Abstract:
  In recent works, we proposed a hypothesis that the turbulence in gases could
be produced by particles interacting via a potential, and examined the proposed
mechanics of turbulence formation in a simple model of two particles for a
variety of different potentials. In this work, we use the same hypothesis to
develop new fluid mechanics equations which model turbulent gas flow on a
macroscopic scale. The main difference between our approach and the
conventional formalism is that we avoid replacing the potential interaction
between particles with the Boltzmann collision integral. Due to this
difference, the velocity moment closure, which we implement for the shear
stress and heat flux, relies upon the high Reynolds number condition, rather
than the Newton law of viscosity and the Fourier law of heat conduction. The
resulting system of equations of fluid mechanics differs considerably from the
standard Euler and Navier-Stokes equations. A numerical simulation of our
system shows that a laminar Bernoulli jet of an argon-like hard sphere gas in a
straight pipe rapidly becomes a turbulent flow. The time-averaged Fourier
spectra of the kinetic energy of this flow exhibit Kolmogorov's negative
five-thirds power decay rate.


Abstract:
  Nested case-control (NCC) is a sampling method widely used for developing and
evaluating risk models with expensive biomarkers on large prospective cohort
studies. The biomarker values are typically obtained on a sub-cohort,
consisting of all the events and a subset of non-events. However, when the
number of events is not small, it might not be affordable to measure the
biomarkers on all of them. Due to the costs and limited availability of
bio-specimens, only a subset of events is selected to the sub-cohort as cases.
For these "untypical" NCC studies, we propose a new weighting method for the
inverse probability weighted (IPW) estimation. We also design a perturbation
method to estimate the variance of the IPW estimator with our new weights. It
accounts for between-subject correlations induced by the sampling processes for
both cases and controls through perturbing their sampling indicator variables,
and thus, captures all the variations. Furthermore, we demonstrate,
analytically and numerically, that when cases consist of only a subset of
events, our new weight produces more efficient IPW estimators than the weight
proposed in Samuelsen (1997) for a standard NCC design. We illustrate the
estimating procedure with a study that aims to evaluate a biomarker-based risk
prediction model using the Framingham cohort study.


Abstract:
  This paper introduces the notion of quantitative resilience of a control
system. Following prior work, we study systems enduring a loss of control
authority over some of their actuators. Such a malfunction results in actuators
producing possibly undesirable inputs over which the controller has real-time
readings but no control. By definition, a system is resilient if it can still
reach a target after a loss of control authority. However, after a malfunction
a resilient system might be significantly slower to reach a target compared to
its initial capabilities. We quantify this loss of performance through the new
concept of quantitative resilience. We define this metric as the maximal ratio
of the minimal times required to reach any target for the initial and
malfunctioning systems. Na\"ive computation of quantitative resilience directly
from the definition is a time-consuming task as it requires solving four
nested, possibly nonlinear, optimization problems. The main technical
contribution of this work is to provide an efficient method to compute
quantitative resilience. Relying on control theory and on three novel geometric
results we reduce the computation of quantitative resilience to a single linear
optimization problem. We illustrate our method on two numerical examples: an
opinion dynamics scenario and a trajectory controller for low-thrust
spacecrafts.


Abstract:
  We test the anisotropy in the Finslerian cosmological model with the X-ray
and ultraviolet (UV) fluxes of 808 quasars. The dipole amplitude is
$A_D=0.302_{ -0.124}^{ +0.185}$ and the dipole direction points towards $(l, b)
= ( 288.92_{~ -28.80^{\circ}}^{^{\circ}+23.74^{\circ}}, 6.10_{~
-16.40^{\circ}}^{^{\circ} +16.55^{\circ}} )$. We find that the dipole direction
from the X-ray and UV fluxes of quasars is very close to the dipole direction
given by the "Joint Light-curve Analysis" (JLA) compilation in the Finslerian
cosmological model and the angular difference between the two dipole directions
is only $10.44^{\circ}$. We also find the angular difference between the dipole
direction from the 808 quasars in the Finslerian cosmological model and ones
from the supernovae of type Ia (SNe Ia) samples in the dipole-modulated
$\Lambda$CDM model is around $30^{\circ}$. Six gravitationally lensed quasars
are considered to investigate the Hubble constant $H_0$ in the Finslerian
cosmological model. We get a slightly smaller $H_0$ than the result given by
the six gravitationally lensed quasars. Finally, we forecast the future
constraints on the dipole parameters with the X-ray and UV fluxes of quasars.
As the number of simulations increases, the precisions of the parameters
related to anisotropy in the Finslerian cosmological model improve
significantly. The X-ray and UV fluxes of quasars have a promising future as a
probe of anisotropy in Finsler spacetime.


Abstract:
  During a geosteering operation the well path is intentionally adjusted in
response to the new data acquired while drilling. To achieve consistent
high-quality decisions, especially when drilling in complex environments,
decision support systems can help cope with high volumes of data and
interpretation complexities. They can assimilate the real-time measurements
into a probabilistic earth model and use the updated model for decision
recommendations.
  Recently, machine learning (ML) techniques have enabled a wide range of
methods that redistribute computational cost from on-line to off-line
calculations. In this paper, we introduce two ML techniques into the
geosteering decision support framework. Firstly, a complex earth model
representation is generated using a Generative Adversarial Network (GAN).
Secondly, a commercial extra-deep electromagnetic simulator is represented
using a Forward Deep Neural Network (FDNN).
  The numerical experiments demonstrate that the combination of the GAN and the
FDNN in an ensemble randomized maximum likelihood data assimilation scheme
provides real-time estimates of complex geological uncertainty. This yields
reduction of geological uncertainty ahead of the drill-bit from the
measurements gathered behind and around the well bore.


Abstract:
  Associative memory is a fundamental function in the brain. Here, we
generalize the standard associative memory model to include long-range Hebbian
interactions at the learning stage, corresponding to a large synaptic
integration window. In our model, the Hebbian length can be arbitrarily large.
The spectral density of the coupling matrix is derived using the replica
method, which is also shown to be consistent with the results obtained by
applying the free probability method. The maximal eigenvalue is then obtained
by an iterative equation, related to the paramagnetic to spin glass transition
in the model. Altogether, this work establishes the connection between the
associative memory with arbitrary Hebbian length and the asymptotic
eigen-spectrum of the neural-coupling matrix.


Abstract:
  Let $U^+_q$ denote the positive part of the quantized enveloping algebra
$U_q(\widehat{\mathfrak{sl}}_2)$. The algebra $U^+_q$ has a presentation
involving two generators $W_0$, $W_1$ and two relations, called the $q$-Serre
relations. In 1993 I. Damiani obtained a PBW basis for $U^+_q$, consisting of
some elements $\lbrace E_{n \delta+ \alpha_0} \rbrace_{n=0}^\infty$, $\lbrace
E_{n \delta+ \alpha_1} \rbrace_{n=0}^\infty$, $\lbrace E_{n \delta}
\rbrace_{n=1}^\infty$. In 2019 we introduced the alternating central extension
$\mathcal U^+_q$ of $U^+_q$. We defined $\mathcal U^+_q$ by generators and
relations. The generators, said to be alternating, are denoted $\lbrace
\mathcal W_{-k}\rbrace_{k=0}^\infty$, $\lbrace \mathcal
W_{k+1}\rbrace_{k=0}^\infty$, $ \lbrace \mathcal G_{k+1}\rbrace_{k=0}^\infty$,
$\lbrace \mathcal {\tilde G}_{k+1}\rbrace_{k=0}^\infty$. Let $\langle \mathcal
W_0, \mathcal W_1 \rangle$ denote the subalgebra of $\mathcal U^+_q$ generated
by $\mathcal W_0$, $\mathcal W_1$. It is known that there exists an algebra
isomorphism $U^+_q\to \langle \mathcal W_0, \mathcal W_1 \rangle$ that sends
$W_0 \mapsto \mathcal W_0$ and $W_1 \mapsto \mathcal W_1$. Via this isomorphism
we identify $U^+_q$ with $\langle \mathcal W_0, \mathcal W_1 \rangle$. In our
main result, we express the Damiani PBW basis elements in terms of the
alternating generators. We give the answer in terms of generating functions.


Abstract:
  Explainable machine learning has become increasingly prevalent, especially in
healthcare where explainable models are vital for ethical and trusted automated
decision making. Work on the susceptibility of deep learning models to
adversarial attacks has shown the ease of designing samples to mislead a model
into making incorrect predictions. In this work, we propose a model agnostic
explainability-based method for the accurate detection of adversarial samples
on two datasets with different complexity and properties: Electronic Health
Record (EHR) and chest X-ray (CXR) data. On the MIMIC-III and Henan-Renmin EHR
datasets, we report a detection accuracy of 77% against the Longitudinal
Adversarial Attack. On the MIMIC-CXR dataset, we achieve an accuracy of 88%;
significantly improving on the state of the art of adversarial detection in
both datasets by over 10% in all settings. We propose an anomaly detection
based method using explainability techniques to detect adversarial samples
which is able to generalise to different attack methods without a need for
retraining.


Abstract:
  We present a supersymmetric extension of the exotic Newtonian Chern-Simons
gravity theory in three spacetime dimensions. The underlying new
non-relativistic superalgebra is obtained by expanding the $\mathcal{N}=2$ AdS
superalgebra and can be written as two copies of the enhanced Nappi-Witten
algebra, one of which is augmented by supersymmetry. We show that the exotic
Newtonian superalgebra allows to introduce a cosmological constant to the
extended Newtonian supergravity. Interestingly, the obtained supergravity
action contains the extended Newton-Hooke supergravity as a sub-case.


