Abstract:
  Three dimensional space is said to be spherically symmetric if it admits
SO(3) as the group of isometries. Under this symmetry condition, the Einsteins
Field equations for vacuum, yields the Schwarzschild Metric as the unique
solution, which essentially is the statement of the well known Birkhoffs
Theorem. Geometrically speaking this theorem claims that the pseudo-Riemanian
space-times provide more isometries than expected from the original metric
holonomy/ansatz. In this paper we use the method of Lie Symmetry Analysis to
analyze the Einsteins Vacuum Field Equations so as to obtain the Symmetry
Generators of the corresponding Differential Equation. Additionally, applying
the Noether Point Symmetry method we have obtained the conserved quantities
corresponding to the generators of the Schwarzschild Lagrangian and paving way
to reformulate the Birkhoffs Theorem from a different approach.


Abstract:
  Scanning quantum dot microscopy is a recently developed high-resolution
microscopy technique that is based on atomic force microscopy and is capable of
imaging the electrostatic potential of nanostructures like molecules or single
atoms. Recently, it could be shown that it not only yields qualitatively but
also quantitatively cutting edge images even on an atomic level. In this paper
we present how control is a key enabling element to this. The developed control
approach consists of a two-degree-of-freedom control framework that comprises a
feedforward and a feedback part. For the latter we design two tailored feedback
controllers. The feedforward part generates a reference for the current scanned
line based on the previously scanned one. We discuss in detail various aspects
of the presented control approach and its implications for scanning quantum dot
microscopy. We evaluate the influence of the feedforward part and compare the
two proposed feedback controllers. The proposed control algorithms speed up
scanning quantum dot microscopy by more than a magnitude and enable to scan
large sample areas.


Abstract:
  Low resolution fine-grained classification has widespread applicability for
applications where data is captured at a distance such as surveillance and
mobile photography. While fine-grained classification with high resolution
images has received significant attention, limited attention has been given to
low resolution images. These images suffer from the inherent challenge of
limited information content and the absence of fine details useful for
sub-category classification. This results in low inter-class variations across
samples of visually similar classes. In order to address these challenges, this
research proposes a novel attribute-assisted loss, which utilizes ancillary
information to learn discriminative features for classification. The proposed
loss function enables a model to learn class-specific discriminative features,
while incorporating attribute-level separability. Evaluation is performed on
multiple datasets with different models, for four resolutions varying from
32x32 to 224x224. Different experiments demonstrate the efficacy of the
proposed attributeassisted loss for low resolution fine-grained classification.


Abstract:
  What is the power of constant-depth circuits with $MOD_m$ gates, that can
count modulo $m$? Can they efficiently compute MAJORITY and other symmetric
functions? When $m$ is a constant prime power, the answer is well understood:
Razborov and Smolensky proved in the 1980s that MAJORITY and $MOD_m$ require
super-polynomial-size $MOD_q$ circuits, where $q$ is any prime power not
dividing $m$. However, relatively little is known about the power of $MOD_m$
circuits for non-prime-power $m$. For example, it is still open whether every
problem in $EXP$ can be computed by depth-$3$ circuits of polynomial size and
only $MOD_6$ gates.
  We shed some light on the difficulty of proving lower bounds for $MOD_m$
circuits, by giving new upper bounds. We construct $MOD_m$ circuits computing
symmetric functions with non-prime power $m$, with size-depth tradeoffs that
beat the longstanding lower bounds for $AC^0[m]$ circuits for prime power $m$.
Our size-depth tradeoff circuits have essentially optimal dependence on $m$ and
$d$ in the exponent, under a natural circuit complexity hypothesis.
  For example, we show for every $\varepsilon > 0$ that every symmetric
function can be computed with depth-3 $MOD_m$ circuits of
$\exp(O(n^{\varepsilon}))$ size, for a constant $m$ depending only on
$\varepsilon > 0$. That is, depth-$3$ $CC^0$ circuits can compute any symmetric
function in \emph{subexponential} size. This demonstrates a significant
difference in the power of depth-$3$ $CC^0$ circuits, compared to other models:
for certain symmetric functions, depth-$3$ $AC^0$ circuits require
$2^{\Omega(\sqrt{n})}$ size [H{\aa}stad 1986], and depth-$3$ $AC^0[p^k]$
circuits (for fixed prime power $p^k$) require $2^{\Omega(n^{1/6})}$ size
[Smolensky 1987]. Even for depth-two $MOD_p \circ MOD_m$ circuits,
$2^{\Omega(n)}$ lower bounds were known [Barrington Straubing Th\'erien 1990].


Abstract:
  We discuss stiffening of matter in quark-hadron continuity. We introduce a
model that relates quark wave functions in a baryon and the occupation
probability of states for baryons and quarks in dense matter. In a dilute
regime, the confined quarks contribute to the energy density through the masses
of baryons, but do not directly contribute to the pressure; hence, the
equations of state are very soft. This dilute regime continues until the low
momentum states for quarks get saturated; this may happen even before baryons
fully overlap, possibly at density slightly above the nuclear saturation
density. After the saturation the pressure grows rapidly while changes in
energy density are modest, producing a peak in the speed of sound. If we use
baryonic descriptions for quark distributions near the Fermi surface, we reach
a description similar to the quarkyonic matter model of McLerran and Reddy.
With a simple adjustment of quark interactions to get the nucleon mass, our
model becomes consistent with the constraints from 1.4-solar mass neutron
stars, but the high density part is too soft to account for two-solar mass
neutron stars. We delineate the relation between the saturation effects and
short range interactions of quarks, suggesting interactions that leave low
density equations of state unchanged but stiffen the high density part.


Abstract:
  The coherent superposition of non-orthogonal fermionic Gaussian states has
been shown to be an efficient approximation to the ground states of quantum
impurity problems [Bravyi and Gosset,Comm. Math. Phys.,356 451 (2017)]. We
present a practical approach for performing a variational calculation based on
such states. Our method is based on approximate imaginary-time equations of
motion that decouple the dynamics of each Gaussian state forming the ansatz. It
is independent of the lattice connectivity of the model and the implementation
is highly parallelizable. To benchmark our variational method, we calculate the
spin-spin correlation function and R\'enyi entanglement entropy of an Anderson
impurity, allowing us to identify the screening cloud and compare to density
matrix renormalization group calculations. Secondly, we study the screening
cloud of the two-channel Kondo model, a problem difficult to tackle using
existing numerical tools.


