title:
Inference for Cluster Randomized Experiments with Non-ignorable Cluster
  Sizes

abstract:
  This paper considers the problem of inference in cluster randomized
experiments when cluster sizes are non-ignorable. Here, by a cluster randomized
experiment, we mean one in which treatment is assigned at the level of the
cluster; by non-ignorable cluster sizes we mean that "large" clusters and
"small" clusters may be heterogeneous, and, in particular, the effects of the
treatment may vary across clusters of differing sizes. In order to permit this
sort of flexibility, we consider a sampling framework in which cluster sizes
themselves are random. In this way, our analysis departs from earlier analyses
of cluster randomized experiments in which cluster sizes are treated as
non-random. We distinguish between two different parameters of interest: the
equally-weighted cluster-level average treatment effect, and the size-weighted
cluster-level average treatment effect. For each parameter, we provide methods
for inference in an asymptotic framework where the number of clusters tends to
infinity and treatment is assigned using simple random sampling. We
additionally permit the experimenter to sample only a subset of the units
within each cluster rather than the entire cluster and demonstrate the
implications of such sampling for some commonly used estimators. A small
simulation study shows the practical relevance of our theoretical results.


title:
Hybrid FSO/THz-based Backhaul Network for mmWave Terrestrial
  Communication

abstract:
  In this work, a hybrid free-space optics (FSO)/ teraHertz (THz) based
backhaul network is considered to provide high-data rate reliable communication
to the terrestrial mobile users (MUs) operating at millimeter wave (mmWave)
bands. The FSO link is affected by the atmospheric turbulence and pointing
error impairments which are characterized with Gamma-Gamma and Rayleigh fading,
respectively. At the FSO receiver, both the intensity modulated direct
detection and heterodyne detection techniques are considered. The multi-antenna
THz link suffers from both high path-loss and misalignment error. The THz
channel is characterized with $\alpha-\mu$ distribution and misalignment error
is characterized with Rayleigh fading. To minimize the effect of back-and-forth
switching, soft switching method is introduced at the access point (AP) to
select the signal coming through the hybrid FSO/THz link, and a comparison with
hard switching method is presented. Selective decode-and-forward relaying is
considered at the AP which is forwarding the successfully decoded backhaul
signals to the terrestrial MUs. In this context, we derive closed-form
expressions of the individual link's outage probability, end-to-end (E2E)
outage probability, asymptotic outage probability, ergodic capacity, and
average bit-error-rate of various modulation schemes. Finally, we study the
effect of different parameters such as atmospheric turbulence,
pointing/misalignment errors, link distance, path-loss, fading parameters of
the THz and access links, and number of antennas on the network performance.
Our results indicate that, with a proper switching method, the joint
implementation of FSO/THz links, improves the rate/reliability of the backhaul
links with limited switching overhead.


title:
AutoMLBench: A Comprehensive Experimental Evaluation of Automated
  Machine Learning Frameworks

abstract:
  Nowadays, machine learning is playing a crucial role in harnessing the power
of the massive amounts of data that we are currently producing every day in our
digital world. With the booming demand for machine learning applications, it
has been recognized that the number of knowledgeable data scientists can not
scale with the growing data volumes and application needs in our digital world.
In response to this demand, several automated machine learning (AutoML)
techniques and frameworks have been developed to fill the gap of human
expertise by automating the process of building machine learning pipelines. In
this study, we present a comprehensive evaluation and comparison of the
performance characteristics of six popular AutoML frameworks, namely,
Auto-Weka, AutoSKlearn, TPOT, Recipe, ATM, and SmartML across 100 data sets
from established AutoML benchmark suites. Our experimental evaluation considers
different aspects for its comparison including the performance impact of
several design decisions including time budget, size of search space,
meta-learning, and ensemble construction. The results of our study reveal
various interesting insights that can significantly guide and impact the design
of AutoML frameworks.


title: Sleeping is Superefficient: MIS in Exponentially Better Awake Complexity

abstract:
  Maximal Independent Set (MIS) is one of the central and most well-studied
problems in distributed computing. Even after four decades of intensive
research, the best-known (randomized) MIS algorithms take $O(\log{n})$
worst-case rounds on general graphs (where $n$ is the number of nodes), while
the best-known lower bound is
$\Omega\left(\sqrt{\frac{\log{n}}{\log{\log{n}}}}\right)$ rounds. Breaking past
the $O(\log{n})$ worst-case bound or showing stronger lower bounds have been
longstanding open problems.
  Our main contribution is that we show that MIS can be computed in
(worst-case) awake complexity of $O(\log \log n)$ rounds that is (essentially)
exponentially better compared to the (traditional) round complexity lower bound
of $\Omega\left(\sqrt{\frac{\log{n}}{\log{\log{n}}}}\right)$. Specifically, we
present the following results. (1) We present a randomized distributed (Monte
Carlo) algorithm for MIS that with high probability computes an MIS and has
$O(\log\log{n})$-rounds awake complexity. This algorithm has (traditional) {\em
round complexity} that is $O(poly(n))$. Our bounds hold in the
$CONGEST(O(polylog n))$ model where only $O(polylog n)$ (specifically $O(\log^3
n)$) bits are allowed to be sent per edge per round. (2) We also show that we
can drastically reduce the round complexity at the cost of a slight increase in
awake complexity by presenting a randomized MIS algorithm with $O(\log \log n
\log^* n )$ awake complexity and $O(\log^3 n \log \log n \log^*n)$ round
complexity in the $CONGEST(O(polylog n))$ model.


title: Zero-Shot Program Representation Learning

abstract:
  Learning program representations has been the core prerequisite of code
intelligent tasks such as code search and code clone detection. The
state-of-the-art pre-trained models such as CodeBERT require the availability
of large-scale code corpora. However, gathering training samples can be costly
and infeasible for domain-specific languages such as Solidity for smart
contracts. In this paper, we propose Zecoler, a zero-shot learning approach for
code representations. Zecoler is built upon a pre-trained programming language
model. In order to elicit knowledge from the pre-trained models efficiently,
Zecoler casts the downstream tasks to the same form of pre-training tasks by
inserting trainable prompts into the original input. Then, it employs the
prompt learning technique which optimizes the pre-trained model by merely
adjusting the original input. This enables the representation model to
efficiently fit the scarce task-oriented data while reusing pre-trained
knowledge. We evaluate Zecoler in three code intelligent tasks in two program
languages that have no training samples, namely, Solidity and Go, with model
trained in corpora of common languages such as Java. Experimental results show
that our approach significantly outperforms baseline models in both zero-shot
and few-shot settings.


title: A Predictive Model for Micrometeoroid Damage to Gossamer Structures

abstract:
  A typical inflatable reflector for space application consists of two thin
membranes with a parabolic shape. It is critical to understand the interaction
of the inflatable and the micrometeoroid environment to which it is exposed.
This interaction leads to a series of penetrations of the inflatable membrane
on entrance and exit of the impacting particle, creating a pathway for gas
escape. To increase the fidelity of the damage expected, we examine the
literature for descriptions of micrometeoroid fragmentation and present a
theoretical formulation for the damage caused by an impacting particle to the
entrance and exit membranes. This theory is compared to an initial set of
hyper-velocity tests for micrometeoroid-sized particles on thin film membranes.
We use the results of these tests to produce a predictive model. This model is
applied to estimate the damage rate near the 1 AU location and output
predictions for the effectiveness of a micrometeoroid shield to reduce the
damage on the lenticular and effectively optimize its lifetime. Lastly, we
apply the kinetic theory of gasses to develop expressions for the expenditure
of gas over a specified mission lifetime due to penetrations. Although this
paper examines the specific case of an inflated lenticular protected by extra
membrane layers, our predictive model can be applied for any gossamer structure
composed of polyimide membranes.


title:
Hardware-algorithm collaborative computing with photonic spiking neuron
  chip based on integrated Fabry-P\'erot laser with saturable absorber

abstract:
  Photonic neuromorphic computing has emerged as a promising avenue toward
building a low-latency and energy-efficient non-von-Neuman computing system.
Photonic spiking neural network (PSNN) exploits brain-like spatiotemporal
processing to realize high-performance neuromorphic computing. However, the
nonlinear computation of PSNN remains a significant challenging. Here, we
proposed and fabricated a photonic spiking neuron chip based on an integrated
Fabry-P\'erot laser with a saturable absorber (FP-SA) for the first time. The
nonlinear neuron-like dynamics including temporal integration, threshold and
spike generation, refractory period, and cascadability were experimentally
demonstrated, which offers an indispensable fundamental building block to
construct the PSNN hardware. Furthermore, we proposed time-multiplexed spike
encoding to realize functional PSNN far beyond the hardware integration scale
limit. PSNNs with single/cascaded photonic spiking neurons were experimentally
demonstrated to realize hardware-algorithm collaborative computing, showing
capability in performing classification tasks with supervised learning
algorithm, which paves the way for multi-layer PSNN for solving complex tasks.


title:
Observing Supernova Neutrino Light Curves with Super-Kamiokande. III.
  Extraction of Mass and Radius of Neutron Stars from Synthetic Data

abstract:
  Neutrinos are guaranteed to be observable from the next galactic supernova
(SN). Optical light and gravitational waves are also observable, but may be
difficult to observe if the location of the SN in the galaxy or the details of
the explosion are unsuitable. The key to observing the next supernova is to
first use neutrinos to understand various physical quantities and then link
them to other signals. In this paper, we present Monte Carlo sampling
calculations of neutrino events from galactic supernova explosions observed
with Super-Kamiokande. The analytical solution of neutrino emission, which
represents the long-term evolution of neutrino-light curve from supernovae, is
used as a theoretical template. It gives the event rate and event spectrum
through inverse beta decay interactions with explicit model parameter
dependence. Parameter estimation is performed on these simulated sample data by
fitting least squares using the analytical solution. The results show that the
mass, radius and total energy of a remnant neutron star produced by a SN can be
determined with an accuracy of $\sim 0.1M_\odot$, $\sim 1$ km, and $\sim
10^{51}$ erg, respectively, for a galactic SN at 8 kpc.


title:
Detecting, Tracking and Counting Motorcycle Rider Traffic Violations on
  Unconstrained Roads

abstract:
  In many Asian countries with unconstrained road traffic conditions, driving
violations such as not wearing helmets and triple-riding are a significant
source of fatalities involving motorcycles. Identifying and penalizing such
riders is vital in curbing road accidents and improving citizens' safety. With
this motivation, we propose an approach for detecting, tracking, and counting
motorcycle riding violations in videos taken from a vehicle-mounted dashboard
camera. We employ a curriculum learning-based object detector to better tackle
challenging scenarios such as occlusions. We introduce a novel trapezium-shaped
object boundary representation to increase robustness and tackle the
rider-motorcycle association. We also introduce an amodal regressor that
generates bounding boxes for the occluded riders. Experimental results on a
large-scale unconstrained driving dataset demonstrate the superiority of our
approach compared to existing approaches and other ablative variants.


