title:
High-dimensional properties for empirical priors in linear regression
  with unknown error variance

abstract:
  We study full Bayesian procedures for high-dimensional linear regression. We
adopt data-dependent empirical priors introduced in [1]. In their paper, these
priors have nice posterior contraction properties and are easy to compute. Our
paper extend their theoretical results to the case of unknown error variance .
Under proper sparsity assumption, we achieve model selection consistency,
posterior contraction rates as well as Bernstein von-Mises theorem by analyzing
multivariate t-distribution.


title:
A Characterization of Semi-Supervised Adversarially-Robust PAC
  Learnability

abstract:
  We study the problem of semi-supervised learning of an adversarially-robust
predictor in the PAC model, where the learner has access to both labeled and
unlabeled examples. The sample complexity in semi-supervised learning has two
parameters, the number of labeled examples and the number of unlabeled
examples. We consider the complexity measures, $VC_U \leq dim_U \leq VC$ and
$VC^*$, where $VC$ is the standard $VC$-dimension, $VC^*$ is its dual, and the
other two measures appeared in Montasser et al. (2019). The best sample bound
known for robust supervised PAC learning is $O(VC \cdot VC^*)$, and we will
compare our sample bounds to $\Lambda$ which is the minimal number of labeled
examples required by any robust supervised PAC learning algorithm. Our main
results are the following: (1) in the realizable setting it is sufficient to
have $O(VC_U)$ labeled examples and $O(\Lambda)$ unlabeled examples. (2) In the
agnostic setting, let $\eta$ be the minimal agnostic error. The sample
complexity depends on the resulting error rate. If we allow an error of
$2\eta+\epsilon$, it is still sufficient to have $O(VC_U)$ labeled examples and
$O(\Lambda)$ unlabeled examples. If we insist on having an error
$\eta+\epsilon$ then $\Omega(dim_U)$ labeled examples are necessary, as in the
supervised case. The above results show that there is a significant benefit in
semi-supervised robust learning, as there are hypothesis classes with $VC_U=0$
and $dim_U$ arbitrary large. In supervised learning, having access only to
labeled examples requires at least $\Lambda \geq dim_U$ labeled examples.
Semi-supervised require only $O(1)$ labeled examples and $O(\Lambda)$ unlabeled
examples. A byproduct of our result is that if we assume that the distribution
is robustly realizable by a hypothesis class, then with respect to the 0-1 loss
we can learn with only $O(VC_U)$ labeled examples, even if the $VC$ is
infinite.


title:
Incorporating Berry Force Effects into The Fewest Switches Surface
  Hopping Algorithm: Intersystem Crossing and The Case of Electronic Degeneracy

abstract:
  We present a preliminary surface-hopping approach for modeling intersystem
crossing (ISC) dynamics between four electronic states: one singlet and one
(triply degenerate) triplet. In order to incorporate all Berry force effects,
the algorithm requires that, when moving along an adiabatic surface associated
with the triplet manifold, \mycomment{one must also keep track of a
quasi-diabatic index (akin to a "$m_s$" quantum number) for each trajectory.
For a simple model problem, we find that a great deal of new physics can be
captured by our algorithm, setting the stage for larger, more realistic (or
perhaps even {\em ab initio}) simulations in the future.


title: Posterior Consistency for Bayesian Relevance Vector Machines

abstract:
  Statistical modeling and inference problems with sample sizes substantially
smaller than the number of available covariates are challenging. Chakraborty et
al. (2012) did a full hierarchical Bayesian analysis of nonlinear regression in
such situations using relevance vector machines based on reproducing kernel
Hilbert space (RKHS). But they did not provide any theoretical properties
associated with their procedure. The present paper revisits their problem,
introduces a new class of global-local priors different from theirs, and
provides results on posterior consistency as well as posterior contraction
rates


title:
Understanding Curriculum Learning in Policy Optimization for Solving
  Combinatorial Optimization Problems

abstract:
  Over the recent years, reinforcement learning (RL) has shown impressive
performance in finding strategic solutions for game environments, and recently
starts to show promising results in solving combinatorial optimization (CO)
problems, inparticular when coupled with curriculum learning to facilitate
training. Despite emerging empirical evidence, theoretical study on why RL
helps is still at its early stage. This paper presents the first systematic
study on policy optimization methods for solving CO problems. We show that CO
problems can be naturally formulated as latent Markov Decision Processes
(LMDPs), and prove convergence bounds on natural policy gradient (NPG) for
solving LMDPs. Furthermore, our theory explains the benefit of curriculum
learning: it can find a strong sampling policy and reduce the distribution
shift, a critical quantity that governs the convergence rate in our theorem.
For a canonical combinatorial problem, Secretary Problem, we formally prove
that distribution shift is reduced exponentially with curriculum learning. Our
theory also shows we can simplify the curriculum learning scheme used in prior
work from multi-step to single-step. Lastly, we provide extensive experiments
on Secretary Problem and Online Knapsack to empirically verify our findings.


title:
X-ray emission from candidate stellar merger remnant TYC 2597-735-1 and
  its Blue Ring Nebula

abstract:
  Tight binary or multiple star systems can interact through mass transfer and
follow vastly different evolutionary pathways than single stars. The star TYC
2597-735-1 is a candidate for a recent stellar merger remnant resulting from a
coalescence of a low-mass companion with a primary star a few thousand years
ago. This violent event is evident in a conical outflow ("Blue Ring Nebula")
emitting in UV light and surrounded by leading shock filaments observed in
H$\alpha$ and UV emission. From Chandra data, we report the detection of X-ray
emission from the location of TYC 2597-735-1 with a luminosity
$\log(L_\mathrm{X}/L_\mathrm{bol})=-5.5$. Together with a previously reported
period around 14~days, this indicates ongoing stellar activity and the presence
of strong magnetic fields on TYC 2597-735-1. Supported by stellar evolution
models of merger remnants, we interpret the inferred stellar magnetic field as
dynamo action associated with a newly formed convection zone in the atmosphere
of TYC 2597-735-1, though internal shocks at the base of an accretion-powered
jet cannot be ruled out. We speculate that this object will evolve into an FK
Com type source, i.e. a class of rapidly spinning magnetically active stars for
which a merger origin has been proposed but for which no relic accretion or
large-scale nebula remains visible. We also detect likely X-ray emission from
two small regions close to the outer shock fronts in the Blue Ring Nebula,
which may arise from either inhomogenities in the circumstellar medium or in
the mass and velocity distribution in the merger-driven outflow.


title:
Modular symmetry anomaly and non-perturbative neutrino mass terms in
  magnetized orbifold models

abstract:
  We study the modular symmetry anomaly in magnetized orbifold models. The
non-perturbative effects such as D-brane instanton effects can break tree-level
symmetry. We study which part of the modular symmetry is broken explicitly by
Majorana mass terms with three generations of neutrinos. The modular weight of
neutrino mass terms does not match with other coupling terms in tree-level
Lagrangian. In addition, the $Z_N$ symmetry of the modular flavor symmetry is
broken and a certain normal subgroup of the modular flavor symmetry remains in
neutrino mass terms.


title:
The $1D$-wave bottom-strange baryons and possible interpretation of
  $\Xi_{b}(6327)^{0}$ and $\Xi_{b}(6333)^{0}$

abstract:
  Inspired by the LHCb's newest observation of two new excited $\Xi_b^0$
states, we systematically study the strong decays of the low-lying $\lambda$-
and $\rho$-modes $1D$-wave $\Xi_{b}$ and $\Xi^{'}_{b}$ baryons using the chiral
quark model within the $j$-$j$ coupling scheme. Based on the measured masses
and strong decay properties of $\Xi_{b}(6327)^{0}$ and $\Xi_{b}(6333)^{0}$, we
explain the two states as the $\lambda$-mode $1D$ $\Xi_{b}$ states with $
J^{P}=3/2^{+} $ and $ J^{P}=5/2^{+} $, respectively. Moreover, under this
assignment, another dominant decay channel of $\Xi_{b}(6327)^{0}$ is
$\Xi'_b\pi$ and that of $\Xi_{b}(6333)^{0}$ is $\Xi_b^*\pi$. Hence, the decay
modes $\Xi'_b\pi$ and $\Xi_b^*\pi$ may be another ideal channels as well to
decode the inner structure of $\Xi_{b}(6327)^{0}$ and $\Xi_{b}(6333)^{0}$,
respectively. For other unseen $1D$ $\Xi_b$ and $\Xi'_b$ states, our results
indicate: (i) $\Xi_b|J^P=\frac{3}{2}^+,2\rangle_{\rho}$ and
$\Xi_b|J^P=\frac{5}{2}^+,2\rangle_{\rho}$ are most likely to be narrow states
with a width of $\Gamma\simeq(12-30)$ MeV, and dominantly decay into
$\Sigma_bK$ and $\Sigma^*_bK$, respectively; (ii) The $1D$ $\Xi'_b$ baryons are
not broad states, and the widths vary in the range of $\Gamma\simeq(14-46)$
MeV. These states have a good potential to be observed in their dominant decay
processes.


title: The discovery of a radio galaxy of at least 5 Mpc

abstract:
  We discover what is in projection the largest known structure of galactic
origin: a giant radio galaxy with a projected proper length of $4.99 \pm 0.04\
\mathrm{Mpc}$. The source, named Alcyoneus, was first identified in
low-resolution LOFAR Two-metre Sky Survey images from which angularly compact
sources had been removed. Being an extreme example in its class, Alcyoneus
could shed light on the main mechanisms that drive radio galaxy growth. We find
that - beyond geometry - Alcyoneus and its host galaxy appear suspiciously
ordinary: the total low-frequency luminosity density, stellar mass and
supermassive black hole mass are all lower than, though similar to, those of
the medial giant radio galaxy (percentiles $45 \pm 3\%$, $25 \pm 9 \%$ and $23
\pm 11 \%$, respectively). The source resides in a filament of the Cosmic Web,
with which it might have significant thermodynamic interaction. At $5 \cdot
10^{-16}\ \mathrm{Pa}$, the pressures in the lobes are the lowest hitherto
found, and Alcyoneus therefore represents one of the most promising radio
galaxies yet to probe the warm-hot intergalactic medium.


title: Quasi-stationary distributions for queueing and other models

abstract:
  This note presents conjectures on polynomial/algebraic/sub-exponential
convergence of transition probabilities for $\lambda$-null recurrent and
$\lambda$-transient Markov chains in continuous time. The only known positive
examples are in queueing, branching, and related models. Implications for the
existence of limiting conditional distributions for $\lambda$-transient chains
are discussed.


