title:
A Simple Approach to Improve Single-Model Deep Uncertainty via
  Distance-Awareness

abstract:
  Accurate uncertainty quantification is a major challenge in deep learning, as
neural networks can make overconfident errors and assign high confidence
predictions to out-of-distribution (OOD) inputs. The most popular approaches to
estimate predictive uncertainty in deep learning are methods that combine
predictions from multiple neural networks, such as Bayesian neural networks
(BNNs) and deep ensembles. However their practicality in real-time,
industrial-scale applications are limited due to the high memory and
computational cost. Furthermore, ensembles and BNNs do not necessarily fix all
the issues with the underlying member networks. In this work, we study
principled approaches to improve uncertainty property of a single network,
based on a single, deterministic representation. By formalizing the uncertainty
quantification as a minimax learning problem, we first identify distance
awareness, i.e., the model's ability to quantify the distance of a testing
example from the training data, as a necessary condition for a DNN to achieve
high-quality (i.e., minimax optimal) uncertainty estimation. We then propose
Spectral-normalized Neural Gaussian Process (SNGP), a simple method that
improves the distance-awareness ability of modern DNNs with two simple changes:
(1) applying spectral normalization to hidden weights to enforce bi-Lipschitz
smoothness in representations and (2) replacing the last output layer with a
Gaussian process layer. On a suite of vision and language understanding
benchmarks, SNGP outperforms other single-model approaches in prediction,
calibration and out-of-domain detection. Furthermore, SNGP provides
complementary benefits to popular techniques such as deep ensembles and data
augmentation, making it a simple and scalable building block for probabilistic
deep learning. Code is open-sourced at
https://github.com/google/uncertainty-baselines


title:
Accurate Fruit Localisation for Robotic Harvesting using High Resolution
  LiDAR-Camera Fusion

abstract:
  Accurate depth-sensing plays a crucial role in securing a high success rate
of robotic harvesting in natural orchard environments. Solid-state LiDAR (SSL),
a recently introduced LiDAR technique, can perceive high-resolution geometric
information of the scenes, which can be potential utilised to receive accurate
depth information. Meanwhile, the fusion of the sensory information from LiDAR
and camera can significantly enhance the sensing ability of the harvesting
robots. This work introduces a LiDAR-camera fusion-based visual sensing and
perception strategy to perform accurate fruit localisation for a harvesting
robot in the apple orchards. Two SOTA extrinsic calibration methods,
target-based and targetless-based, are applied and evaluated to obtain the
accurate extrinsic matrix between the LiDAR and camera. With the extrinsic
calibration, the point clouds and color images are fused to perform fruit
localisation using a one-stage instance segmentation network. Experimental
shows that LiDAR-camera achieves better quality on visual sensing in the
natural environments. Meanwhile, introducing the LiDAR-camera fusion largely
improves the accuracy and robustness of the fruit localisation. Specifically,
the standard deviations of fruit localisation by using LiDAR-camera at 0.5 m,
1.2 m, and 1.8 m are 0.245, 0.227, and 0.275 cm respectively. These measurement
error is only one one fifth of that from Realsense D455. Lastly, we have
attached our visualised point cloud to demonstrate the highly accurate sensing
method.


title: Odd-gon relations and their cohomology

abstract:
  A cohomology theory for "odd polygon" relations -- algebraic imitations of
Pachner moves in dimensions 3, 5, ... -- is constructed. Manifold invariants
based on polygon relations and nontrivial polygon cocycles are proposed.
Example calculation results are presented.


title:
Coordinated Pilot Transmissions for Detecting the Signal Sparsity Level
  in a Massive IoT Network under Rayleigh Fading

abstract:
  Grant-free protocols exploiting compressed sensing (CS) multi-user detection
(MUD) are appealing for solving the random access problem in massive
machine-type communications (mMTC) with sporadic device activity. Such
protocols would greatly benefit from a prior deterministic knowledge of the
sparsity level, i.e., instantaneous number of simultaneously active devices
$K$. Aiming at this, herein we introduce a framework relying on coordinated
pilot transmissions (CPT) over a short phase at the beginning of the
transmission block for detecting $K$ in mMTC scenarios under Rayleigh fading.
CPT can be implemented either as: i) U-CPT, which exploits only uplink
transmissions, or A-CPT, which includes also downlink transmissions for channel
state information (CSI) acquisition that resolve fading uncertainty. We discuss
two specific implementations of A-CPT: ii) A-CPT-F, which implements CSI-based
phase corrections while leveraging the same statistical inverse power control
used by U-CPT, and iii) A-CPT-D, which implements a dynamic CSI-based inverse
power control, although it requires some active devices to remain in silence if
their corresponding channels are too faded. We derive a signal sparsity level
detector for each CPT mechanism by relaxing the original integer
detection/classification problem to an estimation problem in the continuous
real domain followed by a rounding operation. We show that the variance of the
relaxed estimator increases with $K^2$ and $K$ when operating with U-CPT and
A-CPT mechanisms, respectively. The distribution of the estimators under U-CPT,
A-CPT-F and A-CPT-D is found to follow an exponential, Gaussian, and Student's
$t-$like distribution, respectively. Analyses evince the superiority of
A-CPT-D, which is also corroborated via numerical results. We reveal several
interesting trade-offs and highlight potential research directions.


title:
Quality-Aware Real-Time Augmented Reality Visualization under Delay
  Constraints

abstract:
  Augmented reality (AR) is one of emerging applications in modern multimedia
systems research. Due to intensive time-consuming computations for AR
visualization in mobile devices, quality-aware real-time computing under delay
constraints is essentially required. Inspired by Lyapunov optimization
framework, this paper proposes a time-average quality maximization method for
the AR visualization under delay considerations.


title:
Tracing Astrophysical Black Hole Seeds and Primordial Black Holes with
  LISA-Taiji Network

abstract:
  In this work, we discuss the improvement that the joint network of LISA and
Taiji could provide on exploring two kinds of black hole formation mechanisms.
For astrophysical origin, we consider light seed and heavy seed scenarios, and
generate populations accordingly. We find that the joint network has the
potential to observe growing light seeds in the range 15 < z < 20, while single
detector can hardly see, which would shed light on the light seeding mechanism.
For the heavy seeds, the joint network only improves the signal-to-noise ratio.
For primordial origin, we calculate the event rate at z > 20 and detection
rates of LISA and the joint network. The joint network expands LISA's horizon
towards lower mass end, where the event rate is high, so we have better chance
observing primordial black holes with the joint network. We also estimate the
parameters using Fisher matrices of LISA and the joint network, and find that
the joint network significantly improves the estimation.


title:
Tunneling spectroscopic signatures of charge doping and Mott-phase
  transition in ${\alpha}$-RuCl${_3}$ in proximity to graphite

abstract:
  Layered Mott insulator ${\alpha}$-RuCl${_3}$ has been intensely investigated
as a possible candidate for Kitaev quantum spin liquid. In this letter, we
report electron tunneling measurements on few-layer ${\alpha}$-RuCl${_3}$ in
proximity to graphite, using a scanning tunneling microscopy. Signatures of
charge doping have been observed in ${\alpha}$-RuCl${_3}$ layers stacking on
the surface of graphite. Upon charge doping, we observed characteristic
tunneling spectra that are dependent on the number of layers of
${\alpha}$-RuCl${_3}$. For a single ${\alpha}$-RuCl${_3}$ layer that is in
direct contact with graphite, data shows charge states emerging in the Mott-gap
regime with conservation of the Hubbard bands. For a bilayer of
${\alpha}$-RuCl${_3}$, data indicates an unconventional Mott-phase transition,
where the Hubbard bands collapse accompanied by a dramatical gap-reduction. The
results have thus demonstrated that tunneling into doped few-layer
${\alpha}$-RuCl${_3}$ is a useful probe to investigate this otherwise
insulating spin-liquid candidate, providing fundamental information concerning
electronic properties and theoretically proposed strong correlation physics in
${\alpha}$-RuCl${_3}$.


title: On geography of symplectic fillings of contact branched covers

abstract:
  In this paper, we determine the Euler characteristics and signatures of the
exact symplectic fillings of the contact double, 3-fold or 4-fold branched
covers of the standard contact 3-sphere along certain transverse quasi-positive
links. These links include all quasi-positive knots with crossing numbers
smaller than 11 and all quasi-positive links with crossing numbers smaller than
12 and nonzero nullity.


title:
Stable Reinforcement Learning for Optimal Frequency Control: A
  Distributed Averaging-Based Integral Approach

abstract:
  Frequency control plays a pivotal role in reliable power system operations.
It is conventionally performed in a hierarchical way that first rapidly
stabilizes the frequency deviations and then slowly recovers the nominal
frequency. However, as the generation mix shifts from synchronous generators to
renewable resources, power systems experience larger and faster frequency
fluctuations due to the loss of inertia, which adversely impacts the frequency
stability. This has motivated active research in algorithms that jointly
address frequency degradation and economic efficiency in a fast timescale,
among which the distributed averaging-based integral (DAI) control is a notable
one that sets controllable power injections directly proportional to the
integrals of frequency deviation and economic inefficiency signals.
Nevertheless, DAI do not typically consider the transient performance of the
system following power disturbances and has been restricted to quadratic
operational cost functions. This manuscript aims to leverage nonlinear optimal
controllers to simultaneously achieve optimal transient frequency control and
find the most economic power dispatch for frequency restoration. To this end,
we integrate reinforcement learning (RL) to the classic DAI, which results in
RL-DAI. Specifically, we use RL to learn a neural network-based control policy
mapping from the integral variables of DAI to the controllable power injections
which provides optimal transient frequency control, while DAI inherently
ensures the frequency restoration and optimal economic dispatch. Compared to
existing methods, we provide provable guarantees on the stability of the
learned controllers and extend allowable cost functions to a much larger class.
Simulations on the 39-bus New England system illustrate our results.


title: Promises and challenges of high-energy vortex states collisions

abstract:
  Vortex states of photons, electrons, and other particles are non--plane-wave
solutions of the corresponding wave equation with helicoidal wave fronts. These
states possess an intrinsic orbital angular momentum with respect to the
average propagation direction, which represents a new degree of freedom,
previously unexplored in particle or nuclear collisions. Vortex states of
photons, electrons, neutrons, and neutral atoms have been experimentally
produced, albeit at low energies, and are being intensively explored.
Anticipating future experimental progress, one can ask what additional insights
on nuclei and particles one can gain once collisions of high-energy vortex
states become possible. This review describes the present-day landscape of
physics opportunities, experimental progress and suggestions relevant to vortex
states in high energy collisions. The aim is to familiarize the community with
this emergent cross-disciplinary topic and to provide a sufficiently complete
literature coverage, highlighting some results and calculational techniques.


