title:
A Quantum Polynomial-Time Solution to The Dihedral Hidden Subgroup
  Problem

abstract:
  We present a polynomial-time quantum algorithm for the Hidden Subgroup
Problem over $\mathbb{D}_{2^n}$. The usual approach to the Hidden Subgroup
Problem relies on harmonic analysis in the domain of the problem, and the best
known algorithm using this approach has time complexity in
$2^{\mathcal{O}(\sqrt{n})}$. By focusing on structure encoded in the codomain
of the problem, we develop a polynomial-time algorithm which uses this
structure to direct a "walk" down the subgroup lattice of $\mathbb{D}_{2^n}$
terminating at the hidden subgroup.


title:
Analyzing Adaptive Scaffolds that Help Students Develop Self-Regulated
  Learning Behaviors

abstract:
  Providing adaptive scaffolds to help learners develop self-regulated learning
(SRL) processes has been an important goal for intelligent learning
environments. In this paper, we develop a systematic framework for adaptive
scaffolding in Betty's Brain, an open-ended learning-by-teaching environment
that helps middle school students learn science by constructing a causal model
to teach a virtual agent, generically named Betty. Given the open ended nature
of the environment, novice learners often face difficulties in their learning
and teaching tasks. We detect key cognitive-metacognitive inflection points,
i.e., instances where students' behaviors and performance change as they work
on their learning and teaching tasks. At such inflection points, Mr. Davis (a
mentor agent) or Betty (the teachable agent) provide conversational feedback,
focused on strategies to help students become productive learners. We analyze
data collected from a classroom study with 98 middle school students to analyze
the impact of the scaffolds on students' learning performance and behaviors. We
discuss how our findings will support the next iteration of our adaptive
scaffolding framework to help students develop their SRL behaviors when working
in OELEs.


title: Selective Credit Assignment

abstract:
  Efficient credit assignment is essential for reinforcement learning
algorithms in both prediction and control settings. We describe a unified view
on temporal-difference algorithms for selective credit assignment. These
selective algorithms apply weightings to quantify the contribution of learning
updates. We present insights into applying weightings to value-based learning
and planning algorithms, and describe their role in mediating the backward
credit distribution in prediction and control. Within this space, we identify
some existing online learning algorithms that can assign credit selectively as
special cases, as well as add new algorithms that assign credit backward in
time counterfactually, allowing credit to be assigned off-trajectory and
off-policy.


title: On Matrix Method of Symmetric Games

abstract:
  This paper provides a new version of matrix semi-tensor product method based
on adjacent transpositions to test symmetric games. The advantage of using
adjacent transpositions lies in the great simplification of analysis of
symmetric games. By using the new method, new necessary and sufficient
conditions for symmetric games are proposed, and a group of bases of a
symmetric game space can be easily calculated. Moreover, the testing equations
with the minimum number can be concretely determined. Finally, two examples are
displayed to show the effectiveness of the proposed method.


title: A History of Meta-gradient: Gradient Methods for Meta-learning

abstract:
  The history of meta-learning methods based on gradient descent is reviewed,
focusing primarily on methods that adapt step-size (learning rate)
meta-parameters.


title: Tachibana-type theorems on complete manifolds

abstract:
  We prove that a compact Riemannian manifold of dimension $m \geq 3$ with
harmonic curvature and $\lfloor\frac{m-1}{2}\rfloor$-positive curvature
operator has constant sectional curvature, extending the classical Tachibana
theorem for manifolds with positive curvature operator. The condition of
$\lfloor\frac{m-1}{2}\rfloor$-positivity originates from recent work of
Petersen and Wink, who proved a similar Tachibana-type theorem under the
stronger condition that the manifold be Einstein. We show that the same
rigidity property holds for complete manifolds assuming either parabolicity, an
integral bound on the Weyl tensor or a stronger pointwise positive lower bound
on the average of the first $\lfloor\frac{m-1}{2}\rfloor$ eigenvalues of the
curvature operator. For 3-manifolds, we show that positivity of the curvature
operator can be relaxed to positivity of the Ricci tensor.


title: Model-Based Reconstruction for Collimated Beam Ultrasound Systems

abstract:
  Collimated beam ultrasound systems are a novel technology for imaging inside
multi-layered structures such as geothermal wells. Such systems include a
transmitter and multiple receivers to capture reflected signals. Common
algorithms for ultrasound reconstruction use delay-and-sum (DAS) approaches;
these have low computational complexity but produce inaccurate images in the
presence of complex structures and specialized geometries such as collimated
beams.
  In this paper, we propose a multi-layer, ultrasonic, model-based iterative
reconstruction algorithm designed for collimated beam systems. We introduce a
physics-based forward model to accurately account for the propagation of a
collimated ultrasonic beam in multi-layer media and describe an efficient
implementation using binary search. We model direct arrival signals, detector
noise, and a spatially varying image prior, then cast the reconstruction as a
maximum a posteriori estimation problem. Using simulated and experimental data
we obtain significantly fewer artifacts relative to DAS while running in near
real time using commodity compute resources.


title: MANet: Improving Video Denoising with a Multi-Alignment Network

abstract:
  In video denoising, the adjacent frames often provide very useful
information, but accurate alignment is needed before such information can be
harnassed. In this work, we present a multi-alignment network, which generates
multiple flow proposals followed by attention-based averaging. It serves to
mimics the non-local mechanism, suppressing noise by averaging multiple
observations. Our approach can be applied to various state-of-the-art models
that are based on flow estimation. Experiments on a large-scale video dataset
demonstrate that our method improves the denoising baseline model by 0.2dB, and
further reduces the parameters by 47% with model distillation.


title:
The minimal size of a generating set for primitive
  $\frac{3}{2}$-transitive groups

abstract:
  We refer to $d(G)$ as the minimal cardinality of a generating set of a finite
group $G$, and say that $G$ is $d$-generated if $d(G)\leq d$. A transitive
permutation group $G$ is called $\frac{3}{2}$-transitive if a point stabilizer
$G_\alpha$ is nontrivial and its orbits distinct from $\{\alpha\}$ are of the
same size. We prove that $d(G)\leq4$ for every primitive
$\frac{3}{2}$-transitive permutation group $G$, moreover, $G$ is $2$-generated
except for the very particular solvable affine groups that we completely
describe. In particular, all finite $2$-transitive and $2$-homogeneous groups
are $2$-generated. We also show that every finite group whose abelian subgroups
are cyclic is $2$-generated, and so is every Frobenius complement.


title:
Mushroom-instability-driven Magnetic Reconnections in Collisionless
  Relativistic Jets

abstract:
  We study the kinetic plasma dynamics in collisionless relativistic jets with
velocity shear, by carrying out particle-in-cell simulations in the transverse
plane of a jet. It is discovered that intermittent magnetic reconnections (MRs)
are driven by Mushroom instability (MI), which is an important kinetic-scale
plasma instability in the plasma shear-flows with relativistic bulk speed. We
refer to this sequence of kinetic plasma phenomena as "MI-driven MR". The
MI-driven MRs intermittently occur with moving the location of the reconnection
points from the vicinity of the initial velocity-shear surface towards the
center of the jet. As a consequence, the number density of high energy
electrons, which are accelerated by MI-driven MRs, increases with time in the
region inside the initial velocity-shear surface with accompanying the
generation and subsequent amplification of magnetic fields by MI. The maximum
Lorentz factor of electrons increases with initial bulk Lorentz factor of the
jet. A possible relation of MI-driven MR to the bright synchrotron emission in
jet-spine of active galactic nucleus jets is also discussed.


title:
Lie symmetries, Jacobi last multipliers and new non-standard Lagrangians
  for dissipative dynamical systems

abstract:
  We present a new method based on Lie symmetries and Jacobi last multipliers
which allows one to find many non-standard Lagrangians for dissipative
dynamical systems. In particular, it is demonstrated that for every
non-standard Lagrangian one can generate a new non-standard Lagrangian
associated to a new equation of motion. We point out that the knowledge of Lie
symmetries for a given dynamical system generates Jacobi last multipliers which
can be used to obtain new non-standard Lagrangians for dissipative dynamical
systems in a simple and straightforward way. We exemplify the new method by
applying it to the case of the free particle and the simple harmonic oscillator
in order to obtain new non-standard Lagrangians for dissipative systems.


title:
Statistical and Topological Summaries Aid Disease Detection for
  Segmented Retinal Vascular Images

abstract:
  Disease complications can alter vascular network morphology and disrupt
tissue functioning. Diabetic retinopathy, for example, is a complication of
type 1 and 2 diabetus mellitus that can cause blindness. Microvascular diseases
are assessed by visual inspection of retinal images, but this can be
challenging when diseases exhibit silent symptoms or patients cannot attend
in-person meetings. We examine the performance of machine learning algorithms
in detecting microvascular disease when trained on either statistical or
topological summaries of segmented retinal vascular images. We apply our
methods to four publicly-available datasets and find that the fractal dimension
performs best for high resolution images. By contrast, we find that topological
descriptor vectors quantifying the number of loops in the data achieve the
highest accuracy for low resolution images. Further analysis, using the
topological approach, reveals that microvascular disease may alter morphology
by reducing the number of loops in the retinal vasculature. Our work provides
preliminary guidelines on which methods are most appropriate for assessing
disease in high and low resolution images. In the longer term, these methods
could be incorporated into automated disease assessment tools.


title: Delay-line based adiabatic spin-dependent kicks on a hyperfine manifold

abstract:
  High speed control of spinor matterwaves is instrumental to atom
interferometry and ion-based quantum information processing. In this work, we
extend the Raman adiabatic spin-dependent kick (SDK) technique into the
nanosecond regime. Counter-propagating frequency-chirped laser pulses are
programmed on an optical delay line to parallelly drive five $\Delta m=0$
hyperfine Raman transition of $^{85}$Rb atoms within $\tau=40$~nanoseconds. An
average SDK fidelity of $f_{\rm SDK}\approx 97.6\%$ is inferred from
spin-dependent momentum transfer and Raman population measurements, combined
with precise numerical modeling. At such a high speed, coherent spin leakage is
driven by the weakly allowed $\Delta m=\pm 2$ transitions. We theoretically
investigate the intricate dynamics to demonstrate that the leakage can be
substantially suppressed by a chirp-alternating SDK sequence with precisely
cancelled dynamic phases. The technique should thus enable high fidelity,
parallel control of multi-Zeeman spinor matterwave within nanoseconds, for
various quantum technological applications.