title:
Galactic center gamma-ray production by cosmic rays from stellar winds
  and Sgr A East

abstract:
  The High Energy Stereoscopic System (HESS), the Major Atmospheric Gamma-ray
Imaging Cherenkov Telescope (MAGIC), and the Very Energetic Radiation Imaging
Telescope Array System (VERITAS) have observed diffuse gamma-ray emission
strongly correlated with the central molecular zone in the Galactic center. The
most accepted scenario to generate this emission is via a hadronic interaction
between cosmic rays (CRs) and ambient gas, where CRs are accelerated from a
central and continuous source of 1 PeV protons (PeVatron). We explore the
influence of the three-dimensional (3D) shape of the central molecular zone on
the indirect observation of the CR energy density via gamma-ray detection. We
simulated synthetic gamma-ray maps using a CR diffusion model with spherical
injection, one isotropic diffusion coefficient, no advection, and
mono-energetic particles of 1 PeV. Also, we used two different 3D gas
distributions considering the observed gas column density, both with and
without an inner cavity. We find that when using a persistent CR source, a
disk-like gas distribution is needed to reproduce the existing CR indirect
observations. This is in agreement with the continuous gas distribution implied
by some dynamical models and studies based on the comparison of emission and
absorption molecular lines. However, it contradicts several models of the
central molecular zone, which imply that this structure has a significant inner
cavity. This tension can be reconciled by an additional, impulsive CR
injection. If the central molecular zone has a cavity, a composite CR
population, coming from the stellar winds of the Wolf-Rayet stars in the
central 0.5 pc and the supernova Sgr A East, produces a good match to the
observed gamma-ray morphology in the Galactic center.


title:
Wind power ramp prediction algorithm based on wavelet deep belief
  network

abstract:
  The wind power ramp events threaten the power grid safety significantly. To
improve the ramp prediction accuracy, a hybrid wavelet deep belief network
algorithm with adaptive feature selection (WDBNAFS) is proposed. First, the
wind power characteristic is analyzed. Then, wavelet decomposition is addressed
to the time series, and an adaptive feature selection algorithm is proposed to
select the inputs of the prediction model. Finally, a deep belief network is
employed to predict the wind power ramp event, and the proposed WDBNAFS was
testified with the experiments based on the practical data. The simulation
results demonstrate that the prediction accuracy of the proposed algorithm is
more than 90%.


title:
Pseudopotentials for Two-dimentional Ultracold Scattering in the
  Presence of Synthetic Spin-orbit-coupling

abstract:
  We derive a pseudopotential in two dimensions (2D) with the presence of a 2D
Rashba spin-orbit-coupling (SOC), following the same spirit of frame
transformation in {[}Phys. Rev. A 95, 020702(R) (2017){]}. The frame
transformation correctly describes the non-trivial phase accumulation and
partial wave couplings due to the presence of SOC and gives rise to a different
pseudopotential than the free-space one, even when the length scale of SOC is
significantly larger than the two-body potential range. As an application, we
apply our pseudopotential with the Lippmann-Schwinger equation to obtain an
analytical scattering matrix. To demonstrate the validity, we compare our
results with a numerical scattering calculation of finite-range potential and
show perfect agreement over a wide range of scattering energy and SOC strength.
Our results also indicate that the differences between our pseudopotential and
the original free-space pseudopotential are essential to reproduce scattering
observables correctly.


title:
Global existence and stability of de Sitter-like solutions to the
  Einstein-Yang-Mills equations in spacetime dimensions $n\geq 4$

abstract:
  We establish the global existence and stability to the future of non-linear
perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in
$n\geq 4$ spacetime dimension. This generalizes Friedrich's Einstein-Yang-Mills
stability results in dimension $n=4$ [11] to all higher dimensions.


title: A Survey on Programmatic Weak Supervision

abstract:
  Labeling training data has become one of the major roadblocks to using
machine learning. Among various weak supervision paradigms, programmatic weak
supervision (PWS) has achieved remarkable success in easing the manual labeling
bottleneck by programmatically synthesizing training labels from multiple
potentially noisy supervision sources. This paper presents a comprehensive
survey of recent advances in PWS. In particular, we give a brief introduction
of the PWS learning paradigm, and review representative approaches for each
component within PWS's learning workflow. In addition, we discuss complementary
learning paradigms for tackling limited labeled data scenarios and how these
related approaches can be used in conjunction with PWS. Finally, we identify
several critical challenges that remain under-explored in the area to hopefully
inspire future research directions in the field.


title:
Getting started: How a supersonic stellar wind is initiated from a
  hydrostatic surface

abstract:
  Most of a star's mass is bound in a hydrostatic equilibrium in which pressure
balances gravity. But if at some near-surface layer additional outward forces
overcome gravity, this can transition to a supersonic, outflowing wind, with
the sonic point, where the outward force cancels gravity, marking the division
between hydrostatic atmosphere and wind outflow. This talk will review general
issues with such transonic initiation of a stellar wind outflow, and how this
helps set the wind mass loss rate. The main discussion contrasts the flow
initiation in four prominent classes of steady-state winds: (1) the
pressure-driven coronal wind of the sun and other cool stars; (2) line-driven
winds from OB stars; (3) a two-stage initiation model for the much denser winds
from Wolf-Rayet (WR) stars; and (4) the slow "overflow" mass loss from highly
evolved giant stars. A follow on discussion briefly reviews eruptive mass loss,
with particular focus on the giant eruption of eta Carinae.


title: Dual Task Framework for Improving Persona-grounded Dialogue Dataset

abstract:
  This paper introduces a simple yet effective data-centric approach for the
task of improving persona-conditioned dialogue agents. Prior model-centric
approaches unquestioningly depend on the raw crowdsourced benchmark datasets
such as Persona-Chat. In contrast, we aim to fix annotation artifacts in
benchmarking, which is orthogonally applicable to any dialogue model.
Specifically, we augment relevant personas to improve dialogue dataset/agent,
by leveraging the primal-dual structure of the two tasks, predicting dialogue
responses and personas based on each other. Experiments on Persona-Chat show
that our approach outperforms pre-trained LMs by an 11.7 point gain in terms of
accuracy.


title:
Minimax Regret Optimization for Robust Machine Learning under
  Distribution Shift

abstract:
  In this paper, we consider learning scenarios where the learned model is
evaluated under an unknown test distribution which potentially differs from the
training distribution (i.e. distribution shift). The learner has access to a
family of weight functions such that the test distribution is a reweighting of
the training distribution under one of these functions, a setting typically
studied under the name of Distributionally Robust Optimization (DRO). We
consider the problem of deriving regret bounds in the classical learning theory
setting, and require that the resulting regret bounds hold uniformly for all
potential test distributions. We show that the DRO formulation does not
guarantee uniformly small regret under distribution shift. We instead propose
an alternative method called Minimax Regret Optimization (MRO), and show that
under suitable conditions this method achieves uniformly low regret across all
test distributions. We also adapt our technique to have stronger guarantees
when the test distributions are heterogeneous in their similarity to the
training data. Given the widespead optimization of worst case risks in current
approaches to robust machine learning, we believe that MRO can be a strong
alternative to address distribution shift scenarios.


title: Transverse Goldstone mode in holographic fluids with broken translations

abstract:
  In this paper we investigate the low energy shear modes in fluid systems with
spontaneously broken translations by a specific holographic model. In absence
of momentum relaxation, we find that there exist two decoupled gapless modes in
the transverse channel, one of which is purely diffusive and the other is
non-dynamical due to the lack of rigidity. The diffusive mode is associated
with the conservation of momentum while the non-dynamical one is the Goldstone
mode of the spontaneous symmetry breaking. Switching on an external source
which breaks the translations explicitly but weakly, the would-be gapless modes
both get relaxed and acquire a tiny mass gap. Finally, in the strong momentum
relaxation regime, we find a (pseudo-)diffusive-to-sound crossover that is set
by a momentum gap.


title:
Fixed point theorem for an infinite Toeplitz matrix and its extension to
  general infinite matrices

abstract:
  In [V. M. Abramov, \emph{Bull. Aust. Math. Soc.} \textbf{104} (2021),
108--117] the fixed point equation for an infinite nonnegative Toeplitz matrix
has been studied. It was found the conditions for existence of a positive
solution and bounded positive solution. However, the proof of the existence of
a positive solution was entirely straightforward, not admitting extensions for
more general types of matrices. In the present note, we provide an alternative
proof for the existence of a positive solution in more general case. The
presented proof is based on an application of the fixed point theorem of M. A.
Krasnosel'skii. The results are then extended for the equations with infinite
matrices of a general type.


title:
Determination the Solution of a Stochastic Parabolic Equation by the
  Terminal Value

abstract:
  This paper studies the inverse problem of determination the history for a
stochastic diffusion process, by means of the value at the final time $T$. By
establishing a new Carleman estimate, the conditional stability of the problem
is proven. Based on the idea of Tikhonov method, a regularized solution is
proposed. The analysis of the existence and uniqueness of the regularized
solution, and proof for error estimate under an a-proior assumption are
present. Numerical verification of the regularization, including numerical
algorithm and examples are also illustrated.


title: Non-Parametric Spherical Jeans Mass Estimation with B-splines

abstract:
  Spherical Jeans modeling is widely used to estimate mass profiles of systems
from star clusters to galactic stellar haloes to clusters of galaxies. It
derives the cumulative mass profile, M(<r), from kinematics of tracers of the
potential under the assumptions of spherical symmetry and dynamical
equilibrium. We consider the application of Jeans modeling to mapping the dark
matter distribution in the outer reaches of the Milky Way using field halo
stars. We present a novel non-parametric routine for solving the spherical
Jeans equation by fitting B-splines to the velocity and density profiles of
halo stars. While most implementations assume parametric forms for these
profiles, B-splines provide non-parametric fitting curves with analytical
derivatives. Our routine recovers the mass profiles of equilibrium systems with
flattened haloes or a stellar disc and bulge excellently (<~ 10% error at most
radii). Tests with non-equilibrium, Milky Way-like galaxies from the Latte
suite of FIRE-2 simulations perform quite well (<~ 15% error for r <~ 100 kpc).
We also create observationally motivated datasets for the Latte suite by
imposing selection functions and errors on phase space coordinates
characteristic of Gaia and the DESI Milky Way Survey. The resulting imprecise
and incomplete data require us to introduce an MCMC-based subroutine to obtain
deconvolved density and velocity dispersion profiles from the tracer
population. With these observational effects taken into account, the accuracy
of the Jeans mass estimate remains at the level 20% or better.


