title: Coprime permutations

abstract:
  Let $C(n)$ denote the number of permutations $\sigma$ of
$[n]=\{1,2,\dots,n\}$ such that $\gcd(j,\sigma(j))=1$ for each $j\in[n]$. We
prove that for $n$ sufficiently large, $n!/3.73^n < C(n) < n!/2.5^n$.


title: Dynamic Nonlocal Passive Scalar Subgrid-Scale Turbulence Modeling

abstract:
  Extensive experimental evidence highlight that scalar turbulence exhibits
anomalous diffusion and stronger intermittency levels at small scales compared
to that in fluid turbulence. This renders the corresponding subgrid-scale
dynamics modeling for scalar turbulence a greater challenge to date. We develop
a new large eddy simulation (LES) paradigm for efficiently and dynamically
nonlocal LES modeling of the scalar turbulence. To this end, we formulate the
underlying nonlocal model starting from the filtered Boltzmann kinetic
transport equation, where the divergence of subgrid-scale scalar fluxes emerges
as a fractional-order Laplacian term in the filtered advection-diffusion model,
coding the corresponding supper-diffusive nature of scalar turbulence.
Subsequently, we develop a robust data-driven algorithm for estimation of the
fractional (non-integer) Laplacian exponent, where we on-the-fly calculate the
corresponding model coefficient employing a new dynamic procedure. Our
$\textit{a priori}$ tests show that our new dynamically nonlocal LES paradigm
provides better agreements with the ground-truth filtered DNS data in
comparison to the conventional static and dynamic Prandtl-Smagorisnky models.
Moreover, in order to analyze the numerical stability and assessing the model's
performance, we carry out a comprehensive $\textit{a posteriori}$ tests. They
unanimously illustrate that our new model considerably outperforms other
existing functional models, correctly predicting the backscattering phenomena
at the same time and providing higher correlations at small-to-large filter
sizes. We conclude that our proposed nonlocal subgrid-scale model for scalar
turbulence is amenable for coarse LES and VLES frameworks even with strong
anisotropies, applicable to environmental applications.


title:
HAR-GCNN: Deep Graph CNNs for Human Activity Recognition From Highly
  Unlabeled Mobile Sensor Data

abstract:
  The problem of human activity recognition from mobile sensor data applies to
multiple domains, such as health monitoring, personal fitness, daily life
logging, and senior care. A critical challenge for training human activity
recognition models is data quality. Acquiring balanced datasets containing
accurate activity labels requires humans to correctly annotate and potentially
interfere with the subjects' normal activities in real-time. Despite the
likelihood of incorrect annotation or lack thereof, there is often an inherent
chronology to human behavior. For example, we take a shower after we exercise.
This implicit chronology can be used to learn unknown labels and classify
future activities. In this work, we propose HAR-GCCN, a deep graph CNN model
that leverages the correlation between chronologically adjacent sensor
measurements to predict the correct labels for unclassified activities that
have at least one activity label. We propose a new training strategy enforcing
that the model predicts the missing activity labels by leveraging the known
ones. HAR-GCCN shows superior performance relative to previously used baseline
methods, improving classification accuracy by about 25% and up to 68% on
different datasets. Code is available at
\url{https://github.com/abduallahmohamed/HAR-GCNN}.


title:
An algorithm to regularize static spherically symmetric black hole
  spacetimes

abstract:
  A simple algorithm to transform a singular, asymptotically flat, static and
spherically symmetric black hole into a regular black hole spacetime is
presented. The regular black hole is a solution of General Relativity theory
coupled to nonlinear electrodynamics (NLED), even if the original metric is not
a vacuum, or electro-vacuum, solution of General Relativity.


title: CPPF: Towards Robust Category-Level 9D Pose Estimation in the Wild

abstract:
  In this paper, we tackle the problem of category-level 9D pose estimation in
the wild, given a single RGB-D frame. Using supervised data of real-world 9D
poses is tedious and erroneous, and also fails to generalize to unseen
scenarios. Besides, category-level pose estimation requires a method to be able
to generalize to unseen objects at test time, which is also challenging.
Drawing inspirations from traditional point pair features (PPFs), in this
paper, we design a novel Category-level PPF (CPPF) voting method to achieve
accurate, robust and generalizable 9D pose estimation in the wild. To obtain
robust pose estimation, we sample numerous point pairs on an object, and for
each pair our model predicts necessary SE(3)-invariant voting statistics on
object centers, orientations and scales. A novel coarse-to-fine voting
algorithm is proposed to eliminate noisy point pair samples and generate final
predictions from the population. To get rid of false positives in the
orientation voting process, an auxiliary binary disambiguating classification
task is introduced for each sampled point pair. In order to detect objects in
the wild, we carefully design our sim-to-real pipeline by training on synthetic
point clouds only, unless objects have ambiguous poses in geometry. Under this
circumstance, color information is leveraged to disambiguate these poses.
Results on standard benchmarks show that our method is on par with current
state of the arts with real-world training data. Extensive experiments further
show that our method is robust to noise and gives promising results under
extremely challenging scenarios. Our code is available on
https://github.com/qq456cvb/CPPF.


title: Functorial resolution by torus actions

abstract:
  We show a simple and fast embedded resolution of varieties and
principalization of ideals in the language of torus actions on ambient smooth
schemes with or without SNC divisors. The canonical functorial resolution of
varieties in characteristic zero is given by, the introduced here, operations
of cobordant blow-ups with smooth weighted centers. The centers are defined by
the geometric invariant measuring the singularities on smooth schemes with SNC
divisors.
  As the result of the procedure we obtain a smooth variety with a torus action
and the exceptional divisor having simple normal crossings. Moreover, its
geometric quotient is birational to the resolved variety, has abelian quotient
singularities, and can be desingularized directly by combinatorial methods. The
paper is based upon the ideas of the joint work with Abramovich and Temkin and
a similar result by McQuillan on resolution in characteristic zero via
stack-theoretic weighted blow-ups.
  As an application of the method we show the resolution of a certain class of
isolated singularities in positive and mixed characteristic.


title: Modeling Field-level Factor Interactions for Fashion Recommendation

abstract:
  Personalized fashion recommendation aims to explore patterns from historical
interactions between users and fashion items and thereby predict the future
ones. It is challenging due to the sparsity of the interaction data and the
diversity of user preference in fashion. To tackle the challenge, this paper
investigates multiple factor fields in fashion domain, such as colour, style,
brand, and tries to specify the implicit user-item interaction into field
level. Specifically, an attentional factor field interaction graph (AFFIG)
approach is proposed which models both the user-factor interactions and
cross-field factors interactions for predicting the recommendation probability
at specific field. In addition, an attention mechanism is equipped to aggregate
the cross-field factor interactions for each field. Extensive experiments have
been conducted on three E-Commerce fashion datasets and the results demonstrate
the effectiveness of the proposed method for fashion recommendation. The
influence of various factor fields on recommendation in fashion domain is also
discussed through experiments.


title: Systematic Comparison of Path Planning Algorithms using PathBench

abstract:
  Path planning is an essential component of mobile robotics. Classical path
planning algorithms, such as wavefront and rapidly-exploring random tree (RRT)
are used heavily in autonomous robots. With the recent advances in machine
learning, development of learning-based path planning algorithms has been
experiencing rapid growth. An unified path planning interface that facilitates
the development and benchmarking of existing and new algorithms is needed. This
paper presents PathBench, a platform for developing, visualizing, training,
testing, and benchmarking of existing and future, classical and learning-based
path planning algorithms in 2D and 3D grid world environments. Many existing
path planning algorithms are supported; e.g. A*, Dijkstra, waypoint planning
networks, value iteration networks, gated path planning networks; and
integrating new algorithms is easy and clearly specified. The benchmarking
ability of PathBench is explored in this paper by comparing algorithms across
five different hardware systems and three different map types, including
built-in PathBench maps, video game maps, and maps from real world databases.
Metrics, such as path length, success rate, and computational time, were used
to evaluate algorithms. Algorithmic analysis was also performed on a real world
robot to demonstrate PathBench's support for Robot Operating System (ROS).
PathBench is open source.


title:
Derivative-Free Placement Optimization for Multi-UAV Wireless Networks
  with Channel Knowledge Map

abstract:
  This paper studies a multi-UAV wireless network, in which multiple UAV users
share the same spectrum to send individual messages to their respectively
associated ground base stations (GBSs). The UAV users aim to optimize their
locations to maximize the weighted sum rate. While most existing work considers
simplified line-of-sight (LoS) or statistic air-to-ground (A2G) channel models,
we exploit the location-specific channel knowledge map (CKM) to enhance the
placement performance in practice. However, as the CKMs normally contain
discrete site- and location-specific channel data without analytic model
functions, the corresponding weighted sum rate function becomes
non-differentiable in general. In this case, conventional optimization
techniques relying on function derivatives are inapplicable to solve the
resultant placement optimization problem. To address this issue, we propose a
novel iterative algorithm based on the derivative-free optimization. In each
iteration, we first construct a quadratic function to approximate the
non-differentiable weighted sum rate under a set of interpolation conditions,
and then update the UAVs' placement locations by maximizing the approximate
quadratic function subject to a trust region constraint. Numerical results show
the convergence of the proposed algorithm. It is also shown that the proposed
algorithm achieves a weighted sum rate close to the optimal design based on
exhaustive search with much lower implementation complexity, and it
significantly outperforms the conventional optimization method based on
simplified LoS channel models and the heuristic design with each UAV hovering
above its associated GBS.


title: SurvSet: An open-source time-to-event dataset repository

abstract:
  Time-to-event (T2E) analysis is a branch of statistics that models the
duration of time it takes for an event to occur. Such events can include
outcomes like death, unemployment, or product failure. Most modern machine
learning (ML) algorithms, like decision trees and kernel methods, are supported
for T2E modelling with data science software (python and R). To complement
these developments, SurvSet is the first open-source T2E dataset repository
designed for a rapid benchmarking of ML algorithms and statistical methods. The
data in SurvSet have been consistently formatted so that a single preprocessing
method will work for all datasets. SurvSet currently has 76 datasets which vary
in dimensionality, time dependency, and background (the majority of which come
from biomedicine). SurvSet is available on PyPI and can be installed with pip
install SurvSet. R users can download the data directly from the corresponding
git repository.


