title:
Deterministic Generation and Guided Motion of Magnetic Skyrmions by
  Focused He$^+$-Ion Irradiation

abstract:
  Magnetic skyrmions are quasiparticles with non-trivial topology, envisioned
to play a key role in next-generation data technology while simultaneously
attracting fundamental research interest due to their emerging topological
charge. In chiral magnetic multilayers, current-generated spin-orbit torques or
ultrafast laser excitation can be used to nucleate isolated skyrmions on a
picosecond timescale. Both methods, however, produce randomly arranged
skyrmions, which inherently limits the precision on the location at which the
skyrmions are nucleated. Here, we show that nanopatterning of the anisotropy
landscape with a He$^+$-ion beam creates well-defined skyrmion nucleation
sites, thereby transforming the skyrmion localization into a deterministic
process. This approach allows to realize control of individual skyrmion
nucleation as well as guided skyrmion motion with nanometer-scale precision,
which is pivotal for both future fundamental studies of skyrmion dynamics and
applications.


title: Exploring the Unfairness of DP-SGD Across Settings

abstract:
  End users and regulators require private and fair artificial intelligence
models, but previous work suggests these objectives may be at odds. We use the
CivilComments to evaluate the impact of applying the {\em de facto} standard
approach to privacy, DP-SGD, across several fairness metrics. We evaluate three
implementations of DP-SGD: for dimensionality reduction (PCA), linear
classification (logistic regression), and robust deep learning (Group-DRO). We
establish a negative, logarithmic correlation between privacy and fairness in
the case of linear classification and robust deep learning. DP-SGD had no
significant impact on fairness for PCA, but upon inspection, also did not seem
to lead to private representations.


title: AFFDEX 2.0: A Real-Time Facial Expression Analysis Toolkit

abstract:
  In this paper we introduce AFFDEX 2.0 - a toolkit for analyzing facial
expressions in the wild, that is, it is intended for users aiming to; a)
estimate the 3D head pose, b) detect facial Action Units (AUs), c) recognize
basic emotions and 2 new emotional states (sentimentality and confusion), and
d) detect high-level expressive metrics like blink and attention. AFFDEX 2.0
models are mainly based on Deep Learning, and are trained using a large-scale
naturalistic dataset consisting of thousands of participants from different
demographic groups. AFFDEX 2.0 is an enhanced version of our previous toolkit
[1], that is capable of tracking efficiently faces at more challenging
conditions, detecting more accurately facial expressions, and recognizing new
emotional states (sentimentality and confusion). AFFDEX 2.0 can process
multiple faces in real time, and is working across the Windows and Linux
platforms.


title:
Conversion of gravitational and electromagnetic waves without any
  external background fields

abstract:
  Applying a simple harmonic map method to the cylindrically symmetric
Einstein-Maxwell system, we obtain exact solutions representing strong
nonlinear interaction between gravitational waves and electromagnetic waves in
the case without any background field. As an interesting fact, we can show that
with adjusted parameters the solutions represent occurrences of large
conversion phenomena in the intense region of fields near the cylindrically
symmetric axis.


title: On tetrahedron type equations associated with $B_3,C_3, F_4$ and $H_3$

abstract:
  Tetrahedron equation is a three dimensional analogue of the Yang-Baxter
equation. It allows a formulation in terms of the Coxeter group $A_3$. This
short note includes miscellaneous remarks on the generalizations along $B_3,
C_3, F_4$ and the non-crystallographic Coxeter group $H_3$. It is a supplement
to the author's talk in the online workshop, Combinatorial Representation
Theory and Connections with Related Fields, at RIMS, Kyoto University in
November 2021.


title: Semiparametric Estimation of Dynamic Binary Choice Panel Data Models

abstract:
  We propose a new approach to the semiparametric analysis of panel data binary
choice models with fixed effects and dynamics (lagged dependent variables). The
model we consider has the same random utility framework as in Honore and
Kyriazidou (2000). We demonstrate that, with additional serial dependence
conditions on the process of deterministic utility and tail restrictions on the
error distribution, the (point) identification of the model can proceed in two
steps, and only requires matching the value of an index function of explanatory
variables over time, as opposed to that of each explanatory variable. Our
identification approach motivates an easily implementable, two-step maximum
score (2SMS) procedure -- producing estimators whose rates of convergence, in
contrast to Honore and Kyriazidou's (2000) methods, are independent of the
model dimension. We then derive the asymptotic properties of the 2SMS procedure
and propose bootstrap-based distributional approximations for inference. Monte
Carlo evidence indicates that our procedure performs adequately in finite
samples. We then apply the proposed estimators to study labor market dependence
and the effects of health shocks, using data from the Household, Income and
Labor Dynamics in Australia (HILDA) survey.


title: Robust Mediation Analysis: The R Package robmed

abstract:
  Mediation analysis is one of the most widely used statistical techniques in
the social, behavioral, and medical sciences. Mediation models allow to study
how an independent variable affects a dependent variable indirectly through one
or more intervening variables, which are called mediators. The analysis is
often carried out via a series of linear regressions, in which case the
indirect effects can be computed as products of coefficients from those
regressions. Statistical significance of the indirect effects is typically
assessed via a bootstrap test based on ordinary least-squares estimates.
However, this test is sensitive to outliers or other deviations from normality
assumptions, which poses a serious threat to empirical testing of theory about
mediation mechanisms. The R package robmed implements a robust procedure for
mediation analysis based on the fast-and-robust bootstrap methodology for
robust regression estimators, which yields reliable results even when the data
deviate from the usual normality assumptions. Various other procedures for
mediation analysis are included in package robmed as well. Moreover, robmed
introduces a new formula interface that allows to specify mediation models with
a single formula, and provides various plots for diagnostics or visual
representation of the results.


title: Interfering Paths in Decision Trees: A Note on Deodata Predictors

abstract:
  A technique for improving the prediction accuracy of decision trees is
proposed. It consists in evaluating the tree's branches in parallel over
multiple paths. The technique enables predictions that are more aligned with
the ones generated by the nearest neighborhood variant of the deodata
algorithms. The technique also enables the hybridization of the decision tree
algorithm with the nearest neighborhood variant.


title: Activation Functions: Dive into an optimal activation function

abstract:
  Activation functions have come up as one of the essential components of
neural networks. The choice of adequate activation function can impact the
accuracy of these methods. In this study, we experiment for finding an optimal
activation function by defining it as a weighted sum of existing activation
functions and then further optimizing these weights while training the network.
The study uses three activation functions, ReLU, tanh, and sin, over three
popular image datasets, MNIST, FashionMNIST, and KMNIST. We observe that the
ReLU activation function can easily overlook other activation functions. Also,
we see that initial layers prefer to have ReLU or LeakyReLU type of activation
functions, but deeper layers tend to prefer more convergent activation
functions.


title: Small-scale intermittency of premixed turbulent flames

abstract:
  Premixed turbulent flames, encountered in power generation and propulsion
engines, are an archetype of a randomly advected, self-propagating surface.
While such a flame is known to exhibit large-scale intermittent flapping, the
possible intermittency of its small-scale fluctuations has been largely
disregarded. Here, we experimentally reveal the inner intermittency of a
premixed turbulent V-flame, while clearly distinguishing this small-scale
feature from large-scale outer intermittency. From temporal measurements of the
fluctuations of the flame, we find a frequency spectra that has a power-law
subrange with an exponent close to $-2$, which is shown to follow from
Kolmogorov phenomenology. Crucially, however, the moments of the temporal
increment of the flame position are found to scale anomalously, with exponents
that saturate at higher-orders. The implied extremely rapid, small-scale
fluctuation events, hitherto overlooked, are relevant for modeling the heat
release rate and other key properties of premixed turbulent flames.


title:
A 2D Levy-flight model for the complex dynamics of real-life financial
  markets

abstract:
  We report on the emergence of scaling laws in the temporal evolution of the
daily closing values of the S\&P 500 index prices and its modeling based on the
L\'evy flights in two dimensions (2D). The efficacy of our proposed model is
verified and validated by using the extreme value statistics in random matrix
theory. We find that the random evolution of each pair of stocks in a 2D price
space is a scale-invariant complex trajectory whose tortuosity is governed by a
$2/3$ geometric law between the gyration radius $R_g(t)$ and the total length
$\ell(t)$ of the path, i.e., $R_g(t)\sim\ell(t)^{2/3}$. We construct a Wishart
matrix containing all stocks up to a specific variable period and look at its
spectral properties over 30 years. In contrast to the standard random matrix
theory, we find that the distribution of eigenvalues has a power-law tail with
a decreasing exponent over time -- a quantitative indicator of the temporal
correlations. We find that the time evolution of the distance of a 2D L\'evy
flights with index $\alpha=3/2$ from origin generates the same empirical
spectral properties. The statistics of the largest eigenvalues of the model and
the observations are in perfect agreement.


title:
Quantum Lifshitz transitions generated by order from quantum disorder in
  strongly correlated Rashba spin-orbital coupled systems

abstract:
  We study the system of strongly interacting spinor bosons in a square lattice
subject to the isotropic Rashba SOC $ \alpha=\beta $. It supports collinear
spin-bond correlated magnetic Y-x phase, a gapped in-commensurate (IC-)
co-planar IC-XY-y phase, a non-coplanar commensurate (C-) $ 3 \times 3 $
Skyrmion crystal phase (SkX). The state at the Abelian point $
\alpha=\beta=\pi/2 $ is just an AFM state in a rotated basis. Slightly away
from the point, we identify a spurious $ U(1) $ symmetry, develop a novel and
non-perturbative method to calculate not only the gap, but also the excitation
spectrum due to the order from quantum disorder (OFQD) mechanism. We construct
a symmetry based effective action to investigate the quantum Lifshitz
transition from the Y-x state to the IC-XY-y state and establish the connection
between the phenomenological parameters in the effective action and those
evaluated by the microscopic non-perturbative OFQD analysis in the large $ S $
limits. Experimental implications on cold atoms and some 4d or 5d Kitaev
materials are discussed.


