title: BMO with respect to Banach function spaces

abstract:
  For every cube $Q \subset \mathbb{R}^n$ we let $X_Q$ be a quasi-Banach
function space over $Q$ such that $\|\chi_Q\|_{X_Q} \simeq 1$, and for $X=
\{X_Q\}$ define \begin{align*} \|f\|_{\mathrm{BMO}_X} &:=\sup_Q
\,\|f-{\textstyle\frac{1}{|Q|}\int_Qf} \|_{X_Q},\\ \|f\|_{\mathrm{BMO}_X^*}
&:=\sup_Q \,\inf_c\, \|f-c\|_{X_Q}. \end{align*} We study necessary and
sufficient conditions on $X$ such that $$ \mathrm{BMO} = \mathrm{BMO}_X =
\mathrm{BMO}_{X}^*. $$ In particular, we give a full characterization of the
embedding $\mathrm{BMO} \hookrightarrow \mathrm{BMO}_X$ in terms of so-called
sparse collections of cubes and we give easily checkable and rather weak
sufficient conditions for the embedding $\mathrm{BMO}_X^* \hookrightarrow
\mathrm{BMO}$. Our main theorems recover and improve all previously known
results in this area.


title: Partitioning into degenerate graphs in linear time

abstract:
  Let $G$ be a connected graph with maximum degree $\Delta \geq 3$ distinct
from $K_{\Delta + 1}$. Generalizing Brooks' Theorem, Borodin, Kostochka and
Toft proved that if $p_1, \dots, p_s$ are non-negative integers such that $p_1
+ \dots + p_s \geq \Delta - s$, then $G$ admits a vertex partition into parts
$A_1, \dots, A_s$ such that, for $1 \leq i \leq s$, $G[A_i]$ is
$p_i$-degenerate. Here we show that such a partition can be performed in linear
time. This generalizes previous results that treated subcases of a conjecture
of Abu-Khzam, Feghali and Heggernes~\cite{abu2020partitioning}, which our
result settles in full.


title: Socio-Political Feedback on the Path to Net Zero

abstract:
  Anthropogenic emissions of CO2 must soon approach net-zero to stabilize the
global mean temperature. Although several international agreements have
advocated for coordinated climate actions, their implementation has remained
below expectations. One of the main challenges of international cooperation is
the different degrees of socio-political acceptance of decarbonization. Here we
interrogate a minimalistic model of the coupled natural-human system
representing the impact of such socio-political acceptance on clean energy
investments and the path to net-zero emissions. We show that incentives and
carbon pricing are essential tools to achieve net-zero before critical CO2
concentrations are reached, and deep international coordination is necessary
for a rapid and effective transition. Although a perfect coordination scenario
remains unlikely, as investments in clean energy are ultimately limited by
myopic economic strategies and a policy system that promotes free-riding, more
realistic decentralized cooperation with partial efforts from each actor could
still lead to significant emissions cuts.


title:
Driving rapidly while remaining in control: classical shortcuts from
  Hamiltonian to stochastic dynamics

abstract:
  Stochastic thermodynamics lays down a broad framework to revisit the
venerable concepts of heat, work and entropy production for individual
stochastic trajectories of mesoscopic systems. Remarkably, this approach,
relying on stochastic equations of motion, introduces time into the description
of thermodynamic processes -- which opens the way to fine control them. As a
result, the field of finite-time thermodynamics of mesoscopic systems has
blossomed. In this article, after introducing a few concepts of control for
isolated mechanical systems evolving according to deterministic equations of
motion, we review the different strategies that have been developed to realize
finite-time state-to-state transformations in both over and underdamped
regimes, by the proper design of time-dependent control parameters/driving. The
systems under study are stochastic, epitomized by a Brownian object immersed in
a fluid; they thus strongly coupled to their environment playing the role of a
reservoir. Interestingly, a few of those methods (inverse engineering,
counterdiabatic driving, fast-forward) are directly inspired by their
counterpart in quantum control. The review also analyzes the control through
reservoir engineering. Besides the reachability of a given target state from a
known initial state, the question of the optimal path is discussed. Optimality
is here defined with respect to a cost function, a subject intimately related
to the field of information thermodynamics and the question of speed limit.
Another natural extension discussed deals with the connection between arbitrary
states or non-equilibrium steady states. This field of control in stochastic
thermodynamics enjoys a wealth of applications, ranging from optimal mesoscopic
heat engines to population control in biological systems.


title:
Validating galaxy clustering models with Fixed & Paired and Matched-ICs
  simulations: application to Primordial Non-Gaussianities

abstract:
  The Fix and Pair techniques were designed to generate simulations with
reduced variance in the 2-point statistics by modifying the Initial Conditions
(ICs). In this paper we show that this technique is also valid when the initial
conditions have local Primordial non-Gaussianities (PNG), parametrised by
$f_{\rm NL}$, without biasing the 2-point statistics but reducing significantly
their variance. We show how to quantitatively use these techniques to test the
accuracy of galaxy/halo clustering models down to a much reduced uncertainty
and we apply them to test the standard model for halo clustering in the
presence of PNG. Additionally, we show that by Matching the stochastic part of
the ICs for two different cosmologies (Gaussian and non-Gaussian) we obtain a
large correlation between the (2-point) statistics that can explicitly be used
to further reduce the uncertainty of the model testing. For our reference
analysis ($f_{\rm NL}=100$, $V=1 [h^{-1}{\rm Gpc}]^3$, $n= 2.5\times
10^{-4}[h^{-1}{\rm Mpc}]^{-3}$, $b=2.32$), we obtain an uncertainty of
$\sigma(f_{\rm NL})=60$ with a standard simulation, whereas using Fixed
[Fixed-Paired] initial conditions it reduces to $\sigma(f_{\rm NL})=12$
[$\sigma(f_{\rm NL})=12$]. When also Matching the ICs we obtain $\sigma (f_{\rm
NL})=18$ for the standard case, and $\sigma (f_{\rm NL})=8$ [$\sigma (f_{\rm
NL})=7$] for Fixed [Fixed-Paired]. The combination of the Fix, Pair and Match
techniques can be used in the context of PNG to create simulations with an
effective volume incremented by a factor $\sim 70$ at given computational
resources.


title: WikiMulti: a Corpus for Cross-Lingual Summarization

abstract:
  Cross-lingual summarization (CLS) is the task to produce a summary in one
particular language for a source document in a different language. We introduce
WikiMulti - a new dataset for cross-lingual summarization based on Wikipedia
articles in 15 languages. As a set of baselines for further studies, we
evaluate the performance of existing cross-lingual abstractive summarization
methods on our dataset. We make our dataset publicly available here:
https://github.com/tikhonovpavel/wikimulti


title: Excitonic effects in graphene-like C$_3$N

abstract:
  Monolayer C$_3$N is an emerging two-dimensional indirect band gap
semiconductor with interesting mechanical, thermal, and electronic properties.
In this work we present a description of C$_3$N electronic and dielectric
properties, focusing on the so-called momentum-resolved exciton band structure.
Excitation energies and oscillator strengths are computed in order to
characterize bright and dark states, and discussed also with respect to the
crystal symmetry. Activation of excitonic states is observed for finite
transferred momenta: Indeed, we find an active indirect exciton at $\sim$ 0.9
eV, significantly lower than the direct optical gap of 1.96 eV, with excitonic
binding energies in the range 0.6-0.9 eV for the lowest states. As for other 2D
materials, we find a quasi-linear excitonic dispersion close to $\Gamma$, which
however shows a downward convexity related to the indirect band gap of C$_3$N
as well as to the dark nature of the involved excitons.


title:
Approximation Algorithms for Interdiction Problem with Packing
  Constraints

abstract:
  We study a bilevel optimization problem which is a zero-sum Stackelberg game.
In this problem, there are two players, a leader and a follower, who pick items
from a common set. Both the leader and the follower have their own
(multi-dimensional) budgets, respectively. Each item is associated with a
profit, which is the same to the leader and the follower, and will consume the
leader's (follower's) budget if it is selected by the leader (follower). The
leader and the follower will select items in a sequential way: First, the
leader selects items within the leader's budget. Then the follower selects
items from the remaining items within the follower's budget. The goal of the
leader is to minimize the maximum profit that the follower can obtain. Let
$s_A$ and $s_B$ be the dimension of the leader's and follower's budget,
respectively. A special case of our problem is the bilevel knapsack problem
studied by Caprara et al. [SIAM Journal on Optimization, 2014], where
$s_A=s_B=1$. We consider the general problem and obtain an
$(s_B+\epsilon)$-approximation algorithm when $s_A$ and $s_B$ are both
constant. In particular, if $s_B=1$, our algorithm implies a PTAS for the
bilevel knapsack problem, which is the first O(1)-approximation algorithm. We
also complement our result by showing that there does not exist any
$(4/3-\epsilon)$-approximation algorithm even if $s_A=1$ and $s_B=2$. We also
consider a variant of our problem with resource augmentation when $s_A$ and
$s_B$ are both part of the input. We obtain an O(1)-approximation algorithm
with O(1)-resource augmentation, that is, we give an algorithm that returns a
solution which exceeds the given leader's budget by O(1) times, and the
objective value achieved by the solution is O(1) times the optimal objective
value that respects the leader's budget.


title: Debt-Financed Collateral and Stability Risks in the DeFi Ecosystem

abstract:
  The rise of Decentralized Finance ("DeFi") on the Ethereum blockchain has
enabled the creation of lending platforms, which serve as marketplaces to lend
and borrow digital currencies. We first categorize the activity of lending
platforms within a standard regulatory framework. We then employ a novel
grouping and classification algorithm to calculate the percentage of fund flows
into DeFi lending platforms that can be attributed to debt created elsewhere in
the system ("debt-financed collateral"). Based on our results, we conclude that
the wide-spread use of stablecoins as debt-financed collateral increases
financial stability risks in the DeFi ecosystem.


title:
Coherent Atomic Orbital Polarization Probes the Geometric Phase in
  Photodissociation of Polyatomic Molecules

abstract:
  Quantum interference between multiple pathways in molecular photodissociation
often results in angular momentum polarization of atomic products and this can
give deep insight into fundamental physical processes. For dissociation of
diatomic molecules the resulting orbital polarization is fully understood and
consistent with quantum mechanical theory. For polyatomic molecules, however,
coherent photofragment orbital polarization is frequently observed but so far
has eluded theoretical explanation, and physical insight is lacking. Here we
present a model of these effects for ozone photodissociation that reveals the
importance of a novel manifestation of the geometric phase. We show this
geometric phase effect permits the existence of coherent polarization in cases
where it would otherwise vanish, and cancels it in some cases where it might
otherwise exist. The model accounts for measurements in ozone that have
hitherto defied explanation, and represents a step toward a deeper
understanding of coherent electronic excitation in polyatomic molecules and a
new role of the geometric phase.