title: On First Integrals of Hamiltonian System with Holonomic Hamiltonian

abstract:
  In this study, the solution of the Hamilton-Jacobi equation (HJE) with
holonomic Hamiltonian is investigated in terms of the first integrals of the
corresponding Hamiltonian system. Holonomic functions are related to a specific
type of partial differential equations called Pfaffian systems, whose solution
space can be regarded as a finite-dimensional real vector space. In the
finite-dimensional solution space, the existence of first integrals that define
a solution of the HJE is characterized by a finite number of algebraic
equations for finite-dimensional vectors, which can be easily solved and
verified. The derived characterization was illustrated through a numerical
example.


title: Bottom-up holographic models for cosmology

abstract:
  In this note, we investigate some simple generalizations of a bottom-up
holographic approach to cosmology introduced in arXiv:1810.10601. Our models
utilize the Karch/Randall/Takayanagi ansatz for the gravitational dual of a
boundary conformal field theory, involving pure AdS gravity and an
end-of-the-world brane. Following a suggestion made in arXiv:2102.05057, we
consider models with an additional interface brane in the bulk. We find that
solutions with a viable cosmological interpretation exist only if our model is
further generalized, for example by including an Einstein-Hilbert term or
higher order geometric terms in the ETW brane action. The physical validity of
such models is discussed from the perspective of the effective theory.


title:
Behavior Recognition Based on the Integration of Multigranular Motion
  Features

abstract:
  The recognition of behaviors in videos usually requires a combinatorial
analysis of the spatial information about objects and their dynamic action
information in the temporal dimension. Specifically, behavior recognition may
even rely more on the modeling of temporal information containing short-range
and long-range motions; this contrasts with computer vision tasks involving
images that focus on the understanding of spatial information. However, current
solutions fail to jointly and comprehensively analyze short-range motion
between adjacent frames and long-range temporal aggregations at large scales in
videos. In this paper, we propose a novel behavior recognition method based on
the integration of multigranular (IMG) motion features. In particular, we
achieve reliable motion information modeling through the synergy of a channel
attention-based short-term motion feature enhancement module (CMEM) and a
cascaded long-term motion feature integration module (CLIM). We evaluate our
model on several action recognition benchmarks such as HMDB51,
Something-Something and UCF101. The experimental results demonstrate that our
approach outperforms the previous state-of-the-art methods, which confirms its
effectiveness and efficiency.


title:
RumorLens: Interactive Analysis and Validation of Suspected Rumors on
  Social Media

abstract:
  With the development of social media, various rumors can be easily spread on
the Internet and such rumors can have serious negative effects on society.
Thus, it has become a critical task for social media platforms to deal with
suspected rumors. However, due to the lack of effective tools, it is often
difficult for platform administrators to analyze and validate rumors from a
large volume of information on a social media platform efficiently. We have
worked closely with social media platform administrators for four months to
summarize their requirements of identifying and analyzing rumors, and further
proposed an interactive visual analytics system, RumorLens, to help them deal
with the rumor efficiently and gain an in-depth understanding of the patterns
of rumor spreading. RumorLens integrates natural language processing (NLP) and
other data processing techniques with visualization techniques to facilitate
interactive analysis and validation of suspected rumors. We propose
well-coordinated visualizations to provide users with three levels of details
of suspected rumors: an overview displays both spatial distribution and
temporal evolution of suspected rumors; a projection view leverages a
metaphor-based glyph to represent each suspected rumor and further enable users
to gain a quick understanding of their overall characteristics and similarity
with each other; a propagation view visualizes the dynamic spreading details of
a suspected rumor with a novel circular visualization design, and facilitates
interactive analysis and validation of rumors in a compact manner. By using a
real-world dataset collected from Sina Weibo, one case study with a domain
expert is conducted to evaluate


title: Singular Value Perturbation and Deep Network Optimization

abstract:
  We develop new theoretical results on matrix perturbation to shed light on
the impact of architecture on the performance of a deep network. In particular,
we explain analytically what deep learning practitioners have long observed
empirically: the parameters of some deep architectures (e.g., residual
networks, ResNets, and Dense networks, DenseNets) are easier to optimize than
others (e.g., convolutional networks, ConvNets). Building on our earlier work
connecting deep networks with continuous piecewise-affine splines, we develop
an exact local linear representation of a deep network layer for a family of
modern deep networks that includes ConvNets at one end of a spectrum and
ResNets, DenseNets, and other networks with skip connections at the other. For
regression and classification tasks that optimize the squared-error loss, we
show that the optimization loss surface of a modern deep network is piecewise
quadratic in the parameters, with local shape governed by the singular values
of a matrix that is a function of the local linear representation. We develop
new perturbation results for how the singular values of matrices of this sort
behave as we add a fraction of the identity and multiply by certain diagonal
matrices. A direct application of our perturbation results explains
analytically why a network with skip connections (such as a ResNet or DenseNet)
is easier to optimize than a ConvNet: thanks to its more stable singular values
and smaller condition number, the local loss surface of such a network is less
erratic, less eccentric, and features local minima that are more accommodating
to gradient-based optimization. Our results also shed new light on the impact
of different nonlinear activation functions on a deep network's singular
values, regardless of its architecture.


title:
HintNet: Hierarchical Knowledge Transfer Networks for Traffic Accident
  Forecasting on Heterogeneous Spatio-Temporal Data

abstract:
  Traffic accident forecasting is a significant problem for transportation
management and public safety. However, this problem is challenging due to the
spatial heterogeneity of the environment and the sparsity of accidents in space
and time. The occurrence of traffic accidents is affected by complex
dependencies among spatial and temporal features. Recent traffic accident
prediction methods have attempted to use deep learning models to improve
accuracy. However, most of these methods either focus on small-scale and
homogeneous areas such as populous cities or simply use sliding-window-based
ensemble methods, which are inadequate to handle heterogeneity in large
regions. To address these limitations, this paper proposes a novel Hierarchical
Knowledge Transfer Network (HintNet) model to better capture irregular
heterogeneity patterns. HintNet performs a multi-level spatial partitioning to
separate sub-regions with different risks and learns a deep network model for
each level using spatio-temporal and graph convolutions. Through knowledge
transfer across levels, HintNet archives both higher accuracy and higher
training efficiency. Extensive experiments on a real-world accident dataset
from the state of Iowa demonstrate that HintNet outperforms the
state-of-the-art methods on spatially heterogeneous and large-scale areas.


title:
On the stability of orthogonal additivity in $\beta$-homogeneous
  $F$-spaces and quasi-Banach spaces

abstract:
  In this paper, we study the stability of the orthogonal equation,which is
closely related to the results by Wlodzimierz Fechner and Justyna Sikorska in
2010. There are some differences that we consider the target space with the
\b{eta}-homogeneous norm and quasi-norm. Overcoming the \b{eta}-homogeneous
norm and quasi-norm bottlenecks, we get some new results.


title:
The free factor complex and the dualizing module for the automorphism
  group of a free group

abstract:
  Answering a question of Hatcher-Vogtmann, we prove that the top homology
group of the free factor complex is not the dualizing module for
$\text{Aut}(F_n)$, at least for $n = 5$.


title:
Prediction of transport property via machine learning molecular
  movements

abstract:
  Molecular dynamics (MD) simulations are increasingly being combined with
machine learning (ML) to predict material properties. The molecular
configurations obtained from MD are represented by multiple features, such as
thermodynamic properties, and are used as the ML input. However, to accurately
find the input--output patterns, ML requires a sufficiently sized dataset that
depends on the complexity of the ML model. Generating such a large dataset from
MD simulations is not ideal because of their high computation cost. In this
study, we present a simple supervised ML method to predict the transport
properties of materials. To simplify the model, an unsupervised ML method
obtains an efficient representation of molecular movements. This method was
applied to predict the viscosity of lubricant molecules in confinement with
shear flow. Furthermore, simplicity facilitates the interpretation of the model
to understand the molecular mechanics of viscosity. We revealed two types of
molecular mechanisms that contribute to low viscosity.


title: Convergence Speed and Approximation Accuracy of Numerical MCMC

abstract:
  When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation
caused by numerical errors is sometimes inevitable. This paper studies how
perturbation of MCMC affects the convergence speed and Monte Carlo estimation
accuracy. Our results show that when the original Markov chain converges to
stationarity fast enough and the perturbed transition kernel is a good
approximation to the original transition kernel, the corresponding perturbed
sampler has similar convergence speed and high approximation accuracy as well.
We discuss two different analysis frameworks: ergodicity and spectral gap, both
are widely used in the literature. Our results can be easily extended to obtain
non-asymptotic error bounds for MCMC estimators.
  We also demonstrate how to apply our convergence and approximation results to
the analysis of specific sampling algorithms, including Random walk Metropolis
and Metropolis adjusted Langevin algorithm with perturbed target densities, and
parallel tempering Monte Carlo with perturbed densities. Finally we present
some simple numerical examples to verify our theoretical claims.


title:
The ${\cal N}=2$ Supersymmetric $w_{1+\infty}$ Symmetry in the
  Two-Dimensional SYK Models

abstract:
  We identify the rank $(q_{syk}+1)$ of the interaction of the two-dimensional
${\cal N}=(2,2)$ SYK model with the deformation parameter $\lambda$ in the
Bergshoeff, de Wit and Vasiliev(in 1991)'s linear $W_{\infty}[\lambda]$ algebra
via $\lambda =\frac{1}{2(q_{syk}+1)}$ by using a matrix generalization. At the
vanishing $\lambda$ (or the infinity limit of $q_{syk}$), the ${\cal N}=2$
supersymmetric linear $W_{\infty}^{N,N}[\lambda=0]$ algebra contains the matrix
version of known ${\cal N}=2$ $W_{\infty}$ algebra, as a subalgebra, by
realizing that the $N$-chiral multiplets and the $N$-Fermi multiplets in the
above SYK models play the role of the same number of $\beta\, \gamma$ and $b\,
c$ ghost systems in the linear $W_{\infty}^{N,N}[\lambda=0]$ algebra. For the
nonzero $\lambda$, we determine the complete ${\cal N}=2$ supersymmetric linear
$W_{\infty}^{N,N}[\lambda]$ algebra where the structure constants are given by
the linear combinations of two different generalized hypergeometric functions
having the $\lambda$ dependence. The weight-$1, \frac{1}{2}$ currents occur in
the right hand sides of this algebra and their structure constants have the
$\lambda$ factors. We also describe the $\lambda =\frac{1}{4}$ (or $q_{syk}=1$)
case in the truncated subalgebras by calculating the vanishing structure
constants.