title: Runtime-Assured, Real-Time Neural Control of Microgrids

abstract:
  We present SimpleMG, a new, provably correct design methodology for runtime
assurance of microgrids (MGs) with neural controllers. Our approach is centered
around the Neural Simplex Architecture, which in turn is based on Sha et al.'s
Simplex Control Architecture. Reinforcement Learning is used to synthesize
high-performance neural controllers for MGs. Barrier Certificates are used to
establish SimpleMG's runtime-assurance guarantees. We present a novel method to
derive the condition for switching from the unverified neural controller to the
verified-safe baseline controller, and we prove that the method is correct. We
conduct an extensive experimental evaluation of SimpleMG using RTDS, a
high-fidelity, real-time simulation environment for power systems, on a
realistic model of a microgrid comprising three distributed energy resources
(battery, photovoltaic, and diesel generator). Our experiments confirm that
SimpleMG can be used to develop high-performance neural controllers for complex
microgrids while assuring runtime safety, even in the presence of adversarial
input attacks on the neural controller. Our experiments also demonstrate the
benefits of online retraining of the neural controller while the baseline
controller is in control


title:
Compact polarized X-ray source based on all-optical inverse Compton
  scattering

abstract:
  Polarized X-ray source is an important probe for many fields such as
fluorescence imaging, magnetic microscopy, and nuclear physics research.
All-optical inverse Compton scattering source (AOCS) based on laser wakefield
accelerator (LWFA) has drawn great attention in recent years due to its compact
scale and high performance, especially its potential to generate polarized
X-rays. Here, polarization-tunable X-rays are generated by a
plasma-mirror-based AOCS scheme. The linearly and circularly polarized AOCS
pulses are achieved with the mean photon energy of 60($\pm$5)/64($\pm$3) keV
and the single-shot photon yield of $\sim$1.1/1.3$\times10^7$. A Compton
polarimeter is designed to diagnose the photon polarization states,
demonstrating AOCS's polarization-tunable property, and indicating the average
polarization degree of the linearly polarized AOCS is 75($\pm$3)%.


title:
Physics-informed neural networks for learning the homogenized
  coefficients of multiscale elliptic equations

abstract:
  Multiscale elliptic equations with scale separation are often approximated by
the corresponding homogenized equations with slowly varying homogenized
coefficients (the G-limit). The traditional homogenization techniques typically
rely on the periodicity of the multiscale coefficients, thus finding the
G-limits often requires sophisticated techniques in more general settings even
when multiscale coefficient is known, if possible. Alternatively, we propose a
simple approach to estimate the G-limits from (noisy-free or noisy) multiscale
solution data, either from the existing forward multiscale solvers or sensor
measurements. By casting this problem into an inverse problem, our approach
adopts physics-informed neural networks (PINNs) algorithm to estimate the
G-limits from the multiscale solution data by leveraging a priori knowledge of
the underlying homogenized equations. Unlike the existing approaches, our
approach does not rely on the periodicity assumption or the known multiscale
coefficient during the learning stage, allowing us to estimate homogenized
coefficients in more general settings beyond the periodic setting. We
demonstrate that the proposed approach can deliver reasonable and accurate
approximations to the G-limits as well as homogenized solutions through several
benchmark problems.


title:
Curvature-Controlled Geometrical Lensing Behavior in Self-Propelled
  Colloidal Particle Systems

abstract:
  In many biological systems, the curvature of the surfaces cells live on
influence their collective properties. Curvature should likewise influence the
behavior of active colloidal particles. We show using molecular simulation of
self-propelled active particles on surfaces of Gaussian curvature (both
positive and negative) that curvature sign and magnitude can alter the system's
collective behavior. Curvature acts as a geometrical lens and shifts the
critical density of motility-induced phase separation (MIPS) to lower values
for positive curvature and higher values for negative curvature, which we
explain theoretically by the nature of parallel lines in spherical and
hyperbolic space. Curvature also fluidizes dense MIPS clusters due to the
emergence of defect patterns disrupting the crystalline order inside the
clusters. Using our findings, we engineer three confining surfaces that
strategically combine regions of different curvature to produce a host of novel
dynamic phases, including cyclic MIPS on sphercylinders, wave-like MIPS on
spherocones, and cluster fluctuations on metaballs.


title:
Differentiable Robotic Manipulation of Deformable Rope-like Objects
  Using Compliant Position-based Dynamics

abstract:
  Robot manipulation of rope-like objects is an interesting problem that has
some critical applications, such as autonomous robotic suturing. Solving for
and controlling rope is difficult due to the complexity of rope physics and the
challenge of building fast and accurate models of deformable materials. While
more data-driven approaches have become more popular for finding controllers
that learn to do a single task, there is still a strong motivation for a
model-based method that could be used to solve a large variety of optimization
problems. Towards this end, we introduced compliant, position-based dynamics
(XPBD) to model rope-like objects. Using geometric constraints, the model can
represent the coupling of shear/stretch and bend/twist effects. Of crucial
importance is that our formulation is differentiable, which can solve parameter
estimation problems and improve the matching of rope physics to real-life
scenarios (i.e., the real-to-sim problem). For the generality of rope-like
objects, two different solvers are proposed to handle the inextensible and
extensible effects of varied material stiffness for the rope. We demonstrate
our framework's robustness and accuracy on real-to-sim experimental setups
using the Baxter robot and the da Vinci research kit (DVRK). Our work leads to
a new path for robotic manipulation of the deformable rope-like object taking
advantage of the ready-to-use gradients.


title: ARM3D: Attention-based relation module for indoor 3D object detection

abstract:
  Relation context has been proved to be useful for many challenging vision
tasks. In the field of 3D object detection, previous methods have been taking
the advantage of context encoding, graph embedding, or explicit relation
reasoning to extract relation context. However, there exists inevitably
redundant relation context due to noisy or low-quality proposals. In fact,
invalid relation context usually indicates underlying scene misunderstanding
and ambiguity, which may, on the contrary, reduce the performance in complex
scenes. Inspired by recent attention mechanism like Transformer, we propose a
novel 3D attention-based relation module (ARM3D). It encompasses object-aware
relation reasoning to extract pair-wise relation contexts among qualified
proposals and an attention module to distribute attention weights towards
different relation contexts. In this way, ARM3D can take full advantage of the
useful relation context and filter those less relevant or even confusing
contexts, which mitigates the ambiguity in detection. We have evaluated the
effectiveness of ARM3D by plugging it into several state-of-the-art 3D object
detectors and showing more accurate and robust detection results. Extensive
experiments show the capability and generalization of ARM3D on 3D object
detection. Our source code is available at https://github.com/lanlan96/ARM3D.


title:
Towards a Unified Approach to Homography Estimation Using Image Features
  and Pixel Intensities

abstract:
  The homography matrix is a key component in various vision-based robotic
tasks. Traditionally, homography estimation algorithms are classified into
feature- or intensity-based. The main advantages of the latter are their
versatility, accuracy, and robustness to arbitrary illumination changes. On the
other hand, they have a smaller domain of convergence than the feature-based
solutions. Their combination is hence promising, but existing techniques only
apply them sequentially. This paper proposes a new hybrid method that unifies
both classes into a single nonlinear optimization procedure, applies the same
minimization method, and uses the same homography parametrization and warping
function. Experimental validation using a classical testing framework shows
that the proposed unified approach has improved convergence properties compared
to each individual class. These are also demonstrated in a visual tracking
application. As a final contribution, our ready-to-use implementation of the
algorithm is made publicly available to the research community.


title: Understanding Robust Generalization in Learning Regular Languages

abstract:
  A key feature of human intelligence is the ability to generalize beyond the
training distribution, for instance, parsing longer sentences than seen in the
past. Currently, deep neural networks struggle to generalize robustly to such
shifts in the data distribution. We study robust generalization in the context
of using recurrent neural networks (RNNs) to learn regular languages. We
hypothesize that standard end-to-end modeling strategies cannot generalize well
to systematic distribution shifts and propose a compositional strategy to
address this. We compare an end-to-end strategy that maps strings to labels
with a compositional strategy that predicts the structure of the deterministic
finite-state automaton (DFA) that accepts the regular language. We
theoretically prove that the compositional strategy generalizes significantly
better than the end-to-end strategy. In our experiments, we implement the
compositional strategy via an auxiliary task where the goal is to predict the
intermediate states visited by the DFA when parsing a string. Our empirical
results support our hypothesis, showing that auxiliary tasks can enable robust
generalization. Interestingly, the end-to-end RNN generalizes significantly
better than the theoretical lower bound, suggesting that it is able to achieve
at least some degree of robust generalization.


title: Finding shortest non-separating and non-disconnecting paths

abstract:
  For a connected graph $G = (V, E)$ and $s, t \in V$, a non-separating $s$-$t$
path is a path $P$ between $s$ and $t$ such that the set of vertices of $P$
does not separate $G$, that is, $G - V(P)$ is connected. An $s$-$t$ path is
non-disconnecting if $G - E(P)$ is connected. The problems of finding shortest
non-separating and non-disconnecting paths are both known to be NP-hard. In
this paper, we consider the problems from the viewpoint of parameterized
complexity. We show that the problem of finding a non-separating $s$-$t$ path
of length at most $k$ is W[1]-hard parameterized by $k$, while the
non-disconnecting counterpart is fixed-parameter tractable parameterized by
$k$. We also consider the shortest non-separating path problem on several
classes of graphs and show that this problem is NP-hard even on bipartite
graphs, split graphs, and planar graphs. As for positive results, the shortest
non-separating path problem is fixed-parameter tractable parameterized by $k$
on planar graphs and polynomial-time solvable on chordal graphs if $k$ is the
shortest path distance between $s$ and $t$.


title: Analytic continuation from limited noisy Matsubara data

abstract:
  This note proposes a new algorithm for estimating spectral function from
limited noisy Matsubara data. We consider both the molecule and condensed
matter cases. In each case, the algorithm constructs an interpolant of the
Matsubara data and uses conformal mapping and Prony's method to estimate the
spectral function. Numerical results are provided to demonstrate the
performance of the algorithm.