Abstract:
  We investigate what the orbits of globular clusters (GCs) in the Fornax dwarf
spheroidal (dSph) galaxy can teach us about dark matter (DM). This problem was
recently studied for ultralight dark matter (ULDM). We consider two additional
models: (i) fermionic degenerate dark matter (DDM), where Pauli blocking should
be taken into account in the dynamical friction computation; and (ii)
self-interacting dark matter (SIDM). We give a simple and direct Fokker-Planck
derivation of dynamical friction, new in the case of DDM and reproducing
previous results in the literature for ULDM and cold DM. ULDM, DDM and SIDM
were considered in the past as leading to cores in dSphs, a feature that acts
to suppress dynamical friction and prolong GC orbits. For DDM we derive a
version of the cosmological free streaming limit that is independent of the DM
production mechanism, finding that DDM cannot produce an appreciable core in
Fornax without violating Ly-$\alpha$ limits. If the Ly-$\alpha$ limit is
discounted for some reason, then stellar kinematics data does allow a DDM core
which could prolong GC orbits. For SIDM we find that significant prolongation
of GC orbits could be obtained for values of the self-interaction cross section
considered in previous works. In addition to reassessing the inspiral time
using updated observational data, we give a new perspective on the so-called GC
timing problem, demonstrating that for a cuspy cold DM profile dynamical
friction predicts a $z=0$ radial distribution for the innermost GCs that is
independent of initial conditions. The observed orbits of Fornax GCs are
consistent with this expectation with a mild apparent fine-tuning at the level
of $\sim25\%$.


Abstract:
  A classical result of Rothschild and van Lint asserts that if every non-zero
Fourier coefficient of a Boolean function $f$ over $\mathbb{F}_2^{n}$ has the
same absolute value, namely $|\hat{f}(\alpha)|=1/2^k$ for every $\alpha$ in the
Fourier support of $f$, then $f$ must be the indicator function of some affine
subspace of dimension $n-k$. In this paper we slightly generalize their result.
Our main result shows that, roughly speaking, Boolean functions whose Fourier
coefficients take values in the set $\{-2/2^k, -1/2^k, 0, 1/2^k, 2/2^k\}$ are
indicator functions of two disjoint affine subspaces of dimension $n-k$ or four
disjoint affine subspace of dimension $n-k-1$. Our main technical tools are
results from additive combinatorics which offer tight bounds on the affine span
size of a subset of $\mathbb{F}_2^{n}$ when the doubling constant of the subset
is small.


Abstract:
  We study the generalization performance of $\text{full-batch}$ optimization
algorithms for stochastic convex optimization: these are first-order methods
that only access the exact gradient of the empirical risk (rather than
gradients with respect to individual data points), that include a wide range of
algorithms such as gradient descent, mirror descent, and their regularized
and/or accelerated variants. We provide a new separation result showing that,
while algorithms such as stochastic gradient descent can generalize and
optimize the population risk to within $\epsilon$ after $O(1/\epsilon^2)$
iterations, full-batch methods either need at least $\Omega(1/\epsilon^4)$
iterations or exhibit a dimension-dependent sample complexity.


Abstract:
  Several works have shown that the regularization mechanisms underlying deep
neural networks' generalization performances are still poorly understood. In
this paper, we hypothesize that deep neural networks are regularized through
their ability to extract meaningful clusters among the samples of a class. This
constitutes an implicit form of regularization, as no explicit training
mechanisms or supervision target such behaviour. To support our hypothesis, we
design four different measures of intraclass clustering, based on the neuron-
and layer-level representations of the training data. We then show that these
measures constitute accurate predictors of generalization performance across
variations of a large set of hyperparameters (learning rate, batch size,
optimizer, weight decay, dropout rate, data augmentation, network depth and
width).


Abstract:
  In this paper, we consider quasi-Newton methods and solve two open problems
mentioned in Rodomanov and Nesterov's discussion section. First, we extent
Rodomanov and Nesterov's results to random general quasi-Newton methods, which
include common DFP, BFGS, SR1 methods. Such random methods adopt a random
direction for updating the approximate Hessian matrix. Second, we focus on the
specific quasi-Newton methods: SR1 and BFGS methods. We provide improved
versions of greedy and random methods with provable better explicit (local)
superlinear convergence rates. Our analysis is closely related to the
approximation of a given Hessian matrix, unconstrained quadratic objective, as
well as the general strongly convex, smooth, and strongly self-concordant
functions.


Abstract:
  This study derives a method to consistently recover the second-order
convergence of the lattice Boltzmann method (LBM), which is frequently degraded
by the improper discretisation of required source terms. The work focuses on
advection-diffusion models in which the source terms are dependent on the
intensity of transported fields. The main findings are applicable to a wide
range of formulations within the LBM framework. All considered source terms are
interpreted as contributions to the zeroth-moment of the distribution function.
These account for sources in a scalar field, such as density, concentration or
temperature. In addition to this, certain immersed boundary methods can be
interpreted as a source term in their formulation, highlighting a further
application for this work.
  This paper makes three primary contributions to the current state-of-the-art.
Firstly, it identifies the differences observed between the ways source terms
are included in the LBM schemes present in the literature. The algebraic
manipulations are explicitly presented in this paper to clarify the differences
observed, and identify their origin. Secondly, it derives in full detail, the
implicit relation between the value of the transported macroscopic field, and
the sum of the LBM densities. Moreover, this relation is valid for any source
term discretization scheme, and three equivalent forms of the second-order
accurate collision operator are presented. Finally, closed-form solutions of
this implicit relation are shown for a variety of common models.
  The second-order convergence of the proposed LBM schemes is verified on both
linear and non-linear source terms. Commonly used diffusive and acoustic
scalings are discussed, and their pitfalls are identified. Moreover, for a
simplified case, the competing errors are shown visually with isolines of error
in the space of spatial and temporal resolutions.


Abstract:
  The field of DNA nanotechnology has made it possible to assemble, with high
yields, different structures that have actionable properties. For example,
researchers have created components that can be actuated. An exciting next step
is to combine these components into multifunctional nanorobots that could,
potentially, perform complex tasks like swimming to a target location in the
human body, detect an adverse reaction and then release a drug load to stop it.
However, as we start to assemble more complex nanorobots, the yield of the
desired nanorobot begins to decrease as the number of possible component
combinations increases. Therefore, the ultimate goal of this work is to develop
a predictive model to maximize yield. However, training predictive models
typically requires a large dataset. For the nanorobots we are interested in
assembling, this will be difficult to collect. This is because high-fidelity
data, which allows us to characterize the shape and size of individual
structures, is very time-consuming to collect, whereas low-fidelity data is
readily available but only captures bulk statistics for different processes.
Therefore, this work combines low- and high-fidelity data to train a generative
model using a two-step process. We first use a relatively small, high-fidelity
dataset to train a generative model. At run time, the model takes low-fidelity
data and uses it to approximate the high-fidelity content. We do this by
biasing the model towards samples with specific properties as measured by
low-fidelity data. In this work we bias our distribution towards a desired node
degree of a graphical model that we take as a surrogate representation of the
nanorobots that this work will ultimately focus on. We have not yet accumulated
a high-fidelity dataset of nanorobots, so we leverage the MolGAN architecture
[1] and the QM9 small molecule dataset [2-3] to demonstrate our approach.


Abstract:
  Groundstate magnetism of the one-band Hubbard model on the frustrated square
lattice where both nearest-neighbour $t_1$ and next-nearest-neighbour $t_2$
hoppings are considered at half-filling are revisited within mean field
approximation. Two new magnetic phases are detected at intermediate strength of
Hubbard $U$ and relative strong frustration of $t_2/t_1$, named double-stripe
and plaquette antiferromagnetic states, both of which are metallic and stable
even at finite temperature and electron doping. The nature of the phase
transitions between different phases and the properties of the two new states
are analyzed in detail. Our results of various magnetic states emerging from
geometric frustration in the minimal model suggests that distinct
antiferromagnetism observed experimentally in the parent states of two
high-T$_c$ superconducting families, i.e., cuprates and iron-based
superconductors, may be understood from a unified microscopic origin,
irrespective of orbital degrees of freedom, or hoppings further than
next-nearest neighbour, etc.


Abstract:
  A major trend in academia and data science is the rapid adoption of Bayesian
statistics for data analysis and modeling, leading to the development of
probabilistic programming languages (PPL). A PPL provides a framework that
allows users to easily specify a probabilistic model and perform inference
automatically. PyAutoFit is a Python-based PPL which interfaces with all
aspects of the modeling (e.g., the model, data, fitting procedure,
visualization, results) and therefore provides complete management of every
aspect of modeling. This includes composing high-dimensionality models from
individual model components, customizing the fitting procedure and performing
data augmentation before a model-fit. Advanced features include database tools
for analysing large suites of modeling results and exploiting domain-specific
knowledge of a problem via non-linear search chaining. Accompanying PyAutoFit
is the autofit workspace (see https://github.com/Jammy2211/autofit_workspace),
which includes example scripts and the HowToFit lecture series which introduces
non-experts to model-fitting and provides a guide on how to begin a project
using PyAutoFit. Readers can try PyAutoFit right now by going to the
introduction Jupyter notebook on Binder (see
https://mybinder.org/v2/gh/Jammy2211/autofit_workspace/HEAD) or checkout our
readthedocs(see https://pyautofit.readthedocs.io/en/latest/) for a complete
overview of PyAutoFit's features.


Abstract:
  Carton detection is an important technique in the automatic logistics system
and can be applied to many applications such as the stacking and unstacking of
cartons, the unloading of cartons in the containers. However, there is no
public large-scale carton dataset for the research community to train and
evaluate the carton detection models up to now, which hinders the development
of carton detection. In this paper, we present a large-scale carton dataset
named Stacked Carton Dataset(SCD) with the goal of advancing the
state-of-the-art in carton detection. Images are collected from the internet
and several warehourses, and objects are labeled using per-instance
segmentation for precise localization. There are totally 250,000 instance masks
from 16,136 images. In addition, we design a carton detector based on RetinaNet
by embedding Offset Prediction between Classification and Localization
module(OPCL) and Boundary Guided Supervision module(BGS). OPCL alleviates the
imbalance problem between classification and localization quality which boosts
AP by 3.1% - 4.7% on SCD while BGS guides the detector to pay more attention to
boundary information of cartons and decouple repeated carton textures. To
demonstrate the generalization of OPCL to other datasets, we conduct extensive
experiments on MS COCO and PASCAL VOC. The improvement of AP on MS COCO and
PASCAL VOC is 1.8% - 2.2% and 3.4% - 4.3% respectively.