title: Invariance Principle Meets Out-of-Distribution Generalization on Graphs

abstract:
  Despite recent developments in using the invariance principle from causality
to enable out-of-distribution (OOD) generalization on Euclidean data, e.g.,
images, studies on graph data are limited. Different from images, the complex
nature of graphs poses unique challenges that thwart the adoption of the
invariance principle for OOD generalization. In particular, distribution shifts
on graphs can happen at both structure-level and attribute-level, which
increases the difficulty of capturing the invariance. Moreover, domain or
environment partitions, which are often required by OOD methods developed on
Euclidean data, can be expensive to obtain for graphs. Aiming to bridge this
gap, we characterize distribution shifts on graphs with causal models, and show
that the OOD generalization on graphs with invariance principle is possible by
identifying an invariant subgraph for making predictions. We propose a novel
framework to explicitly model this process using a contrastive strategy. By
contrasting the estimated invariant subgraphs, our framework can provably
identify the underlying invariant subgraph under mild assumptions. Experiments
across several synthetic and real-world datasets demonstrate the
state-of-the-art OOD generalization ability of our method.


title:
Three-dimensional quantum cellular automata from chiral semion surface
  topological order and beyond

abstract:
  We construct a novel three-dimensional quantum cellular automaton (QCA) based
on a system with short-range entangled bulk and chiral semion boundary
topological order. We argue that either the QCA is nontrivial, i.e. not a
finite-depth circuit of local quantum gates, or there exists a two-dimensional
commuting projector Hamiltonian realizing the chiral semion topological order
(characterized by $U(1)_2$ Chern-Simons theory). Our QCA is obtained by first
constructing the Walker-Wang Hamiltonian of a certain premodular tensor
category of order four, then condensing the deconfined bulk boson at the level
of lattice operators. We show that the resulting Hamiltonian hosts chiral
semion surface topological order in the presence of a boundary and can be
realized as a non-Pauli stabilizer code on qubits, from which the QCA is
defined. The construction is then generalized to a class of QCAs defined by
non-Pauli stabilizer codes on ${2^n}$-dimensional qudits that feature surface
anyons described by $U(1)_{2^n}$ Chern-Simons theory. Our results support the
conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to
the Witt group of non-degenerate braided fusion categories.

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


title: An Introduction To Langer's Theory

abstract:
  This note provides a pedagogical introduction to Langer's theory for
activated rate processes in multiple dimensions at the high friction limit,
with an emphasis on the connection between the theory and the property of the
backward committor/splitting probability near the saddle point. The intended
audience is assumed to have some familiarity with linear algebra and
statistical mechanics while knowledge of stochastic processes is not strictly
necessary.


title: Computational-Statistical Gaps in Reinforcement Learning

abstract:
  Reinforcement learning with function approximation has recently achieved
tremendous results in applications with large state spaces. This empirical
success has motivated a growing body of theoretical work proposing necessary
and sufficient conditions under which efficient reinforcement learning is
possible. From this line of work, a remarkably simple minimal sufficient
condition has emerged for sample efficient reinforcement learning: MDPs with
optimal value function $V^*$ and $Q^*$ linear in some known low-dimensional
features. In this setting, recent works have designed sample efficient
algorithms which require a number of samples polynomial in the feature
dimension and independent of the size of state space. They however leave
finding computationally efficient algorithms as future work and this is
considered a major open problem in the community.
  In this work, we make progress on this open problem by presenting the first
computational lower bound for RL with linear function approximation: unless
NP=RP, no randomized polynomial time algorithm exists for deterministic
transition MDPs with a constant number of actions and linear optimal value
functions. To prove this, we show a reduction from Unique-Sat, where we convert
a CNF formula into an MDP with deterministic transitions, constant number of
actions and low dimensional linear optimal value functions. This result also
exhibits the first computational-statistical gap in reinforcement learning with
linear function approximation, as the underlying statistical problem is
information-theoretically solvable with a polynomial number of queries, but no
computationally efficient algorithm exists unless NP=RP. Finally, we also prove
a quasi-polynomial time lower bound under the Randomized Exponential Time
Hypothesis.


title:
Neutron spectroscopy evidence on the dual nature of magnetic excitations
  in a van der Waals metallic ferromagnet Fe$_{2.72}$GeTe$_{2}$

abstract:
  In the local or itinerant extreme, magnetic excitations can be described by
the Heisenberg model which treats electron spins as localized moments, or by
the itinerant-electron model where the exchange interaction between electrons
leads to unequal numbers of electrons with up and down spins. However, it has
been elusive when both local moments and itinerant electrons are present in the
intermediate range. Using inelastic neutron scattering, we provide direct
spectroscopic evidence on the coexistence of and interplay between local
moments and itinerant electrons in a van der Waals metallic ferromagnet
Fe$_{2.72}$GeTe$_{2}$, which can sustain tunable room-temperature
ferromagnetism down to the monolayer limit. We find that there exist
ferromagnetic spin-wave excitations dispersing from the zone center at low
energies resulting from local moments, and a column-like broad continuum at the
zone boundary at high energies up to over 100 meV resulting from itinerant
electrons. Unlike the two-dimensional crystal structure, the low-energy mode
exhibits a three-dimensional nature, and the high-energy mode also has an
out-of-plane dependence. Both modes persist well above the Curie temperature of
160 K. Our neutron spectroscopic data reveal that the low-energy spin waves at
100 K are more coherent than those at 4 K, which is evidence of the weakening
of the Kondo screening at high temperatures. These results unambiguously
demonstrate the coexistence of local moments and itinerant electrons, and the
Kondo effect between these two components in Fe$_{2.72}$GeTe$_{2}$. Such
behaviors are generally expected in heavy-fermion systems with heavy $f$
electrons but rarely clearly observed in materials with light $d$ electrons.
These findings shed light on the understanding of magnetism in transition-metal
compounds.


title:
Faster No-Regret Learning Dynamics for Extensive-Form Correlated and
  Coarse Correlated Equilibria

abstract:
  A recent emerging trend in the literature on learning in games has been
concerned with providing faster learning dynamics for correlated and coarse
correlated equilibria in normal-form games. Much less is known about the
significantly more challenging setting of extensive-form games, which can
capture both sequential and simultaneous moves, as well as imperfect
information. In this paper we establish faster no-regret learning dynamics for
\textit{extensive-form correlated equilibria (EFCE)} in multiplayer general-sum
imperfect-information extensive-form games. When all players follow our
accelerated dynamics, the correlated distribution of play is an
$O(T^{-3/4})$-approximate EFCE, where the $O(\cdot)$ notation suppresses
parameters polynomial in the description of the game. This significantly
improves over the best prior rate of $O(T^{-1/2})$. To achieve this, we develop
a framework for performing accelerated \emph{Phi-regret minimization} via
predictions. One of our key technical contributions -- that enables us to
employ our generic template -- is to characterize the stability of fixed points
associated with \emph{trigger deviation functions} through a refined
perturbation analysis of a structured Markov chain. Furthermore, for the
simpler solution concept of extensive-form \emph{coarse} correlated equilibrium
(EFCCE) we give a new succinct closed-form characterization of the associated
fixed points, bypassing the expensive computation of stationary distributions
required for EFCE. Our results place EFCCE closer to \emph{normal-form coarse
correlated equilibria} in terms of the per-iteration complexity, although the
former prescribes a much more compelling notion of correlation. Finally,
experiments conducted on standard benchmarks corroborate our theoretical
findings.


title:
PSACCF: Prioritized Online Slice Admission Control Considering Fairness
  in 5G/B5G Networks

abstract:
  5G/B5G is envisioned to support various services with the assistance of
network slices, each slice instance asks for adequate resources to provide the
pre-negotiated service quality to its subscribers. Slice Admission Control
(SAC) algorithm is a necessity for Slice Providers (SPs) to guarantee the QoS
and QoE of each admitted request with limited resources. In that circumstance,
the priority concern of services and the fairness of resource allocation arise
as meaningful topics for researchers. The former originates from the innate
characteristics of various services supported by 5G networks, and the latter
matters because slices are instantiated on shared physical equipment. However,
the two issues are mainly investigated separately in the literature or do not
receive sufficient research simultaneously. In this work, we study the SAC
problem in 5G/B5G networks, aiming at enhancing the fairness degree on the
premise of satisfying the necessary priority requirements. We first reinterpret
priority as a higher cumulative service acceptance ratio (CSAR), and adopt the
uniformity of adjacent CSAR gaps to reflect the fairness. Based on these
adjustments, the SAC problem is formulated as a non-linear and non-convex
multi-objective optimization. Thus, we propose a heuristic algorithm called
Prioritized Slice Admission Control Considering Fairness (PSACCF) to solve it.
It introduces the resource efficiency of services to amend priority violations,
then promotes fairness by setting the target CSARs for each service type and
pushing their actual CSARs toward. Numerous simulations are carried out to
compare the performance of PSACCF with two existing algorithms, termed MHPF and
AHPF. Results show that our algorithm can achieve a nearly identical priority
indicator to the comparisons, as well as at least a 33.6% improvement in
fairness degree and a higher minimum average resource utilization.


title: Achieving Minimax Rates in Pool-Based Batch Active Learning

abstract:
  We consider a batch active learning scenario where the learner adaptively
issues batches of points to a labeling oracle. Sampling labels in batches is
highly desirable in practice due to the smaller number of interactive rounds
with the labeling oracle (often human beings). However, batch active learning
typically pays the price of a reduced adaptivity, leading to suboptimal
results. In this paper we propose a solution which requires a careful trade off
between the informativeness of the queried points and their diversity. We
theoretically investigate batch active learning in the practically relevant
scenario where the unlabeled pool of data is available beforehand (pool-based
active learning). We analyze a novel stage-wise greedy algorithm and show that,
as a function of the label complexity, the excess risk of this algorithm
operating in the realizable setting for which we prove matches the known
minimax rates in standard statistical learning settings. Our results also
exhibit a mild dependence on the batch size. These are the first theoretical
results that employ careful trade offs between informativeness and diversity to
rigorously quantify the statistical performance of batch active learning in the
pool-based scenario.