title:
Power Enhancement and Phase Transitions for Global Testing of the Mixed
  Membership Stochastic Block Model

abstract:
  The mixed-membership stochastic block model (MMSBM) is a common model for
social networks. Given an $n$-node symmetric network generated from a
$K$-community MMSBM, we would like to test $K=1$ versus $K>1$. We first study
the degree-based $\chi^2$ test and the orthodox Signed Quadrilateral (oSQ)
test. These two statistics estimate an order-2 polynomial and an order-4
polynomial of a "signal" matrix, respectively. We derive the asymptotic null
distribution and power for both tests. However, for each test, there exists a
parameter regime where its power is unsatisfactory. It motivates us to propose
a power enhancement (PE) test to combine the strengths of both tests. We show
that the PE test has a tractable null distribution and improves the power of
both tests. To assess the optimality of PE, we consider a randomized setting,
where the $n$ membership vectors are independently drawn from a distribution on
the standard simplex. We show that the success of global testing is governed by
a quantity $\beta_n(K,P,h)$, which depends on the community structure matrix
$P$ and the mean vector $h$ of memberships. For each given $(K, P, h)$, a test
is called $\textit{ optimal}$ if it distinguishes two hypotheses when
$\beta_n(K, P,h)\to\infty$. A test is called $\textit{optimally adaptive}$ if
it is optimal for all $(K, P, h)$. We show that the PE test is optimally
adaptive, while many existing tests are only optimal for some particular $(K,
P, h)$, hence, not optimally adaptive.


title:
Constraints on the extragalactic magnetic field strength from blazar
  spectra based on 145 months of Fermi-LAT observations

abstract:
  Properties of the extragalactic magnetic field (EGMF) outside of clusters and
filaments of the large-scale structure are essentially unknown. The EGMF could
be probed with $\gamma$-ray observations of distant (redshift $z > 0.1$)
blazars. TeV $\gamma$ rays from these sources are strongly absorbed on
extragalactic background light photons; secondary electrons and positrons
produce cascade $\gamma$ rays with the observable flux dependent on EGMF
parameters. We put constraints on the EGMF strength using 145 months of
Fermi-LAT observations of the blazars 1ES 1218+304, 1ES 1101-232, and 1ES
0347-121, and imaging atmospheric Cherenkov telescope observations of the same
sources. We perform a series of full direct Monte Carlo simulations of
intergalactic electromagnetic cascades with the ELMAG 3.01 code and construct a
model of the observable spectra inside the point spread functions of the
observing instruments for a range of EGMF strengths. We compare the observed
spectra with the models for various values of the EGMF strength $B$ and
calculate the exclusion statistical significance for every value of $B$. We
find that the values of the EGMF strength $B \le 10^{-17}$ G are excluded at a
high level of the statistical significance $Z > 4 \sigma$ for all the four
options of the intrinsic spectral shape considered (power-law, power-law with
exponential cutoff, log-parabola, log-parabola with exponential cutoff). The
value of $B = 10^{-16}$ G is not excluded; it is still a viable option of the
EGMF strength. These results were obtained for the case of steady sources.


title: Substitutions to Lebesgue Type Space-Filling Curves

abstract:
  Lebesgue curve is a space-filling curve that fills the unit square through
linear interpolation. We propose an algorithm to generate a space-filling curve
from any given substitution (of any dimension) satisfying a mild condition. The
constructed curves are defined by a linear interpolation method, and typically
have geometric structures akin to the Lebesgue curve.


title: Ultralimits, Amenable actions and Entropy

abstract:
  In this paper we extend and refine the results and the tools of Sayag-Shalom
to study the entropy in amenable actions of discrete countable groups. That is,
we will show that the minimal value of Furstenberg entropy (along all measures,
not restricting to stationary ones) for any amenable action is the same as for
the action of the group on itself. Using the boundary amenability result of S.
Adams, this allows us to compute the minimal value of the entropy over all the
measure classes in the boundary of the free group. Similar results are proved
for the action of a hyperbolic group on its Gromov boundary. Our main tools are
an ultralimit realization of the Poisson boundary of a matrix-valued random
walk on the group, as well as a structure theorem \`a la Furstenberg-Glasner.


title:
Dipoles in blackbody radiation: Momentum fluctuations, decoherence, and
  drag force

abstract:
  A general expression is derived for the momentum diffusion constant of a
small polarizable particle in blackbody radiation, and is shown to be closely
related to the long-wavelength collisional decoherence rate for such a particle
in a thermal environment. We show how this diffusion constant appears in the
steady-state photon emission rate of two dipoles induced by blackbody
radiation. We consider in addition the Einstein--Hopf drag force on a small
polarizable particle moving in a blackbody field, and derive its fully
relativistic form from the Lorentz transformation of forces.


title: Quantum Error Detection Without Using Ancilla Qubits

abstract:
  In this paper, we describe and experimentally demonstrate an error detection
scheme that does not employ ancilla qubits or mid-circuit measurements. This is
achieved by expanding the Hilbert space where a single logical qubit is encoded
using several physical qubits. For example, one possible two qubit encoding
identifies $|0\rangle_L=|01\rangle$ and $|1\rangle_L=|10\rangle$. If during the
final measurement a $|11\rangle$ or $|00\rangle$ is observed an error is
declared and the run is not included in subsequent analysis. We provide
codewords for a simple bit-flip encoding, a way to encode the states, a way to
implement logical $U_3$ and logical $C_x$ gates, and a description of which
errors can be detected. We then run Greenberger-Horne-Zeilinger circuits on the
transmon based IBM quantum computers, with an input space of $N\in\{2,3,4,5\}$
logical qubits and $Q\in\{1,2,3,4,5\}$ physical qubits per logical qubit. The
results are compared relative to $Q=1$ with and without error detection and we
find a significant improvement for $Q\in\{2,3,4\}$.


title: Time Series Forecasting (TSF) Using Various Deep Learning Models

abstract:
  Time Series Forecasting (TSF) is used to predict the target variables at a
future time point based on the learning from previous time points. To keep the
problem tractable, learning methods use data from a fixed length window in the
past as an explicit input. In this paper, we study how the performance of
predictive models change as a function of different look-back window sizes and
different amounts of time to predict into the future. We also consider the
performance of the recent attention-based Transformer models, which has had
good success in the image processing and natural language processing domains.
In all, we compare four different deep learning methods (RNN, LSTM, GRU, and
Transformer) along with a baseline method. The dataset (hourly) we used is the
Beijing Air Quality Dataset from the UCI website, which includes a multivariate
time series of many factors measured on an hourly basis for a period of 5 years
(2010-14). For each model, we also report on the relationship between the
performance and the look-back window sizes and the number of predicted time
points into the future. Our experiments suggest that Transformer models have
the best performance with the lowest Mean Average Errors (MAE = 14.599, 23.273)
and Root Mean Square Errors (RSME = 23.573, 38.131) for most of our single-step
and multi-steps predictions. The best size for the look-back window to predict
1 hour into the future appears to be one day, while 2 or 4 days perform the
best to predict 3 hours into the future.


title:
Human-Robot Shared Control for Surgical Robot Based on Context-Aware
  Sim-to-Real Adaptation

abstract:
  Human-robot shared control, which integrates the advantages of both humans
and robots, is an effective approach to facilitate efficient surgical
operation. Learning from demonstration (LfD) techniques can be used to automate
some of the surgical subtasks for the construction of the shared control
mechanism. However, a sufficient amount of data is required for the robot to
learn the manoeuvres. Using a surgical simulator to collect data is a less
resource-demanding approach. With sim-to-real adaptation, the manoeuvres
learned from a simulator can be transferred to a physical robot. To this end,
we propose a sim-to-real adaptation method to construct a human-robot shared
control framework for robotic surgery.
  In this paper, a desired trajectory is generated from a simulator using LfD
method, while dynamic motion primitives (DMP) is used to transfer the desired
trajectory from the simulator to the physical robotic platform. Moreover, a
role adaptation mechanism is developed such that the robot can adjust its role
according to the surgical operation contexts predicted by a neural network
model. The effectiveness of the proposed framework is validated on the da Vinci
Research Kit (dVRK). Results of the user studies indicated that with the
adaptive human-robot shared control framework, the path length of the remote
controller, the total clutching number and the task completion time can be
reduced significantly. The proposed method outperformed the traditional manual
control via teleoperation.


title:
Exploring the Role of Task Transferability in Large-Scale Multi-Task
  Learning

abstract:
  Recent work has found that multi-task training with a large number of diverse
tasks can uniformly improve downstream performance on unseen target tasks. In
contrast, literature on task transferability has established that the choice of
intermediate tasks can heavily affect downstream task performance. In this
work, we aim to disentangle the effect of scale and relatedness of tasks in
multi-task representation learning. We find that, on average, increasing the
scale of multi-task learning, in terms of the number of tasks, indeed results
in better learned representations than smaller multi-task setups. However, if
the target tasks are known ahead of time, then training on a smaller set of
related tasks is competitive to the large-scale multi-task training at a
reduced computational cost.


title: New features in MathPartner 2021

abstract:
  We introduce new features in the MathPartner service that have recently
become available to users. We highlight the functions for calculating both
arithmetic-geometric mean and geometric-harmonic mean. They allow calculating
complete elliptic integrals of the first kind. They are useful for solving many
physics problems, for example, one can calculate the period of a simple
pendulum. Next, one can calculate the modified arithmetic-geometric mean
proposed by Semjon Adlaj. Consequently, one can calculate the complete elliptic
integrals of the second kind as well as the circumference of an ellipse.
Furthermore, one can also calculate the Sylvester matrices of the first and the
second kind. Thus, by means of a few strings, one can calculate the resultant
of two polynomials as well as the discriminant of a binary form. Some new
matrix functions are also added. So, today the list of matrix functions
includes the transpose, adjugate, conjugate, inverse, generalized inverse, and
pseudo inverse of a matrix, the matrix determinant, the kernel, the echelon
form, the characteristic polynomial, the Bruhat decomposition, the triangular
LSU decomposition, which is an exact block recursive LU decomposition, the QR
block recursive decomposition, and the singular value decomposition. In
addition, two block-recursive functions have been implemented for calculating
the Cholesky decomposition of symmetric positive-definite matrices: one
function for sparse matrices with the standard multiplication algorithm and
another function for dense matrices with multiplication according to the
Winograd--Strassen algorithm. The linear programming problems can be solved
too. So, the MathPartner service has become better and handy. It is freely
available at http://mathpar.ukma.edu.ua/ as well as at http://mathpar.com.