title:
Regulations Aware Motion Planning for Autonomous Surface Vessels in
  Urban Canals

abstract:
  In unstructured urban canals, regulation-aware interactions with other
vessels are essential for collision avoidance and social compliance. In this
paper, we propose a regulations aware motion planning framework for Autonomous
Surface Vessels (ASVs) that accounts for dynamic and static obstacles. Our
method builds upon local model predictive contouring control (LMPCC) to
generate motion plans satisfying kino-dynamic and collision constraints in
real-time while including regulation awareness. To incorporate regulations in
the planning stage, we propose a cost function encouraging compliance with
rules describing interactions with other vessels similar to COLlision avoidance
REGulations at sea (COLREGs). These regulations are essential to make an ASV
behave in a predictable and socially compliant manner with regard to other
vessels. We compare the framework against baseline methods and show more
effective regulation-compliance avoidance of moving obstacles with our motion
planner. Additionally, we present experimental results in an outdoor
environment


title:
Resistivity anisotropy from multiorbital Boltzmann equation in nematic
  FeSe

abstract:
  We compute the resistivity anisotropy in the nematic phase of FeSe from the
static solution of the multiorbital Boltzmann equation. By introducing disorder
at the level of the microscopic multiorbital model we show that even elastic
scattering by localized impurities may lead to non-trivial anisotropic
renormalization of the electronic velocities, challenging the usual
understanding of transport based only on cold- and hot-spots effects. Our model
takes into account both the $xz/yz$ and the recently proposed $xy$ nematic
ordering. We show that the latter one has a crucial role in order to reproduce
the experimentally-measured anisotropy, providing a direct fingerprint of the
different nematic scenarios on the bulk transport property of FeSe.


title:
Formation and fragmentation of quantum droplets in a quasi-one
  dimensional dipolar Bose gas

abstract:
  We theoretically investigate the droplets formation in a tightly trapped
one-dimensional dipolar gas of bosonic atoms. When the strength of the dipolar
interaction becomes sufficiently attractive compared to the contact one, we
show how a solitonic-like density profile evolves into a liquid-like droplet on
increasing the number of particles in the trap. The incipient gas-liquid
transition is also signalled by a steep increase of the breathing mode and a
change in sign of the chemical potential. Upon a sudden release of the trap,
varying the number of trapped atoms and the scattering length, the numerical
solution of a time-dependent generalized Gross-Pitaevskii equation shows either
an evaporation of the cloud, the formation of a single self-bound droplet or a
fragmentation in multiple droplets.These results can be probed with lanthanides
atoms and help in characterizing the effect of the dipolar interaction in a
quasi-one-dimensional geometry.


title: The Superconducting Plateau

abstract:
  Two recent experiments in lightly doped strontium titanate have shown that
the superconducting critical temperature remains constant in a range of carrier
concentrations covering almost three orders of magnitude. The importance of
this phenomenon, hereby dubbed a superconducting plateau, is comparable to the
celebrated superconducting dome. The dramatic empirical evidence impose severe
constraints on any proposal for a superconducting mechanism at low doping. We
analyze the experimental results to see what type of theoretical models can be
suitable in this regime. We show that the low critical current, absence of
diamagnetic screening and the high critical field are all related to the small
momentum of the carriers, which is expected at low densities. We quantify the
dependency of the critical temperature on density by introducing the "density
exponent". We discuss the role of a quantum critical point in the formation of
a plateau and comment on the need for more experimental data.


title: Random primes without primality testing

abstract:
  Numerous algorithms call for computation over the integers modulo a
randomly-chosen large prime. In some cases, the quasi-cubic complexity of
selecting a random prime can dominate the total running time. We propose a new
variant of the classic D5 algorithm for "dynamic evaluation", applied to a
randomly-chosen (composite) integer. Unlike the D5 principle which has been
used in the past to compute over a direct product of fields, our method is
simpler as it only requires following a single path after any modulus splits.
The transformation we propose can apply to any algorithm in the algebraic RAM
model, even allowing randomization. The resulting transformed algorithm avoids
any primality tests and will, with constant positive probability, have the same
result as the original computation modulo a randomly-chosen prime. As an
application, we demonstrate how to compute the exact number of nonzero terms in
an unknown integer polynomial in quasi-linear time. We also show how the same
algorithmic transformation technique can be used for computing modulo random
irreducible polynomials over a finite field.


title:
Investigating the Use of One-Class Support Vector Machine for Software
  Defect Prediction

abstract:
  Early software defect identification is considered an important step towards
software quality assurance. Software defect prediction aims at identifying
software components that are likely to cause faults before a software is made
available to the end-user. To date, this task has been modeled as a two-class
classification problem, however its nature also allows it to be formulated as a
one-class classification task.
  Preliminary results obtained in prior work show that One-Class Support Vector
Machine (OCSVM) can outperform two-class classifiers for defect prediction. If
confirmed, these results would overcome the data imbalance problem researchers
have for long attempted to tackle in this field.
  In this paper, we further investigate whether learning from one class only is
sufficient to produce effective defect prediction models by conducting a
thorough large-scale empirical study investigating 15 real-world software
projects, three validation scenarios, eight classifiers, robust evaluation
measures and statistical significance tests. The results reveal that OCSVM is
more suitable for cross-version and cross-project, rather than for
within-project defect prediction, thus suggesting it performs better with
heterogeneous data. While, we cannot conclude that OCSVM is the best classifier
(Random Forest performs best herein), our results show interesting findings
that open up further research avenues for training accurate defect prediction
classifiers when defective instances are scarce or unavailable.


title: Chaotic spin chains in AdS/CFT

abstract:
  We consider the spectrum of anomalous dimensions in planar $\mathcal{N}=4$
supersymmetric Yang-Mills theory and its $\mathcal{N}=1$ super-conformal
Leigh-Strassler deformations. The two-loop truncation of the integrable
$\mathcal{N}=4$ dilatation operator in the SU$(2)$ sector, which is a
next-to-nearest-neighbour deformation of the XXX spin chain, is not strictly
integrable at finite coupling and we show that it indeed has Wigner-Dyson level
statistics. However, we find that it is only weakly chaotic in the sense that
the cross-over to chaotic dynamics is slower than for generic chaotic systems.
For the Leigh-Strassler deformed theory with generic parameters, we show that
the one-loop dilatation operator in the SU$(3)$ sector is chaotic, with a
spectrum that is well described by GUE Random Matrix Theory. For the
imaginary-$\beta$ deformation, the statistics are GOE and the transition from
the integrable limit is that of a generic system. This provides a weak-coupling
analogue of the chaotic dynamics seen for classical strings in the dual
background. We further study the spin chains in the semi-classical limit
described by generalised Landau-Lifshitz models, which are also known to
describe large-angular-momentum string solutions in the dual theory. We show
that for the higher-derivative theory following from the two-loop
$\mathcal{N}=4$ SU$(2)$ spin chain, the maximal Lyapunov exponent is close to
zero, consistent with the absence of chaotic dynamics. For the
imaginary-$\beta$ SU$(3)$ theory, the resulting Landau-Lifshitz model has
classically chaotic dynamics at finite values of the deformation parameter.


title: Phrase-Based Affordance Detection via Cyclic Bilateral Interaction

abstract:
  Affordance detection, which refers to perceiving objects with potential
action possibilities in images, is a challenging task since the possible
affordance depends on the person's purpose in real-world application scenarios.
The existing works mainly extract the inherent human-object dependencies from
image/video to accommodate affordance properties that change dynamically. In
this paper, we explore to perceive affordance from a vision-language
perspective and consider the challenging phrase-based affordance detection
problem,i.e., given a set of phrases describing the action purposes, all the
object regions in a scene with the same affordance should be detected. To this
end, we propose a cyclic bilateral consistency enhancement network (CBCE-Net)
to align language and vision features progressively. Specifically, the
presented CBCE-Net consists of a mutual guided vision-language module that
updates the common features of vision and language in a progressive manner, and
a cyclic interaction module (CIM) that facilitates the perception of possible
interaction with objects in a cyclic manner. In addition, we extend the public
Purpose-driven Affordance Dataset (PAD) by annotating affordance categories
with short phrases. The contrastive experimental results demonstrate the
superiority of our method over nine typical methods from four relevant fields
in terms of both objective metrics and visual quality. The related code and
dataset will be released at \url{https://github.com/lulsheng/CBCE-Net}.


title:
Solving clustered low-rank semidefinite programs arising from polynomial
  optimization

abstract:
  We give a primal-dual interior point method specialized to clustered low-rank
semidefinite programs, which arise from multivariate polynomial (matrix)
programs through sums-of-squares characterizations and sampling. This extends
the work of Simmons-Duffin [J. High Energ. Phys. 1506, no. 174 (2015)] from
univariate to multivariate polynomial matrix programs and to more general
clustered low-rank semidefinite programs. We study the interplay of sampling
and symmetry reduction as well as a greedy method to obtain numerically good
bases and sample points. We apply this to the computation of three-point bounds
for the kissing number problem, for which we show a significant speedup (by a
factor $28$ for previously computed bounds). This allows for the computation of
improved kissing number bounds in dimensions $11$ through $23$. The approach
performs well for problems with bad numerical conditioning, which we show
through new computations for the binary sphere packing problem.


title:
Confidence Intervals of Treatment Effects in Panel Data Models with
  Interactive Fixed Effects

abstract:
  We consider the construction of confidence intervals for treatment effects
estimated using panel models with interactive fixed effects. We first use the
factor-based matrix completion technique proposed by Bai and Ng (2021) to
estimate the treatment effects, and then use bootstrap method to construct
confidence intervals of the treatment effects for treated units at each
post-treatment period. Our construction of confidence intervals requires
neither specific distributional assumptions on the error terms nor large number
of post-treatment periods. We also establish the validity of the proposed
bootstrap procedure that these confidence intervals have asymptotically correct
coverage probabilities. Simulation studies show that these confidence intervals
have satisfactory finite sample performances, and empirical applications using
classical datasets yield treatment effect estimates of similar magnitudes and
reliable confidence intervals.


title: Robustness of non-locality in many-body open quantum systems

abstract:
  Non-locality consists in the existence of non-classical correlations between
local measurements. So far, it has been investigated mostly in isolated quantum
systems. Here we show that non-local correlations are present, can be detected
and might be robust against noise also in many-body open quantum systems, both
in the steady-state or in the transient regime. We further discuss the
robustness of non-local correlations when the open quantum system undergoes
repeated measurements, a relevant scenario for quantum cryptography.