title:
Centrifugal breakout reconnection as the electron acceleration mechanism
  powering the radio magnetospheres of early-type stars

abstract:
  Magnetic B-stars often exhibit circularly polarized radio emission thought to
arise from gyrosynchrotron emission by energetic electrons trapped in the
circumstellar magnetosphere. Recent empirical analyses show that the onset and
strength of the observed radio emission scale with both the magnetic field
strength and the stellar rotation rate. This challenges the existing paradigm
that the energetic electrons are accelerated in the current sheet between
opposite-polarity field lines in the outer regions of magnetised stellar winds,
which includes no role for stellar rotation. Building on recent success in
explaining a similar rotation-field dependence of H$\alpha$ line emission in
terms of a model in which magnetospheric density is regulated by centrifugal
breakout (CBO), we examine here the potential role of the associated CBO-driven
magnetic reconnection in accelerating the electrons that emit the observed
gyrosynchrotron radio. We show in particular that the theoretical scalings for
energy production by CBO reconnection match well the empirical trends for
observed radio luminosity, with a suitably small, nearly constant conversion
efficiency $\epsilon \approx 10^{-8}$. We summarize the distinct advantages of
our CBO scalings over previous associations with an electromotive force, and
discuss the potential implications of CBO processes for X-rays and other
observed characteristics of rotating magnetic B-stars with centrifugal
magnetospheres.


title:
Evidence for magnetic fractional excitations in a Kitaev
  quantum-spin-liquid candidate $\alpha$-RuCl$_3$

abstract:
  $\alpha$-RuCl$_3$ has been studied extensively because of its proximity to
the Kitaev quantum-spin-liquid (QSL) phase and the possibility of approaching
it by tuning the competing interactions. Here we present the first polarized
inelastic neutron scattering study on $\alpha$-RuCl$_3$ single crystals to
explore the scattering continuum around the $\Gamma$ point at the Brillouin
zone center, which was hypothesized to be resulting from the Kitaev QSL state
but without concrete evidence. With polarization analyses, we find that while
the spin-wave excitations around the M point vanish above the transition
temperature $T_{\rm N}$, the pure magnetic continuous excitations around the
$\Gamma$ point are robust against temperature. Furthermore, by calculating the
dynamical spin-spin correlation function using the cluster perturbation theory,
we derive magnetic dispersion spectra based on the $K$-$\Gamma$ model, which
involves with a ferromagnetic Kitaev interaction of -7.2 meV and an
off-diagonal interaction of 5.6 meV. We find this model can reproduce not only
the spin-wave excitation spectra around the M point, but also the non-spin-wave
continuous magnetic excitations around the $\Gamma$ point. These results
provide evidence for the existence of fractional excitations around the
$\Gamma$ point originating from the Kitaev QSL state, and further support the
validity of the $K$-$\Gamma$ model as the effective minimal spin model to
describe $\alpha$-RuCl$_3$.


title:
ACORT: A Compact Object Relation Transformer for Parameter Efficient
  Image Captioning

abstract:
  Recent research that applies Transformer-based architectures to image
captioning has resulted in state-of-the-art image captioning performance,
capitalising on the success of Transformers on natural language tasks.
Unfortunately, though these models work well, one major flaw is their large
model sizes. To this end, we present three parameter reduction methods for
image captioning Transformers: Radix Encoding, cross-layer parameter sharing,
and attention parameter sharing. By combining these methods, our proposed ACORT
models have 3.7x to 21.6x fewer parameters than the baseline model without
compromising test performance. Results on the MS-COCO dataset demonstrate that
our ACORT models are competitive against baselines and SOTA approaches, with
CIDEr score >=126. Finally, we present qualitative results and ablation studies
to demonstrate the efficacy of the proposed changes further. Code and
pre-trained models are publicly available at
https://github.com/jiahuei/sparse-image-captioning.


title: Information Design for Differential Privacy

abstract:
  Firms and statistical agencies that publish aggregate data face practical and
legal requirements to protect the privacy of individuals. Increasingly, these
organizations meet these standards by using publication mechanisms which
satisfy differential privacy. We consider the problem of choosing such a
mechanism so as to maximize the value of its output to end users. We show that
this is equivalent to a constrained information design problem, and
characterize its solution. Moreover, by introducing a new order on information
structures and showing that it ranks them by their usefulness to agents with
supermodular payoffs, we show that the simple geometric mechanism is optimal
whenever data users face supermodular decision problems.


title: Robust estimation algorithms don't need to know the corruption level

abstract:
  Real data are rarely pure. Hence the past half-century has seen great
interest in robust estimation algorithms that perform well even when part of
the data is corrupt. However, their vast majority approach optimal accuracy
only when given a tight upper bound on the fraction of corrupt data. Such
bounds are not available in practice, resulting in weak guarantees and often
poor performance. This brief note abstracts the complex and pervasive
robustness problem into a simple geometric puzzle. It then applies the puzzle's
solution to derive a universal meta technique that converts any robust
estimation algorithm requiring a tight corruption-level upper bound to achieve
its optimal accuracy into one achieving essentially the same accuracy without
using any upper bounds.


title:
Algebraic approach to quarkyoniclike configuration and stable diquarks
  in dense matter

abstract:
  We study the color-spin interaction energy of a quark, a diquark and a baryon
with their surrounding baryons and/or quark matter. This is accomplished by
classifying all possible flavor and spin states of the resulting multiquark
configuration in both the flavor SU(2) and SU(3) symmetric cases. We find that
while the baryon has the lowest interaction energy when there is only a single
surrounding baryon, the quark has the lowest interaction energy when the
surrounding has more than three baryons or becomes a quark gas. As the short
range nucleon-nucleon interactions are dominated by the color-spin
interactions, our finding suggests that the baryon modes near other baryons are
suppressed due to larger repulsive energy compared to that of a quark and thus
provides a quark model basis for the quarkyoniclike phase in dense matter. At
the same time, when the internal interactions are taken into account, and the
matter density is high so that the color-spin interaction becomes the dominant
interaction, the diquark becomes the lowest energy configuration and will thus
appear in both the dense baryonic and/or quark matter.


title: Deepest nodes in marked ordered trees

abstract:
  A variation of ordered trees, where each rightmost edge might be marked or
not, if it does not lead to an endnode, is investigated. These marked ordered
trees were introduced by E. Deutsch et al.\ to model skew Dyck paths. We study
the number of deepest nodes in such trees. Explicit generating functions are
established and the average number of deepest nodes, which approaches $\frac53$
when the number of nodes gets large. This is to be compared to standard ordered
trees where the average number of deepest nodes approaches $2$.


title:
NEAT: A Label Noise-resistant Complementary Item Recommender System with
  Trustworthy Evaluation

abstract:
  The complementary item recommender system (CIRS) recommends the complementary
items for a given query item. Existing CIRS models consider the item
co-purchase signal as a proxy of the complementary relationship due to the lack
of human-curated labels from the huge transaction records. These methods
represent items in a complementary embedding space and model the complementary
relationship as a point estimation of the similarity between items vectors.
However, co-purchased items are not necessarily complementary to each other.
For example, customers may frequently purchase bananas and bottled water within
the same transaction, but these two items are not complementary. Hence, using
co-purchase signals directly as labels will aggravate the model performance. On
the other hand, the model evaluation will not be trustworthy if the labels for
evaluation are not reflecting the true complementary relatedness. To address
the above challenges from noisy labeling of the copurchase data, we model the
co-purchases of two items as a Gaussian distribution, where the mean denotes
the co-purchases from the complementary relatedness, and covariance denotes the
co-purchases from the noise. To do so, we represent each item as a Gaussian
embedding and parameterize the Gaussian distribution of co-purchases by the
means and covariances from item Gaussian embedding. To reduce the impact of the
noisy labels during evaluation, we propose an independence test-based method to
generate a trustworthy label set with certain confidence. Our extensive
experiments on both the publicly available dataset and the large-scale
real-world dataset justify the effectiveness of our proposed model in
complementary item recommendations compared with the state-of-the-art models.


title:
Hindi/Bengali Sentiment Analysis Using Transfer Learning and Joint Dual
  Input Learning with Self Attention

abstract:
  Sentiment Analysis typically refers to using natural language processing,
text analysis and computational linguistics to extract affect and emotion based
information from text data. Our work explores how we can effectively use deep
neural networks in transfer learning and joint dual input learning settings to
effectively classify sentiments and detect hate speech in Hindi and Bengali
data. We start by training Word2Vec word embeddings for Hindi \textbf{HASOC
dataset} and Bengali hate speech and then train LSTM and subsequently, employ
parameter sharing based transfer learning to Bengali sentiment classifiers by
reusing and fine-tuning the trained weights of Hindi classifiers with both
classifier being used as baseline in our study. Finally, we use BiLSTM with
self attention in joint dual input learning setting where we train a single
neural network on Hindi and Bengali dataset simultaneously using their
respective embeddings.


abstract:
  Conditional contrastive learning frameworks consider the conditional sampling
procedure that constructs positive or negative data pairs conditioned on
specific variables. Fair contrastive learning constructs negative pairs, for
example, from the same gender (conditioning on sensitive information), which in
turn reduces undesirable information from the learned representations; weakly
supervised contrastive learning constructs positive pairs with similar
annotative attributes (conditioning on auxiliary information), which in turn
are incorporated into the representations. Although conditional contrastive
learning enables many applications, the conditional sampling procedure can be
challenging if we cannot obtain sufficient data pairs for some values of the
conditioning variable. This paper presents Conditional Contrastive Learning
with Kernel (CCL-K) that converts existing conditional contrastive objectives
into alternative forms that mitigate the insufficient data problem. Instead of
sampling data according to the value of the conditioning variable, CCL-K uses
the Kernel Conditional Embedding Operator that samples data from all available
data and assigns weights to each sampled data given the kernel similarity
between the values of the conditioning variable. We conduct experiments using
weakly supervised, fair, and hard negatives contrastive learning, showing CCL-K
outperforms state-of-the-art baselines.


