minimal, then the pushforward of the measure by
an eigenfunction associated with the spectral gap is close to a Beta
distribution. The proof combines estimates on the eigenfunction obtained via a
new $L^1$-functional inequality for RCD spaces with Stein's method for
distribution approximation. We also derive analogous, almost sharp, estimates
for infinite and negative values of the dimension parameter.


title:
Impact of Parameter Sparsity on Stochastic Gradient MCMC Methods for
  Bayesian Deep Learning

abstract:
  Bayesian methods hold significant promise for improving the uncertainty
quantification ability and robustness of deep neural network models. Recent
research has seen the investigation of a number of approximate Bayesian
inference methods for deep neural networks, building on both the variational
Bayesian and Markov chain Monte Carlo (MCMC) frameworks. A fundamental issue
with MCMC methods is that the improvements they enable are obtained at the
expense of increased computation time and model storage costs. In this paper,
we investigate the potential of sparse network structures to flexibly trade-off
model storage costs and inference run time against predictive performance and
uncertainty quantification ability. We use stochastic gradient MCMC methods as
the core Bayesian inference method and consider a variety of approaches for
selecting sparse network structures. Surprisingly, our results show that
certain classes of randomly selected substructures can perform as well as
substructures derived from state-of-the-art iterative pruning methods while
drastically reducing model training times.


title:
Energy Management Based on Multi-Agent Deep Reinforcement Learning for A
  Multi-Energy Industrial Park

abstract:
  Owing to large industrial energy consumption, industrial production has
brought a huge burden to the grid in terms of renewable energy access and power
supply. Due to the coupling of multiple energy sources and the uncertainty of
renewable energy and demand, centralized methods require large calculation and
coordination overhead. Thus, this paper proposes a multi-energy management
framework achieved by decentralized execution and centralized training for an
industrial park. The energy management problem is formulated as a
partially-observable Markov decision process, which is intractable by dynamic
programming due to the lack of the prior knowledge of the underlying stochastic
process. The objective is to minimize long-term energy costs while ensuring the
demand of users. To solve this issue and improve the calculation speed, a novel
multi-agent deep reinforcement learning algorithm is proposed, which contains
the following key points: counterfactual baseline for facilitating contributing
agents to learn better policies, soft actor-critic for improving robustness and
exploring optimal solutions. A novel reward is designed by Lagrange multiplier
method to ensure the capacity constraints of energy storage. In addition,
considering that the increase in the number of agents leads to performance
degradation due to large observation spaces, an attention mechanism is
introduced to enhance the stability of policy and enable agents to focus on
important energy-related information, which improves the exploration efficiency
of soft actor-critic. Numerical results based on actual data verify the
performance of the proposed algorithm with high scalability, indicating that
the industrial park can minimize energy costs under different demands.


title: Particle Transformer for Jet Tagging

abstract:
  Jet tagging is a critical yet challenging classification task in particle
physics. While deep learning has transformed jet tagging and significantly
improved performance, the lack of a large-scale public dataset impedes further
enhancement. In this work, we present JetClass, a new comprehensive dataset for
jet tagging. The JetClass dataset consists of 100 M jets, about two orders of
magnitude larger than existing public datasets. A total of 10 types of jets are
simulated, including several types unexplored for tagging so far. Based on the
large dataset, we propose a new Transformer-based architecture for jet tagging,
called Particle Transformer (ParT). By incorporating pairwise particle
interactions in the attention mechanism, ParT achieves higher tagging
performance than a plain Transformer and surpasses the previous
state-of-the-art, ParticleNet, by a large margin. The pre-trained ParT models,
once fine-tuned, also substantially enhance the performance on two widely
adopted jet tagging benchmarks.


title:
A multivariate pseudo-likelihood approach to estimating directional
  ocean wave models

abstract:
  Ocean buoy data in the form of high frequency multivariate time series are
routinely recorded at many locations in the world's oceans. Such data can be
used to characterise the ocean wavefield, which is important for numerous
socio-economic and scientific reasons. This characterisation is typically
achieved by modelling the frequency-direction spectrum, which decomposes
spatiotemporal variability by both frequency and direction. State-of-the-art
methods for estimating the parameters of such models do not make use of the
full spatiotemporal content of the buoy observations due to unnecessary
assumptions and smoothing steps. We explain how the multivariate debiased
Whittle likelihood can be used to jointly estimate all parameters of such
frequency-direction spectra directly from the recorded time series. When
applied to North Sea buoy data, debiased Whittle likelihood inference reveals
smooth evolution of spectral parameters over time. We discuss challenging
practical issues including model misspecification, and provide guidelines for
future application of the method.


title: Modulation of Spin Seebeck Effect by Hydrogenation

abstract:
  We demonstrate the modulation of spin Seebeck effect (SSE) by hydrogenation
in Pd/YIG bilayers. In the presence of 3% hydrogen gas, SSE voltage decreases
by more than 50% from the magnitude observed in pure Ar gas. The modulation of
the SSE voltage is reversible, but the recovery of the SSE voltage to the
prehydrogenation value takes a few days because of a long time constant of
hydrogen desorption. We also demonstrate that the spin Hall magnetoresistance
of the identical sample reduces significantly with hydrogen exposure,
supporting that the observed modulation of spin current signals originates from
hydrogenation of Pd/YIG.


title:
Addressing Data Scarcity in Multimodal User State Recognition by
  Combining Semi-Supervised and Supervised Learning

abstract:
  Detecting mental states of human users is crucial for the development of
cooperative and intelligent robots, as it enables the robot to understand the
user's intentions and desires. Despite their importance, it is difficult to
obtain a large amount of high quality data for training automatic recognition
algorithms as the time and effort required to collect and label such data is
prohibitively high. In this paper we present a multimodal machine learning
approach for detecting dis-/agreement and confusion states in a human-robot
interaction environment, using just a small amount of manually annotated data.
We collect a data set by conducting a human-robot interaction study and develop
a novel preprocessing pipeline for our machine learning approach. By combining
semi-supervised and supervised architectures, we are able to achieve an average
F1-score of 81.1\% for dis-/agreement detection with a small amount of labeled
data and a large unlabeled data set, while simultaneously increasing the
robustness of the model compared to the supervised approach.


title:
Spin-Phonon Relaxation in Magnetic Molecules: Theory, Predictions and
  Insights

abstract:
  Magnetic molecules have played a central role in the development of magnetism
and coordination chemistry and their study keeps leading innovation in
cutting-edge scientific fields such as magnetic resonance, magnetism,
spintronics, and quantum technologies. Crucially, a long spin lifetime well
above cryogenic temperature is a stringent requirement for all these
applications. In this chapter we review the foundations of spin relaxation
theory and provide a detailed overview of first-principles strategies applied
to the problem of spin-phonon relaxation in magnetic molecules. Firstly, we
present a rigorous formalism of spin-phonon relaxation based on open quantum
systems theory. These results are then used to derive classical
phenomenological relations based on the Debye model. Finally, we provide a
prescription of how to map the relaxation formalism onto existing electronic
structure methods to obtain a quantitative picture of spin-phonon relaxation.
Examples from the literature, including both transition metals and lanthanides
compounds, will be discussed in order to illustrate how Direct, Orbach and
Raman relaxation mechanisms can affect spin dynamics for this class of
compounds.


title:
Optimal $L^2$ error estimates of the penalty finite element method for
  the unsteady Navier-Stokes equations with nonsmooth initial data

abstract:
  In this paper, both semidiscrete and fully discrete finite element methods
are analyzed for the penalized two-dimensional unsteady Navier-Stokes equations
with nonsmooth initial data. First order backward Euler method is applied for
the time discretization, whereas conforming finite element method is used for
the spatial discretization. Optimal $L^2$ error estimates for the semidiscrete
as well as the fully discrete approximations of the velocity and of the
pressure are derived for realistically assumed conditions on the data. The main
ingredient in the proof is the appropriate exploitation of the inverse of the
penalized Stokes operator, negative norm estimates and time weighted estimates.
Numerical examples are discussed at the end which conform our theoretical
results.


title:
Correlation effects in Barkhausen noise and magnetic attenuation in soft
  ribbons

abstract:
  The propagation of the effects connected with the occurrence of magnetization
reversals in an amorphous ribbon of Fe$_{63}$B$_{64}$Si$_{8}$Ni$_{15}$ has been
investigated using a method based on two pickup coils separated by a distance
variable between 2 an 40 mm. The ratio $R$ between the voltage signals induced
in the coils contains information on the location where the magnetization
reversal took place. This information can be extracted by knowing the function
$V(x)$ which represents the attenuation of a signal generated by a reversal
that took place at a distance x from the coil. A mathematical model for
extracting this function starting from the histogram of the experimentally
measured values of $R$ is presented. The attenuation function obtained in this
way is relatively independent on the distance between the coils, and this is in
strong support of the correctness of the model adopted.