title:
Resonance Fluorescence from a two-level artificial atom strongly coupled
  to a single-mode cavity

abstract:
  We experimentally demonstrate the resonance fluorescence of a two-level
artificial atom strongly coupled to a single-mode cavity field. The effect was
theoretically predicted thirty years ago by Savage [Phys. Rev. Lett. 63, 1576
(1989)]. The system consists of a superconducting qubit circuit and a
one-dimensional transmission line resonator. In addition, a one-dimensional
transmission line strongly coupled to the atom serves as an open space. The
effect takes place, when a microwave field is applied to the cavity, which in
turn is resonantly coupled to the atom. The fluorescence spectrum is measured
via the emission into the transmission line. We find that the widths of side
peaks are largely determined not by relaxation rate of the atom but by the
coherent coupling between the atom and the cavity, that is, the fluorescence
spectrum here is very different from that of the Mollow triplet. Our
experimental results agree well with theoretical calculations.


title: Community Trend Prediction on Heterogeneous Graph in E-commerce

abstract:
  In online shopping, ever-changing fashion trends make merchants need to
prepare more differentiated products to meet the diversified demands, and
e-commerce platforms need to capture the market trend with a prophetic vision.
For the trend prediction, the attribute tags, as the essential description of
items, can genuinely reflect the decision basis of consumers. However, few
existing works explore the attribute trend in the specific community for
e-commerce. In this paper, we focus on the community trend prediction on the
item attribute and propose a unified framework that combines the dynamic
evolution of two graph patterns to predict the attribute trend in a specific
community. Specifically, we first design a communityattribute bipartite graph
at each time step to learn the collaboration of different communities. Next, we
transform the bipartite graph into a hypergraph to exploit the associations of
different attribute tags in one community. Lastly, we introduce a dynamic
evolution component based on the recurrent neural networks to capture the
fashion trend of attribute tags. Extensive experiments on three real-world
datasets in a large e-commerce platform show the superiority of the proposed
approach over several strong alternatives and demonstrate the ability to
discover the community trend in advance.


title:
Algebraic-Dynamical Theory for Quantum Many-body Hamiltonians: A
  Formalized Approach To Strongly Interacting Systems

abstract:
  Non-commutative algebras and entanglement are two of the most important
hallmarks of many-body quantum systems. Dynamical perturbation methods are the
most widely used approaches for quantum many-body systems. While study of
entanglement-based numerical methods are booming recently, the traditional
dynamical perturbation methods have not benefited from study of quantum
entanglement. In this work, we formulate an algebraic-dynamical theory (ADT) by
combining the power of quantum algebras and dynamical methods in which quantum
entanglement naturally emerges as the organizing principle. We start by
introducing a complete operator basis set (COBS), with which an arbitrary
state, either pure or mixed, can be represented by the expectation values of
COBS. Then we establish a complete mapping from a given state to a complete set
of dynamical correlation functions of the state through the Heisenberg- and
Schwinger-Dyson-equations-of-motion (SDEOM). The completeness of COBS and the
mapping ensures ADT to be a mathematically complete framework in principle.
Applying ADT to many-body systems on lattices, we find that the quantum
entanglement is represented by the cumulant structure of expectation values of
the many-body COBS. The cumulant structure of the state forms a hierarchy in
correlations. More importantly, such static correlational hierarchy is
inherited by the dynamical correlations and their SDEOM. We propose that the
dynamical hierarchy is also carried into any perturbative calculation on that
state. We demonstrate the validity of such perturbation hierarchy with an
explicit example, in which we show that a single-particle-type perturbative
calculation fails while a many-body perturbation following the hierarchy
succeeds. We also discuss the computation and approximation schemes of ADT and
its implications to other strong coupling theories like parton and slave
particle methods.

categories: quant-ph cond-mat.str-el math-ph math.MP


title: Delta-resonances and hyperons in proto-neutron stars and merger remnants

abstract:
  The equation of state (EoS) and composition of dense and hot
$\Delta$-resonance admixed hypernuclear matter is studied under conditions that
are characteristic of neutron star binary merger remnants and supernovas. The
cold, neutrino free regime is also considered as a reference for the
astrophysical constraints on the EoS of dense matter. Our formalism uses the
covariant density functional (CDF) theory successfully adapted to include the
full $J^P=1/2^+$ baryon octet and non-strange members of $J^P=3/2^+$ decouplet
with density-dependent couplings that have been suitably adjusted to the
existing laboratory and astrophysical data in the nuclear and hypernuclear
sectors. The effect of $\Delta$-resonances at finite temperatures is to soften
the EoS of hypernuclear matter at intermediate densities and stiffen it at high
densities. At low temperatures, the heavy baryons $\Lambda$,
$\Delta^-$,$\Xi^-$, $\Xi^0$ and $\Delta^0$ appear in the given order if the
$\Delta$-meson couplings are close to those for the nucleon-meson couplings. As
is the case for hyperons, the thresholds of $\Delta$-resonances move to lower
densities with the increase of temperature indicating a significant fraction of
$\Delta$s in the low-density subnuclear regime. We find that the
$\Delta$-resonances comprise a significant fraction of baryonic matter, of the
order of $10\%$ at temperatures of the order of several tens of MeV in the
neutrino-trapped regime and, thus, may affect the supernova and binary neutron
star dynamics.


title:
Volume fraction determination of microgel composed of interpenetrating
  polymer networks of PNIPAM and polyacrylic acid

abstract:
  Interpenetrated polymer network microgels, composed of crosslinked networks
of poly(N-isopropylacrylamide) and polyacrylic acid (PAAc), have been
investigated through rheological measurements at four different amounts of
polyacrylic acid. Both PAAc content and crosslinking degree modify particle
dimensions, mass and softness, thereby strongly affecting the volume fraction
and the system viscosity. Here the volume fraction is derived from the flow
curves at low concentrations by fitting the zero-shear viscosity with the
Einstein-Batchelor equation which provides a parameter k to shift weight
concentration to volume fraction. We find that particles with higher PAAc
content and crosslinker are characterized by a greater value of k and therefore
by larger volume fractions when compared to softer particles. The packing
fractions obtained from rheological measurements are compared with those from
static light scattering for two PAAc contents revealing a good agreement.
Moreover, the behaviour of the viscosity as a function of packing fraction, at
room temperature, has highlighted an Arrhenius dependence for microgels
synthesized with low PAAc content and a Vogel-Fulcher-Tammann dependence for
the highest investigated PAAc concentration. A comparison with the hard spheres
behaviour indicates a steepest increase of the viscosity with decreasing
particles softness. Finally, the volume fraction dependence of the viscosity at
a fixed PAAc and at two different temperatures, below and above the volume
phase transition, shows a quantitative agreement with the structural relaxation
time measured through dynamic light scattering indicating that IPN microgels
softness can be tuned with PAAc and temperature and that, depending on particle
softness, two different routes are followed.


title: pHGen: A pH-Based Key Generation Mechanism Using ISFETs

abstract:
  Digital keys are a fundamental component of many hardware- and software-based
security mechanisms. However, digital keys are limited to binary values and
easily exploitable when stored in standard memories. In this paper, based on
emerging technologies, we introduce pHGen, a potential-of-hydrogen (pH)-based
key generation mechanism that leverages chemical reactions in the form of a
potential change in ion-sensitive field-effect transistors (ISFETs). The
threshold voltage of ISFETs is manipulated corresponding to a known pH buffer
solution (key) in which the transistors are immersed. To read the chemical
information effectively via ISFETs, we designed a readout circuit for stable
operation and detection of voltage thresholds. To demonstrate the applicability
of the proposed key generation, we utilize pHGen for logic locking -- a
hardware integrity protection scheme. The proposed key-generation method breaks
the limits of binary values and provides the first steps toward the utilization
of multi-valued voltage thresholds of ISFETs controlled by chemical
information. The pHGen approach is expected to be a turning point for using
more sophisticated bio-based analog keys for securing next-generation
electronics.


title: Interpolation of spectra from 3D model atmospheres

abstract:
  The use of 3D hydrodynamical simulations of stellar surface convection for
model atmospheres is computationally expensive. Although these models have been
available for quite some time, their use is limited because of the lack of
extensive grids of simulations and associated spectra. Our goal is to provide a
method to interpolate spectra that can be applied to both 1D and 3D models, and
implement it in a code available to the community. This tool will enable the
routine use of 3D model atmospheres in the analysis of stellar spectra.} We
have developed a code that makes use of radial basis functions to interpolate
the spectra included in the CIFIST grid of 84 three-dimensional model
atmospheres. Spectral synthesis on the hydrodynamical simulations was
previously performed with the code ASS$\epsilon$T. We make a tool for the
interpolation of 3D spectra available to the community. The code provides
interpolated spectra and interpolation errors for a given wavelength interval,
and a combination of effective temperature, surface gravity, and metallicity.
In addition, it optionally provides graphical representations of the RMS and
mean ratio between 1D and 3D spectra, and maps of the errors in the
interpolated spectra across the parameter space.


title:
SQuadMDS: a lean Stochastic Quartet MDS improving global structure
  preservation in neighbor embedding like t-SNE and UMAP

abstract:
  Multidimensional scaling is a statistical process that aims to embed high
dimensional data into a lower-dimensional space; this process is often used for
the purpose of data visualisation. Common multidimensional scaling algorithms
tend to have high computational complexities, making them inapplicable on large
data sets. This work introduces a stochastic, force directed approach to
multidimensional scaling with a time and space complexity of O(N), with N data
points. The method can be combined with force directed layouts of the family of
neighbour embedding such as t-SNE, to produce embeddings that preserve both the
global and the local structures of the data. Experiments assess the quality of
the embeddings produced by the standalone version and its hybrid extension both
quantitatively and qualitatively, showing competitive results outperforming
state-of-the-art approaches. Codes are available at
https://github.com/PierreLambert3/SQuaD-MDS-and-FItSNE-hybrid.


