title: Opinions Vary? Diagnosis First!

abstract:
  In medical image segmentation, images are usually annotated by several
different clinical experts. This clinical routine helps to mitigate the
personal bias. However, Computer Vision models often assume there has a unique
ground-truth for each of the instance. This research gap between Computer
Vision and medical routine is commonly existed but less explored by the current
research.In this paper, we try to answer the following two questions: 1. How to
learn an optimal combination of the multiple segmentation labels? and 2. How to
estimate this segmentation mask from the raw image? We note that in clinical
practice, the image segmentation mask usually exists as an auxiliary
information for disease diagnosis. Adhering to this mindset, we propose a
framework taking the diagnosis result as the gold standard, to estimate the
segmentation mask upon the multi-rater segmentation labels, named DiFF
(Diagnosis First segmentation Framework).DiFF is implemented by two novelty
techniques. First, DFSim (Diagnosis First Simulation of gold label) is learned
as an optimal combination of multi-rater segmentation labels for the disease
diagnosis. Then, toward estimating DFSim mask from the raw image, we further
propose T\&G Module (Take and Give Module) to instill the diagnosis knowledge
into the segmentation network. The experiments show that compared with commonly
used majority vote, the proposed DiFF is able to segment the masks with 6%
improvement on diagnosis AUC score, which also outperforms various
state-of-the-art multi-rater methods by a large margin.


title:
E-Polynomials of Generic $\text{GL}_n\rtimes\!<\!\sigma\!>\!~$-Character
  Varieties: Branched Case

abstract:
  For any branched double covering of compact Riemann surfaces, we consider the
associated character varieties that are unitary in the global sense, which we
call $\text{GL}_n\rtimes\!<\!\sigma\!>\!~$-character varieties. We restrict the
monodromies around the ramification points to generic semi-simple conjugacy
classes contained in $\text{GL}_n\sigma$, and compute the E-polynomials of
these character varieties using the character table of
$\text{GL}_n(q)\rtimes\!<\!\sigma\!>\!$. The result is expressed as the inner
product of certain symmetric functions associated to the wreath products
$(\mathbb{Z}/2\mathbb{Z})^N\rtimes\mathfrak{S}_N$. We are then led to a
conjectural formula for the mixed Hodge polynomial, which involves (modified)
Macdonald polynomials and wreath Macdonald polynomials.


title: EMGSE: Acoustic/EMG Fusion for Multimodal Speech Enhancement

abstract:
  Multimodal learning has been proven to be an effective method to improve
speech enhancement (SE) performance, especially in challenging situations such
as low signal-to-noise ratios, speech noise, or unseen noise types. In previous
studies, several types of auxiliary data have been used to construct multimodal
SE systems, such as lip images, electropalatography, or electromagnetic
midsagittal articulography. In this paper, we propose a novel EMGSE framework
for multimodal SE, which integrates audio and facial electromyography (EMG)
signals. Facial EMG is a biological signal containing articulatory movement
information, which can be measured in a non-invasive way. Experimental results
show that the proposed EMGSE system can achieve better performance than the
audio-only SE system. The benefits of fusing EMG signals with acoustic signals
for SE are notable under challenging circumstances. Furthermore, this study
reveals that cheek EMG is sufficient for SE.


title: Some Cubic and Quartic Inequalities of Four Variables

abstract:
  Let $\mathcal{H} \subset \mathcal{H}_{n,d} := \mathbb{R}[x_1$,$\ldots$,
$x_n]_d$ be a vector space, and $A$ be a compact semialgebraic subset of
$\mathbb{P}_{\mathbb{R}}^{n-1}$. We shall study some PSD cones $\mathcal{P} =
\mathcal{P}(A$, $\mathcal{H}) := \big\{f \in \mathcal{H}$ $\big|$ $f(a) \geq 0$
($\forall a \in A$)$\big\}$. Our interests are (1) to determine the extremal
elements of $\mathcal{P}$, (2) to determine discriminants of $\mathcal{P}$, (3)
to describe $\mathcal{P}$ as a union of basic semialgebraic subsets, and (4) to
find a nice test set when $\dim \mathcal{H}$ is low. In this article, we
present (1), (2), (3) and (4) for $\mathcal{P}(\mathbb{R}^4$,
$\mathcal{H}_{4,4}^{s0})$ and $\mathcal{P}(\mathbb{R}_+^4$,
$\mathcal{H}_{4,4}^{s0})$, where $\mathcal{H}_{n,d}^{s0} := \big\{f \in
\mathcal{H}_{n,d}$ $\big|$ $f$ is symmetric and $f(1,\ldots,1)=0 \big\}$. We
also provide (1) -- (4) for $\mathcal{P}(\mathbb{R}_+^4$,
$\mathcal{H}_{4,3}^{c0})$, where $\mathcal{H}_{n,d}^{c0} := \big\{f \in
\mathcal{H}_{n,d}$ $\big|$ $f$ is cyclic and $f(1,\ldots,1)=0 \big\}$.


title:
A Novel Transfer Learning Framework with Prototypical Representation
  based Pairwise Learning for Cross-Subject Cross-Session EEG-Based Emotion
  Recognition

abstract:
  In this paper, we propose a novel transfer learning framework with
Prototypical Representation based Pairwise Learning (PR-PL) for EEG-based
emotion recognition, which learns discriminative and generalized prototypical
representations for emotion revealing across individuals and formulates emotion
recognition as pairwise learning to alleviate the model reliance on precise
label information. Prototypical learning based adversarial discriminative
domain adaptation method is developed to encode the inherent emotion-related
semantic structure of EEG data. Pairwise learning with an adaptive
pseudo-labeling method is proposed to achieve a reliable and stable model
learning with noisy labels. Through domain adaptation, besides aligning the
feature representation of the source and the target on a shared feature space,
the feature separability of both source and target domains is also considered.
The characterized prototypical representations are evident with a high feature
concentration within one single emotion category and a high feature
separability across different emotion categories. Extensive experiments are
conducted on two benchmark databases (SEED and SEED-IV) for recognizing three
and four emotion categories using four cross-validation evaluation protocols.
The experimental results demonstrate the superiority of the proposed PR-PL
against the state-of-the-art methods on cross-subject cross-session,
cross-subject within-session, within-subject cross-session, and within-subject
within-session evaluation protocols, which shows the power of PR-PL in dealing
with the ambiguity of neurophysiological responses in affective studies.


title:
Mixing and Shifting: Exploiting Global and Local Dependencies in Vision
  MLPs

abstract:
  Token-mixing multi-layer perceptron (MLP) models have shown competitive
performance in computer vision tasks with a simple architecture and relatively
small computational cost. Their success in maintaining computation efficiency
is mainly attributed to avoiding the use of self-attention that is often
computationally heavy, yet this is at the expense of not being able to mix
tokens both globally and locally. In this paper, to exploit both global and
local dependencies without self-attention, we present Mix-Shift-MLP (MS-MLP)
which makes the size of the local receptive field used for mixing increase with
respect to the amount of spatial shifting. In addition to conventional mixing
and shifting techniques, MS-MLP mixes both neighboring and distant tokens from
fine- to coarse-grained levels and then gathers them via a shifting operation.
This directly contributes to the interactions between global and local tokens.
Being simple to implement, MS-MLP achieves competitive performance in multiple
vision benchmarks. For example, an MS-MLP with 85 million parameters achieves
83.8% top-1 classification accuracy on ImageNet-1K. Moreover, by combining
MS-MLP with state-of-the-art Vision Transformers such as the Swin Transformer,
we show MS-MLP achieves further improvements on three different model scales,
e.g., by 0.5% on ImageNet-1K classification with Swin-B. The code is available
at: https://github.com/JegZheng/MS-MLP.


title: GAMMA Challenge:Glaucoma grAding from Multi-Modality imAges

abstract:
  Color fundus photography and Optical Coherence Tomography (OCT) are the two
most cost-effective tools for glaucoma screening. Both two modalities of images
have prominent biomarkers to indicate glaucoma suspected. Clinically, it is
often recommended to take both of the screenings for a more accurate and
reliable diagnosis. However, although numerous algorithms are proposed based on
fundus images or OCT volumes in computer-aided diagnosis, there are still few
methods leveraging both of the modalities for the glaucoma assessment. Inspired
by the success of Retinal Fundus Glaucoma Challenge (REFUGE) we held
previously, we set up the Glaucoma grAding from Multi-Modality imAges (GAMMA)
Challenge to encourage the development of fundus \& OCT-based glaucoma grading.
The primary task of the challenge is to grade glaucoma from both the 2D fundus
images and 3D OCT scanning volumes. As part of GAMMA, we have publicly released
a glaucoma annotated dataset with both 2D fundus color photography and 3D OCT
volumes, which is the first multi-modality dataset for glaucoma grading. In
addition, an evaluation framework is also established to evaluate the
performance of the submitted methods. During the challenge, 1272 results were
submitted, and finally, top-10 teams were selected to the final stage. We
analysis their results and summarize their methods in the paper. Since all
these teams submitted their source code in the challenge, a detailed ablation
study is also conducted to verify the effectiveness of the particular modules
proposed. We find many of the proposed techniques are practical for the
clinical diagnosis of glaucoma. As the first in-depth study of fundus \& OCT
multi-modality glaucoma grading, we believe the GAMMA Challenge will be an
essential starting point for future research.


title: A Comprehensive Benchmark of Deep Learning Libraries on Mobile Devices

abstract:
  Deploying deep learning (DL) on mobile devices has been a notable trend in
recent years. To support fast inference of on-device DL, DL libraries play a
critical role as algorithms and hardware do. Unfortunately, no prior work ever
dives deep into the ecosystem of modern DL libs and provides quantitative
results on their performance. In this paper, we first build a comprehensive
benchmark that includes 6 representative DL libs and 15 diversified DL models.
We then perform extensive experiments on 10 mobile devices, which help reveal a
complete landscape of the current mobile DL libs ecosystem. For example, we
find that the best-performing DL lib is severely fragmented across different
models and hardware, and the gap between those DL libs can be rather huge. In
fact, the impacts of DL libs can overwhelm the optimizations from algorithms or
hardware, e.g., model quantization and GPU/DSP-based heterogeneous computing.
Finally, atop the observations, we summarize practical implications to
different roles in the DL lib ecosystem.