title: Smoothed quantile regression for censored residual life

abstract:
  We consider a regression modeling of the quantiles of residual life,
remaining lifetime at a specific time. We propose a smoothed induced version of
the existing non-smooth estimating equations approaches for estimating
regression parameters. The proposed estimating equations are smooth in
regression parameters, so solutions can be readily obtained via standard
numerical algorithms. Moreover, the smoothness in the proposed estimating
equations enables one to obtain a robust sandwich-type covariance estimator of
regression estimators aided by an efficient resampling method. To handle data
subject to right censoring, the inverse probability of censoring weight are
used as weights. The consistency and asymptotic normality of the proposed
estimator are established. Extensive simulation studies are conducted to
validate the proposed estimator's performance in various finite samples
settings. We apply the proposed method to dental study data evaluating the
longevity of dental restorations.


title: Explore the Origin of SSB from Adaptive Perturbation Method

abstract:
  A non-trivial vacuum is crucial to trigger spontaneous symmetry breaking. The
origin is a non-trivial problem to explore. We focus on the (3+1)d $\phi^4$
theory to tackle the problem due to its simplicity. The absence of other
matters helps clarify the central origin of the non-trivial vacuum. For the
analysis to remain valid in the strong-coupling regime, we adopt the method of
adaptive perturbation, which has shown accurate results for strongly coupled
quantum mechanics. We generalize this method to the scalar field theory. The
unperturbed Hamiltonian does not commute with the usual number operator.
However, the quantized scalar field admits a plane-wave expansion when acting
on the vacuum. The Lorentz symmetry is not manifest in this approach. We
propose an elegant resummation of Feynman diagrams to restore this symmetry.
The one-, two- and four-point results match numerical solutions with coupling
constant $\lambda = 1, 2, 4, 8, 16$. Finally, we find evidence for quantum
triviality, where self-consistency of the theory in the UV requires $\lambda =
0$. This result implies that the $\phi^4$ theory alone does not experience SSB,
and the $\langle \phi\rangle = 0$ phase is protected under the RG-flow by a
boundary of Gaussian fixed-points.


title:
Don't Blame the Annotator: Bias Already Starts in the Annotation
  Instructions

abstract:
  In recent years, progress in NLU has been driven by benchmarks. These
benchmarks are typically collected by crowdsourcing, where annotators write
examples based on annotation instructions crafted by dataset creators. In this
work, we hypothesize that annotators pick up on patterns in the crowdsourcing
instructions, which bias them to write similar examples that are then
over-represented in the collected data. We study this form of bias, termed
instruction bias, in 14 recent NLU benchmarks, showing that instruction
examples often exhibit concrete patterns, which are propagated by crowdworkers
to the collected data. This extends previous work (Geva et al., 2019) and
raises a new concern of whether we are modeling the dataset creator's
instructions, rather than the task. Through a series of experiments, we show
that, indeed, instruction bias can lead to overestimation of model performance,
and that models struggle to generalize beyond biases originating in the
crowdsourcing instructions. We further analyze the influence of instruction
bias in terms of pattern frequency and model size, and derive concrete
recommendations for creating future NLU benchmarks.


title:
Formulation of an extended null channel formalism for a triangular
  gravitational wave interferometer configuration in the case of non-identical
  and correlated noise

abstract:
  Several proposed gravitational wave interferometers have a triangular
configuration, such as the Einstein Telescope (ET) and the Laser Interferometer
Space Antenna (LISA). For such a configuration one can construct a sky location
independent or unique null channel insensitive to gravitational waves from all
directions. We expand on earlier work and describe an extended null channel
formalism applicable to interferometric data with non-identical as well as
correlated noise sources between the different interferometers. Two examples
are shown to illustrate the formalism in the context of the Einstein Telescope.
Finally we highlight future research needed to transition from the mathematical
formalism described here to a framework in which the formalism can be used to
estimate the noise power spectral densities of the observing gravitational-wave
interferometers.


title: Nonrational polytopes and fans in toric geometry

abstract:
  In this survey, we first examine the notion of nonrational polytope and
nonrational fan in the context of toric geometry. We then discuss and
interrelate some recent developments in the subject.


title: Decoherence Mitigation by Embedding a Logical Qubit in a Qudit

abstract:
  Quantum information stored in a qubit is rapidly lost to the environment. The
realization of robust qubits is one of the most important challenges in quantum
computing. Herein we propose to embed a logical qubit within the manifold of a
qudit as a scheme to preserve quantum information over extended periods of
time. Under identical conditions (e.g. decoherence channels) the submanifold of
the logical qubit exhibits extended lifetimes compared to a pure two-level
system (qubit). The retention of quantum information further improves with
separation between the sublevels of the logical qubit. Lifetime enhancement can
be understood in terms of entropy production of the encoding and non-encoding
subspaces during evolution under a quantum map for a $d$-level system. The
additional pathways for coherent evolution through intermediate sublevels
within a $d$-level manifold provide an information-preserving mechanism:
reversible alternative channels to the irreversible loss of information to the
environment characteristic of open quantum systems.


title: Pro-isomorphic zeta functions of some $D^\ast$ Lie lattices of even rank

abstract:
  We compute the local pro-isomorphic zeta functions at all but finitely many
primes for a certain family of class-two-nilpotent Lie lattices of even rank,
parametrized by irreducible non-linear polynomials $f(x) \in \mathbb{Z} [x]$,
that corresponds to a family of groups introduced by Grunewald and Segal. The
result is expressed in terms of a combinatorially defined family of rational
functions satisfying a functional equation upon inversion of the variables.


abstract:
  We introduce Uniform Manifold Approximation with Two-phase Optimization
(UMATO), a dimensionality reduction (DR) technique that improves UMAP to
capture the global structure of high-dimensional data more accurately. In
UMATO, optimization is divided into two phases so that the resulting embeddings
can depict the global structure reliably while preserving the local structure
with sufficient accuracy. As the first phase, hub points are identified and
projected to construct a skeletal layout for the global structure. In the
second phase, the remaining points are added to the embedding preserving the
regional characteristics of local areas. Through quantitative experiments, we
found that UMATO (1) outperformed widely used DR techniques in preserving the
global structure while (2) producing competitive accuracy in representing the
local structure. We also verified that UMATO is preferable in terms of
robustness over diverse initialization methods, number of epochs, and
subsampling techniques.


title: Production of polarized particle beams via ultraintense laser pulses

abstract:
  High-energy spin-polarized electron, positron, and $\gamma$-photon beams have
many significant applications in the study of material properties, nuclear
structure, particle physics, and high-energy astrophysics. Thus, efficient
production of such polarized beams attracts a broad spectrum of research
interests. This is driven mainly by the rapid advancements in ultrashort and
ultraintense laser technology. Currently available laser pulses can achieve
peak intensities in the range of $10^{22}-10^{23}$ Wcm$^{-2}$, with pulse
durations of tens of femtoseconds. The dynamics of particles in laser fields of
the available intensities is dominated by quantum electrodynamics (QED) and the
interaction mechanisms have reached regimes spanned by nonlinear multiphoton
absorbtion (strong-field QED processes). In strong-field QED processes, the
scattering cross sections obviously depend on the spin and polarization of the
particles, and the spin-dependent photon emission and the radiation-reaction
effects can be utilized to produce the polarized particles. An ultraintense
laser-driven polarized particle source possesses the advantages of
high-brilliance and compactness, which could open the way for the unexplored
aspects in a range of researches. In this work, we briefly review the seminal
conclusions from the study of the polarization effects in strong-field QED
processes, as well as the progress made by recent proposals for production of
the polarized particles by laser-beam or laser-plasma interactions.


title:
Well-posedness for Moving Interfaces with Surface Tension in Ideal
  Compressible MHD

abstract:
  We study the local well-posedness for an interface with surface tension that
separates a perfectly conducting inviscid fluid from a vacuum. The fluid flow
is governed by the equations of three-dimensional ideal compressible
magnetohydrodynamics (MHD), while the vacuum magnetic and electric fields are
supposed to satisfy the pre-Maxwell equations. The fluid and vacuum magnetic
fields are tangential to the interface. This renders a nonlinear
hyperbolic-elliptic coupled problem with a characteristic free boundary. We
introduce some suitable regularization to establish the solvability and tame
estimates for the linearized problem. Combining the linear well-posedness
result with a modified Nash--Moser iteration scheme, we prove the local
existence and uniqueness of solutions of the nonlinear problem. The
non-collinearity condition required by Secchi and Trakhinin [Nonlinearity
27(1): 105--169, 2014] for the case of zero surface tension becomes unnecessary
in our result, which verifies the stabilizing effect of surface tension on the
evolution of moving vacuum interfaces in ideal compressible MHD.


title:
UTC: A Unified Transformer with Inter-Task Contrastive Learning for
  Visual Dialog

abstract:
  Visual Dialog aims to answer multi-round, interactive questions based on the
dialog history and image content. Existing methods either consider answer
ranking and generating individually or only weakly capture the relation across
the two tasks implicitly by two separate models. The research on a universal
framework that jointly learns to rank and generate answers in a single model is
seldom explored. In this paper, we propose a contrastive learning-based
framework UTC to unify and facilitate both discriminative and generative tasks
in visual dialog with a single model. Specifically, considering the inherent
limitation of the previous learning paradigm, we devise two inter-task
contrastive losses i.e., context contrastive loss and answer contrastive loss
to make the discriminative and generative tasks mutually reinforce each other.
These two complementary contrastive losses exploit dialog context and target
answer as anchor points to provide representation learning signals from
different perspectives. We evaluate our proposed UTC on the VisDial v1.0
dataset, where our method outperforms the state-of-the-art on both
discriminative and generative tasks and surpasses previous state-of-the-art
generative methods by more than 2 absolute points on Recall@1.