title:
The adoption of non-pharmaceutical interventions and the role of digital
  infrastructure during the COVID-19 Pandemic in Colombia, Ecuador, and El
  Salvador

abstract:
  Adherence to the non-pharmaceutical interventions (NPIs) put in place to
mitigate the spreading of infectious diseases is a multifaceted problem.
Socio-demographic, socio-economic, and epidemiological factors can influence
the perceived susceptibility and risk which are known to affect behavior.
Furthermore, the adoption of NPIs is dependent upon the barriers, real or
perceived, associated with their implementation. We study the determinants of
NPIs adherence during the first wave of the COVID-19 Pandemic in Colombia,
Ecuador, and El Salvador. Analyses are performed at the level of municipalities
and include socio-economic, socio-demographic, and epidemiological indicators.
Furthermore, by leveraging a unique dataset comprising tens of millions of
internet Speedtest measurements from Ookla, we investigate the quality of the
digital infrastructure as a possible barrier to adoption. We use publicly
available data provided by Meta capturing aggregated mobility changes as a
proxy of adherence to NPIs. Across the three countries considered, we find a
significant correlation between mobility drops and digital infrastructure
quality. The relationship remains significant after controlling for several
factors including socio-economic status, population size, and reported COVID-19
cases. This finding suggests that municipalities with better connectivity were
able to afford higher mobility reductions. The link between mobility drops and
digital infrastructure quality is stronger at the peak of NPIs stringency. We
also find that mobility reductions were more pronounced in larger, denser, and
wealthier municipalities. Our work provides new insights on the significance of
access to digital tools as an additional factor influencing the ability to
follow social distancing guidelines during a health emergency


title:
Optimal gradient estimates for the insulated conductivity problem with
  dimensions more than two

abstract:
  In high-contrast composite materials, the electric (or stress) field may blow
up in the narrow region between inclusions. The gradient of solutions depend on
$\epsilon$, the distance between the inclusions, where $\epsilon$ approaches to
$0$. By using the maximum principle techniques, we give another proof of the
Dong-Li-Yang estimates \cite{DLY} for any convex inclusions of arbitrary shape
with $n\geq 3$. This result solves the problem raised by \cite{W}, where the
spherical inclusions with $n\geq 4$ is considered. Moreover, we also generalize
the above results with flatter boundaries near touching points.


title:
Emergence of zero-field non-synthetic single and catenated
  antiferromagnetic skyrmions in thin films

abstract:
  Antiferromagnetic (AFM) skyrmions are envisioned as ideal localized
topological magnetic bits in future information technologies. In contrast to
ferromagnetic (FM) skyrmions, they are immune to the skyrmion Hall effect[1,2],
might offer potential terahertz dynamics [3,4] while being insensitive to
external magnetic fields and dipolar interactions. Although observed in
synthetic AFM structures 5 and as complex meronic textures in intrinsic AFM
bulk materials[6,7], their realization in non-synthetic AFM films, of crucial
importance in racetrack concepts, has been elusive. Here, we unveil their
presence in a row-wise AFM Cr film deposited on PdFe bilayer grown on fcc
Ir(111) surface. Using first principles, we demonstrate the emergence of single
and strikingly interpenetrating catenated AFM skyrmions, which can co-exist
with the rich inhomogeneous exchange field, including that of FM skyrmions,
hosted by PdFe. Besides the identification of an ideal platform of materials
for intrinsic AFM skyrmions, we anticipate the uncovered knotted solitons to be
promising building blocks in AFM spintronics.


title:
Nontrivial topological states in BaSn5 superconductor probed by de
  Haas-van Alphen quantum oscillations

abstract:
  We report herein the nontrivial topological states in an intrinsic type-II
superconductor BaSn5 (Tc ~ 4.4 K) probed via measuring the magnetizations,
specific heat, de Haas-van Alphen (dHvA) effect and performing first principles
calculations. The first principles calculations reveal a topological nodal ring
structure centering at the H point in the kz = {\pi} plane of the Brillouin
zone (BZ), which could be gapped by spin-orbit coupling (SOC), yielding rather
small gaps below and above the Fermi level about 0.04 eV and 0.14 eV,
respectively. The SOC also results in a pair of Dirac points along the
{\Gamma}-A direction and located ~ 0.2 eV above the Fermi level. The analysis
of the dHvA quantum oscillations supports the calculations by revealing
nontrivial Berry phase originated from three hole and one electron pockets
related to the bands forming the Dirac cones. Our study thus provides an
excellent avenue for investigating the interplay between superconductivity and
nontrivial topological states.


title:
Influence of dark matter on gravitational stability of isothermal gas
  clouds

abstract:
  To date, the presence of dark matter (DM) can be judged only by its
gravitational interaction on the visible matter. It is therefore important to
find the consequences of this interaction, which can then help to determine
both the DM properties and parameters and the dynamics and evolution of visible
matter. The gravitational influence of dark matter on the stability of
interstellar medium (ISM), the progenitor of stars and star clusters, was
considered. An isothermal self-gravity gas was taken as a suitable model
describing ISM, particles interacting only gravitationally were considered as
DM. The results obtained by analytical methods show that even a small amount of
fast DM particles significantly increases the stable radius of the gas cloud
and the corresponding mass while a higher relative density of DM destabilizes
the gas. It was shown that with typical parameters of ISM and DM, its presence
increases the maximum stable mass of isothermal cloud by a factor of four and
the radius by five.


title: KESA: A Knowledge Enhanced Approach For Sentiment Analysis

abstract:
  Though some recent works focus on injecting sentiment knowledge into
pre-trained language models, they usually design mask and reconstruction tasks
in the post-training phase. In this paper, we aim to benefit from sentiment
knowledge in a lighter way. To achieve this goal, we study sentence-level
sentiment analysis and, correspondingly, propose two sentiment-aware auxiliary
tasks named sentiment word cloze and conditional sentiment prediction. The
first task learns to select the correct sentiment words within the input, given
the overall sentiment polarity as prior knowledge. On the contrary, the second
task predicts the overall sentiment polarity given the sentiment polarity of
the word as prior knowledge. In addition, two kinds of label combination
methods are investigated to unify multiple types of labels in each task. We
argue that more information can promote the models to learn more profound
semantic representation. We implement it in a straightforward way to verify
this hypothesis. The experimental results demonstrate that our approach
consistently outperforms pre-trained models and is additive to existing
knowledge-enhanced post-trained models. The code and data are released at
https://github.com/lshowway/KESA.


title: Enhanced Cavity Optomechanics with Quantum-well Exciton Polaritons

abstract:
  Semiconductor microresonators embedding quantum wells can host tightly
confined and mutually interacting excitonic, optical and mechanical modes at
once. We theoretically investigate the case where the system operates in the
strong exciton-photon coupling regime, while the optical and excitonic
resonances are parametrically modulated by the interaction with a mechanical
mode. Owing to the large exciton-phonon coupling at play in semiconductors, we
predict an enhancement of polariton-phonon interactions by two orders of
magnitude with respect to mere optomechanical coupling: a near-unity
single-polariton cooperativity is within reach for current semiconductor
resonator platforms. We further analyze how polariton nonlinearities affect
dynamical back-action, modifying the capability to cool or amplify the
mechanical motion.


title:
Glass and Jamming Rheology in Soft Particles Made of PNIPAM and
  Polyacrylic Acid

abstract:
  The phase behaviour of soft colloids has attracted great attention due to the
large variety of new phenomenologies emerging from their ability to pack at
very high volume fractions. Here we report rheological measurements on
interpenetrated polymer network microgels composed of
poly(Nisopropylacrylamide) (PNIPAM) and polyacrylic acid (PAAc) at fixed PAAc
content as a function of weight concentration. We found three different
rheological regimes characteristic of three different states: a Newtonian
shear-thinning fluid, an attractive glass characterized by a yield stress, and
a jamming state. We discuss the possible molecular mechanisms driving the
formation of these states.


title:
Low-energy electron impact dissociative recombination and vibrational
  transitions of N$^+_2$

abstract:
  Cross sections and thermal rate coefficients are computed for electron-impact
dissociative recombination and vibrational excitation/de-excitation of the
N$^+_2$ molecular ion in its lowest six vibrational levels, for collision
energies/temperatures up to 2.3 eV/5000 K.


title: Distinguishing two dark matter component particles at $e^+e^-$ colliders

abstract:
  In this work we demonstrate that a distorted double hump like missing energy
($\slashed{E}$) or missing transverse momentum ($\slashed{E}_T$) or missing
mass ($\slashed{M}$) distribution at $e^+e^-$ colliders may hint towards the
presence of multipartite dark sector. We illustrate the phenomena using a two
component dark matter (DM) model involving an inert scalar doublet stabilised
under a $\mathcal{Z}_2$ symmetry providing a scalar DM, one vector like fermion
doublet and a right handed fermion singlet both stabilised under a different
$\mathcal{Z}^{'}_2$ providing a fermion DM. We indicate the region of parameter
space where the production of the heavy charged particles and their subsequent
decay to DM yield double peak behaviour in $\slashed{E}$ spectrum after
satisfying DM constraints. Importantly, we illustrate why and how $\slashed{E}$
serves as a better variable than $\slashed{E}_T$ in distinguishing two
component DM frameworks and therefore how International Linear Collider (ILC)
does better than the ongoing Large Hadron Collider (LHC). We also chalk out a
set of criteria to identify and segregate the second peak in $\slashed{E}$
spectrum, after a careful analysis of the corresponding Standard Model (SM)
background contribution, which plays a crucial role.


title:
Numerical reconstruction from the Fourier transform on the ball using
  prolate spheroidal wave functions

abstract:
  We implement numerically formulas of [Isaev, Novikov, arXiv:2107.07882] for
finding a compactly supported function $v$ on $\mathbb{R}^d$, $d\geq 1$, from
its Fourier transform $\mathcal{F} [v]$ given within the ball $B_r$. For the
one-dimensional case, these formulas are based on the theory of prolate
spheroidal wave functions, which arise, in particular, in the singular value
decomposition of the aforementioned band-limited Fourier transform for $d = 1$.
In multidimensions, these formulas also include inversion of the Radon
transform. In particular, we give numerical examples of super-resolution, that
is, recovering details beyond the diffraction limit.