title:
Differentially Private Federated Learning with Local Regularization and
  Sparsification

abstract:
  User-level differential privacy (DP) provides certifiable privacy guarantees
to the information that is specific to any user's data in federated learning.
Existing methods that ensure user-level DP come at the cost of severe accuracy
decrease. In this paper, we study the cause of model performance degradation in
federated learning under user-level DP guarantee. We find the key to solving
this issue is to naturally restrict the norm of local updates before executing
operations that guarantee DP. To this end, we propose two techniques, Bounded
Local Update Regularization and Local Update Sparsification, to increase model
quality without sacrificing privacy. We provide theoretical analysis on the
convergence of our framework and give rigorous privacy guarantees. Extensive
experiments show that our framework significantly improves the privacy-utility
trade-off over the state-of-the-arts for federated learning with user-level DP
guarantee.


title: Privacy Leakage in Proactive VR Streaming: Modeling and Tradeoff

abstract:
  Proactive tile-based virtual reality (VR) video streaming employs the
viewpoint of a user to predict the tiles to be requested, renders and delivers
the predicted tiles before playback. Recently, it has been found that the
identity and preference of the user can be inferred from the trace of viewpoint
uploaded for proactive streaming, which indicates that viewpoint leakage incurs
privacy leakage. In this paper, we strive to answer the following questions
regarding viewpoint leakage during proactive VR video streaming. When is the
viewpoint leaked? Can privacy-preserving approaches (e.g., federated or
individual training, using predictors with no need for training, or predicting
locally) avoid viewpoint leakage? We find that if the prediction error or the
quality of experience (QoE) metric is uploaded for adaptive streaming, the real
viewpoint can be inferred even with the privacy-preserving approaches. Then, we
define viewpoint leakage probability to characterize the accuracy of the
inferred viewpoint, and respectively derive the probability when uploading
prediction error and QoE metric. We find that the viewpoint leakage probability
can be reduced by sacrificing QoE or increasing resources. Simulation with the
state-of-the-art predictor over a real dataset shows that such a tradeoff does
not exist only in rare cases.


title:
Load-Flow Solvability under Security Constraints in DC Distribution
  Networks

abstract:
  We present sufficient conditions for the load-flow solvability under security
constraints in DC distribution networks. In addition, we show that a load-flow
solution that fulfills security constraints can be obtained via a convex
optimization.


title:
Combining Individual and Joint Networking Behavior for Intelligent IoT
  Analytics

abstract:
  The IoT vision of a trillion connected devices over the next decade requires
reliable end-to-end connectivity and automated device management platforms.
While we have seen successful efforts for maintaining small IoT testbeds, there
are multiple challenges for the efficient management of large-scale device
deployments. With Industrial IoT, incorporating millions of devices,
traditional management methods do not scale well. In this work, we address
these challenges by designing a set of novel machine learning techniques, which
form a foundation of a new tool, it IoTelligent, for IoT device management,
using traffic characteristics obtained at the network level. The design of our
tool is driven by the analysis of 1-year long networking data, collected from
350 companies with IoT deployments. The exploratory analysis of this data
reveals that IoT environments follow the famous Pareto principle, such as: (i)
10% of the companies in the dataset contribute to 90% of the entire traffic;
(ii) 7% of all the companies in the set own 90% of all the devices. We designed
and evaluated CNN, LSTM, and Convolutional LSTM models for demand forecasting,
with a conclusion of the Convolutional LSTM model being the best. However,
maintaining and updating individual company models is expensive. In this work,
we design a novel, scalable approach, where a general demand forecasting model
is built using the combined data of all the companies with a normalization
factor. Moreover, we introduce a novel technique for device management, based
on autoencoders. They automatically extract relevant device features to
identify device groups with similar behavior to flag anomalous devices.


title:
Cascaded Gaps: Towards Gap-Dependent Regret for Risk-Sensitive
  Reinforcement Learning

abstract:
  In this paper, we study gap-dependent regret guarantees for risk-sensitive
reinforcement learning based on the entropic risk measure. We propose a novel
definition of sub-optimality gaps, which we call cascaded gaps, and we discuss
their key components that adapt to the underlying structures of the problem.
Based on the cascaded gaps, we derive non-asymptotic and logarithmic regret
bounds for two model-free algorithms under episodic Markov decision processes.
We show that, in appropriate settings, these bounds feature exponential
improvement over existing ones that are independent of gaps. We also prove
gap-dependent lower bounds, which certify the near optimality of the upper
bounds.


title: The PEE aspects of entanglement islands from bit threads

abstract:
  We study the partial entanglement entropy (PEE) aspects of the holographic
BCFT setup with an entanglement island, inspired by the holographic triality of
the AdS/BCFT setup developed in the recent study on the black hole information
problem, and the "PEE=CFF (component flow flux)" prescription, which is
proposed recently to investigate the holographic PEE in the framework of bit
thread formulation. Our study provides a bit thread description of the AdS/BCFT
setup, which characterizes the specific entanglement details between the
different parts of the system with an entanglement island, and may provide
further insight into the black hole information problem. Furthermore, we show
that in the context of island, one should distinguish between the fine-grained
PEE and the semi-classical PEE. Interestingly, similar to the island rule of
the fine-grained entropy in the semi-classical picture, we also propose the
island rules of the fine-grained PEE.


title:
Matrix Decomposition Perspective for Accuracy Assessment of Item
  Response Theory

abstract:
  The item response theory obtains the estimates and their confidence intervals
for parameters of abilities of examinees and difficulties of problems by using
the observed item response matrix consisting of 0/1 value elements. Many papers
discuss the performance of the estimates. However, this paper does not. Using
the maximum likelihood estimates, we can reconstruct the estimated item
response matrix. Then we can assess the accuracy of this reconstructed matrix
to the observed response matrix from the matrix decomposition perspective. That
is, this paper focuses on the performance of the reconstructed response matrix.
To compare the performance of the item response theory with others, we provided
the two kinds of low rank response matrix by approximating the observed
response matrix; one is the matrix via the singular value decomposition method
when the response matrix is a complete matrix, and the other is the matrix via
the matrix decomposition method when the response matrix is an incomplete
matrix. We have, firstly, found that the performance of the singular value
decomposition method and the matrix decomposition method is almost the same
when the response matrix is a complete matrix. Here, the performance is
measured by the closeness between the two matrices using the root mean squared
errors and the accuracy. Secondary, we have seen that the closeness of the
reconstructed matrix obtained from the item response theory to the observed
matrix is located between the two approximated low rank response matrices
obtained from the matrix decomposition method of k= and k=2 to the observed
matrix, where k indicates the first k columns use in the decomposed matrices.


title:
Co-Optimization of On-Ramp Merging and Plug-In Hybrid Electric Vehicle
  Power Split Using Deep Reinforcement Learning

abstract:
  Current research on Deep Reinforcement Learning (DRL) for automated on-ramp
merging neglects vehicle powertrain and dynamics. This work considers automated
on-ramp merging for a power-split Plug-In Hybrid Electric Vehicle (PHEV), the
2015 Toyota Prius Plug-In, using DRL. The on-ramp merging control and the PHEV
energy management are co-optimized such that the DRL policy directly outputs
the power split between the engine and the electric motor. The testing results
show that DRL can be successfully used for co-optimization, leading to
collision-free on-ramp merging. When compared with sequential approaches
wherein the upper-level on-ramp merging control and the lower-level PHEV energy
management are performed independently and in sequence, we found that
co-optimization results in economic but jerky on-ramp merging while sequential
approaches may result in collisions due to neglecting powertrain power limit
constraints in designing the upper-level on-ramp merging controller.


title:
Ulam stability of an additive-quadratic functional equation in F-space
  and quasi-Banach spaces

abstract:
  By adopting the direct method and fixed point method, we prove that the
Hyers-Ulam stability of the following additive-quadratic functional equation
\begin{equation}
  f(x+y, z+w)+f(x-y, z-w)-2 f(x, z)-2 f(x, w)=0 \end{equation} in
$\beta$-homogeneous $F$-spaces and quasi-Banach spaces. There are some
differences that we consider the target space with the $\beta$-homogeneous norm
and quasi-norm. Overcoming the $\beta$-homogeneous norm and quasi-norm
bottlenecks, we get some new results.


title:
Finite Element Approximation of Invariant Manifolds by the
  Parameterization Method

abstract:
  We combine the parameterization method for invariant manifolds with the
finite element method for elliptic PDEs,to obtain a new computational framework
for high order approximation of invariant manifolds attached to unstable
equilibrium solutions of nonlinear parabolic PDEs. The parameterization method
provides an infinitesimal invariance equation for the invariant manifold, which
we solve via a power series ansatz. A power matching argument leads to a
recursive system of linear elliptic PDEs -- the so-called homological equations
-- whose solutions are the power series coefficients of the parameterization.
The homological equations are solved recursively to any desired order using
finite element approximation. The end result is a polynomial expansion for a
chart map of the manifold, with coefficients in an appropriate finite element
space. We implement the method for a variety of example problems having both
polynomial and non-polynomial nonlinearities, on non-convex two-dimensional
polygonal domains (not necessary simply connected), for equilibrium solutions
with Morse indices one and two. We implement a-posteriori error indicators
which provide numerical evidence in support of the claim that the manifolds are
computed accurately.


title:
Kernel Packet: An Exact and Scalable Algorithm for Gaussian Process
  Regression with Mat\'ern Correlations

abstract:
  We develop an exact and scalable algorithm for one-dimensional Gaussian
process regression with Mat\'ern correlations whose smoothness parameter $\nu$
is a half-integer. The proposed algorithm only requires $\mathcal{O}(\nu^3 n)$
operations and $\mathcal{O}(\nu n)$ storage. This leads to a linear-cost solver
since $\nu$ is chosen to be fixed and usually very small in most applications.
The proposed method can be applied to multi-dimensional problems if a full grid
or a sparse grid design is used. The proposed method is based on a novel theory
for Mat\'ern correlation functions. We find that a suitable rearrangement of
these correlation functions can produce a compactly supported function, called
a "kernel packet". Using a set of kernel packets as basis functions leads to a
sparse representation of the covariance matrix that results in the proposed
algorithm. Simulation studies show that the proposed algorithm, when
applicable, is significantly superior to the existing alternatives in both the
computational time and predictive accuracy.