title:
Unified Abstract Syntax Tree Representation Learning for Cross-Language
  Program Classification

abstract:
  Program classification can be regarded as a high-level abstraction of code,
laying a foundation for various tasks related to source code comprehension, and
has a very wide range of applications in the field of software engineering,
such as code clone detection, code smell classification, defects
classification, etc. The cross-language program classification can realize code
transfer in different programming languages, and can also promote
cross-language code reuse, thereby helping developers to write code quickly and
reduce the development time of code transfer. Most of the existing studies
focus on the semantic learning of the code, whilst few studies are devoted to
cross-language tasks. The main challenge of cross-language program
classification is how to extract semantic features of different programming
languages. In order to cope with this difficulty, we propose a Unified Abstract
Syntax Tree (namely UAST in this paper) neural network. In detail, the core
idea of UAST consists of two unified mechanisms. First, UAST learns an AST
representation by unifying the AST traversal sequence and graph-like AST
structure for capturing semantic code features. Second, we construct a
mechanism called unified vocabulary, which can reduce the feature gap between
different programming languages, so it can achieve the role of cross-language
program classification. Besides, we collect a dataset containing 20,000 files
of five programming languages, which can be used as a benchmark dataset for the
cross-language program classification task. We have done experiments on two
datasets, and the results show that our proposed approach outperforms the
state-of-the-art baselines in terms of four evaluation metrics (Precision,
Recall, F1-score, and Accuracy).


title:
Analytic Kludge Waveforms for Extreme Mass Ratio Inspirals of Charged
  Object around Kerr-Newman Black Hole

abstract:
  We derive the approximate, "analytic-kludge" (AK) waveforms for the inspiral
of a charged stellar-mass compact object (CO) into a charged massive
Kerr-Newman (KN) black hole (BH). The modifications of the inspiral orbit due
to the charges in this system can be attributed to three sources: the electric
force between the CO and the MBH, the energy flow of the dipole electromagnetic
radiation, and the deformation of the metric caused by the charge of the MBH.
All these are encoded explicitly in the fundamental frequencies of the orbits,
which are calculated analytically in the weak-field regime. By calculating the
mismatch between the waveforms for charged and neutral EMRI systems with
respect to space-borne detectors TianQin and LISA, we show that tiny charges in
the system can produce distinct imprints on the waveforms. Finally, we perform
parameter estimation for the charges using the Fisher information matrix method
and find that the precision can reach the level of $10^{-5}$ in suitable
scenarios. We also study the effects of charges on the parameter estimation of
charge, which can be well explained by their effects on the cutoff of the
inspiral.


title:
Counterexamples to Gerbner's Conjecture on Stability of Maximal $F$-free
  Graphs

abstract:
  Let $F$ be an $(r+1)$-color critical graph with $r\geq 2$, that is,
$\chi(F)=r+1$ and there is an edge $e$ in $F$ such that $\chi(F-e)=r$. Gerbner
recently conjectured that every $n$-vertex maximal $F$-free graph with at least
$(1-\frac{1}{r})\frac{n^2}{2}- o(n^{\frac{r+1}{r}})$ edges contains an induced
complete $r$-partite graph on $n-o(n)$ vertices. Let $F_{s,k}$ be a graph
obtained from $s$ copies of $C_{2k+1}$ by sharing a common edge. In this paper,
we show that for all $k\geq 2$ if $G$ is an $n$-vertex maximal $F_{s,k}$-free
graph with at least $n^{2}/4 - o(n^{\frac{s+2}{s+1}})$ edges, then $G$ contains
an induced complete bipartite graph on $n-o(n)$ vertices. We also show that it
is best possible. This disproves Gerbner's conjecture for $r=2$.


title:
TinyLight: Adaptive Traffic Signal Control on Devices with Extremely
  Limited Resources

abstract:
  Recent advances in deep reinforcement learning (DRL) have largely promoted
the performance of adaptive traffic signal control (ATSC). Nevertheless,
regarding the implementation, most works are cumbersome in terms of storage and
computation. This hinders their deployment on scenarios where resources are
limited. In this work, we propose TinyLight, the first DRL-based ATSC model
that is designed for devices with extremely limited resources. TinyLight first
constructs a super-graph to associate a rich set of candidate features with a
group of light-weighted network blocks. Then, to diminish the model's resource
consumption, we ablate edges in the super-graph automatically with a novel
entropy-minimized objective function. This enables TinyLight to work on a
standalone microcontroller with merely 2KB RAM and 32KB ROM. We evaluate
TinyLight on multiple road networks with real-world traffic demands.
Experiments show that even with extremely limited resources, TinyLight still
achieves competitive performance. The source code and appendix of this work can
be found at \url{https://bit.ly/38hH8t8}.


title:
Analysis of Diffractive Neural Networks for Seeing Through Random
  Diffusers

abstract:
  Imaging through diffusive media is a challenging problem, where the existing
solutions heavily rely on digital computers to reconstruct distorted images. We
provide a detailed analysis of a computer-free, all-optical imaging method for
seeing through random, unknown phase diffusers using diffractive neural
networks, covering different deep learning-based training strategies. By
analyzing various diffractive networks designed to image through random
diffusers with different correlation lengths, a trade-off between the image
reconstruction fidelity and distortion reduction capability of the diffractive
network was observed. During its training, random diffusers with a range of
correlation lengths were used to improve the diffractive network's
generalization performance. Increasing the number of random diffusers used in
each epoch reduced the overfitting of the diffractive network's imaging
performance to known diffusers. We also demonstrated that the use of additional
diffractive layers improved the generalization capability to see through new,
random diffusers. Finally, we introduced deliberate misalignments in training
to 'vaccinate' the network against random layer-to-layer shifts that might
arise due to the imperfect assembly of the diffractive networks. These analyses
provide a comprehensive guide in designing diffractive networks to see through
random diffusers, which might profoundly impact many fields, such as biomedical
imaging, atmospheric physics, and autonomous driving.


title:
Closed-form max-min power control for some cellular and cell-free
  massive MIMO networks

abstract:
  Many common instances of power control problems for cellular and cell-free
massive MIMO networks can be interpreted as max-min utility optimization
problems involving affine interference mappings and polyhedral constraints. We
show that these problems admit a closed-form solution which depends on the
spectral radius of known matrices. In contrast, previous solutions in the
literature have been indirectly obtained using iterative algorithms based on
the bisection method, or on fixed-point iterations. Furthermore, we also show
an asymptotically tight bound for the optimal utility, which in turn provides a
simple rule of thumb for evaluating whether the network is operating in the
noise or interference limited regime. We finally illustrate our results by
focusing on classical max-min fair power control for cell-free massive MIMO
networks.


title: Toric Quasifolds

abstract:
  Toric quasifolds are highly singular spaces that were first introduced in
order to address, from the symplectic viewpoint, the longstanding open problem
of extending the classical constructions of toric geometry to those simple
convex polytopes that are not rational. We illustrate toric quasifolds, and
their atlases, by describing some notable examples. We conclude with a number
of remarks.


title: Positive Consensus for Heterogeneous Multi-agent Systems

abstract:
  In this paper, we consider a positive consensus problem for some high-order
linear multi-agent systems. Compared with existing consensus results, the most
distinct feature of the formulated problem is that the state variables of all
heterogeneous agents are confined to the positive orthant. To solve this
problem, we first present some auxiliary multi-agent systems as positive local
reference generators and then incorporate the reference generator into some
applicable decentralized tracking controller for each agent. The proposed two
different kinds of distributed algorithms are proven to solve the positive
consensus problem fulfilling certain prescribed pattern for this multi-agent
system under switching topology. A simulation example is finally given to
illustrate the effectiveness of our design.


title:
Drone Flocking Optimization using NSGA-II and Principal Component
  Analysis

abstract:
  Individual agents in natural systems like flocks of birds or schools of fish
display a remarkable ability to coordinate and communicate in local groups and
execute a variety of tasks efficiently. Emulating such natural systems into
drone swarms to solve problems in defence, agriculture, industry automation and
humanitarian relief is an emerging technology. However, flocking of aerial
robots while maintaining multiple objectives, like collision avoidance, high
speed etc. is still a challenge. In this paper, optimized flocking of drones in
a confined environment with multiple conflicting objectives is proposed. The
considered objectives are collision avoidance (with each other and the wall),
speed, correlation, and communication (connected and disconnected agents).
Principal Component Analysis (PCA) is applied for dimensionality reduction, and
understanding the collective dynamics of the swarm. The control model is
characterised by 12 parameters which are then optimized using a multi-objective
solver (NSGA-II). The obtained results are reported and compared with that of
the CMA-ES algorithm. The study is particularly useful as the proposed
optimizer outputs a Pareto Front representing different types of swarms which
can applied to different scenarios in the real world.


title: Quantum Magnetometer with Dual-Coupling Optomechanics

abstract:
  We propose an experimentally feasible magnetometer based on a dual-coupling
optomechanical system, where the radiation-pressure coupling transduces the
magnetic signal to the optical phase, and the quadratic optomechanical
interaction induces a periodic squeezing effect. The latter not only amplifies
the signal to be measured, but also accelerates the signal transducing rate
characterized by an experimentally observable phase accumulation efficiency. In
the vicinity of opto-mechanical decoupled time, the ultimate bound to the
estimability of magnetic signal is proportional to $\exp(-6r)$, and then the
optimized accuracy of estimation can be enhanced nearly 3 orders with a
controllable squeezing parameter $r<1$. Moreover, our proposal is robust
against the mechanical thermal noise, and the sensitivity of a specific
measurement can reach to the order of $10^{-17}{\rm T/\sqrt{Hz}}$ in the
presence of dissipations and without ground state cooling of mechanical
oscillator. Our proposal fundamentally broadens the fields of quantum metrology
and cavity optomechanics, with potential application for on-chip magnetic
detection with high precision.


title: Reinforced Swin-Convs Transformer for Underwater Image Enhancement

abstract:
  Underwater Image Enhancement (UIE) technology aims to tackle the challenge of
restoring the degraded underwater images due to light absorption and
scattering. To address problems, a novel U-Net based Reinforced Swin-Convs
Transformer for the Underwater Image Enhancement method (URSCT-UIE) is
proposed. Specifically, with the deficiency of U-Net based on pure
convolutions, we embedded the Swin Transformer into U-Net for improving the
ability to capture the global dependency. Then, given the inadequacy of the
Swin Transformer capturing the local attention, the reintroduction of
convolutions may capture more local attention. Thus, we provide an ingenious
manner for the fusion of convolutions and the core attention mechanism to build
a Reinforced Swin-Convs Transformer Block (RSCTB) for capturing more local
attention, which is reinforced in the channel and the spatial attention of the
Swin Transformer. Finally, the experimental results on available datasets
demonstrate that the proposed URSCT-UIE achieves state-of-the-art performance
compared with other methods in terms of both subjective and objective
evaluations. The code will be released on GitHub after acceptance.