title: Data variation-aware medical image segmentation

abstract:
  Deep learning algorithms have become the golden standard for segmentation of
medical imaging data. In most works, the variability and heterogeneity of real
clinical data is acknowledged to still be a problem. One way to automatically
overcome this is to capture and exploit this variation explicitly. Here, we
propose an approach that improves on our previous work in this area and explain
how it potentially can improve clinical acceptance of (semi-)automatic
segmentation methods. In contrast to a standard neural network that produces
one segmentation, we propose to use a multi-pathUnet network that produces
multiple segmentation variants, presumably corresponding to the variations that
reside in the dataset. Different paths of the network are trained on disjoint
data subsets. Because a priori it may be unclear what variations exist in the
data, the subsets should be automatically determined. This is achieved by
searching for the best data partitioning with an evolutionary optimization
algorithm. Because each network path can become more specialized when trained
on a more homogeneous data subset, better segmentation quality can be achieved.
In practical usage, various automatically produced segmentations can be
presented to a medical expert, from which the preferred segmentation can be
selected. In experiments with a real clinical dataset of CT scans with prostate
segmentations, our approach provides an improvement of several percentage
points in terms of Dice and surface Dice coefficients compared to when all
network paths are trained on all training data. Noticeably, the largest
improvement occurs in the upper part of the prostate that is known to be most
prone to inter-observer segmentation variation.


title:
DeepFusionMOT: A 3D Multi-Object Tracking Framework Based on
  Camera-LiDAR Fusion with Deep Association

abstract:
  In the recent literature, on the one hand, many 3D multi-object tracking
(MOT) works have focused on tracking accuracy and neglected computation speed,
commonly by designing rather complex cost functions and feature extractors. On
the other hand, some methods have focused too much on computation speed at the
expense of tracking accuracy. In view of these issues, this paper proposes a
robust and fast camera-LiDAR fusion-based MOT method that achieves a good
trade-off between accuracy and speed. Relying on the characteristics of camera
and LiDAR sensors, an effective deep association mechanism is designed and
embedded in the proposed MOT method. This association mechanism realizes
tracking of an object in a 2D domain when the object is far away and only
detected by the camera, and updating of the 2D trajectory with 3D information
obtained when the object appears in the LiDAR field of view to achieve a smooth
fusion of 2D and 3D trajectories. Extensive experiments based on the KITTI
dataset indicate that our proposed method presents obvious advantages over the
state-of-the-art MOT methods in terms of both tracking accuracy and processing
speed. Our code is made publicly available for the benefit of the community


title: The first Grushin eigenvalue on cartesian product domains

abstract:
  In this paper we consider the first eigenvalue $\lambda_1(\Omega)$ of the
Grushin operator $\Delta_G:=\Delta_{x_1}+|x_1|^{2s}\Delta_{x_2}$ with Dirichlet
boundary conditions on a bounded domain $\Omega$ of $\mathbb{R}^d=
\mathbb{R}^{d_1+d_2}$. We prove that $\lambda_1(\Omega)$ admits a unique
minimizer in the class of domains with prescribed finite volume which are the
cartesian product of a set in $\mathbb{R}^{d_1}$ and a set in
$\mathbb{R}^{d_2}$, and that the minimizer is the product of two balls
$\Omega^*_1 \subseteq \mathbb{R}^{d_1}$ and $\Omega_2^* \subseteq
\mathbb{R}^{d_2}$. Moreover, we provide a lower bound for $|\Omega^*_1|$ and
for $\lambda_1(\Omega_1^*\times\Omega_2^*)$. Finally, we consider the limiting
problem as $s$ tends to $0$ and to $+\infty$.


title:
Quantum Calculi: differential forms and vector fields in noncommutative
  geometry

abstract:
  In this paper we revisit the notion of noncommutative vector fields
introduced in \cite{AB96,AB97}, extending the framework, adding new results and
clarifying the old one. Using appropriate algebraic tools certain shortcomings
in the previous considerations are filled and made more precise. We are focused
on the correspondence between the so-called Cartan pairs and first-order
differentials. Particularly, the case of free modules and their braidings is
considered in more detail. Bimodules of right/left universal vector fields are
explicitly constructed.


title: A note on M\"{o}bius functions of upho posets

abstract:
  A poset is called upper homogeneous (or "upho") if every principal order
filter of the poset is isomorphic to the whole poset. We observe that the rank
and characteristic generating functions of upho posets are inverses of one
another.


title: A Transformer-based Network for Deformable Medical Image Registration

abstract:
  Deformable medical image registration plays an important role in clinical
diagnosis and treatment. Recently, the deep learning (DL) based image
registration methods have been widely investigated and showed excellent
performance in computational speed. However, these methods cannot provide
enough registration accuracy because of insufficient ability in representing
both the global and local features of the moving and fixed images. To address
this issue, this paper has proposed the transformer based image registration
method. This method uses the distinctive transformer to extract the global and
local image features for generating the deformation fields, based on which the
registered image is produced in an unsupervised way. Our method can improve the
registration accuracy effectively by means of self-attention mechanism and
bi-level information flow. Experimental results on such brain MR image datasets
as LPBA40 and OASIS-1 demonstrate that compared with several traditional and DL
based registration methods, our method provides higher registration accuracy in
terms of dice values.


title:
Temperature Anisotropy of the CMBR and the Non-zero Cosmological
  Constant

abstract:
  We analyze the effect of a spherically symmetric clump on the anisotropy of
the cosmic microwave background radiation temperature in the framework of the
standard model of cosmology with a non-zero cosmological constant $\Lambda$ and
we show that it weakens the Rees-Sciama effect.


title:
Classification of preordered spaces in terms of monotones -- Filling in
  the gaps

abstract:
  Following the recent introduction of new classes of monotones, like injective
monotones or strict monotone multi-utilities, we present the classification of
preordered spaces in terms of both the existence and cardinality of real-valued
monotones and the cardinality of the quotient space. In particular, we take
advantage of a characterization of real-valued monotones in terms of separating
families of increasing sets in order to obtain a more complete classification
consisting of classes that are strictly different from each other.


title:
From Natural Language to Simulations: Applying GPT-3 Codex to Automate
  Simulation Modeling of Logistics Systems

abstract:
  Our work is the first attempt to apply Natural Language Processing to
automate the development of simulation models of logistics systems. We
demonstrated that the framework built on top of the fine-tuned
Transdormer-based language model could produce functionally valid simulations
of queuing and inventory control systems given the verbal description. The
proposed framework has the potential to remove the tedium of programming and
allow experts to focus on the high-level consideration of the problem and
holistic thinking.


title:
Light Robust Monocular Depth Estimation For Outdoor Environment Via
  Monochrome And Color Camera Fusion

abstract:
  Depth estimation plays a important role in SLAM, odometry, and autonomous
driving. Especially, monocular depth estimation is profitable technology
because of its low cost, memory, and computation. However, it is not a
sufficiently predicting depth map due to a camera often failing to get a clean
image because of light conditions. To solve this problem, various sensor fusion
method has been proposed. Even though it is a powerful method, sensor fusion
requires expensive sensors, additional memory, and high computational
performance.
  In this paper, we present color image and monochrome image pixel-level fusion
and stereo matching with partially enhanced correlation coefficient
maximization. Our methods not only outperform the state-of-the-art works across
all metrics but also efficient in terms of cost, memory, and computation. We
also validate the effectiveness of our design with an ablation study.


title:
Prompt for Extraction? PAIE: Prompting Argument Interaction for Event
  Argument Extraction

abstract:
  In this paper, we propose an effective yet efficient model PAIE for both
sentence-level and document-level Event Argument Extraction (EAE), which also
generalizes well when there is a lack of training data. On the one hand, PAIE
utilizes prompt tuning for extractive objectives to take the best advantages of
Pre-trained Language Models (PLMs). It introduces two span selectors based on
the prompt to select start/end tokens among input texts for each role. On the
other hand, it captures argument interactions via multi-role prompts and
conducts joint optimization with optimal span assignments via a bipartite
matching loss. Also, with a flexible prompt design, PAIE can extract multiple
arguments with the same role instead of conventional heuristic threshold
tuning. We have conducted extensive experiments on three benchmarks, including
both sentence- and document-level EAE. The results present promising
improvements from PAIE (3.5\% and 2.3\% F1 gains in average on three
benchmarks, for PAIE-base and PAIE-large respectively). Further analysis
demonstrates the efficiency, generalization to few-shot settings, and
effectiveness of different extractive prompt tuning strategies. Our code is
available at https://github.com/mayubo2333/PAIE.


title:
Multi-fold non-Hermitian phase transitions and exact solution of
  non-Hermitian skin effects

abstract:
  Non-Hermitian systems can exhibit extraordinary sensitivity to boundary
conditions, but also come with the failure of traditional bulk-boundary
correspondence that Bloch band invariants cannot predict the boundary
behaviors. Here, we emphasize that topological boundary modes and non-Hermitian
skin effects can independently appear, thus we can observe four-fold phase
transitions in non-Hermitian open systems, which is beyond any known phenomenon
from Hermitian physics. To reconstruct the bulk-boundary correspondence,
several methods have been proved valid for non-Hermitian Su-Schrieffer-Heeger
model. However, whether these approach are applicable in more complex
non-Hermitian system, and how to establish the four-fold phase-transition
diagram more conveniently should be investigated. We illustrate our general
insights by deriving the phase diagram for a one-dimensional lattice model with
next-nearest inter-cell interaction. Through the combination of non-Bloch wave
approach and exact solution approach, both the existence condition of
topological modes and the localization length of skin modes can be analytically
expressed, which provides a more general routine to study non-Hermitian
boundary behaviors.


title:
An Algorithm for Computing the Covering Radius of a Linear Code Based on
  Vilenkin-Chrestenson Transform

abstract:
  We present a generalization of Walsh-Hadamard transform that is suitable for
applications in Coding Theory, especially for computation of the weight
distribution and the covering radius of a linear code over a finite field. The
transform used in our research, is a modification of Vilenkin-Chrestenson
transform. Instead of using all the vectors in the considered space, we take a
maximal set of nonproportional vectors, which reduces the computational
complexity.


title: Composition Operators on Dirichlet Spaces over the Half-plane

abstract:
  As continuation of the study of polynomial approximation and composition
operators on Dirichlet spaces of unit disk, which has settled a problem posed
by Cima in 1976, the present paper aims to consider the case of the unbounded
domains, such as the half-plane. Specifically, we may obtain the rational
approximations in the Dirichlet spaces and characterize the composition
operators which has dense range on the Dirichlet spaces over the half-plane.
Moreover, this paper also considers the relationship between the Dirichlet
spaces and Hardy spaces on half-plane.