Abstract:
  Motion planning is an essential aspect of autonomous systems and robotics and
is an active area of research. A recently-proposed sampling-based motion
planning algorithm, termed 'Generalized Shape Expansion' (GSE), has been shown
to possess significant improvement in computational time over several existing
well-established algorithms. The GSE has also been shown to be
probabilistically complete. However, asymptotic optimality of the GSE is yet to
be studied. To this end, in this paper we show that the GSE algorithm is not
asymptotically optimal by studying its behaviour for the promenade problem. In
order to obtain a probabilistically complete and asymptotically optimal
generalized shape-based algorithm, a modified version of the GSE, namely 'GSE*'
algorithm, is subsequently presented. The forementioned desired mathematical
properties of the GSE* algorithm are justified by its detailed analysis.
Numerical simulations are found to be in line with the theoretical results on
the GSE* algorithm.


Abstract:
  The declaration of COVID-19 as a pandemic has largely amplified the spread of
related information on social media, such as Twitter, Facebook, and
WeChat.Unlike the previous studies which focused on how to detect the
misinformation or fake news related toCOVID-19, we investigate how the disease
and information co-evolve in the population. We focus onCOVID-19and its
information during the period when the disease was widely spread in China,
i.e., from January 25th to March 24th, 2020. We first explore how the disease
and information co-evolve via the spatial analysis of the two spreading
processes. We visualize the geo-location of both disease and information at the
province level and find that disease is more geo-localized compared to
information. We find a high correlation between the disease and information
data, and also people care about the spread only when it comes to their
neighborhood. Regard to the content of the information, we find that positive
messages are more negatively correlated with the disease compared to negative
and neutral messages. Additionally, we introduce machine learning algorithms,
i.e., linear regression and random forest, to further predict the number of
infected using different disease spatial related and information-related
characteristics. We obtain that the disease spatial related characteristics of
nearby cities can help to improve the prediction accuracy. Meanwhile,
information-related characteristics can also help to improve the prediction
performance, but with a delay, i.e., the improvement comes from using, for
instance, the number of messages 10 days ago, for disease prediction. The
methodology proposed in this paper may shed light on new clues of emerging
infections


Abstract:
  We consider the effects of bound atomic electrons scattered by solar
neutrinos due to the electromagnetic properties of neutrinos. This necessiate
considering the recoil of atomic nucleus, which should be considered in the
momentum conservation, but that effect to the energy conservation is
negligible. This effect changes the kinematic behavior of the scattered
electron compared to that scattered on free electrons. We apply this effect to
the recent XENON1T data, but the bounds obtained from this is not very
restrictive. We obtained the bounds: the (transition) magnetic moment
$|f_{\alpha\beta}|\le 0.86\times 10^{-7}$ (times the electron Bohr magneton)
and the charge radius $|\tilde{r}|< 4.30\times 10^{-17\,}{\rm cm}$. For a
non-vanishing millicharge ($\varepsilon$), the allowed bound is shown in the
$\tilde{r}^2-\varepsilon$ plane.


Abstract:
  Being one of the most abundant atomic/molecular species observed in dense
molecular gas, atomic carbon ($\mathrm{C}^0$) is a potential good tracer of
molecular gas mass in many chemical/physical environments, though the
$\mathrm{C^0}$ abundance variation outside the Galactic disk region is yet to
be fully known. This paper presents a wide-field 500 GHz [CI] map of the
Galactic central molecular zone (CMZ) obtained with the ASTE 10-m telescope.
Principal component analysis and non-LTE multi-transition analysis have shown
that the [CI] emission predominantly originates from the low-excitation gas
component with a 20-50 K temperature and $\sim 10^3\ \mathrm{cm}^{-3}$ density,
whereas $\mathrm{C^0}$ abundance is likely suppressed in the high-excitation
gas component. The average $N(\mathrm{C}^0)$/$N(\mathrm{CO})$ abundance ratio
in the CMZ is 0.3-0.4, which is 2-3 times that in the Galactic disk. The
$N(\mathrm{C}^0)$/$N(\mathrm{CO})$ ratio increases to 0.7 in the innermost 10
pc region and to $\sim2$ in the circumnuclear disk. We discovered
$\mathrm{C^0}$-rich regions distributed in a ring-shape encircling the
supernova remnant (SNR) Sgr A east, indicative that the
$\mathrm{C}^0$-enrichment in the central 10 pc region is a consequence of a
molecular cloud-SNR interaction. In the 15 atom/molecules included in principal
component analysis (PCA), CN is the only other species that increases in the
[CI]-bright ring. The origin of the [CI]-bright ring is likely a cosmic-ray
dominated region created by low-energy cosmic-ray particles accelerated by Sgr
A east or primitive molecular gas collected by the SNR in which the
$\mathrm{C}^0$-to-CO conversion has not reached the equilibrium.


Abstract:
  We present a diffusion-based simulation and theoretical models for
explanation of photoluminescence (PL) emission intensity in semiconductor
nanoplatelets. It is shown that the shape of PL intensity curves can be
reproduced by the interplay of recombination, diffusion and trapping of
excitons. The emission intensity at short times is purely exponential and is
defined by recombination. At long times it is governed by the release of
excitons from surface traps and is characterized by a power-law tail. We show
that the crossover from one limit to another is controlled by diffusion
properties. This intermediate region exhibits a rich behaviour depending on the
value of diffusivity. Proposed approach reproduces all the features of
experimental curves measured for different nanoplatelet systems.


Abstract:
  We study the cohomology of Lie superalgebras for the full complex of forms:
superforms, pseudoforms and integral forms. We use the technique of spectral
sequences to abstractly compute the Chevalley-Eilenberg cohomology. We first
focus on the superalgebra $\mathfrak{osp}(2|2)$ and show that there exist
non-empty cohomology spaces among pseudoforms related to sub-superalgebras. We
then extend some classical theorems by Koszul, as to include pseudoforms and
integral forms. Further, we conjecture that the algebraic Poincar\'e duality
extends to Lie superalgebras, as long as all the complexes of forms are taken
into account and we prove that this holds true for $\mathfrak{osp}(2|2)$. We
finally construct the cohomology representatives explicitly by using a
distributional realisation of pseudoforms and integral forms. On one hand,
these results show that the cohomology of Lie superalgebras is actually larger
than expected, whereas one restricts to superforms only; on the other hand, we
show the emergence of completely new cohomology classes represented by
pseudoforms. These classes realise as integral form classes of
sub-superstructures.


Abstract:
  We analyze Andreev bound states (ABSs) that form in normal sections of a
Rashba nanowire that is only partially covered by a superconducting layer.
These ABSs are localized close to the ends of the superconducting section and
can be pinned to zero energy over a wide range of magnetic field strengths even
if the nanowire is in the non-topological regime. For finite-size nanowires
(typically $\lesssim 1$ $\mu$m in current experiments), the ABS localization
length is comparable to the length of the nanowire. The probability density of
an ABS is therefore non-zero throughout the nanowire and
differential-conductance calculations reveal a correlated zero-bias peak (ZBP)
at both ends of the nanowire. When a second normal section hosts an additional
ABS at the opposite end of the superconducting section, the combination of the
two ABSs can mimic the closing and reopening of the bulk gap in local and
non-local conductances accompanied by the appearance of the ZBP. These
signatures are reminiscent of those expected for Majorana bound states (MBSs)
but occur here in the non-topological regime. Our results demonstrate that
conductance measurements of correlated ZBPs at the ends of a typical
superconducting nanowire or an apparent closing and reopening of the bulk gap
in the local and non-local conductance are not conclusive indicators for the
presence of MBSs.


Abstract:
  At leading order, the $S$-matrices in QED and gravity are known to factorise,
providing unambiguous determinations of the parts divergent due to infrared
contributions. The soft $S$-matrices defined in this fashion are shown to be
defined entirely in terms of $2$ dimensional models on the celestial sphere,
involving two real scalar fields, allowing us to express the soft $S$-matrices
for real as well as virtual divergences as two dimensional correlation
functions. We discuss what this means for finding holographic representations
of scattering amplitudes in QED and gravity and comment on simple double copy
structures that arise during the analysis.


Abstract:
  This paper reports a mass transfer model of a reactant flowing in a large
aspect ratio microfluidic chip made of a channel with electrodes on the side
walls. A semi-analytical solution to the two-dimensional Fickian diffusion of a
reactant in a microchannel, including the electrochemical reaction at the
electrode interface, and the velocity profile obtained from the Navier-Stokes
equations in a fully developed laminar regime is found . The solution is
written in the Laplace domain in terms of transfer functions. The proposed
solution is an extension of the Leveque approximation describing the reactant
diffusion from the electrode to the middle of the microfluidic channel. The
main applications of this work are the use of the obtained transfer functions
for the measurement of the Faradic current density or the chemical
concentration at the electrode interface. The study can also be extended to the
heat transfer in microfluidic electrochemical chips (temperature or heat flux
measurements at the electrode interface).


Abstract:
  We study contract design for welfare maximization in the well known "common
agency" model of [Bernheim and Whinston, 1986]. This model combines the
challenges of coordinating multiple principals with the fundamental challenge
of contract design: that principals have incomplete information of the agent's
choice of action. Motivated by the significant social inefficiency of standard
contracts for such settings (which we formally quantify using a price of
anarchy/stability analysis), we investigate whether and how a recent toolbox
developed for the first set of challenges under a complete-information
assumption, VCG contracts [Lavi and Shamash, 2019], can be extended to
incomplete information.
  We define and characterize the class of "incomplete information VCG contracts
(IIVCG)", and show it is the unique class guaranteeing truthfulness of the
principals and welfare maximization by the agent. Our results reveal an
inherent tradeoff between two important properties required to ensure
participation in the contract: individual rationality (for the principals) and
limited liability (for the agent). We design a polynomial-time algorithm for
determining whether a setting has an IIVCG contract with both properties. As
our main result we design a polynomial-time "algorithmic IIVCG" contract: given
valuation reports from the principals it returns, if possible for the setting,
a payment scheme for the agent that constitutes an IIVCG contract with all
desired properties. We also give a sufficient graph-theoretic condition on the
population of principals that ensures the existence of such an IIVCG contract.


Abstract:
  In these expository notes, we give a proof of regularity of Anosov splitting
for Anosov diffeomorphisms in a torus. We also generalize the idea to higher
dimensions and to Anosov flows.


Abstract:
  Here is a direct problem for Sidon sets: Given a linear form $\varphi = c_1
x_1 + \cdots + c_h x_h $, construct and describe sets $A$ that are Sidon sets
for $\varphi$. This paper considers an inverse problem for Sidon sets: Given a
set $A$, determine the linear forms $\varphi$ such that $A$ is a Sidon set for
$\varphi$.