title:
Context-Preserving Instance-Level Augmentation and Deformable
  Convolution Networks for SAR Ship Detection

abstract:
  Shape deformation of targets in SAR image due to random orientation and
partial information loss caused by occlusion of the radar signal, is an
essential challenge in SAR ship detection. In this paper, we propose a data
augmentation method to train a deep network that is robust to partial
information loss within the targets. Taking advantage of ground-truth
annotations for bounding box and instance segmentation mask, we present a
simple and effective pipeline to simulate information loss on targets in
instance-level, while preserving contextual information. Furthermore, we adopt
deformable convolutional network to adaptively extract shape-invariant deep
features from geometrically translated targets. By learning sampling offset to
the grid of standard convolution, the network can robustly extract the features
from targets with shape variations for SAR ship detection. Experiments on the
HRSID dataset including comparisons with other deep networks and augmentation
methods, as well as ablation study, demonstrate the effectiveness of our
proposed method.


title: Symbol Length of Classes in Milnor $K$-groups

abstract:
  Given a field $F$, a positive integer $m$ and an integer $n\geq 2$, we prove
that the symbol length of classes in Milnor's $K$-groups $K_n F/2^m K_n F$ that
are equivalent to single symbols under the embedding into $K_n F/2^{m+1} K_n F$
is at most $2^{n-1}$ under the assumption that $F \supseteq \mu_{2^{m+1}}$.
Since for $n=2$, $K_2 F/2^m K_n F \cong {_{2^m}Br(F)}$, this coincides with the
upper bound of $2$ for the symbol length of central simple algebras of degree
$2^m$ that are Brauer equivalent to a single symbol algebra of degree $2^{m+1}$
proved by Tignol in 1983. We also consider the cases where the embedding into
$K_n F/2^{m+1} K_n F$ is of symbol length 2, 3 and 4 (the latter when $n=2$).
We finish with studying the symbol length of classes in $K_3/3^m K_3 F$ whose
embedding into $K_3 F/3^{m+1} K_3 F$ is one symbol when $F \supseteq
\mu_{3^{m+1}}$.


title:
Two-thirds law for pairwise velocity and origin of critical MOND
  acceleration from distributions of density, velocity, and acceleration in
  dark matter flow

abstract:
  A halo-based non-projection approach is proposed to study scale/redshift
dependence of distributions (PDF) in dark matter flow. All particles are
divided into halo and out-of-halo particles such that PDF can be studied
separately. Without projecting particle fields onto grid, scale dependence is
analyzed by counting all pairs on different scales $r$. Redshift dependence is
studied via generalized kurtosis. From this analysis, we demonstrate: i)
Root-mean-square acceleration (~$10^{-10}m/s^2$) in halos matches critical
acceleration $a_0$ in MOND that can be determined by the rate of energy
transfer $\epsilon_u$, where $a_0=-(3\pi)^2\epsilon_u/u$ and $u^2(a=1)=u^2_0$
is velocity dispersion. Particle energy is dependent on its speed as
$\propto{v^2}$ if its acceleration $a_p$>>$a_0$ and $\propto{v^1}$ if
$a_p$<<$a_0$. Both deep-MOND and Newtonian behavior can be recovered in dark
matter flow; ii) $m$th moment of pairwise velocity $\langle(\Delta
u_L)^m\rangle$ is analytically modelled. On small scale, even moments can be
modelled by a two-thirds law $\propto{(-\epsilon_ur)}^{2/3}$, odd moments
$\propto{r}$ and satisfy GSCH; iii) Scale dependence is studied for
longitudinal velocity $u_L$ or $u_L^{'}$, pairwise velocity $\Delta
u_L$=$u_L^{'}$-$u_L$ and sum velocity $\Sigma u_L$=$u^{'}_L$+$u_L$. Fully
developed velocity fields are never Gaussian on any scale. On small scale, both
$u_L$ and $\Sigma u_L$ can be modelled by a X distribution for maximum entropy.
PDF of $\Delta u_L$ is different with its moments derived. On large scale, both
$\Delta u_L$ and $\Sigma u_L$ can be modelled by a logistic function. Time
evolution of velocity distributions follows prediction of X distribution with a
decreasing shape parameter $\alpha$ to maximize system entropy; iv) Delaunay
tessellation is used to reconstruct density field. Density
correlations/spectrum are obtained, modeled and compared with theory.


title:
Contact angle measurement on curved wetting surface in multiphase
  lattice Boltzmann method

abstract:
  Contact angle is an essential physical quantity that characterizes the
wettability of a substrate. Although it is widely used in the studies of
surface wetting, capillary phenomena and moving contact lines, measuring
contact angles in experiments and simulations is still complicated and
time-consuming. In this paper, we present an efficient scheme for the real-time
and on-the-spot measurement of contact angles on curved wetting surfaces in
lattice Boltzmann simulations. The measuring results are in excellent agreement
with the theoretical predictions by the spherical cap method without
considering the gravity effect. A series of the simulations with various drop
sizes and surface curvatures confirm that the present scheme is
grid-independent. Then, it is verified in gravitational environments by
simulating the deformations of sessile and pendent droplets on the curved
wetting surface. The numerical results are highly consistent with experimental
observations and support the theoretical analysis that the microscopic contact
angle is independent of gravity. Furthermore, the scheme is applied to capture
the dynamic contact angle hysteresis on homogeneous or chemically heterogeneous
curved surfaces. Importantly, the accurate contact angle measurement enables
the mechanical analysis at moving contact lines. The present measurement is
simple and efficient, and can be extended to implement in various multiphase
lattice Boltzmann models.


title: Semantic Matching from Different Perspectives

abstract:
  In this paper, we pay attention to the issue which is usually overlooked,
i.e., \textit{similarity should be determined from different perspectives}. To
explore this issue, we release a Multi-Perspective Text Similarity (MPTS)
dataset, in which sentence similarities are labeled from twelve perspectives.
Furthermore, we conduct a series of experimental analysis on this task by
retrofitting some famous text matching models. Finally, we obtain several
conclusions and baseline models, laying the foundation for the following
investigation of this issue. The dataset and code are publicly available at
Github\footnote{\url{https://github.com/autoliuweijie/MPTS}


title: Entanglement and Causal Relation in distributed quantum computation

abstract:
  In this thesis, we investigate two different aspects of entanglement and
classical communication in distributed quantum computation (DQC).
  In the first part, we analyze implementable computation over a given quantum
network resource by introducing a new concept, quantum network coding for
quantum computation. We consider a setting of networks where quantum
communication for each edge of a network is restricted to sending one-qubit,
but classical communication is unrestricted. Specifically, we analyze
implementable $k$-qubit unitary operations over a certain class of networks,
called cluster networks. We show that any two-qubit unitary operation is
implementable over the butterfly network and the grail network, which are
fundamental primitive networks for network coding. We also obtain necessary and
sufficient conditions for the probabilistic implementability of unitary
operations over cluster networks.
  In the second part, we investigate resource tradeoffs in DQC. First, we show
that entanglement required for local state discrimination can be substituted by
less entanglement by increasing the rounds of classical communication. Second,
we develop a new framework of deterministic joint quantum operations by using a
causal relation between the outputs and inputs of the local operations without
predefined causal order, called "classical communication" without predefined
causal order (CC*). We show that local operations and CC* (LOCC*) is equivalent
to the separable operation (SEP). This result indicates that
entanglement-assisted LOCC implementing SEP can be simulated by LOCC* without
entanglement. We also investigate the relationship between LOCC* and another
formalism for deterministic joint quantum operations without assuming
predefined causal order based on the quantum process formalism. As a result, we
construct an example of non-LOCC SEP by using LOCC*.


title:
Modified Poisson-Nernst-Planck theory for low-to-mid frequency
  immittance of electric double-layer capacitors

abstract:
  Understanding the system-level spectral immittance response of capacitive
energy storage devices with analytically tractable physics-based models is not
only important for the progress of the technology, but also allows to develop
new physical insights more easily. Here, we report a modified
Poisson--Nernst--Planck (PNP) system describing charge concentration and
electric potential as a model of electro-kinetics for electrodes showing mixed
resistive-capacitive behavior. This is done by (i) incorporating time shifts
between the current fluxes and both concentration gradients of charged species
and the electric field, and (ii) introducing time fractional derivatives in the
continuity equation. The aim is to characterize the deviation of immittance
from that of ideal capacitors both at close-to-dc frequencies where the
impedance angle for example is larger than -90 deg., and also at mid-range
frequencies where the system veers progressively toward resistive behavior.
This latter tendency is important to model in order to identify the extend of
the capacitive bandwidth of the device from the rest. Solution and simulation
results to the one-dimensional modified PNP system for symmetric
electrolyte/blocking electrode configuration are presented and discussed.


title: Doubly heavy tetraquarks in a chiral-diquark picture

abstract:
  Energy spectrum of doubly heavy tetraquarks, $T_{QQ}$ ($QQ \bar{q} \bar{q}$
with $Q = c, b$ and $q = u, d, s$), is studied in the potential chiral-diquark
model. Using the chiral effective theory of diquarks and the
quark-diquark-based potential model, the $T_{bb}$, $T_{cc}$, and $T_{cb}$
tetraquarks are described as a three-body system composed of two heavy quarks
and an antidiquark. We find several $T_{bb}$ bound states, while no $T_{cc}$
and $T_{cb}$ (deep) bound state is seen. We also study the change of the
$T_{QQ}$ tetraquark masses under restoration of chiral symmetry.


title:
Source Code Summarization with Structural Relative Position Guided
  Transformer

abstract:
  Source code summarization aims at generating concise and clear natural
language descriptions for programming languages. Well-written code summaries
are beneficial for programmers to participate in the software development and
maintenance process. To learn the semantic representations of source code,
recent efforts focus on incorporating the syntax structure of code into neural
networks such as Transformer. Such Transformer-based approaches can better
capture the long-range dependencies than other neural networks including
Recurrent Neural Networks (RNNs), however, most of them do not consider the
structural relative correlations between tokens, e.g., relative positions in
Abstract Syntax Trees (ASTs), which is beneficial for code semantics learning.
To model the structural dependency, we propose a Structural Relative Position
guided Transformer, named SCRIPT. SCRIPT first obtains the structural relative
positions between tokens via parsing the ASTs of source code, and then passes
them into two types of Transformer encoders. One Transformer directly adjusts
the input according to the structural relative distance; and the other
Transformer encodes the structural relative positions during computing the
self-attention scores. Finally, we stack these two types of Transformer
encoders to learn representations of source code. Experimental results show
that the proposed SCRIPT outperforms the state-of-the-art methods by at least
1.6%, 1.4% and 2.8% with respect to BLEU, ROUGE-L and METEOR on benchmark
datasets, respectively. We further show that how the proposed SCRIPT captures
the structural relative dependencies.


