title:
Nonconvex and Nonsmooth Approaches for Affine Chance-Constrained
  Stochastic Programs

abstract:
  Chance-constrained programs (CCPs) constitute a difficult class of stochastic
programs due to its possible nondifferentiability and nonconvexity even with
simple linear random functionals. Existing approaches for solving the CCPs
mainly deal with convex random functionals within the probability function. In
the present paper, we consider two generalizations of the class of chance
constraints commonly studied in the literature; one generalization involves
probabilities of disjunctive nonconvex functional events and the other
generalization involves mixed-signed affine combinations of the resulting
probabilities; together, we coin the term affine chance constraint (ACC) system
for these generalized chance constraints. Our proposed treatment of such an ACC
system involves the fusion of several individually known ideas: (a)
parameterized upper and lower approximations of the indicator function in the
expectation formulation of probability; (b) external (i.e., fixed) versus
internal (i.e., sequential) sampling-based approximation of the expectation
operator; (c) constraint penalization as relaxations of feasibility; and (d)
convexification of nonconvexity and nondifferentiability via surrogation. The
integration of these techniques for solving the affine chance-constrained
stochastic program (ACC-SP) with various degrees of practicality and
computational efforts is the main contribution of this paper.


title:
When AUC meets DRO: Optimizing Partial AUC for Deep Learning with
  Non-Convex Convergence Guarantee

abstract:
  In this paper, we propose systematic and efficient gradient-based methods for
both one-way and two-way partial AUC (pAUC) maximization that are applicable to
deep learning. We propose new formulations of pAUC surrogate objectives by
using the distributionally robust optimization (DRO) to define the loss for
each individual positive data. We consider two formulations of DRO, one of
which is based on conditional-value-at-risk (CVaR) that yields a non-smooth but
exact estimator for pAUC, and another one is based on a KL divergence
regularized DRO that yields an inexact but smooth (soft) estimator for pAUC.
For both one-way and two-way pAUC maximization, we propose two algorithms and
prove their convergence for optimizing their two formulations, respectively.
Experiments demonstrate the effectiveness of the proposed algorithms for pAUC
maximization for deep learning on various datasets.


title:
Leveraging the Cayley Hamilton Theorem for Efficiently Solving the
  Jordan Canonical Form Problem

abstract:
  Given an $n \times n$ nonsingular matrix A and the characteristic polynomial
of A as the starting point, we will leverage the Cayley-Hamilton Theorem to
efficiently calculate the maximal length Jordan Chains for each distinct
eigenvalue of the matrix. Efficiency and speed are gained by seeking a certain
type of starting vector as the first step of the algorithm. The method for
finding this starting vector does not require calculating the $ker[(A-\lambda
I)^k]$ which is quite an expensive operation, and which is the usual approach
taken in solving the Jordan Canonical basis problem. Given this starting
vector, all remaining vectors in the Jordan Chain are calculated very quickly
in a loop. The vectors comprising the Jordan Chains will then be used to
minimize the amount of equation solving in order to find the remaining
generalized eigenvector basis. We will prove a theorem that justifies why the
resulting Jordan Chains are of maximal length. We will also justify how to
derive the starting vector which will subsequently be used to calculate the
Maximal Jordan Chains.


title:
Essential self-adjointness for the Klein-Gordon type operators on
  asymptotically static spacetime

abstract:
  Let $X=\mathbb{R}\times M$ be the spacetime, where $M$ is a closed manifold
equipped with a Riemannian metric $g$, and we consider a symmetric Klein-Gordon
type operator $P$ on $X$, which is asymptotically converges to
$\partial_t^2-\triangle_g$ as $|t|\to\infty$, where $\triangle_g$ is the
Laplace-Beltrami operator on $M$. We prove the essential self-adjointness of
$P$ on $C_0^\infty(X)$. The idea of the proof is closely related to a recent
paper by the authors on the essential self-adjointness for Klein-Gordon
operators on asymptotically flat spaces.


title: A Steinberg algebra approach to \'etale groupoid C*-algebras

abstract:
  We construct the full and reduced C*-algebras of an ample groupoid from its
complex Steinberg algebra. We also show that our construction gives the same
C*-algebras as the standard constructions. In the last section, we consider an
arbitrary locally compact, second-countable, \'etale groupoid, possibly
non-Hausdorff. Using the techniques developed for Steinberg algebras, we show
that every $*$-homomorphism from Connes' space of functions to $B(\mathcal{H})$
is automatically I-norm bounded. Previously, this was only known for Hausdorff
groupoids.


title:
Exploring the Quark Transversity and the Collins Fragmentation Functions
  using Polarized $pp$ Collisions at STAR

abstract:
  Understanding the internal spin structure of the nucleon still remains a
challenge in strong interaction physics. Transversity, which describes the
transverse spin structure of quarks in a transversely polarized proton, is
poorly constrained by experimental data. Since it is chiral-odd, it can only be
accessed through channels that couple to other chiral-odd distributions, like
the Collins fragmentation functions (so-called Collins effect) or the
interference fragmentation functions. Recently, a detailed calculation using
the soft-collinear effective theory found that the Collins effect in $pp$
collisions involves a mixture of collinear and transverse momentum dependent
(TMD) factorization. The Collins effect provides a direct probe to the Collins
fragmentation function and enables testing of its evolution, universality and
factorization breaking in the transverse momentum dependent formalism. In 2018,
STAR published the first measurements of Collins asymmetries for charged pions
in jets in polarized $pp$ collisions at $\sqrt{s}$ = 500 GeV based on data
taken during 2011. These measurements probe $Q^2$ scales one to two orders of
magnitude larger than similar measurements in semi-inclusive deep-inelastic
scattering (SIDIS) and the results are consistent with predictions based on
global analyses of $e^{+}e^{-}$ and SIDIS data. In 2012 and 2015, STAR
collected $\sim$14 $\mathrm{pb^{-1}}$ and $\sim$52 $\mathrm{pb^{-1}}$ of
transversely polarized $pp$ data at $\sqrt{s}$ = 200 GeV, respectively. These
datasets provide the most precise measurement of the Collins effect in 200 GeV
$pp$ collisions to date, especially at the quark momentum fractions $0.1 \le x
\le 0.4$. These proceedings present the preliminary results for Collins
asymmetries of identified pions in jets in $pp$ collisions at $\sqrt{s}$ = 200
GeV and comparisons to theory predictions.


title: Bistability, Bifurcations and Chaos in the Mackey-Glass Equation

abstract:
  Numerical bifurcation analysis, and in particular two-parameter continuation,
is used in consort with numerical simulation to reveal complicated dynamics in
the Mackey-Glass equation for moderate values of the delay close to the onset
of chaos. In particular a cusp bifurcation of periodic orbits and resulting
branches of folds of periodic orbits effectively partition the parameter space
into regions where different behaviours are seen. The cusp bifurcation leads
directly to bistability between periodic orbits, and subsequently to
bistability between a periodic orbit and a chaotic attractor. This leads to two
different mechanisms by which the chaotic attractor is destroyed in a global
bifurcation with a periodic orbit in either an interior crisis or a boundary
crisis. In another part of parameter space a sequence of subcritical
period-doublings is found to give rise to bistability between a periodic orbit
and a chaotic attractor. Torus bifurcations, and a codimension-two fold-flip
bifurcation are also identified, and Lyapunov exponent computations are used to
determine chaotic regions and attractor dimension.


title:
Generation of Maximally Entangled States by Lyapunov Control Based on
  Entanglement Measure

abstract:
  The quantum state with the greatest degree of entanglement has the highest
value in quantum information processing. The existing quantum control methods
treat the generation of the maximally entangled state (MES) as a problem of
state transfer by specifying the desired MES as the target state. Current
methods suffer from two major deficiencies: the structure of the MES to be
prepared must be known in advance, and the quantum control can only be designed
for one MES at a time, and when the target MES changes, the quantum control
must be redesigned. In order to solve these two deficiencies, this paper
proposes an improved quantum Lyapunov control method, in which the
establishment of the Lyapunov function is based on the measure of quantum
entanglement rather than the distance between two quantum states. This
innovative approach allows us to prepare all MESs, whether their structures are
known or unknown in advance, through a single control design. Since the control
target is the scalar entanglement measure, not the quantum state vector, the
entanglement control strategy proposed in this paper is not influenced by the
number of entangled particles. The proposed method will be applied to bipartite
pure states first to show that all Bell states and their equivalent states can
be prepared through one control design. Secondly, it is applied to bipartite
mixed states and multipartite states to show that this method has the ability
to generate currently unknown MESs.


title:
$ \text{T}^3 $OMVP: A Transformer-based Time and Team Reinforcement
  Learning Scheme for Observation-constrained Multi-Vehicle Pursuit in Urban
  Area

abstract:
  Smart Internet of Vehicles (IoVs) combined with Artificial Intelligence (AI)
will contribute to vehicle decision-making in the Intelligent Transportation
System (ITS). Multi-Vehicle Pursuit games (MVP), a multi-vehicle cooperative
ability to capture mobile targets, is becoming a hot research topic gradually.
Although there are some achievements in the field of MVP in the open space
environment, the urban area brings complicated road structures and restricted
moving spaces as challenges to the resolution of MVP games. We define an
Observation-constrained MVP (OMVP) problem in this paper and propose a
Transformer-based Time and Team Reinforcement Learning scheme ($ \text{T}^3
$OMVP) to address the problem. First, a new multi-vehicle pursuit model is
constructed based on decentralized partially observed Markov decision processes
(Dec-POMDP) to instantiate this problem. Second, by introducing and modifying
the transformer-based observation sequence, QMIX is redefined to adapt to the
complicated road structure, restricted moving spaces and constrained
observations, so as to control vehicles to pursue the target combining the
vehicle's observations. Third, a multi-intersection urban environment is built
to verify the proposed scheme. Extensive experimental results demonstrate that
the proposed $ \text{T}^3 $OMVP scheme achieves significant improvements
relative to state-of-the-art QMIX approaches by 9.66%~106.25%. Code is
available at https://github.com/pipihaiziguai/T3OMVP.