Abstract:
  There has been a rise in the use of Machine Learning as a Service (MLaaS)
Vision APIs as they offer multiple services including pre-built models and
algorithms, which otherwise take a huge amount of resources if built from
scratch. As these APIs get deployed for high-stakes applications, it's very
important that they are robust to different manipulations. Recent works have
only focused on typical adversarial attacks when evaluating the robustness of
vision APIs. We propose two new aspects of adversarial image generation methods
and evaluate them on the robustness of Google Cloud Vision API's optical
character recognition service and object detection APIs deployed in real-world
settings such as sightengine.com, picpurify.com, Google Cloud Vision API, and
Microsoft Azure's Computer Vision API. Specifically, we go beyond the
conventional small-noise adversarial attacks and introduce secret embedding and
transparent adversarial examples as a simpler way to evaluate robustness. These
methods are so straightforward that even non-specialists can craft such
attacks. As a result, they pose a serious threat where APIs are used for
high-stakes applications. Our transparent adversarial examples successfully
evade state-of-the art object detections APIs such as Azure Cloud Vision
(attack success rate 52%) and Google Cloud Vision (attack success rate 36%).
90% of the images have a secret embedded text that successfully fools the
vision of time-limited humans but is detected by Google Cloud Vision API's
optical character recognition. Complementing to current research, our results
provide simple but unconventional methods on robustness evaluation.


Abstract:
  Periodic water waves generate Stokes drift as manifest from the orbits of
Lagrangian particles not fully closing. Stokes drift can contribute to the
transport of floating marine litter, including plastic. Previously, marine
litter objects have been considered to be perfect Lagrangian tracers,
travelling with the Stokes drift of the waves. However, floating marine litter
objects have large ranges of sizes and densities, which potentially result in
different rates of transport by waves due to the non-Lagrangian behaviour of
the objects. Through a combination of theory and experiments for idealised
spherical objects in deep-water waves, we show that different objects are
transported at different rates depending on their size and density, and that
larger buoyant objects can have increased drift compared with Lagrangian
tracers. We show that the mechanism for the increased drift observed in our
experiments comprises the variable submergence and the corresponding dynamic
buoyancy force components in a direction perpendicular to the local water
surface. This leads to an amplification of the drift of these objects compared
to the Stokes drift when averaged over the wave cycle. Using an expansion in
wave steepness, we derive a closed-form approximation for this increased drift,
which can be included in ocean-scale models of marine litter transport.


Abstract:
  Modern natural language understanding models depend on pretrained subword
embeddings, but applications may need to reason about words that were never or
rarely seen during pretraining. We show that examples that depend critically on
a rarer word are more challenging for natural language inference models. Then
we explore how a model could learn to use definitions, provided in natural
text, to overcome this handicap. Our model's understanding of a definition is
usually weaker than a well-modeled word embedding, but it recovers most of the
performance gap from using a completely untrained word.


Abstract:
  The structure of the mixing matrix, in the electroweak quark sector with four
generations of quarks is investigated. We conclude that the area of the
unitarity quadrangle is not a good choice as a possible measure of the
CP~violation. In search of new physics we analyze how the existence of the 4-th
quark family may influence on the values of the Cabibbo-Kobayashi-Maskawa
matrix and we show that one can test for the existence of the 4-th generation
using the Jarlskog invariants of the known quarks only. The analysis based on
the measured unitary triangle exhibits some tension with the assumption of
three quark generations. The measurement of the unitarity triangle obtained
from the scalar product of the second row/column of the CKM matrix by the
complex conjugate of third row/column can provide information about the
existence of the fourth generation of quarks.


Abstract:
  The turn of the century has seen a tremendous rise in technological advances
in the field of automobiles. With 5G technology on its way and the development
in the IoT sector, cars will start interacting with each other using V2V
communications and become much more autonomous. In this project, an effort is
made to move in the same direction by proposing a model for an automatic car
wiper system that operates on sensing rain and snow on the windshield of a car.
We develop a prototype for our idea by integrating a servo motor and raindrop
sensor with an AT89C51 Microcontroller.


Abstract:
  We propose that the non-linear Hall response with the preserved time-reversal
symmetry can be observed in the Bloch oscillation of the ultracold atoms in
optical lattices. In the short-time limit of Bloch oscillations with a DC
driving field, the non-linear Hall current dominates with time reversal
symmetry and is a second-order response of the external field strength. The
associated Berry curvature dipole, which is the second order nonlinear
coefficient of the driving field, can be extracted from the dynamics. In the
presence of an AC driving field, the nonlinear Hall response will double the
driving frequency in the case of time reversal symmetry.


Abstract:
  We survey aspects of locally nilpotent linear groups. Then we obtain a new
classification; namely, we classify the irreducible maximal locally nilpotent
subgroups of $\mathrm{GL}(q, \mathbb F)$ for prime $q$ and any field $\mathbb
F$.


Abstract:
  Meta-heuristic techniques are important as they are used to find solutions to
computationally intractable problems. Simplistic methods such as exhaustive
search become computationally expensive and unreliable as the solution space
for search algorithms increase. As no method is guaranteed to perform better
than all others in all classes of optimization search problems, there is a need
to constantly find new and/or adapt old search algorithms. This research
proposes an Infrasonic Search Algorithm, inspired from the Gravitational Search
Algorithm and the mating behaviour in peafowls. The Infrasonic Search Algorithm
identified competitive solutions to 23 benchmark unimodal and multimodal test
functions compared to the Genetic Algorithm, Particle Swarm Optimization
Algorithm and the Gravitational Search Algorithm.


Abstract:
  An ultimate goal of the AI and ML fields is artificial general intelligence
(AGI); although such systems remain science fiction, various models exhibit
aspects of AGI. In this work, we look at neuro-symbolic (NS)approaches to
visual question answering (VQA) from the perspective of AGI desiderata. We see
how well these systems meet these desiderata, and how the desiderata often pull
the scientist in opposing directions. It is my hope that through this work we
can temper model evaluation on benchmarks with a discussion of the properties
of these systems and their potential for future extension.


Abstract:
  We study the $(m,b)$ Maker-Breaker percolation game on $\mathbb{Z}^2$,
introduced by Day and Falgas-Ravry. As our first result, we show that Breaker
has a winning strategy for the $(m,b)$-game whenever $b \geq (2-\frac{1}{14} +
o(1))m$, breaking the ratio $2$ barrier proved by Day and Falgas-Ravry.
  Addressing further questions of Day and Falgas-Ravry, we show that Breaker
can win the $(m,2m)$-game even if he allows Maker to claim $c$ edges before the
game starts, for any integer $c$, and that he can moreover win rather fast (as
a function of $c$).
  Finally, we consider the game played on $\mathbb{Z}^2$ after the usual bond
percolation process with parameter $p$ was performed. We show that when $p$ is
not too much larger than $1/2$, Breaker almost surely has a winning strategy
for the $(1,1)$-game, even if Maker is allowed to choose the origin after the
board is determined.


Abstract:
  Automatic video summarization is still an unsolved problem due to several
challenges. The currently available datasets either have very short videos or
have few long videos of only a particular type. We introduce a new benchmarking
video dataset called VISIOCITY (VIdeo SummarIzatiOn based on Continuity, Intent
and DiversiTY) which comprises of longer videos across six different categories
with dense concept annotations capable of supporting different flavors of video
summarization and other vision problems. For long videos, human reference
summaries necessary for supervised video summarization techniques are difficult
to obtain. We explore strategies to automatically generate multiple reference
summaries from indirect ground truth present in VISIOCITY. We show that these
summaries are at par with human summaries. We also present a study of different
desired characteristics of a good summary and demonstrate how it is normal to
have two good summaries with different characteristics. Thus we argue that
evaluating a summary against one or more human summaries and using a single
measure has its shortcomings. We propose an evaluation framework for better
quantitative assessment of summary quality which is closer to human judgment.
Lastly, we present insights into how a model can be enhanced to yield better
summaries. Sepcifically, when multiple diverse ground truth summaries can
exist, learning from them individually and using a combination of loss
functions measuring different characteristics is better than learning from a
single combined (oracle) ground truth summary using a single loss function. We
demonstrate the effectiveness of doing so as compared to some of the
representative state of the art techniques tested on VISIOCITY. We release
VISIOCITY as a benchmarking dataset and invite researchers to test the
effectiveness of their video summarization algorithms on VISIOCITY.


Abstract:
  In this paper, we study the geodesic deviation equation (GDE) within the
context of the Brans-Dicke (BD) theory in $D$ dimensions. Then, we restrict our
attention to the GDE for the fundamental observers and null vector field past
directed. Concerning the latter, in order to apply the retrieved GDE for the
cosmological models as well as examining exact solutions, we study some
cosmological models in general relativity (GR) and in the context of the BD
theory. For the BD framework, we provide two appropriate settings for dynamical
system, which can be considered as the most extended case scenarios with
respect to those studied previously. Then, we investigate a few well-known BD
cosmological models, for which we present the modified and corrected exact
solutions. Moreover, we show that the retrieved formalism of the GDE can also
be properly applicable for the modified BD theory (MBDT), whose matter and
potential emerge from the geometry. For all of our herein cosmological models,
we investigate the energy conditions and depict the behavior of the deviation
vector and observer area distance. We demonstrate that why the MBDT can be
considered as a more appropriate candidate to describe the universe in
accordance with the observational data as well as from theoretical viewpoint.


Abstract:
  Using sample surveys as a cost effective tool to provide estimates for
characteristics of interest at population and sub-populations (area/domain)
level has a long tradition in "small area estimation". However, the existence
of outliers in the sample data can significantly affect the estimation for
areas in which they occur, especially where the domain-sample size is small.
Based on existing robust estimators for small area estimation we propose two
novel approaches for bias calibration. A series of simulations shows that our
methods lead to more efficient estimators in comparison with other existing
bias-calibration methods. As a real data example we apply our estimators to
obtain \textit{Gini} coefficients in labour market areas of the Tuscany region
of Italy, where our sources of information are the EU-SILC survey and the
Italian census. This analysis shows that the new methods reveal a different
picture than existing methods. We extend our ideas to predictions for
non-sampled areas.