title: Symplectic Integrators in Corotating Coordinates

abstract:
  The dynamic equation of mass point in rotating coordinates is governed by
Coriolis and centrifugal force, besides a corotating potential relative to
frame. Such a system is no longer a canonical Hamiltonian system so that the
construction of symplectic integrator is problematic. In this paper, we present
three integrators for this question. It is significant that those schemes have
the good property of near-conservation of energy. We proved that the discrete
symplectic map of $(p_n, x_n) \mapsto (p_{n+1}, x_{n+1})$ in corotating
coordinates exists and the two integrators are variational symplectic. Two
groups of numerical experiments demonstrates the precision and long-term
convergence of these integrators in the examples of corotating top-hat density
and circular restricted three-body system.


title: Semilinear elliptic equations on rough domains

abstract:
  The paper makes use of recent results in the theory of Banach lattices and
positive operators to deal with abstract semilinear equations. The aim is to
work with minimal or no regularity conditions on the boundary of the domains,
where the usual arguments based on maximum principles do not apply. A key
result is an application of Kato's inequality to prove a comparison theorem for
eigenfunctions that only requires interior regularity and avoids the use of the
Hopf boundary maximum principle. We demonstrate the theory on an abstract
degenerate logistic equation by proving the existence, uniqueness and stability
of non-trivial positive solutions. Examples of operators include the Dirichlet
Laplacian on arbitrary bounded domains, a simplified construction of the Robin
Laplacian on arbitrary domains with boundary of finite measure and general
elliptic operators in divergence form.


title:
Coexistence of different pinning mechanisms in Bi-2223 superconductor
  and its implications for using the material for high current applications

abstract:
  We investigate the pinning mechanism in high-critical-current polycrystalline
samples of Bi-2223 (Bi2Sr2Ca2Cu3O10) utilized in high current applications.
Using differential magneto-optical (DMO) imaging technique, we track the
magnetic field penetration in the sample. Our DMO imaging studies show circular
regions with an average diameter of 20 um with dark contrast. We identify these
as strong-pinning regions with a substantially higher local penetration field
than the surrounding regions. A unique feature of these strong-pinning centers
is that they survive upto high temperatures (near Tc) and produce a
non-Gaussian distribution of the penetration field strength. By analysing the
field dependence of the pinning force behaviour, we identify two distinct
pinning mechanisms: at low temperatures, well below Tc, it is predominantly
surface pinning mechanism and at higher temperatures near Tc, we see a
crossover into a purely delTc pinning mechanism. Our studies show that surface
pinning effects are related to grain alignment, grain boundary, and voids in
the sample. The effect of these diminishes near Tc, and the strong-pinning
regions here are related to local stoichiometric fluctuations. We investigate
the impact of these pinning centers on the current distribution in a
macroscopic Bi-2223 superconducting cylindrical tube. We map the current
distribution across the macroscopic cylindrical tube using an array of hall
sensors distributed around the cylinder. The map shows that the current
distribution is non-uniform across the tube at high currents. The
non-uniformity reveals an inhomogeneous distribution of strong-pinning centers
across large length scales in superconductors used for applications.


title:
An Experimental and Theoretical Investigation of the Gas-Phase C(3P) +
  N2O Reaction. Low Temperature Rate Constants and Astrochemical Implications

abstract:
  The reaction between atomic carbon in its ground electronic state, C(3P), and
nitrous oxide, N2O, has been studied below room temperature due to its
potential importance for astrochemistry, with both species considered to be
present at high abundance levels in a range of interstellar environments. On
the experimental side, we measured rate constants for this reaction over the
50-296 K range using a continuous supersonic flow reactor. C(3P) atoms were
generated by the pulsed photolysis of carbon tetrabromide at 266 nm and were
detected by pulsed laser induced fluorescence at 115.8 nm. Additional
measurements allowing the major product channels to be elucidated were also
performed. On the theoretical side, statistical rate theory was used to
calculate low temperature rate constants. These calculations employed the
results of new electronic structure calculations of the 3A" potential energy
surface of CNNO and provided a basis to extrapolate the measured rate constants
to lower temperatures and pressures. The rate constant was found to increase
monotonically as the temperature falls, reaching a value of k(C(3P)+N2O)(50 K)
= (7.9 +- 0.8) x 10-11 cm3 s-1 at 50 K. As current astrochemical models do not
include the C + N2O reaction, we tested the influence of this process on
interstellar N2O and other related species using a gas-grain model of dense
interstellar clouds. These simulations predict that N2O abundances decrease
significantly at intermediate times (10^3 - 10^5 years) when gas-phase C(3P)
abundances are high.


title:
An inverse problem for Hankel operators and turbulent solutions of the
  cubic Szeg\H{o} equation on the line

abstract:
  We construct inverse spectral theory for finite rank Hankel operators acting
on the Hardy space of the upper half-plane. A particular feature of our theory
is that we completely characterise the set of spectral data. As an application
of this theory, we prove the genericity of turbulent solutions of the cubic
Szeg\H{o} equation on the real line.


title: SCR: Smooth Contour Regression with Geometric Priors

abstract:
  While object detection methods traditionally make use of pixel-level masks or
bounding boxes, alternative representations such as polygons or active contours
have recently emerged. Among them, methods based on the regression of Fourier
or Chebyshev coefficients have shown high potential on freeform objects. By
defining object shapes as polar functions, they are however limited to
star-shaped domains. We address this issue with SCR: a method that captures
resolution-free object contours as complex periodic functions. The method
offers a good compromise between accuracy and compactness thanks to the design
of efficient geometric shape priors. We benchmark SCR on the popular COCO 2017
instance segmentation dataset, and show its competitiveness against existing
algorithms in the field. In addition, we design a compact version of our
network, which we benchmark on embedded hardware with a wide range of power
targets, achieving up to real-time performance.


title:
Extended Object Tracking in Curvilinear Road Coordinates for Autonomous
  Driving

abstract:
  In literature, Extended Object Tracking (EOT) algorithms developed for
autonomous driving predominantly provide obstacles state estimation in
cartesian coordinates in the Vehicle Reference Frame. However, in many
scenarios, state representation in road-aligned curvilinear coordinates is
preferred when implementing autonomous driving subsystems like cruise control,
lane-keeping assist, platooning, etc. This paper proposes a Gaussian Mixture
Probability Hypothesis Density~(GM-PHD) filter with an Unscented Kalman
Filter~(UKF) estimator that provides obstacle state estimates in curvilinear
road coordinates. We employ a hybrid sensor fusion architecture between Lidar
and Radar sensors to obtain rich measurement point representations for EOT. The
measurement model for the UKF estimator is developed with the integration of
coordinate conversion from curvilinear road coordinates to cartesian
coordinates by using cubic hermit spline road model. The proposed algorithm is
validated through Matlab Driving Scenario Designer simulation and experimental
data collected at Monza Eni Circuit.


title:
Coordination of resources at the edge of the electricity grid:
  systematic review and taxonomy

abstract:
  This paper proposes a novel taxonomy of coordination strategies for
distributed energy resources at the edge of the electricity grid, based on a
systematic analysis of key literature trends. The coordination of distributed
energy resources such as decentralised generation and flexibility sources is
critical for decarbonising electricity and achieving climate goals. The
literature on the topic is growing exponentially; however, there is ambiguity
in the terminology used to date. We seek to resolve this lack of clarity by
synthesising the categories of coordination strategies in a novel exhaustive,
mutually exclusive taxonomy based on agency, information and game type. The
relevance of these concepts in the literature is illustrated through a
systematic literature review of 84,741 publications using a structured topic
search query. Then 93 selected coordination strategies are analysed in more
detail and mapped onto this framework. Clarity on structural assumptions is key
for selecting appropriate coordination strategies for differing contexts within
energy systems. We argue that a plurality of complementary strategies is needed
to coordinate energy systems' different components and achieve deep
decarbonisation.


title:
Analysis of a fractional cross-diffusion system for multi-species
  populations

abstract:
  The global in time existence of weak solutions to a cross-diffusion system
with fractional diffusion in the whole space is proved. The equations describe
the evolution of multi-species populations in the regime of large-distance
interactions; they have been derived in the many-particle limit from moderately
interacting particle systems with L\'evy noise. The existence proof is based on
a three-level approximation scheme, entropy and moment estimates, and a new
Aubin-Lions compactness lemma in the whole space.


title:
GB6 J2113+1121: A multi-wavelength flaring gamma-ray blazar temporally
  and spatially coincident with the neutrino event IceCube-191001A

abstract:
  A radio-emitting tidal disruption event (AT2019dsg) is proposed as a likely
counterpart of the IceCube neutrino event IceCube-191001A. In this work we have
revisited the Fermi-LAT data in the direction of the neutrino and confirmed no
signal at the site of AT2019dsg. Instead, at the edge of the 90% confidential
level error region of this neutrino there is a gamma-ray transient source
spatially coincident with the blazar GB6 J2113+1121. When IceCube-191001A
arriving, GB6 J2113+1121 is undergoing the strongest gamma-ray flare since the
start of the Fermi-LAT operation, with a variability amplitude as high as over
20-times. Meanwhile, violent infrared and optical flares of GB6 J2113+1121,
unobserved before, have been simultaneously detected. Motivated by the spatial
and temporal coincidence, we suggest that GB6 J2113+1121 is a candidate of the
counterpart of IceCube-191001A. The jet properties of GB6 J2113+1121 are
investigated, which are found to be comparable with that of the
neutrino-emitting blazars (candidates). A specific analysis of archival IceCube
data in this direction and future observations would put a further constraint
on the origin of the neutrino.