title: Dynamics of semigroups of H\'enon-like maps in $\mathbb{C}^2$

abstract:
  The goal of this article is to explore the dynamics of a semigroup of
polynomial automorphisms of $\mathbb{C}^2$, generated by a finite collection of
H\'enon-like maps. In particular, we construct positive and negative dynamical
Green's functions $G_{\mathscr{G}}^\pm$ and corresponding dynamical Green's
currents $\mu_{\mathscr{G}}^\pm$ for a semigroup $\mathcal{S}$, generated by a
collection ${\mathscr{G}}.$ Using them, we show that the positive (or negative)
Julia set of the semigroup $\mathcal{S}$, i.e., $\mathcal{J}_{\mathcal{S}}^+$
(or $\mathcal{J}_{\mathcal{S}}^-$) is equal to the closure of the union of
individual positive (or negative) Julia sets of the maps, in the semigroup
$\mathcal{S}$. Furthermore, we prove that $\mu_{\mathscr{G}}^+$ is supported on
whole of $\mathcal{J}_{\mathcal{S}}^+$ and is also the unique positive closed
$(1,1)$-current supported on $\mathcal{J}_{\mathcal{S}}^+$, satisfying a
semi-invariance relation that depends on the generating set ${\mathscr{G}}$.


title:
MetaShift: A Dataset of Datasets for Evaluating Contextual Distribution
  Shifts and Training Conflicts

abstract:
  Understanding the performance of machine learning models across diverse data
distributions is critically important for reliable applications. Motivated by
this, there is a growing focus on curating benchmark datasets that capture
distribution shifts. While valuable, the existing benchmarks are limited in
that many of them only contain a small number of shifts and they lack
systematic annotation about what is different across different shifts. We
present MetaShift--a collection of 12,868 sets of natural images across 410
classes--to address this challenge. We leverage the natural heterogeneity of
Visual Genome and its annotations to construct MetaShift. The key construction
idea is to cluster images using its metadata, which provides context for each
image (e.g. "cats with cars" or "cats in bathroom") that represent distinct
data distributions. MetaShift has two important benefits: first, it contains
orders of magnitude more natural data shifts than previously available. Second,
it provides explicit explanations of what is unique about each of its data sets
and a distance score that measures the amount of distribution shift between any
two of its data sets. We demonstrate the utility of MetaShift in benchmarking
several recent proposals for training models to be robust to data shifts. We
find that the simple empirical risk minimization performs the best when shifts
are moderate and no method had a systematic advantage for large shifts. We also
show how MetaShift can help to visualize conflicts between data subsets during
model training.


title:
Tight integration of neural- and clustering-based diarization through
  deep unfolding of infinite Gaussian mixture model

abstract:
  Speaker diarization has been investigated extensively as an important central
task for meeting analysis. Recent trend shows that integration of end-to-end
neural (EEND)-and clustering-based diarization is a promising approach to
handle realistic conversational data containing overlapped speech with an
arbitrarily large number of speakers, and achieved state-of-the-art results on
various tasks. However, the approaches proposed so far have not realized {\it
tight} integration yet, because the clustering employed therein was not optimal
in any sense for clustering the speaker embeddings estimated by the EEND
module. To address this problem, this paper introduces a {\it trainable}
clustering algorithm into the integration framework, by deep-unfolding a
non-parametric Bayesian model called the infinite Gaussian mixture model
(iGMM). Specifically, the speaker embeddings are optimized during training such
that it better fits iGMM clustering, based on a novel clustering loss based on
Adjusted Rand Index (ARI). Experimental results based on CALLHOME data show
that the proposed approach outperforms the conventional approach in terms of
diarization error rate (DER), especially by substantially reducing speaker
confusion errors, that indeed reflects the effectiveness of the proposed iGMM
integration.


title: Nonlinear semigroup approach to Hamilton-Jacobi equations -- A toy model

abstract:
  In this paper, we discuss the existence and multiplicity problem of viscosity
solution to the Hamilton-Jacobi equation $$h(x,d_x u)+\lambda(x)u=c,\quad x\in
M,$$ where $M$ is a closed manifold and $\lambda:M\rightarrow\mathbb{R}$
changes signs on $M$, via nonlinear semigroup method. It turns out that a
bifurcation phenomenon occurs when parameter $c$ strides over the critical
value. As an application of the main result, we analyse the structure of the
set of viscosity solutions of an one-dimensional example in detail.


title: Benign Overfitting in Two-layer Convolutional Neural Networks

abstract:
  Modern neural networks often have great expressive power and can be trained
to overfit the training data, while still achieving a good test performance.
This phenomenon is referred to as "benign overfitting". Recently, there emerges
a line of works studying "benign overfitting" from the theoretical perspective.
However, they are limited to linear models or kernel/random feature models, and
there is still a lack of theoretical understanding about when and how benign
overfitting occurs in neural networks. In this paper, we study the benign
overfitting phenomenon in training a two-layer convolutional neural network
(CNN). We show that when the signal-to-noise ratio satisfies a certain
condition, a two-layer CNN trained by gradient descent can achieve arbitrarily
small training and test loss. On the other hand, when this condition does not
hold, overfitting becomes harmful and the obtained CNN can only achieve
constant level test loss. These together demonstrate a sharp phase transition
between benign overfitting and harmful overfitting, driven by the
signal-to-noise ratio. To the best of our knowledge, this is the first work
that precisely characterizes the conditions under which benign overfitting can
occur in training convolutional neural networks.


title: Non-Roelcke precompactness of groups of surface homeomorphisms

abstract:
  We prove that no subgroup of the group of boundary-fixing homeomorphisms of a
compact surface whose action on the interior of the surface is sufficiently
transitive can be Roelcke precompact with the topology inherited from the
compact-open topology.


title:
Photoinduced 120-degree spin order in the Kondo-lattice model on a
  triangular lattice

abstract:
  We theoretically predict the emergence of 120-degree spin order as a
nonequilibrium steady state in the photodriven Kondo-lattice model on a
triangular lattice. In the system away from the half filling with ferromagnetic
ground state, the photoexcitation of conduction electrons and the photoinduced
renormalization of bandwidth cause reconstruction of band structure and
subsequent redistribution of the electrons through relaxations, which result in
an electronic structure similar to that in the half-filled system at
equilibrium, where the 120-degree spin order is stabilized. In this
photoinduced 120-degree spin ordered phase, domains of different spin-ordered
planes are formed, and vortices of spin chirality vectors called $Z_2$ vortices
appear at points where multiple domains meet. We also discuss favorable
conditions and experimental feasibility to observe the predicted photoinduced
magnetic phase transition by investigating dependencies on the light parameters
(amplitude, frequency, and polarization), the electron filling, the strength of
Kondo coupling, and the effects of antiferromagnetic coupling among the
localized spins. Photoinduced magnetic structures proposed so far have been
limited to simple collinear (anti)ferromagnetic orders or local magnetic
defects in magnets. The present work paves a way to optical creation of complex
noncollinear magnetisms as global nonequilibrium steady phase in photodriven
systems.


title:
Polymer Chain with Stochastic Dipolar Active Forces: a Model for Spatial
  Organization of Chromatin

abstract:
  A living cell is an active environment where the organization and dynamics of
chromatin are affected by different forms of activity. Using a bead-spring
polymer chain with stochastic dipolar active forces, we study how the
subdiffusive motion of the loci leads to the large-scale coherent motion of the
chromatin. In the presence of extensile (contractile) activity, the dynamics of
loci grows faster (slower) and the spatial correlation length increases
(decreases) compared to the case with no dipolar forces. Hence, both the
dipolar active forces modify the elasticity of the chain. Interestingly, the
dynamics and organization of such dipolar active chains largely differ from
their thermal counterparts.


title:
Modular Pulse Synthesizer for Transcranial Magnetic Stimulation with
  Flexible User-Defined Pulse Shaping and Rapidly Changing Pulses in Sequences

abstract:
  The temporal shape of a pulse in transcranial magnetic stimulation (TMS)
influences which neuron populations are activated preferentially as well as the
strength and even direction of neuromodulation effects. Furthermore, various
pulse shapes differ in their efficiency, coil heating, sensory perception, and
clicking sound. However, the available TMS pulse shape repertoire is still very
limited to a few pulses with sinusoidal or near-rectangular shapes. Monophasic
pulses, though found to be more selective and stronger in neuromodulation, are
generated inefficiently and therefore only available in simple low-frequency
repetitive protocols. Despite a strong interest to exploit the temporal effects
of TMS pulse shapes and pulse sequences, waveform control is relatively
inflexible and only possible parametrically within certain limits. Previously
proposed approaches for flexible pulse shape control, such as through power
electronic inverters, have significant limitations: Existing semiconductor
switches can fail under the immense electrical stress associated with free
pulse shaping, and most conventional power inverter topologies are incapable of
generating smooth electric fields or existing pulse shapes. Leveraging
intensive preliminary work on modular power electronics, we present a modular
pulse synthesizer (MPS) technology that can, for the first time, flexibly
generate high-power TMS pulses with user-defined electric field shape as well
as rapid sequences of pulses with high output quality. The circuit topology
breaks the problem of simultaneous high power and switching speed into smaller,
manageable portions. MPS TMS can synthesize practically any pulse shape,
including conventional ones, with fine quantization of the induced electric
field.


title:
Spectrum of the quantum integrable $D^{(2)}_2$ spin chain with generic
  boundary fields

abstract:
  Exact solution of the quantum integrable $D^{(2)}_2$ spin chain with generic
integrable boundary fields is constructed. It is found that the transfer matrix
of this model can be factorized as the product of those of two open staggered
anisotropic XXZ spin chains. Based on this identity, the eigenvalues and Bethe
ansatz equations of the $D^{(2)}_2$ model are derived via off-diagonal Bethe
ansatz.