title: Imaginary reflections and discrete symmetries in the heterotic Monster

abstract:
  Let $\mathbb{M}$ be the Monster finite simple group. We give an
interpretation of certain discrete symmetries of a family of heterotic string
compactifications to $1 + 1$ dimensions in terms of discrete symmetries of the
Monster Lie algebra $\frak m$, and more generally Carnahan's family of
Monstrous Lie algebras $\frak m_g$, for $g\in\mathbb{M}$ of Fricke type. We
relate a Weyl group-type reflection $w_{\im}$, with respect to an imaginary
simple root, to a composition of T-duality, time reversal, and parity reversal
transformations in the compactified heterotic string. The transformation
$w_{\im}$ also has a natural permutation action on the BPS states of the
compactified heterotic string.


title: 3DRM:Pair-wise relation module for 3D object detection

abstract:
  Context has proven to be one of the most important factors in object layout
reasoning for 3D scene understanding. Existing deep contextual models either
learn holistic features for context encoding or rely on pre-defined scene
templates for context modeling. We argue that scene understanding benefits from
object relation reasoning, which is capable of mitigating the ambiguity of 3D
object detections and thus helps locate and classify the 3D objects more
accurately and robustly. To achieve this, we propose a novel 3D relation module
(3DRM) which reasons about object relations at pair-wise levels. The 3DRM
predicts the semantic and spatial relationships between objects and extracts
the object-wise relation features. We demonstrate the effects of 3DRM by
plugging it into proposal-based and voting-based 3D object detection pipelines,
respectively. Extensive evaluations show the effectiveness and generalization
of 3DRM on 3D object detection. Our source code is available at
https://github.com/lanlan96/3DRM.


title:
PooL: Pheromone-inspired Communication Framework forLarge Scale
  Multi-Agent Reinforcement Learning

abstract:
  Being difficult to scale poses great problems in multi-agent coordination.
Multi-agent Reinforcement Learning (MARL) algorithms applied in small-scale
multi-agent systems are hard to extend to large-scale ones because the latter
is far more dynamic and the number of interactions increases exponentially with
the growing number of agents. Some swarm intelligence algorithms simulate the
release and utilization mechanism of pheromones to control large-scale agent
coordination. Inspired by such algorithms, \textbf{PooL}, an
\textbf{p}her\textbf{o}m\textbf{o}ne-based indirect communication framework
applied to large scale multi-agent reinforcement \textbf{l}earning is proposed
in order to solve the large-scale multi-agent coordination problem. Pheromones
released by agents of PooL are defined as outputs of most reinforcement
learning algorithms, which reflect agents' views of the current environment.
The pheromone update mechanism can efficiently organize the information of all
agents and simplify the complex interactions among agents into low-dimensional
representations. Pheromones perceived by agents can be regarded as a summary of
the views of nearby agents which can better reflect the real situation of the
environment. Q-Learning is taken as our base model to implement PooL and PooL
is evaluated in various large-scale cooperative environments. Experiments show
agents can capture effective information through PooL and achieve higher
rewards than other state-of-arts methods with lower communication costs.


title:
Smooth multi-period forecasting with application to prediction of
  COVID-19 cases

abstract:
  Forecasting methodologies have always attracted a lot of attention and have
become an especially hot topic since the beginning of the COVID-19 pandemic. In
this paper we consider the problem of multi-period forecasting that aims to
predict several horizons at once. We propose a novel approach that forces the
prediction to be "smooth" across horizons and apply it to two tasks: point
estimation via regression and interval prediction via quantile regression. This
methodology was developed for real-time distributed COVID-19 forecasting. We
illustrate the proposed technique with the CovidCast dataset as well as a small
simulation example.


title: Bayes-Optimal Classifiers under Group Fairness

abstract:
  Machine learning algorithms are becoming integrated into more and more
high-stakes decision-making processes, such as in social welfare issues. Due to
the need of mitigating the potentially disparate impacts from algorithmic
predictions, many approaches have been proposed in the emerging area of fair
machine learning. However, the fundamental problem of characterizing
Bayes-optimal classifiers under various group fairness constraints has only
been investigated in some special cases. Based on the classical Neyman-Pearson
argument (Neyman and Pearson, 1933; Shao, 2003) for optimal hypothesis testing,
this paper provides a unified framework for deriving Bayes-optimal classifiers
under group fairness. This enables us to propose a group-based thresholding
method that can directly control disparity, and more importantly, achieve an
optimal fairness-accuracy tradeoff. These advantages are supported by
experiments.


title:
Generalized nanoscale electromagnetic boundary conditions and
  interfacial photonics

abstract:
  Classical electromagnetic boundary conditions (EMBCs) fail to describe
quantum interface phenomena at nanoscale. Here, we construct the interface
model with a transition layer describing the electromagnetic field
inhomogeneity across the interface. Generalized nanoscale EMBCs are derived by
introducing the magnetic interfacial response functions (IRFs) and are
rewritten as three different forms based on Maxwell's equations in first order
approximation. The corresponding Fresnel formula are further used to analyze
the interfacial photonic phenomenon, demonstrating interesting behaviors of
Brewster angle shifting, non-extinction at Brewster angle and distinctive
non-classical absorption or gain effect at Brewster angle and the total
internal reflection angles. IRFs-controlled GH-shifts of Gaussian beam near
Brewster angle are generated by the non-classical interface. These unique
phenomena give us some guidance to measure the IRFs and expand interface
photonics in nanoscale.


title:
A path to precision cosmology: Synergy between four promising
  late-universe cosmological probes

abstract:
  In the next decades, it is necessary to forge new late-universe cosmological
probes to precisely constrain the Hubble constant and the equation of state of
dark energy simultaneously. In this work, we show that the four typical
late-universe cosmological probes, the 21 cm intensity mapping (IM), fast radio
burst (FRB), gravitational wave (GW) standard siren, and strong gravitational
lensing (SGL), are expected to be forged into useful tools in solving the
Hubble tension and exploring dark energy. We propose that the synergy of them
is rather important in cosmology. We simulate the 21 cm IM, FRB, GW, and SGL
data based on the hypothetical observations of the Hydrogen Intensity and
Real-time Analysis eXperiment (HIRAX), the Square Kilometre Array (SKA), the
Einstein Telescope (ET), and the Large Synoptic Survey Telescope (LSST),
respectively. We find that the four probes show obviously different parameter
degeneracy orientations in cosmological constraints, so any combination of them
can break the parameter degeneracies and thus significantly improve the
constraint precision. The joint 21 cm IM+FRB+GW+SGL data can provide the
constraint errors of $\sigma(\Omega_{\rm m})=0.0022$ and $\sigma(H_0)=0.16\ \rm
km\ s^{-1}\ Mpc^{-1}$ in the $\Lambda$CDM model, which meet the standard of
precision cosmology, i.e., the constraint precision of parameters is better
than 1%. In addition, the joint data give $\sigma(w)=0.020$ in the $w$CDM
model, and $\sigma(w_0)=0.066$ and $\sigma(w_a)=0.25$ in the $w_0w_a$CDM model,
which are all better than the constraints obtained by the CMB+BAO+SN data. We
show that the synergy between the four late-universe cosmological probes has
magnificent prospects.


title: Online Platforms and the Fair Exposure Problem Under Homophily

abstract:
  In the wake of increasing political extremism, online platforms have been
criticized for contributing to polarization. One line of criticism has focused
on echo chambers and the recommended content served to users by these
platforms. In this work, we introduce the fair exposure problem: given limited
intervention power of the platform, the goal is to enforce balance in the
spread of content (e.g., news articles) among two groups of users through
constraints similar to those imposed by the Fairness Doctrine in the United
States in the past. Groups are characterized by different affiliations (e.g.,
political views) and have different preferences for content. We develop a
stylized framework that models intra- and inter-group content propagation under
homophily, and we formulate the platform's decision as an optimization problem
that aims at maximizing user engagement, potentially under fairness
constraints. Our main notion of fairness requires that each group see a mixture
of their preferred and non-preferred content, encouraging information
diversity. Promoting such information diversity is often viewed as desirable
and a potential means for breaking out of harmful echo chambers. We study the
solutions to both the fairness-agnostic and fairness-aware problems. We prove
that a fairness-agnostic approach inevitably leads to group-homogeneous
targeting by the platform. This is only partially mitigated by imposing
fairness constraints: we show that there exist optimal fairness-aware solutions
which target one group with different types of content and the other group with
only one type that is not necessarily the group's most preferred. Finally,
using simulations with real-world data, we study the system dynamics and
quantify the price of fairness.


title:
The Effects of System Initiative during Conversational Collaborative
  Search

abstract:
  Our research in this paper lies at the intersection of collaborative and
conversational search. We report on a Wizard of Oz lab study in which 27 pairs
of participants collaborated on search tasks over the Slack messaging platform.
To complete tasks, pairs of collaborators interacted with a so-called
\emph{searchbot} with conversational capabilities. The role of the searchbot
was played by a reference librarian. It is widely accepted that conversational
search systems should be able to engage in \emph{mixed-initiative interaction}
-- take and relinquish control of a multi-agent conversation as appropriate.
Research in discourse analysis differentiates between dialog- and task-level
initiative. Taking \emph{dialog-level} initiative involves leading a
conversation for the sole purpose of establishing mutual belief between agents.
Conversely, taking \emph{task-level} initiative involves leading a conversation
with the intent to influence the goals of the other agent(s). Participants in
our study experienced three \emph{searchbot conditions}, which varied based on
the level of initiative the human searchbot was able to take: (1) no
initiative, (2) only dialog-level initiative, and (3) both dialog- and
task-level initiative. We investigate the effects of the searchbot condition on
six different types of outcomes: (RQ1) perceptions of the searchbot's utility,
(RQ2) perceptions of workload, (RQ3) perceptions of the collaboration, (RQ4)
patterns of communication and collaboration, and perceived (RQ5) benefits and
(RQ6) challenges from engaging with the searchbot.


title: It's Raw! Audio Generation with State-Space Models

abstract:
  Developing architectures suitable for modeling raw audio is a challenging
problem due to the high sampling rates of audio waveforms. Standard sequence
modeling approaches like RNNs and CNNs have previously been tailored to fit the
demands of audio, but the resultant architectures make undesirable
computational tradeoffs and struggle to model waveforms effectively. We propose
SaShiMi, a new multi-scale architecture for waveform modeling built around the
recently introduced S4 model for long sequence modeling. We identify that S4
can be unstable during autoregressive generation, and provide a simple
improvement to its parameterization by drawing connections to Hurwitz matrices.
SaShiMi yields state-of-the-art performance for unconditional waveform
generation in the autoregressive setting. Additionally, SaShiMi improves
non-autoregressive generation performance when used as the backbone
architecture for a diffusion model. Compared to prior architectures in the
autoregressive generation setting, SaShiMi generates piano and speech waveforms
which humans find more musical and coherent respectively, e.g. 2x better mean
opinion scores than WaveNet on an unconditional speech generation task. On a
music generation task, SaShiMi outperforms WaveNet on density estimation and
speed at both training and inference even when using 3x fewer parameters. Code
can be found at https://github.com/HazyResearch/state-spaces and samples at
https://hazyresearch.stanford.edu/sashimi-examples.