Abstract:
  As an industry of primarily small and mid-size businesses, it is becoming
increasingly more difficult for British Columbia (BC)'s tree fruit growers to
compete with large, often vertically integrated producers from other regions.
New ways of managing information and resources collaboratively are needed to
develop competitive strengths. This case study seeks to understand the
information and knowledge management capabilities of the BC tree fruit cluster
across the value chain for six different data domains. A qualitative
methodology design of 21 in-depth interviews with cluster stakeholders provides
insights into the data quality, completeness and integration points, and then
applies CMMI level criteria to assess the information management capabilities
of the industry. Significant data and process gaps are identified. This paper
explores how the BC tree fruit industry can move forward from this position
using technology solutions to support the development of information and
knowledge, and collective decision-making.


Abstract:
  Using the example of the harmonic oscillator, we illustrate the use of hybrid
dynamical brackets in analyzing quantum-classical interaction. We only assume
that a hybrid dynamical bracket exists, is bilinear, and reduces to the pure
quantum/classical bracket when acting on pure quantum/classical variables. Any
hybrid bracket obeying these natural requirements will produce the same
dynamics for pure classical or quantum variables, given a hybrid Hamiltonian.
Backreaction is manifested in the evolution of a nonvanishing commutator
between classical variables. The more massive the classical system is, the less
it is affected by backreaction. Interestingly, we show that while pure
variables evolve to violate the pure canonical relations, they always obey the
hybrid canonical relations. The dynamics of hybrid variables, on the other
hand, is shown to require a fully specified and consistent hybrid bracket,
otherwise evolution cannot be defined.


Abstract:
  Anomalous users detection in social network is an imperative task for
security problems. Motivated by the great power of Graph Neural Networks(GNNs),
many current researches adopt GNN-based detectors to reveal the anomalous
users. However, the increasing scale of social activities, explosive growth of
users and manifold technical disguise render the user detection a difficult
task. In this paper, we propose an innovate Relevance-aware Anomalous Users
Detection model (RAU-GNN) to obtain a fine-grained detection result. RAU-GNN
first extracts multiple relations of all types of users in social network,
including both benign and anomalous users, and accordingly constructs the
multiple user relation graph. Secondly, we employ relevance-aware GNN framework
to learn the hidden features of users, and discriminate the anomalous users
after discriminating. Concretely, by integrating Graph Convolution Network(GCN)
and Graph Attention Network(GAT), we design a GCN-based relation fusion layer
to aggregate initial information from different relations, and a GAT-based
embedding layer to obtain the high-level embeddings. Lastly, we feed the
learned representations to the following GNN layer in order to consolidate the
node embedding by aggregating the final users' embeddings. We conduct extensive
experiment on real-world datasets. The experimental results show that our
approach can achieve high accuracy for anomalous users detection.


Abstract:
  Anytime motion planners are widely used in robotics. However, the
relationship between their solution quality and computation time is not well
understood, and thus, determining when to quit planning and start execution is
unclear. In this paper, we address the problem of deciding when to stop
deliberation under bounded computational capacity, so called meta-reasoning,
for anytime motion planning. We propose data-driven learning methods,
model-based and model-free meta-reasoning, that are applicable to different
environment distributions and agnostic to the choice of anytime motion
planners. As a part of the framework, we design a convolutional neural
network-based optimal solution predictor that predicts the optimal path length
from a given 2D workspace image. We empirically evaluate the performance of the
proposed methods in simulation in comparison with baselines.


Abstract:
  Let $V$ be a vector space endowed with a non-degenerate quadratic form $Q$.
If the base field $\mathbb{F}$ is different from $\mathbb{F}_2$, it is known
that every isometry can be written as a product of reflections. In this
article, we detail the structure of the poset of all minimal length reflection
factorizations of an isometry. If $\mathbb{F}$ is an ordered field, we also
study factorizations into positive reflections, i.e., reflections defined by
vectors of positive norm. We characterize such factorizations, under the
hypothesis that the squares of $\mathbb{F}$ are dense in the positive elements
(this includes Archimedean and Euclidean fields). In particular, we show that
an isometry is a product of positive reflections if and only if its spinor norm
is positive. As a final application, we explicitly describe the poset of all
factorizations of isometries of the hyperbolic space.


Abstract:
  We describe the construction of CMC surfaces with symmetries in $\mathbb S^3$
and $\mathbb R^3$ using a CMC quadrilateral in a fundamental tetrahedron of a
tessellation of the space. The fundamental piece is constructed by the
generalized Weierstrass representation using a geometric flow on the space of
potentials.


Abstract:
  Optimal zero-delay coding (quantization) of $\mathbb{R}^d$-valued linearly
generated Markov sources is studied under quadratic distortion. The structure
and existence of deterministic and stationary coding policies that are optimal
for the infinite horizon average cost (distortion) problem are established.
Prior results studying the optimality of zero-delay codes for Markov sources
for infinite horizons either considered finite alphabet sources or, for the
$\mathbb{R}^d$-valued case, only showed the existence of deterministic and
non-stationary Markov coding policies or those which are randomized. In
addition to existence results, for finite blocklength (horizon) $T$ the
performance of an optimal coding policy is shown to approach the infinite time
horizon optimum at a rate $O(\frac{1}{T})$. This gives an explicit rate of
convergence that quantifies the near-optimality of finite window
(finite-memory) codes among all optimal zero-delay codes.


Abstract:
  This paper presents a framework for Convolutional Neural Network (CNN)-based
quality enhancement task, by taking advantage of coding information in the
compressed video signal. The motivation is that normative decisions made by the
encoder can significantly impact the type and strength of artifacts in the
decoded images. In this paper, the main focus has been put on decisions
defining the prediction signal in intra and inter frames. This information has
been used in the training phase as well as input to help the process of
learning artifacts that are specific to each coding type. Furthermore, to
retain a low memory requirement for the proposed method, one model is used for
all Quantization Parameters (QPs) with a QP-map, which is also shared between
luma and chroma components. In addition to the Post Processing (PP) approach,
the In-Loop Filtering (ILF) codec integration has also been considered, where
the characteristics of the Group of Pictures (GoP) are taken into account to
boost the performance. The proposed CNN-based Quality Enhancement(QE) framework
has been implemented on top of the VVC Test Model (VTM-10). Experiments show
that the prediction-aware aspect of the proposed method improves the coding
efficiency gain of the default CNN-based QE method by 1.52%, in terms of BD-BR,
at the same network complexity compared to the default CNN-based QE filter.


Abstract:
  Cross-lingual speech adaptation aims to solve the problem of leveraging
multiple rich-resource languages to build models for a low-resource target
language. Since the low-resource language has limited training data, speech
recognition models can easily overfit. In this paper, we propose to use
adapters to investigate the performance of multiple adapters for
parameter-efficient cross-lingual speech adaptation. Based on our previous
MetaAdapter that implicitly leverages adapters, we propose a novel algorithms
called SimAdapter for explicitly learning knowledge from adapters. Our
algorithm leverages adapters which can be easily integrated into the
Transformer structure.MetaAdapter leverages meta-learning to transfer the
general knowledge from training data to the test language. SimAdapter aims to
learn the similarities between the source and target languages during
fine-tuning using the adapters. We conduct extensive experiments on
five-low-resource languages in Common Voice dataset. Results demonstrate that
our MetaAdapter and SimAdapter methods can reduce WER by 2.98% and 2.55% with
only 2.5% and 15.5% of trainable parameters compared to the strong full-model
fine-tuning baseline. Moreover, we also show that these two novel algorithms
can be integrated for better performance with up to 3.55% relative WER
reduction.


Abstract:
  Magnetic confinement devices for nuclear fusion can be large and expensive.
Compact stellarators are promising candidates for costreduction, but introduce
new difficulties: confinement in smaller volumes requires higher magnetic
field, which calls for higher coil-currents and ultimately causes higher
Laplace forces on the coils-if everything else remains the same. This motivates
the inclusion of force reduction in stellarator coil optimization. In the
present paper we consider a coil winding surface, we prove that there is a
natural and rigorous way to define the Laplace force (despite the magnetic
field discontinuity across the current-sheet), we provide examples of cost
associated (peak force, surface-integral of the force squared) and discuss easy
generalizations to parallel and normal force-components, as these will be
subject to different engineering constraints. Such costs can then be easily
added to the figure of merit in any multi-objective stellarator coil
optimization code. We demonstrate this for a generalization of the REGCOIL code
[1], which we rewrote in python, and provide numerical examples for the NCSX
(now QUASAR) design. We present results for various definitions of the cost
function, including peak force reductions by up to 40 %, and outline future
work for further reduction.


Abstract:
  Detecting, predicting, and alleviating traffic congestion are targeted at
improving the level of service of the transportation network. With increasing
access to larger datasets of higher resolution, the relevance of deep learning
for such tasks is increasing. Several comprehensive survey papers in recent
years have summarised the deep learning applications in the transportation
domain. However, the system dynamics of the transportation network vary greatly
between the non-congested state and the congested state -- thereby
necessitating the need for a clear understanding of the challenges specific to
congestion prediction. In this survey, we present the current state of deep
learning applications in the tasks related to detection, prediction, and
alleviation of congestion. Recurring and non-recurring congestion are discussed
separately. Our survey leads us to uncover inherent challenges and gaps in the
current state of research. Finally, we present some suggestions for future
research directions as answers to the identified challenges.


Abstract:
  We present a simplified, task-agnostic multi-modal pre-training approach that
can accept either video or text input, or both for a variety of end tasks.
Existing pre-training are task-specific by adopting either a single cross-modal
encoder that requires both modalities, limiting their use for retrieval-style
end tasks or more complex multitask learning with two unimodal encoders,
limiting early cross-modal fusion. We instead introduce new pretraining masking
schemes that better mix across modalities (e.g. by forcing masks for text to
predict the closest video embeddings) while also maintaining separability (e.g.
unimodal predictions are sometimes required, without using all the input).
Experimental results show strong performance across a wider range of tasks than
any previous methods, often outperforming task-specific pre-training. Code is
made available at https://github.com/pytorch/fairseq/tree/main/examples/MMPT.