categories: math-ph cond-mat.str-el hep-th math.MP nlin.SI


title:
Joint Design of Hybrid Beamforming and Reflection Coefficients in
  RIS-aided mmWave MIMO Systems

abstract:
  This paper considers a reconfigurable intelligent surface (RIS)-aided
millimeter wave (mmWave) downlink communication system where hybrid
analog-digital beamforming is employed at the base station (BS). We formulate a
power minimization problem by jointly optimizing hybrid beamforming at the BS
and the response matrix at the RIS, under the signal-to-interference-plus-noise
ratio (SINR) constraints at all users. The problem is highly challenging to
solve due to the non-convex SINR constraints as well as the unit-modulus phase
shift constraints for both the RIS reflection coefficients and the analog
beamformer. A two-layer penalty-based algorithm is proposed to decouple
variables in SINR constraints, and manifold optimization is adopted to handle
the non-convex unit-modulus constraints. {We also propose a low-complexity
sequential optimization method, which optimizes the RIS reflection
coefficients, the analog beamformer, and the digital beamformer sequentially
without iteration.} Furthermore, the relationship between the power
minimization problem and the max-min fairness (MMF) problem is discussed.
Simulation results show that the proposed penalty-based algorithm outperforms
the state-of-the-art semidefinite relaxation (SDR)-based algorithm. Results
also demonstrate that the RIS plays an important role in the power reduction.


title: An Introduction to Neural Data Compression

abstract:
  Neural compression is the application of neural networks and other machine
learning methods to data compression. While machine learning deals with many
concepts closely related to compression, entering the field of neural
compression can be difficult due to its reliance on information theory,
perceptual metrics, and other knowledge specific to the field. This
introduction hopes to fill in the necessary background by reviewing basic
coding topics such as entropy coding and rate-distortion theory, related
machine learning ideas such as bits-back coding and perceptual metrics, and
providing a guide through the representative works in the literature so far.


title: Super-replication prices with multiple-priors in discrete time

abstract:
  In the frictionless discrete time financial market of Bouchard and Nutz
(2015), we propose a full characterization of the quasi-sure super-replication
price: as the supremum of the mono-prior super-replication prices, through an
extreme prior and through martingale measures.


title:
Coefficient Decomposition of Spatial Regressive Models Based on
  Standardized Variables

abstract:
  Spatial autocorrelation analysis is the basis for spatial autoregressive
modeling. However, the relationships between spatial correlation coefficients
and spatial regression models are not yet well clarified. The paper is devoted
to explore the deep structure of spatial regression coefficients. By means of
mathematical reasoning, a pair of formulae of canonical spatial regression
coefficients are derived from a general spatial regression model based on
standardized variables. The spatial auto- and lag-regression coefficients are
reduced to a series of statistic parameters and measurements, including
conventional regressive coefficient, Pearson correlation coefficient, Moran's
indexes, spatial cross-correlation coefficients, and the variance of prediction
residuals. The formulae show determinate inherent relationships between spatial
correlation coefficients and spatial regression coefficients. New finding is as
below: the spatial autoregressive coefficient mainly depends on the Moran's
index of the independent variable, while the spatial lag-regressive coefficient
chiefly depends on the cross-correlation coefficient of independent variable
and dependent variable. The observational data of an urban system in Beijing,
Tianjin, and Hebei region of China were employed to verify the newly derived
formulae, and the results are satisfying. The new formulae and their variates
are helpful for understand spatial regression models from the perspective of
spatial correlation and can be used to assist spatial regression modeling.


title: The conformal cosmological potential

abstract:
  We discuss qualitative features of the conformal relation between certain
classes of gravity theories and general relativity, common to different themes
such as $f(R)$, Brans-Dicke-type, and string theories. We focus primarily on
the frame relations of the fields involved, slice energy, traceless and
Palatini extensions, and selected cosmological applications.


title:
Counter-intuitive Ferroelectric Property And Non-negligible Orbital
  Magnetic Moment In Cr/Cu Based Perovskite Metal-Organic Frameworks

abstract:
  Metal-organic frameworks (MOFs) possess a hybrid nature, combining the
inorganic properties from the metal ions and the organic properties from the
molecular linkers. Stroppa, \textit{et al.}, showed that the perovskite-type
MOF [C(NH$_2$)$_3$]M[(HCOO)$_3$] (M = Cr, Cu) exhibits the magneto-electric
coupled multiferroicity [Angew. Chem. Int. Ed. 50, 5847 (2011) and Adv. Mater.
25, 2284 (2013)]. Moreover, their ferroelectricity arises from the hybrid
improper mechanism, which also explains the magneto-electric coupling. In this
work, we further examine the electric and magnetic properties of
[C(NH$_2$)$_3$]M[(HCOO)$_3$]. We find that the hybrid mode composed of
non-polar modes induces purely electronic polarization even without the polar
mode. The polar mode compensates for the purely electronic polarization. It
leads to a counter-intuitive argument that the inversion of the polar mode
rather enhances the polarization. We provide microscopic origin and macroscopic
analysis for this polarization property. In addition, we find that the orbital
magnetic moment is comparable to the spin contribution in the Cu-based MOF.
Finally, we establish the model for the orbital magnetic moment based on the
perturbation theory.


title:
QA4QG: Using Question Answering to Constrain Multi-Hop Question
  Generation

abstract:
  Multi-hop question generation (MQG) aims to generate complex questions which
require reasoning over multiple pieces of information of the input passage.
Most existing work on MQG has focused on exploring graph-based networks to
equip the traditional Sequence-to-sequence framework with reasoning ability.
However, these models do not take full advantage of the constraint between
questions and answers. Furthermore, studies on multi-hop question answering
(QA) suggest that Transformers can replace the graph structure for multi-hop
reasoning. Therefore, in this work, we propose a novel framework, QA4QG, a
QA-augmented BART-based framework for MQG. It augments the standard BART model
with an additional multi-hop QA module to further constrain the generated
question. Our results on the HotpotQA dataset show that QA4QG outperforms all
state-of-the-art models, with an increase of 8 BLEU-4 and 8 ROUGE points
compared to the best results previously reported. Our work suggests the
advantage of introducing pre-trained language models and QA module for the MQG
task.


title: Deduplicating Training Data Mitigates Privacy Risks in Language Models

abstract:
  Past work has shown that large language models are susceptible to privacy
attacks, where adversaries generate sequences from a trained model and detect
which sequences are memorized from the training set. In this work, we show that
the success of these attacks is largely due to duplication in commonly used
web-scraped training sets. We first show that the rate at which language models
regenerate training sequences is superlinearly related to a sequence's count in
the training set. For instance, a sequence that is present 10 times in the
training data is on average generated ~1000 times more often than a sequence
that is present only once. We next show that existing methods for detecting
memorized sequences have near-chance accuracy on non-duplicated training
sequences. Finally, we find that after applying methods to deduplicate training
data, language models are considerably more secure against these types of
privacy attacks. Taken together, our results motivate an increased focus on
deduplication in privacy-sensitive applications and a reevaluation of the
practicality of existing privacy attacks.


title:
GeMSE: a Low-Background Facility for Gamma-Spectrometry at Moderate Rock
  Overburden

abstract:
  The GeMSE (Germanium Material and meteorite Screening Experiment) facility
operates a low-background HPGe crystal in an underground laboratory with a
moderate rock overburden of 620$\,$m.w.e. in Switzerland. It has been optimized
for continuous remote operation. A multi-layer passive shielding, a muon veto,
and a boil-off nitrogen purge line inside the measurement cavity minimize the
instrument's background rate, which decreased by 33% to
(164$\pm$2)$\,$counts/day (100-2700$\,$keV) after five years of underground
operation. This agrees with the prediction based on the expected decay of
short-lived isotopes. A fit to the known background components, modeled via a
precise simulation of the detector, shows that the GeMSE background is now
muon-dominated. We also present updates towards a more accurate detection
efficiency calculation for the screened samples: the thickness of the crystal's
outer dead-layer is precisely determined and the efficiency can now be easily
calculated for any sample geometry. The advantage of this feature is showcased
via the determination of the $^{40}$K content in the screening of a
complex-shaped object: a banana.


title: Pathway: a protocol for algorithmic pricing of a DAO governance token

abstract:
  In this paper, we will consider a governance token pricing algorithm that
conducts liquidity operations on AMM (CPMM) DEXs (automated market maker
decentralized exchanges) with liquidity that belongs to a decentralized
autonomous organization (DAO), also called protocol-owned liquidity (POL). The
primary aim of the protocol is maintaining a price peg by determining
algorithmically when and how to carry out interventions that consist of two
steps: extracting liquidity from an AMM liquidity pool and conducting "token
swap" operations. We will cover setting up an optimal peg function as a
weighted sum of certain normalized factors, which are to be determined
collectively by the DAO. In particular, we will review various arithmetic
invariants of liquidity intervention, which brings the price to a peg while
leaving total liquidity intact, and show how such interventions can be
substituted in practice by so-called PMM (proactive market maker) protocols.


title: Tensionless Strings and Killing(-Yano) Tensors

abstract:
  We construct invariants for bosonic and spinning tensionless (null) strings
in backgrounds that carry Killing tensors or Killing-Yano tensors of mixed
type. This is facilitated by the close relation of these strings to point
particles. We apply the construction to the Minkowski and to the Kerr-Newman
backgrounds.


title:
Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional
  Lattices

abstract:
  We study the dynamical properties of hard-core anyons in one-dimensional
lattices. We present a general method to calculate exactly the dynamical
correlations such as the Green's function, its spectral function and the
out-of-time-ordered correlators (OTOCs), valid for any type of confining
potential and any temperature. We find that the anyonic spectral function
displays three main singularity lines whose dispersion relations can be given
analytically. The three lines cross at a \emph{hot point} near which the
spectral weight is largest in the whole $(q,\omega)$ plane. We also find that
the anyonic statistics can induces spatial asymmetry in the Green's function
and its spectrum. Moreover, the information spreading characterized by the
OTOCs shows light-cone dynamics, asymmetric for general statistics and low
temperatures, but symmetric at infinite temperature. Our results pave the way
toward studying the non-equilibrium dynamics of hard-core anyons and allow
direct comparison with state-of-the-art experiments.


title:
Exact SOHS decompositions of trigonometric univariate polynomials with
  Gaussian coefficients

abstract:
  Certifying the positivity of trigonometric polynomials is of first importance
for design problems in discrete-time signal processing. It is well known from
the Riesz-Fej\'ez spectral factorization theorem that any trigonometric
univariate polynomial positive on the unit circle can be decomposed as a
Hermitian square with complex coefficients. Here we focus on the case of
polynomials with Gaussian integer coefficients, i.e., with real and imaginary
parts being integers. We design, analyze and compare, theoretically and
practically,three hybrid numeric-symbolic algorithms computing weighted sums of
Hermitian squares decompositions for trigonometric univariate polynomials
positive on the unit circle with Gaussian coefficients. The numerical steps the
first and second algorithm rely on are complex root isolation and semidefinite
programming, respectively. An exact sum of Hermitian squares decomposition is
obtained thanks to compensation techniques. The third algorithm, also based on
complex semidefinite programming, is an adaptation of the rounding and
projection algorithm by Peyrl and Parrilo. For all three algorithms, we prove
bit complexity and output size estimates that are polynomial in the degree of
the input and linear in the maximum bitsize of its coefficients. We compare
their performance on randomly chosen benchmarks, and further design a certified
finite impulse filter.