title:
Asymmetric electrostatic properties of an electric double layer: a
  generalized Poisson-Boltzmann approach taking into account non-uniform size
  effects and water polarization

abstract:
  We theoretically study electrostatic properties of electric double layer
using a generalized Poisson-Boltzmann approach taking into account the
orientational ordering of water dipoles and the excluded volume effect of water
molecules as well as those of positive and negative ions with different sizes
in electrolyte solution. Our approach enables one to predict that the number
densities of water molecules, counterions and coions and the permittivity of
electrolyte solution close to a charged surface, asymmetrically vary depending
on both of sign and magnitude of the surface charge density and the volume of
counterion. We treat several phenomena in more detail. Firstly, an increase in
the volume of counterions and an increase in the surface charge density can
cause the position of the minimum number density of water molecules to be
farther from the charged surface. Secondly, width of the range of voltage in
which the properties at the charged surface symmetrically vary decreases with
increasing bulk salt concentration. In addition, we show that the excluded
volume effect of water molecules and the orientational ordering of water
dipoles can lead to early onset and lowering of the maximum of electric
capacitance according to surface voltage. Our approach and results can be
applied to describing electrostatic properties of biological membranes and
electric double layer capacitor for which excluded volume effects of water
molecules and ions with different sizes may be important.


title:
Reduced order modeling for flow and transport problems with Barlow Twins
  self-supervised learning

abstract:
  We propose a unified data-driven reduced order model (ROM) that bridges the
performance gap between linear and nonlinear manifold approaches. Deep learning
ROM (DL-ROM) using deep-convolutional autoencoders (DC-AE) has been shown to
capture nonlinear solution manifolds but fails to perform adequately when
linear subspace approaches such as proper orthogonal decomposition (POD) would
be optimal. Besides, most DL-ROM models rely on convolutional layers, which
might limit its application to only a structured mesh. The proposed framework
in this study relies on the combination of an autoencoder (AE) and Barlow Twins
(BT) self-supervised learning, where BT maximizes the information content of
the embedding with the latent space through a joint embedding architecture.
Through a series of benchmark problems of natural convection in porous media,
BT-AE performs better than the previous DL-ROM framework by providing
comparable results to POD-based approaches for problems where the solution lies
within a linear subspace as well as DL-ROM autoencoder-based techniques where
the solution lies on a nonlinear manifold; consequently, bridges the gap
between linear and nonlinear reduced manifolds. Furthermore, this BT-AE
framework can operate on unstructured meshes, which provides flexibility in its
application to standard numerical solvers, on-site measurements, experimental
data, or a combination of these sources.


title:
Jordan $*$-homomorphisms on the spaces of continuous maps taking values
  in $C^{*}$-algebras

abstract:
  Let $\mathcal{A}$ be a unital $C^{*}$-algebra. We consider Jordan
$*$-homomorphisms on $C(X, \mathcal{A})$ and Jordan $*$-homomorphisms on
$\operatorname{Lip}(X,\mathcal{A})$. More precisely, for any unital
$C^{*}$-algebra $\mathcal{A}$, we prove that every Jordan $*$-homomorphism on
$C(X, \mathcal{A})$ and every Jordan $*$-homomorphism on
$\operatorname{Lip}(X,\mathcal{A})$ is represented as a weighted composition
operator by using the irreducible representations of $\mathcal{A}$. In
addition, when $\mathcal{A}_1$ and $\mathcal{A}_2$ are primitive
$C^{*}$-algebras, we characterize the Jordan $*$-isomorphisms. These results
unify and enrich previous works on algebra $*$-homomorphisms on $C(X,
\mathcal{A})$ and $\operatorname{Lip}(X,\mathcal{A})$ for several concrete
examples of $\mathcal{A}$.


title:
Disorder-induced broadening of the spin waves in a triangular-lattice
  quantum-spin-liquid candidate YbZnGaO$_4$

abstract:
  Disorder is important in the study of quantum spin liquids, but its role on
the spin dynamics remains elusive. Here, we explore the disorder effect by
investigating the magnetic-field dependence of the low-energy magnetic
excitations in a triangular-lattice frustrated magnet YbZnGaO$_4$ with
inelastic neutron scattering. With an intermediate field of 2.5 T applied along
the $c$-axis, the broad continuum at zero field becomes more smeared both in
energy and momentum. With a field up to 10 T, which fully polarizes the
magnetic moments, we observe clear spin-wave excitations with a gap of
$\sim$1.4 meV comparable to the bandwidth. However, the spectra are
significantly broadened. The excitation spectra both at zero and high fields
can be reproduced by performing classical Monte Carlo simulations which take
into account the disorder effect arising from the random site mixing of
nonmagnetic Zn$^{2+}$ and Ga$^{3+}$ ions. These results elucidate the critical
role of disorder in broadening the magnetic excitation spectra and mimicking
the spin-liquid features in frustrated quantum magnets.


title: Infrastructure-enabled GPS Spoofing Detection and Correction

abstract:
  Accurate and robust localization is crucial for supporting high-level driving
automation and safety. Modern localization solutions rely on various sensors,
among which GPS has been and will continue to be essential. However, GPS can be
vulnerable to malicious attacks and GPS spoofing has been identified as a high
threat. GPS spoofing injects false information into true GPS measurements,
aiming to deviate a vehicle from its true trajectory, endangering the safety of
road users. With various types of vehicle-based sensors emerging, recent
studies propose to detect GPS spoofing by deploying and identifying
inconsistencies among multiple sensors. Yet, these methods often require
sophisticated algorithms and cannot handle stealthy or coordinated attacks
targeting multiple sensors. With roadside infrastructure becoming increasingly
important in supporting emerging vehicle technologies and systems, this study
explores the potential of applying infrastructure data in defending against GPS
spoofing. We propose an infrastructure-enabled method by deploying roadside
infrastructure as an independent, secured data source. A real-time detector,
based on the Isolation Forest, is constructed to detect GPS spoofing. Once
spoofing is detected, GPS measurements are isolated, and the potentially
compromised location estimator is corrected using the infrastructure data. We
test the proposed method using both simulation and real-world data and show its
effectiveness in defending against various GPS spoofing attacks, including
stealthy attacks that are proposed to fail the production-grade autonomous
driving systems.


title:
Unravelling the stability, electronic and physical properties in bulk
  and (001)-surfacesof newlysynthesized Ti2ZnX (X=C, N)MAX phases

abstract:
  MAX phase family has been extended by the addition of late transition metals
at the A-site with the expectation of diverse functional properties, such as
magnetism and catalysis. Here, we present our systematic density functional
investigation on the phase stability and physical properties of newly
synthesized Ti2ZnX (X = C, N) phasesin comparison with conventional Ti2AlX (X =
C, N).Due to smaller size of N as compared to C, the unit cell dimensionis
reduced when C atoms are replaced by N atoms atthe X-site. The thermodynamic,
mechanical and dynamical stabilities are validatedby estimating the formation
energies, elastic constants and phonon dispersions, respectively. The elastic
properties of Ti2ZnN are nearly isotropic while those of Ti2ZnC are completely
anisotropic. To understand the thin-film characteristicsin Ti2ZnX, the surface
properties with (001)-terminated slabs are investigated. Both Ti2ZnX bulk and
(001)-surfaces exhibit metal-like electronic structure. There is a strong
covalent bonding between Ti-X and Ti-Zn atoms.Additional states are generated
at the Fermi level (EF) due to the unusual d-pstates hybridization between Ti
and Zn atoms.The anisotropy in chemical bonding is confirmed by the cleavage
energy difference between Ti-X and Ti-Zn atoms. Here,Ti(X)-001 and Zn-001
terminations are stable surfaces, however, in terms of chemical potentials,
Zn-001 termination is the most favorable.


title:
WAD-CMSN: Wasserstein Distance based Cross-Modal Semantic Network for
  Zero-Shot Sketch-Based Image Retrieval

abstract:
  Zero-shot sketch-based image retrieval (ZSSBIR), as a popular studied branch
of computer vision, attracts wide attention recently. Unlike sketch-based image
retrieval (SBIR), the main aim of ZSSBIR is to retrieve natural images given
free hand-drawn sketches that may not appear during training. Previous
approaches used semantic aligned sketch-image pairs or utilized memory
expensive fusion layer for projecting the visual information to a low
dimensional subspace, which ignores the significant heterogeneous cross-domain
discrepancy between highly abstract sketch and relevant image. This may yield
poor performance in the training phase. To tackle this issue and overcome this
drawback, we propose a Wasserstein distance based cross-modal semantic network
(WAD-CMSN) for ZSSBIR. Specifically, it first projects the visual information
of each branch (sketch, image) to a common low dimensional semantic subspace
via Wasserstein distance in an adversarial training manner. Furthermore,
identity matching loss is employed to select useful features, which can not
only capture complete semantic knowledge, but also alleviate the over-fitting
phenomenon caused by the WAD-CMSN model. Experimental results on the
challenging Sketchy (Extended) and TU-Berlin (Extended) datasets indicate the
effectiveness of the proposed WAD-CMSN model over several competitors.


title: Characterization of Rational Solutions of a KdV-Like Equation

abstract:
  We characterize the rational solutions to a KdV-like equation which are
generated from polynomial solutions to the corresponding generalized bilinear
equation. We use a particular class of polynomials satisfying a quadratic
difference equation to obtain that there are no solutions of the bilinear
equation with degree (in the spatial variable) greater than 5. As a byproduct,
we answer positively a conjecture of Yi Zhang and Wen-Xiu Ma about these
solutions.


title:
Evidence for strong correlations at finite temperatures in the dimerized
  magnet Na$_2$Cu$_2$TeO$_6$

abstract:
  Dimerized magnets forming alternating Heisenberg chains exhibit quantum
coherence and entanglement and thus can find potential applications in quantum
information and computation. However, magnetic systems typically undergo
thermal decoherence at finite temperatures. Here, we show inelastic neutron
scattering results on an alternating antiferromagnetic-ferromagnetic chain
compound Na$_2$Cu$_2$TeO$_6$ that the excited quasiparticles can counter
thermal decoherence and maintain strong correlations at elevated temperatures.
At low temperatures, we observe clear dispersive singlet-triplet excitations
arising from the dimers formed along the crystalline $b$-axis. The excitation
gap is of $\sim$18 meV and the bandwidth is about half of the gap. The band top
energy has a weak modulation along the [100] direction, indicative of a small
interchain coupling. The gap increases while the bandwidth decreases with
increasing temperature, leading to a strong reduction in the available phase
space for the triplons. As a result, the Lorentzian-type energy broadening
becomes highly asymmetric as the temperature is raised. These results are
associated with a strongly correlated state resulting from hard-core constraint
and quasiparticle interactions. We consider these results to be not only
evidence for strong correlations at finite temperatures in Na$_2$Cu$_2$TeO$_6$,
but also for the universality of the strongly correlated state in a broad range
of quantum magnetic systems.