title:
Core-level photoemission time delay in heteronuclear diatomic molecules
  at high energy via multiple scattering theory

abstract:
  We present analytical expressions of momentum-resolved core-level
photoemission time delay in a molecular frame of a heteronuclear diatomic
molecule upon photoionization by a linearly polarized soft x-rays attosecond
pulse. For this purpose, we start to derive a general expression of
photoemission time delay based on the first order time dependent perturbation
theory within the one electron and single channel model in the fixed-in-space
system (atoms, molecules and crystals) and apply it to the core-level
photoemission within the electric dipole approximation. By using multiple
scattering theory and applying series expansion, plane wave and muffin-tin
approximations, the core-level photoemission time delay $t$ is divided into
three components, $t_{\rm abs}$, $t_{\rm path}$ and $t_{\rm sc}$, which are
atomic photoemission time delay, delays caused by the propagation of
photoelectron among the surrounding atoms and the scattering of photoelectron
by them, respectively. We applied single scattering approximation to $t_{\rm
path}$ and obtained $t_{\rm path}^{(1)}(k,\theta)$ with polarization vector
parallel to the molecular axis for a heteronuclear diatomic molecule, where
$\theta$ is the angle of measured photoelectron from the molecular axis. $t$ is
approximated well with this simplified expression $t_{\rm
path}^{(1)}(k,\theta)$ in the high energy regime ($k\gtrsim 3.5\,\, {\rm
a.u.}^{-1}$), and the validity of this estimated result is confirmed by
comparing it with multiple scattering calculations for C 1$s$ core-level
photoemission time delay of CO molecules. $t_{\rm path}^{(1)}(k,\theta)$ shows
characteristic dependence on $\theta$, it becomes zero at $\theta=0$, exhibits
EXAFS type oscillation with $2kR$ at $\theta=\pi$, where $R$ is the bondlength,
and gives just the travelling time of photoelectron from the absorbing atom to
the neighbouring atom at $\theta=\pi/2$.


title: Effective dynamics and applications in periodic kicks systems

abstract:
  In this work, we study the kick dynamics of periodically driven quantum
systems, and provide a time-independent effective Hamiltonian with the
analytical form to reasonably describe the effective dynamics in a long
timescale. We find that the effective coupling strength can be much larger than
the coupling strength of the original system in some parameter regions, which
stems from the zero time duration of kicks. Furthermore, different regimes can
be transformed from and to each other in the same three-level system by only
modulating the period of periodic kicks. In particular, the population of
excited states can be selectively suppressed in periodic kicks, benefiting from
the large detuning regime of the original system. Finally, we demonstrate some
applications and physical implementation of periodic kicks in quantum systems.
Those unique features would make periodic kicks becoming a powerful tool for
quantum state manipulations.


title: Fabchain: Managing Audit-able 3D Print Job over Blockchain

abstract:
  Improvements in fabrication devices such as 3D printers are becoming possible
for personal fabrication to freely fabricate any products. To clarify who is
liable for the product, the fabricator should keep the fabrication history in
an immutable and sustainably accessible manner. In this paper, we propose a new
scheme, "Fabchain," that can record the fabrication history in such a manner.
By utilizing a scheme that employs a blockchain as an audit-able communication
channel, Fabchain manages print jobs for the fabricator's 3D printer over the
blockchain, while maintaining a history of a print job. We implemented Fabchain
on Ethereum and evaluated the performance for recording a print job. Our
results demonstrate that Fabchain can complete communication of a print job
sequence in less than 1 minute on the Ethereum test network. We conclude that
Fabchain can manage a print job in a reasonable duration for 3D printing, while
satisfying the requirements for immutability and sustainability.


title: Numerable open covers and representability of topological stacks

abstract:
  In this note, we establish an analogue of the Brown--Gersten property for
numerable open covers of topological spaces: a simplicial presheaf on the site
of topological spaces with numerable open covers satisfies the homotopy descent
property for all open covers if and only if it satisfies it for covers with two
elements and covers with pairwise disjoint elements. We apply this result to
deduce a representability criterion for stacks on topological spaces similar to
arXiv:1912.10544. We also use this result to establish new simple criteria for
chain complexes of sheaves of abelian groups to satisfy the homotopy descent
property.


title:
Protecting Facial Privacy: Generating Adversarial Identity Masks via
  Style-robust Makeup Transfer

abstract:
  While deep face recognition (FR) systems have shown amazing performance in
identification and verification, they also arouse privacy concerns for their
excessive surveillance on users, especially for public face images widely
spread on social networks. Recently, some studies adopt adversarial examples to
protect photos from being identified by unauthorized face recognition systems.
However, existing methods of generating adversarial face images suffer from
many limitations, such as awkward visual, white-box setting, weak
transferability, making them difficult to be applied to protect face privacy in
reality. In this paper, we propose adversarial makeup transfer GAN (AMT-GAN), a
novel face protection method aiming at constructing adversarial face images
that preserve stronger black-box transferability and better visual quality
simultaneously. AMT-GAN leverages generative adversarial networks (GAN) to
synthesize adversarial face images with makeup transferred from reference
images. In particular, we introduce a new regularization module along with a
joint training strategy to reconcile the conflicts between the adversarial
noises and the cycle consistence loss in makeup transfer, achieving a desirable
balance between the attack strength and visual changes. Extensive experiments
verify that compared with state of the arts, AMT-GAN can not only preserve a
comfortable visual quality, but also achieve a higher attack success rate over
commercial FR APIs, including Face++, Aliyun, and Microsoft.


title:
Physical discovery in representation learning via conditioning on prior
  knowledge: applications for ferroelectric domain dynamics

abstract:
  Recent advances in electron, scanning probe, optical, and chemical imaging
and spectroscopy yield bespoke data sets containing the information of
structure and functionality of complex systems. In many cases, the resulting
data sets are underpinned by low-dimensional simple representations encoding
the factors of variability within the data. The representation learning methods
seek to discover these factors of variability, ideally further connecting them
with relevant physical mechanisms. However, generally the task of identifying
the latent variables corresponding to actual physical mechanisms is extremely
complex. Here, we explore an approach based on conditioning the data on the
known (continuous) physical parameters, and systematically compare it with the
previously introduced approach based on the invariant variational autoencoders.
The conditional variational autoencoders (cVAE) approach does not rely on the
existence of the invariant transforms, and hence allows for much greater
flexibility and applicability. Interestingly, cVAE allows for limited
extrapolation outside of the original domain of the conditional variable.
However, this extrapolation is limited compared to the cases when true physical
mechanisms are known, and the physical factor of variability can be
disentangled in full. We further show that introducing the known conditioning
results in the simplification of the latent distribution if the conditioning
vector is correlated with the factor of variability in the data, thus allowing
to separate relevant physical factors. We initially demonstrate this approach
using 1D and 2D examples on a synthetic dataset and then extend it to the
analysis of experimental data on ferroelectric domain dynamics visualized via
Piezoresponse Force Microscopy.


title:
Mismatch between Multi-turn Dialogue and its Evaluation Metric in
  Dialogue State Tracking

abstract:
  Dialogue state tracking (DST) aims to extract essential information from
multi-turn dialogue situations and take appropriate actions. A belief state,
one of the core pieces of information, refers to the subject and its specific
content, and appears in the form of domain-slot-value. The trained model
predicts "accumulated" belief states in every turn, and joint goal accuracy and
slot accuracy are mainly used to evaluate the prediction; however, we specify
that the current evaluation metrics have a critical limitation when evaluating
belief states accumulated as the dialogue proceeds, especially in the most used
MultiWOZ dataset. Additionally, we propose relative slot accuracy to complement
existing metrics. Relative slot accuracy does not depend on the number of
predefined slots, and allows intuitive evaluation by assigning relative scores
according to the turn of each dialogue. This study also encourages not solely
the reporting of joint goal accuracy, but also various complementary metrics in
DST tasks for the sake of a realistic evaluation.


title: Axion electrodynamics and magnetohydrodynamics

abstract:
  We formulate axion-electrodynamics and magnetohydrodynamics (MHD) in the
cosmological context assuming weak gravity. The two formulations are made for a
general scalar field with general $f(\phi)$-coupling, and an axion as a massive
scalar field with $\phi^2$-coupling, with the helical electromagnetic field.
The $\alpha$-dynamo term appears naturally from the helical-coupling in the MHD
formulation. In the presence of the electromagnetic coupling, however, the
Schr\"odinger and hydrodynamic formulations of the coherently oscillating axion
are not available for the conventional $\phi$ coupling; instead, $\phi^2$
coupling allows successful formulations preserving the dark matter nature of
the axion to nonlinear order.


title: Shape of eigenvectors for the decaying potential model

abstract:
  We consider the 1d Schr\"odinger operator with decaying random potential, and
study the joint scaling limit of the eigenvalues and the measures associated
with the corresponding eigenfunctions which is based on the formulation by
Rifkind-Virag. As a result, we have completely different behavior depending on
the decaying rate $\alpha > 0$ of the potential : the limiting measure is equal
to (1) Lebesgue measure for the super-critical case ($\alpha > 1/2$), (2) a
measure of which the density has power-law decay with Brownian fluctuation for
critical case ($\alpha=1/2$), and (3) the delta measure with its atom being
uniformly distributed for the sub-critical case($\alpha<1/2$). This result is
consistent with previous study on spectral and statistical properties.


title: Measurements of Rayleigh Ratios in Linear Alkylbenzene

abstract:
  In present work an experiment has been designed to measure the Rayleigh ratio
directly at $405$ nm and $432$ nm for linear alkylbenzene which is a common
solvent used in liquid scintillator detectors of neutrino experiments. The
perpendicularly polarized Rayleigh ratio is determined to be $(4.52\pm
0.28)\times 10^{-6}$ m$^{-1}\cdot$ sr$^{-1}$ at $405$ nm and $(3.82\pm
0.24)\times 10^{-6}$ m$^{-1}\cdot$ sr$^{-1}$ at $432$ nm, and the corresponding
Rayleigh scattering length is $L_{Ray} = 22.9\pm 0.3(\mathrm{stat.})\pm
1.7(\mathrm{sys.})$ m at $405$ nm and $L_{Ray}= 27.0\pm 0.9(\mathrm{stat.})\pm
1.8(\mathrm{sys.})$ m at $432$ nm.