title: On the impact of outliers in loss reserving

abstract:
  The sensitivity of loss reserving techniques to outliers in the data or
deviations from model assumptions is a well known challenge. It has been shown
that the popular chain-ladder reserving approach is at significant risk to such
aberrant observations in that reserve estimates can be significantly shifted in
the presence of even one outlier. As a consequence the chain-ladder reserving
technique is non-robust. In this paper we investigate the sensitivity of
reserves and mean squared errors of prediction under Mack's Model (Mack, 1993).
This is done through the derivation of impact functions which are calculated by
taking the first derivative of the relevant statistic of interest with respect
to an observation. We also provide and discuss the impact functions for
quantiles when total reserves are assumed to be lognormally distributed.
Additionally, comparisons are made between the impact functions for individual
accident year reserves under Mack's Model and the Bornhuetter-Ferguson
methodology. It is shown that the impact of incremental claims on these
statistics of interest varies widely throughout a loss triangle and is heavily
dependent on other cells in the triangle.
  Results are illustrated using data from a Belgian non-life insurer.


title:
Deep Extragalactic VIsible Legacy Survey (DEVILS): The emergence of
  bulges and decline of disk growth since $z = 1$

abstract:
  The majority of the stellar mass in the Universe today resides in galaxies
with two primary structural components (bulge and disk). In this work, we use
the largest contiguous HST imaging region (COSMOS), the Deep Extragalactic
VIsible Legacy Survey (DEVILS), and the galaxy structural fitting code {\sc
ProFit}, to deconstruct $\sim 35,000$ galaxies into their sub-structures. We
use this sample to determine the stellar mass density (SMD) sub-divided by
structural components and its evolution since $z = 1$. We find that the
majority of stellar mass at all epochs lies in disk-like structures. The SMD in
the disk population increases in $z = 1-0.35$ and stabilizes/decreases to $z =
0$ (contributing $\sim 60\%$ to the total SMD at $z = 1$ and declining to $\sim
30\%$ at $z = 0$). This decline is countered by a rapid rise of the SMD in
pseudo-bulge population and a consistent growth of spheroidal structures
(classical bulges and ellipticals) with significant stellar mass growth in $z =
1-0.35$ and a somewhat flattened trend to $z = 0$. While the physical
mechanisms for this are not obvious, the results are consistent with a
transition from a Universe dominated by disk growth, to a Universe in which
pseudo-bulges are emerging and spheroids are growing. Further study is required
before this can be apportioned to internal secular processes, gas accretion,
minor and major mergers. However, it is clear that since $z = 0.35$ the
processes mentioned above now dominate over quiescent disk growth as the cosmic
star-formation history declines.


title:
ACTIVE:Augmentation-Free Graph Contrastive Learning for Partial
  Multi-View Clustering

abstract:
  In this paper, we propose an augmentation-free graph contrastive learning
framework, namely ACTIVE, to solve the problem of partial multi-view
clustering. Notably, we suppose that the representations of similar samples
(i.e., belonging to the same cluster) and their multiply views features should
be similar. This is distinct from the general unsupervised contrastive learning
that assumes an image and its augmentations share a similar representation.
Specifically, relation graphs are constructed using the nearest neighbours to
identify existing similar samples, then the constructed inter-instance relation
graphs are transferred to the missing views to build graphs on the
corresponding missing data. Subsequently, two main components, within-view
graph contrastive learning (WGC) and cross-view graph consistency learning
(CGC), are devised to maximize the mutual information of different views within
a cluster. The proposed approach elevates instance-level contrastive learning
and missing data inference to the cluster-level, effectively mitigating the
impact of individual missing data on clustering. Experiments on several
challenging datasets demonstrate the superiority of our proposed methods.


title:
Robots Autonomously Detecting People: A Multimodal Deep Contrastive
  Learning Method Robust to Intraclass Variations

abstract:
  Robotic detection of people in crowded and/or cluttered human-centered
environments including hospitals, long-term care, stores and airports is
challenging as people can become occluded by other people or objects, and
deform due to variations in clothing or pose. There can also be loss of
discriminative visual features due to poor lighting. In this paper, we present
a novel multimodal person detection architecture to address the mobile robot
problem of person detection under intraclass variations. We present a two-stage
training approach using 1) a unique pretraining method we define as Temporal
Invariant Multimodal Contrastive Learning (TimCLR), and 2) a Multimodal Faster
R-CNN (MFRCNN) detector. TimCLR learns person representations that are
invariant under intraclass variations through unsupervised learning. Our
approach is unique in that it generates image pairs from natural variations
within multimodal image sequences, in addition to synthetic data augmentation,
and contrasts crossmodal features to transfer invariances between different
modalities. These pretrained features are used by the MFRCNN detector for
finetuning and person detection from RGB-D images. Extensive experiments
validate the performance of our DL architecture in both human-centered crowded
and cluttered environments. Results show that our method outperforms existing
unimodal and multimodal person detection approaches in terms of detection
accuracy in detecting people with body occlusions and pose deformations in
different lighting conditions.


title: Three-Port Impedance Model and Validation of VSCs for Stability Analysis

abstract:
  Modern power system is undergoing a paradigm shift from the synchronous
generators-based system to the power electronics converters-dominated system.
With the high penetration of converters, serious stability problems are
provoked, especially the wideband oscillations. Various studies have been
conducted in this respect, while most of them separate the ac-side stability
with the dc-side stability. However, for the stability analysis of the hybrid
AC/DC grid, it is necessary to consider the converter ac-side and dc-side,
simultaneously. In this paper, the stability analysis of voltage source
converters (VSCs) considering both ac and dc dynamics is carried out. At first,
the three-port AC/DC admittance model of VSCs is established, and the
corresponding measurement method from simulations is presented to validate its
accuracy. Secondly, based on such three-port model, two stability analysis
methods are presented: the one is based on the system open-loop model, where
the stability can be judged via the Generalized Nyquist Criterion (GNC); the
other one is based on the system closed-loop model, whose stability can be
predicted through the pole-zero calculation. At last, a test AC/DC system is
built in MATLAB/Simulink, by which the effectiveness of the three-port
model-based stability analysis is validated.


title:
Efficient and Robust Entanglement Generation with Deep Reinforcement
  Learning for Quantum Metrology

abstract:
  Quantum metrology exploits quantum resources and strategies to improve
measurement precision of unknown parameters. One crucial issue is how to
prepare a quantum entangled state suitable for high-precision measurement
beyond the standard quantum limit. Here, we propose a scheme to find optimal
pulse sequence to accelerate the one-axis twisting dynamics for entanglement
generation with the aid of deep reinforcement learning (DRL). We consider the
pulse train as a sequence of $\pi/2$ pulses along one axis or two orthogonal
axes, and the operation is determined by maximizing the quantum Fisher
information using DRL. Within a limited evolution time, the ultimate precision
bounds of the prepared entangled states follow the Heisenberg-limited scalings.
These states can also be used as the input states for Ramsey interferometry and
the final measurement precisions still follow the Heisenberg-limited scalings.
While the pulse train along only one axis is more simple and efficient, the
scheme using pulse sequence along two orthogonal axes show better robustness
against atom number deviation. Our protocol with DRL is efficient and easy to
be implemented in state-of-the-art experiments.


title:
Semi-supervised Deep Learning for Image Classification with Distribution
  Mismatch: A Survey

abstract:
  Deep learning methodologies have been employed in several different fields,
with an outstanding success in image recognition applications, such as material
quality control, medical imaging, autonomous driving, etc. Deep learning models
rely on the abundance of labelled observations to train a prospective model.
These models are composed of millions of parameters to estimate, increasing the
need of more training observations. Frequently it is expensive to gather
labelled observations of data, making the usage of deep learning models not
ideal, as the model might over-fit data. In a semi-supervised setting,
unlabelled data is used to improve the levels of accuracy and generalization of
a model with small labelled datasets. Nevertheless, in many situations
different unlabelled data sources might be available. This raises the risk of a
significant distribution mismatch between the labelled and unlabelled datasets.
Such phenomena can cause a considerable performance hit to typical
semi-supervised deep learning frameworks, which often assume that both labelled
and unlabelled datasets are drawn from similar distributions. Therefore, in
this paper we study the latest approaches for semi-supervised deep learning for
image recognition. Emphasis is made in semi-supervised deep learning models
designed to deal with a distribution mismatch between the labelled and
unlabelled datasets. We address open challenges with the aim to encourage the
community to tackle them, and overcome the high data demand of traditional deep
learning pipelines under real-world usage settings.


title:
NeuRecover: Regression-Controlled Repair of Deep Neural Networks with
  Training History

abstract:
  Systematic techniques to improve quality of deep neural networks (DNNs) are
critical given the increasing demand for practical applications including
safety-critical ones. The key challenge comes from the little controllability
in updating DNNs. Retraining to fix some behavior often has a destructive
impact on other behavior, causing regressions, i.e., the updated DNN fails with
inputs correctly handled by the original one. This problem is crucial when
engineers are required to investigate failures in intensive assurance
activities for safety or trust. Search-based repair techniques for DNNs have
potentials to tackle this challenge by enabling localized updates only on
"responsible parameters" inside the DNN. However, the potentials have not been
explored to realize sufficient controllability to suppress regressions in DNN
repair tasks. In this paper, we propose a novel DNN repair method that makes
use of the training history for judging which DNN parameters should be changed
or not to suppress regressions. We implemented the method into a tool called
NeuRecover and evaluated it with three datasets. Our method outperformed the
existing method by achieving often less than a quarter, even a tenth in some
cases, number of regressions. Our method is especially effective when the
repair requirements are tight to fix specific failure types. In such cases, our
method showed stably low rates (<2%) of regressions, which were in many cases a
tenth of regressions caused by retraining.


title: Layer Adaptive Deep Neural Networks for Out-of-distribution Detection

abstract:
  During the forward pass of Deep Neural Networks (DNNs), inputs gradually
transformed from low-level features to high-level conceptual labels. While
features at different layers could summarize the important factors of the
inputs at varying levels, modern out-of-distribution (OOD) detection methods
mostly focus on utilizing their ending layer features. In this paper, we
proposed a novel layer-adaptive OOD detection framework (LA-OOD) for DNNs that
can fully utilize the intermediate layers' outputs. Specifically, instead of
training a unified OOD detector at a fixed ending layer, we train multiple
One-Class SVM OOD detectors simultaneously at the intermediate layers to
exploit the full spectrum characteristics encoded at varying depths of DNNs. We
develop a simple yet effective layer-adaptive policy to identify the best layer
for detecting each potential OOD example. LA-OOD can be applied to any existing
DNNs and does not require access to OOD samples during the training. Using
three DNNs of varying depth and architectures, our experiments demonstrate that
LA-OOD is robust against OODs of varying complexity and can outperform
state-of-the-art competitors by a large margin on some real-world datasets.