title: Criticality in stochastic SIR model for infectious diseases

abstract:
  We discuss the criticality in the stochastic SIR model for infectious
diseases. We adopt the path-integral formalism for the propagation of
infections among susceptible, infectious, and removed individuals, and perform
the perturbative and nonperturbative analyses to evaluate the critical value of
the basic reproduction number ${\cal R}$. In the perturbation theory, we
calculate the mean values and the variances of the number of infectious
individuals near the initial time, and find that the critical value ${\cal
R}_{\text{c}}=1/3$-$2/3$ should be adopted in order to suppress the stochastic
spread of infections sufficiently. In the nonperturbative approach, we derive
the effective potential by integrating out the stochastic fluctuations, and
obtain the effective Euler-Lagrange equations for the time-evolution of the
numbers of susceptible, infectious, and removed individuals. From the
asymptotic behaviors for a long time, we find that the critical value ${\cal
R}_{\text{c}}=2/3$ should be adopted for the sufficient convergence of
infections. We also find that the endemic state can be generated dynamically by
the stochastic fluctuation which is absent in the conventional SIR model. Those
analyses show that the critical value of the basic reproduction number should
be less than one, against the usually known critical value ${\cal
R}_{\text{c}}=1$, when the stochastic fluctuations are taken into account in
the SIR model.


title:
Privacy-preserving Generative Framework Against Membership Inference
  Attacks

abstract:
  Artificial intelligence and machine learning have been integrated into all
aspects of our lives and the privacy of personal data has attracted more and
more attention. Since the generation of the model needs to extract the
effective information of the training data, the model has the risk of leaking
the privacy of the training data. Membership inference attacks can measure the
model leakage of source data to a certain degree. In this paper, we design a
privacy-preserving generative framework against membership inference attacks,
through the information extraction and data generation capabilities of the
generative model variational autoencoder (VAE) to generate synthetic data that
meets the needs of differential privacy. Instead of adding noise to the model
output or tampering with the training process of the target model, we directly
process the original data. We first map the source data to the latent space
through the VAE model to get the latent code, then perform noise process
satisfying metric privacy on the latent code, and finally use the VAE model to
reconstruct the synthetic data. Our experimental evaluation demonstrates that
the machine learning model trained with newly generated synthetic data can
effectively resist membership inference attacks and still maintain high
utility.


title: Jigsaw Puzzle: Selective Backdoor Attack to Subvert Malware Classifiers

abstract:
  Malware classifiers are subject to training-time exploitation due to the need
to regularly retrain using samples collected from the wild. Recent work has
demonstrated the feasibility of backdoor attacks against malware classifiers,
and yet the stealthiness of such attacks is not well understood. In this paper,
we investigate this phenomenon under the clean-label setting (i.e., attackers
do not have complete control over the training or labeling process).
Empirically, we show that existing backdoor attacks in malware classifiers are
still detectable by recent defenses such as MNTD. To improve stealthiness, we
propose a new attack, Jigsaw Puzzle (JP), based on the key observation that
malware authors have little to no incentive to protect any other authors'
malware but their own. As such, Jigsaw Puzzle learns a trigger to complement
the latent patterns of the malware author's samples, and activates the backdoor
only when the trigger and the latent pattern are pieced together in a sample.
We further focus on realizable triggers in the problem space (e.g., software
code) using bytecode gadgets broadly harvested from benign software. Our
evaluation confirms that Jigsaw Puzzle is effective as a backdoor, remains
stealthy against state-of-the-art defenses, and is a threat in realistic
settings that depart from reasoning about feature-space only attacks. We
conclude by exploring promising approaches to improve backdoor defenses.


title: Totally geodesic discs in bounded symmetric domains

abstract:
  In this paper, we characterize $C^2$-smooth totally geodesic isometric
embeddings $f\colon \Omega\to\Omega'$ between bounded symmetric domains
$\Omega$ and $\Omega'$ which extend $C^1$-smoothly over some open subset in the
Shilov boundaries and have nontrivial normal derivatives on it. In particular,
if $\Omega$ is irreducible, there exist totally geodesic bounded symmetric
subdomains $\Omega_1$ and $\Omega_2$ of $\Omega'$ such that $f = (f_1, f_2)$
maps into $\Omega_1\times \Omega_2\subset \Omega$ where $f_1$ is holomorphic
and $f_2$ is anti-holomorphic totally geodesic isometric embeddings. If
$\text{rank}(\Omega')<2\text{rank}(\Omega)$, then either $f$ or $\bar f$ is a
standard holomorphic embedding.


title: Dandelion: Certified Approximations of Elementary Functions

abstract:
  Elementary function operations such as sin and exp cannot in general be
computed exactly on today's digital computers, and thus have to be
approximated. The standard approximations in library functions typically
provide only a limited set of precisions, and are too inefficient for many
applications. Polynomial approximations that are customized to a limited input
domain and output accuracy can provide superior performance. In fact, the Remez
algorithm computes the best possible approximation for a given polynomial
degree, but has so far not been formally verified.
  This paper presents Dandelion, an automated certificate checker for
polynomial approximations of elementary functions computed with Remez-like
algorithms that is fully verified in the HOL4 theorem prover. Dandelion checks
whether the difference between a polynomial approximation and its target
reference elementary function remains below a given error bound for all inputs
in a given constraint. By extracting a verified binary with the CakeML
compiler, Dandelion can validate certificates within a reasonable time, fully
automating previous manually verified approximations.


title:
Holomorphicity of totally geodesic Kobayashi isometry between bounded
  symmetric domains

abstract:
  In this paper, we study the holomorphicity of totally geodesic Kobayashi
isometric embeddings between bounded symmetric domains. First we show that for
a $C^1$-smooth totally geodesic Kobayashi isometric embedding $f\colon
\Omega\to\Omega'$ where $\Omega$, $\Omega'$ are bounded symmetric domains, if
$\Omega$ is irreducible and $\text{rank}(\Omega) \geq \text{rank}(\Omega')$ or
more generally, $\text{rank}(\Omega) \geq \text{rank}(f_*v)$ for any tangent
vector $v$ of $\Omega$, then $f$ is either holomorphic or anti-holomorphic.
Secondly we characterize $C^1$ Kobayashi isometries from a reducible bounded
symmetric domain to itself.


title:
Bench-Marking And Improving Arabic Automatic Image Captioning Through
  The Use Of Multi-Task Learning Paradigm

abstract:
  The continuous increase in the use of social media and the visual content on
the internet have accelerated the research in computer vision field in general
and the image captioning task in specific. The process of generating a caption
that best describes an image is a useful task for various applications such as
it can be used in image indexing and as a hearing aid for the visually
impaired. In recent years, the image captioning task has witnessed remarkable
advances regarding both datasets and architectures, and as a result, the
captioning quality has reached an astounding performance. However, the majority
of these advances especially in datasets are targeted for English, which left
other languages such as Arabic lagging behind. Although Arabic language, being
spoken by more than 450 million people and being the most growing language on
the internet, lacks the fundamental pillars it needs to advance its image
captioning research, such as benchmarks or unified datasets. This works is an
attempt to expedite the synergy in this task by providing unified datasets and
benchmarks, while also exploring methods and techniques that could enhance the
performance of Arabic image captioning. The use of multi-task learning is
explored, alongside exploring various word representations and different
features. The results showed that the use of multi-task learning and
pre-trained word embeddings noticeably enhanced the quality of image
captioning, however the presented results shows that Arabic captioning still
lags behind when compared to the English language. The used dataset and code
are available at this link.


title:
Circular polarisation of fast radio bursts in the curvature radiation
  scenario

abstract:
  The curvature radiation is applied to the explain the circular polarisation
of FRBs. Significant circular polarisation is reported in both apparent
non-repeating and repeating FRBs. Curvature radiation can produce significant
circular polarisation at the wing of the radiation beam. In the curvature
radiation scenario, in order to see significant circular polarisation in FRBs
(1) more energetic bursts, (2) burst with electrons having higher Lorentz
factor, (3) a slowly rotating neutron star at the centre are required.
Different rotational period of the central neutron star may explain why some
FRBs have high circular polarisation, while others don't. Considering possible
difference in refractive index for the parallel and perpendicular component of
electric field, the position angle may change rapidly over the narrow pulse
window of the radiation beam. The position angle swing in FRBs may also be
explained by this non-geometric origin, besides that of the rotating vector
model.


title:
Physics-Informed PointNet: A Deep Learning Solver for Steady-State
  Incompressible Flows and Thermal Fields on Multiple Sets of Irregular
  Geometries

abstract:
  We present a novel physics-informed deep learning framework for solving
steady-state incompressible flow on multiple sets of irregular geometries by
incorporating two main elements: using a point-cloud based neural network to
capture geometric features of computational domains, and using the mean squared
residuals of the governing partial differential equations, boundary conditions,
and sparse observations as the loss function of the network to capture the
physics. While the solution of the continuity and Navier-Stokes equations is a
function of the geometry of the computational domain, current versions of
physics-informed neural networks have no mechanism to express this functionally
in their outputs, and thus are restricted to obtain the solutions only for one
computational domain with each training procedure. Using the proposed
framework, three new facilities become available. First, the governing
equations are solvable on a set of computational domains containing irregular
geometries with high variations with respect to each other but requiring
training only once. Second, after training the introduced framework on the set,
it is now able to predict the solutions on domains with unseen geometries from
seen and unseen categories as well. The former and the latter both lead to
savings in computational costs. Finally, all the advantages of the point-cloud
based neural network for irregular geometries, already used for supervised
learning, are transferred to the proposed physics-informed framework. The
effectiveness of our framework is shown through the method of manufactured
solutions and thermally-driven flow for forward and inverse problems.


title:
Vacuum Birefringence in a Supercritical Magnetic Field and a Subcritical
  Electric Field

abstract:
  Recent ultra-intense lasers of subcritical fields and proposed observations
of the x-rays polarization from highly magnetized neutron stars of
supercritical fields have attracted attention to vacuum birefringence, a unique
feature of nonlinear electrodynamics. We propose a formulation of vacuum
birefringence that incorporates the effects of the weaker electric field added
to the extremely strong magnetic field. To do so, we first derive a closed
analytical expression for the one-loop effective Lagrangian for the combined
magnetic and electric fields by using an explicit formula of the one-loop
effective Lagrangian for an arbitrarily strong magnetic field. We then employ
the expression to derive the polarization and magnetization of the vacuum, from
which the permittivity and permeability for weak probe fields are obtained.
Finally, we find the refractive indices and the associated polarization vectors
for the case of parallel magnetic and electric fields. The proposed formulation
predicts that an electric field along the magnetic field reduces the
birefringence and rotates the polarization vectors. Such effects should be
taken into account for accurate polarimetry of the x-rays from magnetized
neutron stars, which will prove the fundamental aspect of the strong field
quantum electrodynamics (QED) and explore the extreme fields of astrophysical
bodies.