Abstract:
  The production of polarized proton beams with multi-GeV energies in
ultra-intense laser interaction with targets is studied with three-dimensional
Particle-In-Cell simulations. A near-critical density plasma target with
pre-polarized proton and tritium ions is considered for the proton
acceleration. The pre-polarized protons are initially accelerated by laser
radiation pressure before injection and further acceleration in a bubble-like
wakefield. The temporal dynamics of proton polarization is tracked via the
T-BMT equation, and it is found that the proton polarization state can be
altered both by the laser field and the magnetic component of the wakefield.
The dependence of the proton acceleration and polarization on the ratio of the
ion species is determined, and it is found that the protons can be efficiently
accelerated as long as their relative fraction is less than 20%, in which case
the bubble size is large enough for the protons to obtain sufficient energy to
overcome the bubble injection threshold.


Abstract:
  This work presents the derivation of a model for the heating process of the
air of a glass dome, where an indoor swimming pool is located in the bottom of
the dome. The problem can be reduced from a three dimensional to a two
dimensional one. The main goal is the formulation of a proper optimization
problem for computing the optimal heating of the air after a given time. For
that, the model of the heating process as a partial differential equation is
formulated as well as the optimization problem subject to the time-dependent
partial differential equation. This yields the optimal heating of the air under
the glass dome such that the desired temperature distribution is attained after
a given time. The discrete formulation of the optimization problem and a proper
numerical method for it, the projected gradient method, are discussed. Finally,
numerical experiments are presented which show the practical performance of the
optimal control problem and its numerical solution method discussed.


Abstract:
  Constituted with a massive black hole and a stellar mass compact object,
Extreme Mass Ratio Inspiral (EMRI) events hold unique opportunity for the study
of massive black holes, such as by measuring and checking the relations among
the mass, spin and quadrupole moment of a massive black hole, putting the
no-hair theorem to test. TianQin is a planned space-based gravitational wave
observatory and EMRI is one of its main types of sources. It is important to
estimate the capacity of TianQin on testing the no-hair theorem with EMRIs. In
this work, we use the analytic kludge waveform with quadrupole moment
corrections and study how the quadrupole moment can be constrained with
TianQin. We find that TianQin can measure the dimensionless quadrupole moment
parameter with accuracy to the level of $10^{-5}$ under suitable scenarios. The
choice of the waveform cutoff is found to have significant effect on the
result: if the Schwarzschild cutoff is used, the accuracy depends strongly on
the mass of the massive black hole, while the spin has negligible impact; if
the Kerr cutoff is used, however, the dependence on the spin is more
significant. We have also analyzed the cases when TianQin is observing
simultaneously with other detectors such as LISA.


Abstract:
  In this paper, we investigate the Dirac equation with the Killingbeck
potential under the external magnetic field in non-commutative space.
Corresponding to the expressions of the energy level and wave functions in spin
symmetry limit and pseudo-spin symmetry limit are derived by using the Bethe
ansatz method. The parameter B associated with the external magnetic field and
non-commutative parameter {\theta} make to modify the energy level for
considered systems.


Abstract:
  A 360{\deg} perception of scene geometry is essential for automated driving,
notably for parking and urban driving scenarios. Typically, it is achieved
using surround-view fisheye cameras, focusing on the near-field area around the
vehicle. The majority of current depth estimation approaches focus on employing
just a single camera, which cannot be straightforwardly generalized to multiple
cameras. The depth estimation model must be tested on a variety of cameras
equipped to millions of cars with varying camera geometries. Even within a
single car, intrinsics vary due to manufacturing tolerances. Deep learning
models are sensitive to these changes, and it is practically infeasible to
train and test on each camera variant. As a result, we present novel
camera-geometry adaptive multi-scale convolutions which utilize the camera
parameters as a conditional input, enabling the model to generalize to
previously unseen fisheye cameras. Additionally, we improve the distance
estimation by pairwise and patchwise vector-based self-attention encoder
networks. We evaluate our approach on the Fisheye WoodScape surround-view
dataset, significantly improving over previous approaches. We also show a
generalization of our approach across different camera viewing angles and
perform extensive experiments to support our contributions. To enable
comparison with other approaches, we evaluate the front camera data on the
KITTI dataset (pinhole camera images) and achieve state-of-the-art performance
among self-supervised monocular methods. An overview video with qualitative
results is provided at https://youtu.be/bmX0UcU9wtA. Baseline code and dataset
will be made public.


Abstract:
  We report on the data set, data handling, and detailed analysis techniques of
the first neutrino-mass measurement by the Karlsruhe Tritium Neutrino (KATRIN)
experiment, which probes the absolute neutrino-mass scale via the $\beta$-decay
kinematics of molecular tritium. The source is highly pure, cryogenic T$_2$
gas. The $\beta$ electrons are guided along magnetic field lines toward a
high-resolution, integrating spectrometer for energy analysis. A silicon
detector counts $\beta$ electrons above the energy threshold of the
spectrometer, so that a scan of the thresholds produces a precise measurement
of the high-energy spectral tail. After detailed theoretical studies,
simulations, and commissioning measurements, extending from the molecular
final-state distribution to inelastic scattering in the source to subtleties of
the electromagnetic fields, our independent, blind analyses allow us to set an
upper limit of 1.1 eV on the neutrino-mass scale at a 90\% confidence level.
This first result, based on a few weeks of running at a reduced source
intensity and dominated by statistical uncertainty, improves on prior limits by
nearly a factor of two. This result establishes an analysis framework for
future KATRIN measurements, and provides important input to both particle
theory and cosmology.


Abstract:
  Formed by using laser inter-satellite links (LISLs) among satellites in
upcoming low Earth orbit and very low Earth orbit satellite constellations,
optical wireless satellite networks (OWSNs), also known as free-space optical
satellite networks, can provide a better alternative to existing optical fiber
terrestrial networks (OFTNs) for long-distance inter-continental data
communications. The LISLs operate at the speed of light in vacuum in space,
which gives OWSNs a crucial advantage over OFTNs in terms of latency. In this
paper, we employ the satellite constellation for Phase I of Starlink and LISLs
between satellites to simulate an OWSN. Then, we compare the network latency of
this OWSN and the OFTN under three different scenarios for long-distance
inter-continental data communications. The results show that the OWSN performs
better than the OFTN in all scenarios. It is observed that the longer the
length of the inter-continental connection between the source and the
destination, the better the latency improvement offered by the OWSN compared to
OFTN.


Abstract:
  We propose a useful integral representation of the quenched free energy which
is applicable to any random systems. Our formula involves the generating
function of multi-boundary correlators, which can be interpreted on the bulk
gravity side as spacetime D-branes introduced by Marolf and Maxfield in
[arXiv:2002.08950]. As an example, we apply our formalism to the Airy limit of
the random matrix model and compute its quenched free energy under certain
approximations of the generating function of correlators. It turns out that the
resulting quenched free energy is a monotonically decreasing function of the
temperature, as expected.