title:
Primitive decompositions of idempotents of the group algebras of
  dihedral groups and generalized quaternion groups

abstract:
  In this paper, the primitive decompositions of idempotents of the dihedral
group algebras $\mathbb{C}[D_{2n}]$ and generalized quaternion group algebras
$\mathbb{C}[Q_{4m}]$ are calculated by their Wedderburn decomposition. Inspired
by the orthogonality relations of the character tables of these two families of
groups, we obtain two sets of trigonometric identities. Furthermore, a group
algebra isomorphism between $\mathbb{C}[D_{8}]$ and $\mathbb{C}[Q_{8}]$ is
described, under which our two complete sets of primitive orthogonal
idempotents of these two group algebras correspond to each other bijectively.


title:
Differentially Private Multivariate Time Series Forecasting of
  Aggregated Human Mobility With Deep Learning: Input or Gradient Perturbation?

abstract:
  This paper investigates the problem of forecasting multivariate aggregated
human mobility while preserving the privacy of the individuals concerned.
Differential privacy, a state-of-the-art formal notion, has been used as the
privacy guarantee in two different and independent steps when training deep
learning models. On one hand, we considered \textit{gradient perturbation},
which uses the differentially private stochastic gradient descent algorithm to
guarantee the privacy of each time series sample in the learning stage. On the
other hand, we considered \textit{input perturbation}, which adds differential
privacy guarantees in each sample of the series before applying any learning.
We compared four state-of-the-art recurrent neural networks: Long Short-Term
Memory, Gated Recurrent Unit, and their Bidirectional architectures, i.e.,
Bidirectional-LSTM and Bidirectional-GRU. Extensive experiments were conducted
with a real-world multivariate mobility dataset, which we published openly
along with this paper. As shown in the results, differentially private deep
learning models trained under gradient or input perturbation achieve nearly the
same performance as non-private deep learning models, with loss in performance
varying between $0.57\%$ to $2.8\%$. The contribution of this paper is
significant for those involved in urban planning and decision-making, providing
a solution to the human mobility multivariate forecast problem through
differentially private deep learning models.


title:
Anisotropic suppression of hyperuniformity of elastic systems in media
  with planar disorder

abstract:
  Disordered hyperuniform materials with vanishing long-wavelength density
fluctuations are attracting attention due to their unique physical properties.
In these systems, the large-scale density fluctuations are strongly suppressed
as in a perfect crystal, even though the system can be disordered like a
liquid. Yet, hyperuniformity can be affected by the different types of quenched
disorder unavoidably present in the host medium where constituents are
nucleated. Here, we use vortex matter in superconductors as a model elastic
system to study how planar correlated disorder impacts the otherwise
hyperuniform structure nucleated in samples with weak point disorder. Planes of
defects suppress hyperuniformity in an anisotropic fashion: While in the
transverse direction to defects the long-wavelength density fluctuations are
non-vanishing, in the longitudinal direction they are smaller and the system
can eventually recover hyperuniformity for sufficiently thick samples. Our
findings stress the need of considering the nature of disorder and
thickness-dependent dimensional crossovers in the search for novel hyperuniform
materials.

categories: cond-mat.supr-con cond-mat.mtrl-sci cond-mat.soft physics.comp-ph


title:
On the combinatorial and rank properties of certain subsemigroups of
  full contractions of a finite chain

abstract:
  Let $[n]=\{1,2,\ldots,n\}$ be a finite chain and let $\mathcal{CT}_{n}$ be
the semigroup of full contractions on $[n]$. Denote $\mathcal{ORCT}_{n}$ and
$\mathcal{OCT}_{n}$ to be the subsemigroup of order preserving or reversing and
the subsemigroup of order preserving full contractions, respectively. It was
shown in [17] that the collection of all regular elements (denoted by,
Reg$(\mathcal{ORCT}_{n})$ and Reg$(\mathcal{OCT}_{n}$), respectively) and the
collection of all idempotent elements (denoted by E$(\mathcal{ORCT}_{n})$ and
E$(\mathcal{OCT}_{n}$), respectively) of the subsemigroups $\mathcal{ORCT}_{n}$
and $\mathcal{OCT}_{n}$, respectively are subsemigroups. In this paper, we
study some combinatorial and rank properties of these subsemigroups.


title: A surface constraint approach for solar sail orbits

abstract:
  In this paper, a surface geometric constraint approach is used in designing
the orbits of a solar sail. We solve the solar sail equation of motion by
obtaining a generalized Laplace-Runge-Lenz (LRL) vector with the assumption
that the cone angle is constant throughout the mission. A family of orbit
equation solutions can then be specified by defining a constraint equation that
relates the radial and polar velocities of the spacecraft and is dependent on
the geometry of the surface where the spacecraft is expected to move. The
proposed method is successfully applied in the design of orbits constrained on
cylinders and to displaced non-Keplerian orbits.


title:
ETMS@IITKGP at SemEval-2022 Task 10: Structured Sentiment Analysis Using
  A Generative Approach

abstract:
  Structured Sentiment Analysis (SSA) deals with extracting opinion tuples in a
text, where each tuple (h, e, t, p) consists of h, the holder, who expresses a
sentiment polarity p towards a target t through a sentiment expression e. While
prior works explore graph-based or sequence labeling-based approaches for the
task, we in this paper present a novel unified generative method to solve SSA,
a SemEval2022 shared task. We leverage a BART-based encoder-decoder
architecture and suitably modify it to generate, given a sentence, a sequence
of opinion tuples. Each generated tuple consists of seven integers respectively
representing the indices corresponding to the start and end positions of the
holder, target, and expression spans, followed by the sentiment polarity class
associated between the target and the sentiment expression. We perform rigorous
experiments for both Monolingual and Cross-lingual subtasks, and achieve
competitive Sentiment F1 scores on the leaderboard in both settings.


title: Dynamic data structures for parameterized string problems

abstract:
  We revisit classic string problems considered in the area of parameterized
complexity, and study them through the lens of dynamic data structures. That
is, instead of asking for a static algorithm that solves the given instance
efficiently, our goal is to design a data structure that efficiently maintains
a solution, or reports a lack thereof, upon updates in the instance.
  We first consider the Closest String problem, for which we design randomized
dynamic data structures with amortized update times $d^{\mathcal{O}(d)}$ and
$|\Sigma|^{\mathcal{O}(d)}$, respectively, where $\Sigma$ is the alphabet and
$d$ is the assumed bound on the maximum distance. These are obtained by
combining known static approaches to Closest String with color-coding.
  Next, we note that from a result of Frandsen et al.~[J. ACM'97] one can
easily infer a meta-theorem that provides dynamic data structures for
parameterized string problems with worst-case update time of the form
$\mathcal{O}(\log \log n)$, where $k$ is the parameter in question and $n$ is
the length of the string. We showcase the utility of this meta-theorem by
giving such data structures for problems Disjoint Factors and Edit Distance. We
also give explicit data structures for these problems, with worst-case update
times $\mathcal{O}(k2^{k}\log \log n)$ and $\mathcal{O}(k^2\log \log n)$,
respectively. Finally, we discuss how a lower bound methodology introduced by
Amarilli et al.~[ICALP'21] can be used to show that obtaining update time
$\mathcal{O}(f(k))$ for Disjoint Factors and Edit Distance is unlikely already
for a constant value of the parameter $k$.


title: On Binary Networked Public Goods Game with Altruism

abstract:
  In the classical Binary Networked Public Goods (BNPG) game, a player can
either invest in a public project or decide not to invest. Based on the
decisions of all the players, each player receives a reward as per his/her
utility function. However, classical models of BNPG game do not consider
altruism, which players often exhibit and can significantly affect equilibrium
behavior. Yu et al. [24] extended the classical BNPG game to capture the
altruistic aspect of the players. We, in this paper, first study the problem of
deciding the existence of a Pure Strategy Nash Equilibrium (PSNE) in a BNPG
game with altruism. This problem is already known to be NP-complete. We
complement this hardness result by showing that the problem admits efficient
algorithms when the input network is either a tree or a complete graph. We
further study the Altruistic Network Modification problem, where the task is to
compute if a target strategy profile can be made a PSNE by adding or deleting a
few edges. This problem is also known to be NP-complete. We strengthen this
hardness result by exhibiting intractability results even for trees. A perhaps
surprising finding of our work is that the above problem remains NP-hard even
for bounded degree graphs when the altruism network is undirected, but becomes
polynomial-time solvable when the altruism network is directed. We also show
some results on computing an MSNE and some parameterized complexity results. In
summary, our results show that it is much easier to predict how the players in
a BNPG game will behave compared to how the players in a BNPG game can be made
to behave in a desirable way.


title: A basis for the cohomology of compact models of toric arrangements

abstract:
  In this paper we find monomial bases for the integer cohomology rings of
compact wonderful models of toric arrangements. In the description of the
monomials various combinatorial objects come into play: building sets, nested
sets, and the fan of a suitable toric variety. We provide some examples
computed via a SageMath program and then we focus on the case of the toric
arrangements associated with root systems of type A. Here the combinatorial
description of our basis offers a geometrical point of view on the relation
between some Eulerian statistics on the symmetric group.


title:
The algebraic and geometric classification of nilpotent weakly
  associative and symmetric Leibniz algebras

abstract:
  This paper is devoted to the complete algebraic and geometric classification
of complex $4$-dimensional nilpotent weakly associative, complex
$4$-dimensional symmetric Leibniz algebras, and complex $5$-dimensional
nilpotent symmetric Leibniz algebras. In particular, we proved that the variety
of complex $4$-dimensional symmetric Leibniz algebras has no
Vergne--Grunewald--O'Halloran Property (there is an irreducible component
formed by only nilpotent algebras), but on the other hand, it has Vergne
Property (there are no rigid nilpotent algebras).