title:
Dissipation and geometry in nonlinear quantum transports of multiband
  electronic systems

abstract:
  Nonlinear responses in condensed matters attract recent intensive interest
because they provide rich information about the materials and hold the
possibility of being applied in diodes or high-frequency optical devices.
Nonlinear responses are often closely related to the multiband nature of the
system which can be taken into account by the geometric quantities such as the
Berry curvature as shown in the nonlinear Hall effect. Theoretically, the
semi-classical Boltzmann treatment or the reduced density matrix method have
been often employed, in which the effect of dissipation is included through the
relaxation time approximation. In the diagrammatic method, the relaxation is
treated through the imaginary part of the self-energy of the Green function and
the consequent broadening of the spectral function for the integration over the
real frequency. Therefore, the poles of the Green function do not play explicit
pole when there is finite dissipation. In this paper, in stark contrast to this
conventional picture, we show that the poles of the Green function determine
mostly the nonlinear response functions with dissipation, which leads to the
terms with the Fermi distribution function of complex argument and results in
the dissipation-induced geometric term. We elucidate the geometric origin of
the nonreciprocal conductivity, which is related to the Berry curvature
generalized to the higher derivative. Finally, we derive the analytical results
on the geometric terms of the nonlinear conductivities in the type-I and
type-II Weyl Hamiltonian to demonstrate their crucial roles.


title: On the nature of Fast Blue Optical Transients

abstract:
  Short rise times of Fast Blue Optical Transients (FBOTs) require very light
ejected envelopes, $M_{ej} \leq 10^{-1} M_\odot$, much smaller than of a
typical supernova. Short peak times also mean that FBOTs should be
hydrodynamically, not radioactively powered. The detection by Chandra of X-ray
emission in AT2020mrf of $L_X \sim 10^{42} $ erg s$^{-1}$ after 328 days
implies total, overall dominant, X-ray energetics at the Gamma Ray Bursts
(GRBs) level of $\sim 6 \times 10^{49}$ erg. We further develop a model of
Lyutikov & Toonen (2019), whereby FBOTs are the results of a late accretion
induced collapse (AIC) of the product of super-Chandrasekhar double white dwarf
(WD) merger between ONeMg WD and another WD. Small ejecta mass, and the rarity
of FBOTs, result from the competition between mass loss from the merger product
to the wind, and ashes added to the core, on time scale of $\sim 10^3-10^4$
years. FBOTs occur only when the envelope mass before AIC is $\leq 10^{-1}
M_\odot$. FBOTs proper come from central engine-powered radiation-dominated
forward shock as it propagates through ejecta. FBOTs' duration is determined by
the diffusion time of photons produced by the NS-driven forward shock within
the expanding ejecta. All the photons produced by the central source deep
inside the ejecta escape almost simultaneously, producing a short bright event.
The high energy emission is generated at the highly relativistic and highly
magnetized termination shock, qualitatively similar to Pulsar Wind Nebulae. The
X-ray bump observed in AT2020mrf by SRG/eROSITA, predicted by Lyutikov & Toonen
(2019), is coming from the break-out of the engine-powered shock from the
ejecta into the preceding wind. The model requires total energetics of just few
$\times 10^{50}$ ergs, slightly above the observed X-rays. We predict that the
system is hydrogen poor.


title:
Online RIS Configuration Learning for Arbitrary Large Numbers of $1$-Bit
  Phase Resolution Elements

abstract:
  Reinforcement Learning (RL) approaches are lately deployed for orchestrating
wireless communications empowered by Reconfigurable Intelligent Surfaces
(RISs), leveraging their online optimization capabilities. Most commonly, in
RL-based formulations for realistic RISs with low resolution phase-tunable
elements, each configuration is modeled as a distinct reflection action,
resulting to inefficient exploration due to the exponential nature of the
search space. In this paper, we consider RISs with 1-bit phase resolution
elements, and model the action of each of them as a binary vector including the
feasible reflection coefficients. We then introduce two variations of the
well-established Deep Q-Network (DQN) and Deep Deterministic Policy Gradient
(DDPG) agents, aiming for effective exploration of the binary action spaces.
For the case of DQN, we make use of an efficient approximation of the
Q-function, whereas a discretization post-processing step is applied to the
output of DDPG. Our simulation results showcase that the proposed techniques
greatly outperform the baseline in terms of the rate maximization objective,
when large-scale RISs are considered. In addition, when dealing with moderate
scale RIS sizes, where the conventional DQN based on configuration-based action
spaces is feasible, the performance of the latter technique is similar to the
proposed learning approach.


title:
Estimating the potential demand for Demand-Responsive Transport based on
  smartcard transactions

abstract:
  The future of Demand-Responsive Transport (DRT) is investigated in respect to
the potential travelers' demand. The potential demand for the DRT service is
studied based on a database of 63 million records of the public transportation
(PT) trips made in Israel using a smartcard in June, 2019. Our major assumption
is that travelers may prefer a DRT service over conventional PT for making a
non-routine trip that occurs only once a month. The behavioral patterns of PT
users were revealed by clustering their boarding records based on the location
of the boarding stops and the boarding time of day using an extended DBSCAN
algorithm. We make three major discoveries: at least 30 percent of the PT trips
do not belong to any cluster of monthly user activity; conventional
home-work-home commuters are a minority and constitute less than 15 percent of
the drivers; the vast majority of the users make, during the month, both
recurrent and occasional trips. The share of occasional trips is 25 percent for
frequent users who make over 40 trips a month, and as high as 60 percent for
those who board PT up to 10 times a month. We uncover the dependencies of trip
regularity on population group, time of day and land use composition around the
location of trip origin. We conclude that in high-density urban areas,
conventional PT may lose substantial ridership to DRT. The spillover to DRT may
be prevented by improving the level of service and incentivizing conventional
PT users. We discuss using our approach to identify city areas and PT lines
where occasional ridership is common, and user groups that are more likely to
switch from conventional PT to DRT.


title:
Benign Overfitting in Time Series Linear Model with
  Over-Parameterization

abstract:
  The success of large-scale models in recent years has increased the
importance of statistical models with numerous parameters. Several studies have
analyzed over-parameterized linear models with high-dimensional data that may
not be sparse; however, existing results depend on the independent setting of
samples. In this study, we analyze a linear regression model with dependent
time series data under over-parameterization settings. We consider an estimator
via interpolation and developed a theory for excess risk of the estimator under
multiple dependence types. This theory can treat infinite-dimensional data
without sparsity and handle long-memory processes in a unified manner.
Moreover, we bound the risk in our theory via the integrated covariance and
nondegeneracy of autocorrelation matrices. The results show that the
convergence rate of risks with short-memory processes is identical to that of
cases with independent data, while long-memory processes slow the convergence
rate. We also present several examples of specific dependent processes that can
be applied to our setting.


title:
Parabolic fractal dimension of forward-singularities for Navier-Stokes
  and liquid crystals inequalities

abstract:
  In 1985, V. Scheffer discussed partial regularity results for what he called
solutions to the "Navier-Stokes inequality". These maps essentially satisfy the
incompressibility condition as well as the local and global energy inequalities
and the pressure equation which may be derived formally from the Navier-Stokes
system of equations, but they are not required to satisfy the Navier-Stokes
system itself. One may extend this notion to a system considered by Fang-Hua
Lin and Chun Liu in the mid 1990s related to models of the flow of nematic
liquid crystals, which include the Navier-Stokes system when the "director
field" $d$ is taken to be zero. In addition to an extended Navier-Stokes
system, the Lin-Liu model includes a further parabolic system which implies an
a priori maximum principle for $d$, which is lost when one considers the
analogous 'inequality'.
  In 2018, Qiao Liu proved a partial regularity result for certain solutions to
the Lin-Liu model in terms of the parabolic fractal dimension
$\textrm{dim}_{\textrm{pf}}$, relying on the boundedness of $d$ coming from the
maximum principle. Specifically, Q. Liu proves
$\textrm{dim}_{\textrm{pf}}(\Sigma_{-} \cap \mathcal{K}) \leq \tfrac{95}{63}$
for any compact $\mathcal{K}$, where $\Sigma_{-}$ is the set of
"forward-singular" space-time points, near which the solution blows up forwards
in time. For solutions to the corresponding "inequality", we prove that,
without any compensation for the lack of maximum principle, one has
$\textrm{dim}_{\textrm{pf}}(\Sigma_{-} \cap \mathcal{K}) \leq \tfrac {55}{13}$.
We also provide a range of criteria, including as just one example the
boundedness of $d$, any one of which would furthermore imply that
$\textrm{dim}_{\textrm{pf}}(\Sigma_{-} \cap \mathcal{K}) \leq \tfrac{95}{63}$
for solutions to the inequality, just as Q. Liu proved for solutions to the
Lin-Liu system itself.


title:
The solution to the problem of time in quantum gravity also solves the
  time of arrival problem in quantum mechanics

abstract:
  We introduced with coauthors some years ago a solution to the problem of time
in quantum gravity which consists in formulating the quantum theory in terms of
real clocks. It combines Page and Wootters' relational proposal with Rovelli's
evolving constants of the motion. Time is associated with an operator and not a
classical parameter. We show here that this construction provides a natural
solution to the time of arrival problem in quantum mechanics and leads to a
well defined time-energy uncertainty relation for the clocks.


title:
Suppression of Nonlinear Optical Rogue Wave Formation Using
  Polarization-Structured Beams

abstract:
  A nonlinear self-focusing material can amplify random small-amplitude phase
modulations present in an optical beam, leading to the formation of amplitude
singularities commonly referred to as optical caustics. By imposing
polarization structuring on the beam, we demonstrate the suppression of
amplitude singularities caused by nonlinear self-phase modulation. Our results
are the first to indicate that polarization-structured beams can suppress
nonlinear caustic formation in a saturable self-focusing medium and add to the
growing understanding of catastrophic self-focusing effects in beams containing
polarization structure.