Abstract:
  Let $\phi:X\rightarrow \mathbb{P}^n$ be a morphism of varieties. Given a
hyperplane $H$ in $\mathbb{P}^n$, there is a Gysin map from the compactly
supported cohomology of $\phi^{-1}(H)$ to that of $X$. We give conditions on
the degree of the cohomology under which this map is an isomorphism for all but
a low-dimensional set of hyperplanes, generalizing results due to Skorobogatov,
Benoist, and Poonen-Slavov. Our argument is based on Beilinson's theory of
singular supports for \'etale sheaves.


Abstract:
  We present FedScale, a diverse set of challenging and realistic benchmark
datasets to facilitate scalable, comprehensive, and reproducible federated
learning (FL) research. FedScale datasets are large-scale, encompassing a
diverse range of important FL tasks, such as image classification, object
detection, word prediction, and speech recognition. For each dataset, we
provide a unified evaluation protocol using realistic data splits and
evaluation metrics. To meet the pressing need for reproducing realistic FL at
scale, we have also built an efficient evaluation platform to simplify and
standardize the process of FL experimental setup and model evaluation. Our
evaluation platform provides flexible APIs to implement new FL algorithms and
includes new execution backends with minimal developer efforts. Finally, we
perform in-depth benchmark experiments on these datasets. Our experiments
suggest fruitful opportunities in heterogeneity-aware co-optimizations of the
system and statistical efficiency under realistic FL characteristics. FedScale
is open-source with permissive licenses and actively maintained, and we welcome
feedback and contributions from the community.


Abstract:
  State-of-the-art motor vehicles are able to break for pedestrians in an
emergency. We investigate what it would take to issue an early warning to the
driver so he/she has time to react. We have identified that predicting the
intention of a pedestrian reliably by position is a particularly hard
challenge. This paper describes an early pedestrian warning demonstration
system.


Abstract:
  This paper concerns the verification of continuous-time polynomial spline
trajectories against linear temporal logic specifications (LTL without 'next').
Each atomic proposition is assumed to represent a state space region described
by a multivariate polynomial inequality. The proposed approach samples a
trajectory strategically, to capture every one of its region transitions. This
yields a discrete word called a trace, which is amenable to established formal
methods for path checking. The original continuous-time trajectory is shown to
satisfy the specification if and only if its trace does. General topological
conditions on the sample points are derived that ensure a trace is recorded for
arbitrary continuous paths, given arbitrary region descriptions. Using
techniques from computer algebra, a trace generation algorithm is developed to
satisfy these conditions when the path and region boundaries are defined by
polynomials. The proposed PolyTrace algorithm has polynomial complexity in the
number of atomic propositions, and is guaranteed to produce a trace of any
polynomial path. Its performance is demonstrated via numerical examples and a
case study from robotics.


Abstract:
  As a part of science of science (SciSci) research, the evolution of
scientific disciplines has been attracting a great deal of attention recently.
This kind of discipline level analysis not only give insights of one particular
field but also shed light on general principles of scientific enterprise. In
this paper we focus on graphene research, a fast growing field covers both
theoretical and applied study. Using co-clustering method, we split graphene
literature into two groups and confirm that one group is about theoretical
research (T) and another corresponds to applied research (A). We analyze the
proportion of T/A and found applied research becomes more and more popular
after 2007. Geographical analysis demonstrated that countries have different
preference in terms of T/A and they reacted differently to research trend. The
interaction between two groups has been analyzed and shows that T extremely
relies on T and A heavily relies on A, however the situation is very stable for
T but changed markedly for A. No geographic difference is found for the
interaction dynamics. Our results give a comprehensive picture of graphene
research evolution and also provide a general framework which is able to
analyze other disciplines.


Abstract:
  Free-space optical communication is emerging as a low-power, low-cost, and
high data rate alternative to radio-frequency communication in short-to
medium-range applications. However, it requires a close-to-line-of-sight link
between the transmitter and the receiver. This paper proposes a robust $\cHi$
control law for free-space optical (FSO) beam pointing error systems under
controlled weak turbulence conditions. The objective is to maintain the
transmitter-receiver line, which means the center of the optical beam as close
as possible to the center of the receiving aperture within a prescribed
disturbance attenuation level. First, we derive an augmented nonlinear
discrete-time model for pointing error loss due to misalignment caused by weak
atmospheric turbulence. We then investigate the $\cHi$-norm optimization
problem that guarantees the closed-loop pointing error is stable and ensures
the prescribed weak disturbance attenuation. Furthermore, we evaluate the
closed-loop outage probability error and bit error rate (BER) that quantify the
free-space optical communication performance in fading channels. Finally, the
paper concludes with a numerical simulation of the proposed approach to the FSO
link's error performance.


Abstract:
  Fake news has now grown into a big problem for societies and also a major
challenge for people fighting disinformation. This phenomenon plagues
democratic elections, reputations of individual persons or organizations, and
has negatively impacted citizens, (e.g., during the COVID-19 pandemic in the US
or Brazil). Hence, developing effective tools to fight this phenomenon by
employing advanced Machine Learning (ML) methods poses a significant challenge.
The following paper displays the present body of knowledge on the application
of such intelligent tools in the fight against disinformation. It starts by
showing the historical perspective and the current role of fake news in the
information war. Proposed solutions based solely on the work of experts are
analysed and the most important directions of the application of intelligent
systems in the detection of misinformation sources are pointed out.
Additionally, the paper presents some useful resources (mainly datasets useful
when assessing ML solutions for fake news detection) and provides a short
overview of the most important R&D projects related to this subject. The main
purpose of this work is to analyse the current state of knowledge in detecting
fake news; on the one hand to show possible solutions, and on the other hand to
identify the main challenges and methodological gaps to motivate future
research.


Abstract:
  We study adaptive methods for differentially private convex optimization,
proposing and analyzing differentially private variants of a Stochastic
Gradient Descent (SGD) algorithm with adaptive stepsizes, as well as the
AdaGrad algorithm. We provide upper bounds on the regret of both algorithms and
show that the bounds are (worst-case) optimal. As a consequence of our
development, we show that our private versions of AdaGrad outperform adaptive
SGD, which in turn outperforms traditional SGD in scenarios with non-isotropic
gradients where (non-private) Adagrad provably outperforms SGD. The major
challenge is that the isotropic noise typically added for privacy dominates the
signal in gradient geometry for high-dimensional problems; approaches to this
that effectively optimize over lower-dimensional subspaces simply ignore the
actual problems that varying gradient geometries introduce. In contrast, we
study non-isotropic clipping and noise addition, developing a principled
theoretical approach; the consequent procedures also enjoy significantly
stronger empirical performance than prior approaches.