title:
Provably Efficient Causal Model-Based Reinforcement Learning for
  Systematic Generalization

abstract:
  In the sequential decision making setting, an agent aims to achieve
systematic generalization over a large, possibly infinite, set of environments.
Such environments are modeled as discrete Markov decision processes with both
states and actions represented through a feature vector. The underlying
structure of the environments allows the transition dynamics to be factored
into two components: one that is environment-specific and another one that is
shared. Consider a set of environments that share the laws of motion as an
illustrative example. In this setting, the agent can take a finite amount of
reward-free interactions from a subset of these environments. The agent then
must be able to approximately solve any planning task defined over any
environment in the original set, relying on the above interactions only. Can we
design a provably efficient algorithm that achieves this ambitious goal of
systematic generalization? In this paper, we give a partially positive answer
to this question. First, we provide the first tractable formulation of
systematic generalization by employing a causal viewpoint. Then, under specific
structural assumptions, we provide a simple learning algorithm that allows us
to guarantee any desired planning error up to an unavoidable sub-optimality
term, while showcasing a polynomial sample complexity.


title: Coalgebraic Semantics for Nominal Automata

abstract:
  This paper provides a coalgebraic approach to the language semantics of two
types of non-deterministic automata over nominal sets: non-deterministic
orbit-finite automata (NOFAs) and regular nominal non-deterministic automata
(RNNAs), which were introduced in previous work. While NOFAs are a
straightforward nominal version of non-deterministic automata, RNNAs feature
ordinary as well as name binding transitions. Correspondingly, words accepted
by RNNAs are strings formed by ordinary letters and name binding letters. Bar
languages are sets of such words modulo $\alpha$-equivalence, and to every
state of an RNNA one associates its accepted bar language. We show that the
semantics of NOFAs and RNNAs, respectively, arise both as an instance of the
Kleisli-style coalgebraic trace semantics as well as an instance of the
coalgebraic language semantics obtained via generalized determinization. On the
way we revisit coalgebraic trace semantics in general and give a new compact
proof for the main result in that theory stating that an initial algebra for a
functor yields the terminal coalgebra for the Kleisli extension of the functor.
Our proof requires fewer assumptions on the functor than all previous ones.


title: Video2IMU: Realistic IMU features and signals from videos

abstract:
  Human Activity Recognition (HAR) from wearable sensor data identifies
movements or activities in unconstrained environments. HAR is a challenging
problem as it presents great variability across subjects. Obtaining large
amounts of labelled data is not straightforward, since wearable sensor signals
are not easy to label upon simple human inspection. In our work, we propose the
use of neural networks for the generation of realistic signals and features
using human activity monocular videos. We show how these generated features and
signals can be utilized, instead of their real counterparts, to train HAR
models that can recognize activities using signals obtained with wearable
sensors. To prove the validity of our methods, we perform experiments on an
activity recognition dataset created for the improvement of industrial work
safety. We show that our model is able to realistically generate virtual sensor
signals and features usable to train a HAR classifier with comparable
performance as the one trained using real sensor data. Our results enable the
use of available, labelled video data for training HAR models to classify
signals from wearable sensors.


title:
A resource-efficient deep learning framework for low-dose brain PET
  image reconstruction and analysis

abstract:
  18F-fluorodeoxyglucose (18F-FDG) Positron Emission Tomography (PET) imaging
usually needs a full-dose radioactive tracer to obtain satisfactory diagnostic
results, which raises concerns about the potential health risks of radiation
exposure, especially for pediatric patients. Reconstructing the low-dose PET
(L-PET) images to the high-quality full-dose PET (F-PET) ones is an effective
way that both reduces the radiation exposure and remains diagnostic accuracy.
In this paper, we propose a resource-efficient deep learning framework for
L-PET reconstruction and analysis, referred to as transGAN-SDAM, to generate
F-PET from corresponding L-PET, and quantify the standard uptake value ratios
(SUVRs) of these generated F-PET at whole brain. The transGAN-SDAM consists of
two modules: a transformer-encoded Generative Adversarial Network (transGAN)
and a Spatial Deformable Aggregation Module (SDAM). The transGAN generates
higher quality F-PET images, and then the SDAM integrates the spatial
information of a sequence of generated F-PET slices to synthesize whole-brain
F-PET images. Experimental results demonstrate the superiority and rationality
of our approach.


title:
High-flux neutron generation by laser-accelerated ions from single- and
  double-layer targets

abstract:
  Contemporary ultraintense, short-pulse laser systems provide extremely
compact setups for the production of high-flux neutron beams, such as required
for nondestructive probing of dense matter, research on neutron-induced damage
in fusion devices or laboratory astrophysics studies. Here, by coupling
particle-in-cell and Monte Carlo numerical simulations, we examine possible
strategies to optimize neutron sources from ion-induced nuclear reactions using
1-PW, 20-fs-class laser systems. To improve the ion acceleration, the
laser-irradiated targets are chosen to be ultrathin solid foils, either
standing alone or preceded by a near-critical-density plasma to enhance the
laser focusing. We compare the performance of these single- and double-layer
targets, and determine their optimum parameters in terms of energy and angular
spectra of the accelerated ions. These are then sent into a converter to
generate neutrons, either traditionally through (p,n) reactions on beryllium
nuclei or through spallation in lead. Overall, we identify configurations that
result in a neutron yield as high as $\sim 10^9\,\rm n\,sr^{-1}$ and an
instantaneous neutron flux above $10^{23}\,\rm n\,cm^{-2}\,s^{-1}$. Considering
a realistic repetition rate of one laser shot per minute, the corresponding
time-averaged neutron yield is predicted to reach values $7\times 10^{6}\,\rm n
\,~sr^{-1}\,s^{-1}$ well above the current experimental record, and this even
with a mere thin foil as a primary target. A further increase in the
time-averaged yield up to above $5\times 10^7\,\rm sr^{-1}\,s^{-1}$ is foreseen
using double-layer targets with a deuterated solid substrate.


title:
Effect of combined pitching and heaving on propulsion of tandem flapping
  foils

abstract:
  Flow dynamics across flapping foils in tandem arrangement at Reynolds number
of Re = 1100 has been numerically investigated in the present study. The
kinematic motion of the foils consists of sinusoidal heaving and pitching
motion. The effects of the heave amplitude, pitch amplitude and the flapping
frequency on the propulsive performance have been comprehensively studied for a
single as well as tandem system of foils at two gaps of 4 and 7 times the
downstream foil's chord length. It is found that the effective angle of attack,
effective projected area, type of vortex interaction and the timing of the
interaction during the downstroke of the flapping motion influence the
propulsive performance. Increasing the heave amplitude of the upstream foil
leads to an increase in the average thrust generated by the downstream foil for
the gap of 7, while the opposite effect is observed for gap of 4. The
propulsion of the downstream foil increases monotonically with the heave
amplitude of the downstream foil. Upstream foil's pitch amplitude is noticed to
have a minor effect on the performance of the downstream foil, while an
increase in the pitch amplitude of the downstream foil increases the thrust for
larger gap between the foils. The study of the propulsive performance in the
frequency-pitch amplitude parametric space for the tandem foils has been
performed for the first time, where a more complex behavior is observed. The
trends in the thrust coefficient and the propulsive efficiency are corroborated
by the study of various vortex interaction mechanisms leading to favorable or
unfavorable thrust generating conditions. Finally, the three-dimensional
flapping dynamics of the tandem configuration is demonstrated, where no
spanwise wake structures are noted, indicating the wake interaction to be
inherently two-dimensional.


title: Topological Quadrupole Phase in Two-dimensional C2N

abstract:
  Quadrupole phase, as a novel high-order topological phase, exhibits
nontrivial gapless states at the boundaries whose dimension is lower than bulk
by two. However, this phase has not been observed experimentally in
two-dimensional (2D) materials up to now. In this work, using first-principles
calculations and tight-binding (TB) model, we propose that the experimentally
synthesized C2N is a 2D quadrupole topological insulator with one-dimensional
gapped edge states and zero-dimensional gapless corner states. C2N is found to
have a large bulk gap of 2.45 eV and an edge gap of 0.32 eV, making it an
excellent candidate to evidently present the nontrivial corner states in
experiments. The robustness of the corner states against the edge disorders has
been explicitly identified. Moreover, another three C2N-like materials are also
found to host the nontrivial quadrupole phase including an experimentally
synthesized material aza-fused microporous polymers (CMP). The four 2D
quadrupole topological phases proposed in our present work provide excellent
candidates for studying the novel high-order topological properties in future
experiments.


title: An excursion to multiplications and convolutions on modulation spaces

abstract:
  We give a self-contained introduction to (quasi-)Banach modulation spaces of
ultradistributions, and review results on boundedness for multiplications and
convolutions for elements in such spaces. Furthermore, we use these results to
study the Gabor product. As an example, we show how it appears in a phase-space
formulation of the nonlinear cubic Schr\"odinger equation.


title: Composition operators on Harmonic Bloch-type spaces

abstract:
  In this paper we consider composition operators on Harmonic-Bloch type spaces
and we compute the spectrum of composition operators. Also, we characterize
isometric composition operators on harmonic Bloch type spaces.


title:
Analog Physical-Layer Relay Attacks with Application to Bluetooth and
  Phase-Based Ranging

abstract:
  Today, we use smartphones as multi-purpose devices that communicate with
their environment to implement context-aware services, including asset
tracking, indoor localization, contact tracing, or access control. As a
de-facto standard, Bluetooth is available in virtually every smartphone to
provide short-range wireless communication. Importantly, many Bluetooth-driven
applications such as Phone as a Key (PaaK) for vehicles and buildings require
proximity of legitimate devices, which must be protected against unauthorized
access. In earlier access control systems, attackers were able to violate
proximity-verification through relay station attacks. However, the
vulnerability of Bluetooth against such attacks was yet unclear as existing
relay attack strategies are not applicable or can be defeated through wireless
distance measurement. In this paper, we design and implement an analog
physical-layer relay attack based on low-cost off-the-shelf radio hardware to
simultaneously increase the wireless communication range and manipulate
distance measurements. Using our setup, we successfully demonstrate relay
attacks against Bluetooth-based access control of a car and a smart lock.
Further, we show that our attack can arbitrarily manipulate Multi-Carrier
Phase-based Ranging (MCPR) while relaying signals over 90 m.