title: Learning to Execute Actions or Ask Clarification Questions

abstract:
  Collaborative tasks are ubiquitous activities where a form of communication
is required in order to reach a joint goal. Collaborative building is one of
such tasks. We wish to develop an intelligent builder agent in a simulated
building environment (Minecraft) that can build whatever users wish to build by
just talking to the agent. In order to achieve this goal, such agents need to
be able to take the initiative by asking clarification questions when further
information is needed. Existing works on Minecraft Corpus Dataset only learn to
execute instructions neglecting the importance of asking for clarifications. In
this paper, we extend the Minecraft Corpus Dataset by annotating all builder
utterances into eight types, including clarification questions, and propose a
new builder agent model capable of determining when to ask or execute
instructions. Experimental results show that our model achieves
state-of-the-art performance on the collaborative building task with a
substantial improvement. We also define two new tasks, the learning to ask task
and the joint learning task. The latter consists of solving both collaborating
building and learning to ask tasks jointly.


title: Untangled: A Complete Dynamic Topological Logic

abstract:
  Dynamic topological logic ($\mathbf{DTL}$) is a trimodal logic designed for
reasoning about dynamic topological systems. It was shown by Fern\'andez-Duque
that the natural set of axioms for $\mathbf{DTL}$ is incomplete, but he
provided a complete axiomatisation in an extended language. In this paper, we
consider dynamic topological logic over scattered spaces, which are topological
spaces where every nonempty subspace has an isolated point. Scattered spaces
appear in the context of computational logic as they provide semantics for
provability and enjoy definable fixed points. We exhibit the first sound and
complete dynamic topological logic in the original trimodal language. In
particular, we show that the version of $\mathbf{DTL}$ based on the class of
scattered spaces is finitely axiomatisable over the original language, and that
the natural axiomatisation is sound and complete.


title:
Orbit pseudometrics and a universality property of the Gromov-Hausdorff
  distance

abstract:
  We consider the notion of Borel reducibility between pseudometrics on
standard Borel spaces introduced and studied recently by C\'{u}th, Doucha and
Kurka, as well as the notion of an orbit pseudometric, a continuous version of
the notion of an orbit equivalence relation. It is well known that the relation
of isometry of Polish metric spaces is bireducible with a universal orbit
equivalence relation. We prove a version of this result for pseudometrics,
showing that the Gromov-Hausdorff distance of Polish metric spaces is
bireducible with a universal element in a certain class of orbit pseudometrics.


title: Detecting Deepfakes with Self-Blended Images

abstract:
  In this paper, we present novel synthetic training data called self-blended
images (SBIs) to detect deepfakes. SBIs are generated by blending pseudo source
and target images from single pristine images, reproducing common forgery
artifacts (e.g., blending boundaries and statistical inconsistencies between
source and target images). The key idea behind SBIs is that more general and
hardly recognizable fake samples encourage classifiers to learn generic and
robust representations without overfitting to manipulation-specific artifacts.
We compare our approach with state-of-the-art methods on FF++, CDF, DFD, DFDC,
DFDCP, and FFIW datasets by following the standard cross-dataset and
cross-manipulation protocols. Extensive experiments show that our method
improves the model generalization to unknown manipulations and scenes. In
particular, on DFDC and DFDCP where existing methods suffer from the domain gap
between the training and test sets, our approach outperforms the baseline by
4.90% and 11.78% points in the cross-dataset evaluation, respectively.


title: Strengthening Subcommunities: Towards Sustainable Growth in AI Research

abstract:
  AI's rapid growth has been felt acutely by scholarly venues, leading to
growing pains within the peer review process. These challenges largely center
on the inability of specific subareas to identify and evaluate work that is
appropriate according to criteria relevant to each subcommunity as determined
by stakeholders of that subarea. We set forth a proposal that re-focuses
efforts within these subcommunities through a decentralization of the reviewing
and publication process. Through this re-centering effort, we hope to encourage
each subarea to confront the issues specific to their process of academic
publication and incentivization. This model has historically been successful
for several subcommunities in AI, and we highlight those instances as examples
for how the broader field can continue to evolve despite its continually
growing size.


title:
Targeted search for the stochastic gravitational-wave background from
  the galactic millisecond pulsar population

abstract:
  The millisecond pulsars, old-recycled objects spinning with high frequency
$\mathcal{O}$(kHz) sustaining the deformation from their spherical shape, may
emit gravitational-waves (GW). These are one of the potential candidates
contributing to the anisotropic stochastic gravitational-wave background (SGWB)
observable in the ground-based GW detectors. Here, we present the results from
a likelihood-based targeted search for the SGWB due to millisecond pulsars in
the Milky Way, by analyzing the data from the first three observing runs of
Advanced LIGO and Advanced Virgo detector. We assume that the shape of SGWB
power spectra and the sky distribution is known a priori from the population
synthesis model. The information of the ensemble source properties, i.e., the
in-band number of pulsars, $N_{obs}$ and the averaged ellipticity,
$\mu_\epsilon$ is encoded in the maximum likelihood statistic. We do not find
significant evidence for the SGWB signal from the considered source population.
The best Bayesian upper limit with $95\%$ confidence for the parameters are
$N_{obs}\leq8.8\times10^{4}$ and $\mu_\epsilon\leq1.1\times10^{-7}$, which is
comparable to the bounds on mean ellipticity with the GW observations of the
individual pulsars. Finally, we show that for the plausible case of
$N_{obs}=40,000$, with the one year of observations, the one-sigma sensitivity
on $\mu_\epsilon$ might reach $10^{-8}$ and $2.7\times10^{-9}$ for the
second-generation detector network having A+ sensitivity and third-generation
detector network respectively.


title:
The role of the bile salt surfactant sodium deoxycholate in aqueous
  two-phase separation of single-wall carbon nanotubes revealed by systematic
  parameter variations

abstract:
  Aqueous two-phase (ATP) extraction has been demonstrated as a fast, scalable,
and effective separation technique to sort single-wall carbon nanotubes
(SWCNTs) according to their diameter and chiral structure. The exact mechanism
behind the chirality-dependent migration of SWCNTs between the two phases is
however not completely understood, and depends on many parameters (e.g., choice
of surfactants and their concentration, pH, temperature, ...), making it
difficult to optimize the multivariable parameter space. In this work, we
present a systematic study of the choice and concentration of specific
surfactants on the ATP sorting, by performing a series of single-step ATP
separations in which each time only one parameter is systematically varied,
while monitoring the structure-specific migration of every SWCNT chirality
between both phases with detailed wavelength-dependent spectroscopy. These
systematic studies reveal that the diameter-dependent stacking of a discrete
number of sodium deoxycholate molecules fitting around the SWCNT circumference
determines the separation order in the form of a periodically modulated pattern
as a function of SWCNT diameter. Addition of cosurfactants can be used to
compete with the bile salt surfactant to enhance the separation yields, but
does not affect the sorting order. The results are afterwards directly applied
to predict the parameters required to separate specific chiral structures in
just two ATP steps.


title: The $\Gamma$-distinguished $\Gamma$-contractions

abstract:
  The symmetrized bidisc, which is the symmetrization of the bidisc $\mathbb
D^2$, is defined by
  \[
  \mathbb{G}=\{(z_1+z_2, z_1z_2) \ : \ |z_1|<1, |z_2|<1 \} \subseteq
\mathbb{C}^2.
  \]
  A distinguished variety in $\mathbb{G}$ is an affine algebraic variety that
intersects $\mathbb{G}$ and exits $\mathbb{G}$ through its distinguished
boundary $b\Gamma,$ where $\Gamma=\overline{\mathbb{G}}.$ A commuting pair of
Hilbert space operators $(S,P),$ for which $\Gamma$ is a spectral set, is
called a $\Gamma$-contraction. We study $\Gamma$-contractions that are
annihilated by a polynomial whose zero set defines a distinguished variety in
$\mathbb{G}$ and we call such $\Gamma$-contractions to be
$\Gamma$-distinguished. We characterize the $\Gamma$-distinguished pure
$\Gamma$-contractions on a finite dimensional Hilbert space. Along with several
results we find a necessary and sufficient condition under which a minimal
$\Gamma$-isometric dilation of a $\Gamma$-distinguished $\Gamma$-contraction
becomes $\Gamma$-distinguished.


title:
Multiple-environment Self-adaptive Network for Aerial-view
  Geo-localization

abstract:
  Aerial-view geo-localization tends to determine an unknown position through
matching the drone-view image with the geo-tagged satellite-view image. This
task is mostly regarded as an image retrieval problem. The key underpinning
this task is to design a series of deep neural networks to learn discriminative
image descriptors. However, existing methods meet large performance drops under
realistic weather, such as rain and fog, since they do not take the domain
shift between the training data and multiple test environments into
consideration. To minor this domain gap, we propose a Multiple-environment
Self-adaptive Network (MuSe-Net) to dynamically adjust the domain shift caused
by environmental changing. In particular, MuSe-Net employs a two-branch neural
network containing one multiple-environment style extraction network and one
self-adaptive feature extraction network. As the name implies, the
multiple-environment style extraction network is to extract the
environment-related style information, while the self-adaptive feature
extraction network utilizes an adaptive modulation module to dynamically
minimize the environment-related style gap. Extensive experiments on two
widely-used benchmarks, i.e., University-1652 and CVUSA, demonstrate that the
proposed MuSe-Net achieves a competitive result for geo-localization in
multiple environments. Furthermore, we observe that the proposed method also
shows great potential to the unseen extreme weather, such as mixing the fog,
rain and snow.


title: Subspace Nonnegative Matrix Factorization for Feature Representation

abstract:
  Traditional nonnegative matrix factorization (NMF) learns a new feature
representation on the whole data space, which means treating all features
equally. However, a subspace is often sufficient for accurate representation in
practical applications, and redundant features can be invalid or even harmful.
For example, if a camera has some sensors destroyed, then the corresponding
pixels in the photos from this camera are not helpful to identify the content,
which means only the subspace consisting of remaining pixels is worthy of
attention. This paper proposes a new NMF method by introducing adaptive weights
to identify key features in the original space so that only a subspace involves
generating the new representation. Two strategies are proposed to achieve this:
the fuzzier weighted technique and entropy regularized weighted technique, both
of which result in an iterative solution with a simple form. Experimental
results on several real-world datasets demonstrated that the proposed methods
can generate a more accurate feature representation than existing methods. The
code developed in this study is available at
https://github.com/WNMF1/FWNMF-ERWNMF.