title: NFS: A Hand Gesture Recognition Based Game Using MediaPipe and PyGame

abstract:
  This paper represents a game which interacts with humans via hand gesture
movement. Nowadays, apps like this seem rare, and there seems to be a window
opening for this kind of application to be more prevalent and useful in the
near future. This application is based on hand gesture movement instead of
being dependent on a keyboard and mouse. The main issue was to figure out how
to utilize machine learning to make this application work as it should be.
First, two games were selected one with a traditional controller and another
with hand gesture method. Then these two games based on the difficulty to use,
fun elements, gameplay, and replayability were compared. Though the difficulty
increases but the other three aspects improve significantly. After going
through all of that a conclusion can be drawn that people are more likely to
play a simple hand gesture-based game.


title:
Privacy-Preserving Cloud Computing: Ecosystem, Life Cycle, Layered
  Architecture and Future Roadmap

abstract:
  Privacy-Preserving Cloud Computing is an emerging technology with many
applications in various fields. Cloud computing is important because it allows
for scalability, adaptability, and improved security. Likewise, privacy in
cloud computing is important because it ensures that the integrity of data
stored on the cloud maintains intact. This survey paper on privacy-preserving
cloud computing can help pave the way for future research in related areas.
This paper helps to identify existing trends by establishing a layered
architecture along with a life cycle and an ecosystem for privacy-preserving
cloud systems in addition to identifying the existing trends in research on
this area.


title: Configuration mixing in particle decay and reaction

abstract:
  Background: Decay constants of unstable nuclei and particles are quantum
constants. Recent controversy on the existence (versus non-existence) of
variability in the observation of decay rate can be settled by considering
mixing in decay configuration. Purpose: Variability in decay rate was
investigated based on the available information of beta decay rate data, solar
neutrino flux, and energy distribution. Method: Full systematic analysis of the
oscillatory behavior was carried out. Based on the zero threshold energy for
neutrino absorption in beta emitters, a model for configuration mixing between
two distinct beta disintegration modes $\beta^\nu$-disintegration (electron
from neutrino interaction) and the $\beta^-$-disintegration (electron from
natural decay) was proposed. Results: The phenomenon of variability in beta
decay rate was related to the possible exothermic neutrino absorption by
unstable nuclei which, in principle, should include the whole range of flux
energies involving flux with energy below the $^{71}$Ga threshold at 0.23 MeV.
These two disintegration modes occur independently and model for their apparent
mixing rate was proposed. Conclusions: The configuration mixing between the two
modes causes depletion of radioactive nuclei which is subject to change with
seasonal solar neutrino variability. Ability to detect this variability was
found to be dependent on the Q-value of the $\beta^\nu$ disintegration and
detection instrument setup. Value of neutrino cross section weighted by the
ratio between $\beta^\nu$ and $\beta^-$ detection efficiencies was found to be
in the range $10^{-44}$ to $10^{-36}$ cm$^{2}$. For experiments that uses the
end point to determine the neutrino mass, interference due to mixing should be
taken into account.


title: Can domain adaptation make object recognition work for everyone?

abstract:
  Despite the rapid progress in deep visual recognition, modern computer vision
datasets significantly overrepresent the developed world and models trained on
such datasets underperform on images from unseen geographies. We investigate
the effectiveness of unsupervised domain adaptation (UDA) of such models across
geographies at closing this performance gap. To do so, we first curate two
shifts from existing datasets to study the Geographical DA problem, and
discover new challenges beyond data distribution shift: context shift, wherein
object surroundings may change significantly across geographies, and
subpopulation shift, wherein the intra-category distributions may shift. We
demonstrate the inefficacy of standard DA methods at Geographical DA,
highlighting the need for specialized geographical adaptation solutions to
address the challenge of making object recognition work for everyone.


title:
Gelation, Clustering and Crowding in the Electrical Double Layer of
  Ionic Liquids

abstract:
  Understanding the bulk and interfacial properties of super-concentrated
electrolytes, such as ionic liquids (ILs), has attracted significant attention
lately for their promising applications in supercapacitors and batteries.
Recently, McEldrew \textit{et al.} developed a theory for reversible ion
associations in bulk ILs, which accounted for the formation of all possible
Cayley tree clusters and a percolating ionic network (gel). Here we adopt and
develop this approach to understand the associations of ILs in the electrical
double layer at electrified interfaces. With increasing charge of the
electrode, the theory predicts a transition from a regime dominated by a gelled
or clustered state to a regime dominated by free, crowded ions. This transition
from gelation to crowding is conceptually similar to the overscreening to
crowding transition.


title:
On the randomness and correlation in the trajectories of alpha particle
  emitted from ${}^{241}$Am: Statistical inference based on information entropy

abstract:
  Most particle detectors are based on the hypothesis that particles are
emitted randomly upon nuclear decay. In the present work, we tested the
hypothesis of the existence of correlation in the random trajectories of alpha
particles emitted from ${}^{241}$Am source and the null hypothesis of random
trajectories. The trajectories were clued through the registration of track in
a solid-state nuclear track detector. The experimental parameters were
optimized to identify the possible sources of correlation in the track
registration and the detector conditions upon exposure and etching to avoid
misleading results. The optimization included authentication of linearity in
registration efficiency with exposure time to prevent coalescence of registered
tracks. The statistical inference processes were based upon adaptive quadrates
analysis of the spatial data, and entropy and divergence analysis of the
quadrate data together with the null hypothesis of Poisson distribution of
random trajectories. The clustering and dispersion analysis were performed with
central deviation tendency, empirical K-function, radial distribution analysis,
and proximity Analysis. Results showed a pattern of gained information within
the registered tracks that may be attributed to being a consequence of the
structure of the source.


title: An affine Weyl group characterization of polynomial Heisenberg algebras

abstract:
  We study deformations of the harmonic oscillator algebra known as polynomial
Heisenberg algebras (PHAs), and establish a connection between them and
extended affine Weyl groups of type $A^{(1)}_m$, where $m$ is the degree of the
PHA. To establish this connection, we employ supersymmetric quantum mechanics
to first connect a polynomial Heisenberg algebra to symmetric systems of
differential equations. This connection has been previously used to relate
quantum systems to non-linear differential equations; most notably, the fourth
and fifth Painlev\'e equations. Once this is done, we use previous studies on
the B\"acklund transformations of Painlev\'e equations and generalizations of
their symmetric forms characterized by extended affine Weyl groups. This work
contributes to better understand quantum systems and the algebraic structures
characterizing them.


title:
Near-real-time diagnosis of electron optical phase aberrations in
  scanning transmission electron microscopy using an artificial neural network

abstract:
  The key to optimizing spatial resolution in a state-of-the-art scanning
transmission electron microscope is the ability to precisely measure and
correct for electron optical aberrations of the probe-forming lenses. Several
diagnostic methods for aberration measurement and correction with maximum
precision and accuracy have been proposed, albeit often at the cost of
relatively long acquisition times. Here, we illustrate how artificial
intelligence can be used to provide near-real-time diagnosis of aberrations
from individual Ronchigrams. The demonstrated speed of aberration measurement
is important as microscope conditions can change rapidly, as well as for the
operation of MEMS-based hardware correction elements that have less intrinsic
stability than conventional electromagnetic lenses.


title: U-NO: U-shaped Neural Operators

abstract:
  Neural operators generalize classical neural networks to maps between
infinite-dimensional spaces, e.g. function spaces. Prior works on neural
operators proposed a series of novel architectures to learn such maps and
demonstrated unprecedented success in solving partial differential equations
(PDEs). In this paper, we propose U-shaped Neural Operators U-NO, an
architecture that allows for deeper neural operators compared to prior works.
U-NOs exploit the problems structures in function predictions, demonstrate fast
training, data efficiency, and robustness w.r.t hyperparameters choices. We
study the performance of U-NO on PDE benchmarks, namely, Darcy's flow law and
the Navier-Stokes equations. We show that U-NO results in average of 14% and
38% prediction improvement on the Darcy's flow and Navier-Stokes equations,
respectively, over the state of art.


title:
Quantitatively linking morphology and optical response of individual
  silver nanohedra

abstract:
  The optical response of metal nanoparticles is governed by plasmonic
resonances, which are dictated by the particle morphology. A thorough
understanding of the link between morphology and optical response requires
quantitatively measuring optical and structural properties of the same
particle. Here we present such a study, correlating electron tomography and
optical micro-spectroscopy. The optical measurements determine the scattering
and absorption cross-section spectra in absolute units, and electron tomography
determines the 3D morphology. Numerical simulations of the spectra for the
individual particle geometry, and the specific optical setup used, allow for a
quantitative comparison including the cross-section magnitude. Silver
nanoparticles produced by photochemically driven colloidal synthesis, including
decahedra, tetrahedra and bi-tetrahedra are investigated. A mismatch of
measured and simulated spectra is found when assuming pure silver particles,
which is resolved by the presence of a few atomic layers of tarnish (Ag2S) on
the surface, not evident in electron tomography. The presented method tightens
the link between particle morphology and optical response, supporting the
predictive design of plasmonic nanomaterials


title:
L-shell X-ray conversion yields for laser-irradiated tin and silver
  foils

abstract:
  We have employed the VULCAN laser facility to generate a laser plasma X-ray
source for use in photoionisation experiments. A nanosecond laser pulse with an
intensity of order ${10}^{15}$ W{cm}$^{-2}$ was used to irradiate thin Ag or Sn
foil targets coated onto a parylene substrate, and the L-shell emission in the
$3.3-4.4$ keV range was recorded for both the laser-irradiated and
non-irradiated sides. Both the experimental and simulation results show higher
laser to X-ray conversion yields for Ag compared with Sn, with our simulations
indicating yields approximately a factor of two higher than found in the
experiments. Although detailed angular data were not available experimentally,
the simulations indicate that the emission is quite isotropic on the
laser-irradiated side, but shows close to a cosine variation on the
non-irradiated side of the target as seen experimentally in previous work.