title: Graph-based Extractive Explainer for Recommendations

abstract:
  Explanations in a recommender system assist users in making informed
decisions among a set of recommended items. Great research attention has been
devoted to generating natural language explanations to depict how the
recommendations are generated and why the users should pay attention to them.
However, due to different limitations of those solutions, e.g., template-based
or generation-based, it is hard to make the explanations easily perceivable,
reliable and personalized at the same time.
  In this work, we develop a graph attentive neural network model that
seamlessly integrates user, item, attributes, and sentences for
extraction-based explanation. The attributes of items are selected as the
intermediary to facilitate message passing for user-item specific evaluation of
sentence relevance. And to balance individual sentence relevance, overall
attribute coverage, and content redundancy, we solve an integer linear
programming problem to make the final selection of sentences. Extensive
empirical evaluations against a set of state-of-the-art baseline methods on two
benchmark review datasets demonstrated the generation quality of the proposed
solution.


title:
Slow light with fractional optical angular momentum in a photonic
  crystal ring

abstract:
  Whispering gallery modes (WGMs) in circularly symmetric optical
microresonators exhibit integer quantized angular momentum numbers due to the
boundary condition imposed by the geometry. Here, we show that incorporating a
photonic crystal pattern in an integrated microring can result in WGMs with
fractional optical angular momentum. By choosing the photonic crystal
periodicity to open a photonic bandgap with a band-edge momentum lying between
that of two WGMs of the unperturbed ring, we observe hybridized WGMs with
half-integer quantized angular momentum numbers ($m \in \mathbb{Z}$ + 1/2).
Moreover, we show that these modes with fractional angular momenta exhibit high
optical quality factors with good cavity-waveguide coupling, an order of
magnitude reduced group velocity, and also can co-exist with more localized
states when a defect is introduced in the photonic crystal lattice. Our work
unveils WGMs with fractional angular momentum, which can be used in
sensing/metrology, nonlinear optics, and cavity quantum electrodynamics.


title: Magneto-optical Spectroscopy with RAMBO: A Table-Top 30 T Magnet

abstract:
  Optically probing materials in high magnetic fields can provide enlightening
insight into field-modified electronic states and phases, while optically
driving materials in high magnetic fields can induce novel nonequilibrium
many-body dynamics of spin and charge carriers. While there are high-field
magnets compatible with standard optical spectroscopy methods, they are
generally bulky and have limited optical access, which prohibit performing
state-of-the-art ultrafast and/or nonlinear optical experiments. The Rice
Advanced Magnet with Broadband Optics (RAMBO), a unique 30-T pulsed mini-coil
magnet system with direct optical access, has enabled previously challenging
experiments using femtosecond optical pulses, including time-domain terahertz
spectroscopy, in cutting-edge materials placed in strong magnetic fields. Here,
we review recent experimental advances made possible by the first-generation
RAMBO setup. After summarizing technological aspects of combining optical
spectroscopic techniques with the mini-coil magnet, we describe results of
magneto-optical studies of a wide variety of materials, providing new insight
into the states and dynamics of four types of quasiparticles in solids -
excitons, plasmons, magnons, and phonons - in high magnetic fields.


title:
Nonlinear p-multigrid preconditioner for implicit time integration of
  compressible Navier--Stokes equations

abstract:
  Within the framework of $ p $-adaptive flux reconstruction, we aim to
construct efficient polynomial multigrid ($p$MG) preconditioners for implicit
time integration of the Navier--Stokes equations using Jacobian-free
Newton--Krylov (JFNK) methods. We hypothesise that in pseudo transient
continuation (PTC), as the residual drops, the frequency of error modes that
dictates the convergence rate gets higher and higher. We apply nonlinear $p$MG
solvers to stiff steady problems at low Mach number ($\mathrm{Ma}=10^{-3}$) to
verify our hypothesis. It is demonstrated that once the residual drops by a few
orders of magnitude, improved smoothing on intermediate $ p $-sublevels will
not only maintain the stability of $ p $MG at large time steps but also improve
the convergence rate. For the unsteady Navier--Stokes equations, we elaborate
how to construct nonlinear preconditioners using pseudo transient continuation
for the matrix-free generalized minimal residual (GMRES) method used in
explicit first stage, singly diagonally implicit Runge--Kutta (ESDIRK) methods,
and linearly implicit Rosenbrock--Wanner (ROW) methods. Given that at each time
step the initial guess in the nonlinear solver is not distant from the
converged solution, we recommend a two-level $p\{p_0\text{-}p_0/2\} $ or even $
p\{p_0\text{-}(p_0-1)\} $ $p$-hierarchy for optimal efficiency with a
matrix-based smoother on the coarser level based on our hypothesis. It is
demonstrated that insufficient smoothing on intermediate $p$-sublevels will
deteriorate the performance of $p$MG preconditioner greatly. (See full abstract
in the paper.)


title:
Schr\"{o}dinger Meets Kuramoto via Feynman-Kac: Minimum Effort
  Distribution Steering for Noisy Nonuniform Kuramoto Oscillators

abstract:
  We formulate and solve the problem of finite horizon minimum control effort
steering of the state probability distribution between prescribed endpoint
joints for a finite population of networked noisy nonuniform Kuramoto
oscillators. We consider both the first and second order stochastic Kuramoto
models. For numerical solution of the associated stochastic optimal control, we
propose combining certain measure-valued proximal recursions and the
Feynman-Kac path integral computation. We illustrate the proposed framework via
numerical examples.


title:
Overparametrization improves robustness against adversarial attacks: A
  replication study

abstract:
  Overparametrization has become a de facto standard in machine learning.
Despite numerous efforts, our understanding of how and where
overparametrization helps model accuracy and robustness is still limited. To
this end, here we conduct an empirical investigation to systemically study and
replicate previous findings in this area, in particular the study by Madry et
al. Together with this study, our findings support the "universal law of
robustness" recently proposed by Bubeck et al. We argue that while critical for
robust perception, overparametrization may not be enough to achieve full
robustness and smarter architectures e.g. the ones implemented by the human
visual cortex) seem inevitable.


title: Virus Assembly Pathways inside a Host Cell

abstract:
  Simple RNA viruses self-assemble spontaneously and encapsulate their genome
into a shell called the capsid. This process is mainly driven by the attractive
electrostatic interaction between the positive charges on capsid proteins and
the negative charges on the genome. Despite its importance and many decades of
intense research, how the virus selects and packages its native RNA inside the
crowded environment of a host cell cytoplasm in the presence of an abundance of
non-viral RNA and other anionic polymers, has remained a mystery. In this
paper, we perform a series of simulations to monitor the growth of viral shells
and find the mechanism by which cargo-coat protein interactions can impact the
structure and stability of the viral shells. We show that coat protein subunits
can assemble around a globular nucleic acid core by forming non-icosahedral
cages, which have been recently observed in assembly experiments involving
small pieces of RNA. We find that the resulting cages are strained and can
easily be split into fragments along stress lines. This suggests that such
metastable non-icosahedral intermediates could be easily re-assembled into the
stable native icosahedral shells if the larger wild-type genome becomes
available, despite the presence of myriad of non-viral RNAs.


title: Amplification of Gravitationally Induced Entanglement

abstract:
  Observation of gravitationally induced entanglement between two massive
particles is the evidence of quantum nature of gravity. However, quantum
effects in the gravitational field are exceptionally small so that the existing
quantum-gravity proposals are extremely hard to test in practice. For
addressing this key challenge, here we propose a criterion based on the logical
contradictions of weak entanglement, which may boost the sensitivity of the
signal due to the gravitationally induced entanglement. Specifically, we make
use of the weak-value scenario and Einstein-Podolsky-Rosen (EPR) steering. We
prove that it is impossible for a classical mediator to act on two local
quantum objects to simulate amplified-weak-value phenomenon in two-setting EPR
steering. Compared to the previous protocols, our approach can amplify the
signal of quantum gravity by any desired factor that depends on the magnitude
of the weak value. Our results not only open up the possibility of detecting
quantum gravity in the near future, but also pave the way for weak entanglement
criterion of a more general nature.


title:
The Loop Game: Quality Assessment and Optimization for Low-Light Image
  Enhancement

abstract:
  There is an increasing consensus that the design and optimization of low
light image enhancement methods need to be fully driven by perceptual quality.
With numerous approaches proposed to enhance low-light images, much less work
has been dedicated to quality assessment and quality optimization of low-light
enhancement. In this paper, to close the gap between enhancement and
assessment, we propose a loop enhancement framework that produces a clear
picture of how the enhancement of low-light images could be optimized towards
better visual quality. In particular, we create a large-scale database for
QUality assessment Of The Enhanced LOw-Light Image (QUOTE-LOL), which serves as
the foundation in studying and developing objective quality assessment
measures. The objective quality assessment measure plays a critical bridging
role between visual quality and enhancement and is further incorporated in the
optimization in learning the enhancement model towards perceptual optimally.
Finally, we iteratively perform the enhancement and optimization tasks,
enhancing the low-light images continuously. The superiority of the proposed
scheme is validated based on various low-light scenes. The database as well as
the code will be available.


title: Radio Constraints on $r$-process Nucleosynthesis by Collapsars

abstract:
  The heaviest elements in the Universe are synthesized through rapid neutron
capture ($r$-process) in extremely neutron rich outflows. Neutron star mergers
were established as an important $r$-process source through the multi-messenger
observation of GW170817. Collapsars were also proposed as a potentially major
source of heavy elements; however, this is difficult to probe through optical
observations due to contamination by other emission mechanisms. Here we present
observational constraints on $r$-process nucleosynthesis by collapsars based on
radio follow-up observations of nearby long gamma-ray bursts. We make the
hypothesis that late-time radio emission arises from the collapsar wind ejecta
responsible for forging $r$-process elements, and consider the constraints that
can be set on this scenario using radio observations of a sample of Swift/BAT
GRBs located within 2 Gpc. No radio counterpart was identified in excess of the
radio afterglow of the GRBs in our sample, limiting the collapsar $r$-process
contribution to $\lesssim0.2$ M$_\odot$ under the models we considered, with
constant circum-merger densities giving more stringent constraints. While our
results are in tension with collapsars being the majority $r$-process
production sites, the ejecta mass and velocity profile of collapsar winds is
not yet well modeled. As such, our results are currently subject to large
uncertainties, but further theoretical work could greatly improve them.