Abstract:
  In this paper, we propose an algorithmic framework dubbed inertial
alternating direction methods of multipliers (iADMM), for solving a class of
nonconvex nonsmooth multiblock composite optimization problems with linear
constraints. Our framework employs the general minimization-majorization (MM)
principle to update each block of variables so as to not only unify the
convergence analysis of previous ADMM that use specific surrogate functions in
the MM step, but also lead to new efficient ADMM schemes. To the best of our
knowledge, in the \emph{nonconvex nonsmooth} setting, ADMM used in combination
with the MM principle to update each block of variables, and ADMM combined with
inertial terms for the primal variables have not been studied in the
literature. Under standard assumptions, we prove the subsequential convergence
and global convergence for the generated sequence of iterates. We illustrate
the effectiveness of iADMM on a class of nonconvex low-rank representation
problems.


Abstract:
  Recommender systems, which merely leverage user-item interactions for user
preference prediction (such as the collaborative filtering-based ones), often
face dramatic performance degradation when the interactions of users or items
are insufficient. In recent years, various types of side information have been
explored to alleviate this problem. Among them, knowledge graph (KG) has
attracted extensive research interests as it can encode users/items and their
associated attributes in the graph structure to preserve the relation
information. In contrast, less attention has been paid to the item-item
co-occurrence information (i.e., \textit{co-view}), which contains rich
item-item similarity information. It provides information from a perspective
different from the user/item-attribute graph and is also valuable for the CF
recommendation models. In this work, we make an effort to study the potential
of integrating both types of side information (i.e., KG and item-item
co-occurrence data) for recommendation. To achieve the goal, we propose a
unified graph-based recommendation model (UGRec), which integrates the
traditional directed relations in KG and the undirected item-item co-occurrence
relations simultaneously. In particular, for a directed relation, we transform
the head and tail entities into the corresponding relation space to model their
relation; and for an undirected co-occurrence relation, we project head and
tail entities into a unique hyperplane in the entity space to minimize their
distance. In addition, a head-tail relation-aware attentive mechanism is
designed for fine-grained relation modeling. Extensive experiments have been
conducted on several publicly accessible datasets to evaluate the proposed
model. Results show that our model outperforms several previous
state-of-the-art methods and demonstrate the effectiveness of our UGRec model.


Abstract:
  We introduce an inversion based method, denoted as IMAge-Guided model
INvErsion (IMAGINE), to generate high-quality and diverse images from only a
single training sample. We leverage the knowledge of image semantics from a
pre-trained classifier to achieve plausible generations via matching
multi-level feature representations in the classifier, associated with
adversarial training with an external discriminator. IMAGINE enables the
synthesis procedure to simultaneously 1) enforce semantic specificity
constraints during the synthesis, 2) produce realistic images without generator
training, and 3) give users intuitive control over the generation process. With
extensive experimental results, we demonstrate qualitatively and quantitatively
that IMAGINE performs favorably against state-of-the-art GAN-based and
inversion-based methods, across three different image domains (i.e., objects,
scenes, and textures).


Abstract:
  Deep learning play a vital role in classifying different arrhythmias using
the electrocardiography (ECG) data. Nevertheless, training deep learning models
normally requires a large amount of data and it can lead to privacy concerns.
Unfortunately, a large amount of healthcare data cannot be easily collected
from a single silo. Additionally, deep learning models are like black-box, with
no explainability of the predicted results, which is often required in clinical
healthcare. This limits the application of deep learning in real-world health
systems. In this paper, we design a new explainable artificial intelligence
(XAI) based deep learning framework in a federated setting for ECG-based
healthcare applications. The federated setting is used to solve issues such as
data availability and privacy concerns. Furthermore, the proposed framework
setting effectively classifies arrhythmia's using an autoencoder and a
classifier, both based on a convolutional neural network (CNN). Additionally,
we propose an XAI-based module on top of the proposed classifier to explain the
classification results, which help clinical practitioners make quick and
reliable decisions. The proposed framework was trained and tested using the
MIT-BIH Arrhythmia database. The classifier achieved accuracy up to 94% and 98%
for arrhythmia detection using noisy and clean data, respectively, with
five-fold cross-validation.


Abstract:
  For all positive non-square integer multiplier k, there is an infinity of
multiples of triangular numbers which are also triangular numbers. With a
simple change of variables, these triangular numbers can be found using
solutions of Pell equations. With some conditions on parities of fundamental
solutions of the simple and generalized Pell equations, only odd solutions of
the generalized Pell equation are retained to provide many infinitely solutions
found on branches corresponding to each of the generalized fundamental
solutions. General algebraic expressions of fundamental solutions of the Pell
equations are found for some values of the multiplier k in function of the
closest natural square. Further, among the expressions of Pell equation
solutions, a set of recurrent relations is identical to those found previously
without the Pell equation solving method. It is found also that two constants
of the problem of multiples of triangular numbers are directly related to the
fundamental solutions of the simple Pell equation, which is an unexpected
result as it means that simple Pell equation fundamental solutions in all
generality are related to constants in recurrent relations of the problem of
finding triangular numbers multiple of other triangular numbers.


Abstract:
  Executing computer vision models on streaming visual data, or streaming
perception is an emerging problem, with applications in self-driving, embodied
agents, and augmented/virtual reality. The development of such systems is
largely governed by the accuracy and latency of the processing pipeline. While
past work has proposed numerous approximate execution frameworks, their
decision functions solely focus on optimizing latency, accuracy, or energy,
etc. This results in sub-optimum decisions, affecting the overall system
performance. We argue that the streaming perception systems should holistically
maximize the overall system performance (i.e., considering both accuracy and
latency simultaneously). To this end, we describe a new approach based on deep
reinforcement learning to learn these tradeoffs at runtime for streaming
perception. This tradeoff optimization is formulated as a novel deep contextual
bandit problem and we design a new reward function that holistically integrates
latency and accuracy into a single metric. We show that our agent can learn a
competitive policy across multiple decision dimensions, which outperforms
state-of-the-art policies on public datasets.


Abstract:
  We discuss the interconnections between AO*, adversarial game-searching
algorithms, e.g., proof number search and minimax search. The former was
developed in the context of a general AND/OR graph model, while the latter were
mostly presented in game-trees which are sometimes modeled using AND/OR trees.
It is thus worth investigating to what extent these algorithms are related and
how they are connected. In this paper, we explicate the interconnections
between these search paradigms. We argue that generalized proof number search
might be regarded as a more informed replacement of AO* for solving arbitrary
AND/OR graphs, and the minimax principle might also extended to use dual
heuristics.


Abstract:
  The classical Cauchy rigidity theorem for convex polytopes reads that if two
convex polytopes have isometric developments then they are congruent. In other
words, we can decide whether two polyhedra are isometric or not by using their
developments only. In this article, we study a similar problem about whether it
is possible, using only the developments of two convex polyhedra of Euclidean
3-space, to understand that these polyhedra are (or are not) affine-equivalent.


Abstract:
  An element $g$ in a group $G$ is called reversible (or real) if it is
conjugate to $g^{-1}$ in $G$, i.e. there is a $h$ in $G$ such that $g^{-1}=
hgh^{-1}$. The element $g$ in $G$ is called strongly reversible (or strongly
real) if $g$ is a product of two involutions (i.e. order one or two elements)
in $G$. In this paper, we classify reversible and strongly reversible elements
in the isometry groups of $\mathbb F$-Hermitian spaces, where $\mathbb F
=\mathbb C$ or $\mathbb H$. More precisely, we classify reversible and strongly
reversible elements in the groups $\mathrm{Sp}(n) \ltimes \mathbb H^n$,
$\mathrm{U}(n) \ltimes \mathbb C^n$ and $\mathrm{SU}n) \ltimes \mathbb C^n$. We
also give a new proof to the classification of strongly reversible elements in
$\mathrm{Sp}(n)$.


Abstract:
  Minimizing cross-entropy is a widely used method for training artificial
neural networks. Many training procedures based on backpropagation use
cross-entropy directly as their loss function. Instead, this theoretical essay
investigates a dual process model with two processes, in which one process
minimizes the Kullback-Leibler divergence while its dual counterpart minimizes
the Shannon entropy. Postulating that learning consists of two dual processes
complementing each other, the model defines an equilibrium state for both
processes in which the loss function assumes its minimum. An advantage of the
proposed model is that it allows deriving the optimal learning rate and
momentum weight to update network weights for backpropagation. Furthermore, the
model introduces the golden ratio and complex numbers as important new concepts
in machine learning.


Abstract:
  The topology of a network associated with a reservoir computer is often taken
so that the connectivity and the weights are chosen randomly. Optimization is
hardly considered as the parameter space is typically too large. Here we
investigate this problem for a class of reservoir computers for which we obtain
a decomposition of the reservoir dynamics into modes, which can be computed
independently of one another. Each mode depends on an eigenvalue of the network
adjacency matrix. We then take a parametric approach in which the eigenvalues
are parameters that can be appropriately designed and optimized. In addition,
we introduce the application of a time shift to each individual mode. We show
that manipulations of the individual modes, either in terms of the eigenvalues
or the time shifts, can lead to dramatic reductions in the training error.


Abstract:
  Robust travel time predictions are of prime importance in managing any
transportation infrastructure, and particularly in rail networks where they
have major impacts both on traffic regulation and passenger satisfaction. We
aim at predicting the travel time of trains on rail sections at the scale of an
entire rail network in real-time, by estimating trains' delays relative to a
theoretical circulation plan. Existing implementations within railway companies
generally work using the approximation that a train's delay will stay constant
for the rest of its trip.
  Predicting the evolution of a given train's delay is a uniquely hard problem,
distinct from mainstream road traffic forecasting problems, since it involves
several hard-to-model phenomena: train spacing, station congestion and
heterogeneous rolling stock among others. We first offer empirical evidence of
the previously unexplored phenomenon of delay propagation in the French
National Railway Network, leading to delays being amplified by interactions
between trains. We then contribute a novel technique using the transformer
architecture and pre-trained embeddings to make real-time massively parallel
predictions for train delays at the scale of the whole rail network (over 3k
trains at peak hours, making predictions at an average horizon of 70 minutes).
Our approach yields very positive results on real-world data when compared to
currently-used and experimental prediction techniques. Our work is in the early
stages of implementation for industrial use at the French railway company SNCF
for passenger information systems, and a contender as a tool to aid traffic
regulation decisions.