title:
MRKL Systems: A modular, neuro-symbolic architecture that combines large
  language models, external knowledge sources and discrete reasoning

abstract:
  Huge language models (LMs) have ushered in a new era for AI, serving as a
gateway to natural-language-based knowledge tasks. Although an essential
element of modern AI, LMs are also inherently limited in a number of ways. We
discuss these limitations and how they can be avoided by adopting a systems
approach. Conceptualizing the challenge as one that involves knowledge and
reasoning in addition to linguistic processing, we define a flexible
architecture with multiple neural models, complemented by discrete knowledge
and reasoning modules. We describe this neuro-symbolic architecture, dubbed the
Modular Reasoning, Knowledge and Language (MRKL, pronounced "miracle") system,
some of the technical challenges in implementing it, and Jurassic-X, AI21 Labs'
MRKL system implementation.


title:
Adaptive Online Optimization with Predictions: Static and Dynamic
  Environments

abstract:
  In the past few years, Online Convex Optimization (OCO) has received notable
attention in the control literature thanks to its flexible real-time nature and
powerful performance guarantees. In this paper, we propose new step-size rules
and OCO algorithms that simultaneously exploit gradient predictions, function
predictions and dynamics, features particularly pertinent to control
applications. The proposed algorithms enjoy static and dynamic regret bounds in
terms of the dynamics of the reference action sequence, gradient prediction
error and function prediction error, which are generalizations of known
regularity measures from the literature. We present results for both convex and
strongly convex costs. We validate the performance of the proposed algorithms
in a trajectory tracking case study, as well as portfolio optimization using
real-world datasets.


title:
Molecular Identification with Atomic Force Microscopy and Conditional
  Generative Adversarial Networks

abstract:
  Frequency modulation (FM) Atomic Force Microscopy (AFM) with metal tips
functionalized with a CO molecule at the tip apex has provided access to the
internal structure of molecules with totally unprecedented resolution. We
propose a model to extract the chemical information from those AFM images in
order to achieve a complete identification of the imaged molecule. Our
Conditional Generative Adversarial Network (CGAN) converts a stack of AFM
images at various tip-sample distances into a ball-and-stick depiction, where
balls of different color and size represent the chemical species and sticks
represent the bonds, providing complete information on the structure and
chemical composition. The CGAN has been trained and tested with the QUAM-AFM
data set, that contains simulated AFM images for a collection of 686,000
molecules that include all the chemical species relevant in organic chemistry.
Tests with a large set of theoretical images and few experimental examples
demonstrate the accuracy and potential of our approach for molecular
identification.


title: Uniform Interpolation in Coalgebraic Modal Logic

abstract:
  A logic has uniform interpolation if its formulas can be projected down to
given subsignatures, preserving all logical consequences that do not mention
the removed symbols; the weaker property of (Craig) interpolation allows the
projected formula -- the interpolant -- to be different for each logical
consequence of the original formula. These properties are of importance, e.g.,
in the modularization of logical theories. We study interpolation in the
context of coalgebraic modal logics, i.e. modal logics axiomatized in rank 1,
restricting for clarity to the case with finitely many modalities. Examples of
such logics include the modal logics K and KD, neighbourhood logic and its
monotone variant, finite-monoid-weighted logics, and coalition logic. We
introduce a notion of one-step (uniform) interpolation, which refers only to a
restricted logic without nesting of modalities, and show that a coalgebraic
modal logic has uniform interpolation if it has one-step interpolation.
Moreover, we identify preservation of finite surjective weak pullbacks as a
sufficient, and in the monotone case necessary, condition for one-step
interpolation. We thus prove or reprove uniform interpolation for most of the
examples listed above.


title:
Molecular Identification from AFM images using the IUPAC Nomenclature
  and Attribute Multimodal Recurrent Neural Networks

abstract:
  Despite being the main tool to visualize molecules at the atomic scale, AFM
with CO-functionalized metal tips is unable to chemically identify the observed
molecules. Here we present a strategy to address this challenging task using
deep learning techniques. Instead of identifying a finite number of molecules
following a traditional classification approach, we define the molecular
identification as an image captioning problem. We design an architecture,
composed of two multimodal recurrent neural networks, capable of identifying
the structure and composition of an unknown molecule using a 3D-AFM image stack
as input. The neural network is trained to provide the name of each molecule
according to the IUPAC nomenclature rules. To train and test this algorithm we
use the novel QUAM-AFM dataset, which contains almost 700,000 molecules and 165
million AFM images. The accuracy of the predictions is remarkable, achieving a
high score quantified by the cumulative BLEU 4-gram, a common metric in
language recognition studies.


title: On priority in multi-issue bankruptcy problems with crossed claims

abstract:
  In this paper, we analyze the problem of how to adapt the concept of priority
to situations where several perfectly divisible resources have to be allocated
among certain set of agents that have exactly one claim which is used for all
resources. In particular, we introduce constrained sequential priority rules
and the constrained random arrival rule, which extend the classical sequential
priority rules and the random arrival rule to these situations. Moreover, we
provide an axiomatic analysis of these rules.


title: The Ludii Game Description Language is Universal

abstract:
  There are several different game description languages (GDLs), each intended
to allow wide ranges of arbitrary games (i.e., general games) to be described
in a single higher-level language than general-purpose programming languages.
Games described in such formats can subsequently be presented as challenges for
automated general game playing agents, which are expected to be capable of
playing any arbitrary game described in such a language without prior knowledge
about the games to be played. The language used by the Ludii general game
system was previously shown to be capable of representing equivalent games for
any arbitrary, finite, deterministic, fully observable extensive-form game. In
this paper, we prove its universality by extending this to include finite
non-deterministic and imperfect-information games.


title:
The use of Data Augmentation as a technique for improving neural network
  accuracy in detecting fake news about COVID-19

abstract:
  This paper aims to present how the application of Natural Language Processing
(NLP) and data augmentation techniques can improve the performance of a neural
network for better detection of fake news in the Portuguese language. Fake news
is one of the main controversies during the growth of the internet in the last
decade. Verifying what is fact and what is false has proven to be a difficult
task, while the dissemination of false news is much faster, which leads to the
need for the creation of tools that, automated, assist in the process of
verification of what is fact and what is false. In order to bring a solution,
an experiment was developed with neural network using news, real and fake,
which were never seen by artificial intelligence (AI). There was a significant
performance in the news classification after the application of the mentioned
techniques.


title: Quantum Groups and Asymptotic Symmetries

abstract:
  This thesis is devoted to the study of Lie bialgebra and Hopf algebra
structures related to certain versions of non-commutative geometry constructed
on infinite-dimensional Lie algebras that arise in the context of asymptotic
symmetries of spacetime. We prove a number of theorems about cohomology groups
that aid the classification of the Lie bialgebras and explicitly construct and
analyze selected Hopf algebras. Particularly interesting behavior was found by
studying the contraction limit of spacetimes with cosmological constant and the
inclusion of central charges on the level of Lie bialgebras and Hopf algebras.
Phenomenological consequences, like deformed in-vacuo dispersion relations,
known from the study of $\kappa$-Poincar\'e quantum groups, are investigated.
Furthermore, we examine how a new proposal in the context of the black hole
information loss paradox and counterarguments against it are affected.


title: Cloud formation in Exoplanetary Atmospheres

abstract:
  This invited review for young researchers presents key ideas on cloud
formation as key part for virtual laboratories for exoplanet atmospheres. The
basic concepts are presented, followed by utilising a time-scale analysis to
disentangle process hierarchies. The kinetic approach to cloud formation
modelling is described in some detail to allow the discussion of cloud
structures as prerequisite for future extrasolar weather forecasts.

categories: astro-ph.EP astro-ph.SR physics.comp-ph physics.space-ph


title: Quantum-inspired algorithm for truncated total least squares solution

abstract:
  Total least squares (TLS) methods have been widely used in data fitting.
Compared with the least squares method, for TLS problem we takes into account
not only the observation errors, but also the errors in the measurement matrix.
This is more realistic in practical applications. For the large-scale discrete
ill-posed problem $Ax \approx b$, we introduce the quantum-inspired techniques
to approximate the truncated total least squares (TTLS) solution. We analyze
the accuracy of the quantum-inspired truncated total least squares algorithm
and perform numerical experiments to demonstrate the efficiency of our method.


title: An Analysis of the Features Considerable for NFT Recommendations

abstract:
  This research explores the methods that NFTs can be recommended to people who
interact with NFT-marketplaces to explore NFTs of preference and similarity to
what they have been searching for. While exploring past methods that can be
adopted for recommendations, the use of NFT traits for recommendations has been
explored. The outcome of the research highlights the necessity of using
multiple Recommender Systems to present the user with the best possible NFTs
when interacting with decentralized systems.


title: Metzler/Zeta Correspondence

abstract:
  We present an explicit formula for the determinant on the Metzler matrix of a
digraph $D$. Furthermore, we introduce a walk-type zeta function with respect
to this Metzler matrix of the symmetric digraph of a finite torus, and express
its limit formula by using the integral expression.


title:
Ringing the universe with cosmic emptiness: void properties through a
  combined analysis of stacked weak gravitational and Doppler lensing

abstract:
  An essential aspect of cosmic voids is that these underdense regions provide
complementary information about the properties of our Universe. Unlike dense
regions, voids are avoided by matter and are less contaminated by baryonic
processes. The first step to understanding the properties of cosmic voids is to
correctly infer their mass profiles. In the literature, various techniques have
been implemented. In this paper, we review them and implement a new technique
that is based on Doppler lensing. We use a relativistic $N$-body code,
\textsc{Gevolution}, to generate cosmological mass perturbations and implement
a three-dimensional ray-tracing technique, which follows the evolution of a
ray-bundles. We focus on the various properties of cosmic voids (e.g. void size
function, 2-point correlation function, and the density profile of voids), and
compare the results with their universal trends. We show that when weak-lensing
is combined with the Doppler lensing we obtain even tighter constraints than
weak-lensing alone. We also obtain better agreement between density profiles
within central parts of voids inferred from lensing and density profiles
inferred from halo tracers. The implication of the result relevant to the
ongoing and prospective low-redshift spectroscopic surveys is briefly
discussed.