title:
Thermo-optical reshaping of SHG emission from dimerall-dielectric
  nanoresonators

abstract:
  In recent years resonant semiconductor and all-dielectric nanophotonics
offered a lot of possibilities for thermally-induced light manipulation at the
nanoscale. Owing to high-quality resonant states, such nanostructures allow for
efficient light-to-heat conversion supported by various temperature detection
approaches based on thermally sensitive intrinsic optical responses
(photoluminescence, Raman scattering, thermorefraction etc.). In this work, we
study theoretically a phenomenon of the photothermal reshaping of the radiation
pattern of second-harmonic generation (SHG) that occurs in resonant
all-dielectric systems. In the suggested geometry near-IR pulsed laser is
utilized for excitation of SHG while simultaneous continuous wave visible laser
heats the structure. The thermooptical switching of the resonant optical states
in the nanostructures governs the reconfiguration of the emission pattern,
without significant loss in the magnitude of the SHG. We believe, that our
findings will pave the way for subwavelength-size near-IR thermally switchable
nonlinear optical devices.


title: Development of the Berezin number inequalities

abstract:
  We present new bounds for the Berezin number inequalities which improve on
the existing bounds. We also obtain bounds for the Berezin norm of operators as
well as the sum of two operators.


title: A Kleene Theorem for Higher-Dimensional Automata

abstract:
  We prove a Kleene theorem for higher-dimensional automata. It states that the
languages they recognise are precisely the rational subsumption-closed sets of
labelled interval orders. Higher-dimensional automata are general models of
concurrency that subsume, for instance, Petri nets, event structures and
asynchronous transition systems. We formalise them as presheaves over labelled
precube categories. Interval orders are used as non-interleaving semantics of
concurrent or distributed systems where events have duration. For the proof, we
introduce higher-dimensional automata with interfaces and several tools
inspired by model categories, such as cylinders, necessary for handling cycles,
and (co)fibrations.


title: Counterfactual Multi-Token Fairness in Text Classification

abstract:
  The counterfactual token generation has been limited to perturbing only a
single token in texts that are generally short and single sentences. These
tokens are often associated with one of many sensitive attributes. With limited
counterfactuals generated, the goal to achieve invariant nature for machine
learning classification models towards any sensitive attribute gets bounded,
and the formulation of Counterfactual Fairness gets narrowed. In this paper, we
overcome these limitations by solving root problems and opening bigger domains
for understanding. We have curated a resource of sensitive tokens and their
corresponding perturbation tokens, even extending the support beyond
traditionally used sensitive attributes like Age, Gender, Race to Nationality,
Disability, and Religion. The concept of Counterfactual Generation has been
extended to multi-token support valid over all forms of texts and documents. We
define the method of generating counterfactuals by perturbing multiple
sensitive tokens as Counterfactual Multi-token Generation. The method has been
conceptualized to showcase significant performance improvement over
single-token methods and validated over multiple benchmark datasets. The
emendation in counterfactual generation propagates in achieving improved
Counterfactual Multi-token Fairness.


title:
Coefficientwise Hankel-total positivity of row-generating polynomials
  for the $m$-Jacobi-Rogers triangle

abstract:
  The aim of this paper is to study the criteria for the row-generating
polynomial sequence of the $m$-Jacobi-Rogers triangle being coefficientwise
Hankel-totally positive and their applications.
  Using the theory of production matrices, we gain a criterion for the
coefficientwise Hankel-total positivity of the row-generating polynomial
sequence of the $m$-Jacobi-Rogers triangle. This immediately implies that the
corresponding $m$-Jacobi-Rogers triangular convolution preserves the Stieltjes
moment property of sequences and its zeroth column sequence is coefficientwise
Hankel-totally positive and log-convex of higher order in all the
indeterminates. In consequence, for $m=1$, we immediately obtain some results
on coefficientwise Hankel-total positivity for the Catalan-Stieltjes matrices.
For the general $m$, combining our criterion and a function satisfying an
autonomous differential equation, we present different criteria for
coefficientwise Hankel-total positivity of the row-generating polynomial
sequence for exponential Rirodan arrays. In addition, we also derive some
results for the coefficientwise Hankel-total positivity in terms of
compositional functions and $m$-branched Stieltjes continued fractions. We
apply our results to many combinatorial polynomials in a unified manner. In
particular, we also solve some conjcetures proposed by Sokal.


title:
Hidden Kac-Moody Structures in the Fermionic Sector of Five-Dimensional
  Supergravity

abstract:
  We study the supersymmetric quantum dynamics of the cosmological models
obtained by reducing $D=5$ supergravity to one timelike dimension. This
consistent truncation has fourteen bosonic degrees of freedom, while the
quantization of the homogeneous gravitino field leads to a
$2^{16}$--dimensional fermionic Hilbert space. We construct a consistent
quantization of the model in which the wave function of the Universe is a
$2^{16}$--component spinor %\textcolor{red}{of Spin(24,8)} depending on
fourteen continuous coordinates, which satisfies eight Dirac-like wave
equations (supersymmetry constraints) and one Klein-Gordon-like equation
(Hamiltonian constraint). The fermionic part of the quantum Hamiltonian is
built from operators that generate a $2^{16}$-dimensional representation of the
(infinite-dimensional) maximally compact sub-algebra $K(G_2^{++})$ of the
rank-4 hyperbolic Kac--Moody algebra $G_2^{++}$. The (quartic-in-fermions)
squared-mass term $\widehat \mu^2$ entering the Klein-Gordon-like equation has
several remarkable properties: (i) it commutes with the generators of
$K(G_2^{++})$; and (ii) it is a quadratic polynomial in the fermion number $N_F
\sim \overline\Psi \Psi$, and a symplectic fermion bilinear $C_F \sim \Psi
C\Psi$. Some aspects of the structure of the solutions of our model are
discussed, and notably the Kac-Moody meaning of the operators describing the
reflection of the wave function on the fermion-dependent potential walls
("quantum fermionic Kac-Moody billiard").


title:
Feature subset selection for Big Data via Chaotic Binary Differential
  Evolution under Apache Spark

abstract:
  Feature subset selection (FSS) using a wrapper approach is essentially a
combinatorial optimization problem having two objective functions namely
cardinality of the selected-feature-subset, which should be minimized and the
corresponding area under the ROC curve (AUC) to be maximized. In this research
study, we propose a novel multiplicative single objective function involving
cardinality and AUC. The randomness involved in the Binary Differential
Evolution (BDE) may yield less diverse solutions thereby getting trapped in
local minima. Hence, we embed Logistic and Tent chaotic maps into the BDE and
named it as Chaotic Binary Differential Evolution (CBDE). Designing a scalable
solution to the FSS is critical when dealing with high-dimensional and
voluminous datasets. Hence, we propose a scalable island (iS) based
parallelization approach where the data is divided into multiple
partitions/islands thereby the solution evolves individually and gets combined
eventually in a migration strategy. The results empirically show that the
proposed parallel Chaotic Binary Differential Evolution (P-CBDE-iS) is able to
find the better quality feature subsets than the Parallel Bi-nary Differential
Evolution (P-BDE-iS). Logistic Regression (LR) is used as a classifier owing to
its simplicity and power. The speedup attained by the proposed parallel
approach signifies the importance.


title: Weak commutativity, virtually nilpotent groups, and Dehn functions

abstract:
  The group $\mathfrak{X}(G)$ is obtained from $G\ast G$ by forcing each
element $g$ in the first free factor to commute with the copy of $g$ in the
second free factor. We make significant additions to the list of properties
that the functor $\mathfrak{X}$ is known to preserve. We also investigate the
geometry and complexity of the word problem for $\mathfrak{X}(G)$. Subtle
features of $\mathfrak{X}$ are encoded in a normal abelian subgroup
$W<\mathfrak{X}(G)$ that is a module over $\mathbb{Z} Q$, where $Q=
H_1(G,\mathbb{Z})$. We establish a structural result for this module and
illustrate its utility by proving that $\mathfrak{X}$ preserves virtual
nilpotence, the Engel condition, and growth type -- polynomial, exponential, or
intermediate. We also use it to establish isoperimetric inequalities for
$\mathfrak{X}(G)$ when $G$ lies in a class that includes Thompson's group $F$
and all non-fibered K\"ahler groups. The word problem is solvable in
$\mathfrak{X}(G)$ if and only if it is solvable in $G$. The Dehn function of
$\mathfrak{X}(G)$ is bounded below by a cubic polynomial if $G$ maps onto a
non-abelian free group.