Abstract:
  We present a theoretical framework for characterizing incremental stability
of nonlinear stochastic systems perturbed by compound Poisson shot noise and
finite-measure L\'{e}vy noise. For each noise type, we compare trajectories of
the perturbed system with distinct noise sample paths against trajectories of
the nominal, unperturbed system. We show that for a finite number of jumps
arising from the noise process, the mean-squared error between the trajectories
exponentially converge towards a bounded error ball across a finite interval of
time under practical boundedness assumptions. The convergence rate for shot
noise systems is the same as the exponentially-stable nominal system, but with
a tradeoff between the parameters of the shot noise process and the size of the
error ball. The convergence rate and the error ball for the L\'{e}vy noise
system are shown to be nearly direct sums of the respective quantities for the
shot and white noise systems separately, a result which is analogous to the
L\'{e}vy-Khintchine theorem. We demonstrate our results using several simple
case studies: a 1D linear reference-tracking system, 2D linear time-varying
systems, a 2D nonlinear system, and a 2D nonlinear observer design problem.


Abstract:
  Thermodynamics tells us to expect underwater contact between two hydrophobic
surfaces to result in stronger adhesion compared to two hydrophilic surfaces.
However, presence of water changes not only energetics, but also the dynamic
process of reaching a final state, which couples solid deformation and liquid
evacuation. These dynamics can create challenges for achieving strong
underwater adhesion/friction, which affects diverse fields including soft
robotics, bio-locomotion and tire traction. Closer investigation, requiring
sufficiently precise resolution of film evacuation while simultaneously
controlling surface wettability has been lacking. We perform high resolution
in-situ frustrated total internal reflection imaging to track underwater
contact evolution between soft-elastic hemispheres of varying stiffness and
smooth-hard surfaces of varying wettability. Surprisingly, we find exponential
rate of water evacuation from hydrophobic-hydrophobic (adhesive) contact is 3
orders of magnitude lower than that from hydrophobic-hydrophilic (non-adhesive)
contact. The trend of decreasing rate with decreasing wettability of glass
sharply changes about a point where thermodynamic adhesion crosses zero,
suggesting a transition in mode of evacuation, which is illuminated by
3-Dimensional spatiotemporal heightmaps. Adhesive contact is characterized by
the early localization of sealed puddles, whereas non-adhesive contact remains
smooth, with film-wise evacuation from one central puddle. Measurements with a
human thumb and alternatively hydrophobic/hydrophilic glass surface demonstrate
practical consequences of the same dynamics: adhesive interactions cause
instability in valleys and lead to a state of more trapped water and less
intimate solid-solid contact.


Abstract:
  Bacteria live in environments that are continuously fluctuating and changing.
Exploiting any predictability of such fluctuations can lead to an increased
fitness. On longer timescales bacteria can "learn" the structure of these
fluctuations through evolution. However, on shorter timescales, inferring the
statistics of the environment and acting upon this information would need to be
accomplished by physiological mechanisms. Here, we use a model of metabolism to
show that a simple generalization of a common regulatory motif (end-product
inhibition) is sufficient both for learning continuous-valued features of the
statistical structure of the environment and for translating this information
into predictive behavior; moreover, it accomplishes these tasks near-optimally.
We discuss plausible genetic circuits that could instantiate the mechanism we
describe, including one similar to the architecture of two-component signaling,
and argue that the key ingredients required for such predictive behavior are
readily accessible to bacteria.


Abstract:
  Graph generative models are a highly active branch of machine learning. Given
the steady development of new models of ever-increasing complexity, it is
necessary to provide a principled way to evaluate and compare them. In this
paper, we enumerate the desirable criteria for such a comparison metric and
provide an overview of the status quo of graph generative model comparison in
use today, which predominantly relies on maximum mean discrepancy (MMD). We
perform a systematic evaluation of MMD in the context of graph generative model
comparison, highlighting some of the challenges and pitfalls researchers
inadvertently may encounter. After conducting a thorough analysis of the
behaviour of MMD on synthetically-generated perturbed graphs as well as on
recently-proposed graph generative models, we are able to provide a suitable
procedure to mitigate these challenges and pitfalls. We aggregate our findings
into a list of practical recommendations for researchers to use when evaluating
graph generative models.


Abstract:
  The problem of achieving ultra-reliable and low-latency communication (URLLC)
in multi-terminal networks has gained traction in the recent past owing to new
wireless applications in vehicular networks. In the context of multi-hop
networks, which is a classic example for multi-party communication, recent
studies have shown that automatic-repeat-request (ARQ) based decode-and-forward
(DF) strategies are suitable for URLLC since the idea of distributing a given
number of ARQs across the nodes provides fine control on the features of
reliability and latency. Inspired by these developments, in this work, we
propose a cooperative ARQ sharing strategy for URLLC in multi-hop networks. At
the heart of the proposed scheme lies the idea that every node is given the
knowledge of the number of ARQs allotted to its preceding node in addition to
the ARQs allotted to itself. As a result, each node only needs to count the
number of unsuccessful attempts of its preceding node, and then borrow the
unused ARQs, thereby improving the reliability feature with no compromise in
the latency constraint. Using packet-drop-probability (PDP) as the reliability
metric for the proposed cooperative strategy, we formulate an optimization
problem of minimizing the PDP subject to a sum constraint on the total number
of ARQs allotted across all the nodes. Supported by theoretical analysis on the
behavior of PDP, we present low-complexity algorithms to compute near-optimal
ARQ distributions for our strategy, and show that our strategy outperforms the
existing non-cooperative strategies.


Abstract:
  Although ultra-luminous X-ray sources (ULX) are important for astrophysics
due to their extreme apparent super-Eddington luminosities, their nature is
still poorly known. Theoretical and observational studies suggest that ULXs
could be a diversified group of objects composed of low-mass X-ray binaries,
high-mass X-ray binaries and marginally also systems containing
intermediate-mass black holes, which is supported by their presence in a
variety of environments. Observational data on the ULX donors could
significantly boost our understanding of these systems, but only a few were
detected. There are several candidates, mostly red supergiants (RSGs), but
surveys are typically biased toward luminous near-infrared objects.
Nevertheless, it is worth exploring if RSGs can be members of ULX binaries. In
such systems matter accreted onto the compact body would have to be provided by
the stellar wind of the companion, since a Roche-lobe overflow could be
unstable for relevant mass-ratios. Here we present a comprehensive study of the
evolution and population of wind-fed ULXs and provide a theoretical support for
the link between RSGs and ULXs. Our estimated upper limit on contribution of
wind-fed ULX to the overall ULX population is $\sim75$--$96\%$ for young
($<100$ Myr) star forming environments, $\sim 49$--$87\%$ for prolonged
constant star formation (e.g., disk of Milky Way), and $\lesssim1\%$ for
environments in which star formation ceased long time ($>2$ Gyr) ago. We show
also that some wind-fed ULXs (up to $6\%$) may evolve into merging double
compact objects (DCOs), but typical systems are not viable progenitors of such
binaries because of their large separations. We demonstrate that, the exclusion
of wind-fed ULXs from population studies of ULXs, might have lead to
systematical errors in their conclusions.


Abstract:
  These lecture notes provide an informal introduction to the theory of
nonnegative polynomials and sums of squares. We highlight the history and some
recent developments, especially the new connections with classical (complex)
algebraic geometry and commutative algebra. We briefly discuss the connection
to semidefinite programming and applications. We expect the reader to be
familiar with algebra and fundamentals of algebraic geometry, on the level of a
graduate course, and know basic facts about positive semidefinite matrices.


Abstract:
  A macroscopic effect can be induced by a local non-Hermitian term, when it
manifests simultaneously level coalescence of a full real degeneracy spectrum,
leading to exceptional spectrum. In this paper, we propose a family of systems
that support such an intriguing property. It is generally consisted of two
arbitrary identical Hermitian sub-lattices in association with unidirectional
couplings between them. We show exactly that all single-particle eigenstates
coalesce in pairs, even only single unidirectional coupling appears. As an
application, we study the dynamic magnetization induced by complex fields in an
itinerant electron system. It shows that an initial saturated ferromagnetic
state at half-filling can be driven into its opposite state according to the
dynamics of high-order exceptional point. Numerical simulations for the
dynamical processes of magnetization are performed for several representative
situations, including lattice dimensions, global random and local impurity
distributions. It shows that the dynamic magnetization processes exhibit
universal behavior.


Abstract:
  The calculus of Dependent Object Types (DOT) has enabled a more principled
and robust implementation of Scala, but its support for type-level computation
has proven insufficient. As a remedy, we propose $F^\omega_{..}$, a rigorous
theoretical foundation for Scala's higher-kinded types. $F^\omega_{..}$ extends
$F^\omega_{<:}$ with interval kinds, which afford a unified treatment of
important type- and kind-level abstraction mechanisms found in Scala, such as
bounded quantification, bounded operator abstractions, translucent type
definitions and first-class subtyping constraints. The result is a flexible and
general theory of higher-order subtyping. We prove type and kind safety of
$F^\omega_{..}$, as well as weak normalization of types and undecidability of
subtyping. All our proofs are mechanized in Agda using a fully syntactic
approach based on hereditary substitution.


Abstract:
  We report the detection of an atmosphere on a rocky exoplanet, GJ 1132 b,
which is similar to Earth in terms of size and density. The atmospheric
transmission spectrum was detected using Hubble WFC3 measurements and shows
spectral signatures of aerosol scattering, HCN, and CH$_{4}$ in a low mean
molecular weight atmosphere. We model the atmospheric loss process and conclude
that GJ 1132 b likely lost the original H/He envelope, suggesting that the
atmosphere that we detect has been reestablished. We explore the possibility of
H$_{2}$ mantle degassing, previously identified as a possibility for this
planet by theoretical studies, and find that outgassing from ultrareduced magma
could produce the observed atmosphere. In this way we use the observed
exoplanet transmission spectrum to gain insights into magma composition for a
terrestrial planet. The detection of an atmosphere on this rocky planet raises
the possibility that the numerous powerfully irradiated Super-Earth planets,
believed to be the evaporated cores of Sub-Neptunes, may, under favorable
circumstances, host detectable atmospheres.