title: Semiseparable functors

abstract:
  In this paper we introduce and investigate the notion of semiseparable
functor. One of its first features is that it allows a novel description of
separable and naturally full functors in terms of faithful and full functors,
respectively. To any semiseparable functor we attach an invariant, given by an
idempotent natural transformation, which controls when the functor is separable
and yields a characterization of separable functors in terms of (dual) Maschke
and conservative functors. We prove that any semiseparable functor admits a
canonical factorization as a naturally full functor followed by a separable
functor. Here the main tool is the construction of the coidentifier category
attached to the associated idempotent natural transformation. Then we move our
attention to the semiseparability of functors that have an adjoint. First we
obtain a Rafael-type Theorem. Next we characterize the semiseparability of
adjoint functors in terms of the (co)separability of the associated (co)monads
and the natural fullness of the corresponding (co)comparison functor. We also
focus on functors that are part of an adjoint triple. In particular, we
describe bireflections as semiseparable (co)reflections, or equivalently, as
either Frobenius or naturally full (co)reflections. As an application of our
results, we study the semiseparability of functors traditionally attached to
ring homomorphisms, coalgebra maps, corings and bimodules, introducing the
notions of semicosplit coring and semiseparability relative to a bimodule which
extend those of cosplit coring and Sugano's separability relative to a
bimodule, respectively.


title:
Born probability estimation via gate merging and dynamic frame
  optimisation

abstract:
  Outcome probability estimation via classical methods is an important task for
validating quantum computing devices. Outcome probabilities of any quantum
circuit can be estimated using Monte Carlo sampling, where the amount of
negativity present in the circuit frame representation quantifies the overhead
on the number of samples required to achieve a certain precision. In this
paper, we propose two classical sub-routines: circuit gate merging and dynamic
frame optimisation, which optimise the circuit representation to reduce the
sampling overhead. We show that the runtimes of both sub-routines scale
polynomially in circuit size and gate depth. Our methods are applicable to
general circuits, regardless of generating gate sets, qudit dimensions and the
chosen frame representations for the circuit components. We numerically
demonstrate that our methods provide improved scaling in the negativity
overhead for all tested cases of random circuits with Clifford+$T$ and
Haar-random gates, and that the performance of our methods compares favourably
with prior quasi-probability samplers as the number of non-Clifford gates
increases.


title:
Methodology for estimating the magnetic Prandtl number and application
  to solar surface small-scale dynamo simulations

abstract:
  Context. A crucial step in the numerical investigation of small-scale dynamos
in the solar atmosphere consists of an accurate determination of the magnetic
Prandtl number, Prm, stemming from radiative magneto-hydrodynamic (MHD)
simulations. Aims. The aims are to provide a reliable methodology for
estimating the effective Reynolds and magnetic Reynolds numbers, Re and Rem,
and their ratio Prm=Rem/Re (the magnetic Prandlt number), that characterise MHD
simulations and to categorise small-scale dynamo simulations in terms of these
dimensionless parameters. Methods. The methodology proposed for computing Re
and Rem is based on the method of projection on proper elements and it relies
on a post-processing step carried out using higher order accurate numerical
operators than the ones in the simulation code. A number of radiative MHD
simulations with different effective viscosities and plasma resistivities were
carried out with the CO5BOLD code, and the resulting growth rate of the
magnetic energy and saturated magnetic field strengths were characterised in
terms of Re and Rem. Results. Overall, the proposed methodology provides a
solid estimate of the dissipation coefficients affecting the momentum and
induction equations of MHD simulation codes, and consequently also a reliable
evaluation of the magnetic Prandtl number characterising the numerical results.
Additionally, it is found that small-scale dynamos are active and can amplify a
small seed magnetic field up to significant values in CO5BOLD simulations with
a grid spacing smaller than h=12 km, even at Prm=0.65. However, it is also
evident that it is difficult to categorise dynamo simulations in terms of Prm
alone, because it is not only important to estimate the amplitude of the
dissipation coefficients, but also at which scales energy dissipation takes
place.


title: Slow-Fast Visual Tempo Learning for Video-based Action Recognition

abstract:
  Action visual tempo characterizes the dynamics and the temporal scale of an
action, which is helpful to distinguish human actions that share high
similarities in visual dynamics and appearance. Previous methods capture the
visual tempo either by sampling raw videos with multiple rates, which requires
a costly multi-layer network to handle each rate, or by hierarchically sampling
backbone features, which relies heavily on high-level features that miss
fine-grained temporal dynamics. In this work, we propose a Temporal Correlation
Module (TCM), which can be easily embedded into the current action recognition
backbones in a plug-in-and-play manner, to extract action visual tempo from
low-level backbone features at single-layer remarkably. Specifically, our TCM
contains two main components: a Multi-scale Temporal Dynamics Module (MTDM) and
a Temporal Attention Module (TAM). MTDM applies a correlation operation to
learn pixel-wise fine-grained temporal dynamics for both fast-tempo and
slow-tempo. TAM adaptively emphasizes expressive features and suppresses
inessential ones via analyzing the global information across various tempos.
Extensive experiments conducted on several action recognition benchmarks, e.g.
Something-Something V1 & V2, Kinetics-400, UCF-101, and HMDB-51, have
demonstrated that the proposed TCM is effective to promote the performance of
the existing video-based action recognition models for a large margin. The
source code is publicly released at https://github.com/zphyix/TCM.


title:
Universal framework for the long-time position distribution of free
  active particles

abstract:
  Active particles self-propel themselves with a stochastically evolving
velocity, generating a persistent motion leading to a non-diffusive behavior of
the position distribution. Nevertheless, an effective diffusive behavior
emerges at times much larger than the persistence time. Here we develop a
general framework for studying the long-time behaviour for a class of active
particle dynamics and illustrate it using the examples of run-and-tumble
particle, active Ornstein-Uhlenbeck particle, active Brownian particle, and
direction reversing active Brownian particle. Treating the ratio of the
persistence-time to the observation time as the small parameter, we show that
the position distribution generically satisfies the diffusion equation at the
leading order. We further show that the sub-leading contributions, at each
order, satisfies an inhomogeneous diffusion equation, where the source term
depends on the previous order solutions. We explicitly obtain a few sub-leading
contributions to the Gaussian position distribution. As a part of our
framework, we also prescribe a way to find the position moments recursively and
compute the first few explicitly for each model.


title:
Gap probability and full counting statistics in the one dimensional
  one-component plasma

abstract:
  We consider the $1d$ one-component plasma (OCP) in thermal equilibrium,
consisting of $N$ equally charged particles on a line, with pairwise Coulomb
repulsion and confined by an external harmonic potential. We study two
observables: (i) the distribution of the gap between two consecutive particles
in the bulk and (ii) the distribution of the number of particles $N_I$ in a
fixed interval $I=[-L,+L]$ inside the bulk, the so-called
full-counting-statistics (FCS). For both observables, we compute, for large
$N$, the distribution of the typical as well as atypical large fluctuations. We
show that the distribution of the typical fluctuations of the gap are described
by the scaling form ${\cal P}_{\rm gap, bulk}(g,N) \sim N H_\alpha(g\,N)$,
where $\alpha$ is the interaction coupling and the scaling function
$H_\alpha(z)$ is computed explicitly. It has a faster than Gaussian tail for
large $z$: $H_\alpha(z) \sim e^{-z^3/(96 \alpha)}$ as $z \to \infty$.
Similarly, for the FCS, we show that the distribution of the typical
fluctuations of $N_I$ is described by the scaling form ${\cal P}_{\rm
FCS}(N_I,N) \sim 2\alpha \, U_\alpha[2 \alpha(N_I - \bar{N}_I)]$, where
$\bar{N}_I = L\,N/(2 \alpha)$ is the average value of $N_I$ and the scaling
function $U_\alpha(z)$ is obtained explicitly. For both observables, we show
that the probability of large fluctuations are described by large deviations
forms with respective rate functions that we compute explicitly. Our numerical
Monte-Carlo simulations are in good agreement with our analytical predictions.

categories: cond-mat.stat-mech math-ph math.MP math.PR


title:
Optimal Learning Rates of Deep Convolutional Neural Networks: Additive
  Ridge Functions

abstract:
  Convolutional neural networks have shown extraordinary abilities in many
applications, especially those related to the classification tasks. However,
for the regression problem, the abilities of convolutional structures have not
been fully understood, and further investigation is needed. In this paper, we
consider the mean squared error analysis for deep convolutional neural
networks. We show that, for additive ridge functions, convolutional neural
networks followed by one fully connected layer with ReLU activation functions
can reach optimal mini-max rates (up to a log factor). The convergence rates
are dimension independent. This work shows the statistical optimality of
convolutional neural networks and may shed light on why convolutional neural
networks are able to behave well for high dimensional input.


title:
Temporal Convolution Domain Adaptation Learning for Crops Growth
  Prediction

abstract:
  Existing Deep Neural Nets on crops growth prediction mostly rely on
availability of a large amount of data. In practice, it is difficult to collect
enough high-quality data to utilize the full potential of these deep learning
models. In this paper, we construct an innovative network architecture based on
domain adaptation learning to predict crops growth curves with limited
available crop data. This network architecture overcomes the challenge of data
availability by incorporating generated data from the developed crops
simulation model. We are the first to use the temporal convolution filters as
the backbone to construct a domain adaptation network architecture which is
suitable for deep learning regression models with very limited training data of
the target domain. We conduct experiments to test the performance of the
network and compare our proposed architecture with other state-of-the-art
methods, including a recent LSTM-based domain adaptation network architecture.
The results show that the proposed temporal convolution-based network
architecture outperforms all benchmarks not only in accuracy but also in model
size and convergence rate.


title:
Modeling and Predicting Spatio-temporal Dynamics of PM$_{2.5}$
  Concentrations Through Time-evolving Covariance Models

abstract:
  Fine particulate matter (PM$_{2.5}$) has become a great concern worldwide due
to its adverse health effects. PM$_{2.5}$ concentrations typically exhibit
complex spatio-temporal variations. Both the mean and the spatio-temporal
dependence evolve with time due to seasonality, which makes the statistical
analysis of PM$_{2.5}$ challenging. In geostatistics, Gaussian process is a
powerful tool for characterizing and predicting such spatio-temporal dynamics,
for which the specification of a spatio-temporal covariance function is the
key. While the extant literature offers a wide range of choices for flexible
stationary spatio-temporal covariance models, the temporally evolving
spatio-temporal dependence has received scant attention only. To this end, we
propose a time-varying spatio-temporal covariance model for describing the
time-evolving spatio-temporal dependence in PM$_{2.5}$ concentrations. For
estimation, we develop a composite likelihood-based procedure to handle large
spatio-temporal datasets.The proposed model is shown to outperform
traditionally used models through simulation studies in terms of predictions.
We apply our model to analyze the PM$_{2.5}$ data in the state of Oregon, US.
Therein, we show that the spatial scale and smoothness exhibit periodicity. The
proposed model is also shown to be beneficial over traditionally used models on
this dataset for predictions.