title: Thin film extensional flow of a transversely isotropic viscous fluid

abstract:
  Many biological materials such as cervical mucus and collagen gel possess a
fibrous micro-structure. This micro-structure affects the emergent mechanical
properties of the material, and hence the functional behaviour of the system.
We consider the canonical problem of stretching a thin sheet of
transversely-isotropic viscous fluid as a simplified version of the
spinnbarkeit test for cervical mucus. We propose a novel solution to the model
constructed by Green & Friedman by manipulating the model to a form amenable to
arbitrary Lagrangian-Eulerian techniques. The system of equations, reduced by
exploiting the slender nature of the sheet, are solved numerically and we
discover that the bulk properties of the sheet are controlled by an effective
viscosity dependent on the evolving angle of the fibres. In addition, we
confirm a previous conjecture by demonstrating that the centre-line of the
sheet need not be flat, and perform a short timescale analysis to capture the
full behaviour of the centre-line.


title:
Deep learning fluid flow reconstruction around arbitrary two-dimensional
  objects from sparse sensors using conformal mappings

abstract:
  The usage of neural networks (NNs) for flow reconstruction (FR) tasks from a
limited number of sensors is attracting strong research interest, owing to NNs'
ability to replicate high dimensional relationships. Trained on a single flow
case for a given Reynolds number or over a reduced range of Reynolds numbers,
these models are unfortunately not able to handle flows around different
objects without re-training. We propose a new framework called Spatial
Multi-Geometry FR (SMGFR) task, capable of reconstructing fluid flows around
different two-dimensional objects without re-training, mapping the
computational domain as an annulus. Different NNs for different sensor setups
(where information about the flow is collected) are trained with high-fidelity
simulation data for a Reynolds number equal to approximately $300$ for 64
objects randomly generated using Bezier curves. The performance of the models
and sensor setups are then assessed for the flow around 16 unseen objects. It
is shown that our mapping approach improves percentage errors by up to 15\% in
SMGFR when compared to a more conventional approach where the models are
trained on a Cartesian grid, and achieves errors under 3\%, 10\% and 30\% for
pressure, velocity and vorticity fields predictions, respectively. Finally,
SMGFR is extended to predictions of snapshots in the future, introducing the
Spatio-temporal MGFR (STMGFR) task. A novel approach is developed for STMGFR
involving splitting DNNs into a spatial and a temporal component. We
demonstrate that this approach is able to reproduce, in time and in space, the
main features of flows around arbitrary objects.


title: What are the best systems? New perspectives on NLP Benchmarking

abstract:
  In Machine Learning, a benchmark refers to an ensemble of datasets associated
with one or multiple metrics together with a way to aggregate different systems
performances. They are instrumental in (i) assessing the progress of new
methods along different axes and (ii) selecting the best systems for practical
use. This is particularly the case for NLP with the development of large
pre-trained models (e.g. GPT, BERT) that are expected to generalize well on a
variety of tasks. While the community mainly focused on developing new datasets
and metrics, there has been little interest in the aggregation procedure, which
is often reduced to a simple average over various performance measures.
However, this procedure can be problematic when the metrics are on a different
scale, which may lead to spurious conclusions. This paper proposes a new
procedure to rank systems based on their performance across different tasks.
Motivated by the social choice theory, the final system ordering is obtained
through aggregating the rankings induced by each task and is theoretically
grounded. We conduct extensive numerical experiments (on over 270k scores) to
assess the soundness of our approach both on synthetic and real scores (e.g.
GLUE, EXTREM, SEVAL, TAC, FLICKR). In particular, we show that our method
yields different conclusions on state-of-the-art systems than the
mean-aggregation procedure while being both more reliable and robust.


title:
Ada-NETS: Face Clustering via Adaptive Neighbour Discovery in the
  Structure Space

abstract:
  Face clustering has attracted rising research interest recently to take
advantage of massive amounts of face images on the web. State-of-the-art
performance has been achieved by Graph Convolutional Networks (GCN) due to
their powerful representation capacity. However, existing GCN-based methods
build face graphs mainly according to kNN relations in the feature space, which
may lead to a lot of noise edges connecting two faces of different classes. The
face features will be polluted when messages pass along these noise edges, thus
degrading the performance of GCNs. In this paper, a novel algorithm named
Ada-NETS is proposed to cluster faces by constructing clean graphs for GCNs. In
Ada-NETS, each face is transformed to a new structure space, obtaining robust
features by considering face features of the neighbour images. Then, an
adaptive neighbour discovery strategy is proposed to determine a proper number
of edges connecting to each face image. It significantly reduces the noise
edges while maintaining the good ones to build a graph with clean yet rich
edges for GCNs to cluster faces. Experiments on multiple public clustering
datasets show that Ada-NETS significantly outperforms current state-of-the-art
methods, proving its superiority and generalization. Code is available at
https://github.com/damo-cv/Ada-NETS.


title:
Design and Implementation of Electronic Infrastructure For Academic
  Establishment

abstract:
  Most establishments including academic institutions under goes the lengthy
process of study-based document handling such as direct mailing, indexing and
tracking. This daily task is time consuming and resource-intensive. Using a
private network dedicated for such document management would benefit the
establishment increasing operational efficiency. In this study, the Information
and Communication Engineering (ICE) Department was used as a model to determine
the requirements needed to build the intranet network. A packet tracer
simulator was used to build a virtual intranet architecture.Then the simulation
report was examined to ensure optimum functionality. Upon establishing a stable
behavior an intranet infrastructure building commenced using the available
hardware components and software.The system architecture was based on Windows
2012R2 server to manage 3 separated sub-networks connected to three switches
and one router. Running the intranet for one semester proved its success in
providing a fast, cheap and simplified service for all department needs. The
accomplished system is a step forward to achieve a full electronic department
in scientific establishments.


title:
On $C^*$-algebras associated to transfer operators for countable-to-one
  maps

abstract:
  Our initial data is a transfer operator $L$ for a continuous,
countable-to-one map $\varphi:\Delta \to X$ defined on an open subset of a
locally compact Hausdorff space $X$. Then $L$ may be identified with a
`potential', i.e. a map $\varrho:\Delta\to X$ that need not be continuous
unless $\varphi$ is a local homeomorphism. We define the crossed product
$C_0(X)\rtimes L$ as a universal $C^*$-algebra with explicit generators and
relations, and give an explicit faithful representation of $C_0(X)\rtimes L$
under which it is generated by weighted composition operators. We explain its
relationship with Exel-Royer's crossed products, quiver $C^*$-algebras of Muhly
and Tomforde, $C^*$-algebras associated to complex or self-similar dynamics by
Kajiwara and Watatani, and groupoid $C^*$-algebras associated to
Deaconu-Renault groupoids.
  We describe spectra of core subalgebras of $C_0(X)\rtimes L$ and use it to
characterise simplicity of $C_0(X)\rtimes L$ and prove the uniqueness theorem
for $C_0(X)\rtimes L$. We give efficient criteria for $C_0(X)\rtimes L$ to be a
Kirchberg algebra, and we discuss relationship between KMS states on the core
subalgebra of $C_0(X)\rtimes L$ and conformal measures for $\varphi$.


title: Private Information Delivery with Coded Storage

abstract:
  In private information delivery (PID) problem, there are $K$ messages stored
across $N$ servers, each capable of storing $M$ messages and a user. Servers
want to convey one of the $K$ messages to the user without revealing the
identity (index) of the message conveyed. The capacity of PID problem is
defined as maximum number of bits of the desired message that can be conveyed
privately, per bit of total communication, to the user. For the restricted case
of replicated systems, where coded messages or splitting one message into
several servers is not allowed, the capacity of PID has been characterized by
Hua Sun in "Private Information Delivery, IEEE Transactions on Information
Theory, December 2020" in terms of $K, N$ and $M.$ In this paper, we study the
problem of PID with coded storage at the servers. For a class of problems
called {\it bi-regular PID} we characterize the capacity for $N=K/M$ and for
$N>K/M$ we provide an achievable scheme. In both the cases the rates achieved
are more than the rates achievable with the replicated systems.


title:
The numerical Hodge standard conjecture for the square of a simple
  abelian variety of prime dimension

abstract:
  We prove the numerical Hodge standard conjecture for the square of a simple
abelian variety of prime dimension, and also in some related cases.


title: Quantifying the topic disparity of scientific articles

abstract:
  Citation count is a popular index for assessing scientific papers. However,
it depends on not only the quality of a paper but also various factors, such as
conventionality, team size, and gender. Here, we examine the extent to which
the conventionality of a paper is related to its citation percentile in a
discipline by using our measure, topic disparity. The topic disparity is the
cosine distance between a paper and its discipline on a neural embedding space.
Using this measure, we show that the topic disparity is negatively associated
with the citation percentile in many disciplines, even after controlling team
size and the genders of the first and last authors. This result indicates that
less conventional research tends to receive fewer citations than conventional
research. Our proposed method can be used to complement the raw citation counts
and to recommend papers at the periphery of a discipline because of their less
conventional topics.