Abstract:
  In this paper we show that wormholes in (2+1) dimensions (3-D) cannot be
sourced solely by both Casimir energy and tension, differently from what
happens in a 4-D scenario, in which case it has been shown recently, by the
direct computation of the exact shape and redshift functions of a wormhole
solution, that this is possible. We show that in a 3-D spacetime the same is
not true since the arising of at least an event horizon is inevitable. We do
the analysis for massive and massless fermions, as well as for scalar fields,
considering quasi-periodic boundary conditions and find that a possibility to
circumvent such a restriction is to introduce, besides the 3-D Casimir energy
density and tension, a cosmological constant, embedding the surface in a 4-D
manifold and applying a perpendicular weak magnetic field. This causes an
additional tension on it, which contributes to the formation of the wormhole.
Finally, we discuss the possibility of producing the condensed matter analogous
of this wormhole in a graphene sheet and analyze the electronic transport
through it.


Abstract:
  We propose the Automatic-differentiated Physics-Informed Echo State Network
(API-ESN). The network is constrained by the physical equations through the
reservoir's exact time-derivative, which is computed by automatic
differentiation. As compared to the original Physics-Informed Echo State
Network, the accuracy of the time-derivative is increased by up to seven orders
of magnitude. This increased accuracy is key in chaotic dynamical systems,
where errors grows exponentially in time. The network is showcased in the
reconstruction of unmeasured (hidden) states of a chaotic system. The API-ESN
eliminates a source of error, which is present in existing physics-informed
echo state networks, in the computation of the time-derivative. This opens up
new possibilities for an accurate reconstruction of chaotic dynamical states.


Abstract:
  The aerodynamic performance of the high-lift configuration greatly influences
the safety and economy of commercial aircraft. Accurately predicting the
aerodynamic performance of the high-lift configuration, especially the stall
behavior, is important for aircraft design. However, the complex flow phenomena
of high-lift configurations pose substantial difficulties to current turbulence
models. In this paper, a three-equation k-(v^2)-{\omega} turbulence model for
the Reynolds-averaged Navier-Stokes equations is used to compute the stall
behavior of high-lift configurations. A separated shear layer fixed function is
implemented in the turbulence model to better capture the nonequilibrium
characteristics of turbulence. Different high-lift configurations, including
the two-dimensional multielement NLR7301 and Omar airfoils and a complex
full-configuration model (JAXA Standard Model), are numerically tested. The
results indicate that the effect of the nonequilibrium characteristics of
turbulence is significant in the free shear layer, which is key to accurately
predicting the stall behavior of high-lift devices. The modified SPF k-(v^2
)-{\omega} model is more accurate in predicting stall behavior than the
Spalart-Allmaras, shear stress transport, and original k-(v^2)-{\omega} models
for the full high-lift configuration. The relative errors in the predicted
maximum lift coefficients are within 3% of the experimental data.


Abstract:
  Aberration-corrected scanning electron microscopy (AC-STEM) can provide
valuable information on the atomic structure of nanoclusters, an essential
input for gaining an understanding of their physical and chemical properties. A
systematic method is presented here for the extraction of atom coordinates from
an AC-STEM image in a way that is general enough to be applicable to irregular
structures. The two-dimensional information from the image is complemented with
an approximate description of the atomic interactions so as to construct a
three-dimensional structure and, at a final stage, the structure is refined
using electron density functional theory (DFT) calculations. The method is
applied to an AC-STEM image of Au55. Analysis of the local structure shows that
the cluster is a combination of a part with icosahedral structure elements and
a part with local atomic arrangement characteristic of crystal packing,
including a segment of a flat surface facet. The energy landscape of the
cluster is explored in calculations of minimum energy paths between the optimal
fit structure and other candidates generated in the analysis. This reveals low
energy barriers for conformational changes, showing that such transitions can
occur on laboratory timescale even at room temperature and lead to large
changes in the AC-STEM image. The paths furthermore reveal additional cluster
configurations, some with lower DFT energy and providing nearly as good fit to
the experimental image.


Abstract:
  We present a method for exploring analogue Hawking radiation using a laser
pulse propagating through an underdense plasma. The propagating fields in the
Hawking effect are local perturbations of the plasma density and laser
amplitude. We derive the dependence of the resulting Hawking temperature on the
dimensionless amplitude of the laser and the behaviour of the spot area of the
laser at the analogue event horizon. We demonstrate one possible way of
obtaining the analogue Hawking temperature in terms of the plasma wavelength,
and our analysis shows that for a high intensity near-IR laser the analogue
Hawking temperature is less than approximately 25K for a reasonable choice of
parameters.


Abstract:
  Ionic polymer-metal composites consist in a thin film of electro-active
polymers (Nafion R for example) sandwiched between two metallic electrodes.
They can be used as sensors or actuators. The polymer is saturated with water,
which causes a complete dissociation and the release of small cations. The
strip undergoes large bending motions when it is submitted to an orthogonal
electric field and vice versa. We used a continuous medium approach and a
coarse grain model; the system is depicted as a deformable porous medium in
which flows an ionic solution. We write microscale balance laws and
thermodynamic relations for each phase, then for the complete material using an
average technique. Entropy production, then constitutive equations are deduced
: a Kelvin-Voigt stress-strain relation, generalized Fourier's and Darcy's laws
and a Nernst-Planck equation. We applied this model to a cantilever E.A.P.
strip undergoing a continuous potential difference (static case); a shear force
may be applied to the free end to prevent its displacement. Applied forces and
deflection are calculated using a beam model in large displacements. The
results obtained are in good agreement with the experimental data published in
the literature.


Abstract:
  Learning representation for source code is a foundation of many program
analysis tasks. In recent years, neural networks have already shown success in
this area, but most existing models did not make full use of the unique
structural information of programs. Although abstract syntax tree-based neural
models can handle the tree structure in the source code, they cannot capture
the richness of different types of substructure in programs. In this paper, we
propose a modular tree network (MTN) which dynamically composes different
neural network units into tree structures based on the input abstract syntax
tree. Different from previous tree-structural neural network models, MTN can
capture the semantic differences between types of ASTsubstructures. We evaluate
our model on two tasks: program classification and code clone detection.
Ourmodel achieves the best performance compared with state-of-the-art
approaches in both tasks, showing the advantage of leveraging more elaborate
structure information of the source code.