title: Demonstrating BrainScaleS-2 Inter-Chip Pulse-Communication using EXTOLL

abstract:
  The BrainScaleS-2 (BSS-2) Neuromorphic Computing System currently consists of
multiple single-chip setups, which are connected to a compute cluster via
Gigabit-Ethernet network technology. This is convenient for small experiments,
where the neural networks fit into a single chip. When modeling networks of
larger size, neurons have to be connected across chip boundaries. We implement
these connections for BSS-2 using the EXTOLL networking technology. This
provides high bandwidths and low latencies, as well as high message rates.
Here, we describe the targeted pulse-routing implementation and required
extensions to the BSS-2 software stack. We as well demonstrate feed-forward
pulse-routing on BSS-2 using a scaled-down version without temporal merging.


title:
An Information-theoretical Approach to Semi-supervised Learning under
  Covariate-shift

abstract:
  A common assumption in semi-supervised learning is that the labeled,
unlabeled, and test data are drawn from the same distribution. However, this
assumption is not satisfied in many applications. In many scenarios, the data
is collected sequentially (e.g., healthcare) and the distribution of the data
may change over time often exhibiting so-called covariate shifts. In this
paper, we propose an approach for semi-supervised learning algorithms that is
capable of addressing this issue. Our framework also recovers some popular
methods, including entropy minimization and pseudo-labeling. We provide new
information-theoretical based generalization error upper bounds inspired by our
novel framework. Our bounds are applicable to both general semi-supervised
learning and the covariate-shift scenario. Finally, we show numerically that
our method outperforms previous approaches proposed for semi-supervised
learning under the covariate shift.


title:
Projected gradient-tracking in multi-cluster games and its application
  to power management

abstract:
  We are concerned with a distributed approach to solve multi-cluster games
arising in multi-agent systems. In such games, agents are separated into
distinct clusters. The agents belonging to the same cluster cooperate with each
other to achieve a common cluster goal while a non-cooperative game is played
between the clusters. To be able to deal with the sparsity of information, as
each agent only knows a specific part of the problem, we combine
gradient-tracking and consensus methods for information distribution into an
algorithm that can solve both the cooperative and non-cooperative problem in a
single run. The constraints of the problem are taken into account by the
corresponding projection operators and linear convergence is proven given an
appropriate constant step size. The algorithm is applied to a day-ahead power
management problem, posed as a multi-cluster game, and its efficiency is
demonstrated by simulations.


title: Extremal problems for trinomials with fold symmetry

abstract:
  The famous T. Suffridge polynomials have many extremal properties: the
maximality of coefficients when the leading coefficient is maximal; the zeros
of the derivative are located on the unit circle; the maximum radius of
stretching the unit disk with the schlicht normalization $F(0)=0$, $F'(0)=1$;
the maximum size of the unit disk contraction in the direction of the real axis
for univalent polynomials with the normalization $F(0)=0$, $F(1)=1.$ However,
under the standard symmetrization method $\sqrt[T]{F(z^T)}$, these polynomials
go to functions, which are not polynomials. How can we construct the
polynomials with fold symmetry that have properties similar to those of the
Suffridge polynomial? What values will the corresponding extremal quantities
take in the above-mentioned extremal problems? The paper is devoted to solving
these questions for the case of the trinomials $F(z)=z+az^{1+T}+bz^{1+2T}$.
Also, there are suggested hypotheses for the general case in the work.


title:
Zeros of derivatives of $L$-functions in the Selberg class on
  $\Re(s)<1/2$

abstract:
  In this article, we show that the Riemann hypothesis for an $L$-function $F$
belonging to the Selberg class implies that all the derivatives of $F$ can have
at most finitely many zeros on the left of the critical line with imaginary
part greater than a certain constant. This was shown for the Riemann zeta
function by Levinson and Montgomery in 1974.


title:
Robust random walk-like Metropolis-Hastings algorithms for concentrating
  posteriors

abstract:
  Motivated by Bayesian inference with highly informative data we analyze the
performance of random walk-like Metropolis-Hastings algorithms for approximate
sampling of increasingly concentrating target distributions. We focus on
Gaussian proposals which use a Hessian-based approximation of the target
covariance. By means of pushforward transition kernels we show that for
Gaussian target measures the spectral gap of the corresponding
Metropolis-Hastings algorithm is independent of the concentration of the
posterior, i.e., the noise level in the observational data that is used for
Bayesian inference. Moreover, by exploiting the convergence of the
concentrating posteriors to their Laplace approximation we extend the analysis
to non-Gaussian target measures which either concentrate around a single point
or along a linear manifold. In particular, in that setting we show that the
average acceptance rate as well as the expected squared jump distance of
suitable Metropolis-Hastings Markov chains do not deteriorate as the target
concentrates.

categories: stat.CO cs.NA math.NA math.PR math.ST stat.TH


title: Optimal policy structure for system upgrades during an asset's lifetime

abstract:
  We consider a continuous-time stochastic model that aims to find an optimal
upgrade policy for a single system in an asset with a fixed overhaul planning.
In a novel model, we include the key critical factors that may drive an asset
owner to upgrade a system: increasing functionality requirements due to
evolving technology, age-dependent maintenance costs, a predetermined overhaul
plan, and a finite lifetime of the asset. We characterize the structure of the
optimal upgrade policy through analytical results, and use these to establish
an efficient solution approach based on dynamic programming. We also consider
the effects of the input parameters on the optimal total costs, both
analytically as well as numerically.


title: Symmetries at Causal Boundaries in 2D and 3D Gravity

abstract:
  We study 2d and 3d gravity theories on spacetimes with causal (timelike or
null) codimension one boundaries while allowing for variations in the position
of the boundary. We construct the corresponding solution phase space and
specify boundary degrees freedom by analysing boundary (surface) charges
labelling them. We discuss Y and W freedoms and change of slicing in the
solution space. For D dimensional case we find D+1 surface charges, which are
generic functions over the causal boundary. We show that there exist solution
space slicings in which the charges are integrable. For the 3d case there
exists an integrable slicing where charge algebra takes the form of Heisenberg
\oplus\ {\cal A}_3 where {\cal A}_3 is two copies of Virasoro at Brown-Henneaux
central charge for AdS_3 gravity and BMS_3 for the 3d flat space gravity.


title:
Lipschitz stable determination of polyhedral conductivity inclusions
  from local boundary measurements

abstract:
  We consider the problem of determining a polyhedral conductivity inclusion
embedded in a homogeneous isotropic medium from boundary measurements. We prove
global Lipschitz stability for the polyhedral inclusion from the local
Dirichlet-to-Neumann map extending in a highly nontrivial way the results
obtained in [18] and [19] in the two-dimensional case to the three-dimensional
setting.


title: The Shortest Path with Increasing Chords in a Simple Polygon

abstract:
  We study the problem of finding the shortest path with increasing chords in a
simple polygon. A path has increasing chords if and only if for any points a,
b, c, and d that lie on the path in that order, |ad| >= |bc|. In this paper we
show that the shortest path with increasing chords is unique and present an
algorithm to construct it.


title:
"splink" is happy and "phrouth" is scary: Emotion Intensity Analysis for
  Nonsense Words

abstract:
  People associate affective meanings to words - "death" is scary and sad while
"party" is connotated with surprise and joy. This raises the question if the
association is purely a product of the learned affective imports inherent to
semantic meanings, or is also an effect of other features of words, e.g.,
morphological and phonological patterns. We approach this question with an
annotation-based analysis leveraging nonsense words. Specifically, we conduct a
best-worst scaling crowdsourcing study in which participants assign intensity
scores for joy, sadness, anger, disgust, fear, and surprise to 272 non-sense
words and, for comparison of the results to previous work, to 68 real words.
Based on this resource, we develop character-level and phonology-based
intensity regressors. We evaluate them on both nonsense words and real words
(making use of the NRC emotion intensity lexicon of 7493 words), across six
emotion categories. The analysis of our data reveals that some phonetic
patterns show clear differences between emotion intensities. For instance, s as
a first phoneme contributes to joy, sh to surprise, p as last phoneme more to
disgust than to anger and fear. In the modelling experiments, a regressor
trained on real words from the NRC emotion intensity lexicon shows a higher
performance (r = 0.17) than regressors that aim at learning the emotion
connotation purely from nonsense words. We conclude that humans do associate
affective meaning to words based on surface patterns, but also based on
similarities to existing words ("juy" to "joy", or "flike" to "like").


title:
Conformally curved initial data for charged, spinning black hole
  binaries on arbitrary orbits

abstract:
  We present a method to construct conformally curved initial data for charged
black hole binaries with spin on arbitrary orbits. We generalize the superposed
Kerr-Schild, extended conformal thin sandwich construction from [Lovelace et
al., Phys. Rev. D {78}, 084017 (2008)] to use Kerr-Newman metrics for the
superposed black holes and to solve the electromagnetic constraint equations.
We implement the construction in the pseudospectral code SGRID. The code thus
provides a complementary and completely independent excision-based
construction, compared to the existing charged black hole initial data
constructed using the puncture method [Bozzola and Paschalidis, Phys. Rev. D
{99}, 104044 (2019)]. It also provides an independent implementation (with some
small changes) of the Lovelace et al. vacuum construction. We construct initial
data for different configurations of orbiting binaries, e.g., with black holes
that are highly charged or rapidly spinning (90 and 80 percent of the extremal
values, respectively, for this initial test, though the code should be able to
produce data with even higher values of these parameters using higher
resolutions), as well as for generic spinning, charged black holes. We carry
out exploratory evolutions with the finite difference, moving punctures codes
BAM (in the vacuum case) and HAD (for head-on collisions including charge),
filling inside the excision surfaces. In the charged case, evolutions of these
initial data provide a proxy for binary black hole waveforms in modified
theories of gravity. Moreover, the generalization of the construction to
Einstein-Maxwell-dilaton theory should be straightforward.