title: High-Dimensional Dynamic Stochastic Model Representation

abstract:
  We propose a scalable method for computing global solutions of nonlinear,
high-dimensional dynamic stochastic economic models. First, within a time
iteration framework, we approximate economic policy functions using an
adaptive, high-dimensional model representation scheme, combined with adaptive
sparse grids to address the ubiquitous challenge of the curse of
dimensionality. Moreover, the adaptivity within the individual component
functions increases sparsity since grid points are added only where they are
most needed, that is, in regions with steep gradients or at
nondifferentiabilities. Second, we introduce a performant vectorization scheme
for the interpolation compute kernel. Third, the algorithm is hybrid
parallelized, leveraging both distributed- and shared-memory architectures. We
observe significant speedups over the state-of-the-art techniques, and almost
ideal strong scaling up to at least $1,000$ compute nodes of a Cray XC$50$
system at the Swiss National Supercomputing Center. Finally, to demonstrate our
method's broad applicability, we compute global solutions to two variates of a
high-dimensional international real business cycle model up to $300$ continuous
state variables. In addition, we highlight a complementary advantage of the
framework, which allows for a priori analysis of the model complexity.


title:
In-beam PET and Compton imaging for enhanced accuracy proton-range
  verification

abstract:
  We report on a combined in-beam PET and prompt-gamma Compton imaging system
aimed at ion-range verification in proton-therapy treatments. A
proof-of-concept experiment was carried out at the radiobiology beam line of
the CNA cyclotron facility using a set of two synchronous Compton imagers and
different target materials. The time structure of the 18 MeV proton beam was
shaped with a series of beam-on and beam-off intervals, thereby mimicking a
pulsed proton beam on a long time scale. During beam-on Compton imaging was
performed utilizing the high energy $\gamma$-rays promptly emitted from the
nuclear reactions in the target. In the course of the beam-off intervals
in-situ positron-emission tomography was accomplished with the same imagers
using the $\beta^{+}$ decay of short-lived activated nuclei. The targets used
were stacks of different materials covering also various proton ranges and
energies. The experimental results obtained in this work are compared with a
Monte Carlo model of the experimental setup. The results demonstrate the
possibility to combine both imaging techniques in a concomitant way, where
high-efficiency Compton imaging is complemented with the high spatial accuracy
of PET. Empowered by these results we discuss a new methodology for enhanced
accuracy and real-time ion-range monitoring. We suggest that a pulsed beam with
a suitable duty cycle, in conjunction with in-situ Compton- and PET-imaging may
help to attain both real-time and high-accuracy range monitoring.


title:
Reinforcement Learning in Presence of Discrete Markovian Context
  Evolution

abstract:
  We consider a context-dependent Reinforcement Learning (RL) setting, which is
characterized by: a) an unknown finite number of not directly observable
contexts; b) abrupt (discontinuous) context changes occurring during an
episode; and c) Markovian context evolution. We argue that this challenging
case is often met in applications and we tackle it using a Bayesian approach
and variational inference. We adapt a sticky Hierarchical Dirichlet Process
(HDP) prior for model learning, which is arguably best-suited for Markov
process modeling. We then derive a context distillation procedure, which
identifies and removes spurious contexts in an unsupervised fashion. We argue
that the combination of these two components allows to infer the number of
contexts from data thus dealing with the context cardinality assumption. We
then find the representation of the optimal policy enabling efficient policy
learning using off-the-shelf RL algorithms. Finally, we demonstrate empirically
(using gym environments cart-pole swing-up, drone, intersection) that our
approach succeeds where state-of-the-art methods of other frameworks fail and
elaborate on the reasons for such failures.


title:
SAUTE RL: Almost Surely Safe Reinforcement Learning Using State
  Augmentation

abstract:
  Satisfying safety constraints almost surely (or with probability one) can be
critical for deployment of Reinforcement Learning (RL) in real-life
applications. For example, plane landing and take-off should ideally occur with
probability one. We address the problem by introducing Safety Augmented (Saute)
Markov Decision Processes (MDPs), where the safety constraints are eliminated
by augmenting them into the state-space and reshaping the objective. We show
that Saute MDP satisfies the Bellman equation and moves us closer to solving
Safe RL with constraints satisfied almost surely. We argue that Saute MDP
allows to view Safe RL problem from a different perspective enabling new
features. For instance, our approach has a plug-and-play nature, i.e., any RL
algorithm can be "sauteed". Additionally, state augmentation allows for policy
generalization across safety constraints. We finally show that Saute RL
algorithms can outperform their state-of-the-art counterparts when constraint
satisfaction is of high importance.


title: Modelling Underwater Acoustic Propagation using One-way Wave Equations

abstract:
  The primary contribution of this paper is to characterize the propagation of
acoustic signal carrying information through any medium and the interaction of
the travelling acoustic signal with the surrounding medium. We will use the
concept of damped harmonic oscillator to model the medium and Milne's
oscillator technique to map the interaction of the acoustic signal with the
medium. The acoustic signal itself will be modelled using the one-way wave
equation formulated in terms of acoustic pressure and velocity of acoustic
waves through the medium. Using the above-mentioned concepts, we calculated the
effective signal strength, phase shift and time period of the communicated
signal. Numerical results are generated to present the evolution of signal
strength and received signal envelope in underwater environment.


title:
General relativistic Lagrangian continuum theories -- Part I: reduced
  variational principles and junction conditions for hydrodynamics and
  elasticity

abstract:
  We establish a Lagrangian variational framework for general relativistic
continuum theories that permits the development of the process of Lagrangian
reduction by symmetry in the relativistic context. Starting with a continuum
version of the Hamilton principle for the relativistic particle, we deduce two
classes of reduced variational principles that are associated to either
spacetime covariance, which is an axiom of the continuum theory, or material
covariance, which is related to particular properties of the system such as
isotropy. The covariance hypotheses and the Lagrangian reduction process are
efficiently formulated by making explicit the dependence of the theory on given
material and spacetime tensor fields that are transported by the world-tube of
the continuum via the push-forward and pull-back operations. It is shown that
the variational formulation, when augmented with the Gibbons-Hawking-York (GHY)
boundary terms, also yields the Israel-Darmois junction conditions between the
solution at the interior of the relativistic continua and the solution
describing the gravity field produced outside from it. The expression of the
first variation of the GHY term with respect to the hypersurface involves some
extensions of previous results that we also derive in the paper. We consider in
details the application of the variational framework to relativistic fluids and
relativistic elasticity. For the latter case, our setting also allows to
clarify the relation between formulations of relativistic elasticity based on
the relativistic right Cauchy-Green tensor or on the relativistic Cauchy
deformation tensor. The setting developed here will be further exploited for
modelling purpose in subsequent parts of the paper.


title:
Decreasing Minimization on Base-Polyhedra: Relation Between Discrete and
  Continuous Cases

abstract:
  This paper is concerned with the relationship between the discrete and the
continuous decreasing minimization problem on base-polyhedra. The continuous
version (under the name of lexicographically optimal base of a polymatroid) was
solved by Fujishige in 1980, with subsequent elaborations described in his book
(1991). The discrete counterpart of the dec-min problem (concerning M-convex
sets) was settled only recently by the present authors, with a strongly
polynomial algorithm to compute not only a single decreasing minimal element
but also the matroidal structure of all decreasing minimal elements and the
dual object called the canonical partition. The objective of this paper is to
offer a complete picture on the relationship between the continuous and
discrete dec-min problems on base-polyhedra by establishing novel technical
results and integrating known results. In particular, we derive proximity
results, asserting the geometric closeness of the decreasingly minimal elements
in the continuous and discrete cases, by revealing the relation between the
principal partition and the canonical partition. We also describe
decomposition-type algorithms for the discrete case following the approach of
Fujishige and Groenevelt.


title: Gamekins: Gamifying Software Testing in Jenkins

abstract:
  Developers have to write thorough tests for their software in order to find
bugs and to prevent regressions. Writing tests, however, is not every
developer's favourite occupation, and if a lack of motivation leads to a lack
of tests, then this may have dire consequences, such as programs with poor
quality or even project failures. This paper introduces Gamekins, a tool that
uses gamification to motivate developers to write more and better tests.
Gamekins is integrated into the Jenkins continuous integration platform where
game elements are based on commits to the source code repository: Developers
can earn points for completing test challenges and quests posed by Gamekins,
compete with other developers or developer teams on a leaderboard, and are
rewarded for their test-related achievements.


title: Saving RNN Computations with a Neuron-Level Fuzzy Memoization Scheme

abstract:
  Recurrent Neural Networks (RNNs) are a key technology for applications such
as automatic speech recognition or machine translation. Unlike conventional
feed-forward DNNs, RNNs remember past information to improve the accuracy of
future predictions and, therefore, they are very effective for sequence
processing problems. For each application run, recurrent layers are executed
many times for processing a potentially large sequence of inputs (words,
images, audio frames, etc.). In this paper, we observe that the output of a
neuron exhibits small changes in consecutive invocations.~We exploit this
property to build a neuron-level fuzzy memoization scheme, which dynamically
caches each neuron's output and reuses it whenever it is predicted that the
current output will be similar to a previously computed result, avoiding in
this way the output computations.
  The main challenge in this scheme is determining whether the new neuron's
output for the current input in the sequence will be similar to a recently
computed result. To this end, we extend the recurrent layer with a much simpler
Bitwise Neural Network (BNN), and show that the BNN and RNN outputs are highly
correlated: if two BNN outputs are very similar, the corresponding outputs in
the original RNN layer are likely to exhibit negligible changes. The BNN
provides a low-cost and effective mechanism for deciding when fuzzy memoization
can be applied with a small impact on accuracy. We evaluate our memoization
scheme on top of a state-of-the-art accelerator for RNNs, for a variety of
different neural networks from multiple application domains. We show that our
technique avoids more than 26.7\% of computations, resulting in 21\% energy
savings and 1.4x speedup on average.