title:
EPPAC: Entity Pre-typing Relation Classification with Prompt
  AnswerCentralizing

abstract:
  Relation classification (RC) aims to predict the relationship between a pair
of subject and object in a given context. Recently, prompt tuning approaches
have achieved high performance in RC. However, existing prompt tuning
approaches have the following issues: (1) numerous categories decrease RC
performance; (2) manually designed prompts require intensive labor. To address
these issues, a novel paradigm, Entity Pre-typing Relation Classification with
Prompt Answer Centralizing(EPPAC) is proposed in this paper. The entity
pre-tying in EPPAC is presented to address the first issue using a double-level
framework that pre-types entities before RC and prompt answer centralizing is
proposed to address the second issue. Extensive experiments show that our
proposed EPPAC outperformed state-of-the-art approaches on TACRED and TACREV by
14.4% and 11.1%, respectively. The code is provided in the Supplementary
Materials.


title: Private Frequency Estimation via Projective Geometry

abstract:
  In this work, we propose a new algorithm ProjectiveGeometryResponse (PGR) for
locally differentially private (LDP) frequency estimation. For a universe size
of $k$ and with $n$ users, our $\varepsilon$-LDP algorithm has communication
cost $\lceil\log_2k\rceil$ bits in the private coin setting and
$\varepsilon\log_2 e + O(1)$ in the public coin setting, and has computation
cost $O(n + k\exp(\varepsilon) \log k)$ for the server to approximately
reconstruct the frequency histogram, while achieving the state-of-the-art
privacy-utility tradeoff. In many parameter settings used in practice this is a
significant improvement over the $ O(n+k^2)$ computation cost that is achieved
by the recent PI-RAPPOR algorithm (Feldman and Talwar; 2021). Our empirical
evaluation shows a speedup of over 50x over PI-RAPPOR while using approximately
75x less memory for practically relevant parameter settings. In addition, the
running time of our algorithm is within an order of magnitude of
HadamardResponse (Acharya, Sun, and Zhang; 2019) and RecursiveHadamardResponse
(Chen, Kairouz, and Ozgur; 2020) which have significantly worse reconstruction
error. The error of our algorithm essentially matches that of the
communication- and time-inefficient but utility-optimal SubsetSelection (SS)
algorithm (Ye and Barg; 2017). Our new algorithm is based on using Projective
Planes over a finite field to define a small collection of sets that are close
to being pairwise independent and a dynamic programming algorithm for
approximate histogram reconstruction on the server side. We also give an
extension of PGR, which we call HybridProjectiveGeometryResponse, that allows
trading off computation time with utility smoothly.


title: Do Atoms Age?

abstract:
  Time evolution generically entangles a quantum state with environmental
degrees of freedom. The resulting increase in entropy changes the properties of
that quantum system leading to "aging". It is interesting to ask if this
familiar property also applies to simple, single particle quantum systems such
as the decay of a radioactive particle. We propose a test of such aging in an
ion clock setup where we probe for temporal changes to the energies of the
electronic state of an ion containing a radioactive nucleus. Such effects are
absent in standard quantum mechanics and this test is thus a potent null test
for violations of quantum mechanics. As a proof of principle, we show that
these effects exist in causal non-linear modifications of quantum mechanics.


title: Atmospheric aerosol clearing by femtosecond filaments

abstract:
  Atmospheric aerosols, such as water droplets in fog, interfere with laser
propagation through scattering and absorption. Femtosecond optical filaments
have been shown to clear foggy regions, improving transmission of subsequent
pulses. However, the detailed fog clearing mechanism had yet to be determined.
Here we directly measure and simulate the dynamics of ~5 micron radius water
droplets, typical of fog, under the influence of optical and acoustic
interactions characteristic of femtosecond filaments. We find that for
filaments generated by the collapse of collimated near-infrared femtosecond
pulses, the main droplet clearing mechanism is optical shattering by laser
light. For such filaments, the single cycle acoustic wave launched by filament
energy deposition in air leaves droplets intact and drives negligible
transverse displacement, and therefore negligible fog clearing. Only for
tightly focused non-filamentary pulses, where local energy deposition greatly
exceeds that of a filament, do acoustic waves significantly displace aerosols.


title:
Online Gradient Descent for Flexible Power Point Tracking Under a Highly
  Fluctuating Weather and Load

abstract:
  The increasing electricity demand and the need for clean and renewable energy
resources to satisfy this demand in a cost-effective manner, imposes new
challenges on researchers and developers to maximize the output of these
renewable resources at all times. However, the increasing penetration of
renewable energy into the grid imposes new challenges on the grid operators.
All of these challenges and issues gave rise to the need of Maximum Power Point
Tracker (MPPT) and Flexible Power Point Trackers (FPPT) in order to maximize
the power extracted from Photovoltaic (PV) systems and meet the grid operation
constraints. Existing solutions for these algorithms do not take into
consideration the very high dynamical nature of weather conditions that affects
the output power that can be extracted from the PV modules, whereas in
practice, the weather changes dynamically faster than what the algorithms time
needed to converge. The work in this document is an attempt to address this
shortcoming address shortcoming by utilizing online optimization algorithms for
this purpose. Numerical analysis and verification are presented in the
document. Code for the algorithms can be found at this link


title:
Predicting the Future Performance of the Planned Seismic Network in
  Mainland China: II. Earthquake Early Warning

abstract:
  The China Earthquake Administration (CEA) has launched an ambitious
nationwide earthquake early warning (EEW) system project that is currently
under development, which will consist of approximately 15,000 seismic stations
and be the largest EEW system in the world. The new EEW system is planned to go
online by the end of 2022. In 23% and 3% of Mainland China, the inter-station
distance will soon be smaller than 50 km and 25 km, respectively. The
effectiveness of the EEW system expected inside Mainland China can be
quantified via the metric given by the radius of the blind zone (no-warning
zone). Using theoretical network-based method, we generate the spatial
distribution of the blind zone radii predicted for the new seismic network
based on its configuration. The densified new seismic network is expected to
have excellent EEW performance from the perspective of blind zone. The area
covered by blind zones that are smaller than 30 km will soon rise from 1.6% to
24.3% inside Mainland China, which means that the area will increase by 2.6
million km2 (almost the size of Kazakhstan). We claim that every 1,000,000 RMB
(158,000 USD) invested to densifying the planned network will increase the area
where the blind zone radius is smaller than 30 km by 3,000 km2. Continuing to
increase the density of stations in some key regions with the blind zone radii
ranging from 20 to 40 km is still necessary to control the unexpected expansion
of blind zones due to the possible (and common) stations failure. Our
investigation provides a useful reference for the real functioning and further
optimization of the EEW system in Mainland China.


title:
Equivariant and Stable Positional Encoding for More Powerful Graph
  Neural Networks

abstract:
  Graph neural networks (GNN) have shown great advantages in many graph-based
learning tasks but often fail to predict accurately for a task-based on sets of
nodes such as link/motif prediction and so on. Many works have recently
proposed to address this problem by using random node features or node distance
features. However, they suffer from either slow convergence, inaccurate
prediction, or high complexity. In this work, we revisit GNNs that allow using
positional features of nodes given by positional encoding (PE) techniques such
as Laplacian Eigenmap, Deepwalk, etc. GNNs with PE often get criticized because
they are not generalizable to unseen graphs (inductive) or stable. Here, we
study these issues in a principled way and propose a provable solution, a class
of GNN layers termed PEG with rigorous mathematical analysis. PEG uses separate
channels to update the original node features and positional features. PEG
imposes permutation equivariance w.r.t. the original node features and rotation
equivariance w.r.t. the positional features simultaneously. Extensive link
prediction experiments over 8 real-world networks demonstrate the advantages of
PEG in generalization and scalability.


title:
Topological susceptibility and fourth cumulant in a uniform magnetic
  field

abstract:
  We study the topological susceptibility and fourth cumulant of the QCD vacuum
in a background magnetic field using three-flavor chiral perturbation theory
($\chi$PT) for arbitrary quark masses and $n$-flavor $\chi$PT with degenerate
quark masses. We find that the enhancement of the topological susceptibility is
larger in the three-flavor $\chi$PT compared to two-flavor $\chi$PT.
Additionally, in comparing the fourth cumulant, we find that its suppression is
comparable for magnetic fields, $eH\lesssim 0.8m_{\pi}^{2}$, and weaker for
larger magnetic fields in three-flavor $\chi$PT with its enhancement beginning
at a significantly lower critical magnetic field compared to two-flavor
$\chi$PT. We also find that the enhancement of the topological susceptibility
in $n$-flavor $\chi$PT with degenerate quarks is significantly larger and the
suppression of the topological cumulant significantly greater at weak fields
with the critical magnetic field pushed out to larger magnetic fields compared
to both two and three-flavor $\chi$PT.


title:
RMBR: A Regularized Minimum Bayes Risk Reranking Framework for Machine
  Translation

abstract:
  Beam search is the most widely used decoding method for neural machine
translation (NMT). In practice, the top-1 candidate with the highest
log-probability among the n candidates is selected as the preferred one.
However, this top-1 candidate may not be the best overall translation among the
n-best list. Recently, Minimum Bayes Risk (MBR) decoding has been proposed to
improve the quality for NMT, which seeks for a consensus translation that is
closest on average to other candidates from the n-best list. We argue that MBR
still suffers from the following problems: The utility function only considers
the lexical-level similarity between candidates; The expected utility considers
the entire n-best list which is time-consuming and inadequate candidates in the
tail list may hurt the performance; Only the relationship between candidates is
considered. To solve these issues, we design a regularized MBR reranking
framework (RMBR), which considers semantic-based similarity and computes the
expected utility for each candidate by truncating the list. We expect the
proposed framework to further consider the translation quality and model
uncertainty of each candidate. Thus the proposed quality regularizer and
uncertainty regularizer are incorporated into the framework. Extensive
experiments on multiple translation tasks demonstrate the effectiveness of our
method.