title:
'I think I discovered a military base in the middle of the ocean' --
  Null Island, the most real of fictional places

abstract:
  This paper explores Null Island, a fictional place located at 0$^\circ$
latitude and 0$^\circ$ longitude in the WGS84 geographic coordinate system.
Null Island is erroneously associated with large amounts of geographic data in
a wide variety of location-based services, place databases, social media and
web-based maps. While it was originally considered a joke within the geospatial
community, this article will demonstrate implications of its existence, both
technological and social in nature, promoting Null Island as a fundamental
issue of geographic information that requires more widespread awareness. The
article summarizes error sources that lead to data being associated with Null
Island. We identify four evolutionary phases which help explain how this
fictional place evolved and established itself as an entity reaching beyond the
geospatial profession to the point of being discovered by the visual arts and
the general population. After providing an accurate account of data that can be
found at (0, 0), geospatial, technological and social implications of Null
Island are discussed. Guidelines to avoid misplacing data to Null Island are
provided. Since data will likely continue to appear at this location, our
contribution is aimed at both GIScientists and the general population to
promote awareness of this error source.


title: Projective geometry of 3-Sasaki structures

abstract:
  We show that $3$-Sasaki structures admit a natural description in terms of
projective differential geometry. This description provides a concrete link
between $3$-Sasaki structures and several other geometries and constructions
via a single unifying picture. First we establish that a $3$-Sasaki structure
may be understood as a projective structure equipped with a certain holonomy
reduction to the (possibly indefinite) unitary quaternionic group
$\textrm{Sp}(p,q)$, namely a parallel hyperk\"ahler structure on the projective
tractor bundle satisfying a particular genericity condition. For the converse,
where one begins with a general parallel hyperk\"ahler structure on the
projective tractor bundle, the genericity condition is not automatic. Indeed we
prove that generically such a reduction decomposes the underlying manifold into
a disjoint union of strata including open manifolds with (indefinite)
$3$-Sasaki structures and a closed separating hypersurface at infinity with
respect to the $3$-Sasaki metrics. Moreover, it is shown that the latter
hypersurface inherits a Biquard-Fefferman conformal structure, which thus
(locally) fibres over a quaternionic contact structure, and which in turn
compactifies the natural quaternionic K\"ahler quotients of the $3$-Sasaki
structures on the open manifolds. As an application we describe the projective
compactification of (suitably) complete, non-compact (indefinite) $3$-Sasaki
manifolds and recover Biquard's notion of asymptotically hyperbolic
quaternionic K\"ahler metrics.


title:
Distributed MST Computation in the Sleeping Model: Awake-Optimal
  Algorithms and Lower Bounds

abstract:
  We study the distributed minimum spanning tree (MST) problem, a fundamental
problem in distributed computing. It is well-known that distributed MST can be
solved in $\tilde{O}(D+\sqrt{n})$ rounds in the standard CONGEST model (where
$n$ is the network size and $D$ is the network diameter) and this is
essentially the best possible round complexity (up to logarithmic factors).
However, in resource-constrained networks such as ad hoc wireless and sensor
networks, nodes spending so much time can lead to significant spending of
resources such as energy.
  Motivated by the above consideration, we study distributed algorithms for MST
under the \emph{sleeping model} [Chatterjee et al., PODC 2020], a model for
design and analysis of resource-efficient distributed algorithms. In the
sleeping model, a node can be in one of two modes in any round --
\emph{sleeping} or \emph{awake} (unlike the traditional model where nodes are
always awake). Only the rounds in which a node is \emph{awake} are counted,
while \emph{sleeping} rounds are ignored. A node spends resources only in the
awake rounds and hence the main goal is to minimize the \emph{awake complexity}
of a distributed algorithm, the worst-case number of rounds any node is awake.
  We present deterministic and randomized distributed MST algorithms that have
an \emph{optimal} awake complexity of $O(\log n)$ time with a matching lower
bound. We also show that our randomized awake-optimal algorithm has essentially
the best possible round complexity by presenting a lower bound of
$\tilde{\Omega}(n)$ on the product of the awake and round complexity of any
distributed algorithm (including randomized) that outputs an MST, where
$\tilde{\Omega}$ hides a $1/(\text{polylog } n)$ factor.


title: Optimal Subsampling for High-dimensional Ridge Regression

abstract:
  We investigate the feature compression of high-dimensional ridge regression
using the optimal subsampling technique. Specifically, based on the basic
framework of random sampling algorithm on feature for ridge regression and the
A-optimal design criterion, we first obtain a set of optimal subsampling
probabilities. Considering that the obtained probabilities are uneconomical, we
then propose the nearly optimal ones. With these probabilities, a two step
iterative algorithm is established which has lower computational cost and
higher accuracy. We provide theoretical analysis and numerical experiments to
support the proposed methods. Numerical results demonstrate the decent
performance of our methods.


title:
LayoutLMv3: Pre-training for Document AI with Unified Text and Image
  Masking

abstract:
  Self-supervised pre-training techniques have achieved remarkable progress in
Document AI. Most multimodal pre-trained models use a masked language modeling
objective to learn bidirectional representations on the text modality, but they
differ in pre-training objectives for the image modality. This discrepancy adds
difficulty to multimodal representation learning. In this paper, we propose
LayoutLMv3 to pre-train multimodal Transformers for Document AI with unified
text and image masking. Additionally, LayoutLMv3 is pre-trained with a
word-patch alignment objective to learn cross-modal alignment by predicting
whether the corresponding image patch of a text word is masked. The simple
unified architecture and training objectives make LayoutLMv3 a general-purpose
pre-trained model for both text-centric and image-centric Document AI tasks.
Experimental results show that LayoutLMv3 achieves state-of-the-art performance
not only in text-centric tasks, including form understanding, receipt
understanding, and document visual question answering, but also in
image-centric tasks such as document image classification and document layout
analysis. The code and models are publicly available at
https://aka.ms/layoutlmv3.


title: A remark on the component group of the Sato-Tate group

abstract:
  In this paper, we give a complete characterization of the component group of
the Sato-Tate group of an abelian variety $A$ of arbitrary dimension, defined
over a number field $K,$ in terms of the connectedness of the Lefschetz group
associated to $A.$


title: Boson Sampling for Generalized Bosons

abstract:
  We introduce the notion of "generalized bosons" whose exchange statistics
resemble those of bosons, but the local bosonic commutator
$[a_i,a_i^\dagger]=1$ is replaced by an arbitrary single-mode operator that is
diagonal in the generalized Fock basis. Examples of generalized bosons include
boson pairs and spins. We consider the analogue of the boson sampling task for
these particles and observe that its output probabilities are still given by
permanents, so that the results regarding hardness of sampling directly carry
over. Finally, we propose implementations of generalized boson sampling in
circuit-QED and ion-trap platforms.


title: $W$ boson mass shift and muon magnetic moment in the Zee model

abstract:
  The CDF collaboration at Fermilab has recently reported a new precision
measurement of the $W$ boson mass showing a substantial $7\sigma$ deviation
from the Standard Model prediction. Moreover, Fermilab has recently confirmed
the longstanding tension in the $(g-2)_\mu$ measurement. We propose a unified
solution to these deviations within the simplest radiative neutrino mass model:
the Zee model. Our analysis establishes non-trivial links between the origin of
neutrino mass, the $(g-2)_\mu$ anomaly, and the $W$ boson mass shift while
being consistent with lepton flavor violation and all other experimental
constraints. We find that the mass spectrum of the physical scalars must be
hierarchical to be consistent with the $W$ boson mass shift; remarkably, this
is also the key to resolving the $(g-2)_\mu$ tension. Furthermore, this mass
splitting offers a unique same-sign dimuon signal through which our model can
be tested at the LHC.


title: Colors of Irregular Satellites of Saturn with DECam

abstract:
  We report g-r and r-i new colors for 21 Saturn Irregular Satellites, among
them, 4 previously unreported. This is the highest number of Saturn Irregular
satellites reported in a single survey. These satellites were measured by
"stacking" their observations to increase their signal without trailing. This
work describes a novel processing algorithm that enables the detection of faint
sources under significant background noise and in front of a severely crowded
field.
  Our survey shows these new color measurements of Saturn Irregular Satellites
are consistent with other Irregular Satellites populations as found in previous
works and reinforcing the observation that the lack of ultra red objects among
the irregular satellites is a real feature that separates them from the
trans-Neptunian objects (their posited source population).


title: Quasihomomorphisms from the integers into Hamming metrics

abstract:
  A function $f: \mathbb{Z} \to \mathbb{Q}^n$ is a $c$-quasihomomorphism if the
Hamming distance between $f(x+y)$ and $f(x)+f(y)$ is at most $c$ for all $x,y
\in \mathbb{Z}$. We show that any $c$-quasihomomorphism has distance at most
some constant $C(c)$ to an actual group homomorphism; here $C(c)$ depends only
on $c$ and not on $n$ or $f$. This gives a positive answer to a special case of
a question posed by Kazhdan and Ziegler.


title: Proton Stability: From the Standard Model to Ultra Unification

abstract:
  For the 4d Standard Model (SM) with Lie group $G_{{\rm SM}_q} \equiv$
SU(3)$\times$SU(2)$\times$U(1)$_{\tilde Y}/\mathbb{Z}_q$ of $q=1,2,3,6$ with
$N_f$ family of 15 or 16 Weyl fermions, in addition to the continuous baryon
minus lepton U(1)$_{\bf B - L}$ symmetry, there is also a compatible discrete
baryon plus lepton $\mathbb{Z}_{2N_f, \bf B + L}$ symmetry. The
$\mathbb{Z}_{2N_f, \bf B + L}$ is discrete due to the ABJ anomaly under the
BPST SU(2) instanton. Although both U(1)$_{\bf B - L}$ and $\mathbb{Z}_{2N_f,
\bf B + L}$ symmetries are anomaly-free under the dynamically gauged $G_{{\rm
SM}_q}$, it is important to check whether they have mixed anomalies with the
gravitational background field (spacetime diffeomorphism under Spin group
rotation) and higher symmetries (whose charged objects are Wilson electric or
't Hooft magnetic line operators) of SM. We can also replace the U(1)$_{\bf B -
L}$ with a discrete variant $\mathbb{Z}_{4,X}$ for $X \equiv 5({\bf B -
L})-\frac{2}{3} {\tilde Y}$ of electroweak hypercharge ${\tilde Y}$. We explore
a systematic classification of candidate perturbative local and nonperturbative
global anomalies of the 4d SM, including all these gauge and gravitational
backgrounds, via a cobordism theory, which controls the SM's deformation class.
We discuss the proton stability of the SM and Ultra Unification in the presence
of (U(1)$_{\bf B - L} \times \mathbb{Z}_{2N_f,\bf B + L})/{\mathbb{Z}_2^{\rm
F}}$ or $(\mathbb{Z}_{4,X} \times \mathbb{Z}_{2N_f, \bf B +
L})/{\mathbb{Z}_2^{\rm F}}$ symmetry protection with the fermion parity
$\mathbb{Z}_2^{\rm F}$. While many Grand Unified Theories violating the
discrete $\bf B + L$ symmetry suffer from the proton decay, the SM and some
versions of Ultra Unification can have a stable proton.