Abstract:
  Motivated by the recent surge of criminal activities with
cross-cryptocurrency trades, we introduce a new topological perspective to
structural anomaly detection in dynamic multilayer networks. We postulate that
anomalies in the underlying blockchain transaction graph that are composed of
multiple layers are likely to also be manifested in anomalous patterns of the
network shape properties. As such, we invoke the machinery of clique persistent
homology on graphs to systematically and efficiently track evolution of the
network shape and, as a result, to detect changes in the underlying network
topology and geometry. We develop a new persistence summary for multilayer
networks, called stacked persistence diagram, and prove its stability under
input data perturbations. We validate our new topological anomaly detection
framework in application to dynamic multilayer networks from the Ethereum
Blockchain and the Ripple Credit Network, and demonstrate that our stacked PD
approach substantially outperforms state-of-art techniques.


Abstract:
  Consider a deterministically growing surface of any dimension, where the
growth at a point is an arbitrary nonlinear function of the heights at that
point and its neighboring points. Assuming that this nonlinear function is
monotone, invariant under the symmetries of the lattice, equivariant under
constant shifts, and twice continuously differentiable, it is shown that any
such growing surface approaches a solution of the deterministic KPZ equation in
a suitable space-time scaling limit.


Abstract:
  Extracting the interaction rules of biological agents from movement sequences
pose challenges in various domains. Granger causality is a practical framework
for analyzing the interactions from observed time-series data; however, this
framework ignores the structures and assumptions of the generative process in
animal behaviors, which may lead to interpretational problems and sometimes
erroneous assessments of causality. In this paper, we propose a new framework
for learning Granger causality from multi-animal trajectories via augmented
theory-based behavioral models with interpretable data-driven models. We adopt
an approach for augmenting incomplete multi-agent behavioral models described
by time-varying dynamical systems with neural networks. For efficient and
interpretable learning, our model leverages theory-based architectures
separating navigation and motion processes, and the theory-guided
regularization for reliable behavioral modeling. This can provide interpretable
signs of Granger-causal effects over time, i.e., when specific others cause the
approach or separation. In experiments using synthetic datasets, our method
achieved better performance than various baselines. We then analyzed
multi-animal datasets of mice, flies, birds, and bats, which verified our
method and obtained novel biological insights.


Abstract:
  While attention-based encoder-decoder (AED) models have been successfully
extended to the online variants for streaming automatic speech recognition
(ASR), such as monotonic chunkwise attention (MoChA), the models still have a
large label emission latency because of the unconstrained end-to-end training
objective. Previous works tackled this problem by leveraging alignment
information to control the timing to emit tokens during training. In this work,
we propose a simple alignment-free regularization method, StableEmit, to
encourage MoChA to emit tokens earlier. StableEmit discounts the selection
probabilities in hard monotonic attention for token boundary detection by a
constant factor and regularizes them to recover the total attention mass during
training. As a result, the scale of the selection probabilities is increased,
and the values can reach a threshold for token emission earlier, leading to a
reduction of emission latency and deletion errors. Moreover, StableEmit can be
combined with methods that constraint alignments to further improve the
accuracy and latency. Experimental evaluations with LSTM and Conformer encoders
demonstrate that StableEmit significantly reduces the recognition errors and
the emission latency simultaneously. We also show that the use of alignment
information is complementary in both metrics.


Abstract:
  This paper describes a test and case study of self-evaluation of online
courses during the pandemic time. Due to the Covid-19, the whole world needs to
sit on lockdown in different periods. Many things need to be done in all kinds
of business including the education sector of countries. To sustain the
education development teaching methods had to switch from traditional
face-to-face teaching to online courses. The government made decisions in a
short time and educational institutions had no time to prepare the materials
for the online teaching. All courses of the Mongolian University of
Pharmaceutical Sciences switched to online lessons. Challenges were raised
before professors and tutors during online teaching. Our university did not
have a specific learning management system for online teaching and e-learning.
Therefore professors used different platforms for their online teaching such as
Zoom, Microsoft teams for instance. Moreover, different social networking
platforms played an active role in communication between students and
professors. The situation is very difficult for professors and students. To
measure the quality of online courses and to figure out the positive and weak
points of online teaching we need an evaluation of e-learning. The focus of
this paper is to share the evaluation process of e-learning based on a
structure-oriented evaluation model.


Abstract:
  This report contains the description of two novel job shop scheduling
benchmarks that resemble instances of real scheduling problem as they appear in
industry. In particular, the aim was to provide large-scale benchmarks (up to 1
million operations) to test the state-of-the-art scheduling solutions on
problems that are closer to what occurs in a real industrial context. The first
benchmark is an extension of the well known Taillard benchmark (1992), while
the second is a collection of scheduling instances with a known-optimum
solution.


Abstract:
  Sentiment analysis can provide a suitable lead for the tools used in software
engineering along with the API recommendation systems and relevant libraries to
be used. In this context, the existing tools like SentiCR, SentiStrength-SE,
etc. exhibited low f1-scores that completely defeats the purpose of deployment
of such strategies, thereby there is enough scope for performance improvement.
Recent advancements show that transformer based pre-trained models (e.g., BERT,
RoBERTa, ALBERT, etc.) have displayed better results in the text classification
task. Following this context, the present research explores different
BERT-based models to analyze the sentences in GitHub comments, Jira comments,
and Stack Overflow posts. The paper presents three different strategies to
analyse BERT based model for sentiment analysis, where in the first strategy
the BERT based pre-trained models are fine-tuned; in the second strategy an
ensemble model is developed from BERT variants, and in the third strategy a
compressed model (Distil BERT) is used. The experimental results show that the
BERT based ensemble approach and the compressed BERT model attain improvements
by 6-12% over prevailing tools for the F1 measure on all three datasets.


Abstract:
  Neural networks notoriously suffer from the problem of catastrophic
forgetting, the phenomenon of forgetting the past knowledge when acquiring new
knowledge. Overcoming catastrophic forgetting is of significant importance to
emulate the process of "incremental learning", where the model is capable of
learning from sequential experience in an efficient and robust way.
State-of-the-art techniques for incremental learning make use of knowledge
distillation towards preventing catastrophic forgetting. Therein, one updates
the network while ensuring that the network's responses to previously seen
concepts remain stable throughout updates. This in practice is done by
minimizing the dissimilarity between current and previous responses of the
network one way or another. Our work contributes a novel method to the arsenal
of distillation techniques. In contrast to the previous state of the art, we
propose to firstly construct low-dimensional manifolds for previous and current
responses and minimize the dissimilarity between the responses along the
geodesic connecting the manifolds. This induces a more formidable knowledge
distillation with smooth properties which preserves the past knowledge more
efficiently as observed by our comprehensive empirical study.