title:
Evaluation of Controllers and Development of a new in-house Controller
  for the Teledyne HxRG Focal Plane Array for the IRSIS satellite payload

abstract:
  The Infrared Astronomy Group (Department of Astronomy and Astrophysics) at
Tata Institute of Fundamental Research (TIFR) is presently developing
controllers for the Teledyne HxRG Focal Plane Arrays (FPAs) to be used on board
the Infrared Spectroscopic Imaging Survey (IRSIS) satellite payload. In this
manuscript we discuss the results of our tests with different FPA controllers
like the Astronomical Research Cameras (ARC) controller, Teledyne's SIDECAR
ASIC as well as our new in-house designed Array controller. As part of the
development phase of the IRSIS instrument, which is an optical fibre based
Integral Field Unit (IFU) Near-Infrared (NIR) Spectrometer, a laboratory model
with limited NIR bandwidth was built which consisted of various subsystems like
a Ritchey-Chretien (RC) 30 cm telescope, optical fibre IFU, spectrometer
optics, and the Teledyne H2RG detector module. We discuss the various
developments during the building and testing of the IRSIS laboratory model and
the technical aspects of the prototype in-house H2RG controller.


title: The Hirota Variety of a Rational Nodal Curve

abstract:
  The Hirota variety parametrizes solutions to the KP equation arising from a
degenerate Riemann theta function. In this work we study in detail the Hirota
variety arising from a rational nodal curve. Of particular interest is the
irreducible subvariety defined as the image of a parametrization map, we call
this the main component. Proving that this is an irreducible component of the
Hirota variety corresponds to solving a weak Schottky problem for rational
nodal curves. We solve this problem up to genus seven using computational
tools.


title:
Riemannian statistics meets random matrix theory: towards learning from
  high-dimensional covariance matrices

abstract:
  Riemannian Gaussian distributions were initially introduced as basic building
blocks for learning models which aim to capture the intrinsic structure of
statistical populations of positive-definite matrices (here called covariance
matrices). While the potential applications of such models have attracted
significant attention, a major obstacle still stands in the way of these
applications: there seems to exist no practical method of computing the
normalising factors associated with Riemannian Gaussian distributions on spaces
of high-dimensional covariance matrices. The present paper shows that this
missing method comes from an unexpected new connection with random matrix
theory. Its main contribution is to prove that Riemannian Gaussian
distributions of real, complex, or quaternion covariance matrices are
equivalent to orthogonal, unitary, or symplectic log-normal matrix ensembles.
This equivalence yields a highly efficient approximation of the normalising
factors, in terms of a rather simple analytic expression. The error due to this
approximation decreases like the inverse square of dimension. Numerical
experiments are conducted which demonstrate how this new approximation can
unlock the difficulties which have impeded applications to real-world datasets
of high-dimensional covariance matrices. The paper then turns to Riemannian
Gaussian distributions of block-Toeplitz covariance matrices. These are
equivalent to yet another kind of random matrix ensembles, here called
"acosh-normal" ensembles. Orthogonal and unitary "acosh-normal" ensembles
correspond to the cases of block-Toeplitz with Toeplitz blocks, and
block-Toeplitz (with general blocks) covariance matrices, respectively.


title:
Predicting the Future Performance of the Planned Seismic Network in
  Mainland China

abstract:
  The new broadband seismic network in China will increase the number of
stations from approximately 950 to 2000. The higher-resolution monitoring of
the frequent smaller earthquakes expected inside Mainland China can be
quantified via the completeness magnitude (Mc) metric. Using the Bayesian
Magnitude of Completeness (BMC) method, we generate the spatial distribution of
Mc predicted for the new network, based on the prior model calibrated on the
current earthquake catalog (2012 to 2021) and network configuration. If 99% of
Mainland China is at present covered down to Mc = 2.7, this threshold will soon
fall to Mc = 2.0. This means approximately 3 times more earthquakes available
per year. Based on the observation that seismic precursors are most likely to
be observed at least at 3 units below the mainshock magnitude, the new seismic
network shall achieve the goal of almost total coverage for optimal
seismic-based earthquake prediction research.


title:
Observation of fractional quantum numbers at photonic topological edges
  and corners

abstract:
  Topological phases of matter are featured with exotic edge states. However,
the fractional quantum numbers at edges, though predicted long ago by Jackiw
and Rebbi, remain elusive in topological photonic systems. Here, we report on
the observation of fractional quantum numbers at the topological edges and
corners in one- and two-dimensional photonic crystals. The fractional quantum
numbers are determined via the measurements of the photonic local
density-of-states. In one-dimensional photonic crystals, we witness a rapid
change of the fractional quantum number at the edges rising from 0 to 1/2 when
the photonic band gap experiences a topological transition, confirming the
well-known prediction of Jackiw and Rebbi. In two-dimensional systems, we
discover that the fractional quantum number in the corner region varies from 0
to 1/2 and 1/4 in different photonic band gap phases. Our study paves a
promising way toward topological manipulation of fractional quantum numbers in
photonics.


title: Generalized hypergeometric $G$-functions take linear independent values

abstract:
  In this article, we show a new general linear independence criterion related
to values of $G$-functions, including the linear independence of values at
algebraic points of contiguous hypergeometric functions, which is not known
before. Let $K$ be any algebraic number field and $v$ be a place of $K$. Let
$r\in\mathbb{Z}$ with $r\ge2$. Consider $a_1,\ldots,a_{r},
b_1,\ldots,b_{r-1}\in \mathbb{Q}\setminus\{0\}$ not being negative integers.
Assume neither $a_k$ nor $a_k+1-b_j$ be strictly positive integers $(1\le k \le
r, 1\le j \le r-1)$. Let $\alpha_1,\ldots,\alpha_m\in K\setminus\{0\}$ with
$\alpha_1,\ldots,\alpha_m$ pairwise distinct. By choosing sufficiently large
$\beta\in \mathbb{Z}$ depending on $K$ and $v$ such that the points
$\alpha_1/\beta,\ldots,\alpha_m/\beta$ are closed enough to the origin, we
prove that the $rm+1$ numbers~$:$ \begin{align*} &{}_{r}F_{r-1}
\biggl(\begin{matrix} a_1,\ldots, a_r\\ b_1, \ldots, b_{r-1} \end{matrix}
\biggm| \dfrac{\alpha_i}{\beta}\biggr)\enspace, \ \ {}_{r}F_{r-1}
\biggl(\begin{matrix} a_1+1,\ldots,\ldots,\ldots,a_r+1\\ b_1+1, \ldots,
b_{r-s}+1,b_{r-s+1},\ldots,b_{r-1} \end{matrix} \biggm|
\dfrac{\alpha_i}{\beta}\biggr)\enspace\\ &(1\le i \le m, 1\le s \le
r-1)\end{align*} and $1$ are linearly independent over $K$. The essential
ingredient is our term-wise formal construction of type II of Pad\'e
approximants together with new non-vanishing argument for the generalized
Wronskian.


title: Automorphisms and representations of quasi Laurent polynomial algebras

abstract:
  We study automorphisms and representations of quasi polynomial algebras
(QPAs) and quasi Laurent polynomial algebras (QLPAs). For any QLPA defined by
an arbitrary skew symmetric integral matrix, we explicitly describe its
automorphism groups at generic $q$ and at roots of unity. Any QLPA is
isomorphic to the tensor product of copies of the QLPA of degree $2$ at
different powers of $q$ and the centre, thus the study of representations of
QPAs and QLPAs largely reduces to that of ${\mathcal L}_q(2)$ and ${\mathcal
A}_q(2)$, the QLPA and QPA of degree $2$. We study a category of ${\mathcal
A}_q(2)$-modules which have finite covers by submodules with natural local
finiteness properties and satisfy some condition under localisation,
determining its blocks, classifying the simple objects and providing two
explicitly constructions for the simples. One construction produces the simple
${\mathcal A}_q(2)$-modules from ${\mathcal L}_q(2)$-modules via monomorphisms
composed of the natural embedding of ${\mathcal A}_q(2)$ in ${\mathcal L}_q(2)$
and automorphisms of ${\mathcal L}_q(2)$, and the other explores a class of
holonomic ${\mathcal D}_q$-modules for the algebra ${\mathcal D}_q$ of
$q$-differential operators.


title: Tail bounds for detection times in mobile hyperbolic graphs

abstract:
  Motivated by Krioukov et al.'s model of random hyperbolic graphs for
real-world networks, and inspired by the analysis of a dynamic model of graphs
in Euclidean space by Peres et al., we introduce a dynamic model of hyperbolic
graphs in which vertices are allowed to move according to a Brownian motion
maintaining the distribution of vertices in hyperbolic space invariant. For
different parameters of the speed of angular and radial motion, we analyze tail
bounds for detection times of a fixed target and obtain a complete picture, for
very different regimes, of how and when the target is detected: as a function
of the time passed, we characterize the subset of the hyperbolic space where
particles typically detecting the target are initially located.
  We overcome several substantial technical difficulties not present in
Euclidean space, and provide a complete picture on tail bounds. On the way, we
obtain also new results for the time more general continuous processes with
drift and reflecting barrier spent in certain regions, and we also obtain
improved bounds for independent sums of Pareto random variables.


title:
Interactive Human-in-the-loop Coordination of Manipulation Skills
  Learned from Demonstration

abstract:
  Learning from demonstration (LfD) provides a fast, intuitive and efficient
framework to program robot skills, which has gained growing interest both in
research and industrial applications. Most complex manipulation tasks are
long-term and involve a set of skill primitives. Thus it is crucial to have a
reliable coordination scheme that selects the correct sequence of skill
primitive and the correct parameters for each skill, under various scenarios.
Instead of relying on a precise simulator, this work proposes a
human-in-the-loop coordination framework for LfD skills that: builds
parameterized skill models from kinesthetic demonstrations; constructs a
geometric task network (GTN) on-the-fly from human instructions; learns a
hierarchical control policy incrementally during execution. This framework can
reduce significantly the manual design efforts, while improving the
adaptability to new scenes. We show on a 7-DoF robotic manipulator that the
proposed approach can teach complex industrial tasks such as bin sorting and
assembly in less than 30 minutes.


title:
Investigating Selective Prediction Approaches Across Several Tasks in
  IID, OOD, and Adversarial Settings

abstract:
  In order to equip NLP systems with selective prediction capability, several
task-specific approaches have been proposed. However, which approaches work
best across tasks or even if they consistently outperform the simplest baseline
'MaxProb' remains to be explored. To this end, we systematically study
'selective prediction' in a large-scale setup of 17 datasets across several NLP
tasks. Through comprehensive experiments under in-domain (IID), out-of-domain
(OOD), and adversarial (ADV) settings, we show that despite leveraging
additional resources (held-out data/computation), none of the existing
approaches consistently and considerably outperforms MaxProb in all three
settings. Furthermore, their performance does not translate well across tasks.
For instance, Monte-Carlo Dropout outperforms all other approaches on Duplicate
Detection datasets but does not fare well on NLI datasets, especially in the
OOD setting. Thus, we recommend that future selective prediction approaches
should be evaluated across tasks and settings for reliable estimation of their
capabilities.