title:
Cuierzhuang Phenomenon: A model of rural industrialization in north
  China

abstract:
  Cuierzhuang Phenomenon (or Cuierzhuang Model) is a regional development
phenomenon or rural revitalization model driven by ICT in the information era,
characterized by the storage and transportation, processing, packaging and
online sales of agricultural products, as well as online and offline
coordination, long-distance and cross-regional economic cooperation, ethnic
blending, equality, and mutual benefit. Unlike the Wenzhou Model, South Jiangsu
Model, and Pearl River Model in the 1980s and 1990s, the Cuierzhuang Model is
not only a rural revitalization brought about by the industrialization and
modernization of northern rural areas with the characteristics of industrial
development in the information age, but also an innovative regional economic
cooperation and development model with folk nature, spontaneous formation,
equality, and mutual benefit. Taking southern Xinjiang as the production base,
Xinjiang jujubes from Hotan and Ruoqiang are continuously transported to
Cuierzhuang, Cangzhou City, Hebei Province, where they are transferred,
cleaned, dried and packaged, and finally sold all over the country. With red
dates as a link, the eastern town of Cuierzhuang, which is more than 4,000
kilometers apart, connected with Xinjiang in the western region. Along the
ancient Silk Road, the farthest route can reach as far as Kashgar through the
southern Xinjiang route. Then, how did this long-distance and cross-regional
economic cooperation channel form, what are the regional economics or economic
geography principles of Cuierzhuang attracting Xinjiang jujube, and the
challenges and opportunities faced by Cuierzhuang phenomenon, etc. A
preliminary economic analysis has been carried out in this paper.


title: Indy Autonomous Challenge -- Autonomous Race Cars at the Handling Limits

abstract:
  Motorsport has always been an enabler for technological advancement, and the
same applies to the autonomous driving industry. The team TUM Auton-omous
Motorsports will participate in the Indy Autonomous Challenge in Octo-ber 2021
to benchmark its self-driving software-stack by racing one out of ten
autonomous Dallara AV-21 racecars at the Indianapolis Motor Speedway. The first
part of this paper explains the reasons for entering an autonomous vehicle race
from an academic perspective: It allows focusing on several edge cases
en-countered by autonomous vehicles, such as challenging evasion maneuvers and
unstructured scenarios. At the same time, it is inherently safe due to the
motor-sport related track safety precautions. It is therefore an ideal testing
ground for the development of autonomous driving algorithms capable of
mastering the most challenging and rare situations. In addition, we provide
insight into our soft-ware development workflow and present our
Hardware-in-the-Loop simulation setup. It is capable of running simulations of
up to eight autonomous vehicles in real time. The second part of the paper
gives a high-level overview of the soft-ware architecture and covers our
development priorities in building a high-per-formance autonomous racing
software: maximum sensor detection range, relia-ble handling of multi-vehicle
situations, as well as reliable motion control under uncertainty.


title:
NIMSA: Non-Interactive Multihoming Security Authentication Scheme for
  vehicular communications in Mobile Heterogeneous Networks

abstract:
  In vehicular communications, in-vehicle devices' mobile and multihoming
characteristics bring new requirements for devicevsecurity authentication. On
the one hand, the existing network layer authentication methods rely on the PKI
system; on the other hand, key negotiation needs interaction. These two points
determine that the traditional security authentication method requires
bandwidth consumption and additional delay. It is unsuitable for heterogeneous
wireless scenarios with a high packet loss rate and limited bandwidth
resources. In addition, the establishment of a security association state is
contrary to the original design that the network layer only provides a
forwarding function. We proposed a non-interactive multihoming security
authentication (NIMSA) scheme, a stateless network layer security
authentication scheme triggered by data forwarding. Our scheme adopts an
identity-based non-interactive key agreement strategy to avoid the interaction
of signaling information, which is lightweight and has good support for mobile
and multipath parallel transmission scenarios. The comparison with IKEv2 and
its mobility and multihoming extension scheme (MOBIKE) shows that the proposed
scheme has shorter authentication and handover delay and data transmission
delay and can bring better bandwidth aggregation effect in the scenario of
multipath parallel transmission.


title:
Light ring images of double photon spheres in black hole and wormhole
  space-times

abstract:
  The silhouette of a black hole having a critical curve (an unstable bound
photon orbit) when illuminated by an optically thin accretion disk whose
emission is confined to the equatorial plane shows a distinctive central
brightness depression (the shadow) whose outer edge consists of a series of
strongly lensed, self-similar rings superimposed with the disk's direct
emission. While the size and shape of the critical curve depend only on the
background geometry, the pattern of bright and dark regions (including the size
and depth of the shadow itself) in the image is strongly influenced by the
(astro)physics of the accretion disk. This aspect makes it difficult to extract
clean and clear observational discriminators between the Kerr black hole and
other compact objects. In the presence of a second critical curve, however,
observational differences become apparent. In this work we shall consider some
spherically symmetric black hole and wormhole geometries characterized by the
presence of a second critical curve, via a uniparametric family of extensions
of the Schwarzschild metric. By assuming three toy models of geometrically thin
accretion disks, we show the presence of additional light rings in the
intermediate region between the two critical curves. The observation of such
rings could represent a compelling evidence for the existence of black hole
mimickers having multiple critical curves.


title: Perfect state transfer on bi-Cayley graphs over abelian groups

abstract:
  The study of perfect state transfer on graphs has attracted a great deal of
attention during the past ten years because of its applications to quantum
information processing and quantum computation. Perfect state transfer is
understood to be a rare phenomenon. This paper establishes necessary and
sufficient conditions for a bi-Cayley graph having perfect state transfer over
any given finite abelian group. As corollaries, many known and new results are
obtained on Cayley graphs having perfect state transfer over abelian groups,
(generalized) dihedral groups, semi-dihedral groups and generalized quaternion
groups. Especially, we give an example of a connected non-normal Cayley graph
over a dihedral group having perfect state transfer between two distinct
vertices, which was thought impossible.


title:
Predictive Beamforming for Integrated Sensing and Communication in
  Vehicular Networks: A Deep Learning Approach

abstract:
  The implementation of integrated sensing and communication (ISAC) highly
depends on the effective beamforming design exploiting accurate instantaneous
channel state information (ICSI). However, channel tracking in ISAC requires
large amount of training overhead and prohibitively large computational
complexity. To address this problem, in this paper, we focus on ISAC-assisted
vehicular networks and exploit a deep learning approach to implicitly learn the
features of historical channels and directly predict the beamforming matrix for
the next time slot to maximize the average achievable sum-rate of system, thus
bypassing the need of explicit channel tracking for reducing the system
signaling overhead. To this end, a general sum-rate maximization problem with
Cramer-Rao lower bounds-based sensing constraints is first formulated for the
considered ISAC system. Then, a historical channels-based convolutional long
short-term memory network is designed for predictive beamforming that can
exploit the spatial and temporal dependencies of communication channels to
further improve the learning performance. Finally, simulation results show that
the proposed method can satisfy the requirement of sensing performance, while
its achievable sum-rate can approach the upper bound obtained by a genie-aided
scheme with perfect ICSI available.


title:
A possible role of salt-induced intermediates in the liquid-liquid phase
  transitions of globular protein dispersions

abstract:
  A probable model of the liquid-liquid (L-L) type phase transitions in
water-salt dispersions of native (N*, N) globular proteins in the temperature
range between thermal (D*) and cold (D) denaturation has been proposed. Protein
intermediates (I, I*) arising as a result of the ion non-equilibrium
(de)sorption in the process of D <-> N and D* <-> N* transitions are assumed to
be involved in the L-L micro-phase transition forming clusters and fibrils in
the main phase of N and N* proteins. Thus, they compensate for their excess
chemical potential (ChPot) caused by unbalanced distribution of adsorbed salt
ions in protein structure as compared to N-protein. A temperature model is
proposed for the behavior of ChPots (delta mui) of various states of the
protein: low-temperature i = D, N, I and high-temperature i = D*, N*, I*, as
well as the transition between them. On this basis, the temperature dependence
of the solvent ChPot delta mu1 is proposed. The relationship between the
extreme values of delta mu1 and the temperatures of the critical points (upper
and lower critical solution temperatures) of L-L transitions is established.
The reasons for the nonideal behavior of osmotic pressure at different
temperatures in water-salt protein dispersions are discussed on the basis of
the phase diagrams.


title: Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters

abstract:
  This paper introduces a novel and generic framework to solve the flagship
task of supervised labeled graph prediction by leveraging Optimal Transport
tools. We formulate the problem as regression with the Fused Gromov-Wasserstein
(FGW) loss and propose a predictive model relying on a FGW barycenter whose
weights depend on inputs. First we introduce a non-parametric estimator based
on kernel ridge regression for which theoretical results such as consistency
and excess risk bound are proved. Next we propose an interpretable parametric
model where the barycenter weights are modeled with a neural network and the
graphs on which the FGW barycenter is calculated are additionally learned.
Numerical experiments show the strength of the method and its ability to
interpolate in the labeled graph space on simulated data and on a difficult
metabolic identification problem where it can reach very good performance with
very little engineering.


title: Optimal Transport of Binary Classifiers to Fairness

abstract:
  Much of the past work on fairness in machine learning has focused on forcing
the predictions of classifiers to have similar statistical properties for
individuals of different demographics. Yet, such methods often simply perform a
rescaling of the classifier scores and ignore whether individuals of different
groups have similar features. Our proposed method, Optimal Transport to
Fairness (OTF), applies Optimal Transport (OT) to take this similarity into
account by quantifying unfairness as the smallest cost of OT between a
classifier and any score function that satisfies fairness constraints. For a
flexible class of linear fairness constraints, we show a practical way to
compute OTF as an unfairness cost term that can be added to any standard
classification setting. Experiments show that OTF can be used to achieve an
effective trade-off between predictive power and fairness.