Abstract:
  One of the problems of conventional visual quality evaluation criteria such
as PSNR and MSE is the lack of appropriate standards based on the human visual
system (HVS). They are calculated based on the difference of the corresponding
pixels in the original and manipulated image. Hence, they practically do not
provide a correct understanding of the image quality. Watermarking is an image
processing application in which the image's visual quality is an essential
criterion for its evaluation. Watermarking requires a criterion based on the
HVS that provides more accurate values than conventional measures such as PSNR.
This paper proposes a weighted fuzzy-based criterion that tries to find
essential parts of an image based on the HVS. Then these parts will have larger
weights in computing the final value of PSNR. We compare our results against
standard PSNR, and our experiments show considerable consequences.


Abstract:
  Hermite best approximation vectors of a real number $\theta$ were introduced
by Lagarias. A nonzero vector (p, q) $\in$ Z x N is a Hermite best
approximation vector of $\theta$ if there exists $\Delta$ > 0 such that (p --
q$\theta$) 2 + q 2 /$\Delta$ $\le$ (a -- b$\theta$) 2 + b 2 /$\Delta$ for all
nonzero (a, b) $\in$ Z 2. Hermite observed that if q > 0 then the fraction p/q
must be a convergent of the continued fraction expansion of $\theta$ and
Lagarias pointed out that some convergents are not associated with a Hermite
best approximation vectors. In this note we show that the almost sure
proportion of Hermite best approximation vectors among convergents is ln 3/ ln
4. The main tool of the proof is the natural extension of the Gauss map x
$\in$]0, 1[$\rightarrow$ {1/x}.


Abstract:
  To make off-screen interaction without specialized hardware practical, we
investigate using deep learning methods to process the common built-in IMU
sensor (accelerometers and gyroscopes) on mobile phones into a useful set of
one-handed interaction events. We present the design, training, implementation
and applications of TapNet, a multi-task network that detects tapping on the
smartphone. With phone form factor as auxiliary information, TapNet can jointly
learn from data across devices and simultaneously recognize multiple tap
properties, including tap direction and tap location. We developed two datasets
consisting of over 135K training samples, 38K testing samples, and 32
participants in total. Experimental evaluation demonstrated the effectiveness
of the TapNet design and its significant improvement over the state of the art.
Along with the datasets,
(https://sites.google.com/site/michaelxlhuang/datasets/tapnet-dataset), and
extensive experiments, TapNet establishes a new technical foundation for
off-screen mobile input.


Abstract:
  In this report we are aiming at introducing a global measure of
non-classicality of the state space of $N$-level quantum systems and estimating
it in the limit of large $N$. For this purpose we employ the Wigner function
negativity as a non-classicality criteria. Thus, the specific volume of the
support of negative values of Wigner function is treated as a measure of
non-classicality of an individual state. Assuming that the states of an
$N$-level quantum system are distributed by Hilbert-Schmidt measure
(Hilbert-Schmidt ensemble), we define the global measure as the average
non-classicality of the individual states over the Hilbert-Schmidt ensemble. We
present the numerical estimate of this quantity as a result of random
generation of states, and prove a proposition claiming its exact value in the
limit of $N\to \infty$


Abstract:
  While language identification is a fundamental speech and language processing
task, for many languages and language families it remains a challenging task.
For many low-resource and endangered languages this is in part due to resource
availability: where larger datasets exist, they may be single-speaker or have
different domains than desired application scenarios, demanding a need for
domain and speaker-invariant language identification systems. This year's
shared task on robust spoken language identification sought to investigate just
this scenario: systems were to be trained on largely single-speaker speech from
one domain, but evaluated on data in other domains recorded from speakers under
different recording circumstances, mimicking realistic low-resource scenarios.
We see that domain and speaker mismatch proves very challenging for current
methods which can perform above 95% accuracy in-domain, which domain adaptation
can address to some degree, but that these conditions merit further
investigation to make spoken language identification accessible in many
scenarios.


Abstract:
  We establish an uncountable amenable ergodic Roth theorem, in which the
acting group is not assumed to be countable and the space need not be
separable. This extends a previous result of Bergelson, McCutcheon and Zhang.
Using this uncountable Roth theorem, we establish the following two additional
results.
  [(i)] We establish a combinatorial application about triangular patterns in
certain subsets of the Cartesian square of arbitrary amenable groups, extending
a result of Bergelson, McCutcheon and Zhang for countable amenable groups.
  [(ii)] We establish a uniform bound on the lower Banach density of the set of
double recurrence times along all $\Gamma$-systems, where $\Gamma$ is any group
in a class of uniformly amenable groups. As a special case, we obtain this
uniformity over all $\mathbb{Z}$-systems, and our result seems to be novel
already in this particular case.
  Our uncountable Roth theorem is crucial in the proof of both of these
results.


Abstract:
  We consider a class of anisotropic spin-$\frac{1}{2}$ models with competing
ferro- and antiferromagnetic interactions on two-dimensional Tasaki and kagome
lattices consisting of corner sharing triangles. For certain values of the
interactions the ground state is macroscopically degenerated in zero magnetic
field. In this case the ground state manifold consists of isolated magnons as
well as the bound magnon complexes. The ground state degeneracy is estimated
using a special form of exact wave function which admits arrow configuration
representation on two-dimensional lattice. The comparison of this estimate with
the result for some special exactly solved models shows that the used approach
determines the number of the ground states with exponential accuracy. It is
shown that the main contribution to the ground state degeneracy and the
residual entropy is given by the bound magnon complexes.


Abstract:
  We introduce a method where particle physics processes in cosmology may be
calculated by the usual perturbative flat space quantum field theory through an
effective Minkowski space description at small time intervals provided that the
running of the effective particle masses are sufficiently slow. We discuss the
necessary conditions for the applicability of this method and illustrate the
method through a simple example. This method has the advantage of avoiding the
effects of gravitational particle creation in the calculation of rates and
cross sections i.e. giving directly the rates and the cross sections due to the
scatterings or the decay processes.


Abstract:
  Complex linear differential equations with entire coefficients are studied in
the situation where one of the coefficients is an exponential polynomial and
dominates the growth of all the other coefficients. If such an equation has an
exponential polynomial solution $f$, then the order of $f$ and of the dominant
coefficient are equal, and the two functions possess a certain duality
property. The results presented in this paper improve earlier results by some
of the present authors, and the paper adjoins with two open problems.