title:
Influence in Completely Bounded Block-multilinear Forms and Classical
  Simulation of Quantum Algorithms

abstract:
  The Aaronson-Ambainis conjecture (Theory of Computing '14) says that every
low-degree bounded polynomial on the Boolean hypercube has an influential
variable. This conjecture, if true, would imply that the acceptance probability
of every $d$-query quantum algorithm can be well-approximated almost everywhere
(i.e., on almost all inputs) by a $\mathrm{poly}(d)$-query classical algorithm.
We prove a special case of the conjecture: in every completely bounded
degree-$d$ block-multilinear form with constant variance, there always exists a
variable with influence at least $1/\mathrm{poly}(d)$. In a certain sense, such
polynomials characterize the acceptance probability of quantum query
algorithms, as shown by Arunachalam, Bri\"et and Palazuelos (SICOMP '19). As a
corollary we obtain efficient classical almost-everywhere simulation for a
particular class of quantum algorithms that includes for instance $k$-fold
Forrelation. Our main technical result relies on connections to free
probability theory.


title:
Optimal Routing for Multi-user Multi-hop Relay Networks via Dynamic
  Programming

abstract:
  In this paper, we study the relay selection problem in multi-user, multi-hop
relay networks with the objective of minimizing the maximum outage probability
across all users. When only one user is present, it is well known that the
optimal relay selection problem can be solved efficiently via dynamic
programming. This solution breaks down in the multi-user scenario due to
dependence between users. We resolve this challenge using a novel relay
aggregation approach. On the expanded trellis, dynamic programming can be used
to solve the optimal relay selection problem with computational complexity
linear in the number of hops. Numerical examples illustrate the efficient use
of this algorithm for relay networks.


title:
Understanding the Challenges When 3D Semantic Segmentation Faces Class
  Imbalanced and OOD Data

abstract:
  3D semantic segmentation (3DSS) is an essential process in the creation of a
safe autonomous driving system. However, deep learning models for 3D semantic
segmentation often suffer from the class imbalance problem and
out-of-distribution (OOD) data. In this study, we explore how the class
imbalance problem affects 3DSS performance and whether the model can detect the
category prediction correctness, or whether data is ID (in-distribution) or
OOD. For these purposes, we conduct two experiments using three representative
3DSS models and five trust scoring methods, and conduct both a confusion and
feature analysis of each class. Furthermore, a data augmentation method for the
3D LiDAR dataset is proposed to create a new dataset based on SemanticKITTI and
SemanticPOSS, called AugKITTI. We propose the wPre metric and TSD for a more
in-depth analysis of the results, and follow are proposals with an insightful
discussion. Based on the experimental results, we find that: (1) the classes
are not only imbalanced in their data size but also in the basic properties of
each semantic category. (2) The intraclass diversity and interclass ambiguity
make class learning difficult and greatly limit the models' performance,
creating the challenges of semantic and data gaps. (3) The trust scores are
unreliable for classes whose features are confused with other classes. For 3DSS
models, those misclassified ID classes and OODs may also be given high trust
scores, making the 3DSS predictions unreliable, and leading to the challenges
in judging 3DSS result trustworthiness. All of these outcomes point to several
research directions for improving the performance and reliability of the 3DSS
models used for real-world applications.


title:
Ultrafast laser inscribed waveguides in tailored fluoride glasses: An
  enabling technology for mid-infrared integrated photonics devices

abstract:
  Zirconium fluoride (ZBLAN) glass, the standard material used in fiber-based
mid-infrared photonics, has been re-designed to enable the fabrication of high
index-contrast low-loss waveguides via femtosecond laser direct writing. We
demonstrate that in contrast to pure ZBLAN, a positive index change of close to
10$^{-2}$ can be induced in hybrid zirconium/hafnium (Z/HBLAN) glasses during
ultrafast laser inscription and show that this can be explained by an electron
cloud distortion effect that is driven by the existence of two glass formers
with contrasting polarizability. High numerical aperture (NA) type-I waveguides
that support a well confined 3.1 $\mu$m wavelength mode with a mode-field
diameter (MFD) as small as 12 $\mu$m have successfully been fabricated. These
findings open the door for the fabrication of mid-infrared integrated photonic
devices that can readily be pigtailed to existing ZBLAN fibers.


title:
Induced Current Due to Electromagnetic Shock Produced by Charge Impact
  on a Conducting Surface

abstract:
  This paper compares the transient induced current due to the electromagnetic
shock produced by a charged particle impacting a perfectly conducting plate,
with the classical, quasi-static induced current of Ramo and Shockley (RS). We
consider the simple model of a line charge, removed upon striking the plate. We
find that the induced current due to the shock is negligible compared with the
RS current for nonrelativistic impact energies, but is more significant as the
impact energy becomes mildly relativistic. The implications of these findings
are discussed.


title: Some results on degenerate Fubini and degenerate Bell polynomials

abstract:
  The aim of this paper is to further study some properties and identities on
the degenerate Fubini and the degenerate Bell polynomials which are degenerate
versions of the Fubini and the Bell polynomials, respectively. Especially, we
find several expressions for the generating function of the sum of the values
of the generalized falling factorials at positive consecutive integers.


title:
Specialized Accelerators and Compiler Flows: Replacing Accelerator APIs
  with a Formal Software/Hardware Interface

abstract:
  Specialized accelerators are increasingly used to meet the power-performance
goals of emerging applications such as machine learning, image processing, and
graph analysis. Existing accelerator programming methodologies using APIs have
several limitations: (1) The application code lacks portability to other
platforms and compiler frameworks; (2) the lack of integration of accelerator
code in the compiler limits useful optimizations such as instruction selection
and operator fusion; and (3) the opacity of the accelerator function semantics
limits the ability to check the final code for correctness. The root of these
limitations is the lack of a formal software/hardware interface specification
for accelerators.
  In this paper, we use the recently developed Instruction-Level Abstraction
(ILA) for accelerators to serve this purpose, similar to how the Instruction
Set Architecture (ISA) has been used as the software/hardware interface for
processors. We propose a compiler flow termed D2A using the ILA and present a
prototype that demonstrates this flow for deep learning (DL) applications. This
prototype compiles programs from high-level domain-specific languages, e.g.,
PyTorch and MxNet, to multiple target accelerators with no target-specific
extensions to the application or compiler - thus demonstrating application
portability. It includes compiler optimizations through instruction selection
using equality saturation-based flexible matching. Finally, we show checking
the correctness of the resulting code through formal verification of individual
matched operations and fully automated simulation-based validation of complete
applications. The evaluation of the prototype compiler is based on six
different DL applications and three different accelerators. Overall, this
methodology lays the foundation for integrating accelerators in compiler flows
using a formal software/hardware interface.


title:
FedREP: Towards Horizontal Federated Load Forecasting for Retail Energy
  Providers

abstract:
  As Smart Meters are collecting and transmitting household energy consumption
data to Retail Energy Providers (REP), the main challenge is to ensure the
effective use of fine-grained consumer data while ensuring data privacy. In
this manuscript, we tackle this challenge for energy load consumption
forecasting in regards to REPs which is essential to energy demand management,
load switching and infrastructure development. Specifically, we note that
existing energy load forecasting is centralized, which are not scalable and
most importantly, vulnerable to data privacy threats. Besides, REPs are
individual market participants and liable to ensure the privacy of their own
customers. To address this issue, we propose a novel horizontal
privacy-preserving federated learning framework for REPs energy load
forecasting, namely FedREP. We consider a federated learning system consisting
of a control centre and multiple retailers by enabling multiple REPs to build a
common, robust machine learning model without sharing data, thus addressing
critical issues such as data privacy, data security and scalability. For
forecasting, we use a state-of-the-art Long Short-Term Memory (LSTM) neural
network due to its ability to learn long term sequences of observations and
promises of higher accuracy with time-series data while solving the vanishing
gradient problem. Finally, we conduct extensive data-driven experiments using a
real energy consumption dataset. Experimental results demonstrate that our
proposed federated learning framework can achieve sufficient performance in
terms of MSE ranging between 0.3 to 0.4 and is relatively similar to that of a
centralized approach while preserving privacy and improving scalability.


title:
On Minimal Surfaces of Revolutions Immersed in Deformed Hyperbolic
  Kropina Space

abstract:
  In this paper we consider three dimensional upper half space $\mathbb{H}^3 $
equipped with various Kropina metrics obtained by deformation of hyperbolic
metric of $\mathbb{H}^3$ through $1$-forms and obtain a partial differential
equation that characterizes minimal surfaces immersed in it. We prove that such
minimal surfaces can only be obtained when the hyperbolic metric is deformed
along $x^3$ direction. Then we classify such minimal surfaces and show that
flag curvature of these surfaces is always non-positive. We also obtain the
geodesics of this surface. In particular, it follows that such surfaces neither
have forward conjugate points nor they are forward complete.


title:
Hitting a New Low: The Unique 28 h Cessation of Accretion in the TESS
  Light Curve of YY Dra (DO Dra)

abstract:
  We present the Transiting Exoplanet Surveying Satellite (TESS) light curve of
the intermediate polar YY Draconis (YY Dra, also known as DO Dra). The power
spectrum indicates that while there is stream-fed accretion for most of the
observational period, there is a day-long, flat-bottomed low state at the
beginning of 2020 during which the only periodic signal is ellipsoidal
variation and there is no appreciable flickering. We interpret this low state
to be a complete cessation of accretion, a phenomenon that has been observed
only once before in an intermediate polar. Simultaneous ground-based
observations of this faint state establish that when accretion is negligible,
YY Dra fades to $g=17.37\pm0.12$, which we infer to be the magnitude of the
combined photospheric contributions of the white dwarf and its red dwarf
companion. Using survey photometry, we identify additional low states in
2018-2019 during which YY Dra repeatedly fades to -- but never below -- this
threshold. This implies relatively frequent cessations in accretion.
Spectroscopic observations during future episodes of negligible accretion can
be used to directly measure the field strength of the white dwarf by Zeeman
splitting. Separately, we search newly available catalogs of variable stars in
an attempt to resolve the long-standing dispute over the proper identifier of
this system.