title: Vetting Asteroseismic $\Delta\nu$ Measurements using Neural Networks

abstract:
  Precise asteroseismic parameters allow one to quickly estimate radius and
mass distributions for large samples of stars. A number of automated methods
are available to calculate the frequency of maximum acoustic power
($\nu_{\mathrm{max}}$) and the frequency separation between overtone modes
($\Delta\nu$) from the power spectra of red giants. However, filtering through
the results requires either manual vetting, elaborate averaging across multiple
methods, or sharp cuts in certain parameters to ensure robust samples of stars
free of outliers. Given the importance of ensemble studies for Galactic
archaeology and the surge in data availability, faster methods for obtaining
reliable asteroseismic parameters are desirable. We present a neural network
classifier that vets $\Delta\nu$ by combining multiple features from the visual
$\Delta\nu$ vetting process. Our classifier is able to analyse large numbers of
stars determining whether their measured $\Delta\nu$ are reliable thus
delivering clean samples of oscillating stars with minimal effort. Our
classifier is independent of the method used to obtain $\nu_{\mathrm{max}}$ and
$\Delta\nu$, and therefore can be applied as a final step to any such method.
Tests of our classifier's performance on manually vetted $\Delta\nu$
measurements reach an accuracy of 95%. We apply the method to giants observed
by K2 Galactic Archaeology Program and find that our results retain stars with
astrophysical oscillation parameters consistent with the parameter
distributions already defined by well-characterised Kepler red giants.


title:
When models fail: an introduction to posterior predictive checks and
  model misspecification in gravitational-wave astronomy

abstract:
  Bayesian inference is a powerful tool in gravitational-wave astronomy. It
enables us to deduce the properties of merging compact-object binaries and to
determine how these mergers are distributed as a population according to mass,
spin, and redshift. As key results are increasingly derived using Bayesian
inference, there is increasing scrutiny on Bayesian methods. In this review, we
discuss the phenomenon of \textit{model misspecification}, in which results
obtained with Bayesian inference are misleading because of deficiencies in the
assumed model(s). Such deficiencies can impede our inferences of the true
parameters describing physical systems. They can also reduce our ability to
distinguish the "best fitting" model: it can be misleading to say that Model~A
is preferred over Model~B if both models are manifestly poor descriptions of
reality. Broadly speaking, there are two ways in which models fail: models that
fail to adequately describe the data (either the signal or the noise) have
misspecified likelihoods. Population models -- designed, for example, to
describe the distribution of black hole masses -- may fail to adequately
describe the true population due to a misspecified prior. We recommend tests
and checks that are useful for spotting misspecified models using examples
inspired by gravitational-wave astronomy. We include companion python notebooks
to illustrate essential concepts.


title: The CYGNO Experiment

abstract:
  The search for a novel technology able to detect and reconstruct nuclear and
electron recoil events with the energy of a few keV has become more and more
important now that large regions of high-mass dark matter (DM) candidates have
been excluded. Moreover, a detector sensitive to incoming particle direction
will be crucial in the case of DM discovery to open the possibility of studying
its properties. Gaseous time projection chambers (TPC) with optical readout are
very promising detectors combining the detailed event information provided by
the TPC technique with the high sensitivity and granularity of
latest-generation scientific light sensors. The CYGNO experiment (a CYGNus
module with Optical readout) aims to exploit the optical readout approach of
multiple-GEM structures in large volume TPCs for the study of rare events as
interactions of low-mass DM or solar neutrinos. The combined use of
high-granularity sCMOS cameras and fast light sensors allows the reconstruction
of the 3D direction of the tracks, offering good energy resolution and very
high sensitivity in the few keV energy range, together with a very good
particle identification useful for distinguishing nuclear recoils from
electronic recoils. This experiment is part of the CYGNUS proto-collaboration,
which aims at constructing a network of underground observatories for
directional DM search. A one cubic meter demonstrator is expected to be built
in 2022/23 aiming at a larger scale apparatus (30 m$^3$--100 m$^3$) at a later
stage.


title:
Concurrent Training of a Control Policy and a State Estimator for
  Dynamic and Robust Legged Locomotion

abstract:
  In this paper, we propose a locomotion training framework where a control
policy and a state estimator are trained concurrently. The framework consists
of a policy network which outputs the desired joint positions and a state
estimation network which outputs estimates of the robot's states such as the
base linear velocity, foot height, and contact probability. We exploit a fast
simulation environment to train the networks and the trained networks are
transferred to the real robot. The trained policy and state estimator are
capable of traversing diverse terrains such as a hill, slippery plate, and
bumpy road. We also demonstrate that the learned policy can run at up to 3.75
m/s on normal flat ground and 3.54 m/s on a slippery plate with the coefficient
of friction of 0.22.


title:
Is the black-widow pulsar PSR J1555-2908 in a hierarchical triple
  system?

abstract:
  The 559 Hz black-widow pulsar PSR J1555-2908, originally discovered in radio,
is also a bright gamma-ray pulsar. Timing its pulsations using 12 yr of
Fermi-LAT gamma-ray data reveals long-term variations in its spin frequency
that are much larger than is observed from other millisecond pulsars. While
this variability in the pulsar rotation rate could be intrinsic "timing noise",
here we consider an alternative explanation: the variations arise from the
presence of a very-low-mass third object in a wide multi-year orbit around the
neutron star and its low-mass companion. With current data, this
hierarchical-triple-system model describes the pulsar's rotation slightly more
accurately than the best-fitting timing-noise model. Future observations will
show if this alternative explanation is correct.


title: Parametrization of the nuclear structure function

abstract:
  In this paper, the parametrization of the nuclear structure function which is
directly constrained by the dynamics of QCD in its high-energy limit is
considered. This simple parameterization of the nuclear structure function is
obtained from the proton experimental data by relying on a Froissart-bounded
parametrization of the proton structure function. This phenomenological model
describes high-energy QCD in the presence of saturation effects. In the region
of small $x$, the effect of nuclear shadowing manifests itself as an inequality
$F_{2}^{A}/AF^{p}_{2}<1$ and satisfying geometrical scaling at very small $x$.
The magnitude of nuclear shadowing is predicted for various kinematic regions
and can be applied as well in analysis of ultra-high energy processes by future
experiments at electron-ion colliders. Numerical calculations and comparison
with available data from NMC, EMC and E665 Collaborations demonstrate that the
suggested method by N.Armesto, C.A.Salgado and U.A. Wiedemann (ASW model)
provides reliable ratio of nuclear structure functions $F_{2}^{A}/AF^{p}_{2}$
at low $x$ for light and heavy nuclei.


title:
Strong core and Pareto-optimal solutions for the multiple partners
  matching problem under lexicographic preferences

abstract:
  In a multiple partners matching problem the agents can have multiple partners
up to their capacities. In this paper we consider both the two-sided
many-to-many stable matching problem and the one-sided stable fixtures problem
under lexicographic preferences. We study strong core and Pareto-optimal
solutions for this setting from a computational point of view. First we provide
an example to show that the strong core can be empty even under these severe
restrictions for many-to-many problems, and that deciding the non-emptiness of
the strong core is NP-hard. We also show that for a given matching checking
Pareto-optimality and the strong core properties are co-NP-complete problems
for the many-to-many problem, and deciding the existence of a complete
Pareto-optimal matching is also NP-hard for the fixtures problem. On the
positive side, we give efficient algorithms for finding a near feasible strong
core solution, where the capacities are only violated by at most one unit for
each agent, and also for finding a half-matching in the strong core of
fractional matchings. These polynomial time algorithms are based on the Top
Trading Cycle algorithm. Finally, we also show that finding a maximum size
matching that is Pareto-optimal can be done efficiently for many-to-many
problems, which is in contrast with the hardness result for the fixtures
problem.


title:
Fitting Sparse Markov Models to Categorical Time Series Using
  Regularization

abstract:
  The major problem of fitting a higher order Markov model is the exponentially
growing number of parameters. The most popular approach is to use a Variable
Length Markov Chain (VLMC), which determines relevant contexts (recent pasts)
of variable orders and form a context tree. A more general approach is called
Sparse Markov Model (SMM), where all possible histories of order $m$ form a
partition so that the transition probability vectors are identical for the
histories belonging to a particular group. We develop an elegant method of
fitting SMM using convex clustering, which involves regularization. The
regularization parameter is selected using BIC criterion. Theoretical results
demonstrate the model selection consistency of our method for large sample
size. Extensive simulation studies under different set-up have been presented
to measure the performance of our method. We apply this method to classify
genome sequences, obtained from individuals affected by different viruses.


title: On the conjugates of Christoffel words

abstract:
  We introduce a parametrization of the conjugates of Christoffel words based
on the integer Ostrowski numeration system. We use it to give a precise
description of the borders (prefixes which are also suffixes) of the conjugates
of Christoffel words and to revisit the notion of Sturmian graph introduced by
Epifanio et al.


title:
Kevin: de Bruijn-based topology with demand-aware links and greedy
  routing

abstract:
  We propose Kevin, a novel demand-aware reconfigurable rack-to-rack datacenter
network realized with a simple and efficient control plane. In particular,
Kevin makes effective use of the network capacity by supporting integrated and
multi-hop routing as well as work-conserving scheduling. To this end, Kevin
relies on local greedy routing with small forwarding tables which require local
updates only during topological reconfigurations, making this approach ideal
for dynamic networks. Specifically, Kevin is based on a de Bruijn topology
(using a small number of optical circuit switches) in which static links are
enhanced with opportunistic links.