title:
Superposition of Random Plane Waves in High Spatial Dimensions: Random
  Matrix Approach to Landscape Complexity

abstract:
  Motivated by current interest in understanding statistical properties of
random landscapes in high-dimensional spaces, we consider a model of the
landscape in $\mathbb{R}^N$ obtained by superimposing $M>N$ plane waves of
random wavevectors and amplitudes. For this landscape we show how to compute
the "annealed complexity" controlling the asymptotic growth rate of the mean
number of stationary points as $N\to \infty$ at fixed ratio $\alpha=M/N>1$. The
framework of this computation requires us to study spectral properties of
$N\times N$ matrices $W=KTK^T$, where $T$ is diagonal with $M$ mean zero i.i.d.
real normally distributed entries, and all $MN$ entries of $K$ are also i.i.d.
real normal random variables. We suggest to call the latter Gaussian
Marchenko-Pastur Ensemble, as such matrices appeared in the seminal 1967 paper
by those authors. We compute the associated mean spectral density and evaluate
some moments and correlation functions involving products of characteristic
polynomials for such and related matrices.

categories: cond-mat.stat-mech cond-mat.dis-nn math-ph math.MP


title:
Clustering of eclipsing binary light curves through functional principal
  component analysis

abstract:
  In this paper, we revisit the problem of clustering 1318 new variable stars
found in the Milky way. Our recent work distinguishes these stars based on
their light curves which are univariate series of brightness from the stars
observed at discrete time points. This work proposes a new approach to look at
these discrete series as continuous curves over time by transforming them into
functional data. Then, functional principal component analysis is performed
using these functional light curves. Clustering based on the significant
functional principal components reveals two distinct groups of eclipsing
binaries with consistency and superiority compared to our previous results.
This method is established as a new powerful light curve-based classifier,
where implementation of a simple clustering algorithm is effective enough to
uncover the true clusters based merely on the first few relevant functional
principal components. Simultaneously we discard the noise from the data study
involving the higher order functional principal components. Thus the suggested
method is very useful for clustering big light curve data sets which is also
verified by our simulation study.


title: New results on vectorial dual-bent functions and partial difference sets

abstract:
  Bent functions $f: V_{n}\rightarrow \mathbb{F}_{p}$ with certain additional
properties play an important role in constructing partial difference sets,
where $V_{n}$ denotes an $n$-dimensional vector space over $\mathbb{F}_{p}$,
$p$ is an odd prime. In \cite{Cesmelioglu1,Cesmelioglu2}, the so-called
vectorial dual-bent functions are considered to construct partial difference
sets. In \cite{Cesmelioglu1}, \c{C}e\c{s}melio\v{g}lu \emph{et al.} showed that
for vectorial dual-bent functions $F: V_{n}\rightarrow V_{s}$ with certain
additional properties, the preimage set of $0$ for $F$ forms a partial
difference set. In \cite{Cesmelioglu2}, \c{C}e\c{s}melio\v{g}lu \emph{et al.}
showed that for a class of Maiorana-McFarland vectorial dual-bent functions $F:
V_{n}\rightarrow \mathbb{F}_{p^s}$, the preimage set of the squares
(non-squares) in $\mathbb{F}_{p^s}^{*}$ for $F$ forms a partial difference set.
In this paper, we further study vectorial dual-bent functions and partial
difference sets. We prove that for vectorial dual-bent functions $F:
V_{n}\rightarrow \mathbb{F}_{p^s}$ with certain additional properties, the
preimage set of the squares (non-squares) in $\mathbb{F}_{p^s}^{*}$ for $F$ and
the preimage set of any coset of some subgroup of $\mathbb{F}_{p^s}^{*}$ for
$F$ form partial difference sets. Furthermore, explicit constructions of
partial difference sets are yielded from some (non)-quadratic vectorial
dual-bent functions. In this paper, we illustrate that almost all the results
of using weakly regular $p$-ary bent functions to construct partial difference
sets are special cases of our results.


title:
Sub-ps thermionic electron injection effects on exciton-formation
  dynamics at a van der Waals semiconductor/metal interface

abstract:
  Inorganic van der Waals bonded semiconductors like transition metal
dichalcogenides are subject of intense research due to their electronic and
optical properties which are promising for next-generation optoelectronic
devices. In this context, understanding the ultrafast carrier dynamics, as well
as charge and energy transfer at the interface between metals and
semiconductors is crucial and yet quite unexplored. Here, we present an
experimental study on how thermally induced ultrafast charge carrier injection
affects the exciton formation dynamics in bulk WS2 by employing a
pump-push-probe scheme, where a pump pulse induces thermionic injection of
electrons from the gold substrate into the conduction band of the
semiconductor, and another delayed push pulse excites direct transitions in the
WS2. The transient response shows different dynamics on the sub-ps timescale by
varying the delay between pump and push pulses or by changing the pump fluence,
thus disclosing the important role of ultrafast hot electron injection on the
exciton formation dynamics. Our findings might have potential impact on
research fields that target the integration of ultrafast optics at the boundary
of photonics and electronics, as well as in optically-driven CMOS and quantum
technologies.


title: Mr. Bayes and the classics: a suggested interpretation

abstract:
  The main hypothesis about Thomas Bayes's intentions to write his famous Essay
on probability is that he wanted to refute the arguments of David Hume against
the reliability of the occurrence of miracles, published in 1748. In this paper
we argue that it was not Bayes's intention to rebut Hume but that his interest
on the "inverse problem" came about as result of his study of the second
edition of Abraham De Moivre's book, The Doctrine of Chances, published in
1738.
  A possible communication of Bayes's breakthrough might have annoyed De
Moivre, leading to a response written for Bayes in the third edition of De
Moivre's book, published in 1756. Among other points, the response claims that
De Moivre was the first to solve the mentioned inverse problem. Under this
perspective Richard Price's letter, written as preface to Bayes's essay, has a
new interpretation, appearing also as a defense of Bayes premiership on a
satisfactory or proper solution.


title:
Tunable Magnetic Anisotropy in Patterned SrRuO3 Quantum Structures:
  Competition between Lattice Anisotropy and Oxygen Octahedral Rotation

abstract:
  Artificial perovskite-oxide nanostructures possess intriguing magnetic
properties due to their tailorable electron-electron interactions, which are
extremely sensitive to the oxygen coordination environment. To date,
perovskite-oxide nanodots with sizes below 50 nm have rarely been reported.
Furthermore, the oxygen octahedral distortion and its relation to magnetic
properties in perovskite oxide nanodots remain unexplored yet. Here, we have
studied the magnetic anisotropy in patterned SrRuO3 (SRO) nanodots as small as
30 nm while performing atomic-resolution electron microscopy and spectroscopy
to directly visualize the constituent elements, in particular oxygen ions. We
observe that the magnetic anisotropy and RuO6 octahedra distortion in SRO
nanodots are both nanodots' size-dependent but remain unchanged in the first
3-unit-cell interfacial SRO monolayers regardless of the dots' size. Combined
with the first principle calculations, we unravel a unique structural mechanism
behind the nanodots' size-dependent magnetic anisotropy in SRO nanodots,
sugguesting that the competition between lattice anisotropy and oxygen
octahedral rotation mediates anisotropic exchange interactions in SRO nanodots.
These findings demonstrate a new avenue towards tuning magnetic properties of
correlated perovskite oxides and imply that patterned nanodots could be a
promising playground for engineering emergent functional behaviors.


title: A Lower Bound on the Failed Zero Forcing Number of a Graph

abstract:
  Given a graph $G=(V,E)$ and a set of vertices marked as filled, we consider a
color-change rule known as zero forcing. A set $S$ is a zero forcing set if
filling $S$ and applying all possible instances of the color change rule causes
all vertices in $V$ to be filled. A failed zero forcing set is a set of
vertices that is not a zero forcing set. Given a graph $G$, the failed zero
forcing number $F(G)$ is the maximum size of a failed zero forcing set. An open
question was whether given any $k$ there is a an $\ell$ such that all graphs
with at least $\ell$ vertices must satisfy $F(G)\geq k$. We answer this
question affirmatively by proving that for a graph $G$ with $n$ vertices,
$F(G)\geq \lfloor\frac{n-1}{2}\rfloor$.


title: A Novel Plug-in Module for Fine-Grained Visual Classification

abstract:
  Visual classification can be divided into coarse-grained and fine-grained
classification. Coarse-grained classification represents categories with a
large degree of dissimilarity, such as the classification of cats and dogs,
while fine-grained classification represents classifications with a large
degree of similarity, such as cat species, bird species, and the makes or
models of vehicles. Unlike coarse-grained visual classification, fine-grained
visual classification often requires professional experts to label data, which
makes data more expensive. To meet this challenge, many approaches propose to
automatically find the most discriminative regions and use local features to
provide more precise features. These approaches only require image-level
annotations, thereby reducing the cost of annotation. However, most of these
methods require two- or multi-stage architectures and cannot be trained
end-to-end. Therefore, we propose a novel plug-in module that can be integrated
to many common backbones, including CNN-based or Transformer-based networks to
provide strongly discriminative regions. The plugin module can output
pixel-level feature maps and fuse filtered features to enhance fine-grained
visual classification. Experimental results show that the proposed plugin
module outperforms state-of-the-art approaches and significantly improves the
accuracy to 92.77\% and 92.83\% on CUB200-2011 and NABirds, respectively. We
have released our source code in Github
https://github.com/chou141253/FGVC-PIM.git.