title:
On The Hydrosphere Stability of TESS Targets: Applications to 700 d, 256
  b, and 203 b

abstract:
  A main determinant of the habitability of exoplanets is the presence of
stable liquid surface water. In an era of abundant possible targets, the
potential to find a habitable world remains a driving force in prioritization.
We present here a data-forward method to investigate the likelihood of a stable
hydrosphere on the timescales of the formation of life, 1 Gyr, and beyond. As
our primary application, we use this method to examine the potential
hydrospheres of TESS Objects of Interest 700 d, 256 b, and 203 b. We first
present our selection criteria, which is based on an implementation of the
Earth Similarity Index, as well as the results of an initial investigation into
the desiccation of the targets, which reveals that TOI 203 b is almost
certainly desiccated based on TESS observations. We then describe the
characterization of the remaining targets and their host stars from 2MASS,
Gaia, and TESS data and the derivation of sampled probability distributions for
their parameters. Following this, we describe our process of simulating the
desiccation of the targets hydrospheres using the Virtual Planet Simulator,
VPLanet, with inputs directly linked to the previously derived probability
distributions. We find that 50.86 percent of the likely cases for TOI 700 d are
desiccated and no modeled cases for TOI 256 b are without water. In addition,
we calculate the remaining water inventory for the targets, the percentage of
cases that are continuing to lose water, and the rate at which these cases are
losing water.


title: From boxes to polynomials: a story of generalisation

abstract:
  Here we will embark on a journey starting with some ostensibly inauspicious
boxes. Carefully stacking them in different ways yields amazing identities.
From humble beginnings at the integer version: `how many steps does it take to
get from row $i$ to row $j$?' to the first upgrade: the polynomial version,
before finally reaching the final upgrade: the elliptic version. Each upgrade
gives a more general theorem than before. Secretly, everything is controlled by
the symmetric Macdonald polynomials. Setting $q = t$ in the Macdonald
polynomial takes the elliptic version of the theorem to the polynomial version.
Then, letting $t$ approach $1$ reduces the polynomial version to the integer
version. All the beautiful theorems and ideas come merely from stacking boxes.


title: On Orthogonal Approximate Message Passing

abstract:
  Approximate Message Passing (AMP) is an efficient iterative
parameter-estimation technique for certain high-dimensional linear systems with
non-Gaussian distributions, such as sparse systems. In AMP, a so-called Onsager
term is added to keep estimation errors approximately Gaussian. Orthogonal AMP
(OAMP) does not require this Onsager term, relying instead on an
orthogonalization procedure to keep the current errors uncorrelated with (i.e.,
orthogonal to) past errors. In this paper, we show that the orthogonality in
OAMP ensures that errors are "asymptotically independently and identically
distributed Gaussian" (AIIDG). This AIIDG property, which is essential for the
attractive performance of OAMP, holds for separable functions. We present a
procedure to realize the required orthogonality for OAMP through Gram-Schmidt
orthogonalization (GSO). We show that expectation propagation (EP), AMP, OAMP
and some other algorithms can be unified under this orthogonality framework.
The simplicity and generality of OAMP provide efficient solutions for
estimation problems beyond the classical linear models; related applications
will be discussed in a companion paper where new algorithms are developed for
problems with multiple constraints and multiple measurement variables.


title:
INAQS, a generic interface for non-adiabatic QM/MM dynamics: Design,
  implementation, and validation for GROMACS/Q-CHEM simulations

abstract:
  The accurate description of large molecular systems in complex environments
remains an ongoing challenge for the field of computational chemistry. This
problem is even more pronounced for photo-induced processes, as multiple
excited electronic states and their corresponding non-adiabatic couplings must
be taken into account. Multiscale approaches such as hybrid quantum
mechanics/molecular mechanics (QM/MM) offer a balanced compromise between
accuracy and computational burden. Here, we introduce an open-source software
package (INAQS) for non-adiabatic QM/MM simulations that bridges the sampling
capabilities of the GROMACS MD package and the excited-state infrastructure of
the Q-CHEM electronic structure software. The interface is simple and can be
adapted easily to other MD codes. The code supports a variety of different
trajectory based molecular dynamics, ranging from Born-Oppenheimer to surface
hopping dynamics. To illustrate the power of this combination, we simulate
electronic absorption spectra, free energy surfaces along a reaction
coordinate, and the excited state dynamics of 1,3-cyclohexadiene in solution.


title:
Fast tunable coupling scheme of Kerr-nonlinear parametric oscillators
  based on shortcuts to adiabaticity

abstract:
  Kerr-nonlinear parametric oscillators (KPOs), which can be implemented with
superconducting parametrons possessing large Kerr nonlinearity, have been
attracting much attention in terms of their applications to quantum annealing,
universal quantum computation and studies of quantum many-body systems. It is
of practical importance for these studies to realize fast and accurate tunable
coupling between KPOs in a simple manner. We develop a simple scheme of fast
tunable coupling of KPOs with high tunability in speed and amplitude using the
fast transitionless rotation of a KPO in the phase space based on the shortcuts
to adiabaticity. Our scheme enables rapid switching of the effective coupling
between KPOs, and can be implemented with always-on linear coupling between
KPOs, simply by controlling the phase and frequency of the pump field without
controlling the amplitude of the pump field nor using additional drive fields.
We apply the coupling scheme to a two-qubit gate, and show that our scheme
realizes high gate fidelity compared to a purely adiabatic one, by mitigating
undesired nonadiabatic transitions.


title:
$C_3$ symmetry breaking metal-insulator transitions near a flat band in
  the half-filled Hubbard model on the decorated honeycomb lattice

abstract:
  We study the single-orbital Hubbard model on the half-filled decorated
honeycomb lattice. In the non-interacting theory at half-filling the Fermi
energy lies within a flat bland where strong correlations are enhanced and the
lattice exhibits frustration. We find a correlation driven first-order
metal-insulator transition to two different insulating ground states - a dimer
valence bond solid Mott insulator when inter-triangle correlations dominate,
and a broken $\mathcal{C}_3$ symmetry antiferromagnet that arises from
frustration when intra-triangle correlations dominate. The metal-insulator
transitions into these two phases have very different characters. The
metal-broken $\mathcal{C}_3$ antiferromagnetic transition is driven by
spontaneous $\mathcal{C}_3$ symmetry breaking that lifts the topologically
required degeneracy at the Fermi energy and opens an energy gap in the
quasiparticle spectrum. The metal-dimer valence bond solid transition breaks no
symmetries of the Hamiltonian. It is caused by strong correlations
renormalizing the electronic structure into a phase that is adiabatically
connected to both the trivial band insulator and the ground state of the
spin-1/2 Heisenberg model in the relevant parameter regime. Therefore, neither
of these metal-insulator transitions can be understood in either the
Brinkmann-Rice or Slater paradigms.


title: When is a subcategory Serre or torsionfree?

abstract:
  Let R be a commutative noetherian ring. Denote by mod R the category of
finitely generated R-modules. In the present paper, we first provide various
sufficient (and necessary) conditions for a full subcategory of mod R to be a
Serre subcategory, which include several refinements of theorems of Stanley and
Wang and of Takahashi with simpler proofs. Next we consider when an IKE-closed
subcategory of mod R is a torsionfree class. We investigate certain modules out
of which all modules of finite length can be built by taking direct summands
and extensions, and then we apply it to show that the IKE-closed subcategories
of mod R are torsionfree classes in the case where R is a certain numerical
semigroup ring.


title:
Fitting a Stochastic Model of Intensive Care Occupancy to Noisy
  Hospitalization Time Series

abstract:
  Intensive care occupancy is an important indicator of health care stress that
has been used to guide policy decisions during the COVID-19 pandemic. To
reliably forecast this occupancy, the rate at which patients are admitted to
hospitals and intensive care units (ICUs) and the rate at which patients leave
ICUs are crucial. Since individual-level hospital data are rarely available to
modelers in each geographic locality of interest, it is important to be able to
estimate these rates from publicly available daily numbers of hospital and ICU
beds occupied. We develop such an estimation approach based on an
immigration-death process that models fluctuations of ICU occupancy. Our
flexible framework allows for immigration and death rates to depend on
covariates, such as hospital bed occupancy and daily SARS-CoV-2 test positivity
rate, which may drive changes in hospital ICU operations. We demonstrate via
simulation studies that the proposed method performs well on noisy time series
data, and apply our statistical framework to hospitalization data from the
University of California, Irvine (UCI) Health and Orange County, California. By
introducing a likelihood-based framework where immigration and death rates can
vary with covariates, we find through rigorous model selection that
hospitalization and positivity rates are crucial covariates for modeling ICU
stay dynamics, and validate our per-patient ICU stay estimates using anonymized
patient-level UCI hospital data.


title: Chandrasekhar-Kendall-Woltjer-Taylor state in a resistive plasma

abstract:
  We give a criterion for the Chandrasekhar-Kendall-Woltjer-Taylor (CKWT) state
in a resistive plasma. We find that the lowest momentum (longest wavelength) of
the initial helicity amplitudes of magnetic fields are the key to the CKWT
state which can be reached if one helicity is favored over the other. This
indicates that the imbalance between two helicities at the lowest momentum or
longest wavelength in the initial conditions is essential to the CKWT state. A
few examples of initial conditions for helicity amplitudes are taken to support
the above statement both analytically and numerically.


title: Self-Propulsion of Boiling Droplets on Thin Heated Oil Films

abstract:
  We report on the self-propulsion of boiling droplets which, despite their
contact with viscous, immiscible oil films, attain high velocities comparable
to those of levitating Leidenfrost droplets. Experiments and model reveal that
droplet propulsion originates from a coupling between seemingly disparate short
and long timescale phenomena due to microsecond fluctuations induced by boiling
events at the droplet-oil interface. This interplay of phenomena leads to
continuous asymmetric vapor release and momentum transfer for high droplet
velocities.


title: Extended Graph Temporal Classification for Multi-Speaker End-to-End ASR

abstract:
  Graph-based temporal classification (GTC), a generalized form of the
connectionist temporal classification loss, was recently proposed to improve
automatic speech recognition (ASR) systems using graph-based supervision. For
example, GTC was first used to encode an N-best list of pseudo-label sequences
into a graph for semi-supervised learning. In this paper, we propose an
extension of GTC to model the posteriors of both labels and label transitions
by a neural network, which can be applied to a wider range of tasks. As an
example application, we use the extended GTC (GTC-e) for the multi-speaker
speech recognition task. The transcriptions and speaker information of
multi-speaker speech are represented by a graph, where the speaker information
is associated with the transitions and ASR outputs with the nodes. Using GTC-e,
multi-speaker ASR modelling becomes very similar to single-speaker ASR
modeling, in that tokens by multiple speakers are recognized as a single merged
sequence in chronological order. For evaluation, we perform experiments on a
simulated multi-speaker speech dataset derived from LibriSpeech, obtaining
promising results with performance close to classical benchmarks for the task.