title:
Noise Augmentation Is All You Need For FGSM Fast Adversarial Training:
  Catastrophic Overfitting And Robust Overfitting Require Different
  Augmentation

abstract:
  Adversarial training (AT) and its variants are the most effective approaches
for obtaining adversarially robust models. A unique characteristic of AT is
that an inner maximization problem needs to be solved repeatedly before the
model weights can be updated, which makes the training slow. FGSM AT
significantly improves its efficiency but it fails when the step size grows.
The SOTA GradAlign makes FGSM AT compatible with a higher step size, however,
its regularization on input gradient makes it 3 to 4 times slower than FGSM AT.
Our proposed NoiseAug removes the extra computation overhead by directly
regularizing on the input itself. The key contribution of this work lies in an
empirical finding that single-step FGSM AT is not as hard as suggested in the
past line of work: noise augmentation is all you need for (FGSM) fast AT.
Towards understanding the success of our NoiseAug, we perform an extensive
analysis and find that mitigating Catastrophic Overfitting (CO) and Robust
Overfitting (RO) need different augmentations. Instead of more samples caused
by data augmentation, we identify what makes NoiseAug effective for preventing
CO might lie in its improved local linearity.


title:
Radiation condition for the 3-dimensional Helmholtz equation on the
  boundary of a bounded domain

abstract:
  In the formulation of the problem of scattering of monochromatic waves and
the numerical simulation of the solution to the Helmholtz equation, there is a
computational inconvenience: the calculation is performed on a finite grid of
discretization nodes of the finite scattering region, while the radiation
conditions for the scattered wave are formulated at the infinitely distant
boundary. Overcoming this inconvenience leads to a new type of boundary
condition: a nonlocal boundary condition (or condition of the 4th kind).


title: Bananas: multi-edge graphs and their Feynman integrals

abstract:
  We consider multi-edge or banana graphs $b_n$ on $n$ internal edges $e_i$
with different masses $m_i$. We focus on the cut banana graphs
$\Im(\Phi_R(b_n))$ from which the full result $\Phi_R(b_n)$ can be derived
through dispersion. We give a recursive definition of $\Im(\Phi_R(b_n))$
through iterated integrals. We discuss the structure of this iterated integral
in detail. A discussion of accompanying differential equations, of monodromy
and of a basis of master integrals is included.


title: Exemplar-free Online Continual Learning

abstract:
  Targeted for real world scenarios, online continual learning aims to learn
new tasks from sequentially available data under the condition that each data
is observed only once by the learner. Though recent works have made remarkable
achievements by storing part of learned task data as exemplars for knowledge
replay, the performance is greatly relied on the size of stored exemplars while
the storage consumption is a significant constraint in continual learning. In
addition, storing exemplars may not always be feasible for certain applications
due to privacy concerns. In this work, we propose a novel exemplar-free method
by leveraging nearest-class-mean (NCM) classifier where the class mean is
estimated during training phase on all data seen so far through online mean
update criteria. We focus on image classification task and conduct extensive
experiments on benchmark datasets including CIFAR-100 and Food-1k. The results
demonstrate that our method without using any exemplar outperforms
state-of-the-art exemplar-based approaches with large margins under standard
protocol (20 exemplars per class) and is able to achieve competitive
performance even with larger exemplar size (100 exemplars per class).


title:
Entroformer: A Transformer-based Entropy Model for Learned Image
  Compression

abstract:
  One critical component in lossy deep image compression is the entropy model,
which predicts the probability distribution of the quantized latent
representation in the encoding and decoding modules. Previous works build
entropy models upon convolutional neural networks which are inefficient in
capturing global dependencies. In this work, we propose a novel
transformer-based entropy model, termed Entroformer, to capture long-range
dependencies in probability distribution estimation effectively and
efficiently. Different from vision transformers in image classification, the
Entroformer is highly optimized for image compression, including a top-k
self-attention and a diamond relative position encoding. Meanwhile, we further
expand this architecture with a parallel bidirectional context model to speed
up the decoding process. The experiments show that the Entroformer achieves
state-of-the-art performance on image compression while being time-efficient.


title: On Grothendieck--Serre conjecture in mixed characteristic for SL_1(D)

abstract:
  Let R be an unramified regular local ring of mixed characteristic, D an
Azumaya R-algebra, K the fraction field of R, Nrd the reduced norm homomorphism
for the Azumaya R-algebra D. Let a be a unit in R. It is proved the following:
suppose the equation Nrd=a has a solution over K, then it has a solution over
R.
  Similar results are proved for regular local rings, which are geometrically
regular over a discrete valuation ring of mixed characteristic. These results
extend result proven by A.Sulin and the author in the middle of 90's.


title: Input-constrained funnel control of nonlinear systems

abstract:
  We study tracking control for uncertain nonlinear multi-input, multi-output
systems modelled by $r$-th order functional differential equations
(encompassing systems with arbitrary strict relative degree) in the presence of
input constraints. The objective is to guarantee the evolution of the tracking
error within a performance funnel with prescribed asymptotic shape (thus
achieving desired transient and asymptotic accuracy objectives), for any
sufficiently smooth reference signal. We design a novel funnel controller
which, in order to satisfy the input constraints, contains a dynamic component
which widens the funnel boundary whenever the input saturation is active. This
design is model-free, of low-complexity and extends earlier funnel control
approaches. We present a simulation where the controller is compared to these
approaches.


title: Inference for Projection-Based Wasserstein Distances on Finite Spaces

abstract:
  The Wasserstein distance is a distance between two probability distributions
and has recently gained increasing popularity in statistics and machine
learning, owing to its attractive properties. One important approach to
extending this distance is using low-dimensional projections of distributions
to avoid a high computational cost and the curse of dimensionality in empirical
estimation, such as the sliced Wasserstein or max-sliced Wasserstein distances.
Despite their practical success in machine learning tasks, the availability of
statistical inferences for projection-based Wasserstein distances is limited
owing to the lack of distributional limit results. In this paper, we consider
distances defined by integrating or maximizing Wasserstein distances between
low-dimensional projections of two probability distributions. Then we derive
limit distributions regarding these distances when the two distributions are
supported on finite points. We also propose a bootstrap procedure to estimate
quantiles of limit distributions from data. This facilitates asymptotically
exact interval estimation and hypothesis testing for these distances. Our
theoretical results are based on the arguments of Sommerfeld and Munk (2018)
for deriving distributional limits regarding the original Wasserstein distance
on finite spaces and the theory of sensitivity analysis in nonlinear
programming. Finally, we conduct numerical experiments to illustrate the
theoretical results and demonstrate the applicability of our inferential
methods to real data analysis.


title:
Ribbon tensor structure on the full representation categories of the
  singlet vertex algebras

abstract:
  We show that the category of finite-length generalized modules for the
singlet vertex algebra $\mathcal{M}(p)$, $p\in\mathbb{Z}_{>1}$, is equal to the
category $\mathcal{O}_{\mathcal{M}(p)}$ of $C_1$-cofinite
$\mathcal{M}(p)$-modules, and that this category admits the vertex algebraic
braided tensor category structure of Huang-Lepowsky-Zhang. Since
$\mathcal{O}_{\mathcal{M}(p)}$ includes the uncountably many typical
$\mathcal{M}(p)$-modules, which are simple $\mathcal{M}(p)$-module structures
on Heisenberg Fock modules, our results substantially extend our previous work
on tensor categories of atypical $\mathcal{M}(p)$-modules. We also introduce a
tensor subcategory $\mathcal{O}_{\mathcal{M}(p)}^T$, graded by an algebraic
torus $T$, which has enough projectives and is conjecturally tensor equivalent
to the category of finite-dimensional weight modules for the unrolled
restricted quantum group of $\mathfrak{sl}_2$ at a $2p$th root of unity. We
compute all tensor products involving simple and projective
$\mathcal{M}(p)$-modules, and we prove that both tensor categories
$\mathcal{O}_{\mathcal{M}(p)}$ and $\mathcal{O}_{\mathcal{M}(p)}^T$ are rigid
and thus also ribbon. As an application, we use vertex operator algebra
extension theory to show that the representation categories of all finite
cyclic orbifolds of the triplet vertex algebras $\mathcal{W}(p)$ are
non-semisimple modular tensor categories, and we confirm a conjecture of
Adamovi\'{c}-Lin-Milas on the classification of simple modules for these finite
cyclic orbifolds.


title:
Temporal evolution of the Covid19 pandemic reproduction number:
  Estimations from proximal optimization to Monte Carlo sampling

abstract:
  Monitoring the evolution of the Covid19 pandemic constitutes a critical step
in sanitary policy design. Yet, the assessment of the pandemic intensity within
the pandemic period remains a challenging task because of the limited quality
of data made available by public health authorities (missing data, outliers and
pseudoseasonalities, notably), that calls for cumbersome and ad-hoc
preprocessing (denoising) prior to estimation. Recently, the estimation of the
reproduction number, a measure of the pandemic intensity, was formulated as an
inverse problem, combining data-model fidelity and space-time regularity
constraints, solved by nonsmooth convex proximal minimizations. Though
promising, that formulation lacks robustness against the limited quality of the
Covid19 data and confidence assessment. The present work aims to address both
limitations: First, it discusses solutions to produce a robust assessment of
the pandemic intensity by accounting for the low quality of the data directly
within the inverse problem formulation. Second, exploiting a Bayesian
interpretation of the inverse problem formulation, it devises a Monte Carlo
sampling strategy, tailored to a nonsmooth log-concave a posteriori
distribution, to produce relevant credibility intervalbased estimates for the
Covid19 reproduction number. Clinical relevance Applied to daily counts of new
infections made publicly available by the Health Authorities for around 200
countries, the proposed procedures permit robust assessments of the time
evolution of the Covid19 pandemic intensity, updated automatically and on a
daily basis.


title:
Fast and Robust Sparsity Learning over Networks: A Decentralized
  Surrogate Median Regression Approach

abstract:
  Decentralized sparsity learning has attracted a significant amount of
attention recently due to its rapidly growing applications. To obtain the
robust and sparse estimators, a natural idea is to adopt the non-smooth median
loss combined with a $\ell_1$ sparsity regularizer. However, most of the
existing methods suffer from slow convergence performance caused by the {\em
double} non-smooth objective. To accelerate the computation, in this paper, we
proposed a decentralized surrogate median regression (deSMR) method for
efficiently solving the decentralized sparsity learning problem. We show that
our proposed algorithm enjoys a linear convergence rate with a simple
implementation. We also investigate the statistical guarantee, and it shows
that our proposed estimator achieves a near-oracle convergence rate without any
restriction on the number of network nodes. Moreover, we establish the
theoretical results for sparse support recovery. Thorough numerical experiments
and real data study are provided to demonstrate the effectiveness of our
method.