title:
Measurements of differential cross-sections in top-quark pair events
  with a high transverse momentum top quark and limits on beyond the Standard
  Model contributions to top-quark pair production with the ATLAS detector at
  $\sqrt{s}=13$ TeV

abstract:
  Cross-section measurements of top-quark pair production where the
hadronically decaying top quark has transverse momentum greater than $355$ GeV
and the other top quark decays into $\ell \nu b$ are presented using 139
fb$^{-1}$ of data collected by the ATLAS experiment during proton-proton
collisions at the LHC. The fiducial cross-section at $\sqrt{s}=13$ TeV is
measured to be $\sigma = 1.267 \pm 0.005 \pm 0.053$ pb, where the uncertainties
reflect the limited number of data events and the systematic uncertainties,
giving a total uncertainty of $4.2\%$. The cross-section is measured
differentially as a function of variables characterising the $t\bar{t}$ system
and additional radiation in the events. The results are compared with various
Monte Carlo generators, including comparisons where the generators are
reweighted to match a parton-level calculation at next-to-next-to-leading
order. The reweighting improves the agreement between data and theory. The
measured distribution of the top-quark transverse momentum is used to set
limits on the Wilson coefficients of the dimension-six operators $O_{tG}$ and
$O_{tq}^{(8)}$ in the effective field theory framework.


title: McKay correspondence and orbifold equivalence

abstract:
  We prove that a pair of singularities related by a transformation arising
from the McKay correspondence are orbifold equivalent.


title:
A phase-field approach for detecting cavities via a Kohn-Vogelius type
  functional

abstract:
  We deal with the geometrical inverse problem of the shape reconstruction of
cavities in a bounded linear isotropic medium by means of boundary data. The
problem is addressed from the point of view of optimal control: the goal is to
minimize in the class of Lipschitz domains a Kohn-Vogelius type functional with
a perimeter regularization term which penalizes the perimeter of the cavity to
be reconstructed. To solve numerically the optimization problem, we use a
phase-field approach, approximating the perimeter functional with a
Modica-Mortola relaxation and modeling the cavity as an inclusion with a very
small elastic tensor. We provide a detailed analysis showing the robustness of
the algorithm through some numerical experiments.


title:
From Zero-Intelligence to Queue-Reactive: Limit Order Book modeling for
  high-frequency volatility estimation and optimal execution

abstract:
  The estimation of the volatility with high-frequency data is plagued by the
presence of microstructure noise, which leads to biased measures. Alternative
estimators have been developed and tested either on specific structures of the
noise or by the speed of convergence to their asymptotic distributions.
Gatheral and Oomen (2010) proposed to use the Zero-Intelligence model of the
limit order book to test the finite-sample performance of several estimators of
the integrated variance. Building on this approach, in this paper we introduce
three main innovations: (i) we use as data-generating process the
Queue-Reactive model of the limit order book (Huang et al. (2015)), which -
compared to the Zero-Intelligence model - generates more realistic
microstructure dynamics, as shown here by using an Hausman test; (ii) we
consider not only estimators of the integrated volatility but also of the spot
volatility; (iii) we show the relevance of the estimator in the prediction of
the variance of the cost of a simulated VWAP execution. Overall we find that,
for the integrated volatility, the pre-averaging estimator optimizes the
estimation bias, while the unified and the alternation estimator lead to
optimal mean squared error values. Instead, in the case of the spot volatility,
the Fourier estimator yields the optimal accuracy, both in terms of bias and
mean squared error. The latter estimator leads also to the optimal prediction
of the cost variance of a VWAP execution.


title:
How reparametrization trick broke differentially-private text
  representation learning

abstract:
  As privacy gains traction in the NLP community, researchers have started
adopting various approaches to privacy-preserving methods. One of the favorite
privacy frameworks, differential privacy (DP), is perhaps the most compelling
thanks to its fundamental theoretical guarantees. Despite the apparent
simplicity of the general concept of differential privacy, it seems non-trivial
to get it right when applying it to NLP. In this short paper, we formally
analyze several recent NLP papers proposing text representation learning using
DPText (Beigi et al., 2019a,b; Alnasser et al., 2021; Beigi et al., 2021) and
reveal their false claims of being differentially private. Furthermore, we also
show a simple yet general empirical sanity check to determine whether a given
implementation of a DP mechanism almost certainly violates the privacy loss
guarantees. Our main goal is to raise awareness and help the community
understand potential pitfalls of applying differential privacy to text
representation learning.


title:
Testing Deep Learning Models: A First Comparative Study of Multiple
  Testing Techniques

abstract:
  Deep Learning (DL) has revolutionized the capabilities of vision-based
systems (VBS) in critical applications such as autonomous driving, robotic
surgery, critical infrastructure surveillance, air and maritime traffic
control, etc. By analyzing images, voice, videos, or any type of complex
signals, DL has considerably increased the situation awareness of these
systems. At the same time, while relying more and more on trained DL models,
the reliability and robustness of VBS have been challenged and it has become
crucial to test thoroughly these models to assess their capabilities and
potential errors. To discover faults in DL models, existing software testing
methods have been adapted and refined accordingly. In this article, we provide
an overview of these software testing methods, namely differential,
metamorphic, mutation, and combinatorial testing, as well as adversarial
perturbation testing and review some challenges in their deployment for
boosting perception systems used in VBS. We also provide a first experimental
comparative study on a classical benchmark used in VBS and discuss its results.


title: Studying Aspects of the Early Universe with Primordial Black Holes

abstract:
  This thesis by publication is devoted to the study of aspects of the early
universe in the context of primordial black hole (PBH) physics. Firstly, we
review the fundamentals of the early universe cosmology and we recap the basics
of the PBHs physics. In particular, we propose a refinement in the
determination of the PBH formation threshold, a fundamental quantity in PBH
physics, in the context of a time-dependent equation-of-state parameter.
Afterwards, we briefly present the theory of inflationary perturbations, which
is the theoretical framework within which PBHs are studied in this thesis.
Then, in the second part of the thesis, we review the core of the research
conducted within my PhD, in which aspects of the early universe and the
gravitational wave physics are combined with the physics of PBHs. Moreover,
aspects of the PBH gravitational collapse process are studied in the presence
of anisotropies. Specifically, we study PBHs produced from the preheating
instability in the context of single-field inflation. Interestingly, we find
that PBHs produced during preheating can potentially dominate the universe's
content and drive reheating through their evaporation. Then, we focus on the
scalar induced second-order stochastic gravitational wave background (SGWB)
induced from Poisson energy density fluctuations of ultralight PBHs. By taking
then into account gravitational wave backreaction effects we set
model-independent constraints on the initial abundance of ultralight PBHs as a
function of their mass. Afterwards, we study in a covariant way the anisotropic
spherical gravitational collapse of PBHs during a radiation-dominated era in
which one can compute the PBH formation threshold as a function of the
anisotropy. Finally, we summarize our research results by discussing future
prospects opened up as a result of the research work conducted within this
thesis.


title: Bilateral series and Ramanujan's radial limits

abstract:
  Ramanujan's last letter to Hardy explored the asymptotic properties of
modular forms, as well as those of certain interesting $q$-series which he
called \emph{mock theta functions}. For his mock theta function $f(q)$, he
claimed that as $q$ approaches an even order $2k$ root of unity $\zeta$,
\[\lim_{q\to \zeta} \big(f(q) - (-1)^k (1-q)(1-q^3)(1-q^5)\cdots (1-2q + 2q^4 -
\cdots)\big) = O(1),\] and hinted at the existence of similar statements for
his other mock theta functions. Recent work of Folsom-Ono-Rhoades provides a
closed formula for the implied constant in this radial limit of $f(q)$. Here,
by different methods, we prove similar results for all of Ramanujan's 5th order
mock theta functions. Namely, we show that each 5th order mock theta function
may be related to a modular bilateral series, and exploit this connection to
obtain our results. We further explore other mock theta functions to which this
method can be applied.


title:
Pretraining without Wordpieces: Learning Over a Vocabulary of Millions
  of Words

abstract:
  The standard BERT adopts subword-based tokenization, which may break a word
into two or more wordpieces (e.g., converting "lossless" to "loss" and "less").
This will bring inconvenience in following situations: (1) what is the best way
to obtain the contextual vector of a word that is divided into multiple
wordpieces? (2) how to predict a word via cloze test without knowing the number
of wordpieces in advance? In this work, we explore the possibility of
developing BERT-style pretrained model over a vocabulary of words instead of
wordpieces. We call such word-level BERT model as WordBERT. We train models
with different vocabulary sizes, initialization configurations and languages.
Results show that, compared to standard wordpiece-based BERT, WordBERT makes
significant improvements on cloze test and machine reading comprehension. On
many other natural language understanding tasks, including POS tagging,
chunking and NER, WordBERT consistently performs better than BERT. Model
analysis indicates that the major advantage of WordBERT over BERT lies in the
understanding for low-frequency words and rare words. Furthermore, since the
pipeline is language-independent, we train WordBERT for Chinese language and
obtain significant gains on five natural language understanding datasets.
Lastly, the analyse on inference speed illustrates WordBERT has comparable time
cost to BERT in natural language understanding tasks.


title:
Flexural deformations and collapse of bilayer two-dimensional crystals
  by interlayer exciton

abstract:
  We develop a consistent theory of the interlayer exciton-polaron formed in
atomically-thin bilayers. Coulomb attraction between an electron and a hole
situated in the different layers results in their flexural deformation and
provides an efficient mechanism of the exciton coupling with flexural phonons.
We study the effect of layers tension on the polaron binding energy and
effective mass leading to suppression of polaron formation by the tension both
in the weak and strong coupling regimes. We also consider the role of the
nonlinearity related to the interaction between the out- and in-plane lattice
displacements and obtain the criterion of the layer sticking, where the exciton
collapses, due to the Coulomb attraction between the charge carriers.


title:
A note on the minimal tensor product and the C*-envelope of operator
  systems

abstract:
  In this article, we show that the $C^*$-envelope of the minimal tensor
product of two operator systems is isomorphic to the minimal tensor product of
their $C^*$-envelopes. We do this by identifying the Silov boundary ideal of
the minimal tensor product of two operator systems. Finally, as an application
of this result, we show that the propagation number of the minimal tensor
product of operator systems is the maximum of the propagation numbers of the
factors.