title:
Training High-Performance Low-Latency Spiking Neural Networks by
  Differentiation on Spike Representation

abstract:
  Spiking Neural Network (SNN) is a promising energy-efficient AI model when
implemented on neuromorphic hardware. However, it is a challenge to efficiently
train SNNs due to their non-differentiability. Most existing methods either
suffer from high latency (i.e., long simulation time steps), or cannot achieve
as high performance as Artificial Neural Networks (ANNs). In this paper, we
propose the Differentiation on Spike Representation (DSR) method, which could
achieve high performance that is competitive to ANNs yet with low latency.
First, we encode the spike trains into spike representation using (weighted)
firing rate coding. Based on the spike representation, we systematically derive
that the spiking dynamics with common neural models can be represented as some
sub-differentiable mapping. With this viewpoint, our proposed DSR method trains
SNNs through gradients of the mapping and avoids the common
non-differentiability problem in SNN training. Then we analyze the error when
representing the specific mapping with the forward computation of the SNN. To
reduce such error, we propose to train the spike threshold in each layer, and
to introduce a new hyperparameter for the neural models. With these components,
the DSR method can achieve state-of-the-art SNN performance with low latency on
both static and neuromorphic datasets, including CIFAR-10, CIFAR-100, ImageNet,
and DVS-CIFAR10.


title:
Controller Hardware-in-the-loop (C-HIL) Testing of Decentralized EV-Grid
  Integration

abstract:
  Present grid infrastructure is unprepared for the wide-scale integration of
electric vehicles (EVs). Real-time grid simulation and hardware testing are
necessary for the fast and accurate development of EV charging control
strategies that are applicable in the field to mitigate their adverse effects.
To help facilitate this goal, in this study, we develop a controller
verification testbed using a baseline bidirectional AC/DC converter, commonly
used in on-board EV chargers, within a hardware-in-the-loop (HIL) test system.
The converter runs real-time on a very-fast time scale and integrates into an
external grid simulator. We utilize the strength of the HIL device in
simulating power electronics while simultaneously realizing a complex
distribution grid operation in real-time. The whole system holistically
provides an opportunity to see the implementation benefits of a decentralized
charging algorithm on the voltage stability of the distribution grid. The study
presents a step-by-step approach to developing and testing controllers,
providing an essential contribution in the field demonstration of decentralized
EV charger control strategies.


title: A Lojasiewicz Inequality in Hypocomplex Structures of $\mathbb{R}^2$

abstract:
  For a real analytic complex vector field $L$ in an open set of
$\mathbb{R}^2$, with local first integrals that are open maps, we attach a
number $\mu \ge 1$ (obtained through Lojasiewicz inequalities) and show that
the equation $Lu=f$ has bounded solutions when $f\in L^p$ with $p>1+\mu$. We
also establish a similarity principle between the bounded solutions of the
equation $Lu=Au+B\overline{u}$ (with $A,B\in L^p$) and holomorphic functions.


title:
The use of Semantic Technologies in Computer Science Curriculum: A
  Systematic Review

abstract:
  Semantic technologies are evolving and being applied in several research
areas, including the education domain. This paper aims to present the results
of a systematic review carried out to provide an overview of the application of
Semantic technologies in the context of the Computer Science curriculum and
discuss the limitations in this field whilst offering insights for future
research. In total, 4,510 studies were reviewed, and 37 were analysed and
reported. As a result, while there has been increasing use of semantic
technologies to develop Computer Science curricula in recent years, the
alignment of ontologies and accurate curricula assessment appears to be the
most significant limitations to the widespread adoption of such technologies.


title: Dataset-free Deep learning Method for Low-Dose CT Image Reconstruction

abstract:
  Low-dose CT (LDCT) imaging attracted a considerable interest for the
reduction of the object's exposure to X-ray radiation. In recent years,
supervised deep learning has been extensively studied for LDCT image
reconstruction, which trains a network over a dataset containing many pairs of
normal-dose and low-dose images. However, the challenge on collecting many such
pairs in the clinical setup limits the application of such
supervised-learning-based methods for LDCT image reconstruction in practice.
Aiming at addressing the challenges raised by the collection of training
dataset, this paper proposed a unsupervised deep learning method for LDCT image
reconstruction, which does not require any external training data. The proposed
method is built on a re-parametrization technique for Bayesian inference via
deep network with random weights, combined with additional total variational
(TV) regularization. The experiments show that the proposed method noticeably
outperforms existing dataset-free image reconstruction methods on the test
data.


title: Quadrature formulas for Bessel polynomials

abstract:
  A quadrature formula is a formula computing a definite integration at finite
points. Sawa and Uchida proved existence and non-existence of certain rational
quadrature formulas for the weight function of certain classical orthogonal
polynomials. In this article, we extend the work of Sawa and Uchida to the
weight function of the Bessel polynomials. In the proofs, we use the
Riesz--Shohat theorem and Newton polygons. Proofs of some results are reduced
to determining the set of rational points on an elliptic curve.


title: Conceptualizing Treatment Leakage in Text-based Causal Inference

abstract:
  Causal inference methods that control for text-based confounders are becoming
increasingly important in the social sciences and other disciplines where text
is readily available. However, these methods rely on a critical assumption that
there is no treatment leakage: that is, the text only contains information
about the confounder and no information about treatment assignment. When this
assumption does not hold, methods that control for text to adjust for
confounders face the problem of post-treatment (collider) bias. However, the
assumption that there is no treatment leakage may be unrealistic in real-world
situations involving text, as human language is rich and flexible. Language
appearing in a public policy document or health records may refer to the future
and the past simultaneously, and thereby reveal information about the treatment
assignment.
  In this article, we define the treatment-leakage problem, and discuss the
identification as well as the estimation challenges it raises. Second, we
delineate the conditions under which leakage can be addressed by removing the
treatment-related signal from the text in a pre-processing step we define as
text distillation. Lastly, using simulation, we show how treatment leakage
introduces a bias in estimates of the average treatment effect (ATE) and how
text distillation can mitigate this bias.


title: Categorical Semantics for Feynman Diagrams

abstract:
  We introduce a novel compositional description of Feynman diagrams, with
well-defined categorical semantics as morphisms in a dagger-compact category.
Our chosen setting is suitable for infinite-dimensional diagrammatic reasoning,
generalising the ZX calculus and other algebraic gadgets familiar to the
categorical quantum theory community.
  The Feynman diagrams we define look very similar to their traditional
counterparts, but are more general: instead of depicting scattering amplitude,
they embody the linear maps from which the amplitudes themselves are computed,
for any given initial and final particle states. This shift in perspective
reflects into a formal transition from the syntactic, graph-theoretic
compositionality of traditional Feynman diagrams to a semantic,
categorical-diagrammatic compositionality.
  Because we work in a concrete categorical setting -- powered by non-standard
analysis -- we are able to take direct advantage of complex additive structure
in our description. This makes it possible to derive a particularly compelling
characterisation for the sequential composition of categorical Feynman
diagrams, which automatically results in the superposition of all possible
graph-theoretic combinations of the individual diagrams themselves.


title: Shape Change and Control of Pressure-based Soft Agents

abstract:
  Biological agents possess bodies that are mostly of soft tissues. Researchers
have resorted to soft bodies to investigate Artificial Life (ALife)-related
questions; similarly, a new era of soft-bodied robots has just begun.
Nevertheless, because of their infinite degrees of freedom, soft bodies pose
unique challenges in terms of simulation, control, and optimization. Here we
propose a novel soft-bodied agents formalism, namely Pressure-based Soft Agents
(PSAs): they are bodies of gas enveloped by a chain of springs and masses, with
pressure pushing on the masses from inside the body. Pressure endows the agents
with structure, while springs and masses simulate softness and allow the agents
to assume a large gamut of shapes. Actuation takes place by changing the length
of springs or modulating global pressure. We optimize the controller of PSAs
for a locomotion task on hilly terrain and an escape task from a cage; the
latter is particularly suitable for soft-bodied agents, as it requires the
agent to contort itself to squeeze through a small aperture. Our results
suggest that PSAs are indeed effective at those tasks and that controlling
pressure is fundamental for shape-changing. Looking forward, we envision PSAs
to play a role in the modeling of soft-bodied agents, including soft robots and
biological cells. Videos of evolved agents are available at
https://pressuresoftagents.github.io.


title:
QCD at finite temperature and density within the fRG approach: An
  overview

abstract:
  In this paper we present an overview on recent progress in studies of QCD at
finite temperature and densities within the functional renormalization group
(fRG) approach. The fRG is a nonperturbative continuum field approach, in which
quantum, thermal and density fluctuations are integrated in successively with
the evolution of the renormalization group (RG) scale. The fRG results for the
QCD phase structure and the location of the critical end point (CEP), the QCD
equation of state (EoS), the magnetic EoS, baryon number fluctuations
confronted with recent experimental measurements, various critical exponents,
spectral functions in the critical region, the dynamical critical exponent,
etc., are presented. Recent estimates of the location of the CEP from
first-principle QCD calculations within fRG and Dyson-Schwinger Equations,
which passes through lattice benchmark tests at small baryon chemical
potentials, converge in a rather small region at baryon chemical potentials of
about 600 MeV. A region of inhomogeneous instability indicated by a negative
wave function renormalization is found with $\mu_B\gtrsim 420$ MeV. It is found
that the non-monotonic dependence of the kurtosis of the net-proton number
distributions on the beam collision energy observed in experiments, could arise
from the increasingly sharp crossover in the regime of low collision energy.


title:
The orientation of Jesuit churches in the Chiquitos missions of eastern
  Bolivia

abstract:
  The Jesuit missions in South America were an important and unique advance in
Christian evangelisation on the continent until the expulsion of the Order in
1767. Although the history and cultural aspects of these missions and their
most iconic buildings have been extensively studied, the archaeoastronomy of
the Guaran\'i peoples of the Province of Paraquaria (Province of Paraguay) has
only been recently considered, with the existing studies focusing primarily on
the orientation of their churches. The paper presented here, which is the first
archaeoastronomical study of the Jesuit missions of Chiquitos in eastern
Bolivia, is an attempt to continue and complement the previous
archaeoastronomical studies of the region. The methodologies employed involved
the analysis of the Jesuit churches that currently exist in this region,
namely, the on-site measurements of the orientations of eight churches
currently standing and the ruins of a ninth church of which only a
free-standing bell tower and parts of the side walls remain preserved. The
orientation measurements of a tenth church, which we were unable to visit, were
determined via the use of satellite maps. The landscape surrounding these
churches was then examined in detail and furthermore, a detailed cultural and
historical study of the characteristics of the villages where the churches are
located was carried out. Our results show that, unlike the churches of the
Province of Paraquaria where meridian orientations in the north-south direction
stand out, half of the studied churches have shown potential canonical
orientations that seem to be aligned to solar phenomena, with three exhibiting
precise equinoctial orientation. We propose reasons for these orientations,
including the possible relevance of illumination effects on significant
internal elements within the churches - effects that were generally sought in
Baroque church architecture.