title: CenterNet++ for Object Detection

abstract:
  There are two mainstreams for object detection: top-down and bottom-up. The
state-of-the-art approaches mostly belong to the first category. In this paper,
we demonstrate that the bottom-up approaches are as competitive as the top-down
and enjoy higher recall. Our approach, named CenterNet, detects each object as
a triplet keypoints (top-left and bottom-right corners and the center
keypoint). We firstly group the corners by some designed cues and further
confirm the objects by the center keypoints. The corner keypoints equip the
approach with the ability to detect objects of various scales and shapes and
the center keypoint avoids the confusion brought by a large number of
false-positive proposals. Our approach is a kind of anchor-free detector
because it does not need to define explicit anchor boxes. We adapt our approach
to the backbones with different structures, i.e., the 'hourglass' like networks
and the the 'pyramid' like networks, which detect objects on a
single-resolution feature map and multi-resolution feature maps, respectively.
On the MS-COCO dataset, CenterNet with Res2Net-101 and Swin-Transformer
achieves APs of 53.7% and 57.1%, respectively, outperforming all existing
bottom-up detectors and achieving state-of-the-art. We also design a real-time
CenterNet, which achieves a good trade-off between accuracy and speed with an
AP of 43.6% at 30.5 FPS. https://github.com/Duankaiwen/PyCenterNet.


title: Etudes for the inverse spectral problem

abstract:
  In this note we study inverse spectral problems for canonical Hamiltonian
systems, which encompass a broad class of second order differential equations
on a half-line. Our goal is to extend the classical resultss developed in the
work of Marchenko, Gelfand-Levitan, and Krein to broader classes of canonical
systems and to illustrate the solution algorithms and formulas with a variety
of examples. One of the main ingredients of our approach is the use of
truncated Toeplitz operators, which complement the standard toolbox of the
Krein-de Branges theory of canonical systems.


title: StableMoE: Stable Routing Strategy for Mixture of Experts

abstract:
  The Mixture-of-Experts (MoE) technique can scale up the model size of
Transformers with an affordable computational overhead. We point out that
existing learning-to-route MoE methods suffer from the routing fluctuation
issue, i.e., the target expert of the same input may change along with
training, but only one expert will be activated for the input during inference.
The routing fluctuation tends to harm sample efficiency because the same input
updates different experts but only one is finally used. In this paper, we
propose StableMoE with two training stages to address the routing fluctuation
problem. In the first training stage, we learn a balanced and cohesive routing
strategy and distill it into a lightweight router decoupled from the backbone
model. In the second training stage, we utilize the distilled router to
determine the token-to-expert assignment and freeze it for a stable routing
strategy. We validate our method on language modeling and multilingual machine
translation. The results show that StableMoE outperforms existing MoE methods
in terms of both convergence speed and performance.


title:
Fast and Memory-Efficient Network Towards Efficient Image
  Super-Resolution

abstract:
  Runtime and memory consumption are two important aspects for efficient image
super-resolution (EISR) models to be deployed on resource-constrained devices.
Recent advances in EISR exploit distillation and aggregation strategies with
plenty of channel split and concatenation operations to make full use of
limited hierarchical features. In contrast, sequential network operations avoid
frequently accessing preceding states and extra nodes, and thus are beneficial
to reducing the memory consumption and runtime overhead. Following this idea,
we design our lightweight network backbone by mainly stacking multiple highly
optimized convolution and activation layers and decreasing the usage of feature
fusion. We propose a novel sequential attention branch, where every pixel is
assigned an important factor according to local and global contexts, to enhance
high-frequency details. In addition, we tailor the residual block for EISR and
propose an enhanced residual block (ERB) to further accelerate the network
inference. Finally, combining all the above techniques, we construct a fast and
memory-efficient network (FMEN) and its small version FMEN-S, which runs 33%
faster and reduces 74% memory consumption compared with the state-of-the-art
EISR model: E-RFDN, the champion in AIM 2020 efficient super-resolution
challenge. Besides, FMEN-S achieves the lowest memory consumption and the
second shortest runtime in NTIRE 2022 challenge on efficient super-resolution.
Code is available at https://github.com/NJU-Jet/FMEN.


title:
L3Cube-HingCorpus and HingBERT: A Code Mixed Hindi-English Dataset and
  BERT Language Models

abstract:
  Code-switching occurs when more than one language is mixed in a given
sentence or a conversation. This phenomenon is more prominent on social media
platforms and its adoption is increasing over time. Therefore code-mixed NLP
has been extensively studied in the literature. As pre-trained
transformer-based architectures are gaining popularity, we observe that real
code-mixing data are scarce to pre-train large language models. We present
L3Cube-HingCorpus, the first large-scale real Hindi-English code mixed data in
a Roman script. It consists of 52.93M sentences and 1.04B tokens, scraped from
Twitter. We further present HingBERT, HingMBERT, HingRoBERTa, and HingGPT. The
BERT models have been pre-trained on codemixed HingCorpus using masked language
modelling objectives. We show the effectiveness of these BERT models on the
subsequent downstream tasks like code-mixed sentiment analysis, POS tagging,
NER, and LID from the GLUECoS benchmark. The HingGPT is a GPT2 based generative
transformer model capable of generating full tweets. We also release
L3Cube-HingLID Corpus, the largest code-mixed Hindi-English language
identification(LID) dataset and HingBERT-LID, a production-quality LID model to
facilitate capturing of more code-mixed data using the process outlined in this
work. The dataset and models are available at
https://github.com/l3cube-pune/code-mixed-nlp .


title: Unsupervised Contrastive Domain Adaptation for Semantic Segmentation

abstract:
  Semantic segmentation models struggle to generalize in the presence of domain
shift. In this paper, we introduce contrastive learning for feature alignment
in cross-domain adaptation. We assemble both in-domain contrastive pairs and
cross-domain contrastive pairs to learn discriminative features that align
across domains. Based on the resulting well-aligned feature representations we
introduce a label expansion approach that is able to discover samples from hard
classes during the adaptation process to further boost performance. The
proposed approach consistently outperforms state-of-the-art methods for domain
adaptation. It achieves 60.2% mIoU on the Cityscapes dataset when training on
the synthetic GTA5 dataset together with unlabeled Cityscapes images.


title: Dynamic Network Adaptation at Inference

abstract:
  Machine learning (ML) inference is a real-time workload that must comply with
strict Service Level Objectives (SLOs), including latency and accuracy targets.
Unfortunately, ensuring that SLOs are not violated in inference-serving systems
is challenging due to inherent model accuracy-latency tradeoffs, SLO diversity
across and within application domains, evolution of SLOs over time,
unpredictable query patterns, and co-location interference. In this paper, we
observe that neural networks exhibit high degrees of per-input activation
sparsity during inference. . Thus, we propose SLO-Aware Neural Networks which
dynamically drop out nodes per-inference query, thereby tuning the amount of
computation performed, according to specified SLO optimization targets and
machine utilization. SLO-Aware Neural Networks achieve average speedups of
$1.3-56.7\times$ with little to no accuracy loss (less than 0.3%). When
accuracy constrained, SLO-Aware Neural Networks are able to serve a range of
accuracy targets at low latency with the same trained model. When latency
constrained, SLO-Aware Neural Networks can proactively alleviate latency
degradation from co-location interference while maintaining high accuracy to
meet latency constraints.


title:
TranS: Transition-based Knowledge Graph Embedding with Synthetic
  Relation Representation

abstract:
  Knowledge graph embedding (KGE) aims to learn continuous vectors of relations
and entities in knowledge graph. Recently, transition-based KGE methods have
achieved promising performance, where the single relation vector learns to
translate head entity to tail entity. However, this scoring pattern is not
suitable for complex scenarios where the same entity pair has different
relations. Previous models usually focus on the improvement of entity
representation for 1-to-N, N-to-1 and N-to-N relations, but ignore the single
relation vector. In this paper, we propose a novel transition-based method,
TranS, for knowledge graph embedding. The single relation vector in traditional
scoring patterns is replaced with synthetic relation representation, which can
solve these issues effectively and efficiently. Experiments on a large
knowledge graph dataset, ogbl-wikikg2, show that our model achieves
state-of-the-art results.


title: Rank Based Tests for High Dimensional White Noise

abstract:
  The development of high-dimensional white noise test is important in both
statistical theories and applications, where the dimension of the time series
can be comparable to or exceed the length of the time series. This paper
proposes several distribution-free tests using the rank based statistics for
testing the high-dimensional white noise, which are robust to the heavy tails
and do not quire the finite-order moment assumptions for the sample
distributions. Three families of rank based tests are analyzed in this paper,
including the simple linear rank statistics, non-degenerate U-statistics and
degenerate U-statistics. The asymptotic null distributions and rate optimality
are established for each family of these tests. Among these tests, the test
based on degenerate U-statistics can also detect the non-linear and
non-monotone relationships in the autocorrelations. Moreover, this is the first
result on the asymptotic distributions of rank correlation statistics which
allowing for the cross-sectional dependence in high dimensional data.


title:
An Iterative Decoupled Algorithm with Unconditional Stability for Biot
  Model

abstract:
  This paper is concerned with numerical algorithms for Biot model. By
introducing an intermediate variable, the classical 2-field Biot model is
written into a 3-field formulation. Based on such a 3-field formulation, we
propose a coupled algorithm, some time-extrapolation based decoupled
algorithms, and an iterative decoupled algorithm. Our focus is the analysis of
the iterative decoupled algorithm. It is shown that the convergence of the
iterative decoupled algorithm requires no extra assumptions on physical
parameters or stabilization parameters. Numerical experiments are provided to
demonstrate the accuracy and efficiency of the proposed method.