title: Connectedness of a space of branched coverings with a periodic cycle

abstract:
  We prove the connectedness of the following locus: the space of degree-$d$
branched self-coverings of $S^2$ with two critical points of order $d$, one of
which is $n$-periodic.


title:
Data Debugging with Shapley Importance over End-to-End Machine Learning
  Pipelines

abstract:
  Developing modern machine learning (ML) applications is data-centric, of
which one fundamental challenge is to understand the influence of data quality
to ML training -- "Which training examples are 'guilty' in making the trained
ML model predictions inaccurate or unfair?" Modeling data influence for ML
training has attracted intensive interest over the last decade, and one popular
framework is to compute the Shapley value of each training example with respect
to utilities such as validation accuracy and fairness of the trained ML model.
Unfortunately, despite recent intensive interest and research, existing methods
only consider a single ML model "in isolation" and do not consider an
end-to-end ML pipeline that consists of data transformations, feature
extractors, and ML training.
  We present DataScope (ease.ml/datascope), the first system that efficiently
computes Shapley values of training examples over an end-to-end ML pipeline,
and illustrate its applications in data debugging for ML training. To this end,
we first develop a novel algorithmic framework that computes Shapley value over
a specific family of ML pipelines that we call canonical pipelines: a positive
relational algebra query followed by a K-nearest-neighbor (KNN) classifier. We
show that, for many subfamilies of canonical pipelines, computing Shapley value
is in PTIME, contrasting the exponential complexity of computing Shapley value
in general. We then put this to practice -- given an sklearn pipeline, we
approximate it with a canonical pipeline to use as a proxy. We conduct
extensive experiments illustrating different use cases and utilities. Our
results show that DataScope is up to four orders of magnitude faster over
state-of-the-art Monte Carlo-based methods, while being comparably, and often
even more, effective in data debugging.


title: The Geometry of the Centre Symmetry Set of a Planar Curve

abstract:
  The Centre Symmetry Set of a planar curve $M$ is the envelope of affine
chords of $M$, i.e. the lines joining points on $M$ with parallel tangent
lines. In this paper we study global geometrical properties of this set
including the number of singularities and the number of asymptotes.


title:
Towards Bundle Adjustment for Satellite Imaging via Quantum Machine
  Learning

abstract:
  Given is a set of images, where all images show views of the same area at
different points in time and from different viewpoints. The task is the
alignment of all images such that relevant information, e.g., poses, changes,
and terrain, can be extracted from the fused image. In this work, we focus on
quantum methods for keypoint extraction and feature matching, due to the
demanding computational complexity of these sub-tasks. To this end, k-medoids
clustering, kernel density clustering, nearest neighbor search, and kernel
methods are investigated and it is explained how these methods can be
re-formulated for quantum annealers and gate-based quantum computers.
Experimental results obtained on digital quantum emulation hardware, quantum
annealers, and quantum gate computers show that classical systems still deliver
superior results. However, the proposed methods are ready for the current and
upcoming generations of quantum computing devices which have the potential to
outperform classical systems in the near future.


title:
Can Foundation Models Perform Zero-Shot Task Specification For Robot
  Manipulation?

abstract:
  Task specification is at the core of programming autonomous robots. A
low-effort modality for task specification is critical for engagement of
non-expert end-users and ultimate adoption of personalized robot agents. A
widely studied approach to task specification is through goals, using either
compact state vectors or goal images from the same robot scene. The former is
hard to interpret for non-experts and necessitates detailed state estimation
and scene understanding. The latter requires the generation of desired goal
image, which often requires a human to complete the task, defeating the purpose
of having autonomous robots. In this work, we explore alternate and more
general forms of goal specification that are expected to be easier for humans
to specify and use such as images obtained from the internet, hand sketches
that provide a visual description of the desired task, or simple language
descriptions. As a preliminary step towards this, we investigate the
capabilities of large scale pre-trained models (foundation models) for
zero-shot goal specification, and find promising results in a collection of
simulated robot manipulation tasks and real-world datasets.


title:
AZ-whiteness test: a test for uncorrelated noise on spatio-temporal
  graphs

abstract:
  We present the first whiteness test for graphs, i.e., a whiteness test for
multivariate time series associated with the nodes of a dynamic graph. The
statistical test aims at finding serial dependencies among close-in-time
observations, as well as spatial dependencies among neighboring observations
given the underlying graph. The proposed test is a spatio-temporal extension of
traditional tests from the system identification literature and finds
applications in similar, yet more general, application scenarios involving
graph signals. The AZ-test is versatile, allowing the underlying graph to be
dynamic, changing in topology and set of nodes, and weighted, thus accounting
for connections of different strength, as is the case in many application
scenarios like transportation networks and sensor grids. The asymptotic
distribution -- as the number of graph edges or temporal observations increases
-- is known, and does not assume identically distributed data. We validate the
practical value of the test on both synthetic and real-world problems, and show
how the test can be employed to assess the quality of spatio-temporal
forecasting models by analyzing the prediction residuals appended to the graphs
stream.


title:
Renumbering of the Antikythera Mechanism Saros cells, resulting from the
  Saros spiral mechanical apokatastasis

abstract:
  After studying the design geometry of the Antikythera Mechanism Saros spiral,
new critical geometrical/mechanical characteristics of the Back plate design
were detected. The geometrical characteristics related to the symmetry of the
Antikythera Mechanism design, are independent to the present irregular
deformation of the Mechanism parts and were used as calibration points for the
Saros spiral cells positional measurements. The Saros cells numbering was
recalculated using the calibration points position. A correction of minus one
to the currently accepted numbering of the Saros cells was applied. Following
the new numbering, a new proper position for the (displaced) Saros pointer
axis-g, in graphic design environment was calculated. The measurements were
tested on a bronze reconstruction of the Back plate, by the authors. This
research leads to a new important result that the Saros does not start in a
random or arbitrary date but only when a solar eclipse occurs within a month.
Additional results were also calculated regarding the symmetry of the eclipse
events/sequence. The new Saros cell numbering strongly affects the calculations
for the initial starting date of the Saros spiral and the eclipse events scheme
of the Antikythera Mechanism.


title: Evaluating regular path queries under the all-shortest paths semantics

abstract:
  The purpose of this report is to explain how the textbook breadth-first
search algorithm (BFS) can be modified in order to also create a compact
representation of all shortest paths connecting a single source node to all the
nodes reachable from it. From this representation, all these paths can also be
efficiently enumerated. We then apply this algorithm to solve a similar problem
in edge labelled graphs, where paths also have an additional restriction that
their edge labels form a word belonging to a regular language. Namely, we solve
the problem of evaluating regular path queries (RPQs) under the all-shortest
paths semantics.


title:
Use of Multifidelity Training Data and Transfer Learning for Efficient
  Construction of Subsurface Flow Surrogate Models

abstract:
  Data assimilation presents computational challenges because many
high-fidelity models must be simulated. Various deep-learning-based surrogate
modeling techniques have been developed to reduce the simulation costs
associated with these applications. However, to construct data-driven surrogate
models, several thousand high-fidelity simulation runs may be required to
provide training samples, and these computations can make training
prohibitively expensive. To address this issue, in this work we present a
framework where most of the training simulations are performed on coarsened
geomodels. These models are constructed using a flow-based upscaling method.
The framework entails the use of a transfer-learning procedure, incorporated
within an existing recurrent residual U-Net architecture, in which network
training is accomplished in three steps. In the first step. where the bulk of
the training is performed, only low-fidelity simulation results are used. The
second and third steps, in which the output layer is trained and the overall
network is fine-tuned, require a relatively small number of high-fidelity
simulations. Here we use 2500 low-fidelity runs and 200 high-fidelity runs,
which leads to about a 90% reduction in training simulation costs. The method
is applied for two-phase subsurface flow in 3D channelized systems, with flow
driven by wells. The surrogate model trained with multifidelity data is shown
to be nearly as accurate as a reference surrogate trained with only
high-fidelity data in predicting dynamic pressure and saturation fields in new
geomodels. Importantly, the network provides results that are significantly
more accurate than the low-fidelity simulations used for most of the training.
The multifidelity surrogate is also applied for history matching using an
ensemble-based procedure, where accuracy relative to reference results is again
demonstrated.


title:
Musical Stylistic Analysis: A Study of Intervallic Transition Graphs via
  Persistent Homology

abstract:
  Topological data analysis has been recently applied to investigate stylistic
signatures and trends in musical compositions. A useful tool in this area is
Persistent Homology. In this paper, we develop a novel method to represent a
weighted directed graph as a finite metric space and then use persistent
homology to extract useful features. We apply this method to weighted directed
graphs obtained from pitch transitions information of a given musical fragment
and use these techniques to the study of stylistic trends. In particular, we
are interested in using these tools to make quantitative stylistic comparisons.
As a first illustration, we analyze a selection of string quartets by Haydn,
Mozart and Beethoven and discuss possible implications of our results in terms
of different approaches by these composers to stylistic exploration and
variety. We observe that Haydn is stylistically the most conservative, followed
by Mozart, while Beethoven is the most innovative, expanding and modifying the
string quartet as a musical form. Finally we also compare the variability of
different genres, namely minuets, allegros, prestos and adagios, by a given
composer and conclude that the minuet is the most stable form of the string
quartet movements.


title: A diploid population model for copy number variation of genetic elements

abstract:
  We study the following model for a diploid population of constant size $N$:
Every individual carries a random number of (genetic) elements. Upon a
reproduction event (which occurs at rate 1 per pair of individuals), each of
the two parents inherit each element with probability $\tfrac 12$ to the
offspring. We study convergence of $X^N = (X_0^N, X_1^N,...)$, where $X_k^N$ is
the frequency of individuals carrying $k$ elements, as \mbox{$N\to\infty$}. We
find convergence (in some weak sense) to $X = (X_t)_{t\geq 0}$, where $X_t =
\text{Poi}(Z_t)$ and $Z_t$ evolves according to a critical Feller branching
process. We discuss heuristics explaining this finding and some extensions and
limitations.


title:
Hydrodynamic and kinetic representation of the microscopic dynamics as
  the transitions on the macroscopic scale of description and meaning of the
  self-consistent field approximation in these models

abstract:
  The open problem of derivation of the relativistic Vlasov equation for the
systems of charged particles moving with the velocities up to the speed of
light and creating the electromagnetic field in accordance with the full set of
the Maxwell equations is considered. Moreover, the method of derivation is
firstly illustrated on the nonrelativistic kinetic model. Independent
derivation of the relativistic hydrodynamics is also demonstrated. Key role of
these derivations of the hydrodynamic and kinetic equations includes the
explicit operator of averaging on the physically infinitesimal volume suggested
by L.S. Kuzmenkov.