title:
A Foundation for Wireless Channel Prediction and Full Ray Makeup
  Estimation Using an Unmanned Vehicle

abstract:
  In this paper, we consider the problem of wireless channel prediction, where
we are interested in predicting the channel quality at unvisited locations in
an area of interest, based on a small number of prior received power
measurements collected by an unmanned vehicle in the area. We propose a new
framework for channel prediction that can not only predict the detailed
variations of the received power, but can also predict the detailed makeup of
the wireless rays (i.e., amplitude, angle-of-arrival, and phase of all the
incoming paths). More specifically, we show how an enclosure-based robotic
route design ensures that the received power measurements at the prior
measurement locations can be utilized to fully predict detailed ray parameters
at unvisited locations. We then show how to first estimate the detailed ray
parameters at the prior measurement route and then fully extend them to predict
the detailed ray makeup at unvisited locations in the workspace. We
experimentally validate our proposed framework through extensive real-world
experiments in three different areas, and show that our approach can accurately
predict the received channel power and the detailed makeup of the rays at
unvisited locations in an area, considerably outperforming the state-of-the-art
in wireless channel prediction.


title: Visual Attention Network

abstract:
  While originally designed for natural language processing tasks, the
self-attention mechanism has recently taken various computer vision areas by
storm. However, the 2D nature of images brings three challenges for applying
self-attention in computer vision. (1) Treating images as 1D sequences neglects
their 2D structures. (2) The quadratic complexity is too expensive for
high-resolution images. (3) It only captures spatial adaptability but ignores
channel adaptability. In this paper, we propose a novel large kernel attention
(LKA) module to enable self-adaptive and long-range correlations in
self-attention while avoiding the above issues. We further introduce a novel
neural network based on LKA, namely Visual Attention Network (VAN). While
extremely simple, VAN outperforms the state-of-the-art vision transformers and
convolutional neural networks with a large margin in extensive experiments,
including image classification, object detection, semantic segmentation,
instance segmentation, etc. Code is available at
https://github.com/Visual-Attention-Network.


title: Lyapunov stable chain recurrence classes for singular flows

abstract:
  We show that for a $C^1$ generic vector field $X$ away from homoclinic
tangencies, a nontrivial Lyapunov stable chain recurrence class is a homoclinic
class. The proof uses an argument with $C^2$ vector fields approaching $X$ in
$C^1$ topology, with their Gibbs $F$-states converging to a Gibbs $F$-state of
$X$.


title: Measurement of the Ra$^+$ $7p$ $^{2}P_{3/2}$ state lifetime

abstract:
  We report a measurement of the radium ion's $7p$ ${}^{2}P_{3/2}$ state
lifetime, $\tau=4.78(3)$ ns. The measured lifetime is in good agreement with
theoretical calculations, and will enable a determination of the differential
scalar polarizability of the narrow linewidth $7s$ ${}^{2}S_{1/2}\rightarrow$
$6d$ ${}^{2}D_{5/2}$ optical clock transition.


title:
Effective spin model in momentum space: Toward a systematic
  understanding of multiple-$Q$ instability by momentum-resolved anisotropic
  exchange interactions

abstract:
  Multiple-$Q$ magnetic states, such as a skyrmion crystal, become a source of
unusual transport phenomena and dynamics. Recent theoretical and experimental
studies clarify that such multiple-$Q$ states ubiquitously appear under
different crystal structures in metals and insulators. Toward a systematic
understanding of the formation of the multiple-$Q$ states in various crystal
systems, in this theoretical study, we present a low-energy effective spin
model with anisotropic exchange interactions in momentum space. We summarize
specific six symmetry rules for nonzero symmetric and antisymmetric anisotropic
exchange interactions in momentum space, which are regarded as an extension of
Moriya's rule. According to the rules, we construct the effective spin model
for tetragonal, hexagonal, and trigonal magnets with crystal- and
momentum-dependent anisotropic exchange interactions based on magnetic
representation analysis. Furthermore, we describe the origin of the effective
anisotropic exchange interactions in itinerant magnets by perturbatively
analyzing a multi-band periodic Anderson model with the spin-orbit coupling. We
apply the effective spin model to an itinerant magnet in a $P6/mmm$ crystal and
find various multiple-$Q$ states with a spin scalar chirality in the ground
state. Our results provide a foundation of constructing effective
phenomenological spin models for any crystal systems hosting the multiple-$Q$
states, which will stimulate further exploration of exotic multiple-$Q$ states
in materials with the spin-orbit coupling.


title: RDP-Net: Region Detail Preserving Network for Change Detection

abstract:
  Change detection (CD) is an essential earth observation technique. It
captures the dynamic information of land objects. With the rise of deep
learning, neural networks (NN) have shown great potential in CD. However,
current NN models introduce backbone architectures that lose the detail
information during learning. Moreover, current NN models are heavy in
parameters, which prevents their deployment on edge devices such as drones. In
this work, we tackle this issue by proposing RDP-Net: a region detail
preserving network for CD. We propose an efficient training strategy that
quantifies the importance of individual samples during the warmup period of NN
training. Then, we perform non-uniform sampling based on the importance score
so that the NN could learn detail information from easy to hard. Next, we
propose an effective edge loss that improves the network's attention on details
such as boundaries and small regions. As a result, we provide a NN model that
achieves the state-of-the-art empirical performance in CD with only 1.70M
parameters. We hope our RDP-Net would benefit the practical CD applications on
compact devices and could inspire more people to bring change detection to a
new level with the efficient training strategy.


title:
Ultrasensitive refractive index sensor with rotatory biased weak
  measurement

abstract:
  A modified weak measurement scheme, rotatory biased weak measurement, is
proposed to significantly improve the sensitivity and resolution of the
refractive index sensor on a total reflection structure. This method introduces
an additional phase in the post-selected procedure and generates an extinction
point in the spectrum distribution. The biased post-selection makes smaller
coupling strength available, which leads to an enhancement of phase sensitivity
and refractive index sensitivity. In rotatory biased weak measurement, we
achieve an enhanced refractive index sensitivity of 13605 nm/RIU compared to
1644 nm/RIU in standard weak measurement. The performance of sensors with
different sensitivity is analyzed, and we find the optimal refractive index
resolution of sensors increases with sensitivity. In this work, we demonstrate
an optimal refractive index resolution of $4\times10^{-7}$ RIU on a total
reflection structure. The rabbit anti-mouse IgG and mouse IgG binding reaction
experiments demonstrate that our system has a high response to the
concentration of IgG in a wide range and the limit of detection is 15 ng/mL.
The improvements in this work are helpful to the optimizations of other optical
sensors with weak measurement.


title: PGE: Robust Product Graph Embedding Learning for Error Detection

abstract:
  Although product graphs (PGs) have gained increasing attentions in recent
years for their successful applications in product search and recommendations,
the extensive power of PGs can be limited by the inevitable involvement of
various kinds of errors. Thus, it is critical to validate the correctness of
triples in PGs to improve their reliability. Knowledge graph (KG) embedding
methods have strong error detection abilities. Yet, existing KG embedding
methods may not be directly applicable to a PG due to its distinct
characteristics: (1) PG contains rich textual signals, which necessitates a
joint exploration of both text information and graph structure; (2) PG contains
a large number of attribute triples, in which attribute values are represented
by free texts. Since free texts are too flexible to define entities in KGs,
traditional way to map entities to their embeddings using ids is no longer
appropriate for attribute value representation; (3) Noisy triples in a PG
mislead the embedding learning and significantly hurt the performance of error
detection. To address the aforementioned challenges, we propose an end-to-end
noise-tolerant embedding learning framework, PGE, to jointly leverage both text
information and graph structure in PG to learn embeddings for error detection.
Experimental results on real-world product graph demonstrate the effectiveness
of the proposed framework comparing with the state-of-the-art approaches.


title:
Velocity Obstacle Based Risk-Bounded Motion Planning for Stochastic
  Multi-Agent Systems

abstract:
  In this paper, we present an innovative risk-bounded motion planning
methodology for stochastic multi-agent systems. For this methodology, the
disturbance, noise, and model uncertainty are considered; and a velocity
obstacle method is utilized to formulate the collision-avoidance constraints in
the velocity space. With the exploitation of geometric information of static
obstacles and velocity obstacles, a distributed optimization problem with
probabilistic chance constraints is formulated for the stochastic multi-agent
system. Consequently, collision-free trajectories are generated under a
prescribed collision risk bound. Due to the existence of probabilistic and
disjunctive constraints, the distributed chance-constrained optimization
problem is reformulated as a mixed-integer program by introducing the binary
variable to improve computational efficiency. This approach thus renders it
possible to execute the motion planning task in the velocity space instead of
the position space, which leads to smoother collision-free trajectories for
multi-agent systems and higher computational efficiency. Moreover, the risk of
potential collisions is bounded with this robust motion planning methodology.
To validate the effectiveness of the methodology, different scenarios for
multiple agents are investigated, and the simulation results clearly show that
the proposed approach can generate high-quality trajectories under a predefined
collision risk bound and avoid potential collisions effectively in the velocity
space.


title: Van der Waals equation of state for asymmetric nuclear matter

abstract:
  The application of van der Waals equation of state to the asymmetric nuclear
matter is considered in a critical state region. The corrections to the van der
Waals pressure and free energy due to the Fermi statistics are obtained
starting from the Thomas--Fermi entropy expression which ensures the fulfilment
of Nernst theorem. The derived corrections account for the effective nucleon
mass and neutron-proton isotopic asymmetry. The parameters of van der Waals
equation of state are deduced taking the experimental value of critical
temperature for symmetric nuclear matter and testing the model of van der Waals
with statistics corrections included against the theory of Skyrme energy
density functional. Critical line in pressure-temperature-composition space is
considered. Incompressibility coefficient is determined along the critical line
as a function of nuclear matter composition. Jump in the value of specific heat
upon crossing critical line is discussed.