title: Nonlocal capillarity for anisotropic kernels

abstract:
  We study a nonlocal capillarity problem with interaction kernels that are
possibly anisotropic and not necessarily invariant under scaling.
  In particular, the lack of scale invariance will be modeled via two different
fractional exponents $s_1, s_2\in (0,1)$ which take into account the
possibility that the container and the environment present different features
with respect to particle interactions.
  We determine a nonlocal Young's law for the contact angle and discuss the
unique solvability of the corresponding equation in terms of the interaction
kernels and of the relative adhesion coefficient.


title:
On certain elements and the center of the quasi-isometry groups of
  Euclidean spaces

abstract:
  We introduce the notion of $PL_\delta$- homeomorphism between two locally
finite simplicial complexes in $\mathbb{R}^n$ and give a sufficient condition
for a simplicial homeomorphism to be a quasi-isometry. We show that the center
of the group $QI(\mathbb{R}^n)$ of all quasi-isometries of $\mathbb{R}^n$ is
trivial.


title: skrl: Modular and Flexible Library for Reinforcement Learning

abstract:
  skrl is an open-source modular library for reinforcement learning written in
Python and designed with a focus on readability, simplicity, and transparency
of algorithm implementations. Apart from supporting environments that use the
traditional OpenAI Gym interface, it allows loading, configuring, and operating
NVIDIA Isaac Gym environments, enabling the parallel training of several agents
with adjustable scopes, which may or may not share resources, in the same
execution. The library's documentation can be found at
https://skrl.readthedocs.io and its source code is available on GitHub at
url{https://github.com/Toni-SM/skrl.


title: On the Pitfalls of Using the Residual Error as Anomaly Score

abstract:
  Many current state-of-the-art methods for anomaly localization in medical
images rely on calculating a residual image between a potentially anomalous
input image and its "healthy" reconstruction. As the reconstruction of the
unseen anomalous region should be erroneous, this yields large residuals as a
score to detect anomalies in medical images. However, this assumption does not
take into account residuals resulting from imperfect reconstructions of the
machine learning models used. Such errors can easily overshadow residuals of
interest and therefore strongly question the use of residual images as scoring
function. Our work explores this fundamental problem of residual images in
detail. We theoretically define the problem and thoroughly evaluate the
influence of intensity and texture of anomalies against the effect of imperfect
reconstructions in a series of experiments. Code and experiments are available
under https://github.com/FeliMe/residual-score-pitfalls


title:
Universality for random matrices with equi-spaced external source: a
  case study of a biorthogonal ensemble

abstract:
  We prove the edge and bulk universality of random Hermitian matrices with
equi-spaced external source. One feature of our method is that we use neither a
Christoffel-Darboux type formula, nor a double-contour formula, which are
standard methods to prove universality results for exactly solvable models.
This matrix model is an example of a biorthogonal ensemble, which is a special
kind of determinantal point process whose kernel generally does not have a
Christoffel-Darboux type formula or double-contour representation. Our methods
may showcase how to handle universality problems for biorthogonal ensembles in
general.


title: Analysis of the bottom-charm baryon states with QCD sum rules

abstract:
  In this work, we explore the ground state mass spectrum of the bottom-charm
baryon states in the framework of the QCD sum rules in a comprehensive way. In
calculations, we distinguish the contributions of the positive-parity and
negative-parity baryon states unambiguously, and investigate the energy scale
dependence of the QCD sum rules in details and observe that the acceptable
energy scales are $\mu=2.0\sim 2.8\,\rm{GeV}$, while the best energy scale is
$\mu=2.0\,\rm{GeV}$. The predictions can be confronted to the experimental data
in the future and shed light on the QCD low energy dynamics.


title: TimeLMs: Diachronic Language Models from Twitter

abstract:
  Despite its importance, the time variable has been largely neglected in the
NLP and language model literature. In this paper, we present TimeLMs, a set of
language models specialized on diachronic Twitter data. We show that a
continual learning strategy contributes to enhancing Twitter-based language
models' capacity to deal with future and out-of-distribution tweets, while
making them competitive with standardized and more monolithic benchmarks. We
also perform a number of qualitative analyses showing how they cope with trends
and peaks in activity involving specific named entities or concept drift.


title:
Damping of long wavelength gravitational waves by the intergalactic
  medium

abstract:
  The problem of radiation by the charged particles of the intergalactic medium
(IGM) when a passing gravitational wave (GW) accelerate them is investigated.
The largest acceleration (taking a charge from rest to a maximum speed which
remains non-relativistic in the rest frame of the unperturbed spacetime) is
found to be limited by the curvature of a propagating spherical gravitational
wavefront. Interesting physics arises from the ensuing emission of radiation
into the warm hot IGM, which to lowest order is a fully ionized hydrogen plasma
with a frozen-in magnetic field $B$. It is found that for a vast majority of
propagation directions, the right-handed polarized radiation can penetrate the
plasma at frequencies below the plasma frequency $\om_p$, provided $\om<\om_b,$
where $\om_b=eB/m_e$ satisfies $\om_b<\om_p$ for typical IGM conditions.
Moreover, the refractive index under such a scenario is $n\gg 1,$ resulting in
an enhanced radiative dissipation of GW energy (relative to the vacuum
scenario), which is more severe for electrons if both charge species are in
thermal equilibrium and accelerated in the same way. The emission by the
electrons then prevails, and is further amplified by coherent addition of
amplitudes within the size one wavelength. The conversion of GWs of
$\lam\gtrsim 5\times 10^{13}$~cm to electromagnetic waves means such GWs can
only propagate a distance $\lesssim 1$~Gpc before being significantly damped by
an IGM B field of $\sim10^{-8}$ G. The low-frequency GWs
\textcolor{black}{targeted by pulsar-timing-arrays} will not survive unless the
IGM magnetic field is much lower than expected. The \textcolor{black}{mHz}
frequency GW inspirals targeted by future \textcolor{black}{space based}
detectors such as the Laser Interferometer Space Antenna remain intact and can
be detected.


title:
Ultrathin quantum light source enabled by a nonlinear van der Waals
  crystal with vanishing interlayer-electronic-coupling

abstract:
  Interlayer electronic coupling in two-dimensional (2D) materials enables
tunable and emergent properties by stacking engineering. However, it also
brings significant evolution of electronic structures and attenuation of
excitonic effects in 2D semiconductors as exemplified by quickly degrading
excitonic photoluminescence and optical nonlinearities in transition metal
dichalcogenides when monolayers are stacked into van der Waals structures. Here
we report a novel van der Waals crystal, niobium oxide dichloride, featuring a
vanishing interlayer electronic coupling and scalable second harmonic
generation intensity of up to three orders higher than that of exciton-resonant
monolayer WS2. Importantly, the strong second-order nonlinearity enables
correlated parametric photon pair generation, via a spontaneous parametric
down-conversion (SPDC) process, in flakes as thin as ~46 nm. To our knowledge,
this is the first SPDC source unambiguously demonstrated in 2D layered
materials, and the thinnest SPDC source ever reported. Our work opens an avenue
towards developing van der Waals material-based ultracompact on-chip SPDC
sources, and high-performance photon modulators in both classical and quantum
optical technologies.


title:
Joint position and trajectory optimization of flying base station in 5G
  cellular networks, based on users' current and predicted location

abstract:
  Nowadays, Unmanned Aerial Vehicles (UAVs) have been significantly improved,
and one of their most important applications is to provide temporary coverage
for cellular users. Static Base Station cannot service all users due to
temporary crashes because of temporary events such as ground BS breakdowns, bad
weather conditions, natural disasters, transmission errors, etc., drones
equipped with small cellular BS. The Drone Base Station is immediately sent to
the target location and establishes the necessary communication links without
requiring any predetermined infrastructure and covers that area. Finding the
optimal location and the appropriate number (DBS) of drone-BS in this area is a
challenge. Therefore, in this paper, the optimal location and optimal number of
DBSs are distributed in the current state of the users and the subsequent user
states determined by the prediction. Finally, the DBS transition is optimized
from the current state to the predicted future locations. The simulation
results show that the proposed method can provide acceptable coverage on the
network.