title: Graph Neural Network based Agent in Google Research Football

abstract:
  Deep neural networks (DNN) can approximate value functions or policies for
reinforcement learning, which makes the reinforcement learning algorithms more
powerful. However, some DNNs, such as convolutional neural networks (CNN),
cannot extract enough information or take too long to obtain enough features
from the inputs under specific circumstances of reinforcement learning. For
example, the input data of Google Research Football, a reinforcement learning
environment which trains agents to play football, is the small map of players'
locations. The information is contained not only in the coordinates of players,
but also in the relationships between different players. CNNs can neither
extract enough information nor take too long to train. To address this issue,
this paper proposes a deep q-learning network (DQN) with a graph neural network
(GNN) as its model. The GNN transforms the input data into a graph which better
represents the football players' locations so that it extracts more information
of the interactions between different players. With two GNNs to approximate its
local and target value functions, this DQN allows players to learn from their
experience by using value functions to see the prospective value of each
intended action. The proposed model demonstrated the power of GNN in the
football game by outperforming other DRL models with significantly fewer steps.


title: Supplementing Missing Visions via Dialog for Scene Graph Generations

abstract:
  Most current AI systems rely on the premise that the input visual data are
sufficient to achieve competitive performance in various computer vision tasks.
However, the classic task setup rarely considers the challenging, yet common
practical situations where the complete visual data may be inaccessible due to
various reasons (e.g., restricted view range and occlusions). To this end, we
investigate a computer vision task setting with incomplete visual input data.
Specifically, we exploit the Scene Graph Generation (SGG) task with various
levels of visual data missingness as input. While insufficient visual input
intuitively leads to performance drop, we propose to supplement the missing
visions via the natural language dialog interactions to better accomplish the
task objective. We design a model-agnostic Supplementary Interactive Dialog
(SI-Dial) framework that can be jointly learned with most existing models,
endowing the current AI systems with the ability of question-answer
interactions in natural language. We demonstrate the feasibility of such a task
setting with missing visual input and the effectiveness of our proposed dialog
module as the supplementary information source through extensive experiments
and analysis, by achieving promising performance improvement over multiple
baselines.


title: Competitive Physics Informed Networks

abstract:
  Physics Informed Neural Networks (PINNs) solve partial differential equations
(PDEs) by representing them as neural networks. The original PINN
implementation does not provide high accuracy, typically attaining about
$0.1\%$ relative error. We formulate and test an adversarial approach called
competitive PINNs (CPINNs) to overcome this limitation. CPINNs train a
discriminator that is rewarded for predicting PINN mistakes. The discriminator
and PINN participate in a zero-sum game with the exact PDE solution as an
optimal strategy. This approach avoids the issue of squaring the large
condition numbers of PDE discretizations. Numerical experiments show that a
CPINN trained with competitive gradient descent can achieve errors two orders
of magnitude smaller than that of a PINN trained with Adam or stochastic
gradient descent.


title:
Critical Dynamics of the Antiferromagnetic $O(3)$ Nonlinear Sigma Model
  with Conserved Magnetization

abstract:
  We study the near-equilibrium critical dynamics of the $O(3)$ nonlinear sigma
model describing isotropic antiferromagnets with non-conserved order parameter
reversibly coupled to the conserved total magnetization. To calculate response
and correlation functions, we set up a description in terms of Langevin
stochastic equations of motion, and their corresponding Janssen--De~Dominicis
response functional. We find that in equilibrium, the dynamics is
well-separated from the statics, at least to one-loop order in a perturbative
treatment with respect to the static and dynamical nonlinearities. Since the
static nonlinear sigma model must be analyzed in a dimensional $d = 2 +
\varepsilon$ expansion about its lower critical dimension $d_\textrm{lc} = 2$,
whereas the dynamical mode-coupling terms are governed by the upper critical
dimension $d_c = 4$, a simultaneous perturbative dimensional expansion is not
feasible, and the reversible critical dynamics for this model cannot be
accessed at the static critical renormalization group fixed point. However, in
the coexistence limit addressing the long-wavelength properties of the
low-temperature ordered phase, we can perform an $\epsilon = 4 - d$ expansion
near $d_c$. This yields anomalous scaling features induced by the massless
Goldstone modes, namely sub-diffusive relaxation for the conserved
magnetization density with asymptotic scaling exponent $z_\Gamma = d - 2$ which
may be observable in neutron scattering experiments. Intriguingly, if
initialized near the critical point, the renormalization group flow for the
effective dynamical exponents recovers their universal critical values $z_c = d
/ 2$ in an intermediate crossover region.


title:
Gabor is Enough: Interpretable Deep Denoising with a Gabor Synthesis
  Dictionary Prior

abstract:
  Image processing neural networks, natural and artificial, have a long history
with orientation-selectivity, often described mathematically as Gabor filters.
Gabor-like filters have been observed in the early layers of CNN classifiers
and even throughout low-level image processing networks. In this work, we take
this observation to the extreme and explicitly constrain the filters of a
natural-image denoising CNN to be learned 2D real Gabor filters. Surprisingly,
we find that the proposed network (GDLNet) can achieve near state-of-the-art
denoising performance amongst popular fully convolutional neural networks, with
only a fraction of the learned parameters. We further verify that this
parameterization maintains the noise-level generalization (training vs.
inference mismatch) characteristics of the base network, and investigate the
contribution of individual Gabor filter parameters to the performance of the
denoiser. We present positive findings for the interpretation of dictionary
learning networks as performing accelerated sparse-coding via the importance of
untied learned scale parameters between network layers. Our network's success
suggests that representations used by low-level image processing CNNs can be as
simple and interpretable as Gabor filterbanks.


title:
Few-cycle vortex beam generated from self-compression of mid-infrared
  femtosecond vortex beam in thin plates

abstract:
  We demonstrate theoretically that few-cycle vortex beam with subterawatt peak
power can be generated by self-compression of mid-infrared femtosecond vortex
beam using the thin-plate scheme. The 3 {\mu}m femtosecond vortex beam with
input duration of 90 fs is compressed to 15.1 fs with the vortex
characteristics preserved. The conversion efficiency is as high as 91.5% and
the peak power reaches 0.18 TW. The generation of the high-peak-power few-cycle
vortex beam is owing to the proper spatiotemporal match by this novel scheme,
where the spectrum is broadened enough, the negative group velocity dispersion
can compensate the positive chirp induced by nonlinear effects, and multiple
filamentation is inhibited for the keeping of the vortex characteristics. Our
work will help to generate isolated attosecond vortices, opening a new
perspective in ultrafast science.


title: Overbooking with bounded loss

abstract:
  We study a classical problem in revenue management: quantity-based
single-resource revenue management with no-shows. In this problem, a firm
observes a sequence of $T$ customers requesting a service. Each arrival is
drawn independently from a known distribution of $k$ different types, and the
firm needs to decide irrevocably whether to accept or reject requests in an
online fashion. The firm has a capacity of resources $B$, and wants to maximize
its profit. Each accepted service request yields a type-dependent revenue and
has a type-dependent probability of requiring a resource once all arrivals have
occurred (or, be a no-show). If the number of accepted arrivals that require a
resource at the end of the horizon is greater than $B$, the firm needs to pay a
fixed compensation for each service request that it cannot fulfill. With a
clairvoyant, that knows all arrivals ahead of time, as a benchmark, we provide
an algorithm with a uniform additive loss bound, i.e., its expected loss is
independent of $T$. This improves upon prior works achieving $\Omega(\sqrt{T})$
guarantees.


title:
Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond
  $1/2$-Approximation

abstract:
  In this work we give two new algorithms that use similar techniques for
(non-monotone) submodular function maximization subject to a cardinality
constraint.
  The first is an offline fixed parameter tractable algorithm that guarantees a
$0.539$-approximation for all non-negative submodular functions.
  The second algorithm works in the random-order streaming model. It guarantees
a $(1/2+c)$-approximation for symmetric functions, and we complement it by
showing that no space-efficient algorithm can beat $1/2$ for asymmetric
functions. To the best of our knowledge this is the first provable separation
between symmetric and asymmetric submodular function maximization.


title: Learning and Inference in Sparse Coding Models with Langevin Dynamics

abstract:
  We describe a stochastic, dynamical system capable of inference and learning
in a probabilistic latent variable model. The most challenging problem in such
models - sampling the posterior distribution over latent variables - is
proposed to be solved by harnessing natural sources of stochasticity inherent
in electronic and neural systems. We demonstrate this idea for a sparse coding
model by deriving a continuous-time equation for inferring its latent variables
via Langevin dynamics. The model parameters are learned by simultaneously
evolving according to another continuous-time equation, thus bypassing the need
for digital accumulators or a global clock. Moreover we show that Langevin
dynamics lead to an efficient procedure for sampling from the posterior
distribution in the 'L0 sparse' regime, where latent variables are encouraged
to be set to zero as opposed to having a small L1 norm. This allows the model
to properly incorporate the notion of sparsity rather than having to resort to
a relaxed version of sparsity to make optimization tractable. Simulations of
the proposed dynamical system on both synthetic and natural image datasets
demonstrate that the model is capable of probabilistically correct inference,
enabling learning of the dictionary as well as parameters of the prior.


title:
Pre-classification based stochastic reduced-order model for
  time-dependent complex system

abstract:
  We propose a novel stochastic reduced-order model (SROM) for complex systems
by combining clustering and classification strategies. Specifically, the
distance and centroid of centroidal Voronoi tessellation (CVT) are redefined
according to the optimality of proper orthogonal decomposition (POD), thereby
obtaining a time-dependent generalized CVT, and each class can generate a set
of cluster-based POD (CPOD) basis functions. To learn the classification
mechanism of random input, the naive Bayes pre-classifier and clustering
results are applied. Then for a new input, the set of CPOD basis functions
associated with the predicted label is used to reduce the corresponding model.
Rigorous error analysis is shown, and a discussion in stochastic Navier-Stokes
equation is given to provide a context for the application of this model.
Numerical experiments verify that the accuracy of our SROM is improved compared
with the standard POD method.