title:
Ordered Submodularity and its Applications to Diversifying
  Recommendations

abstract:
  A fundamental task underlying many important optimization problems, from
influence maximization to sensor placement to content recommendation, is to
select the optimal group of $k$ items from a larger set. Submodularity has been
very effective in allowing approximation algorithms for such subset selection
problems. However, in several applications, we are interested not only in the
elements of a set, but also the order in which they appear, breaking the
assumption that all selected items receive equal consideration. One such
category of applications involves the presentation of search results, product
recommendations, news articles, and other content, due to the well-documented
phenomenon that humans pay greater attention to higher-ranked items. As a
result, optimization in content presentation for diversity, user coverage,
calibration, or other objectives more accurately represents a sequence
selection problem, to which traditional submodularity approximation results no
longer apply. Although extensions of submodularity to sequences have been
proposed, none is designed to model settings where items contribute based on
their position in a ranked list, and hence they are not able to express these
types of optimization problems. In this paper, we aim to address this modeling
gap.
  Here, we propose a new formalism of ordered submodularity that captures these
ordering problems in content presentation, and more generally a category of
optimization problems over ranked sequences in which different list positions
contribute differently to the objective function. We analyze the natural
ordered analogue of the greedy algorithm and show that it provides a
$2$-approximation. We also show that this bound is tight, establishing that our
new framework is conceptually and quantitatively distinct from previous
formalisms of set and sequence submodularity.


title:
Small infinite partitions and other features of the Nowhere Centered
  ideal

abstract:
  The \textit{nowhere dense ideal} $\mathcal{NC}$ is introduced. It is a
coanalytic ideal of $\omega\times\omega$ whose defining characteristic is that
the sets of the form $X\times Y$, where $X,Y$ are infinite subsets of $\omega$,
are dense in the quotient $\mathcal{P}(\omega\times\omega)\slash\mathcal{NC}$.
This quotient has countable partitions and consistently has partitions of size
$\omega_1$ while $\mathfrak{a}>\omega_1$. This represents a huge contrast with
other definable quotients. Other combinatorial features of this ideal are
presented, as well as some results on a family of similar, higher dimensional
ideals.


title:
Beam Squint-Aware Integrated Sensing and Communications for Hybrid
  Massive MIMO LEO Satellite Systems

abstract:
  The space-air-ground-sea integrated network (SAGSIN) plays an important role
in offering global coverage. To improve the efficient utilization of spectral
and hardware resources in the SAGSIN, integrated sensing and communications
(ISAC) has drawn extensive attention. Most existing ISAC works focus on
terrestrial networks and can not be straightforwardly applied in satellite
systems due to the significantly different electromagnetic wave propagation
properties. In this work, we investigate the application of ISAC in massive
multiple-input multiple-output (MIMO) low earth orbit (LEO) satellite systems.
We first characterize the statistical wave propagation properties by
considering beam squint effects. Based on this analysis, we propose a beam
squint-aware ISAC technique for hybrid analog/digital massive MIMO LEO
satellite systems exploiting statistical channel state information. Simulation
results demonstrate that the proposed scheme can operate both the wireless
communications and the target sensing simultaneously with satisfactory
performance, and the beam-squint effects can be efficiently mitigated with the
proposed method in typical LEO satellite systems.


title: TRILLsson: Distilled Universal Paralinguistic Speech Representations

abstract:
  Recent advances in self-supervision have dramatically improved the quality of
speech representations. However, deployment of state-of-the-art embedding
models on devices has been restricted due to their limited public availability
and large resource footprint. Our work addresses these issues by publicly
releasing a collection of paralinguistic speech models that are small and near
state-of-the-art performance. Our approach is based on knowledge distillation,
and our models are distilled on public data only. We explore different
architectures and thoroughly evaluate our models on the Non-Semantic Speech
(NOSS) benchmark. Our largest distilled model is less than 15% the size of the
original model (314MB vs 2.2GB), achieves over 96% the accuracy on 6 of 7
tasks, and is trained on 6.5% the data. The smallest model is 1% in size (22MB)
and achieves over 90% the accuracy on 6 of 7 tasks. Our models outperform the
open source Wav2Vec 2.0 model on 6 of 7 tasks, and our smallest model
outperforms the open source Wav2Vec 2.0 on both emotion recognition tasks
despite being 7% the size.


title:
Mental Health Pandemic during the COVID-19 Outbreak: Calls for Help on
  Social Media

abstract:
  Heightened social isolation during the COVID-19 outbreak puts individuals at
greater risks of loneliness (Bu et al., 2020) where elevated levels of
loneliness are closely associated with depression (Killgore et al., 2020; Palgi
et al., 2020; Weeks et al., 1980). Prior research has suggested that lonely
individuals are more likely to seek mental health help from an online social
platform (e.g., Reddit), a perceived comfortable environment for lonely people
to seek mental health support through anonymous communication with a broad
social network (Andy, 2021; Bonetti et al., 2010; Morahan-Martin et al., 2003).
Therefore, this study aims to identify and analyze depression-related dialogues
on loneliness subreddits during the COVID-19 outbreak, with the impact on
depression-related infoveillance during the pandemic. With the collected data
using Reddit API, our study utilized logistic regression and topic modeling to
classify and examine depression related discussions on loneliness subreddits
during the outbreak. Our results reveal that lonely individuals engaging in
depression-related discussions are likely to be experiencing elevated risks of
mental health problems and domestic issues, higher level of relationship
seeking, and heightened need of social support. Furthermore, the results
suggest an increase in dog adoption as a coping behavior and challenges in the
online learning environment. Finally, returning users disclose and seek
information on triggering factors of mental health problems, indicating the
significance of peer-to-peer mental health support on loneliness subreddits.
Our future work will clinically validate the current approach, which has
implications on designing surveillance system during the crisis.


title: How certain are your uncertainties?

abstract:
  Having a measure of uncertainty in the output of a deep learning method is
useful in several ways, such as in assisting with interpretation of the
outputs, helping build confidence with end users, and for improving the
training and performance of the networks. Therefore, several different methods
have been proposed to capture various types of uncertainty, including epistemic
(relating to the model used) and aleatoric (relating to the data) sources, with
the most commonly used methods for estimating these being test-time dropout for
epistemic uncertainty and test-time augmentation for aleatoric uncertainty.
However, these methods are parameterised (e.g. amount of dropout or type and
level of augmentation) and so there is a whole range of possible uncertainties
that could be calculated, even with a fixed network and dataset. This work
investigates the stability of these uncertainty measurements, in terms of both
magnitude and spatial pattern. In experiments using the well characterised
BraTS challenge, we demonstrate substantial variability in the magnitude and
spatial pattern of these uncertainties, and discuss the implications for
interpretability, repeatability and confidence in results.


title: Coded Demixing for Unsourced Random Access

abstract:
  Unsourced random access (URA) is a recently proposed multiple access paradigm
tailored to the uplink channel of machine-type communication networks. By
exploiting a strong connection between URA and compressed sensing, the massive
multiple access problem may be cast as a compressed sensing (CS) problem,
albeit one in exceedingly large dimensions. To efficiently handle the
dimensionality of the problem, coded compressed sensing (CCS) has emerged as a
pragmatic signal processing tool that, when applied to URA, offers good
performance at low complexity. While CCS is effective at recovering a signal
that is sparse with respect to a single basis, it is unable to jointly recover
signals that are sparse with respect to separate bases. In this article, the
CCS framework is extended to the demixing setting, yielding a novel technique
called coded demixing. A generalized framework for coded demixing is presented
and a low-complexity recovery algorithm based on approximate message passing
(AMP) is developed. Coded demixing is applied to heterogeneous multi-class URA
networks and traditional single-class networks. Its performance is analyzed and
numerical simulations are presented to highlight the benefits of coded
demixing.


title:
Convergence Criteria of a Three Step Scheme under generalized Lipschitz
  Condition in Banach Spaces

abstract:
  The goal of this study is to investigate the local convergence of a
three-step Newton-Traub technique for solving nonlinear equations in Banach
spaces with a convergence rate of five. The first order derivative of a
nonlinear operator is assumed to satisfy the generalized Lipschitz condition,
i.e. the $\kappa$-average condition. Furthermore, a few results on the
convergence of the same method in Banach spaces are developed under the
assumption that the derivative of the operators satisfies the radius or center
Lipschitz condition with a weak $\kappa$-average, and that $\kappa$ is a
positive integrable function but not necessarily non-decreasing. Our new notion
provides a tighter convergence analysis without the need for new circumstances.
As a result, we broaden the applicability of iterative approaches. Theoretical
results are supported further by illuminating examples. The existence and
uniqueness of the solution $x^*$ are examined in the convergence theorem. In
the end, we achieve weaker sufficient convergence criteria and more specific
information on the position of the solution than previous efforts requiring the
same computational effort. We obtain the convergence theorems as well as some
novel results by applying the results to some specific functions for
$\kappa(u)$. A numerical test is carried out to corroborate the hypothesis
established in this work.


title: First-generation Memory Disaggregation for Cloud Platforms

abstract:
  In Azure, up to 25% of memory is stranded, i.e., it is leftover after the
servers' cores have been rented to VMs. Memory disaggregation promises to
reduce this stranding. However, making disaggregation practical for production
cloud deployment remains challenging. For example, RDMA-based disaggregation
involves too much overhead for common workloads and transparent latency
management is incompatible with virtualization acceleration. The emerging
Compute Express Link (CXL) standard offers a low-overhead substrate to build
memory disaggregation while overcoming these challenges. This paper proposes a
first-generation CXL-based disaggregation system that meets the requirements of
cloud providers. Our system includes a memory pool controller, and
prediction-based system software and distributed control plane designs. Its
predictions of VM latency sensitivity and memory usage allow it to split
workloads across local and pooled memory while mitigating the higher pool
latency.
  Our analysis of production clusters shows that small pools of 8-32 sockets
are sufficient to reduce stranding significantly. It also shows that about 50%
of all VMs never touch 50% of their rented memory. In emulated experiments with
150+ workloads, we show our pooling approach incurs a configurable performance
loss between 1-5%. Finally, we show that disaggregation can achieve a 9-10%
reduction in overall DRAM, which represents hundreds of millions of dollars in
cost savings for a large cloud provider.