title: Picosecond synchronization system for quantum networks

abstract:
  The operation of long-distance quantum networks requires photons to be
synchronized and must account for length variations of quantum channels. We
demonstrate a 200 MHz clock-rate fiber optic-based quantum network using
off-the-shelf components combined with custom-made electronics and
telecommunication C-band photons. The network is backed by a scalable and fully
automated synchronization system with ps-scale timing resolution.
Synchronization of the photons is achieved by distributing O-band-wavelength
laser pulses between network nodes. Specifically, we distribute photon pairs
between three nodes, and measure a reduction of coincidence-to-accidental ratio
from 77 to only 42 when the synchronization system is enabled, which permits
high-fidelity qubit transmission. Our demonstration sheds light on the role of
noise in quantum communication and represents a key step in realizing deployed
co-existing classical-quantum networks.


title:
Searching for Robust Neural Architectures via Comprehensive and Reliable
  Evaluation

abstract:
  Neural architecture search (NAS) could help search for robust network
architectures, where defining robustness evaluation metrics is the important
procedure. However, current robustness evaluations in NAS are not sufficiently
comprehensive and reliable. In particular, the common practice only considers
adversarial noise and quantified metrics such as the Jacobian matrix, whereas,
some studies indicated that the models are also vulnerable to other types of
noises such as natural noise. In addition, existing methods taking adversarial
noise as the evaluation just use the robust accuracy of the FGSM or PGD, but
these adversarial attacks could not provide the adequately reliable evaluation,
leading to the vulnerability of the models under stronger attacks. To alleviate
the above problems, we propose a novel framework, called Auto Adversarial
Attack and Defense (AAAD), where we employ neural architecture search methods,
and four types of robustness evaluations are considered, including adversarial
noise, natural noise, system noise and quantified metrics, thereby assisting in
finding more robust architectures. Also, among the adversarial noise, we use
the composite adversarial attack obtained by random search as the new metric to
evaluate the robustness of the model architectures. The empirical results on
the CIFAR10 dataset show that the searched efficient attack could help find
more robust architectures.


title: Continuum Many Planar Embeddings of the Knaster Accordion

abstract:
  Anusic, Bruin, and Cinc have asked which hereditarily decomposable chainable
continua (HDCC) have uncountably many mutually inequivalent planar embeddings.
It was noted, as per the embedding technique of John C. Mayer with the
$\sin(1/x)$-curve, that any HDCC which is the compactification of a ray with an
arc likely has this property. Here, we show two methods for constructing
$\mathfrak{c}$-many mutually inequivalent planar embeddings of the classic
Knaster $V \Lambda$-continuum, $K$, also referred to as the Knaster accordion.
The first of these two methods produces $\mathfrak{c}$-many planar embeddings
of $K$, all of whose images have a different set of accessible points from the
image of the standard embedding of $K$, while the second method produces
$\mathfrak{c}$-many embeddings of $K$, each of which preserve the accessibility
of all points in the standard embedding.


title: Non-equilibrium many-body dynamics in supersymmetric quenching

abstract:
  We study the dynamics induced by quenching an ultracold quantum many-body
system between two supersymmetric Hamiltonians. Such a quench can be created by
carefully changing the external trapping potential and leads to a situation
where the eigenspectra before and after the quench are nearly identical. We
show that the dynamics originating from this can be conveniently described
using knowledge about the initial state only and apply this insight to the
specific example of a fermionic gas that is initially trapped in an infinite
box potential. Quenching to different, higher order supersymmetric partners
potentials we observe the appearance of many-body revivals in the survival
probability and show that some of these are robust at finite temperatures. This
is in contrast to the well known Talbot effect, which is the standard example
for quenching into a system with a quadratic spectrum.


title: Input-Tuning: Adapting Unfamiliar Inputs to Frozen Pretrained Models

abstract:
  Recently the prompt-tuning paradigm has attracted significant attention. By
only tuning continuous prompts with a frozen pre-trained language model (PLM),
prompt-tuning takes a step towards deploying a shared frozen PLM to serve
numerous downstream tasks. Although prompt-tuning shows good performance on
certain natural language understanding (NLU) tasks, its effectiveness on
natural language generation (NLG) tasks is still under-explored. In this paper,
we argue that one of the factors hindering the development of prompt-tuning on
NLG tasks is the unfamiliar inputs (i.e., inputs are linguistically different
from the pretraining corpus). For example, our preliminary exploration reveals
a large performance gap between prompt-tuning and fine-tuning when unfamiliar
inputs occur frequently in NLG tasks. This motivates us to propose
input-tuning, which fine-tunes both the continuous prompts and the input
representations, leading to a more effective way to adapt unfamiliar inputs to
frozen PLMs. Our proposed input-tuning is conceptually simple and empirically
powerful. Experimental results on seven NLG tasks demonstrate that input-tuning
is significantly and consistently better than prompt-tuning. Furthermore, on
three of these tasks, input-tuning can achieve a comparable or even better
performance than fine-tuning.


title: Quantum spectral clustering algorithm for unsupervised learning

abstract:
  Clustering is one of the most crucial problems in unsupervised learning, and
the well-known $k$-means clustering algorithm has been shown to be
implementable on a quantum computer with a significant speedup. However, many
clustering problems cannot be solved by $k$-means, and a powerful method called
spectral clustering is introduced to solve these problems. In this work, we
propose a circuit design to implement spectral clustering on a quantum
processor with a substantial speedup, by initializing the processor into a
maximally entangled state and encoding the data information into an
efficiently-simulatable Hamiltonian. Compared with the established quantum
$k$-means algorithms, our method does not require a quantum random access
memory or a quantum adiabatic process. It relies on an appropriate embedding of
quantum phase estimation into Grover's search to gain the quantum speedup.
Simulations demonstrate that our method is effective in solving clustering
problems and will serve as an important supplement to quantum $k$-means for
unsupervised learning.


title:
Measurement of the integrated luminosities at BESIII for data samples at
  collision energies around 4 GeV

abstract:
  The integrated luminosities of the XYZ data samples collected in 2016--2017
at center-of-mass energies between 4.19 and 4.28 GeV are measured with a
precision better than 1% by analyzing large-angle Bhabha scattering events. The
integrated luminosities of the data sets collected in 2010--2014 are updated by
considering an additional correction related to the detector performance. These
results are essential for precision measurements of the production cross
sections of the charmonium and charmonium-like states.


title: Determining Atmospheric Electric Fields using MGMR3D

abstract:
  Cosmic-ray particles impinging on the atmosphere induce high-energy particle
cascades in air, an Extensive Air Shower (EAS), emitting coherent radio
emission. This emission is affected by the presence of strong electric fields
during thunderstorm conditions. To reconstruct the atmospheric electric field
from the measured radio footprint of the EAS we use an analytic model for the
calculation of the radio emission, MGMR3D. In this work we make an extensive
comparison between the results of a microscopic model for radio emission,
CoREAS, to obtain an improved parametrization for MGMR3D in the presence of
atmospheric electric fields, as well as confidence intervals. The approach to
extract the electric field structure is applied successfully to an event with a
complicated radio footprint measured by LOFAR during thunderstorm conditions.
This shows that, with the improved parametrization, MGMR3D can be used to
extract the structure of the atmospheric electric field.


title:
Stable phase retrieval for infinite dimensional subspaces of
  $L_2(\mathbb{R})$

abstract:
  Phase retrieval is known to always be unstable when using a frame or
continuous frame for an infinite dimensional Hilbert space. We consider a
generalization of phase retrieval to the setting of subspaces of $L_2$ which
coincides with using a continuous frame for phase retrieval when the subspace
is the range of the analysis operator of a continuous frame. We then prove that
there do exist infinite dimensional subspaces of $L_2$ where phase retrieval is
stable. That is, we give a method for constructing an infinite dimensional
subspace $Y\subseteq L_2$ such that there exists $C\geq 1$ so that
$$\min\big(\big\|f-g\big\|_{L_2},\big\|f+g\big\|_{L_2}\big)\leq C \big\|
|f|-|g| \big\|_{L_2} \qquad\textrm{ for all }f,g\in Y. $$
  This construction also leads to new results on uniform stability of phase
retrieval in finite dimensions. Our construction has a deterministic component
and a random component. When using sub-Gaussian random variables we achieve
phase retrieval with high probability and stability constant independent of the
dimension $n$ when using $m$ on the order of $n$ random vectors. Without
sub-Gaussian or any other higher moment assumptions, we are able to achieve
phase retrieval with high probability and stability constant independent of the
dimension $n$ when using $m$ on the order of $n\log(n)$ random vectors.


title:
Suzaku Observations of Fe K-shell Lines in the Supernova Remnant W51C
  and Hard X-ray Sources in the Proximity

abstract:
  In this paper, we investigated the Fe K-shell lines in the supernova remnant
W51C and hard X-ray sources in the proximity. We measured the intensities of Fe
I K$\alpha$ and Fe XXV He$\alpha$ lines at 6.40 keV and 6.68 keV, respectively,
and found that the intensity of the 6.68 keV line is consistent with the
background level expected from previous studies, while that of the 6.40 keV
line is higher at the significance level of 2.0${\sigma}$. Given the presence
of gamma-ray emission and high ionization rate point spatially coincident with
the remnant, we conclude that the enhanced 6.40 keV line most likely originates
from the interaction between low-energy cosmic rays and molecular clouds. Also,
we discovered an enhanced 6.68 keV line emission from the compact H II region
G49.0-0.3 at the significance level of 3.4${\sigma}$. Spectral analysis
revealed that the temperature and abundance of the thermal plasma with the 6.68
keV line is $kT = 3.0^{+0.8}_{-0.7}$ keV and $Z = 0.5 \pm 0.2$ solar,
respectively. These values are explained by the thermal plasma generated by the
stellar winds of O stars.


title: MSDN: Mutually Semantic Distillation Network for Zero-Shot Learning

abstract:
  The key challenge of zero-shot learning (ZSL) is how to infer the latent
semantic knowledge between visual and attribute features on seen classes, and
thus achieving a desirable knowledge transfer to unseen classes. Prior works
either simply align the global features of an image with its associated class
semantic vector or utilize unidirectional attention to learn the limited latent
semantic representations, which could not effectively discover the intrinsic
semantic knowledge e.g., attribute semantics) between visual and attribute
features. To solve the above dilemma, we propose a Mutually Semantic
Distillation Network (MSDN), which progressively distills the intrinsic
semantic representations between visual and attribute features for ZSL. MSDN
incorporates an attribute$\rightarrow$visual attention sub-net that learns
attribute-based visual features, and a visual$\rightarrow$attribute attention
sub-net that learns visual-based attribute features. By further introducing a
semantic distillation loss, the two mutual attention sub-nets are capable of
learning collaboratively and teaching each other throughout the training
process. The proposed MSDN yields significant improvements over the strong
baselines, leading to new state-of-the-art performances on three popular
challenging benchmarks, i.e., CUB, SUN, and AWA2. Our codes have been available
at: \url{https://github.com/shiming-chen/MSDN}.