Abstract:
  The article reviews the physics of Anderson localization on random regular
graphs (RRG) and its connections to many-body localization (MBL) in disordered
interacting systems. Properties of eigenstate and energy level correlations in
delocalized and localized phases, as well at criticality, are discussed. In the
many-body part, models with short-range and power-law interactions are
considered, as well as the quantum-dot model representing the limit of the
"most long-range" interaction. Central themes -- which are common to the RRG
and MBL problems -- include ergodicity of the delocalized phase, localized
character of the critical point, strong finite-size effects, and fractal
scaling of eigenstate correlations in the localized phase.


Abstract:
  In this letter, we consider an intelligent reflecting surface (IRS)-aided
wireless relaying system, where a decode-and-forward relay (R) is employed to
forward data from a source (S) to a destination (D), aided by M passive
reflecting elements. We consider two practical IRS deployment strategies,
namely, single-IRS deployment where all reflecting elements are mounted on one
single IRS that is deployed near S, R, or D, and multi-IRS deployment where the
reflecting elements are allocated over three separate IRSs which are deployed
near S, R, and D, respectively. Under the line-of-sight (LoS) channel model, we
characterize the capacity scaling orders with respect to an increasing M for
the IRS-aided relay system with different IRS deployment strategies. For
single-IRS deployment, we show that deploying the IRS near R achieves the
highest capacity as compared to that near S or D. While for multi-IRS
deployment, we propose a practical cooperative IRS passive beamforming design
which is analytically shown to achieve a larger capacity scaling order than the
single-IRS deployment (i.e., near R or S/D) when M is sufficiently large.
Numerical examples are provided, which validate our theoretical results.


Abstract:
  Continuous engineering of autonomous driving functions commonly requires
deploying vehicles in road testing to obtain inputs that cause problematic
decisions. Although the discovery leads to producing an improved system, it
also challenges the foundation of testing using equivalence classes and the
associated relative test coverage criterion. In this paper, we propose believed
equivalence, where the establishment of an equivalence class is initially based
on expert belief and is subject to a set of available test cases having a
consistent valuation. Upon a newly encountered test case that breaks the
consistency, one may need to refine the established categorization in order to
split the originally believed equivalence into two. Finally, we focus on
modules implemented using deep neural networks where every category partitions
an input over the real domain. We present both analytical and lazy methods to
suggest the refinement. The concept is demonstrated in analyzing multiple
autonomous driving modules, indicating the potential of our proposed approach.


Abstract:
  Non-alternating Hamiltonian Lie algebras in three variables over a perfect
field of characteristic 2 are considered. A classification of non-alternating
Hamiltonian forms over an algebra of divided powers in three variables and of
the corresponding simple Lie algebras is given. In particular, it is shown that
the non-alternating Hamiltonian form may not be equivalent to its linear part.
It is proved that the Lie algebras which correspond to the nonequivalent forms
are not isomorphic.


Abstract:
  We propose a novel scenario of Dark Matter production naturally connected
with generation of gravitational waves. Dark Matter is modelled as a real
scalar, which interacts with the hot primordial plasma through a portal
coupling to another scalar field. For a particular sign of the coupling, this
system exhibits an inverse second order phase transition. The latter leads to
an abundant Dark Matter production, even if the portal interaction is so weak
that the freeze-in mechanism is inefficient. The model predicts domain wall
formation in the Universe, long time before the inverse phase transition. These
domain walls have a tension decreasing with time, and completely disappear at
the inverse phase transition, so that the problem of overclosing the Universe
is avoided. The domain wall network emits gravitational waves with
characteristics defined by those of Dark Matter. In particular, the peak
frequency of gravitational waves is determined by the portal coupling constant,
and falls in the observable range for currently planned gravitational wave
detectors.


Abstract:
  Determining potential abilities of nanostructures to induce toxicity to
biological molecules is still a convoluted challenge in the realm of
nanomedicine. Based on the unprecedented achievements of twodimensional
nanomaterials in nearly all areas of applied sciences particularly medicine, we
carried out all-atom molecular dynamics simulations to assess the
biologically-important, yet-unmapped issue of the biocompatibility of 2D,
hexagonal \b{eta}-Si3N4 nanosheet via investigating its possible cross
interactions with both human serum albumin (HSA) and p53 tumor suppressor.
Examining the conventional MD indicators in the presence and absence of the
monolayer revealed that hexagonal Si3N4 nanosheet weakly binds to these two
proteins without inducing any important, dramatic change to their secondary
structures, revealing accordingly the biological compatibility of the monolayer
in case it is released as therapeutics or carriers in vivo. This finding was
also broadly supported by the related, time-dependent behaviors of the
protein-monolayer as well as the protein-water interaction energies.


Abstract:
  Impressive progress has been made in audio-driven 3D facial animation
recently, but synthesizing 3D talking-head with rich emotion is still unsolved.
This is due to the lack of 3D generative models and available 3D emotional
dataset with synchronized audios. To address this, we introduce 3D-TalkEmo, a
deep neural network that generates 3D talking head animation with various
emotions. We also create a large 3D dataset with synchronized audios and
videos, rich corpus, as well as various emotion states of different persons
with the sophisticated 3D face reconstruction methods. In the emotion
generation network, we propose a novel 3D face representation structure -
geometry map by classical multi-dimensional scaling analysis. It maps the
coordinates of vertices on a 3D face to a canonical image plane, while
preserving the vertex-to-vertex geodesic distance metric in a least-square
sense. This maintains the adjacency relationship of each vertex and holds the
effective convolutional structure for the 3D facial surface. Taking a neutral
3D mesh and a speech signal as inputs, the 3D-TalkEmo is able to generate vivid
facial animations. Moreover, it provides access to change the emotion state of
the animated speaker.
  We present extensive quantitative and qualitative evaluation of our method,
in addition to user studies, demonstrating the generated talking-heads of
significantly higher quality compared to previous state-of-the-art methods.


Abstract:
  Satoh has defined a map from virtual knots to ribbon surfaces embedded in
$S^4$. Herein, we generalize this map to virtual $m$-links, and use this to
construct generalizations of welded and extended welded knots to higher
dimensions. This also allows us to construct two new geometric pictures of
virtual $m$-links, including 1-links.


Abstract:
  Clustering is a fundamental task in the computer vision and machine learning
community. Although various methods have been proposed, the performance of
existing approaches drops dramatically when handling incomplete
high-dimensional data (which is common in real world applications). To solve
the problem, we propose a novel deep incomplete clustering method, named Deep
Distribution-preserving Incomplete Clustering with Optimal Transport (DDIC-OT).
To avoid insufficient sample utilization in existing methods limited by few
fully-observed samples, we propose to measure distribution distance with the
optimal transport for reconstruction evaluation instead of traditional
pixel-wise loss function. Moreover, the clustering loss of the latent feature
is introduced to regularize the embedding with more discrimination capability.
As a consequence, the network becomes more robust against missing features and
the unified framework which combines clustering and sample imputation enables
the two procedures to negotiate to better serve for each other. Extensive
experiments demonstrate that the proposed network achieves superior and stable
clustering performance improvement against existing state-of-the-art incomplete
clustering methods over different missing ratios.


Abstract:
  For action recognition learning, 2D CNN-based methods are efficient but may
yield redundant features due to applying the same 2D convolution kernel to each
frame. Recent efforts attempt to capture motion information by establishing
inter-frame connections while still suffering the limited temporal receptive
field or high latency. Moreover, the feature enhancement is often only
performed by channel or space dimension in action recognition. To address these
issues, we first devise a Channel-wise Motion Enhancement (CME) module to
adaptively emphasize the channels related to dynamic information with a
channel-wise gate vector. The channel gates generated by CME incorporate the
information from all the other frames in the video. We further propose a
Spatial-wise Motion Enhancement (SME) module to focus on the regions with the
critical target in motion, according to the point-to-point similarity between
adjacent feature maps. The intuition is that the change of background is
typically slower than the motion area. Both CME and SME have clear physical
meaning in capturing action clues. By integrating the two modules into the
off-the-shelf 2D network, we finally obtain a Comprehensive Motion
Representation (CMR) learning method for action recognition, which achieves
competitive performance on Something-Something V1 & V2 and Kinetics-400. On the
temporal reasoning datasets Something-Something V1 and V2, our method
outperforms the current state-of-the-art by 2.3% and 1.9% when using 16 frames
as input, respectively.


Abstract:
  For the most general Polya urn schemes, we establish the almost sure
convergence of its composition. The only requirement is that there are always
enough balls of both colors, so that the extractions can be indefinitely
pursued according to the specifications of the model. We also consider the
method for determining the probability of fulfilling this requirement, as a
function of the initial number of balls of each color.


Abstract:
  We give a computational approach to theorem proving in homological algebra.
This approach is based on computations in the free abelian category of an
additive category $\mathbf{A}$. We show that the free abelian category is
amenable to explicit computations whenever we can decide homotopy equations in
$\mathbf{A}$. As some consequences of our investigations, we recover Dowker's
explicit formula for the connecting homomorphism $\partial$ in the snake lemma,
we find a universal sense in which $\partial$ is unique, and we give a refined
version of the 5-lemma.


Abstract:
  Some observations such as those presented in Walker et al. show that the
observed entropy profiles of the intra-cluster medium (ICM) deviate from the
power-law prediction of adiabatic simulations. This implies that
non-gravitational processes, which are absent in the simulations, may be
important in the evolution of the ICM, and by quantifying the deviation, we may
be able to estimate the feedback energy in the ICM and use it as a probe of the
non-gravitational processes. To address this issue we calculate the ICM entropy
profiles in a sample of 47 galaxy clusters and groups, which have been observed
out to at least $\sim r_{500}$ with Chandra, XMM-Newton and/or Suzaku, by
constructing a physical model to incorporate the effects of both gravity and
non-gravitational processes to fit the observed gas temperature and surface
brightness profiles via Bayesian statistics. After carefully evaluating the
effects of systematic errors, we find that the gas entropy profiles derived
with best-fit results of our model are consistent with the simulation-predicted
power-law profile near the virial radius, while the flattened profiles reported
previously can be explained by introducing the gas clumping effect, the
existence of which is confirmed in 19 luminous targets in our sample. We
calculate the total feedback energy per particle and find that it decreases
from $\sim 10$ keV at the center to about zero at $\sim 0.35$$r_{200}$ and is
consistent with zero outside $\sim 0.35$$r_{200}$, implying the upper limit of
the feedback efficiency $\sim 0.02$ for the super-massive black holes hosted in
the brightest cluster galaxies.