title:
Unsupervised Vision-and-Language Pre-training via Retrieval-based
  Multi-Granular Alignment

abstract:
  Vision-and-Language (V+L) pre-training models have achieved tremendous
success in recent years on various multi-modal benchmarks. However, the
majority of existing models require pre-training on a large set of parallel
image-text data, which is costly to collect, compared to image-only or
text-only data. In this paper, we explore unsupervised Vision-and-Language
pre-training (UVLP) to learn the cross-modal representation from non-parallel
image and text datasets. We found two key factors that lead to good
unsupervised V+L pre-training without parallel data: (i) joint image-and-text
input (ii) overall image-text alignment (even for non-parallel data).
Accordingly, we propose a novel unsupervised V+L pre-training curriculum for
non-parallel texts and images. We first construct a weakly aligned image-text
corpus via a retrieval-based approach, then apply a set of multi-granular
alignment pre-training tasks, including region-to-tag, region-to-phrase, and
image-to-sentence alignment, to bridge the gap between the two modalities. A
comprehensive ablation study shows each granularity is helpful to learn a
stronger pre-trained model. We adapt our pre-trained model to a set of V+L
downstream tasks, including VQA, NLVR2, Visual Entailment, and RefCOCO+. Our
model achieves the state-of-art performance in all these tasks under the
unsupervised setting.


title:
Lattice paths, vector continued fractions, and resolvents of banded
  Hessenberg operators

abstract:
  We give a combinatorial interpretation of vector continued fractions obtained
by applying the Jacobi-Perron algorithm to a vector of $p\geq 1$ resolvent
functions of a banded Hessenberg operator of order $p+1$. The interpretation
consists in the identification of the coefficients in the Laurent series
expansion of the resolvent functions as weight polynomials associated with
certain collections of lattice paths. In the scalar case $p=1$ this reduces to
the relation established by P. Flajolet between Jacobi continued fractions and
Motzkin paths. A fundamental collection of lattice paths we consider is the
collection of partial $p$-Lukasiewicz paths. We also discuss the particular
case of Stieltjes-Rogers polynomials, also known in the literature as genetic
sums, associated with partial $p$-Dyck paths and bi-diagonal Hessenberg
operators.


title:
Impact of the interference between the $1^{--}$ resonance and continuum
  amplitudes on the branching fraction measurement

abstract:
  The measurement of the branching fraction of a heavy quarkonium decaying into
light hadronic final state at $e^{+}e^{-}$ colliders are revisited. The
irreducible background contributions from the continuum amplitude and its
interference with the resonance amplitude become more and more significant as
the precision of experimental measurements improves. While the former can be
easily subtracted with data taken off the resonance peak, the latter depends on
the relative size and phase between the resonance and continuum amplitudes. The
exact formula of the ratio of the interference term with respect to the
resonance term $r_R$ and the ratio to the continuum term $r_c$ are
investigated. For narrow resonances, $r_R$ could be as large as a few percent,
and for broad resonances, both $r_R$ and $r_c$ could be large. The interference
effect is crucial for measurements of the branching fractions aiming at percent
level or better precision and needs to be measured or estimated properly.


title:
On the Causal Interpretation of Randomized Interventional Indirect
  Effects

abstract:
  Identification of standard mediated effects such as the natural indirect
effect relies on heavy causal assumptions. By circumventing such assumptions,
so-called randomized interventional indirect effects have gained popularity in
the causal mediation literature. In this article, I introduce an essential
criterion (the sharp null criterion) that any indirect effect measure ought to
satisfy in order to have a true mediational interpretation. Namely, an indirect
effect measure must be null whenever there is no individual-level indirect
effect. I show that without stronger assumptions, randomized interventional
indirect effects do not satisfy this criterion. I additionally discuss
alternative causal interpretations of such effects.


title: Sample Complexity versus Depth: An Information Theoretic Analysis

abstract:
  Deep learning has proven effective across a range of data sets. In light of
this, a natural inquiry is: "for what data generating processes can deep
learning succeed?" In this work, we study the sample complexity of learning
multilayer data generating processes of a sort for which deep neural networks
seem to be suited. We develop general and elegant information-theoretic tools
that accommodate analysis of any data generating process -- shallow or deep,
parametric or nonparametric, noiseless or noisy. We then use these tools to
characterize the dependence of sample complexity on the depth of multilayer
processes. Our results indicate roughly linear dependence on depth. This is in
contrast to previous results that suggest exponential or high-order polynomial
dependence.


title:
Band structures under non-Hermitian periodic potentials: Connecting
  nearly-free and bi-orthogonal tight-binding models

abstract:
  We explore band structures of one-dimensional open systems described by
periodic non-Hermitian operators, based on continuum models and tight-binding
models. We show that imaginary scalar potentials do not open band gaps but
instead lead to the formation of exceptional points as long as the strength of
the potential exceeds a threshold value, which is contrast to closed systems
where real potentials open a gap with infinitesimally small strength. The
imaginary vector potentials hinder the separation of low energy bands because
of the lifting of degeneracy in the free system. In addition, we construct
tight-binding models through bi-orthogonal Wannier functions based on Bloch
wavefunctions of the non-Hermitian operator and its Hermitian conjugate. We
show that the bi-orthogonal tight-binding model well reproduces the dispersion
relations of the continuum model when the complex scalar potential is
sufficiently large.


title:
Extension of Irreducibility results on Generalised Laguerre Polynomials
  $L_n^{(-1-n-s)}(x)$

abstract:
  We consider the irreducibility of Generalised Laguerre Polynomials for
negative integral values given by
$L_n^{(-1-n-s)}(x)=\displaystyle\sum_{j=0}^{n}\binom{n-j+s}{n-j}\frac{x^j}{j!}.$
For different values of $s,$ this family gives polynomials which are of great
interest. It was proved earlier that for $0 \leq s \leq 60,$ these polynomials
are irreducible over $\mathbb{Q}.$ In this paper we improve this result upto $s
\leq 88.$


title: Exploring and Adapting Chinese GPT to Pinyin Input Method

abstract:
  While GPT has become the de-facto method for text generation tasks, its
application to pinyin input method remains unexplored. In this work, we make
the first exploration to leverage Chinese GPT for pinyin input method. We find
that a frozen GPT achieves state-of-the-art performance on perfect pinyin.
However, the performance drops dramatically when the input includes abbreviated
pinyin. A reason is that an abbreviated pinyin can be mapped to many perfect
pinyin, which links to even larger number of Chinese characters. We mitigate
this issue with two strategies, including enriching the context with pinyin and
optimizing the training process to help distinguish homophones. To further
facilitate the evaluation of pinyin input method, we create a dataset
consisting of 270K instances from 15 domains. Results show that our approach
improves performance on abbreviated pinyin across all domains. Model analysis
demonstrates that both strategies contribute to the performance boost.


title:
A nonlinear weighted anisotropic total variation regularization for
  electrical impedance tomography

abstract:
  This paper proposes a nonlinear weighted anisotropic total variation (NWATV)
regularization technique for electrical impedance tomography (EIT). The key
idea is to incorporate the internal inhomogeneity information (e.g., edges of
the detected objects) into the EIT reconstruction process, aiming to preserve
the conductivity profiles (to be detected). We study the NWATV image
reconstruction by employing a novel soft thresholding based reformulation
included in the alternating direction method of multipliers (ADMM). To evaluate
the proposed approach, 2D and 3D numerical experiments and human EIT lung
imaging are carried out. It is demonstrated that the properties of the internal
inhomogeneity are well preserved and improved with the proposed regularization
approach, in comparison to traditional total variation (TV) and recently
proposed fidelity embedded regularization approaches. Owing to the simplicity
of the proposed method, the computational cost is significantly decreased
compared with the well established primal-dual algorithm. Meanwhile, it was
found that the proposed regularization method is quite robust to the
measurement noise, which is one of the main uncertainties in EIT.


title: FIRL: Fast Imitation and Policy Reuse Learning

abstract:
  Intelligent robotics policies have been widely researched for challenging
applications such as opening doors, washing dishes, and table organization. We
refer to a "Policy Pool", containing skills that be easily accessed and reused.
There are researches to leverage the pool, such as policy reuse, modular
learning, assembly learning, transfer learning, hierarchical reinforcement
learning (HRL), etc. However, most methods generally do not perform well in
learning efficiency and require large datasets for training. This work focuses
on enabling fast learning based on the policy pool. It should learn fast enough
in one-shot or few-shot by avoiding learning from scratch. We also allow it to
interact and learn from humans, but the training period should be within
minutes. We propose FIRL, Fast (one-shot) Imitation, and Policy Reuse Learning.
Instead of learning a new skill from scratch, it performs the one-shot
imitation learning on the higher layer under a 2-layer hierarchical mechanism.
Our method reduces a complex task learning to a simple regression problem that
it could solve in a few offline iterations. The agent could have a good command
of a new task given a one-shot demonstration. We demonstrate this method on the
OpenDoors mini-grid environment, and the code is available on
http://www.github.com/yiwc/firl.


title: Bregman three-operator splitting methods

abstract:
  The paper presents primal-dual proximal splitting methods for convex
optimization, in which generalized Bregman distances are used to define the
primal and dual proximal update steps. The methods extend the primal and dual
Condat-Vu algorithms and the primal-dual three-operator (PD3O) algorithm. The
Bregman extensions of the Condat-Vu algorithms are derived from the Bregman
proximal point method applied to a monotone inclusion problem. Based on this
interpretation, a unified framework for the convergence analysis of the two
methods is presented. We also introduce a line search procedure for stepsize
selection in the Bregman dual Condat-Vu algorithm applied to
equality-constrained problems. Finally, we propose a Bregman extension of PD3O
and analyze its convergence.


title:
Intermediate asymptotics on crossover of scaling law on dynamical impact
  of viscoelastic surface

abstract:
  In this paper, a crossover of scaling laws is described as a result of the
interference from self-similar variable of the higher class of the
self-similarity on the dynamical impact of solid sphere onto a viscoelastic
surface. All the physical factors including the size of spheres, the impact of
velocity are successfully summarized to the primal dimensionless numbers which
construct a self-similar solution of the second kind, which represents the
balance between dimensionless numbers. The self-similar solution gives two
different scaling laws by the perturbation method describing the crossover.
These theoretical predictions are compared with experimental results to show
good agreement. It was suggested that a hierarchical structure of similarity
plays a fundamental role on crossover, which offers a fundamental insight to
self-similarity in general.