title:
Diabatic valence-hole states in the C$_2$ molecule: "Putting Humpty
  Dumpty together again"

abstract:
  Despite the long history of spectroscopic studies of the C$_2$ molecule,
fundamental questions about its chemical bonding are still being hotly debated.
The complex electronic structure of C$_2$ is a consequence of its dense
manifold of near-degenerate, low-lying electronic states. A global multi-state
diabatic model is proposed here to disentangle the numerous configuration
interactions within four symmetry manifolds of C$_2$ ($^{1}\Pi_g$, $^{3}\Pi_g$,
$^{1}\Sigma_u^+$, and $^{3}\Sigma_u^+$). The key concept of our model is the
existence of two "valence-hole" configurations,
$2\sigma_g^22\sigma_u^11\pi_{u}^33\sigma_g^2$ for $^{1,3}\Pi_g$ states and
$2\sigma_g^22\sigma_u^11\pi_{u}^43\sigma_g^1$ for $^{1,3}\Sigma_u^+$ states
that derive from $3\sigma_g\leftarrow2\sigma_u$ electron promotion. The
lowest-energy state from each of the four C$_2$ symmetry species is dominated
by this type of valence-hole configuration at its equilibrium internuclear
separation. As a result of their large binding energy (nominal bond order of 3)
and correlation with the 2s$^2$2p$^2$+2s2p$^3$ separated-atom configurations,
the presence of these valence-hole configurations has a profound impact on the
$global$ electronic structure and unimolecular dynamics of C$_2$.


title:
The nuclear symmetry energy from relativistic Brueckner-Hartree-Fock
  model

abstract:
  The microscopic mechanisms of the symmetry energy in nuclear matter are
investigated in the framework of the relativistic Brueckner-Hartree-Fock (RBHF)
model with a high-precision realistic nuclear potential, pvCDBonn A. The
kinetic energy and potential contributions to symmetry energy are decomposed.
They are explicitly expressed by the nucleon self-energies, which are obtained
through projecting the $G$-matrices from the RBHF model into the terms of
Lorentz covariants. The nuclear medium effects on the nucleon self-energy and
nucleon-nucleon interaction in symmetry energy are discussed by comparing the
results from the RBHF model and those from Hartree-Fock and relativistic
Hartree-Fock models. It is found that the nucleon self-energy including the
nuclear medium effect on the single-nucleon wave function provides a largely
positive contribution to the symmetry energy, while {the nuclear medium effect
on the nucleon-nucleon interaction, i.e., the effective $G$-matrices generates
the negative contribution}. The tensor force plays an essential role in the
symmetry energy around the density. The scalar and vector covariant amplitudes
of nucleon-nucleon interaction dominate the potential component of the symmetry
energy. Furthermore, the isoscalar and isovector terms in the optical potential
are extracted from the RBHF model. The isoscalar part is consistent with the
results from the analysis of global optical potential, while the isovector one
has obvious differences at higher incident energy due to the relativistic
effect.


title:
An Improved Automatic Modulation Classification Scheme Based on Adaptive
  Fusion Network

abstract:
  Due to the over-fitting problem caused by imbalance samples, there is still
room to improve the performance of data-driven automatic modulation
classification (AMC) in noisy scenarios. By fully considering the signal
characteristics, an AMC scheme based on adaptive fusion network (AFNet) is
proposed in this work. The AFNet can extract and aggregate multi-scale spatial
features of in-phase and quadrature (I/Q) signals intelligently, thus improving
the feature representation capability. Moreover, a novel confidence weighted
loss function is proposed to address the imbalance issue and it is implemented
by a two-stage learning scheme.Through the two-stage learning, AFNet can focus
on high-confidence samples with more valid information and extract effective
representations, so as to improve the overall classification performance. In
the simulations, the proposed scheme reaches an average accuracy of 62.66% on a
wide range of SNRs, which outperforms other AMC models. The effects of the loss
function on classification accuracy are further studied.


title:
General relativistic treatment of $f$-mode oscillations of hyperonic
  stars

abstract:
  We present a systematic study of $f$-mode oscillations in neutron stars
containing hyperons, extending recent results obtained within the Cowling
approximation to linearized General Relativity. Employing a relativistic mean
field model, we find that the Cowling approximation can overestimate the
quadrupolar $f$-mode frequency of neutron stars by up to 30\% compared to the
frequency obtained in the linearized general relativistic formalism. Imposing
current astrophysical constraints, we derive updated empirical relations for
gravitational wave asteroseismology. The frequency and damping time of
quadrupole $f$-mode oscillations of hyperonic stars are found to be in the
range of 1.47 - 2.45kHz and 0.13 - 0.51 sec respectively. Our correlation
studies demonstrate that among the various parameters of the nucleonic and
hyperonic sectors of the model, the nucleon effective mass shows the strongest
correlation with mode characteristics and neutron star observables. Estimates
for the detectability of $f$-modes in a transient burst of gravitational waves
from isolated hyperonic stars is also provided.


title: New proofs of stability theorems on spectral graph problems

abstract:
  Both the Simonovits stability theorem and the Nikiforov spectral stability
theorem are powerful tools for solving exact values of Tur\'{a}n numbers in
extremal graph theory. Recently, F\"{u}redi [J. Combin. Theory Ser. B 115
(2015)] provided a concise and contemporary proof of the Simonovits stability
theorem. In this note, we present a unified treatment for some extremal graph
problems, including short proofs of Nikiforov's spectral stability theorem and
the clique stability theorem proved recently by Ma and Qiu [European J. Combin.
84 (2020)]. Moreover, some spectral extremal problems related to the
$p$-spectral radius and signless Laplacian radius are also included.


title:
Tunable optical bistability in grapheme Tamm plasmon/Bragg reflector
  hybrid structure at terahertz frequencies

abstract:
  We propose a composite multilayer structure consist of graphene Tamm plasmon
and Bragg reflector with defect layer to realize the low threshold and tunable
optical bistability (OB) at the terahertz frequencies. This low-threshold OB
originates from the couple of the Tamm plasmon (TP) and the defect mode (DM).
We discuss the influence of graphene and the DM on the hysteretic response of
the TM-polarized reflected light. It is found that the switch-up and
switch-down threshold required to observe the optical bistable behavior are
lowered markedly due to the excitation of the TP and DM. Besides, the switching
threshold value can be further reduced by coupling the TP and DM. We believe
these results will provide a new avenue for realizing the low threshold and
tunable optical bistable devices and other nonlinear optical devices.


title:
Open Source Software Sustainability: Combining Institutional Analysis
  and Socio-Technical Networks

abstract:
  Open Source Software (OSS) forms much of the fabric of our digital society,
especially successful and sustainable ones. But many OSS projects do not become
sustainable, resulting in abandonment and even risks for the world's digital
infrastructure. Prior work has looked at the reasons for this mainly from two
very different perspectives. In software engineering, the focus has been on
understanding success and sustainability from the socio-technical perspective:
the OSS programmers' day-to-day activities and the artifacts they create. In
institutional analysis, on the other hand, emphasis has been on institutional
designs (e.g., policies, rules, and norms) that structure governance. Even
though each is necessary for a comprehensive understanding of OSS projects, the
connection and interaction between the two approaches have been barely
explored.
  In this paper, we make the first effort toward understanding OSS project
sustainability using a dual-view analysis, by combining institutional analysis
with socio-technical systems analysis. In particular, we (i) use linguistic
approaches to extract institutional rules and norms from OSS contributors'
communications to represent the evolution of their governance systems, and (ii)
construct socio-technical networks based on longitudinal collaboration records
to represent each project's organizational structure. We combined the two
methods and applied them to a dataset of developer traces from 253 nascent OSS
projects within the Apache Software Foundation (ASF) incubator. We find that
the socio-technical and institutional features relate to each other, and
provide complementary views into the progress of the ASF's OSS projects.
Refining these combined analyses can help provide a more precise understanding
of the synchronization between the evolution of institutional governance and
organizational structure.


title:
End-to-end video instance segmentation via spatial-temporal graph neural
  networks

abstract:
  Video instance segmentation is a challenging task that extends image instance
segmentation to the video domain. Existing methods either rely only on
single-frame information for the detection and segmentation subproblems or
handle tracking as a separate post-processing step, which limit their
capability to fully leverage and share useful spatial-temporal information for
all the subproblems. In this paper, we propose a novel graph-neural-network
(GNN) based method to handle the aforementioned limitation. Specifically, graph
nodes representing instance features are used for detection and segmentation
while graph edges representing instance relations are used for tracking. Both
inter and intra-frame information is effectively propagated and shared via
graph updates and all the subproblems (i.e. detection, segmentation and
tracking) are jointly optimized in an unified framework. The performance of our
method shows great improvement on the YoutubeVIS validation dataset compared to
existing methods and achieves 35.2% AP with a ResNet-50 backbone, operating at
22 FPS. Code is available at http://github.com/lucaswithai/visgraph.git .


title: Electromagnetic Energy Density in Hyperbolic Metamaterials

abstract:
  We derive the energy density associated with an electromagnetic wave passing
through a hyperbolic metamaterial (HMM). Both types of HMMs are studied. By
considering a dispersive and absorbing HMM as an effective uniaxial crystal, we
find that under the influence of an electromagnetic wave, the response of type
I (type II) HMM in the directions perpendicular to and parallel to the optical
axis are similar to those of Lorentz (Drude) and Drude (Lorentz) media,
respectively. Numerical examples are presented to reveal the general
characteristics of the direction-dependent energy storage capacity of both
types of HMMs.


title:
Automatic Calibration Framework of Agent-Based Models for Dynamic and
  Heterogeneous Parameters

abstract:
  Agent-based models (ABMs) highlight the importance of simulation validation,
such as qualitative face validation and quantitative empirical validation. In
particular, we focused on quantitative validation by adjusting simulation input
parameters of the ABM. This study introduces an automatic calibration framework
that combines the suggested dynamic and heterogeneous calibration methods.
Specifically, the dynamic calibration fits the simulation results to the
real-world data by automatically capturing suitable simulation time to adjust
the simulation parameters. Meanwhile, the heterogeneous calibration reduces the
distributional discrepancy between individuals in the simulation and the real
world by adjusting agent related parameters cluster-wisely.