title: Duoidal $\infty$-categories of operadic modules

abstract:
  In this paper we study duoidal structures on $\infty$-categories of operadic
modules. Let $\mathcal{O}^{\otimes}$ be a small coherent $\infty$-operad and
let $\mathcal{P}^{\otimes}$ be an $\infty$-operad. If a
$\mathcal{P}\otimes\mathcal{O}$-monoidal $\infty$-category
$\mathcal{C}^{\otimes}$ has a sufficient supply of colimits, then we show that
the $\infty$-category ${\rm Mod}_A^{\mathcal{O}}(\mathcal{C})$ of
$\mathcal{O}$-$A$-modules in $\mathcal{C}^{\otimes}$ has a structure of
$(\mathcal{P},\mathcal{O})$-duoidal $\infty$-category for any
$\mathcal{P}\otimes\mathcal{O}$-algebra object $A$.


title: Chain rules for quantum channels

abstract:
  Divergence chain rules for channels relate the divergence of a pair of
channel inputs and to the divergence of the corresponding channel outputs. An
important special case of such a rule is the data-processing inequality, which
tells us that if the same channel is applied to both inputs then the divergence
cannot increase. Based on direct matrix analysis methods, we derive several
R\'enyi divergence chain rules for channels in the quantum setting. Our results
simplify and in some cases generalise previous derivations in the literature.


title:
Dual Skipping Guidance for Document Retrieval with Learned Sparse
  Representations

abstract:
  This paper proposes a dual skipping guidance scheme with hybrid scoring to
accelerate document retrieval that uses learned sparse representations while
still delivering a good relevance. This scheme uses both lexical BM25 and
learned neural term weights to bound and compose the rank score of a candidate
document separately for skipping and final ranking, and maintains two top-k
thresholds during inverted index traversal. This paper evaluates time
efficiency and ranking relevance of the proposed scheme in searching MS MARCO
TREC datasets.


title: Adaptive Tests for Bandedness of High-dimensional Covariance Matrices

abstract:
  Estimation of the high-dimensional banded covariance matrix is widely used in
multivariate statistical analysis. To ensure the validity of estimation, we aim
to test the hypothesis that the covariance matrix is banded with a certain
bandwidth under the high-dimensional framework. Though several testing methods
have been proposed in the literature, the existing tests are only powerful for
some alternatives with certain sparsity levels, whereas they may not be
powerful for alternatives with other sparsity structures. The goal of this
paper is to propose a new test for the bandedness of high-dimensional
covariance matrix, which is powerful for alternatives with various sparsity
levels. The proposed new test also be used for testing the banded structure of
covariance matrices of error vectors in high-dimensional factor models. Based
on these statistics, a consistent bandwidth estimator is also introduced for a
banded high dimensional covariance matrix. Extensive simulation studies and an
application to a prostate cancer dataset from protein mass spectroscopy are
conducted for evaluating the effectiveness of the proposed adaptive tests blue
and bandwidth estimator for the banded covariance matrix.


title: Perspective: New directions in dynamical density functional theory

abstract:
  Classical dynamical density functional theory (DDFT) has become one of the
central modeling approaches in nonequilibrium soft matter physics. Recent years
have seen the emergence of novel and interesting fields of application for
DDFT. In particular, there has been a remarkable growth in the amount of work
related to chemistry. Moreover, DDFT has stimulated research on other theories
such as phase field crystal models and power functional theory. In this
perspective, we summarize the latest developments in the field of DDFT and
discuss a variety of possible directions for future research.

categories: cond-mat.soft cond-mat.mtrl-sci cond-mat.stat-mech physics.chem-ph


title:
On the exact divisibility by $5$ of the class number of some pure
  metacyclic fields

abstract:
  Let $\Gamma \,=\, \mathbb{Q}(\sqrt[5]{n})$ be a pure quintic field, where $n$
is a natural number $5^{th}$ power-free. Let $k = \mathbb{Q}(\sqrt[5]{n},
\zeta_5)$, with $\zeta_5$ is a primitive $5^{th}$ root of unit, be the normal
closure of $\Gamma$, and a pure metacyclic field of degree $20$ over
$\mathbb{Q}$. When $n$ takes some particular forms, we show that $\Gamma$
admits a trivial $5$-class group and $5$ divides exactly the class number of
$k$.


title: Hydrodynamics of the $t$-PNG model via a colored $t$-PNG model

abstract:
  The $t$-PNG model introduced in Aggarwal, Borodin, and Wheeler (2021) is a
deformed version of the polynuclear growth (PNG) model. In this paper, we prove
the hydrodynamic limit of the model using soft techniques. One key element of
the proof is the construction of a colored version of the $t$-PNG model, which
allows us to apply the superadditive ergodic theorem and obtain the
hydrodynamic limit, albeit without identifying the limiting constant. We then
find this constant by proving a law of large numbers for the $\alpha$-points,
which generalizes Groeneboom (2001). Along the way, we construct the stationary
$t$-PNG model and prove a version of Burke's theorem for it.


title: Explainable Fairness in Recommendation

abstract:
  Existing research on fairness-aware recommendation has mainly focused on the
quantification of fairness and the development of fair recommendation models,
neither of which studies a more substantial problem--identifying the underlying
reason of model disparity in recommendation. This information is critical for
recommender system designers to understand the intrinsic recommendation
mechanism and provides insights on how to improve model fairness to decision
makers. Fortunately, with the rapid development of Explainable AI, we can use
model explainability to gain insights into model (un)fairness. In this paper,
we study the problem of explainable fairness, which helps to gain insights
about why a system is fair or unfair, and guides the design of fair recommender
systems with a more informed and unified methodology. Particularly, we focus on
a common setting with feature-aware recommendation and exposure unfairness, but
the proposed explainable fairness framework is general and can be applied to
other recommendation settings and fairness definitions. We propose a
Counterfactual Explainable Fairness framework, called CEF, which generates
explanations about model fairness that can improve the fairness without
significantly hurting the performance.The CEF framework formulates an
optimization problem to learn the "minimal" change of the input features that
changes the recommendation results to a certain level of fairness. Based on the
counterfactual recommendation result of each feature, we calculate an
explainability score in terms of the fairness-utility trade-off to rank all the
feature-based explanations, and select the top ones as fairness explanations.


title:
Discovery of extended structure around open cluster COIN-Gaia 13 based
  on Gaia EDR3

abstract:
  COIN-Gaia 13 is a newly discovered open cluster revealed by Gaia DR2 data. It
is a nearby open cluster with a distance of about 513 pc. Combined with the
five-dimensional astrometric data of Gaia EDR3 with higher accuracy, we use the
membership assignment algorithm (pyUPMASK) to determine the membership of
COIN-Gaia 13 in a large extended spatial region. The cluster has found 478
candidate members. After obtaining reliable cluster members, we further study
its basic properties and spatial distribution. Our results show that there is
an obvious extended structure of the cluster in the X-Y plane. This elongated
structure is distributed along the spiral arm, and the whole length is about
270 pc. The cluster age is 250 Myr, the total mass is about 439 M$_\odot$, and
the tidal radius of the cluster is about 11 pc. Since more than half of the
member stars (352 stars) are located outside twice the tidal radius, it is
suspected that this cluster is undergoing the dynamic dissolution process.
Furthermore, the spatial distribution and kinematic analysis indicate that the
extended structure in COIN-Gaia 13 is more likely to be caused by the
differential rotation of the Galaxy.


title: A Survey on Unsupervised Industrial Anomaly Detection Algorithms

abstract:
  In line with the development of Industry 4.0, more and more attention is
attracted to the field of surface defect detection. Improving efficiency as
well as saving labor costs has steadily become a matter of great concern in
industry field, where deep learning-based algorithms performs better than
traditional vision inspection methods in recent years. While existing deep
learning-based algorithms are biased towards supervised learning, which not
only necessitates a huge amount of labeled data and a significant amount of
labor, but it is also inefficient and has certain limitations. In contrast,
recent research shows that unsupervised learning has great potential in
tackling above disadvantages for visual anomaly detection. In this survey, we
summarize current challenges and provide a thorough overview of recently
proposed unsupervised algorithms for visual anomaly detection covering five
categories, whose innovation points and frameworks are described in detail.
Meanwhile, information on publicly available datasets containing surface image
samples are provided. By comparing different classes of methods, the advantages
and disadvantages of anomaly detection algorithms are summarized. It is
expected to assist both the research community and industry in developing a
broader and cross-domain perspective.


title:
MAP-Elites based Hyper-Heuristic for the Resource Constrained Project
  Scheduling Problem

abstract:
  The resource constrained project scheduling problem (RCPSP) is an NP-Hard
combinatorial optimization problem. The objective of RCPSP is to schedule a set
of activities without violating any activity precedence or resource
constraints. In recent years researchers have moved away from complex solution
methodologies, such as meta heuristics and exact mathematical approaches,
towards more simple intuitive solutions like priority rules. This often
involves using a genetic programming based hyper-heuristic (GPHH) to discover
new priority rules which can be applied to new unseen cases. A common problem
affecting GPHH is diversity in evolution which often leads to poor quality
output. In this paper, we present a MAP-Elites based hyper-heuristic (MEHH) for
the automated discovery of efficient priority rules for RCPSP. MAP-Elites uses
a quality diversity based approach which explicitly maintains an archive of
diverse solutions characterised along multiple feature dimensions. In order to
demonstrate the benefits of our proposed hyper-heuristic, we compare the
overall performance against a traditional GPHH and priority rules proposed by
human experts. Our results indicate strong improvements in both diversity and
performance. In particular we see major improvements for larger instances which
have been under-studied in the existing literature.


title:
Simulating spin measurement with a finite heat bath model for the
  environment

abstract:
  Spin measurement is studied as a unitary time evolution of the spin coupled
to an environment representing the meter and the apparatus. Modelling the
environment as a heat bath comprising only a finite number of boson modes and
represented in a basis of coherent states, following the Davydov ansatz, it can
be fully included in the quantum time evolution of the total system. We perform
numerical simulations of projective measurements of the polarization, with the
spins prepared initially in a neutral pure state. The likewise pure initial
state of the environment is constructed as a product of coherent states of the
boson modes with a random distribution of their centroids around the origin of
phase space. Switching the self-energy of the spin and the coupling to the heat
bath on and off by a time-dependent modulation, we observe the outcome of the
measurement in terms of the long-time behaviour of the spin. Interacting with
the heat bath, the spins get entangled with it and lose coherence, thus
reproduce the "collapse of the wavefunction". The expected quantum randomness
in the final state is manifest in our simulations as a tendency of the spin to
approach either one of the two eigenstates of the measured spin operator,
recovering an almost pure state. The unitary time evolution allows us to
reproducibly relate these random final states to the respective initial states
of the environment and to monitor the exchange of information between the two
subsystems in terms of their purity and mutual entropy.