title:
RIS-assisted Millimeter-Wave MIMO Communication Systems: Ergodic
  Capacity Analysis and Optimization

abstract:
  Reconfigurable intelligent surfaces (RISs) have emerged as a prospective
technology for next-generation wireless networks due to their potential in
coverage and capacity enhancement. The analysis and optimization of ergodic
capacity for RIS-assisted communication systems have been investigated
extensively. However, the Rayleigh or Rician channel model is usually utilized
in the existing work, which is not suitable for millimeter-wave (mmWave)
multiple-input multiple-output (MIMO) systems. Thus, we fill the gap and
consider the ergodic capacity of RIS-assisted mmWave MIMO communication systems
under the Saleh-Valenzuela channel model. Firstly, we derive tight
approximations of ergodic capacity and a tight upper bound in high
signal-to-noise ratio regime. Then, we aim to maximize the ergodic capacity by
jointly designing the transmit covariance matrix at the base station and the
reflection coefficients at the RIS. Specifically, the transmit covariance
matrix is optimized by the water-filling algorithm and the reflection
coefficients are optimized using the Riemanian conjugate gradient algorithm.
Simulation results validate the tightness of the derived ergodic capacity
approximations and the effectiveness of the proposed algorithms.


title:
Single-stage Rotate Object Detector via Two Points with Solar Corona
  Heatmap

abstract:
  Oriented object detection is a crucial task in computer vision. Current
top-down oriented detection methods usually directly detect entire objects, and
not only neglecting the authentic direction of targets, but also do not fully
utilise the key semantic information, which causes a decrease in detection
accuracy. In this study, we developed a single-stage rotating object detector
via two points with a solar corona heatmap (ROTP) to detect oriented objects.
The ROTP predicts parts of the object and then aggregates them to form a whole
image. Herein, we meticulously represent an object in a random direction using
the vertex, centre point with width, and height. Specifically, we regress two
heatmaps that characterise the relative location of each object, which enhances
the accuracy of locating objects and avoids deviations caused by angle
predictions. To rectify the central misjudgement of the Gaussian heatmap on
high-aspect ratio targets, we designed a solar corona heatmap generation method
to improve the perception difference between the central and non-central
samples. Additionally, we predicted the vertex relative to the direction of the
centre point to connect two key points that belong to the same goal.
Experiments on the HRSC 2016, UCASAOD, and DOTA datasets show that our ROTP
achieves the most advanced performance with a simpler modelling and less manual
intervention.


title:
On $p$-adic $L$-functions for
  $\operatorname{GL}(2)\times\operatorname{GL}(3)$ via pullbacks of
  Saito--Kurokawa lifts

abstract:
  We build a one-variable $p$-adic $L$-function attached to two Hida families
of ordinary $p$-stabilised newforms $\mathbf{f}$, $\mathbf{g}$, interpolating
the algebraic part of the central values of the complex $L$-series $L(f \otimes
\textrm{Ad}(g), s)$ when $f$ and $g$ range over the classical specialisations
of $\mathbf{f}$, $\mathbf{g}$ on a suitable line of the weight space. The
construction rests on two major results: an explicit formula for the relevant
complex central $L$-values, and the existence of non-trivial $\Lambda$-adic
Shintani liftings and Saito--Kurokawa liftings studied in a previous work by
the authors. We also illustrate that, under an appropriate sign assumption,
this $p$-adic $L$-function arises as a factor of a triple product $p$-adic
$L$-function attached to $\mathbf{f}$, $\mathbf{g}$, and $\mathbf{g}$.


title:
Observed dependence of characteristics of liquid-pool fires on swirl
  magnitude

abstract:
  One dozen vertically oriented thin rectangular vanes, 62 cm tall and 15.2 cm
wide, were placed 27 cm from the center of heptane and ethanol pool fires in
continuously fed, floor-flush pans 3.2 cm and 5.1 cm in diameter in the
laboratory. The vanes were all oriented at the same fixed angles from the
radial direction, for 9 different angles, ranging from 0 to 85 degrees, thereby
imparting 9 different levels of circulation to the air entrained by each pool
fire. The different swirl levels were observed to engender dramatically
different pool-fire structures. Moderate swirl suppresses the global puffing
instability, replacing it by a global helical instability that generates a tall
fire whirl, the height of which increases with increasing circulation. Except
for the largest heptane pool, higher swirl levels produced vortex breakdown,
resulting in the emergence of a bubble-like recirculation region with a ring
vortex encircling the axis. Measured burning rates increase with increasing
swirl levels as a consequence of the associated increasing inflow velocities
reducing the thickness of the boundary layer within which combustion occurs
right above the liquid surface, eventually forming detached edge flames in the
boundary layer that move closer to the axis as the circulation is increased.
Still higher circulation reduces the burning rate by decreasing the surface
area of the liquid covered by the flame, thereby reducing the height of the
fire whirl. Even higher circulation causes edge-flame detachment, resulting in
formation of the blue whirl identified in recent literature, often meandering
over the surface of the liquid in the present experiments. This sequence of
events is documented herein.


title:
Online-updated High-order Collaborative Networks for Single Image
  Deraining

abstract:
  Single image deraining is an important and challenging task for some
downstream artificial intelligence applications such as video surveillance and
self-driving systems. Most of the existing deep-learning-based methods
constrain the network to generate derained images but few of them explore
features from intermediate layers, different levels, and different modules
which are beneficial for rain streaks removal. In this paper, we propose a
high-order collaborative network with multi-scale compact constraints and a
bidirectional scale-content similarity mining module to exploit features from
deep networks externally and internally for rain streaks removal. Externally,
we design a deraining framework with three sub-networks trained in a
collaborative manner, where the bottom network transmits intermediate features
to the middle network which also receives shallower rainy features from the top
network and sends back features to the bottom network. Internally, we enforce
multi-scale compact constraints on the intermediate layers of deep networks to
learn useful features via a Laplacian pyramid. Further, we develop a
bidirectional scale-content similarity mining module to explore features at
different scales in a down-to-up and up-to-down manner. To improve the model
performance on real-world images, we propose an online-update learning
approach, which uses real-world rainy images to fine-tune the network and
update the deraining results in a self-supervised manner. Extensive experiments
demonstrate that our proposed method performs favorably against eleven
state-of-the-art methods on five public synthetic datasets and one real-world
dataset. The source code will be available at
\url{https://supercong94.wixsite.com/supercong94}.


title: UniParser: A Unified Log Parser for Heterogeneous Log Data

abstract:
  Logs provide first-hand information for engineers to diagnose failures in
large-scale online service systems. Log parsing, which transforms
semi-structured raw log messages into structured data, is a prerequisite of
automated log analysis such as log-based anomaly detection and diagnosis.
Almost all existing log parsers follow the general idea of extracting the
common part as templates and the dynamic part as parameters. However, these log
parsing methods, often neglect the semantic meaning of log messages.
Furthermore, high diversity among various log sources also poses an obstacle in
the generalization of log parsing across different systems. In this paper, we
propose UniParser to capture the common logging behaviours from heterogeneous
log data. UniParser utilizes a Token Encoder module and a Context Encoder
module to learn the patterns from the log token and its neighbouring context. A
Context Similarity module is specially designed to model the commonalities of
learned patterns. We have performed extensive experiments on 16 public log
datasets and our results show that UniParser outperperforms state-of-the-art
log parsers by a large margin.


title:
Anytime Capacity Expansion in Medical Residency Match by Monte Carlo
  Tree Search

abstract:
  This paper considers the capacity expansion problem in two-sided matchings,
where the policymaker is allowed to allocate some extra seats as well as the
standard seats. In medical residency match, each hospital accepts a limited
number of doctors. Such capacity constraints are typically given in advance.
However, such exogenous constraints can compromise the welfare of the doctors;
some popular hospitals inevitably dismiss some of their favorite doctors.
Meanwhile, it is often the case that the hospitals are also benefited to accept
a few extra doctors. To tackle the problem, we propose an anytime method that
the upper confidence tree searches the space of capacity expansions, each of
which has a resident-optimal stable assignment that the deferred acceptance
method finds. Constructing a good search tree representation significantly
boosts the performance of the proposed method. Our simulation shows that the
proposed method identifies an almost optimal capacity expansion with a
significantly smaller computational budget than exact methods based on
mixed-integer programming.


title:
Non-Boussinesq stability analysis of natural-convection gaseous flow on
  inclined hot plates

abstract:
  The buoyancy-driven boundary-layer flow that develops over a semi-infinite
inclined hot plate is known to become unstable at a finite distance from the
leading edge, characterized by a critical value of the Grashof number Gr based
on the local boundary-layer thickness. The nature of the resulting instability
depends on the inclination angle $\phi$, measured from the vertical direction.
For values of $\phi$ below a critical value $\phi_c$ the instability is
characterized by the appearance of spanwise traveling waves, whereas for
$\phi>\phi_c$ the bifurcated flow displays G\"ortler-like streamwise vortices.
The Boussinesq approximation, employed in previous linear stability analyses,
ceases to be valid for gaseous flow when the wall-to-ambient temperature ratio
$\Theta_w$ is not close to unity. The corresponding non-Boussinesq analysis is
presented here, accounting also for the variation with temperature of the
different transport properties. A temporal stability analysis including
nonparallel effects of the base flow is used to determine curves of neutral
stability, which are then employed to delineate the dependences of the critical
Grashof number and of its associated wave length on the inclination angle
$\phi$ and on the temperature ratio $\Theta_w$ for the two instability modes,
giving quantitative information of interest for configurations with
$\Theta_w-1\sim 1$. The analysis provides in particular the predicted
dependence of the crossover inclination angle $\phi_c$ on $\Theta_w$,
indicating that for gaseous flow with $\Theta_w-1\sim 1$ spanwise traveling
waves are predominant over a range of inclination angles $0 \le \phi \le
\phi_c$ that is significantly wider than that predicted in the Boussinesq
approximation.


title: Invariant KAM tori: from theory to applications to exoplanetary systems

abstract:
  We consider the classical problem of the construction of invariant tori
exploiting suitable Hamiltonian normal forms. This kind of approach can be
translated by means of the Lie series method into explicit computational
algorithms, which are particularly suitable for applications in the field of
Celestial Mechanics. First, the algorithm constructing the Kolmogorov normal
form is described in detail. Then, the extension to lower-dimensional elliptic
tori is provided. We adopt the same formalism and notations in both cases, with
the aim of making the latter easier to understand. Finally, they are both used
in a combined way in order to approximate carefully the secular dynamics of the
extrasolar system hosting two planets orbiting around the HD 4732 star.