title:
Enhancing Affective Representations of Music-Induced EEG through
  Multimodal Supervision and latent Domain Adaptation

abstract:
  The study of Music Cognition and neural responses to music has been
invaluable in understanding human emotions. Brain signals, though, manifest a
highly complex structure that makes processing and retrieving meaningful
features challenging, particularly of abstract constructs like affect.
Moreover, the performance of learning models is undermined by the limited
amount of available neuronal data and their severe inter-subject variability.
In this paper we extract efficient, personalized affective representations from
EEG signals during music listening. To this end, we employ music signals as a
supervisory modality to EEG, aiming to project their semantic correspondence
onto a common representation space. We utilize a bi-modal framework by
combining an LSTM-based attention model to process EEG and a pre-trained model
for music tagging, along with a reverse domain discriminator to align the
distributions of the two modalities, further constraining the learning process
with emotion tags. The resulting framework can be utilized for emotion
recognition both directly, by performing supervised predictions from either
modality, and indirectly, by providing relevant music samples to EEG input
queries. The experimental findings show the potential of enhancing neuronal
data through stimulus information for recognition purposes and yield insights
into the distribution and temporal variance of music-induced affective
features.


title:
Floquet analysis of extended Rabi models based on high-frequency
  expansion

abstract:
  The extended quantum Rabi models make a significant contribution to
understand the quantum nature of the atom-light interaction. We transform two
kinds of extended quantum Rabi model, anisotropic Rabi model and asymmetric
Rabi model, into rotating frame, and regard them as periodically driven quantum
systems. The analytical solutions of the quasi-energy spectrum as well as the
Floquet modes for both models are constructed by applying the Floquet theory
and the high-frequency expansion, which is applied to the non-stroboscopic
dynamics of physical observables. For anisotropic Rabi model, the quasi energy
fits well with the numerical results in even the deep-strong coupling regime if
the counterrotating terms is small enough compared to the driving frequency.
Avoided level crossing occurs for quasi energy with the same parity, while the
high frequency expansion fails to predict this due to the conservation of the
total excitation number. Furthermore, we present analytical and numerical study
of the long-time evolution of population and figure out the analytical method
is credible for the population dynamics. For asymmetric Rabi model, we find
that the external bias field which breaks the parity symmetry of total
excitation number tends to cluster the upper and lower branches into two
bundles, and the detuning induced gap in the first temporal Brillouin zone
shows a quadratic dependence on the bias. The Fourier analysis is applied to
extract the frequency composition and the two-frequency driving behavior is
revealed. Varying the bias strength will change the equilibrium value of the
oscillation, which shows how the bias competes with the detuning and atom-field
coupling in the driving dynamics. Both models prove that treating the
Hamiltonian in the rotating frame by Floquet theory gives an alternative tool
in the study of interaction between atom and light.


title:
A simple proof of logarithmic Sobolev inequality on the Heisenberg
  groups

abstract:
  In this note we give a simple, dimension independent, proof of the
logarithmic Sobolev inequality on the Heisenberg groups $H_n=\R^{2n+1}$ using
the measure preserving transformations of the Brownian motion.


title: Learning to Control Partially Observed Systems with Finite Memory

abstract:
  We consider the reinforcement learning problem for partially observed Markov
decision processes (POMDPs) with large or even countably infinite state spaces,
where the controller has access to only noisy observations of the underlying
controlled Markov chain. We consider a natural actor-critic method that employs
a finite internal memory for policy parameterization, and a multi-step temporal
difference learning algorithm for policy evaluation. We establish, to the best
of our knowledge, the first non-asymptotic global convergence of actor-critic
methods for partially observed systems under function approximation. In
particular, in addition to the function approximation and statistical errors
that also arise in MDPs, we explicitly characterize the error due to the use of
finite-state controllers. This additional error is stated in terms of the total
variation distance between the traditional belief state in POMDPs and the
posterior distribution of the hidden state when using a finite-state
controller. Further, we show that this error can be made small in the case of
sliding-block controllers by using larger block sizes.


title: Percolation induced gel-gel phase separation in a dilute polymer network

abstract:
  Cosmic large-scale structures, animal flocks, and living tissues are
non-equilibrium organized systems created by dissipative processes. Despite the
uniqueness, the realization of dissipative structures is still difficult.
Herein, we report that a network formation process in a dilute system is a
dissipative process, leading to percolation induced gel-gel phase separation
(GGPS) in a prominent miscible polymer-water system. The dilute system, which
forms a monophase structure at the percolation threshold, eventually separates
into two gel phases in a longer time scale as the network formation progresses.
The dilute hydrogel with GGPS exhibits an unexpected mesoscale co-continuous
structure and induces adipose growth in subcutaneous. The formation mechanism
of GGPS and a cosmic large-scale structure is analogous, in terms of attractive
interactions in a diluted system driving phase separation. This unique
phenomenon unveils the possibility of dissipative structures enabling advanced
functionalities and will stimulate research fields related to dissipative
structures.


title:
Multi-dimensional Network Security Game: How do attacker and defender
  battle on parallel targets?

abstract:
  In this paper, we consider a new network security game wherein an attacker
and a defender are battling over "multiple" targets. This type of game is
appropriate to model many current network security conflicts such as Internet
phishing, mobile malware or network intrusions. In such attacks, the attacker
and the defender need to decide how to allocate resources on each target so as
to maximize his utility within his resource limit. We model such a
multi-dimensional network security game as a constrained non-zero sum game. Two
security breaching models, the product-form and the proportion-form, are
considered. For each breaching model, we prove the existence of a unique Nash
equilibrium (NE) based on Rosen's theorem and propose efficient algorithms to
find the NE when the games are strictly concave. Furthermore, we show the
existence of multiple NEs in the product-form breaching model when the strict
concavity does not hold. Our study sheds light on the strategic behaviors of
the attacker and the defender, in particular, on how they allocate resources to
the targets which have different weights, and how their utilities as well as
strategies are influenced by the resource constraints.


title:
Bad list assignments for non-$k$-choosable $k$-chromatic graphs with
  $2k+2$-vertices

abstract:
  It was conjectured by Ohba, and proved by Noel, Reed and Wu that
$k$-chromatic graphs $G$ with $|V(G)| \le 2k+1$ are chromatic-choosable. This
upper bound on $|V(G)|$ is tight: if $k$ is even, then $K_{3 \star (k/2+1), 1
\star (k/2-1)}$ and $K_{4, 2 \star (k-1)}$ are $k$-chromatic graphs with $2
k+2$ vertices that are not chromatic-choosable. It was proved in
[arXiv:2201.02060] that these are the only non-$k$-choosable complete
$k$-partite graphs with $2k+2$ vertices. For $G =K_{3 \star (k/2+1), 1 \star
(k/2-1)}$ or $K_{4, 2 \star (k-1)}$, a bad list assignment of $G$ is a $k$-list
assignment $L$ of $G$ such that $G$ is not $L$-colourable. Bad list assignments
for $G=K_{4, 2 \star (k-1)}$ were characterized in [Discrete Mathematics 244
(2002), 55-66]. In this paper, we first give a simpler proof of this result,
and then we characterize bad list assignments for $G=K_{3 \star (k/2+1), 1
\star (k/2-1)}$. Using these results, we characterize all non-$k$-choosable
(non-complete) $k$-partite graphs with $2k+2$ vertices.


title:
Twisted conjugacy in classical groups over certain domains of
  Characteristic $p>0$

abstract:
  Let $F$ be a subfield of the algebraic closure of a finite field
$\mathbb{F}_p$, $p \ne 2$, and let $R$ denote any ring such that $F[t] \subset
R \subsetneq F(t)$. Let $G$ be a classical Chevalley group of adjoint type
defined over $R$. We prove that the group $G(R)$ has the $R_{\infty}$-property.


title:
Submultiplicative and Power Submultiplicative Properties for Generalized
  Hersch-Pfluger Distortion Function

abstract:
  For $a\in(0,1/2]$ and $r\in(0,1)$, and for $K>0$, we investigate
submultiplicative and power submultiplicative properties for generalized
Hersch-Pfluger distortion function $\varphi_K^a(r)$, which generalize the
recent results of Hersch-Pfluger distortion function $\varphi_K(r)$ obtained by
Wang, Qiu and Chu.


title:
A Tseng type stochastic forward-backward algorithm for monotone
  inclusions

abstract:
  In this paper, we propose a stochastic version of the classical Tseng's
forward-backward-forward method with inertial term for solving monotone
inclusions given by the sum of a maximal monotone operator and a single-valued
monotone operator in real Hilbert spaces. We obtain the almost sure convergence
for the general case and the rate $\mathcal{O}(1/n)$ in expectation for the
strong monotone case.
  Furthermore, we derive $\mathcal{O}(1/n)$ rate convergence of the primal-dual
gap for saddle point problems.


title: The strong-interaction limit of density functional theory

abstract:
  This is a comprehensive review of the strong-interaction limit of density
functional theory. It covers the derivation of the limiting strictly correlated
electrons (SCE) functional from exact Hohenberg-Kohn DFT, basic aspects of SCE
physics such as the nonlocal dependence of the SCE potential on the density,
equivalent formulations and the mathematical interpretation as optimal
transport with Coulomb cost, rigorous results (including exactly soluble
cases), approximations, numerical methods, integration into Kohn-Sham DFT (KS
SCE), and applications to molecular systems, an example being that KS SCE,
unlike the local density approximation or generalized gradient approximations,
dissociates H$_2$ correctly. We have made an effort to make this review
accessible to a broad audience of physicists, chemists, and mathematicians.

categories: physics.chem-ph cond-mat.str-el math-ph math.MP


title:
Optimal configuration of cooperative stationary and mobile energy
  storage considering ambient temperature: A case for Winter Olympic Game

abstract:
  The international mega-event, such as the Winter Olympic Game, has been
considered as one of the most carbon intensive activities worldwide. The
commitment of fully renewable energy accommodation and utilization while
ensuring the extreme high reliability has brought significant challenges on
system operation due to the stochastic nature of the renewables. The battery
energy storage system (BESS) composed of stationary energy storage system
(SESS) and shared mobile energy storage system (MESS) can be utilized to meet
the requirements of short-term load surges, renewable accommodation and
emergency power supply for important loads during the mega-event. The BESS can
continue to serve the venues electricity consumption to satisfy the carbon
neutrality after the event. On the other hand, the low ambient temperature of
Winter Olympic game has significant impact on BESSs degradation and performance
which need to be integrated to the charging and discharging model of BESS. To
this end, a joint two-stage optimal configuration method considering the
ambient temperature of SESS and MESS has been developed to support the
mega-event carbon neutrality, to reduce redundant BESS capacity allocation and
improve the system life cycle cost-benefit. Simulation results have
demonstrated the rationality and effectiveness of the collaborative operation
of SESS and the MESS under various scenarios.