title: Subgroup Fairness in Graph-based Spam Detection

abstract:
  Fake reviews are prevalent on review websites such as Amazon and Yelp. GNN is
the state-of-the-art method that can detect suspicious reviewers by exploiting
the topologies of the graph connecting reviewers, reviews, and target products.
However, the discrepancy in the detection accuracy over different groups of
reviewers causes discriminative treatment of different reviewers of the
websites, leading to less engagement and trustworthiness of such websites. The
complex dependencies over the review graph introduce difficulties in teasing
out subgroups of reviewers that are hidden within larger groups and are treated
unfairly. There is no previous study that defines and discovers the subtle
subgroups to improve equitable treatment of reviewers. This paper addresses the
challenges of defining, discovering, and utilizing subgroup memberships for
fair spam detection. We first define a subgroup membership that can lead to
discrepant accuracy in the subgroups. Since the subgroup membership is usually
not observable while also important to guide the GNN detector to balance the
treatment, we design a model that jointly infers the hidden subgroup
memberships and exploits the membership for calibrating the target GNN's
detection accuracy across subgroups. Comprehensive results on two large Yelp
review datasets demonstrate that the proposed model can be trained to treat the
subgroups more fairly.


title:
ReLoop: A Self-Correction Continual Learning Loop for Recommender
  Systems

abstract:
  Deep learning-based recommendation has become a widely adopted technique in
various online applications. Typically, a deployed model undergoes frequent
re-training to capture users' dynamic behaviors from newly collected
interaction logs. However, the current model training process only acquires
users' feedbacks as labels, but fail to take into account the errors made in
previous recommendations. Inspired by the intuition that humans usually reflect
and learn from mistakes, in this paper, we attempt to build a self-correction
learning loop (dubbed ReLoop) for recommender systems. In particular, a new
customized loss is employed to encourage every new model version to reduce
prediction errors over the previous model version during training. Our ReLoop
learning framework enables a continual self-correction process in the long run
and thus is expected to obtain better performance over existing training
strategies. Both offline experiments and an online A/B test have been conducted
to validate the effectiveness of ReLoop.


title:
In-plane anisotropic response to the uniaxial pressure in the hidden
  order state of URu$_2$Si$_2$

abstract:
  We studied the uniaxial-pressure dependence of the resistivity for
URu$_{2-x}$Fe$_x$Si$_2$ samples with $x$ = 0 and 0.2, which host a hidden order
(HO) and a large-moment antiferromagnetic (LMAFM) phase, respectively. For both
samples, the elastoresistivity $\zeta$ shows a seemingly divergent behavior
above the transition temperature $T_0$ and a quick decrease below it. We found
that the temperature dependence of $\zeta$ for both samples can be well
described by assuming the uniaxial pressure effect on the gap or certain energy
scale except for $\zeta_{(110)}$ of the $x$ = 0 sample, which exhibits a
non-zero residual value at 0 K. We show that this provides a qualitative
difference between the HO and LMAFM phases. Our results suggest that there is
an in-plane anisotropic response to the uniaxial pressure that only exists in
the hidden order state without necessarily breaking the rotational lattice
symmetry.


title:
RelViT: Concept-guided Vision Transformer for Visual Relational
  Reasoning

abstract:
  Reasoning about visual relationships is central to how humans interpret the
visual world. This task remains challenging for current deep learning
algorithms since it requires addressing three key technical problems jointly:
1) identifying object entities and their properties, 2) inferring semantic
relations between pairs of entities, and 3) generalizing to novel
object-relation combinations, i.e., systematic generalization. In this work, we
use vision transformers (ViTs) as our base model for visual reasoning and make
better use of concepts defined as object entities and their relations to
improve the reasoning ability of ViTs. Specifically, we introduce a novel
concept-feature dictionary to allow flexible image feature retrieval at
training time with concept keys. This dictionary enables two new concept-guided
auxiliary tasks: 1) a global task for promoting relational reasoning, and 2) a
local task for facilitating semantic object-centric correspondence learning. To
examine the systematic generalization of visual reasoning models, we introduce
systematic splits for the standard HICO and GQA benchmarks. We show the
resulting model, Concept-guided Vision Transformer (or RelViT for short)
significantly outperforms prior approaches on HICO and GQA by 16% and 13% in
the original split, and by 43% and 18% in the systematic split. Our ablation
analyses also reveal our model's compatibility with multiple ViT variants and
robustness to hyper-parameters.


title:
Generalized Lagrange Coded Computing: A Flexible
  Computation-Communication Tradeoff

abstract:
  We consider the problem of evaluating arbitrary multivariate polynomials over
a massive dataset, in a distributed computing system with a master node and
multiple worker nodes. Generalized Lagrange Coded Computing (GLCC) codes are
proposed to provide robustness against stragglers who do not return computation
results in time, adversarial workers who deliberately modify results for their
benefit, and information-theoretic security of the dataset amidst possible
collusion of workers. GLCC codes are constructed by first partitioning the
dataset into multiple groups, and then encoding the dataset using carefully
designed interpolation polynomials, such that interference computation results
across groups can be eliminated at the master. Particularly, GLCC codes include
the state-of-the-art Lagrange Coded Computing (LCC) codes as a special case,
and achieve a more flexible tradeoff between communication and computation
overheads in optimizing system efficiency.


title: Quasinormal modes of black holes in f(T) gravity

abstract:
  We calculate the quasinormal modes (QNM) frequencies of a test massless
scalar field around static black holes in f(T) gravity. Focusing on quadratic
f(T) modifications, which is a good approximation for every realistic f(T)
theory, we first extract the spherically symmetric solutions using the
perturbative method, imposing two ansatze for the metric functions, which
suitably quantify the deviation from the Schwarzschild solution. Moreover, we
extract the effective potential and then we calculate the QNM frequency of the
obtained solutions. Firstly, we solve the Schrodinger-like equation numerically
using the discretization method, and we extract the frequency and the time
evolution of the dominant mode applying the function fit method. Secondly, we
perform a semi-analytical calculation by applying the third-order WKB
approximation method. We show that the results for f(T) gravity are different
comparing to General Relativity, and in particular we obtain a different slope
and period of the field decay behavior for different values of the model
parameter. Hence, under the light of gravitational-wave observations of
increasing accuracy from binary systems, the whole analysis could be used as an
additional tool in order to test General Relativity and examine whether
torsional gravitational modifications are possible.


title: Data compression for quantum machine learning

abstract:
  The advent of noisy-intermediate scale quantum computers has introduced the
exciting possibility of achieving quantum speedups in machine learning tasks.
These devices, however, are composed of a small number of qubits, and can
faithfully run only short circuits. This puts many proposed approaches for
quantum machine learning beyond currently available devices. We address the
problem of efficiently compressing and loading classical data for use on a
quantum computer. Our proposed methods allow both the required number of qubits
and depth of the quantum circuit to be tuned. We achieve this by using a
correspondence between matrix-product states and quantum circuits, and further
propose a hardware-efficient quantum circuit approach, which we benchmark on
the Fashion-MNIST dataset. Finally, we demonstrate that a quantum circuit based
classifier can achieve competitive accuracy with current tensor learning
methods using only 11 qubits.


title: Fixing Knockout Tournaments With Seeds

abstract:
  Knockout tournaments constitute a popular format for organizing sports
competitions. While prior results have shown that it is often possible to
manipulate a knockout tournament by fixing the bracket, these results ignore
the prevalent aspect of player seeds, which can significantly constrain the
chosen bracket. We show that certain structural conditions that guarantee that
a player can win a knockout tournament without seeds are no longer sufficient
in light of seed constraints. On the other hand, we prove that when the
pairwise match outcomes are generated randomly, all players are still likely to
be knockout winners under the same probability threshold with seeds as without
seeds. In addition, we investigate the complexity of deciding whether a
manipulation is possible when seeds are present.


title: New type of solutions for the nonlinear Schr\"odinger-Newton system

abstract:
  The nonlinear Schr\"{o}dinger-Newton system \begin{equation*}
  \begin{cases}
  \Delta u- V(|x|)u + \Psi u=0, &~x\in\mathbb{R}^3,\\ \Delta \Psi+\frac12
u^2=0, &~x\in\mathbb{R}^3, \end{cases} \end{equation*} is a nonlinear system
obtained by coupling the linear Schr\"{o}dinger equation of quantum mechanics
with the gravitation law of Newtonian mechanics. Wei and Yan in (Calc. Var.
Partial Differential Equations 37 (2010),423--439) proved that the
Schr\"{o}dinger equation has infinitely many positive solutions in
$\mathbb{R}^N$ and these solutions have polygonal symmetry in the $(y_{1},
y_{2})$ plane and they are radially symmetric in the other variables. Duan et
al. in (arXiv:2006.16125v1) extended the results got by Wei and Yan and these
solutions have polygonal symmetry in the $(y_{1}, y_{2})$ plane and they are
even in $y_{2}$with one more more parameter in the expression of the
solutions.Hu et al. Under the appropriate assumption on the potential function
V, Hu et al. in (arXiv: 2106.04288v1) constructed infinitely many non-radial
positive solutions for the Schr\"{o}dinger-Newton system and these positive
solutions have polygonal symmetry in the $(y_{1}, y_{2})$ plane and they are
even in $y_{2}$ and $y_{3}$. Assuming that $V(r)$ has the following character
\begin{equation*}
V(r)=V_{1}+\frac{b}{r^q}+O\Big(\frac{1}{r^{q+\sigma}}\Big),~\mbox{ as }
r\rightarrow\infty, \end{equation*} Where $\frac12\leq q<1$ and $b, V_{1},
\sigma$ are some positive constants, $V(y)\geq V_1>0$, we construct infinitely
many non-radial positive solutions which have polygonal symmetry in the
$(y_{1}, y_{2})$ plane and are even in $y_{2}$ for the Schr\"{o}dinger-Newton
system by the Lyapunov-Schmidt reduction method. We extend the results got by
Duan et al. in (arXiv:2006.16125v1) to the nonlinear Schr\"{o}dinger-Newton
system.