title:
Virtual Photon Emission in Leptonic Decays of Charged Pseudoscalar
  Mesons

abstract:
  We study the radiative leptonic decays
$P\to\ell\nu_\ell\,\ell^{\prime\,+}\ell^{\prime\,-}$, where $P$ is a
pseudoscalar meson and $\ell$ and $\ell^\prime$ are charged leptons. In such
decays the emitted photon is off-shell and, in addition to the "point-like"
contribution in which the virtual photon is emitted either from the lepton or
the meson treated as a point-like particle, four structure-dependent (SD) form
factors contribute to the amplitude. We present a strategy for the extraction
of the SD form factors and implement it in an exploratory lattice computation
of the decay rates for the four channels of kaon decays
($\ell,\ell^\prime=e,\mu$). It is the SD form factors which describe the
interaction between the virtual photon and the internal hadronic structure of
the decaying meson, and in our procedure we separate the SD and point-like
contributions to the amplitudes. We demonstrate that the form factors can be
extracted with good precision and, in spite of the unphysical quark masses used
in our simulation ($m_\pi\simeq 320\,$MeV and $m_K\simeq 530\,$MeV), the
results for the decay rates are in reasonable semiquantitative agreement with
experimental data (for the channels where these exist). Following this
preparatory work, the emphasis of our future work will be on obtaining results
at physical quark masses and on the control of the systematic uncertainties
associated with discretisation and finite-volume errors.


title:
FSM: FBS Set Management, An energy efficient multi-drone 3D trajectory
  approach in cellular networks

abstract:
  Nowadays, Unmanned Aerial Vehicles (UAVs) have been significantly improved,
and one of their most important applications is to provide temporary coverage
for cellular users. Terrestrial Base Station cannot service all users due to
disasters or events such as ground BS breakdowns, bad weather conditions,
natural disasters, transmission errors, etc. The UAV can be sent to the target
location and establishes the necessary communication links without requiring
any predetermined infrastructure and covers that area. Finding the optimal
location and the appropriate number (DBS) of drone-BS in this area is a
challenge. In this paper, the optimal location and optimal number of DBSs are
distributed in the current state of the users and the subsequent user states
determined by the prediction. Finally, the DBS transition is optimized from the
current state to the predicted future locations. The simulation results show
that the proposed method can provide acceptable coverage on the network.


title:
A covariant, discrete time-frequency representation tailored for
  zero-based signal detection

abstract:
  Recent work in time-frequency analysis proposed to switch the focus from the
maxima of the spectrogram toward its zeros. The zeros of signals in white
Gaussian noise indeed form a random point pattern with a very stable structure.
Using modern spatial statistics tools on the pattern of zeros of a spectrogram
has led to component disentanglement and signal detection procedures. The major
bottlenecks of this approach are the discretization of the Short-Time Fourier
Transform and the necessarily bounded observation window in the time-frequency
plane. Both impact the estimation of summary statistics of the zeros, which are
then used in standard statistical tests. To circumvent these limitations, we
propose a generalized time-frequency representation, which we call the Kravchuk
transform. It naturally applies to finite signals, i.e., finite-dimensional
vectors. The corresponding phase space, instead of the whole time-frequency
plane, is compact, and particularly amenable to spatial statistics. On top of
this, the Kravchuk transform has several natural properties for signal
processing, among which covariance under the action of SO(3), invertibility and
symmetry with respect to complex conjugation. We further show that the point
process of the zeros of the Kravchuk transform of discrete white Gaussian noise
coincides in law with the zeros of the spherical Gaussian Analytic Function.
This implies that the law of the zeros is invariant under isometries of the
sphere. Elaborating on this theorem, we develop a procedure for signal
detection based on the spatial statistics of the zeros of the Kravchuk
spectrogram. The statistical power of this procedure is assessed by intensive
numerical simulation, and compares favorably with respect to state-of-the-art
zeros-based detection procedures. Furthermore it appears to be particularly
robust to both low signal-to-noise ratio and small number of samples.


title:
An Improved Analysis of Gradient Tracking for Decentralized Machine
  Learning

abstract:
  We consider decentralized machine learning over a network where the training
data is distributed across $n$ agents, each of which can compute stochastic
model updates on their local data. The agent's common goal is to find a model
that minimizes the average of all local loss functions. While gradient tracking
(GT) algorithms can overcome a key challenge, namely accounting for differences
between workers' local data distributions, the known convergence rates for GT
algorithms are not optimal with respect to their dependence on the mixing
parameter $p$ (related to the spectral gap of the connectivity matrix).
  We provide a tighter analysis of the GT method in the stochastic strongly
convex, convex and non-convex settings. We improve the dependency on $p$ from
$\mathcal{O}(p^{-2})$ to $\mathcal{O}(p^{-1}c^{-1})$ in the noiseless case and
from $\mathcal{O}(p^{-3/2})$ to $\mathcal{O}(p^{-1/2}c^{-1})$ in the general
stochastic case, where $c \geq p$ is related to the negative eigenvalues of the
connectivity matrix (and is a constant in most practical applications). This
improvement was possible due to a new proof technique which could be of
independent interest.


title:
Computing the quasinormal modes and eigenfunctions for the Teukolsky
  equation using horizon penetrating, hyperboloidally compactified coordinates

abstract:
  We study the quasinormal modes and eigenfunctions for the Kerr spacetime in a
horizon penetrating, hyperboloidally compactified (HPHC) coordinate system.
Following earlier work by Zengino\u{g}lu (arXiv:1102.2451), we show that the
physical quasinormal eigenfunctions for the Teukolsky equation are regular from
the black hole horizon to future null infinity in these coordinates. We then
present several example eigenfunction solutions, and study some of their
properties in near-extremal Kerr limit.


title: Online error control for platform trials

abstract:
  Platform trials evaluate multiple experimental treatments under a single
master protocol, where new treatment arms are added to the trial over time.
Given the multiple treatment comparisons, there is the potential for inflation
of the overall type I error rate, which is complicated by the fact that the
hypotheses are tested at different times and are not all necessarily
pre-specified. Online error control methodology provides a possible solution to
the problem of multiplicity for platform trials where a relatively large number
of hypotheses are expected to be tested over time. In the online testing
framework, hypotheses are tested in a sequential manner, where at each
time-step an analyst decides whether to reject the current null hypothesis
without knowledge of future tests but based solely on past decisions.
Methodology has recently been developed for online control of the false
discovery rate as well as the familywise error rate (FWER). In this paper, we
describe how to apply online error control to the platform trial setting,
present extensive simulation results, and give some recommendations for the use
of this new methodology in practice. We show that the algorithms for online
error rate control can have a substantially lower FWER than uncorrected
testing, while still achieving noticeable gains in power when compared with the
use of a Bonferroni procedure. We also illustrate how online error control
would have impacted a currently ongoing platform trial.


title: On three general forms of multiple zeta(-star) values

abstract:
  In this paper, we investigate three general forms of multiple zeta(-star)
values. We use these values to give three new sum formulas for multiple
zeta(-star) values with height $\leq 2$ and the evaluation of
$\zeta^\star(\{1\}^m,\{2\}^{n+1})$. We also give a new proof of sum formula of
multiple zeta values.


title: An optimized TEM specimen preparation method of quantum nanostructures

abstract:
  Electron transparent TEM lamella with unaltered microstructure and chemistry
is the prerequisite for successful TEM explorations. Currently, TEM specimen
preparation of quantum nanostructures, such as quantum dots (QDs), remains a
challenge. In this work, we optimize the sample-preparation routine for
achieving high-quality TEM specimens consisting of SrRuO3 (SRO) QDs grown on
SrTiO3 (STO) substrates. We demonstrate that a combination of ion-beam-milling
techniques can produce higher-quality specimens of quantum nanostructures
compared to TEM specimens prepared by a combination of tripod polishing
followed by Ar+ ion milling. In the proposed method, simultaneous imaging in a
focused ion-beam device enables accurate positioning of the QD regions and
assures the presence of dots in the thin lamella by cutting the sample inclined
by 5{\deg} relative to the dots array. Furthermore, the preparation of TEM
lamellae with several large electron-transparent regions that are separated by
thicker walls effectively reduces the bending of the specimen and offers broad
thin areas. The final use of a NanoMill efficiently removes the amorphous layer
without introducing any additional damage.


title: Width is Less Important than Depth in ReLU Neural Networks

abstract:
  We solve an open question from Lu et al. (2017), by showing that any target
network with inputs in $\mathbb{R}^d$ can be approximated by a width $O(d)$
network (independent of the target network's architecture), whose number of
parameters is essentially larger only by a linear factor. In light of previous
depth separation theorems, which imply that a similar result cannot hold when
the roles of width and depth are interchanged, it follows that depth plays a
more significant role than width in the expressive power of neural networks.
  We extend our results to constructing networks with bounded weights, and to
constructing networks with width at most $d+2$, which is close to the minimal
possible width due to previous lower bounds. Both of these constructions cause
an extra polynomial factor in the number of parameters over the target network.
We also show an exact representation of wide and shallow networks using deep
and narrow networks which, in certain cases, does not increase the number of
parameters over the target network.


title: Super-expanding measures

abstract:
  We study the one-dimensional expanding Lorenz maps and show the existence of
dense subset D of Lorens maps such that each f in D has an uncountable set of
ergodic invariant probabilities with infinite Lyapunov exponent and positive
entropy. Such measures may appear when the singularity has fast recurrence to
itself. Conversely, if the singularity has slow recurrence to itself then the
Lorenz map has an upper bound to the Lyapunov exponent of all invariant
measures.