title:
Multi-objective Distributed Optimization for Zonal Distribution System
  with Multi-Microgrids

abstract:
  The issue of voltage variations caused by integration of renewables has been
addressed in this paper through distributed management of Microgrids (MGs). The
distribution network (DN) takes the network losses and voltage quality as
objectives, an alternating direction method of multipliers (ADMM) with adaptive
penalty modulation has been proposed to realize distributed optimization with
improved convergence. On the basis of satisfying the optimization target on the
system level, the individual MG manages the controllable resources inside the
MG to minimize the operating cost on the lower level. The feasibility and
effectiveness of the proposed method has been demonstrated on a modified IEEE
33-bus system.


title: Matrix-free interior point methods for point set matching problems

abstract:
  Point sets matching problems can be handled by optimal transport. The
mechanism behind it is that optimal transport recovers the point-to-point
correspondence associated with the least curl deformation. Optimal transport is
a special form of linear programming with dense constraints. Linear programming
can be handled by interior point methods effectively, provided that the
involved ill-conditioned Hessians can be computed accurately. Recently, matrix
balancing has been employed to compute optimal transport. In this work, we
incorporate sparse support constraints to matrix-balancing based interior point
methods, in which the sparse constraint set fulfilling total support is
iteratively updated according to the multiplier vectors. Total support
condition ensures the existence of matrix balancing. Experiments justify the
effectiveness of the proposed algorithm on point-sets with large cardinality.


title: Holomorphic Koszul-Brylinski homologies of Poisson blow-ups

abstract:
  We derive a blow-up formula for holomorphic Koszul-Brylinski homologies of
compact holomorphic Poisson manifolds. As applications, we investigate the
invariance of the $E_{1}$-degeneracy of the Dolbeault-Koszul-Brylinski spectral
sequence under Poisson blow-ups, and compute the holomorphic Koszul-Brylinski
homology for del Pezzo surfaces and two complex nilmanifolds with holomorphic
Poisson structures.


title: Notes on finite totally $2$-closed permutation groups

abstract:
  Let $N$ be a normal subgroup of a finite group $G$. For a faithful $N$-set
$\Delta$, applying the university embedding theorem one can construct a
faithful $G$-set $\Omega$. In this short note, it is proved that if the
$2$-closure of $N$ in $\Omega$ is equal to $N$, then the $2$-closure of $N$ in
$\Delta$ is also equal to $N$; in addition, it is proved that any abelian
normal subgroup of a finite totally $2$-closed group is cyclic; finally, it is
proved that if a finite nilpotent group is a direct of two nilpotent subgroups
where the two factors have coprime orders and both of them are totally 2-closed
then G is totally $2$-closed. As corollaries, several well-known results on
finite totally 2-closed groups are reproved in more simple ways.


title: GRANDMA Observations of ZTF/Fink Transients during Summer 2021

abstract:
  We present our follow-up observations with GRANDMA of transient sources
revealed by the Zwicky Transient Facility (ZTF). Over a period of six months,
all ZTF triggers were examined in real time by a dedicated science module
implemented in the Fink broker, which will be used for the data processing of
the Vera C. Rubin Observatory. In this article, we present three selection
methods to identify kilonova candidates. Out of more than 35 million
candidates, a hundred sources have passed our selection criteria. Six were then
followed-up by GRANDMA (by both professional and amateur astronomers). The
majority were finally classified either as asteroids or as supernovae events.
We mobilized 37 telescopes, bringing together a large sample of images, taken
under various conditions and quality. To complement the orphan kilonova
candidates (those without associated gamma-ray bursts, which were all), we
included three additional supernovae alerts to conduct further observations of
during summer 2021. We demonstrate the importance of the amateur astronomer
community that contributed images for scientific analyzes of new sources
discovered in a magnitude range r'=17-19 mag. We based our rapid kilonova
classification on the decay rate of the optical source that should exceed 0.3
mag/day. GRANDMA's follow-up determined the fading rate within 1.5+/-1.2 days
post-discovery, without waiting for further observations from ZTF. No confirmed
kilonovae were discovered during our observing campaign. This work will be
continued in the coming months in the view of preparing for kilonova searches
in the next gravitational-wave observing run O4.


title: Geometry of gauged LG-model with compatible boundary conditions

abstract:
  This paper introduces the geometry of the open string Floer theory of gauged
Landau-Ginzburg model via gauged Witten equations. Given a $G$-invariant
Morse-Bott holomorphic function $W$ on a Hamiltonian space $(M,\omega,G),$
Lefschetz thimbles are constructed from proper Lagrangian submanifolds of
critical set of $W.$ We study an energy functional on path space whose gradient
flow equation corresponds to the gauged Witten equations with temporal gauge on
a strip end, and whose critical points are Lagrangian intersections in the
reduced critical space of $W.$


title:
Tropical curves in abelian surfaces II: enumeration of curves in linear
  systems

abstract:
  In this paper, second installment in a series of three, we give a
correspondence theorem to relate the count of genus $g$ curves in a fixed
linear system in an abelian surface to a tropical count. To do this, we relate
the linear system defined by a complex curve to certain integrals of 1-forms
over cycles in the curve. We then give an expression for the tropical
multiplicity provided by the correspondence theorem, and prove the invariance
for the associated refined multiplicity, thus introducing refined invariants of
Block-G\"ottsche type in abelian surfaces.


title: Dynamic Spatial Propagation Network for Depth Completion

abstract:
  Image-guided depth completion aims to generate dense depth maps with sparse
depth measurements and corresponding RGB images. Currently, spatial propagation
networks (SPNs) are the most popular affinity-based methods in depth
completion, but they still suffer from the representation limitation of the
fixed affinity and the over smoothing during iterations. Our solution is to
estimate independent affinity matrices in each SPN iteration, but it is
over-parameterized and heavy calculation. This paper introduces an efficient
model that learns the affinity among neighboring pixels with an
attention-based, dynamic approach. Specifically, the Dynamic Spatial
Propagation Network (DySPN) we proposed makes use of a non-linear propagation
model (NLPM). It decouples the neighborhood into parts regarding to different
distances and recursively generates independent attention maps to refine these
parts into adaptive affinity matrices. Furthermore, we adopt a diffusion
suppression (DS) operation so that the model converges at an early stage to
prevent over-smoothing of dense depth. Finally, in order to decrease the
computational cost required, we also introduce three variations that reduce the
amount of neighbors and attentions needed while still retaining similar
accuracy. In practice, our method requires less iteration to match the
performance of other SPNs and yields better results overall. DySPN outperforms
other state-of-the-art (SoTA) methods on KITTI Depth Completion (DC) evaluation
by the time of submission and is able to yield SoTA performance in NYU Depth v2
dataset as well.


title:
Probability equivalent level of Value at Risk and higher-order Expected
  Shortfalls

abstract:
  We investigate the probability equivalent level of Value at Risk and
$n^{\mathrm{th}}$-order Expected Shortfall (called PELVE_n), which can be
considered as a variant of the notion of the probability equivalent level of
Value at Risk and Expected Shortfall (called PELVE) due to Li and Wang (2019).
We study the finiteness, uniqueness and several properties of PELVE_n, we
calculate PELVE_2 of some notable distributions, PELVE_2 of a random variable
having generalized Pareto excess distribution, and we describe the asymptotic
behaviour of PELVE_2 of regularly varying distributions as the level tends to
$0$. Some properties of $n^{\mathrm{th}}$-order Expected Shortfall are also
investigated. Among others, it turns out that a Gini Shortfall is a linear
combination of Expected Shortfall and $2^{\mathrm{nd}}$-order Expected
Shortfall.


title:
Random periodic solutions for stochastic differential equations with
  non-uniform dissipativity

abstract:
  This paper is concerned with the existence and uniqueness of random periodic
solutions for stochastic differential equations (SDEs), where the drift terms
involved need not to be uniformly dissipative. On the one hand, via the
reflection coupling approach, we investigate the existence of random periodic
solutions in the sense of distribution for SDEs without memory, where the
drifts are merely dissipative at long distance. On the other hand, via the
synchronous coupling strategy, we establish respectively the existence of
pathwise random periodic solutions for functional SDEs with a finite time lag
and an infinite time lag, in which the drifts are only dissipative on average
rather than uniformly dissipative with respect to the time parameters.


title: Context-aware adaptation of mobile video decoding resolution

abstract:
  While the evolution of mobile computing is experiencing a considerable
growth, it is at the same time seriously threatened by the limitations of the
battery technology, which does not keep pace with the evergrowing increase in
energy requirements of mobile applications. A novel approach for reducing the
energy appetite of mobile apps comes from the approximate computing field,
which proposes techniques that in a controlled manner sacrifice computation
accuracy for higher energy savings. Building on this philosophy we propose a
context-aware mobile video quality adaptation that reduces the energy needed
for video playback, while ensuring that a user's quality expectations with
respect to the mobile video are met. We confirm that the decoding resolution
can play a significant role in reducing the overall power consumption of a
mobile device and conduct two user studies to investigate how the context in
which a video is played, its content, and the user's personality, modulate a
user's quality expectations. We discover that a user's physical activity, the
spatial/temporal properties of the video, and the user's personality traits
interact and jointly influence the minimal acceptable playback resolution,
paving the way for context-adaptable approximate mobile computing.