title: Ces\'{a}ro condition for curves in the flat pseudo-hermitian manifolds

abstract:
  By considering the three dimensional Heisenberg group $\mathbb{H}_1$ as a
flat model of pseudo-hermitian manifolds, the authors in [8] derived the
Frenet-Serret formulas for curves in $\mathbb{H}_1$. In this notes we show
three applications of the Frenet-Serret formulas. The first is the Ces\'{a}ro
immobility condition, which provides the criterion of curves being contained in
a given rotationally symmetric surface. Secondly, we show that any horizontally
regular curve is a Bertrand curve, and give all characterizations of those
curves. The final application is a classification of curves depending on
whether the position vector of the curve lies on the planes spanned by any pair
of its unit tangent, normal, and binormal vectors.


title: DIDO: Deep Inertial Quadrotor Dynamical Odometry

abstract:
  In this work, we propose an interoceptive-only state estimation system for a
quadrotor with deep neural network processing, where the quadrotor dynamics is
considered as a perceptive supplement of the inertial kinematics. To improve
the precision of multi-sensor fusion, we train cascaded networks on real-world
quadrotor flight data to learn IMU kinematic properties, quadrotor dynamic
characteristics, and motion states of the quadrotor along with their
uncertainty information, respectively. This encoded information empowers us to
address the issues of IMU bias stability, dynamic constraints, and multi-sensor
calibration during sensor fusion. The above multi-source information is fused
into a two-stage Extended Kalman Filter (EKF) framework for better estimation.
Experiments have demonstrated the advantages of our proposed work over several
conventional and learning-based methods.


title:
On the Construction of Distribution-Free Prediction Intervals for an
  Image Regression Problem in Semiconductor Manufacturing

abstract:
  The high-volume manufacturing of the next generation of semiconductor devices
requires advances in measurement signal analysis. Many in the semiconductor
manufacturing community have reservations about the adoption of deep learning;
they instead prefer other model-based approaches for some image regression
problems, and according to the 2021 IEEE International Roadmap for Devices and
Systems (IRDS) report on Metrology a SEMI standardization committee may endorse
this philosophy. The semiconductor manufacturing community does, however,
communicate a need for state-of-the-art statistical analyses to reduce
measurement uncertainty. Prediction intervals which characterize the
reliability of the predictive performance of regression models can impact
decisions, build trust in machine learning, and be applied to other regression
models. However, we are not aware of effective and sufficiently simple
distribution-free approaches that offer valid coverage for important classes of
image data, so we consider the distribution-free conformal prediction and
conformalized quantile regression framework.The image regression problem that
is the focus of this paper pertains to line edge roughness (LER) estimation
from noisy scanning electron microscopy images. LER affects semiconductor
device performance and reliability as well as the yield of the manufacturing
process; the 2021 IRDS emphasizes the crucial importance of LER by devoting a
white paper to it in addition to mentioning or discussing it in the reports of
multiple international focus teams. It is not immediately apparent how to
effectively use normalized conformal prediction and quantile regression for LER
estimation. The modeling techniques we apply appear to be novel for finding
distribution-free prediction intervals for image data and will be presented at
the 2022 SEMI Advanced Semiconductor Manufacturing Conference.


title: Fast Community Detection based on Graph Autoencoder Reconstruction

abstract:
  With the rapid development of big data, how to efficiently and accurately
discover tight community structures in large-scale networks for knowledge
discovery has attracted more and more attention. In this paper, a community
detection framework based on Graph AutoEncoder Reconstruction (noted as GAER)
is proposed for the first time. GAER is a highly scalable framework which does
not require any prior information. We decompose the graph autoencoder-based
one-step encoding into the two-stage encoding framework to adapt to the
real-world big data system by reducing complexity from the original O(N^2) to
O(N). At the same time, based on the advantages of GAER support module
plug-and-play configuration and incremental community detection, we further
propose a peer awareness based module for real-time large graphs, which can
realize the new nodes community detection at a faster speed, and accelerate
model inference with the 6.15 times - 14.03 times speed. Finally, we apply the
GAER on multiple real-world datasets, including some large-scale networks. The
experimental result verified that GAER has achieved the superior performance on
almost all networks.


title: A global synchronization theorem for oscillators on a random graph

abstract:
  Consider $n$ identical Kuramoto oscillators on a random graph. Specifically,
consider \ER random graphs in which any two oscillators are bidirectionally
coupled with unit strength, independently and at random, with probability
$0\leq p\leq 1$. We say that a network is globally synchronizing if the
oscillators converge to the all-in-phase synchronous state for almost all
initial conditions. Is there a critical threshold for $p$ above which global
synchrony is extremely likely but below which it is extremely rare? It is
suspected that a critical threshold exists and is close to the so-called
connectivity threshold, namely, $p\sim \log(n)/n$ for $n \gg 1$. Ling, Xu, and
Bandeira made the first progress toward proving a result in this direction:
they showed that if $p\gg \log(n)/n^{1/3}$, then \ER networks of Kuramoto
oscillators are globally synchronizing with high probability as
$n\rightarrow\infty$. Here we improve that result by showing that $p\gg
\log^2(n)/n$ suffices. Our estimates are explicit: for example, we can say that
there is more than a $99.9996\%$ chance that a random network with $n = 10^6$
and $p>0.01117$ is globally synchronizing.


title: Scalable Verification of GNN-based Job Schedulers

abstract:
  Recently, Graph Neural Networks (GNNs) have been applied for scheduling jobs
over clusters, achieving better performance than hand-crafted heuristics.
Despite their impressive performance, concerns remain over whether these
GNN-based job schedulers meet users' expectations about other important
properties, such as strategy-proofness, sharing incentive, and stability. In
this work, we consider formal verification of GNN-based job schedulers. We
address several domain-specific challenges such as networks that are deeper and
specifications that are richer than those encountered when verifying image and
NLP classifiers. We develop vegas, the first general framework for verifying
both single-step and multi-step properties of these schedulers based on
carefully designed algorithms that combine abstractions, refinements, solvers,
and proof transfer. Our experimental results show that vegas achieves
significant speed-up when verifying important properties of a state-of-the-art
GNN-based scheduler compared to previous methods.


title: A geometric conjecture about phase transitions

abstract:
  As phenomena that necessarily emerge from the collective behavior of
interacting particles, phase transitions continue to be difficult to predict
using statistical thermodynamics. A recent proposal called the topological
hypothesis suggests that the existence of a phase transition could perhaps be
inferred from changes to the topology of the accessible part of the
configuration space. This paper instead suggests that such a topological change
is often associated with a dramatic change in the configuration space geometry,
and that the geometric change is the actual driver of the phase transition.
More precisely, a geometric change that brings about a discontinuity in the
mixing time required for an initial probability distribution on the
configuration space to reach steady-state is conjectured to be related to the
onset of a phase transition in the thermodynamic limit. This conjecture is
tested by evaluating the diffusion diameter and $\epsilon$-mixing time of the
configuration spaces of hard disk and hard sphere systems of increasing size.
Explicit geometries are constructed for the configuration spaces of these
systems, and numerical evidence suggests that a discontinuity in the
$\epsilon$-mixing time coincides with the solid-fluid phase transition in the
thermodynamic limit.


title: Riemann problem for constant flow with single-point heating source

abstract:
  This work focuses on the Riemann problem of Euler equations with global
constant initial conditions and a single-point heating source, which comes from
the physical problem of heating one-dimensional inviscid compressible constant
flow. In order to deal with the source of Dirac delta-function, we propose an
analytical frame of double classic Riemann problems(CRPs) coupling, which
treats the fluids on both sides of the heating point as two separate Riemann
problems and then couples them. Under the double CRPs frame, the solution is
self-similar, and only three types of solution are found. The theoretical
analysis is also supported by the numerical simulation. Furthermore, the
uniqueness of the Riemann solution is established with some restrictions on the
Mach number of the initial condition.


title:
Multi-physics constraints at different densities to probe nuclear
  symmetry energy in hyperonic neutron stars

abstract:
  The appearance of strangeness in the form of hyperons within the inner core
of neutron stars is expected to affect its detectable properties such as its
global structure or gravitational wave emission. In this work, we explore the
parameter space of hyperonic stars within the framework of the Relativistic
Mean Field model allowed by present uncertainties in state-of-the-art nuclear
and hypernuclear experimental data. We impose multi-physics constraints at
different density regimes to restrict the parameter space: Chiral effective
field theory, heavy-ion collision data as well as multi-messenger astrophysical
observations of neutron stars. We investigate possible correlations between
empirical nuclear and hypernuclear parameters, particularly the symmetry energy
and its slope, with observable properties of neutron stars. We do not find a
correlation for the hyperon parameters and the astrophysical data. However, the
inclusion of hyperons generates a tension between the astrophysical and heavy
ion data constraining considerable the available parameter space.


title: SingleSketch2Mesh : Generating 3D Mesh model from Sketch

abstract:
  Sketching is an important activity in any design process. Designers and
stakeholders share their ideas through hand-drawn sketches. These sketches are
further used to create 3D models. Current methods to generate 3D models from
sketches are either manual or tightly coupled with 3D modeling platforms.
Therefore, it requires users to have an experience of sketching on such
platform. Moreover, most of the existing approaches are based on geometric
manipulation and thus cannot be generalized. We propose a novel AI based
ensemble approach, SingleSketch2Mesh, for generating 3D models from hand-drawn
sketches. Our approach is based on Generative Networks and Encoder-Decoder
Architecture to generate 3D mesh model from a hand-drawn sketch. We evaluate
our solution with existing solutions. Our approach outperforms existing
approaches on both - quantitative and qualitative evaluation criteria.


title: Representations of General Linear Groups in the Verlinde Category

abstract:
  In this article, we construct affine group schemes $GL(X)$ where $X$ is any
object in the Verlinde category in characteristic $p$ and classify their
irreducible representations. We begin by showing that for a simple object $X$
of categorical dimension $i$, this representation category is semisimple and is
equivalent to the connected component of the Verlinde category for $SL_{i}$.
Subsequently, we use this along with a Verma module construction to classify
irreducible representations of $GL(nL)$ for any simple object $L$ and any
natural number $n$. Finally, parabolic induction allows us to classify
irreducible representations of $GL(X)$ where $X$ is any object in the Verlinde
Category.