title: Low Degree Testing over the Reals

abstract:
  We study the problem of testing whether a function $f: \mathbb{R}^n \to
\mathbb{R}$ is a polynomial of degree at most $d$ in the
\emph{distribution-free} testing model. Here, the distance between functions is
measured with respect to an unknown distribution $\mathcal{D}$ over
$\mathbb{R}^n$ from which we can draw samples. In contrast to previous work, we
do not assume that $\mathcal{D}$ has finite support.
  We design a tester that given query access to $f$, and sample access to
$\mathcal{D}$, makes $(d/\varepsilon)^{O(1)}$ many queries to $f$, accepts with
probability $1$ if $f$ is a polynomial of degree $d$, and rejects with
probability at least $2/3$ if every degree-$d$ polynomial $P$ disagrees with
$f$ on a set of mass at least $\varepsilon$ with respect to $\mathcal{D}$. Our
result also holds under mild assumptions when we receive only a polynomial
number of bits of precision for each query to $f$, or when $f$ can only be
queried on rational points representable using a logarithmic number of bits.
Along the way, we prove a new stability theorem for multivariate polynomials
that may be of independent interest.


title:
Zero-shot Entity and Tweet Characterization with Designed Conditional
  Prompts and Contexts

abstract:
  Online news and social media have been the de facto mediums to disseminate
information globally from the beginning of the last decade. However, bias in
content and purpose of intentions are not regulated, and managing bias is the
responsibility of content consumers. In this regard, understanding the stances
and biases of news sources towards specific entities becomes important. To
address this problem, we use pretrained language models, which have been shown
to bring about good results with no task-specific training or few-shot
training. In this work, we approach the problem of characterizing Named
Entities and Tweets as an open-ended text classification and open-ended fact
probing problem.We evaluate the zero-shot language model capabilities of
Generative Pretrained Transformer 2 (GPT-2) to characterize Entities and Tweets
subjectively with human psychology-inspired and logical conditional prefixes
and contexts. First, we fine-tune the GPT-2 model on a sufficiently large news
corpus and evaluate subjective characterization of popular entities in the
corpus by priming with prefixes. Second, we fine-tune GPT-2 with a Tweets
corpus from a few popular hashtags and evaluate characterizing tweets by
priming the language model with prefixes, questions, and contextual synopsis
prompts. Entity characterization results were positive across measures and
human evaluation.


title:
The 2HD+a model for a combined explanation of the possible excesses in
  the CDF $\mathbf{M_W}$ measurement and $\mathbf{(g-2)_\mu}$ with Dark Matter

abstract:
  The new measurement of the $W$ boson mass performed by the CDF experiment at
the Tevatron shows a significant deviation not only with the expectation in the
Standard Model but also with other precision measurements performed at LEP, the
Tevatron and the LHC. We nevertheless take this new measurement at face value
and interpret it as an effect of new physics. We particularly try to link it
with other possible anomalies such as the recent muon $g-2$ and consider a
scenario that addresses some shortcomings of the Standard Model. We show that a
model with two doublets and a light pseudoscalar Higgs fields, supplemented by
a stable isosinglet fermion, can simultaneously explain the possible $M_W$ and
$(g-2)_\mu$ anomalies and accounts for the weakly interacting massive particle
that could be responsible of the dark matter in the universe.


title:
Non-Markovian random walks characterize network robustness to nonlocal
  cascades

abstract:
  Localized perturbations in a real-world network have the potential to trigger
cascade failures at the whole system level, hindering its operations and
functions. Standard approaches analytically tackling this problem are mostly
based either on static descriptions, such as percolation, or on models where
the failure evolves through first-neighbor connections, crucially failing to
capture the nonlocal behavior typical of real cascades. We introduce a
dynamical model that maps the failure propagation across the network to a
self-avoiding random walk that, at each step, has a probability to perform
nonlocal jumps toward operational systems' units. Despite the inherent
non-Markovian nature of the process, we are able to characterize the critical
behavior of the system out of equilibrium, as well as the stopping time
distribution of the cascades. Our numerical experiments on synthetic and
empirical biological and transportation networks are in excellent agreement
with theoretical expectation, demonstrating the ability of our framework to
quantify the vulnerability to nonlocal cascade failures of complex systems with
interconnected structure.


title:
On Ozaki's theorem realizing prescribed $p$-groups as $p$-class tower
  groups

abstract:
  We give a streamlined and effective proof of Ozaki's theorem that any finite
$p$-group $\Gamma$ is the Galois group of the $p$-Hilbert class field tower of
some number field $\rm F$. Our work is inspired by Ozaki's and applies in
broader circumstances. While his theorem is in the totally complex setting, we
obtain the result in any mixed signature setting for which there exists a
number field ${\rm k}_0$ with class number prime to $p$. We construct ${\rm
F}/{\rm k}_0$ by a sequence of ${\mathbb Z}/p$-extensions ramified only at
finite tame primes and also give explicit bounds on $[{\rm F}:{\rm k}_0]$ and
the number of ramified primes of ${\rm F}/{\rm k}_0$ in terms of $\# \Gamma$.


title: Caption Feature Space Regularization for Audio Captioning

abstract:
  Audio captioning aims at describing the content of audio clips with human
language. Due to the ambiguity of audio, different people may perceive the same
audio differently, resulting in caption disparities (i.e., one audio may
correlate to several captions with diverse semantics). For that, general audio
captioning models achieve the one-to-many training by randomly selecting a
correlated caption as the ground truth for each audio. However, it leads to a
significant variation in the optimization directions and weakens the model
stability. To eliminate this negative effect, in this paper, we propose a
two-stage framework for audio captioning: (i) in the first stage, via the
contrastive learning, we construct a proxy feature space to reduce the
distances between captions correlated to the same audio, and (ii) in the second
stage, the proxy feature space is utilized as additional supervision to
encourage the model to be optimized in the direction that benefits all the
correlated captions. We conducted extensive experiments on two datasets using
four commonly used encoder and decoder architectures. Experimental results
demonstrate the effectiveness of the proposed method. The code is available at
https://github.com/PRIS-CV/Caption-Feature-Space-Regularization.


title: Two dimensional perfect evolution algebras over domains

abstract:
  We will study evolution algebras $A$ which are free modules of dimension $2$
over domains. Furthermore, we will assume that these algebras are perfect, that
is $A^2=A$. We start by making some general considerations about algebras over
domains: they are sandwiched between a certain essential $D$-submodule and its
scalar extension over the field of fractions of the domain. We introduce the
notion of quasiperfect algebras and modify slightly the procedure to associate
a graph to an evolution algebra over a field given in \cite{ElduqueGraphs}.
Essentially, we introduce color in the connecting arrows, depending on a
suitable criterion related to the squares of the natural basis elements. Then
we classify the algebras under scope parametrizing the isomorphic classes by
convenient moduli.


title:
Robust, Nonparametric, Efficient Decomposition of Spectral Peaks under
  Distortion and Interference

abstract:
  We propose a decomposition method for the spectral peaks in an observed
frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier
Transform. In contrast to the traditional methods of waveform fitting on the
spectrum, we optimize the problem from a more robust perspective. We model the
peaks in spectrum as pseudo-symmetric functions, where the only constraint is a
nonincreasing behavior around a central frequency when the distance increases.
Our approach is more robust against arbitrary distortion, interference and
noise on the spectrum that may be caused by an observation system. The time
complexity of our method is linear, i.e., $O(N)$ per extracted spectral peak.
Moreover, the decomposed spectral peaks show a pseudo-orthogonal behavior,
where they conform to a power preserving equality.


title: Temporally Efficient Vision Transformer for Video Instance Segmentation

abstract:
  Recently vision transformer has achieved tremendous success on image-level
visual recognition tasks. To effectively and efficiently model the crucial
temporal information within a video clip, we propose a Temporally Efficient
Vision Transformer (TeViT) for video instance segmentation (VIS). Different
from previous transformer-based VIS methods, TeViT is nearly convolution-free,
which contains a transformer backbone and a query-based video instance
segmentation head. In the backbone stage, we propose a nearly parameter-free
messenger shift mechanism for early temporal context fusion. In the head
stages, we propose a parameter-shared spatiotemporal query interaction
mechanism to build the one-to-one correspondence between video instances and
queries. Thus, TeViT fully utilizes both framelevel and instance-level temporal
context information and obtains strong temporal modeling capacity with
negligible extra computational cost. On three widely adopted VIS benchmarks,
i.e., YouTube-VIS-2019, YouTube-VIS-2021, and OVIS, TeViT obtains
state-of-the-art results and maintains high inference speed, e.g., 46.6 AP with
68.9 FPS on YouTube-VIS-2019. Code is available at
https://github.com/hustvl/TeViT.


title: Special theory of regularity

abstract:
  The theory of regularity is a philosophical perspective in which laws of
nature are just descriptions, that is to say, laws of nature do not govern the
world. Moreover, according to the theory of regularity, the number of laws of
nature might be infinite, thus any attempt towards the theory of everything is
doomed. Here I propose a special or restricted theory of regularity. The main
difference as to the well-known version of that theory is both the range of
validity and the scale of the laws of nature. Laws of nature ought to be
considered just inside the observable universe and within certain energy and
length scales. Even so I apply the theory of regularity to the multiverse
scenario. As a consequence, the special theory of regularity supports only two
types of multiverses by comparison with our world: those ones with a different
sequence of unique events and different laws of nature and those ones with the
same sequence of unique events and the same laws of nature instanced by the
unique events. The latter case is some sort of eternal recurrence or a parallel
eternal recurrence.


title: STONet: A Neural-Operator-Driven Spatio-temporal Network

abstract:
  Graph-based spatio-temporal neural networks are effective to model the
spatial dependency among discrete points sampled irregularly from unstructured
grids, thanks to the great expressiveness of graph neural networks. However,
these models are usually spatially-transductive -- only fitting the signals for
discrete spatial nodes fed in models but unable to generalize to `unseen'
spatial points with zero-shot. In comparison, for forecasting tasks on
continuous space such as temperature prediction on the earth's surface, the
\textit{spatially-inductive} property allows the model to generalize to any
point in the spatial domain, demonstrating models' ability to learn the
underlying mechanisms or physics laws of the systems, rather than simply fit
the signals. Besides, in temporal domains, \textit{irregularly-sampled} time
series, e.g. data with missing values, urge models to be temporally-continuous.
Motivated by the two issues, we propose a spatio-temporal framework based on
neural operators for PDEs, which learn the underlying mechanisms governing the
dynamics of spatially-continuous physical quantities. Experiments show our
model's improved performance on forecasting spatially-continuous physic
quantities, and its superior generalization to unseen spatial points and
ability to handle temporally-irregular data.