title: Some homological properties of algebras involving smooth functions

abstract:
  Consider a complex affine variety $\tilde V$ and a real analytic
Zariski-dense submanifold V of $\tilde V$. We compare modules over the ring $O
(\tilde V)$ of regular functions on $\tilde V$ with modules over the ring
$C^\infty (V)$ of smooth complex valued functions on V.
  Under a mild condition on the tangent spaces, we prove that $C^\infty (V)$ is
flat as a module over $O (\tilde V)$. From this we deduce a comparison theorem
for the Hochschild homology of finite type algebras over $O (\tilde V)$ and the
Hochschild homology of similar algebras over $C^\infty (V)$.
  We also establish versions of these results for functions on $\tilde V$
(resp. V) that are invariant under the action of a finite group G. When V is
compact, we check that $C^\infty (V)$ has finite rank as module over $C^\infty
(V)^G$.


title: I-Tuning: Tuning Language Models with Image for Caption Generation

abstract:
  Recently, tuning the pre-trained language model (PLM) in a
parameter-efficient manner becomes a popular topic in the natural language
processing area. However, most of them focus on tuning the PLM with the
text-only information. In this work, we propose a new perspective to tune the
frozen PLM with images for caption generation. We denote our method as
I-Tuning, which can automatically filter the vision information from images to
adjust the output hidden states of PLM. Evaluating on the image captioning
tasks (MSCOCO and Flickr30k Captioning), our method achieves comparable or even
better performance than the previous models which have 2-4 times more trainable
parameters and/or consume a large amount of cross-modal pre-training data.


title:
Dilation properties of measurable Schur multipliers and Fourier
  multipliers

abstract:
  In the article, we find new dilatation results on non-commutative $L_p$
spaces. We prove that any selfadjoint, unital, positive measurable Schur
multiplier on some $B(L^2(\Sigma))$ admits, for all $1\leq p<\infty$, an
invertible isometric dilation on some non-commutative $L^p$-space. We obtain a
similar result for selfadjoint, unital, completely positive Fourier multiplier
on $VN(G)$, when $G$ is a unimodular locally compact group. Furthermore, we
establish multivariable versions of these results.


title: Minimal Steklov eigenvalues on combinatorial graphs

abstract:
  In this paper, we study extremal problems of Steklov eigenvalues on
combinatorial graphs by extending Friedman's theory of nodal domains for
Laplacian eigenfunctions to Steklov eigenfunctions.


title: A Homogenised Model of Fluid-String Interaction

abstract:
  A homogenised model is developed to describe the interaction between aligned
strings and an incompressible, viscous, Newtonian fluid. In the case of many
strings, the ratio of string separation to domain width gives a small parameter
which can be exploited to simplify the problem. Model derivation using
multiscale asymptotics results in a modified Darcy law for fluid flow, with
coefficients determined by averaged solutions to microscale problems. Fluid
flow is coupled to solid deformation via a homogenised force balance obtained
by coarse-graining the balance on each string. This approach offers an
alternative method to systematically derive the equations governing the
interaction of Stokes flow with many flexible structures. The resulting model
of fluid-structure interaction is reduced to a single scalar, linear, partial
differential equation by introducing a potential for the pressure. Analytical
solutions are presented for a cylindrical geometry subject to time harmonic
motion of the string ends. Scaling laws are identified that describe the
variation of shear stress exerted on the string surface with the forcing
frequency.


title:
A Meshfree Peridynamic Model for Brittle Fracture in Randomly
  Heterogeneous Materials

abstract:
  In this work we aim to develop a unified mathematical framework and a
reliable computational approach to model the brittle fracture in heterogeneous
materials with variability in material microstructures, and to provide
statistic metrics for quantities of interest, such as the fracture toughness.
To depict the material responses and naturally describe the nucleation and
growth of fractures, we consider the peridynamics model. In particular, a
stochastic state-based peridynamic model is developed, where the
micromechanical parameters are modeled by a finite-dimensional random vector,
or a combination of random variables truncating the Karhunen-Lo\`{e}ve
decomposition or the principle component analysis (PCA). To solve this
stochastic peridynamic problem, probabilistic collocation method (PCM) is
employed to sample the random field representing the micromechanical
parameters. For each sample, the deterministic peridynamic problem is
discretized with an optimization-based meshfree quadrature rule. We present
rigorous analysis for the proposed scheme and demonstrate its convergence for a
number of benchmark problems, showing that it sustains the asymptotic
compatibility spatially and achieves an algebraic or sub-exponential
convergence rate in the random space as the number of collocation points grows.
Finally, to validate the applicability of this approach on real-world fracture
problems, we consider the problem of crystallization toughening in
glass-ceramic materials, in which the material at the microstructural scale
contains both amorphous glass and crystalline phases. The proposed stochastic
peridynamic solver is employed to capture the crack initiation and growth for
glass-ceramics with different crystal volume fractions, and the averaged
fracture toughness are calculated. The numerical estimates of fracture
toughness show good consistency with experimental measurements.


title: Aerodynamics of planar counterflowing jets

abstract:
  The planar laminar flow resulting from the impingement of two gaseous jets of
different density issuing into an open space from aligned steadily fed slot
nozzles of semi-width $R$ separated a distance $2H$ is investigated by
numerical and analytical methods, with specific consideration given to the
high-Reynolds and low-Mach number conditions typically present in
counterflow-flame experiments, for which the flow is nearly inviscid and
incompressible. It is shown that introduction of a density-weighted
vorticity-stream function formulation effectively reduces the problem to one
involving two jets of equal density, thereby removing the vortex-sheet
character of the interface separating the two jet streams. Besides the
geometric parameter $H/R$, the solution depends only on the shape of the
velocity profiles in the feed streams and on the jet momentum-flux ratio. While
conformal mapping can be used to determine the potential solution corresponding
to uniform velocity profiles, numerical integration is required in general to
compute rotational flows, including those arising with Poiseuille velocity
profiles, with simplified solutions found in the limits $H/R \ll 1$ and $H/R
\gg 1$. The results are used to quantify the near-stagnation-point region, of
interest in counterflow-flame studies, including the local value of the strain
rate as well as the curvature of the separating interface and the variations of
the strain rate away from the stagnation point.


title:
Improved Aggregating and Accelerating Training Methods for Spatial Graph
  Neural Networks on Fraud Detection

abstract:
  Graph neural networks (GNNs) have been widely applied to numerous fields. A
recent work which combines layered structure and residual connection proposes
an improved deep architecture to extend CAmouflage-REsistant GNN (CARE-GNN) to
deep models named as Residual Layered CARE-GNN (RLC-GNN), which forms
self-correcting and incremental learning mechanism, and achieves significant
performance improvements on fraud detection task. However, we spot three issues
of RLC-GNN, which are the usage of neighboring information reaching limitation,
the training difficulty which is inherent problem to deep models and lack of
comprehensive consideration about node features and external patterns. In this
work, we propose three approaches to solve those three problems respectively.
First, we suggest conducting similarity measure via cosine distance to take
both local features and external patterns into consideration. Then, we combine
the similarity measure module and the idea of adjacency-wise normalization with
node-wise and batch-wise normalization and then propound partial neighborhood
normalization methods to overcome the training difficulty while mitigating the
impact of too much noise caused by high-density of graph. Finally, we put
forward intermediate information supplement to solve the information
limitation. Experiments are conducted on Yelp and Amazon datasets. And the
results show that our proposed methods effectively solve the three problems.
After applying the three methods, we achieve 4.81%, 6.62% and 6.81%
improvements in the metrics of recall, AUC and Macro-F1 respectively on the
Yelp dataset. And we obtain 1.65% and 0.29% improvements in recall and AUC
respectively on the Amazon datasets.


title:
On the pressure decline analysis for hydraulic fractures in
  elasto-plastic materials

abstract:
  In this paper the problem of a plane strain hydraulic fracture propagating in
elasto-plastic material is analyzed. The Finite Element Method computations are
employed in the framework of ELFEN package to simulate the Mini-Frac test. The
basic trends of fracture evolution are identified for both, the propagation and
the closure stage. Pressure decline analysis is conducted. The results show
that the standard techniques of the pressure decline analysis can be adopted
also for the case where the fractured material deforms inelastically.


title:
Characterization of $g_2$-minimal normal 3-pseudomanifolds with at most
  four singularities

abstract:
  Let $\Delta$ be a $g_2$-minimal normal 3-pseudomanifold. A vertex in $\Delta$
whose link is not a sphere is called a singular vertex. The combinatorial
characterization of such $\Delta$ is known when $\Delta$ has at most two
singular vertices \cite{BasakSwartz}. In this article we have given the
combinatorial characterization of such $\Delta$, when $\Delta$ contains either
three singular vertices including one $\mathbb{RP}^2$ singularity or four
singular vertices including two $\mathbb{RP}^2$ singularities. In both cases,
we prove that $\Delta$ is obtained from a one-vertex suspension of a surface
and some boundary complex of $4$-simplices by applying the combinatorial
operations connected sum, vertex folding and edge folding.


title:
Individual-based and continuum models of phenotypically heterogeneous
  growing cell populations

abstract:
  Existing studies comparing individual-based models of growing cell
populations and their continuum counterparts have mainly focused on homogeneous
populations, in which all cells have the same phenotypic characteristics.
However, significant intercellular phenotypic variability is commonly observed
in cellular systems. Therefore, we develop here an individual-based model for
the growth of phenotypically heterogeneous cell populations. In this model, the
phenotypic state of each cell is described by a structuring variable that
captures intercellular variability in cell proliferation and migration rates.
The model tracks the spatial evolutionary dynamics of single cells, which
undergo pressure-dependent proliferation, heritable phenotypic changes and
directional movement in response to pressure differentials. We formally show
that the continuum limit of this model comprises a non-local partial
differential equation for the cell population density, which generalises
earlier models of growing cell populations. Results of the individual-based
model illustrate how proliferation-migration tradeoffs shaping the evolution of
single cells can lead to the formation of travelling waves at the population
level where highly-mobile cells locally dominate at the invasive front, while
more-proliferative cells are found at the rear. We demonstrate that there is an
excellent quantitative agreement between these results and the results of
numerical simulations and formal travelling-wave analysis of the continuum
model, when sufficiently large cell numbers are considered. We provide
numerical evidence of scenarios in which the predictions of the two models may
differ due to demographic stochasticity, which cannot be captured by the
continuum model. This indicates the importance of integrating individual-based
and continuum approaches when modelling the growth of phenotypically
heterogeneous cell populations.