Abstract:
  In this article, we study the logarithm of the central value
$L\left(\frac{1}{2}, \chi_D\right)$ in the symplectic family of Dirichlet
$L$-functions associated with the hyperelliptic curve of genus $\delta$ over a
fixed finite field $\mathbb{F}_q$ in the limit as $\delta\to \infty$.
Unconditionally, we show that the distribution of $\log
\big|L\left(\frac{1}{2}, \chi_D\right)\big|$ is asymptotically bounded above by
the Gaussian distribution of mean $\frac{1}{2}\log \deg(D)$ and variance $\log
\deg(D)$. Assuming a mild condition on the distribution of the low-lying zeros
in this family, we obtain the full Gaussian distribution.


Abstract:
  In this article, we obtain a complete list of inequivalent irreducible
representations of the compact quantum group $U_q(2)$ for non-zero complex
deformation parameters $q$, which are not roots of unity. The matrix
coefficients of these representations are described in terms of the little
$q$-Jacobi polynomials. The Haar state is shown to be faithful and an
orthonormal basis of $L^2(U_q(2))$ is obtained. Thus, we have an explicit
description of the Peter-Weyl decomposition of $U_q(2)$. As an application, we
discuss the Fourier transform and establish the Plancherel formula. We also
describe the decomposition of the tensor product of two irreducible
representations into irreducible components. Finally, we classify the compact
quantum groups $U_q(2)$.


Abstract:
  In this work, the $\overline{\partial}$ steepest descent method is employed
to investigate the soliton resolution for the Hirota equation with the initial
value belong to weighted Sobolev space $H^{1,1}(\mathbb{R})=\{f\in
L^{2}(\mathbb{R}): f',xf\in L^{2}(\mathbb{R})\}$. The long-time asymptotic
behavior of the solution $q(x,t)$ is derived in any fixed space-time cone
$C(x_{1},x_{2},v_{1},v_{2})=\left\{(x,t)\in \mathbb{R}\times\mathbb{R}:
x=x_{0}+vt ~\text{with}~ x_{0}\in[x_{1},x_{2}]\right\}$. We show that solution
resolution conjecture of the Hirota equation is characterized by the leading
order term $\mathcal {O}(t^{-1/2})$ in the continuous spectrum, $\mathcal
{N}(\mathcal {I})$ soliton solutions in the discrete spectrum and error order
$\mathcal {O}(t^{-3/4})$ from the $\overline{\partial}$ equation.


Abstract:
  We present the first 3D radiation-hydrodynamic simulations on the formation
and evolution of born-again planetary nebulae (PNe), with particular emphasis
to the case of HuBi1, the inside-out PN. We use the extensively-tested GUACHO
code to simulate the formation of HuBi1 adopting mass-loss and stellar wind
terminal velocity estimates obtained from observations presented by our group.
We found that, if the inner shell of HuBi1 was formed by an explosive very late
thermal pulse (VLTP) ejecting material with velocities of $\sim$300 km
s$^{-1}$, the age of this structure is consistent with that of $\simeq$200 yr
derived from multi-epoch narrow-band imaging. Our simulations predict that, as
a consequence of the dramatic reduction of the stellar wind velocity and photon
ionizing flux during the VLTP, the velocity and pressure structure of the outer
H-rich nebula are affected creating turbulent ionized structures surrounding
the inner shell. These are indeed detected in Gran Telescopio Canarias MEGARA
optical observations. Furthermore, we demonstrate that the current relatively
low ionizing photon flux from the central star of HuBi1 is not able to
completely ionize the inner shell, which favors previous suggestions that its
excitation is dominated by shocks. Our simulations suggest that the kinetic
energy of the H-poor ejecta of HuBi1 is at least 30 times that of the clumps
and filaments in the evolved born-again PNe A30 and A78, making it a truly
unique VLTP event.


Abstract:
  Here we study the effect of an additional interfacial spin-transfer torque,
as well as the well established spin-orbit torque and bulk spin-transfer
torque, on skyrmion collections - group of skyrmions dense enough that they are
not isolated from on another - in ultrathin heavy metal / ferromagnetic
multilayers, by comparing modelling with experimental results. Using a skyrmion
collection with a range of skyrmion diameters and landscape disorder, we study
the dependence of the skyrmion Hall angle on diameter and velocity, as well as
the velocity as a function of diameter. We show the experimental results are in
good agreement with modelling when including the interfacial spin-transfer
torque, and cannot be reproduced by using the spin-orbit torque alone. We also
show that for skyrmion collections the velocity is approximately independent of
diameter, in marked contrast to the motion of isolated skyrmions, as the group
of skyrmions move together at an average group velocity. Moreover, the
calculated skyrmion velocities are comparable to those obtained in experiments
when the interfacial spin-transfer torque in included, whilst modelling using
the spin-orbit torque alone shows large discrepancies with the experimental
data. Our results thus show the significance of the interfacial spin-transfer
torque in ultrathin magnetic multilayers, which is of similar strength to the
spin-orbit torque, and both significantly larger than the bulk spin-transfer
torque. Due to the good agreement with experiments, we conclude that the
interfacial spin-transfer torque should be included in numerical modelling for
correct reproduction of experimental results.


Abstract:
  A method is demonstrated to optimize a stellarator's geometry to eliminate
magnetic islands and achieve other desired physics properties at the same time.
For many physics quantities that have been used in stellarator optimization,
including quasisymmetry, neoclassical transport, and magnetohydrodynamic
stability, it is convenient to use a magnetic equilibrium representation that
assures the existence of magnetic surfaces. However, this representation hides
the possible presence of magnetic islands, which are typically undesirable. To
include both surface-based objectives and island widths in a single
optimization, two fixed-boundary equilibrium calculations are run at each
iteration of the optimization: one that enforces the existence of magnetic
surfaces (VMEC [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553
(1983)]), and one that does not (SPEC [S. R. Hudson, et al, Phys. Plasmas 19,
112502 (2012)]). By penalizing the island residues in the objective function,
the two magnetic field representations are brought into agreement during the
optimization. An example is presented in which, particularly on the surface
where quasisymmetry was targeted, quasisymmetry is achieved more accurately
than in previously published examples.


Abstract:
  This paper discusses relational operations in the first-order logical
environment {FOLE}. Here we demonstrate how FOLE expresses the relational
operations of database theory in a clear and implementable representation. An
analysis of the representation of database tables/relations in FOLE reveals a
principled way to express the relational operations. This representation is
expressed in terms of a distinction between basic components versus composite
relational operations. The 9 basic components fall into three categories:
reflection (2), Booleans or basic operations (3), and adjoint flow (4). Adjoint
flow is given for signatures (2) and for type domains (2), which are then
combined into full adjoint flow. The basic components are used to express
various composite operations, where we illustrate each of these with a
flowchart. Implementation of the composite operations is then expressed in an
input/output table containing four parts: constraint, construction, input, and
output. We explain how limits and colimits are constructed from diagrams of
tables, and then classify composite relational operations into three
categories: limit-like, colimit-like and unorthodox.