title:
Exploring Dimensionality Reduction Techniques in Multilingual
  Transformers

abstract:
  Both in scientific literature and in industry,, Semantic and context-aware
Natural Language Processing-based solutions have been gaining importance in
recent years. The possibilities and performance shown by these models when
dealing with complex Language Understanding tasks is unquestionable, from
conversational agents to the fight against disinformation in social networks.
In addition, considerable attention is also being paid to developing
multilingual models to tackle the language bottleneck. The growing need to
provide more complex models implementing all these features has been
accompanied by an increase in their size, without being conservative in the
number of dimensions required. This paper aims to give a comprehensive account
of the impact of a wide variety of dimensional reduction techniques on the
performance of different state-of-the-art multilingual Siamese Transformers,
including unsupervised dimensional reduction techniques such as linear and
nonlinear feature extraction, feature selection, and manifold techniques. In
order to evaluate the effects of these techniques, we considered the
multilingual extended version of Semantic Textual Similarity Benchmark (mSTSb)
and two different baseline approaches, one using the pre-trained version of
several models and another using their fine-tuned STS version. The results
evidence that it is possible to achieve an average reduction in the number of
dimensions of $91.58\% \pm 2.59\%$ and $54.65\% \pm 32.20\%$, respectively.
This work has also considered the consequences of dimensionality reduction for
visualization purposes. The results of this study will significantly contribute
to the understanding of how different tuning approaches affect performance on
semantic-aware tasks and how dimensional reduction techniques deal with the
high-dimensional embeddings computed for the STS task and their potential for
highly demanding NLP tasks


title: Clustering Coefficient of the Tensor Product of Graphs

abstract:
  Clustering coefficient is one of the most useful indices in complex networks.
However, graph theoretic properties of this metric have not been discussed much
in the literature, especially in graphs resulting from some binary operations.
In this paper we present some expressions for the clustering coefficient of the
tensor product of arbitrary graphs, regular graphs, and strongly regular
graphs. A Vizing-type upperbound and a sharp lower bound for the clustering
coefficient of the tensor product of graphs are also given.


title: Linear codes using simplicial complexes

abstract:
  Certain simplicial complexes are used to construct a subset $D$ of
$\mathbb{F}_{2^n}^m$ and $D$, in turn, defines the linear code $C_{D}$ over
$\mathbb{F}_{2^n}$ that consists of $(v\cdot d)_{d\in D}$ for $v\in
\mathbb{F}_{2^n}^m$. Here we deal with the case $n=3$, that is, when $C_{D}$ is
an octanary code. We establish a relation between $C_{D}$ and its binary
subfield code $C_{D}^{(2)}$ with the help of a generator matrix. For a given
length and dimension, a code is called distance optimal if it has the highest
possible distance. With respect to the Griesmer bound, five infinite families
of distance optimal codes are obtained, and sufficient conditions for certain
linear codes to be minimal are established.


title: Enveloped Sinusoid Parseval Frames

abstract:
  This paper presents a method of constructing Parseval frames from any
collection of complex envelopes. The resulting Enveloped Sinusoid Parseval
(ESP) frames can represent a wide variety of signal types as specified by their
physical morphology. Since the ESP frame retains its Parseval property even
when generated from a variety of envelopes, it is compatible with large scale
and iterative optimization algorithms. ESP frames are constructed by applying
time-shifted enveloping functions to the discrete Fourier Transform basis, and
in this way are similar to the short-time Fourier Transform.
  This work provides examples of ESP frame generation for both synthetic and
experimentally measured signals. Furthermore, the frame's compatibility with
distributed sparse optimization frameworks is demonstrated, and efficient
implementation details are provided. Numerical experiments on acoustics data
reveal that the flexibility of this method allows it to be simultaneously
competitive with the STFT in time-frequency processing and also with Prony's
Method for time-constant parameter estimation, surpassing the shortcomings of
each individual technique.


title:
Probabilistic Modelled Optimal Frame for Erasures under Spectral and
  Operator Norm

abstract:
  Error occurs in data transmission process when some data are missing at the
time of reconstruction. Finding the best dual frame or a dual pair that
minimizes the reconstruction error when erasure occurs,is a deep-rooted problem
in frame theory. The main motivation behind this paper is to characterize the
optimal dual under the spectral and operator norms. Here we give several
equivalent conditions for which the canonical dual is an optimal dual frame for
a given frame. We also go on to characterize the set of dual pairs which
attains the optimal value.


title:
Solvable models in the KPZ class: approach through periodic and free
  boundary Schur measures

abstract:
  We explore probabilistic consequences of correspondences between
$q$-Whittaker measures and periodic and free boundary Schur measures
established by the authors in the recent paper [arXiv:2106.11922]. The result
is a comprehensive theory of solvability of stochastic models in the KPZ class
where exact formulas descend from mapping to explicit determinantal and
pfaffian point processes. We discover new variants of known results as
determinantal formulas for the current distribution of the ASEP on the line and
new results such as Fredholm pfaffian formulas for the distribution of the
point-to-point partition function of the Log Gamma polymer model in half space.
In the latter case, scaling limits and asymptotic analysis allow to establish
Baik-Rains phase transition for height function of the KPZ equation on the half
line at the origin.

categories: math.PR cond-mat.stat-mech math-ph math.MP


title: Bounds on skewness and kurtosis of steady state currents

abstract:
  Current fluctuations are a powerful tool to unreaveal the underlying physics
of the observed transport process. This work discusses some general properties
of the third and the fourth current cumulant (skewness and kurtosis) related to
dynamics and thermodynamics of a transport setup. Specifically, several
distinct bounds on these quanities are either analytically derived or
numerically conjectured, which are applicable to: 1) noninteracting fermionic
systems, 2) nonintereacting bosonic systems, 3) thermally driven classical
Markovian systems, 4) unicyclic Markovian networks. Finally, it is demonstrated
that violation of the obtained inequalities can provide information about the
physics the analyzed system, e.g., enable one to infer presence of interactions
or unitary dynamics as well as characterize the nature of thermodynamic forces
driving the system. In particular, relevant information about the microscopic
dynamics can be gained even at equilibrium when the current variance - a
standard measure of current fluctuations - is determined mostly by the thermal
noise.


title:
On isomorphism conditions for algebra functors with applications to
  Leavitt path algebras

abstract:
  We introduce certain functors from the category of commutative rings (and
related categories) to that of $\mathbb{Z}$-algebras (not necessarily
associative or commutative). One of the motivating examples is the Leavitt path
algebra functor $R\mapsto L_R(E)$ for a given graph $E$. Our goal is to find
"descending" isomorphism results of the type: if $\mathfrak{F},\mathcal{G}$ are
algebra functors and $K\subset K'$ a field extension, under what conditions an
isomorphism $\mathfrak{F}(K')\cong \mathcal{G}(K')$ of $K'$-algebras implies
the existence of an isomorphism $\mathfrak{F}(K)\cong\mathcal{G}(K)$ of
$K$-algebras? We find some positive answers to that problem for the so-called
"extension invariant functors" which include the functors associated to Leavitt
path algebras, Steinberg algebras, path algebras, group algebras, evolution
algebras and others. For our purposes, we employ an extension of the Hilbert's
Nullstellensatz Theorem for polynomials in possibly infinitely many variables,
as one of our main tools. We also remark that for extension invariant functors
$\mathfrak{F},\mathcal{G}$, an isomorphism
$\mathfrak{F}(H)\cong\mathcal{G}(H)$, for some Hopf $K$-algebra $H$, implies
the existence of an isomorphism $\mathfrak{F}(S)\cong\mathcal{G}(S)$ for any
commutative and unital $K$-algebra $S$.


title: Power savings for counting solutions to polynomial-factorial equations

abstract:
  Let $P$ be a polynomial with integer coefficients and degree at least two. We
prove an upper bound on the number of integer solutions $n\leq N$ to $n! =
P(x)$ which yields a power saving over the trivial bound. In particular, this
applies to a century-old problem of Brocard and Ramanujan. The previous best
result was that the number of solutions is $o(N)$. The proof uses techniques of
Diophantine and Pad\'e approximation.


title:
Timelike behavior of the electromagnetic form factor in the functional
  formalism

abstract:
  The electromagnetic form factor of the pion is calculated within the use of
functional formalism. We develop Integral Representation for the minimal set of
Standard Model Green's functions and derive the dispersion relation for the
form factor in two flavor QCD isospin limit $m_u=m_d$. We use dressed quark
propagator as obtained form the gap equation in Minkowski space and derive the
approximate dispersion relation for the form factor. We evaluate the form
factor for the spacelike as well as for the timelike momentum in presented
formalism for the first time. A new Nakanishi like form of integral
representation is proved on the base of vector Bethe-Salpeter equation for the
quark-photon vector with ladder-rainbow kernel. The Gauge Technique turns to be
a part of the entire structure of the vertex.
  In analytic approach presented here, it is shown that the large amount of
$\rho$ meson peak in the cross section
  $e^+e^-\rightarrow \pi^+\pi^-$ is governed by the gauge invariance of
QED/QCD, i.e. by Gauge Technique constructed quark-photon vertex. This
approximation naturally explains the broad shape of the $\rho$ meson peak.


title:
Tomography of stellar halos: what does anisotropy in a stellar halo tell
  us?

abstract:
  The stellar halo of the Milky Way is known to have a highly lumpy structure
due to the presence of tidal debris and streams accreted from the satellite
galaxies. The abundance and distribution of these substructures can provide a
wealth of information on the assembly history of the Milky Way. We use some
information-theoretic measures to study the anisotropy in a set of Milky
Way-sized stellar halos from the Bullock & Johnston suite of simulations. Our
analysis shows that the radial anisotropy in each stellar halo increases with
the distance from its centre and eventually plateaus out beyond a certain
radius. All the stellar halo have a very smooth structure within a radius of
$\sim 50$ kpc and a highly anisotropic structure in the outskirts. At a given
radius, the polar and azimuthal anisotropies in a stellar halo have two
distinct components: (i) a nearly unvarying component from the smooth
distribution of stars and (ii) a highly fluctuating component possibly from the
substructures. We destroy the substructures and any non-spherical shape of the
halo by randomizing the polar and azimuthal coordinates of the stellar
particles while keeping their radial distances fixed. We observe that the
fluctuating part of the anisotropy is completely eliminated, and the unvarying
part of the anisotropy is significantly reduced after the sphericalization. A
comparison between the original halo and its sphericalized versions reveals
that the unvarying part of the anisotropy originates from the discreteness
noise and the non-spherical shape of the halo whereas the substructures
contribute to the fluctuating part. We show that such distinction between the
anisotropies can constrain the shape of the stellar halo and its substructures.
Finally, we map the distribution of the individual substructures by combining
the polar and azimuthal anisotropy profiles of the halo at different radial
distances.