title:
Learning to Help Emergency Vehicles Arrive Faster: A Cooperative
  Vehicle-Road Scheduling Approach

abstract:
  The ever-increasing heavy traffic congestion potentially impedes the
accessibility of emergency vehicles (EVs), resulting in detrimental impacts on
critical services and even safety of people's lives. Hence, it is significant
to propose an efficient scheduling approach to help EVs arrive faster. Existing
vehicle-centric scheduling approaches aim to recommend the optimal paths for
EVs based on the current traffic status while the road-centric scheduling
approaches aim to improve the traffic condition and assign a higher priority
for EVs to pass an intersection. With the intuition that real-time vehicle-road
information interaction and strategy coordination can bring more benefits, we
propose LEVID, a LEarning-based cooperative VehIcle-roaD scheduling approach
including a real-time route planning module and a collaborative traffic signal
control module, which interact with each other and make decisions iteratively.
The real-time route planning module adapts the artificial potential field
method to address the real-time changes of traffic signals and avoid falling
into a local optimum. The collaborative traffic signal control module leverages
a graph attention reinforcement learning framework to extract the latent
features of different intersections and abstract their interplay to learn
cooperative policies. Extensive experiments based on multiple real-world
datasets show that our approach outperforms the state-of-the-art baselines.


title:
Dynamic and Efficient Gray-Box Hyperparameter Optimization for Deep
  Learning

abstract:
  Gray-box hyperparameter optimization techniques have recently emerged as a
promising direction for tuning Deep Learning methods. In this work, we
introduce DyHPO, a method that learns to dynamically decide which configuration
to try next, and for what budget. Our technique is a modification to the
classical Bayesian optimization for a gray-box setup. Concretely, we propose a
new surrogate for Gaussian Processes that embeds the learning curve dynamics
and a new acquisition function that incorporates multi-budget information. We
demonstrate the significant superiority of DyHPO against state-of-the-art
hyperparameter optimization baselines through large-scale experiments
comprising 50 datasets (Tabular, Image, NLP) and diverse neural networks (MLP,
CNN/NAS, RNN).


title:
Non-Abelian Landau-Ginzburg Theory of Ferromagnetic Superconductivity
  and Photon-Magnon Mixing

abstract:
  We present an effective theory of non-Abelian superconductivity, an
SU(2)xU(1) extension of the Abelian Landau-Ginzburg theory, which could be
viewed as an effective theory of ferromagnetic superconductivity made of
spin-up and spin-down Cooper pairs. Just like the Abelian Landau-Ginzburg
theory it has the U(1) electromagnetic interaction, but the new ingredient is
the SU(2) magnon gauge interaction between the spin doublet Cooper pairs. A
remarkable feature of the theory is the mixing between the photon and the
diagonal part of the SU(2) magnons. After the mixing it has massless magnon and
massive photon, in addition to the massive off-diagonal magnon. So, unlike the
ordinary Landau-Ginzburg theory it has a long range interaction mediated by the
massless magnon, which we interpret as the long range magnetic order and spin
waves observed in ferromagnetic superconductors. The theory is characterized by
three scales. In addition to the correlation length fixed by the mass of the
Higgs field it has two different penetration lengths, the one fixed by the mass
of the massive photon and the other fixed by the mass of the off-diagonal
magnon. And the massive off-diagonal magnon generates the non-Abelian Meissner
effect. The non-Abelian structure of the theory naturally accommodates new
topological objects, the non-Abrikosov magnetic vortex and non-Abelian
monopole. We discuss the physical implications of the non-Abelian
Landau-Ginzburg theory.


title: Towards a dichotomy for the Reidemeister zeta function

abstract:
  We prove a dichotomy between rationality and a natural boundary for the
analytic behavior of the Reidemeister zeta function for automorphisms of
non-finitely generated torsion abelian groups and for endomorphisms of groups
$\mathbb Z_p^d,$ where $\mathbb Z_p$ the group of p-adic integers. As a
consequence, we obtain a dichotomy for the Reidemeister zeta function of a
continuous map of a topological space with fundamental group that is
non-finitely generated torsion abelian group. We also prove the rationality of
the coincidence Reidemeister zeta function for tame endomorphisms pairs of
finitely generated torsion-free nilpotent groups, based on a weak commutativity
condition.


title:
An Analysis of Complex-Valued CNNs for RF Data-Driven Wireless Device
  Classification

abstract:
  Recent deep neural network-based device classification studies show that
complex-valued neural networks (CVNNs) yield higher classification accuracy
than real-valued neural networks (RVNNs). Although this improvement is
(intuitively) attributed to the complex nature of the input RF data (i.e., IQ
symbols), no prior work has taken a closer look into analyzing such a trend in
the context of wireless device identification. Our study provides a deeper
understanding of this trend using real LoRa and WiFi RF datasets. We perform a
deep dive into understanding the impact of (i) the input representation/type
and (ii) the architectural layer of the neural network. For the input
representation, we considered the IQ as well as the polar coordinates both
partially and fully. For the architectural layer, we considered a series of
ablation experiments that eliminate parts of the CVNN components. Our results
show that CVNNs consistently outperform RVNNs counterpart in the various
scenarios mentioned above, indicating that CVNNs are able to make better use of
the joint information provided via the in-phase (I) and quadrature (Q)
components of the signal.


title: Pseudo Numerical Methods for Diffusion Models on Manifolds

abstract:
  Denoising Diffusion Probabilistic Models (DDPMs) can generate high-quality
samples such as image and audio samples. However, DDPMs require hundreds to
thousands of iterations to produce final samples. Several prior works have
successfully accelerated DDPMs through adjusting the variance schedule (e.g.,
Improved Denoising Diffusion Probabilistic Models) or the denoising equation
(e.g., Denoising Diffusion Implicit Models (DDIMs)). However, these
acceleration methods cannot maintain the quality of samples and even introduce
new noise at a high speedup rate, which limit their practicability. To
accelerate the inference process while keeping the sample quality, we provide a
fresh perspective that DDPMs should be treated as solving differential
equations on manifolds. Under such a perspective, we propose pseudo numerical
methods for diffusion models (PNDMs). Specifically, we figure out how to solve
differential equations on manifolds and show that DDIMs are simple cases of
pseudo numerical methods. We change several classical numerical methods to
corresponding pseudo numerical methods and find that the pseudo linear
multi-step method is the best in most situations. According to our experiments,
by directly using pre-trained models on Cifar10, CelebA and LSUN, PNDMs can
generate higher quality synthetic images with only 50 steps compared with
1000-step DDIMs (20x speedup), significantly outperform DDIMs with 250 steps
(by around 0.4 in FID) and have good generalization on different variance
schedules. Our implementation is available at
https://github.com/luping-liu/PNDM.


title:
Variably Scaled Persistence Kernels (VSPKs) for persistent homology
  applications

abstract:
  In recent years, various kernels have been proposed in the context of
persistent homology to deal with persistence diagrams in supervised learning
approaches. In this paper, we consider the idea of variably scaled kernels, for
approximating functions and data, and we interpret it in the framework of
persistent homology. We call them Variably Scaled Persistence Kernels (VSPKs).
These new kernels are then tested in different classification experiments. The
obtained results show that they can improve the performance and the efficiency
of existing standard kernels.


title: Fast high-dimensional integration using tensor networks

abstract:
  The design and application of regression-free tensor network representations
for integration is presented. Tensor network methods are demonstrated to
outperform Monte Carlo for test problems, and exponential convergence is shown
to be achievable for a non-analytic integrand.


title: Some new results about $q$-trinomial coefficients

abstract:
  In this paper, we present several new congruences on the $q$-trinomial
coefficients introduced by Andrews and Baxter. A new congruence on sums of
central $q$-binomial coefficients is also established.


title: Tight Wavelet Filter Banks with Prescribed Directions

abstract:
  Constructing tight wavelet filter banks with prescribed directions is
challenging. This paper presents a systematic method for designing a tight
wavelet filter bank, given any prescribed directions. There are two types of
wavelet filters in our tight wavelet filter bank. One type is entirely
determined by the prescribed information about the directionality and makes the
wavelet filter bank directional. The other type helps the wavelet filter bank
to be tight. In addition to the flexibility in choosing the directions, our
construction method has other useful properties. It works for any
multi-dimension, and it allows the user to have any prescribed number of
vanishing moments along the chosen directions. Furthermore, our tight wavelet
filter banks have fast algorithms for analysis and synthesis. Concrete examples
are given to illustrate our construction method and properties of resulting
tight wavelet filter banks.


title:
Analysis and optimization of a novel energy storage flywheel for
  improved energy capacity

abstract:
  Kinetic/Flywheel energy storage systems (FESS) have re-emerged as a vital
technology in many areas such as smart grid, renewable energy, electric
vehicle, and high-power applications. FESSs are designed and optimized to have
higher energy per mass (specific energy) and volume (energy density). Prior
research, such as the use of high-strength materials and the reduction of
stress concentration, primarily focused on designing and optimizing the rotor
itself. However, a modern FESS includes other indispensable components such as
magnetic bearings and a motor/generator that requires a shaft. The shaft
significantly impacts the flywheel design. This paper investigates several
typical flywheel designs and their stress analysis. A simplified analysis
method is given for designing rotor-shaft assembly. It is found that the
shaftless flywheel design approach can double the energy density level when
compared to typical designs. The shaftless flywheel is further optimized using
finite element analysis with the magnetic bearing and motor/generators' design
considerations.


title: Clustering by the Probability Distributions from Extreme Value Theory

abstract:
  Clustering is an essential task to unsupervised learning. It tries to
automatically separate instances into coherent subsets. As one of the most
well-known clustering algorithms, k-means assigns sample points at the boundary
to a unique cluster, while it does not utilize the information of sample
distribution or density. Comparably, it would potentially be more beneficial to
consider the probability of each sample in a possible cluster. To this end,
this paper generalizes k-means to model the distribution of clusters. Our novel
clustering algorithm thus models the distributions of distances to centroids
over a threshold by Generalized Pareto Distribution (GPD) in Extreme Value
Theory (EVT). Notably, we propose the concept of centroid margin distance, use
GPD to establish a probability model for each cluster, and perform a clustering
algorithm based on the covering probability function derived from GPD. Such a
GPD k-means thus enables the clustering algorithm from the probabilistic
perspective. Correspondingly, we also introduce a naive baseline, dubbed as
Generalized Extreme Value (GEV) k-means. GEV fits the distribution of the block
maxima. In contrast, the GPD fits the distribution of distance to the centroid
exceeding a sufficiently large threshold, leading to a more stable performance
of GPD k-means. Notably, GEV k-means can also estimate cluster structure and
thus perform reasonably well over classical k-means. Thus, extensive
experiments on synthetic datasets and real datasets demonstrate that GPD
k-means outperforms competitors. The github codes are released in
https://github.com/sixiaozheng/EVT-K-means.