title: Reward Systems for Trustworthy Medical Federated Learning

abstract:
  Federated learning (FL) has received high interest from researchers and
practitioners to train machine learning (ML) models for healthcare. Ensuring
the trustworthiness of these models is essential. Especially bias, defined as a
disparity in the model's predictive performance across different subgroups, may
cause unfairness against specific subgroups, which is an undesired phenomenon
for trustworthy ML models. In this research, we address the question to which
extent bias occurs in medical FL and how to prevent excessive bias through
reward systems. We first evaluate how to measure the contributions of
institutions toward predictive performance and bias in cross-silo medical FL
with a Shapley value approximation method. In a second step, we design
different reward systems incentivizing contributions toward high predictive
performance or low bias. We then propose a combined reward system that
incentivizes contributions toward both. We evaluate our work using multiple
medical chest X-ray datasets focusing on patient subgroups defined by patient
sex and age. Our results show that we can successfully measure contributions
toward bias, and an integrated reward system successfully incentivizes
contributions toward a well-performing model with low bias. While the
partitioning of scans only slightly influences the overall bias, institutions
with data predominantly from one subgroup introduce a favorable bias for this
subgroup. Our results indicate that reward systems, which focus on predictive
performance only, can transfer model bias against patients to an institutional
level. Our work helps researchers and practitioners design reward systems for
FL with well-aligned incentives for trustworthy ML.


title:
The early stage of the interaction between a planar shock and a
  cylindrical droplet considering cavitation effects: theoretical analysis and
  numerical simulation

abstract:
  The interaction between planar shock waves and droplets, involved the
evolution of high transient unsteady wave structures and the induced cavitation
process, occurs widely in nature and industry. In this paper, a combination of
theoretical analysis and high-resolution numerical simulation is employed to
study the inherent characteristics of the interaction. A multi-component
two-phase compressible flow model, coupled with the phase transition procedure,
is used to capture the spatiotemporal evolution of wave structures and
cavitation behaviours, including the inception, growth and collapse of
cavitation. The ray analysis method is appended to the interaction, and the
evolution of wave structures are characterized by the motion of a series of
rays, whose emission angle is correlated to a dimensionless wave speed, the
ratio of the transmitted shock velocity and incident shock velocity. Under the
influence of cylindrical droplet curvature, those rays focus inside the
droplet. The present study theoretically predicts the focusing position for the
first time, determined by the dimensionless wave speed, and the theoretical
analysis is well consistent with numerical results. Due to the significant
difference in the properties between the upper and lower branches of the second
reflected wave, a high-transient pressure region is observed and its position
is clarified. Numerical results show that if the incident shock wave intensity
is high enough, the focusing zone of the reflected expansion wave can be
identified as a cavity inside the droplet. Furthermore, the cavitation zone is
enlarged, and the stronger collapsing waves are induced by increasing the
incident shock wave intensity.


title: A symmetry of silting quivers

abstract:
  We investigate symmetry of the silting quiver of a given algebra which is
induced by an anti-automorphism of the algebra. In particular, one shows that
if there is a primitive idempotent fixed by the anti-automorphism, then the
2-silting quiver ($=$ the support $\tau$-tilting quiver) has a bisection.
Consequently, in the case, we obtain that the cardinality of the 2-silting
quiver is double.


title: A Survey of Decentralized Online Learning

abstract:
  Decentralized online learning (DOL) has been increasingly researched in the
last decade, mostly motivated by its wide applications in sensor networks,
commercial buildings, robotics (e.g., decentralized target tracking and
formation control), smart grids, deep learning, and so forth. In this problem,
there are a network of agents who may be cooperative (i.e., decentralized
online optimization) or noncooperative (i.e., online game) through local
information exchanges, and the local cost function of each agent is often
time-varying in dynamic and even adversarial environments. At each time, a
decision must be made by each agent based on historical information at hand
without knowing future information on cost functions. Although this problem has
been extensively studied in the last decade, a comprehensive survey is lacking.
Therefore, this paper provides a thorough overview of DOL from the perspective
of problem settings, communication, computation, and performances. In addition,
some potential future directions are also discussed in details.


title: Voting in Two-Crossing Elections

abstract:
  We introduce two-crossing elections as a generalization of single-crossing
elections, showing a number of new results. First, we show that two-crossing
elections can be recognized in polynomial time, by reduction to the
well-studied consecutive ones problem. We also conjecture that recognizing
$k$-crossing elections is NP-complete in general, providing evidence by
relating to a problem similar to consecutive ones proven to be hard in the
literature. Single-crossing elections exhibit a transitive majority relation,
from which many important results follow. On the other hand, we show that the
classical Debord-McGarvey theorem can still be proven two-crossing, implying
that any weighted majority tournament is inducible by a two-crossing election.
This shows that many voting rules are NP-hard under two-crossing elections,
including Kemeny and Slater. This is in contrast to the single-crossing case
and outlines an important complexity boundary between single- and two-crossing.
Subsequently, we show that for two-crossing elections the Young scores of all
candidates can be computed in polynomial time, by formulating a totally
unimodular linear program. Finally, we consider the Chamberlin-Courant rule
with arbitrary disutilities and show that a winning committee can be computed
in polynomial time, using an approach based on dynamic programming.


title: Formal Languages via Theories over Strings

abstract:
  We investigate the properties of formal languages expressible in terms of
formulas over quantifier-free theories of word equations, arithmetic over
length constraints, and language membership predicates for the classes of
regular, visibly pushdown, and deterministic context-free languages. In total,
we consider 20 distinct theories and decidability questions for problems such
as emptiness and universality for formal languages over them. First, we discuss
their relative expressive power and observe a rough division into two
hierarchies based on whether or not word equations are present. Second, we
consider the decidability status of several important decision problems, such
as emptiness and universality. Note that the emptiness problem is equivalent to
the satisfiability problem over the corresponding theory. Third, we consider
the problem of whether a language in one theory is expressible in another and
show several negative results in which this problem is undecidable. These
results are particularly relevant in the context of normal forms in both
practical and theoretical aspects of string solving.


title: None Class Ranking Loss for Document-Level Relation Extraction

abstract:
  Document-level relation extraction (RE) aims at extracting relations among
entities expressed across multiple sentences, which can be viewed as a
multi-label classification problem. In a typical document, most entity pairs do
not express any pre-defined relation and are labeled as "none" or "no
relation". For good document-level RE performance, it is crucial to distinguish
such none class instances (entity pairs) from those of pre-defined classes
(relations). However, most existing methods only estimate the probability of
pre-defined relations independently without considering the probability of "no
relation". This ignores the context of entity pairs and the label correlations
between the none class and pre-defined classes, leading to sub-optimal
predictions. To address this problem, we propose a new multi-label loss that
encourages large margins of label confidence scores between each pre-defined
class and the none class, which enables captured label correlations and
context-dependent thresholding for label prediction. To gain further robustness
against positive-negative imbalance and mislabeled data that could appear in
real-world RE datasets, we propose a margin regularization and a margin
shifting technique. Experimental results demonstrate that our method
significantly outperforms existing multi-label losses for document-level RE and
works well in other multi-label tasks such as emotion classification when none
class instances are available for training.


title: Ridgeless Regression with Random Features

abstract:
  Recent theoretical studies illustrated that kernel ridgeless regression can
guarantee good generalization ability without an explicit regularization. In
this paper, we investigate the statistical properties of ridgeless regression
with random features and stochastic gradient descent. We explore the effect of
factors in the stochastic gradient and random features, respectively.
Specifically, random features error exhibits the double-descent curve.
Motivated by the theoretical findings, we propose a tunable kernel algorithm
that optimizes the spectral density of kernel during training. Our work bridges
the interpolation theory and practical algorithm.


title:
Investigating Possible Existence of Hyper-Heavy Nuclei in Neutron Star
  Environment

abstract:
  The synthesis of hyper-heavy elements is investigated under conditions
simulating neutron star environment. The Constrained Molecular Dynamics (CoMD)
approach is used to simulate low energy collisions of extremely n-rich nuclei.
A new type of the fusion barrier due to a "neutron wind" is observed when the
effect of neutron star environment (screening of Coulomb interaction) is
introduced implicitly. When introducing also a background of surrounding
nuclei, the nuclear fusion becomes possible down to temperatures of 10$^{8}$ K
and synthesis of extremely heavy and n-rich nuclei appears feasible. A possible
existence of hyper-heavy nuclei in a neutron star environment could provide a
mechanism of extra coherent neutrino scattering or an additional mechanism,
resulting in X-ray burst or a gravitational wave signal and, thus, becoming
another crucial process adding new information to the suggested models on
neutron star evolution.


title: Nearest Neighbor Knowledge Distillation for Neural Machine Translation

abstract:
  k-nearest-neighbor machine translation (NN-MT), proposed by Khandelwal et al.
(2021), has achieved many state-of-the-art results in machine translation
tasks. Although effective, NN-MT requires conducting NN searches through the
large datastore for each decoding step during inference, prohibitively
increasing the decoding cost and thus leading to the difficulty for the
deployment in real-world applications. In this paper, we propose to move the
time-consuming NN search forward to the preprocessing phase, and then introduce
Nearest Neighbor Knowledge Distillation (NN-KD) that trains the base NMT model
to directly learn the knowledge of NN. Distilling knowledge retrieved by NN can
encourage the NMT model to take more reasonable target tokens into
consideration, thus addressing the overcorrection problem. Extensive
experimental results show that, the proposed method achieves consistent
improvement over the state-of-the-art baselines including NN-MT, while
maintaining the same training and decoding speed as the standard NMT model.