title:
Exploring the ground state bulk and decay properties of the nuclei in
  superheavy island

abstract:
  The $\alpha$-decay half-lives of 204 superheavy nuclei covering the range
$114 \leq Z \leq 126$ have been investigated using the relativistic mean-field
model (RMF) for NL3$^*$ parameter set. The ground state bulk properties such as
binding energy, quadrupole deformation parameter ($\beta_2$ ), and
root-mean-square charge radii for these nuclei are analyzed. Four different
semi-empirical formulae, namely, the universal decay law (UDL), the
Viola-Seaborg (VSS) formula, the modified universal decay law (MUDL), and the
modified Brown formula (MBrown), are used to obtain the $\alpha$-decay
half-lives for the considered nuclei. To examine the applicability of
relativistic mean-field model within NL3$^*$ parametrization, the
$\alpha$-decay energies, and the half-lives of a few known superheavy nuclei
within the range 102 $\leq$ Z $\leq$ 118 are calculated and the results are
compared with the experimental data along with the theoretical predictions. The
$\alpha$-decay energies ($Q$-values) are estimated from the binding energies of
the parent, and daughter from the RMF (NL3$^*$) parameter set. The calculated
results are compared with macroscopic-microscopic Finite-Range-Droplet-Model
(FRDM), Global Nuclear Mass Model (WS3, WS4), Weizsacker-Skyrme mass model
(WS$^*$) predictions, and the experimental data, wherever available. The
possible standard deviations are also estimated for experimental and various
theoretical predictions. We find a good consistency for the
experimental-to-UDL, FRDM-to-UDL, and WS4-to-UDL estimates of the decay energy
and corresponding half-life. The present analysis provides the theoretical
predictions within the microscopic model for the upcoming experiments on the
superheavy region.


title: Complete Policy Regret Bounds for Tallying Bandits

abstract:
  Policy regret is a well established notion of measuring the performance of an
online learning algorithm against an adaptive adversary. We study restrictions
on the adversary that enable efficient minimization of the \emph{complete
policy regret}, which is the strongest possible version of policy regret. We
identify a gap in the current theoretical understanding of what sorts of
restrictions permit tractability in this challenging setting. To resolve this
gap, we consider a generalization of the stochastic multi armed bandit, which
we call the \emph{tallying bandit}. This is an online learning setting with an
$m$-memory bounded adversary, where the average loss for playing an action is
an unknown function of the number (or tally) of times that the action was
played in the last $m$ timesteps. For tallying bandit problems with $K$ actions
and time horizon $T$, we provide an algorithm that w.h.p achieves a complete
policy regret guarantee of $\tilde{\mathcal{O}}(mK\sqrt{T})$, where the
$\tilde{\mathcal{O}}$ notation hides only logarithmic factors. We additionally
prove an $\tilde\Omega(\sqrt{m K T})$ lower bound on the expected complete
policy regret of any tallying bandit algorithm, demonstrating the near
optimality of our method.


title:
Study of background from accidental coincidence signals in the PandaX-II
  experiment

abstract:
  The PandaX-II experiment employed a 580kg liquid xenon detector to search for
the interactions between dark matter particles and the target xenon atoms. The
accidental coincidences of isolated signals result in a dangerous background
which mimic the signature of the dark matter. We performed a detailed study on
the accidental coincidence background in PandaX-II, including the possible
origin of the isolated signals, the background level and corresponding
background suppression method. With a boosted-decision-tree algorithm, the
accidental coincidence background is reduced by 70% in the dark matter signal
region, thus the sensitivity of dark matter search at PandaX-II is improved.


title:
Cousin Problems for Overdetermined Systems of Partial Differential
  Equations

abstract:
  We construct a resolution of the sheaf of germs of solutions of a
overdetermined system of PDEs. A sufficient condition for global exactness is
obtained in terms of semi-positivity and a lower bound of the rank of a
quadratic form which was originally introduced by L. H{\"o}rmander(\cite{H1}).
As applications of global exactness, we investigate the original overdetermined
system by formulating Cousin type problems which provide approaches to gluing
local solutions of overdetermined systems of PDEs. To establish solvability of
multiplicative Cousin problem, we will introduce a twisted exponential
sequence.


title:
Virtual Rings on Highways: Traffic Control by Connected Automated
  Vehicles

abstract:
  This work gives introduction to traffic control by connected automated
vehicles. The influence of vehicle control on vehicular traffic and traffic
control strategies are discussed and compared. It is highlighted that
vehicle-to-everything connectivity allows connected automated vehicles to
access the state of the traffic behind them such that feedback can be utilized
to mitigate evolving congestions. Numerical simulations demonstrate that such
connectivity-based traffic control is beneficial for smoothness and energy
efficiency of highway traffic. The dynamics and stability of traffic flow,
under the proposed controllers, are analyzed in detail to construct stability
charts that guide the selection of stabilizing control gains.


title:
Engineering Majorana corner modes from two-dimensional hexagonal
  crystals

abstract:
  Second order topological insulator can be engineered from two-dimensional
materials with strong spin-orbit coupling and in-plane Zeeman field. In
proximity to superconductor, topological superconducting phase could be induced
in the two-dimensional materials, which host Majorana corner modes at the
intersection between two zigzag edges. Two types of tight binding models in
hexagonal lattice, which include $p_{z}$ or $p_{x,y}$ orbit(s) in each lattice
site, are applied to engineer two-dimensional materials in topological
superconducting phase. In both models, the condition that induces the second
order topological superconductor requires nonuniform value of either in-plane
Zeeman fields or superconductor pairing parameters in two sublattices. The
finite size effect of the second model is weaker than that of the first model.


title:
Generating Two-dimensional Ferromagnetic Charge Density Waves via
  External Fields

abstract:
  Two-dimensional (2D) ferromagnetic charge density wave (CDW), an exotic
quantum state for exploring the intertwining effect between correlated charge
and spin orders in 2D limit, has not been discovered in the experiments yet.
Here, we propose a feasible strategy to realize 2D ferromagnetic CDWs under
external fields, which is demonstrated in monolayer VSe$_2$ using
first-principles calculations. Under external tensile strain, two novel
ferromagnetic CDWs ($\sqrt{3}$$\times$$\sqrt{3}$ and 2$\times2\sqrt{3}$ CDWs)
can be generated, accompanied by distinguishable lattice reconstructions of
magnetic V atoms. Remarkably, because the driving forces for generating these
two ferromagnetic CDWs are strongly spin-dependent, fundamentally different
from that in conventional CDWs, the $\sqrt{3}$$\times$$\sqrt{3}$ and
2$\times2\sqrt{3}$ CDWs can exhibit two dramatically different half-metallic
phases under a large strain range, along with either a flat band or a Dirac
cone around Fermi level. Our proposed strategy and material demonstration may
open a door to generate and manipulate correlation effect between collective
charge and spin orders via external fields.


title:
Few-Shot Speaker Identification Using Depthwise Separable Convolutional
  Network with Channel Attention

abstract:
  Although few-shot learning has attracted much attention from the fields of
image and audio classification, few efforts have been made on few-shot speaker
identification. In the task of few-shot learning, overfitting is a tough
problem mainly due to the mismatch between training and testing conditions. In
this paper, we propose a few-shot speaker identification method which can
alleviate the overfitting problem. In the proposed method, the model of a
depthwise separable convolutional network with channel attention is trained
with a prototypical loss function. Experimental datasets are extracted from
three public speech corpora: Aishell-2, VoxCeleb1 and TORGO. Experimental
results show that the proposed method exceeds state-of-the-art methods for
few-shot speaker identification in terms of accuracy and F-score.


title: Realistic Evaluation of Transductive Few-Shot Learning

abstract:
  Transductive inference is widely used in few-shot learning, as it leverages
the statistics of the unlabeled query set of a few-shot task, typically
yielding substantially better performances than its inductive counterpart. The
current few-shot benchmarks use perfectly class-balanced tasks at inference. We
argue that such an artificial regularity is unrealistic, as it assumes that the
marginal label probability of the testing samples is known and fixed to the
uniform distribution. In fact, in realistic scenarios, the unlabeled query sets
come with arbitrary and unknown label marginals. We introduce and study the
effect of arbitrary class distributions within the query sets of few-shot tasks
at inference, removing the class-balance artefact. Specifically, we model the
marginal probabilities of the classes as Dirichlet-distributed random
variables, which yields a principled and realistic sampling within the simplex.
This leverages the current few-shot benchmarks, building testing tasks with
arbitrary class distributions. We evaluate experimentally state-of-the-art
transductive methods over 3 widely used data sets, and observe, surprisingly,
substantial performance drops, even below inductive methods in some cases.
Furthermore, we propose a generalization of the mutual-information loss, based
on $\alpha$-divergences, which can handle effectively class-distribution
variations. Empirically, we show that our transductive $\alpha$-divergence
optimization outperforms state-of-the-art methods across several data sets,
models and few-shot settings. Our code is publicly available at
https://github.com/oveilleux/Realistic_Transductive_Few_Shot.


title:
Cyclic cohomology and the extended Heisenberg calculus of Epstein and
  Melrose

abstract:
  In this paper we present a formula for the index of a pseudodifferential
operator with invertible principal symbol in the extended Heisenberg calculus
of Epstein and Melrose. Our results build on the work we did in a previous
paper (arXiv:2010.02900), where we restricted attention to the Heisenberg
calculus proper.


title: Formation of bound states in the continuum in double trapezoidal grating

abstract:
  In the field of optics, bound state in the continuum (BIC) has been
researched in many photonic crystals and periodic structures due to a strong
resonance and an ultrahigh Q factor. Some designs of narrowband transmission
filters, lasers, and sensors were proposed based on excellent optical
properties of BIC. In this paper, we consider symmetrical rectangular grating
structure firstly, then cut off the corner of one of the gratings, the Fano
peak of quasi-BIC can be observed in the spectrum. After that, we further
change the tilt parameter of the other grating, which minimizes the Fano line
width. In the momentum space, the process of structural change corresponds to
topological charges split from q=1 into two half charges q=1/2.We analyze
guided mode resonance (GMR) excitation of the grating structure, and discuss
the dispersion relations in the waveguide layer with the position of BIC in
energy bands. In addition, the reflectance spectrum is found to exhibit
asymmetric line-shapes with different values of the asymmetry parameters, M1
and M2. BIC is transformed into quasi-BIC as the symmetry of the structure is
broken. This work demonstrates a double trapezoid structure with strong
resonance properties, which has significant implications for exploring the
phenomenon of BIC.