title:
Risk Bounds of Multi-Pass SGD for Least Squares in the Interpolation
  Regime

abstract:
  Stochastic gradient descent (SGD) has achieved great success due to its
superior performance in both optimization and generalization. Most of existing
generalization analyses are made for single-pass SGD, which is a less practical
variant compared to the commonly-used multi-pass SGD. Besides, theoretical
analyses for multi-pass SGD often concern a worst-case instance in a class of
problems, which may be pessimistic to explain the superior generalization
ability for some particular problem instance. The goal of this paper is to
sharply characterize the generalization of multi-pass SGD, by developing an
instance-dependent excess risk bound for least squares in the interpolation
regime, which is expressed as a function of the iteration number, stepsize, and
data covariance. We show that the excess risk of SGD can be exactly decomposed
into the excess risk of GD and a positive fluctuation error, suggesting that
SGD always performs worse, instance-wisely, than GD, in generalization. On the
other hand, we show that although SGD needs more iterations than GD to achieve
the same level of excess risk, it saves the number of stochastic gradient
evaluations, and therefore is preferable in terms of computational time.


title:
NMR evidence for energy gap opening in thiol-capped platinum
  nanoparticles

abstract:
  When the particle size of a metal is reduced, it is expected that an energy
gap will open due to the quantum size effect. However, the energy gap in
platinum (Pt) metal nanoparticles has not been observed directly by nuclear
magnetic resonance (NMR). To investigate the particle size dependence of the
electronic state of Pt nanoparticles, we performed 195Pt NMR experiments on
thiol-capped Pt nanoparticles with three different average diameters of less
than 3 nm. For the nanoparticles with a diameter of 2.8 nm, we observed usual
metallic behavior with a smaller density of states than that of the bulk Pt. In
contrast, the temperature dependence of 1/T1T in nanoparticles less than 2.5 nm
in diameter is an activation-energy form above 150 K, which is semiconducting
behavior with an energy gap of the order of 2000 K. The significant decrease in
1/T1T by more than two orders of magnitude in the smaller Pt nanoparticles
compared to the bulk Pt is attributable to the disappearance of the density of
states at the Fermi energy, which is consistent with the opening of an energy
gap. These results indicate a metal-insulator transition below 2.5 nm in
diameter is present in our thiol-capped Pt nanoparticle samples. The effect of
the thiol capping on the electronic structure suggested by the experimental
results is also discussed.


title:
Minimax principle for right eigenvalues of dual quaternion matrices and
  their generalized inverses

abstract:
  Dual quaternions can represent rigid body motion in 3D spaces, and have found
wide applications in robotics, 3D motion modelling and control, and computer
graphics. In this paper, we introduce three different right linear independency
for a set of dual quaternion vectors, and study some related basic properties
for the set of dual quaternion vectors and dual quaternion matrices. We present
a minimax principle for right eigenvalues of dual quaternion Hermitian
matrices. Based upon a newly established Cauchy-Schwarz inequality for dual
quaternion vectors and singular value decomposition of dual quaternion
matrices, we propose an important inequality for singular values of dual
quaternion matrices. We finally introduce the concept of generalized inverse of
dual quaternion matrices, and present the necessary and sufficient conditions
for a dual quaternion matrix to be one of four types of generalized inverses of
another dual quaternion matrix.


title:
Tunable Dirac Semimetals with Higher-order Fermi Arcs in Kagome Lattices
  Pd$_3$Pb$_2$X$_2$ (X = S, Se)

abstract:
  Bulk-boundary correspondence has achieved a great success in the
identification of topological states. However, this elegant strategy doesn't
apply to the Dirac semimetals (DSMs). Here, we propose that kagome lattices
Pd$_3$Pb$_2$X$_2$ (X = S, Se) are unique type-I DSMs without surface Fermi arc
states, which are different from the previous well-known DSMs, such as Na$_3$Bi
and Cd$_3$As$_2$. Pd$_3$Pb$_2$X$_2$ are characterized by nontrivial topological
invariant Z$_3$, guaranteeing a higher-order bulk-hinge correspondence and the
existence of higher-order Fermi arcs, as well as fractional corner charges on
the hinges. The type-I DSMs are located at the phase boundaries of several
topological phases, including type-II DSMs and three-dimensional weak
topological insulators. The phase transitions can be easily manipulated by
external strain. Our results provide feasible platforms for the study of these
unique DSMs and the related phase transitions.


title: Secondary bifurcations in semilinear ordinary differential equations

abstract:
  We consider the Neumann problem for the equation $u_{xx}+\lambda f(u)=0$ in
the punctured interval $(-1,1) \setminus \{0\}$, where $\lambda>0$ is a
bifurcation parameter and $f(u)=u-u^3$. At $x=0$, we impose the conditions
$u(-0)+au_x(-0)=u(+0)-au_x(+0)$ and $u_x(-0)=u_x(+0)$ for a constant $a>0$ (the
symbols $+0$ and $-0$ stand for one-sided limits). The problem appears as a
limiting equation for a semilinear elliptic equation in a higher dimensional
domain shrinking to the interval $(-1,1)$. First we prove that odd solutions
and even solutions form families of branches $\{ \mathcal{C}^o_k\}_{k \in
\mathbb{N}}$ and $\{ \mathcal{C}^e_k\}_{k \in \mathbb{N}}$, respectively. Both
$\mathcal{C}^o_k$ and $\mathcal{C}^e_k$ bifurcate from the trivial solution
$u=0$. We then show that $\mathcal{C}^e_k$ contains no other bifurcation point,
while $\mathcal{C}^o_k$ contains two points where secondary bifurcations occur.
Finally we determine the Morse index of solutions on the branches. General
conditions on $f(u)$ for the same assertions to hold are also given.


title:
Speeding up quantum adiabatic processes with dynamical quantum geometric
  tensor

abstract:
  For adiabatic control of quantum systems, the non-adiabatic transitions are
usually reduced by increasing the operation time of the processes. The quantum
adiabaticity is perfectly reached with infinite operation time. In this paper,
we propose the dynamical quantum geometric tensor, as a metric in the control
parameter space, to speed up quantum adiabatic processes and reach the quantum
adiabaticity in relatively short time. The optimal control is to tune the
control parameter with a constant velocity along the geodesic path according to
the metric. For the system initiated from the $n$-th eigenstate, the
probability of the non-adiabatic transition in the optimal control is bounded
as $P_{n}(t)\leq4\mathcal{L}_{n}^{2}/\tau^{2}$ with the quantum adiabatic
length $\mathcal{L}_{n}$ induced by the metric and the operation time $\tau$.
Our optimization strategy is illustrated via two explicit models, the
Landau-Zener model and the one-dimensional transverse Ising model.


title:
Estimation of the number of logical qubits required for radiation
  transport calculations with a quantum computer

abstract:
  As an application of fault-tolerant quantum computers, we consider radiation
transport calculations in this study. Radiation transport calculation using
Monte Carlo calculation can obtain a solution to even a problem difficult to
solve analytically. However, it is time-consuming depending on the scale and
precision of the problem. Because it is known that the computational complexity
of Monte Carlo calculation can be square rooted by quantum amplitude
estimation, acceleration can be expected if radiation transport calculation is
run on a quantum computer. In this study, we designed and investigated a
quantum circuit for a simplified transport calculation in which the reaction is
only forward scattering or absorption and the energy and time do not change as
well as showed the possibility of acceleration the calculation. Further, we
estimated the number of logical qubits required to solve practical problems
based on the quantum circuit.


title: HRTF measurement for accurate sound localization cues

abstract:
  A new database of head-related transfer functions (HRTFs) for accurate sound
source localization is presented through precise measurement and
post-processing in terms of improved frequency bandwidth and causality of
head-related impulse responses (HRIRs) for accurate spectral cue (SC) and
interaural time difference (ITD), respectively. The improvement effects of the
proposed methods on binaural sound localization cues were investigated. To
achieve sufficient frequency bandwidth with a single source, a one-way sealed
speaker module was designed to obtain wide band frequency response based on
electro-acoustics, whereas most existing HRTF databases rely on a two-way
vented loudspeaker that has multiple sources. The origin transfer function at
the head center was obtained by the proposed measurement scheme using a 0
degree on-axis microphone to ensure accurate spectral cue pattern of HRTFs,
whereas in the previous measurements with a 90 degree off-axis microphone, the
magnitude response of the origin transfer function fluctuated and decreased
with increasing frequency, causing erroneous SCs of HRTFs. To prevent
discontinuity of ITD due to non-causality of ipsilateral HRTFs, obtained HRIRs
were circularly shifted by time delay considering the head radius of the
measurement subject. Finally, various sound localization cues such as ITD,
interaural level difference (ILD), SC, and horizontal plane directivity (HPD)
were derived from the presented HRTFs, and improvements on binaural sound
localization cues were examined. As a result, accurate SC patterns of HRTFs
were confirmed through the proposed measurement scheme using the 0 degree
on-axis microphone, and continuous ITD patterns were obtained due to the
non-causality compensation. Source codes and presented HRTF database are
available to relevant research groups at GitHub
(https://github.com/han-saram/HRTF-HATS-KAIST).


title:
Evolution of interfaces, triple points, and quadruple points using
  discrete interface equations of motion

abstract:
  The evolution of interfaces is intrinsic to many physical processes ranging
from cavitation in fluids to recrystallization in solids. Computational
modeling of interface motion entails a number of challenges, largely due to the
range of topological transitions that can occur over the course of the
simulation. Microstructure evolution in a polycrystalline material that
involves grain boundary motion is a particularly complex example due to the
extreme variety, heterogeneity, and anisotropy of grain boundary properties.
Accurately modeling this process is essential to determining
processing-structure-property relationships in polycrystalline materials
though, making modeling efforts central to the eventual rational design of
materials. Simulations of microstructure evolution often use diffuse interface
methods, and specifically the phase field method; these are advantageous for
their versatility and ease of handling complex geometries, but can be
prohibitively expensive due to the need for high interface resolution. Discrete
interface methods require fewer grid points and can consequently exhibit better
performance but have received comparatively little attention, perhaps due to
the difficulty of consistently implementing topological transitions. This work
considers a recently developed discrete-interface method for microstructure
evolution, and provides an explicit comparison to diffuse interface methods by
comparing against a multiphase field method in a number of classical
microstructure evolution problems: the shrinking of a spherical grain,
determination of a triple junction diheral angle, and determination of a
quadruple point dihedral angle. In each case, the discrete method is found to
meet or outperform the multiphase field method in terms of accuracy for
comparable levels of refinement, demonstrating its potential efficacy as a
numerical approach for microstructure evolution.