title:
CHAI: A CHatbot AI for Task-Oriented Dialogue with Offline Reinforcement
  Learning

abstract:
  Conventionally, generation of natural language for dialogue agents may be
viewed as a statistical learning problem: determine the patterns in
human-provided data and generate appropriate responses with similar statistical
properties. However, dialogue can also be regarded as a goal directed process,
where speakers attempt to accomplish a specific task. Reinforcement learning
(RL) algorithms are designed specifically for solving such goal-directed
problems, but the most direct way to apply RL -- through trial-and-error
learning in human conversations, -- is costly. In this paper, we study how
offline reinforcement learning can instead be used to train dialogue agents
entirely using static datasets collected from human speakers. Our experiments
show that recently developed offline RL methods can be combined with language
models to yield realistic dialogue agents that better accomplish task goals.


title: On energetics and progenitors of Odd Radio Circles

abstract:
  Odd Radio Circles or ORCs are recently discovered low surface brightness
diffuse radio sources, whose progenitors and astrophysical processes
responsible for their origins are presently debated. Some ORCs appear to be
hosted in distant galaxies and some are host-less. Two plausible scenarios
consider ORCs as either nearby supernovae remnants of sizes a few hundred pc in
the intragroup medium of the local group of galaxies or alternatively shocked
halos of sizes a few hundred kpc around distant galaxies. The input energy for
shocks, required to create ORCs of a few hundred kpc size is estimated to be
$10^{56} - 10^{59}$ erg. It is shown here that the energy released in shocks
with a rate of $10^{41} - 10^{44}$ erg s$^{-1}$ due to multiple ($10^{3} -
10^{6}$) tidal disruption events in a short span of time (a few tens of Myr) in
a merger galaxy system, hosting a massive black hole can supply required energy
to generate ORCs around distant galaxies. The most plausible and abundant hosts
for ORCs can be post-starburst galaxies at intermediate redshifts. The
presently observed dominance of tidal disruption events in post-starburst
galaxies, redshift evolution and environments of post-starburst galaxies at
intermediate redshifts favourably support the current observations.


title: Thickness and a gap lemma in $\mathbb{R}^d$

abstract:
  We give a definition of thickness in $\mathbb{R}^d$ that is useful even for
totally disconnected sets, and prove a Gap Lemma type result. We also guarantee
an interval of distances in any direction in thick compact sets, relate thick
sets (for this definition of thickness) with winning sets, give a lower bound
for the Hausdorff dimension of the intersection of countably many of them, a
result guaranteeing the presence of large patterns, and lower bounds for the
Hausdorff dimension of a set in relationship with its thickness.


title:
The Markov model of a dynamic system based on experimental data for
  control problems of bionic prostheses

abstract:
  This article is devoted to a prediction of gait kinematics based on the
Markov chains in the delay space. We use hypercubic grid in the delay space of
angles in the sagittal plane in the knee and hip joints to construct Markov
states. Our experimental signal (obtained from the telemetry of the prosthesis)
provides transition probabilities. The resulting Markov model seems to be
helpful for estimation of attractor dimension, characteristic frequencies of
the system, and so on.


title:
In-Circuit Impedance Measurement Setups of Inductive Coupling Approach:
  A Review

abstract:
  In-circuit impedance measurement provides useful information for many EMC
applications. The inductive coupling approach is a promising in-circuit
impedance measurement method due to its non-contact characteristics and simple
on-site implementation. Many measurement setups of this approach were reported.
However, a comprehensive survey and comparison of these setups have not been
found in the literature. This paper reviews these setups in terms of their
characteristics, limitations, and applications. In addition, recommendations
for future research are also presented.


title:
Energy calibration of nonlinear microcalorimeters with uncertainty
  estimates from Gaussian process regression

abstract:
  The nonlinear energy response of cryogenic microcalorimeters is usually
corrected through an empirical calibration. X-ray or gamma-ray emission lines
of known shape and energy anchor a smooth function that generalizes the
calibration data and converts detector measurements to energies. We argue that
this function should be an approximating spline. The theory of Gaussian process
regression makes a case for this functional form. It also provides an important
benefit previously absent from our calibration method: a quantitative
uncertainty estimate for the calibrated energies, with lower uncertainty near
the best-constrained calibration points.


title: A smartphone-based sensor for measuring the optical properties of snow

abstract:
  Snow is a highly complex medium composed of from ice crystals of various
shapes and sizes. Knowledge of its intrinsic optical properties such as the
scattering and absorption coefficient is tantamount for radiative transfer
models in climate research. The absorption coefficient in particular allows us
to access information about light-absorbing particles contained in the snow. In
contrast to snow's apparent properties like the albedo, measuring the intrinsic
properties is challenging, Here, we present a simple apparatus that can measure
bulk optical properties of snow using readily available components and a
smartphone camera, and a robust diffuse-optical framework for data analysis. We
demonstrate the instrument both on scattering phantoms with known scattering
and absorption coefficient as well as in the field. Its low cost, simplicity
and portability uniquely qualify this setup for large-scale field work,
undergraduate education and citizen science.


title:
Sensitive multi-species photoacoustic gas detection based on
  mid-infrared supercontinuum source and miniature multipass cell

abstract:
  We report multipass broadband photoacoustic spectroscopy of trace gases in
the mid-infrared. The measurement principle of the sensor relies on
supercontinuum-based Fourier transform photoacoustic spectroscopy (FT-PAS), in
which a scanning interferometer modulates the intensity of a mid-infrared
supercontinuum light source and a cantilever microphone is employed for
sensitive photoacoustic detection. With a custom-built external Herriott cell,
the supercontinuum beam propagates ten times through a miniature and
acoustically non-resonant gas cell. The performance of the FT-PAS system is
demonstrated by measuring the fundamental C-H stretch bands of various
hydrocarbons. A noise equivalent detection limit of 11 ppb is obtained for
methane (40 s averaging time, 15 $\mu$W/cm$^{-1}$ incident power spectral
density, 4 cm$^{-1}$ resolution), which is an improvement by a factor of 12
compared to the best previous FT-PAS systems. High linearity and good stability
of the sensor provide reliable identification of individual species from a gas
mixture with strong spectral overlap, laying the foundation for sensitive and
selective multi-species detection in small sample volumes.


title: Better automation of beamline control at HEPS

abstract:
  At the High Energy Photon Source (HEPS) where up to 90 beamlines can be
provided in the future, minimisation of workload for individual beamlines and
maximisation of knowledge about one beamline that can be applied to other
beamlines is essential to minimise the total complexity in beamline control.
Presented in this paper are our efforts to achieve these goals by composing
relatively simple utilities and mechanisms to automate tasks, and always
remembering to keep our automation solutions simple and clear. After an
introduction to our choice of basic software in EPICS-based beamline control,
the issues encountered in introducing package management to EPICS modules, as
well as our solutions to them, are presented; then the design and
implementation of our packaging system is concisely discussed. After a
presentation of our efforts to reduce the need for self-built multi-device
EPICS IOC applications by providing reusable modular IOC executables, our
implementation of easily maintainable multi-IOC setups through the separation
and minimisation of each user's IOC configurations is given. Finally, the
ongoing project of comprehensive beamline services at HEPS to further simplify
configuration management on multiple scales, ranging from individual beamline
devices to all beamlines at HEPS, is introduced.


title: On the existence of twin prime in an interval

abstract:
  Let $S_{(x,y]} = \left\{\frac{p_n}{p_{n+1}-2} :~ n\in I \right\}$ for $I =
\left\{n :~ x<p_n \le y \right\}$, where $x, y \in \mathbb{R}_{>0}$ and $p_n$
is the $n$-th prime. If $M_\alpha(x,y)$ denotes the $\alpha$-power mean of the
elements of $S_{(x,y]}$, it is shown that the existence of a twin prime pair in
$(x,y]$ is implied if $\displaystyle \lim_{\alpha \rightarrow
\infty}M_{\alpha}(x,y) > 1 - 2/y + O(y^{-2})$ for a sufficiently large $y$. We
also find a lower bound for the mean, $\displaystyle \lim_{\alpha \rightarrow
\infty}M_{\alpha}(x,x^\beta)>1-c/x^\beta+O(x^{-\beta}\log^{-1} x)$, where $c>0$
and $\beta = 1+c/\log^2 x$ or equivalently, $x^\beta=x+cx/\log x+O(x/\log^2
x)$. With $c<2$, the lower bound for $\displaystyle \lim_{\alpha \rightarrow
\infty}M_{\alpha}(x,x^\beta)$ satisfies the inequality on the existence of a
twin prime.


title: Some topological results on $\phi$-metric spaces

abstract:
  In this paper, the notion of $\phi$-metric is developed by making a suitable
modification in triangle inequality. It is shown that spaces like S-metric,
b-metric, etc. are $\phi$-metrizable. Unlike metric, concerned $\phi$-metric
can be easily constructed. The structure of $\phi$-metric spaces is studied and
some fixed point theorems are established.


title: Strolling in Room-Scale VR: Hex-Core-MK1 Omnidirectional Treadmill

abstract:
  The natural locomotion interface is critical to the development of many VR
applications. For household VR applications, there are two basic requirements:
natural immersive experience and minimized space occupation. The existing
locomotion strategies generally do not simultaneously satisfy these two
requirements well. This paper presents a novel omnidirectional treadmill (ODT)
system, named Hex-Core-MK1 (HCMK1). By implementing two kinds of mirror
symmetrical spiral rollers to generate the omnidirectional velocity field, this
proposed system is capable of providing real walking experiences with a
full-degree of freedom in an area as small as 1.76 m^2, while delivering great
advantages over several existing ODT systems in terms of weight, volume,
latency and dynamic performance. Compared with the sizes of Infinadeck and HCP,
the two best motor-driven ODTs so far, the 8 cm height of HCMK1 is only 20% of
Infinadeck and 50% of HCP. In addition, HCMK1 is a lightweight device weighing
only 110 kg, which provides possibilities of further expanding VR scenarios,
such as terrain simulation. The latency of HCMK1 is only 23ms. The experiments
show that HCMK1 can deliver on a starting acceleration of 16.00 m/s^2 and a
braking acceleration of 30.00 m/s^2.


title: On Dynamics of Asymptotically Minimal Polynomials

abstract:
  We study dynamical properties of asymptotically extremal polynomials
associated with a non-polar planar compact set E. In particular, we prove that
if the zeros of such polynomials are uniformly bounded then their Brolin
measures converge weakly to the equilibrium measure of E. In addition, if E is
regular and the zeros of such polynomials are sufficiently close to E then we
prove that the filled Julia sets converge to polynomial convex hull of E in the
Klimek topology.