title: On a combinatorial identity of Chaundy and Bullard

abstract:
  We give two new proofs of the Chaundy-Bullard formula $$ (1-x)^{n+1}
\sum_{k=0}^m {n+k\choose k} x^k +x^{m+1}\sum_{k=0}^n {m+k\choose k} (1-x)^k=1
$$ and we prove the "twin formula" $$ \frac{ (1-x)^{(n+1)}}{(n+1)!}
\sum_{k=0}^m \frac{n+1}{n+k+1} \frac{ x^{(k)}}{k!} + \frac{ x^{(m+1)}}{(m+1)!}
\sum_{k=0}^n \frac{m+1}{m+k+1} \frac{ (1-x)^{(k)}}{k!}=1, $$ where $z^{(n)}$
denotes the rising factorial. Moreover, we present identities involving the
incomplete beta function and a certain combinatorial sum.


title:
Boost decoding performance of finite geometry LDPC codes with deep
  learning tactics

abstract:
  It was known a standard min-sum decoder can be unrolled as a neural network
after weighting each edges. We adopt the similar decoding framework to seek a
low-complexity and high-performance decoder for a class of finite geometry LDPC
codes in short and moderate block lengths. It is elaborated on how to generate
high-quality training data effectively, and the strong link is illustrated
between training loss and the bit error rate of a neural decoder after tracing
the evolution curves. Considering there exists a potential conflict between the
neural networks and the error-correction decoders in terms of their objectives,
the necessity of restraining the number of trainable parameters to ensure
training convergence or reduce decoding complexity is highlighted.
Consequently, for the referred LDPC codes, their rigorous algebraic structure
promotes the feasibility of cutting down the number of trainable parameters
even to only one, whereas incurring marginal performance loss in the
simulation.


title: Horizontal decompositions, I

abstract:
  We show that every smooth, closed, orientable 4-manifold X admits a special
kind of handlebody decomposition that we call horizontal. We classify the
closed 4-manifolds with the simplest horizontal decompositions and we describe
all such decompositions of CP^2, showing that they give rise to infinitely many
of the known embeddings of rational homology balls in the complex projective
plane.


title: Fourfolds of Weil type and the spinor map

abstract:
  Recent papers by Markman and O'Grady give, besides their main results on the
Hodge conjecture and on hyperkaehler varieties, surprising and explicit
descriptions of families of abelian fourfolds of Weil type with trivial
discriminant. They also provide a new perspective on the well-known fact that
these abelian varieties are Kuga Satake varieties for certain weight two Hodge
structures of rank six.
  In this paper we give a pedestrian introduction to these results. The spinor
map, which is defined using a half-spin representation of SO(8), is used
intensively. For simplicity, we use basic representation theory and we avoid
the use of triality.


title:
Dynamic Programming in Rank Space: Scaling Structured Inference with
  Low-Rank HMMs and PCFGs

abstract:
  Hidden Markov Models (HMMs) and Probabilistic Context-Free Grammars (PCFGs)
are widely used structured models, both of which can be represented as factor
graph grammars (FGGs), a powerful formalism capable of describing a wide range
of models. Recent research found it beneficial to use large state spaces for
HMMs and PCFGs. However, inference with large state spaces is computationally
demanding, especially for PCFGs. To tackle this challenge, we leverage tensor
rank decomposition (aka.\ CPD) to decrease inference computational complexities
for a subset of FGGs subsuming HMMs and PCFGs. We apply CPD on the factors of
an FGG and then construct a new FGG defined in the rank space. Inference with
the new FGG produces the same result but has a lower time complexity when the
rank size is smaller than the state size. We conduct experiments on HMM
language modeling and unsupervised PCFG parsing, showing better performance
than previous work. Our code is publicly available at
\url{https://github.com/VPeterV/RankSpace-Models}.


title: Bilingual End-to-End ASR with Byte-Level Subwords

abstract:
  In this paper, we investigate how the output representation of an end-to-end
neural network affects multilingual automatic speech recognition (ASR). We
study different representations including character-level, byte-level, byte
pair encoding (BPE), and byte-level byte pair encoding (BBPE) representations,
and analyze their strengths and weaknesses. We focus on developing a single
end-to-end model to support utterance-based bilingual ASR, where speakers do
not alternate between two languages in a single utterance but may change
languages across utterances. We conduct our experiments on English and Mandarin
dictation tasks, and we find that BBPE with penalty schemes can improve
utterance-based bilingual ASR performance by 2% to 5% relative even with
smaller number of outputs and fewer parameters. We conclude with analysis that
indicates directions for further improving multilingual ASR.


title: Pointed semibiproducts of monoids

abstract:
  Semibiproducts of monoids are introduced here as a common generalization to
biproducts (of abelian groups) and to semidirect products (of groups) for
exploring a wide class of monoid extensions. More generally, abstract
semibiproducts exist in any concrete category over sets in which map addition
is meaningful thus reinterpreting Mac Lane's relative biproducts. In the
pointed case they give rise to a special class of extensions called
semibiproduct extensions. Not all monoid extensions are semibiproduct
extensions but all group extensions are. A categorical equivalence is
established between the category of pointed semibiproducts of monoids and the
category of pointed monoid action systems, a new category of actions that
emerges from the equivalence. The main difference to classical extension theory
is that semibiproduct extensions are treated in the same way as split
extensions, even though the section map may fail to be a homomorphism. A list
with all the 14 semibiproduct extensions of 2-element monoids is provided.


title: On the speed of uniform convergence in Mercer's theorem

abstract:
  The classical Mercer's theorem claims that a continuous positive definite
kernel $K({\mathbf x}, {\mathbf y})$ on a compact set can be represented as
$\sum_{i=1}^\infty \lambda_i\phi_i({\mathbf x})\phi_i({\mathbf y})$ where
$\{(\lambda_i,\phi_i)\}$ are eigenvalue-eigenvector pairs of the corresponding
integral operator. This infinite representation is known to converge uniformly
to the kernel $K$. We estimate the speed of this convergence in terms of the
decay rate of eigenvalues and demonstrate that for $3m$ times differentiable
kernels the first $N$ terms of the series approximate $K$ as
$\mathcal{O}\big((\sum_{i=N+1}^\infty\lambda_i)^{\frac{m}{m+n}}\big)$ or
$\mathcal{O}\big((\sum_{i=N+1}^\infty\lambda^2_i)^{\frac{m}{2m+n}}\big)$.


title:
Towards the structure of a cubic interaction vertex for massless integer
  higher spin fields

abstract:
  The structure of a cubic Lagrangian vertex is clarified for irreducible
fields of helicities $s_1, s_2, s_3$ in a $d$-dimensional Minkowski space. An
explicit form of the operator $\mathcal{Z}_j$ entering the vertex in a
non-multiplicative way (examined in arXiv:2105.12030[hep-th] for $j=1$) is
obtained. The solution is found within the BRST approach with complete BRST
operators, which contain all constraints corresponding to the conditions that
extract the irreducible fields, including trace operators.


title: Arrowhead and Diamond Diameters

abstract:
  {\em Arrowhead} and {\em diamond} are two hierarchical Cayley graphs defined
on the triangular grid. In their undirected version, they are isomorphic and
merely define two distinct representations of the same graph. This paper gives
the expression of their diameter, in the oriented and non--oriented case. It
also displays the full distribution of antipodals.


title:
Regeneration of branching processes with immigration in varying
  environments

abstract:
  In this paper, we consider certain linear-fractional branching processes with
immigration in varying environments. For $n\ge0,$ let $Z_n$ counts the number
of individuals of the $n$-th generation, which excludes the immigrant which
enters into the system at time $n.$ We call $n$ a regeneration time if $Z_n=0.$
We give first a criterion for the finiteness or infiniteness of the number of
regeneration times. Then, we construct some concrete examples to exhibit the
strange phenomena caused by the so-called varying environments. It may happen
that the process is extinct but there are only finitely many regeneration
times. Also, when there are infinitely many regeneration times, we show that
for each $\varepsilon>0,$ the number of regeneration times in $[0,n]$ is no
more than $(\log n)^{1+\varepsilon}$ as $n\rightarrow\infty.$


title:
Many a little Makes a Mickle: Probing Backscattering Energy Recycling
  for Backscatter Communications

abstract:
  In this paper, we investigate and analyze full-duplex-based backscatter
communications with multiple backscatter devices (BDs). Different from previous
works where only the energy from the energy source is harvested, BDs are also
allowed to harvest energy from previous BDs by recycling the backscattering
energy. Our objective is to maximize the total energy efficiency (EE) of the
system via joint time scheduling, beamforming design, and reflection
coefficient (RC) adjustment while satisfying the constraints on the total time,
the transmit energy consumption, the circuit energy consumption and the
achievable throughput for each BD by taking the causality and the non-linearity
of energy harvesting into account. To deal with this intractable non-convex
problem, we reformulate the problem by utilizing the Dinkelbach's method.
Subsequently, an alternative iterative algorithm is designed to solve it.
Simulation results show that the proposed algorithm achieves a much better EE
than the benchmark algorithms.


title: Understanding Distance Measures Among Elections

abstract:
  Motivated by putting empirical work based on (synthetic) election data on a
more solid mathematical basis, we analyze six distances among elections,
including, e.g., the challenging-to-compute but very precise swap distance and
the distance used to form the so-called map of elections. Among the six, the
latter seems to strike the best balance between its computational complexity
and expressiveness.


title: Gleason's theorem for composite systems

abstract:
  Gleason's theorem [A. Gleason, J. Math. Mech., \textbf{6}, 885 (1957)] is an
important result in the foundations of quantum mechanics, where it justifies
the Born rule as a mathematical consequence of the quantum formalism. Formally,
it presents a key insight into the projective geometry of Hilbert spaces,
showing that finitely additive measures on the projection lattice $\PH$ extend
to positive linear functionals on the algebra of bounded operators $\BH$. Over
many years, and by the effort of various authors, the theorem has been
broadened in its scope from type I to arbitrary von Neumann algebras (without
type $\text{I}_2$ factors). Here, we prove a generalisation of Gleason's
theorem to composite systems. To this end, we strengthen the original result in
two ways: first, we extend its scope to dilations in the sense of Naimark [M.
A. Naimark, C. R. (Dokl.) Acad. Sci. URSS, n. Ser., \textbf{41}, 359 (1943)]
and Stinespring [W. F. Stinespring, Proc. Am. Math. Soc., \textbf{6}, 211
(1955)] and second, we require consistency with respect to dynamical
correspondences on the respective (local) algebras in the composition [E. M.
Alfsen and F. W. Shultz, Commun. Math. Phys., \textbf{194}, 87 (1998)]. We show
that neither of these conditions changes the result in the single system case,
yet both are necessary to obtain a generalisation to bipartite systems.