Abstract:
  In this paper, the generation of magnetic fields in a nonuniformly rotating
layer of finite thickness of an electrically conducting fluid by thermomagnetic
(TM) instability. This instability arises due to the temperature gradient
$\nabla T_0$ and thermoelectromotive coefficient gradient $\nabla\alpha $. The
influence of the generation of a toroidal magnetic field by TM instability on
convective instability in a nonuniformly rotating layer of an electrically
conductive fluid in the presence of a vertical constant magnetic field
${\bf{B}}_0 \| {\rm OZ}$ is established. As a result of applying the method of
perturbation theory for the small parameter $ \epsilon = \sqrt {(\textrm
{Ra}-\textrm {Ra}_c) / \textrm {Ra}_c} $ of supercriticality of the stationary
Rayleigh number $\textrm {Ra}_c$ a nonlinear equation of the Ginzburg-Landau
type was obtained. This equation describes the evolution of the finite
amplitude of perturbations. Numerical solutions of this equation made it
possible to determine the heat transfer in the fluid layer with and without TM
effects. It is shown that the amplitude of the stationary toroidal magnetic
field noticeably increases with allowance for TM effects.


Abstract:
  Head and Neck Squamous Cell Carcinoma (HNSCC) is one of cancer type that is
most distressing leading to acute pain, effecting speech and primary survival
functions such as swallowing and breathing. The morbidity and mortality of
HNSCC patients have not significantly improved even tough there has been
advancement in surgical and radiotherapy treatments. The high mortality may be
attributed to the complexity and significant changes in the clinical outcomes.
Therefore, it is important to increase the accuracy of predicting the outcome
of cancer survival. Few cancer survival prediction models of HNSCC have been
proposed so far. In this study, genomic data (whole exome sequencing) are
integrated with clinical data to improve the performance of prediction model.
The somatic mutations of every patient is processed using Multifractal
Deterended Fluctuation Analysis (MFDFA) algorithm and the parameter values of
Fractal Dimension (Dq) is included along with clinical data for cancer survival
prediction. Feature ranking proves that the new engineered feature is one of
the important feature in prediction model. In order to improve the performance
index of models, hyperparameters were also tuned in all the classifiers
considered. 10-Fold cross validation is implemented and XGBoost (98% AUROC, 94%
precision, and 93% recall) proves to be best model classifier followed by
Random Forest 93% AUROC, 93% precision, and 93% recall), Support Vector Machine
(84% AUCROC, 79% precision, and 79% recall) and Logistic Regression (80% AUROC,
77% precision, and 76% recall).


Abstract:
  In this paper, the formation of primordial black holes (PBHs) is
reinvestigated using inflationary $\alpha$-attractors. Instead of using the
conventional Press-Schechter theory to compute the abundance, the optimized
peaks theory is used, which was developed in Ref.
\cite{Yoo:2018kvb,Yoo:2020dkz}. This method takes into account how curvature
perturbations play a r\^{o}le in modifying the mass of primordial black holes.
Analyzing the model proposed in \cite{Mahbub:2019uhl} it is seen that the
horizon mass of the collapsed Hubble patch is larger by $\mathcal{O}(10)$
compared to the usual computation. Moreover, PBHs can be formed from curvature
power spectrum, $\mathcal{P}_{\zeta}(k)$, peaked at lower values using
numerically favored threshold overdensities. As a result of the generally
larger masses predicted, the peak of the power spectrum can be placed at larger
$k$ modes than that is typical with which potential future constraints on the
primordial power spectrum through gravitational waves (GWs) can be evaded.


Abstract:
  The Einstein field equations for a class of irrotational non-orthogonally
transitive $G_{2}$ cosmologies are written down as a system of partial
differential equations. The equilibrium points are self-similar and can be
written as a one-parameter, five-dimensional, ordinary differential equation.
The corresponding cosmological models both evolve and have one-dimension of
inhomogeneity. The major mathematical features of this ordinary differential
equation are derived, and a cosmological interpretation is given. The
relationship to the exceptional Bianchi models is explained and exploited to
provide a conjecture about future generalizations.


Abstract:
  Polarimetric observations of Fast Radio Bursts (FRBs) are a powerful resource
for better understanding these mysterious sources by directly probing the
emission mechanism of the source and the magneto-ionic properties of its
environment. We present a pipeline for analysing the polarized signal of FRBs
captured by the triggered baseband recording system operating on the FRB survey
of The Canadian Hydrogen Intensity Mapping Experiment (CHIME/FRB). Using a
combination of simulated and real FRB events, we summarize the main features of
the pipeline and highlight the dominant systematics affecting the polarized
signal. We compare parametric (QU-fitting) and non-parametric (rotation measure
synthesis) methods for determining the Faraday rotation measure (RM) and find
the latter method susceptible to systematic errors from known instrumental
effects of CHIME/FRB observations. These errors include a leakage artefact that
appears as polarized signal near $\rm{RM\sim 0 \; rad \, m^{-2}}$ and an RM
sign ambiguity introduced by path length differences in the system's
electronics. We apply the pipeline to a bright burst previously reported by
\citet[FRB 20191219F;][]{Leung2021}, detecting an $\mathrm{RM}$ of $\rm{+6.074
\pm 0.006 \pm 0.050 \; rad \, m^{-2}}$ with a significant linear polarized
fraction ($\gtrsim0.87$) and strong evidence for a non-negligible circularly
polarized component. Finally, we introduce an RM search method that employs a
phase-coherent de-rotation algorithm to correct for intra-channel
depolarization in data that retain electric field phase information, and
successfully apply it to an unpublished FRB, FRB 20200917A, measuring an
$\mathrm{RM}$ of $\rm{-1294.47 \pm 0.10 \pm 0.05 \; rad \, m^{-2}}$ (the second
largest unambiguous RM detection from any FRB source observed to date).


Abstract:
  We propose a projected Wasserstein gradient descent method (pWGD) for
high-dimensional Bayesian inference problems. The underlying density function
of a particle system of WGD is approximated by kernel density estimation (KDE),
which faces the long-standing curse of dimensionality. We overcome this
challenge by exploiting the intrinsic low-rank structure in the difference
between the posterior and prior distributions. The parameters are projected
into a low-dimensional subspace to alleviate the approximation error of KDE in
high dimensions. We formulate a projected Wasserstein gradient flow and analyze
its convergence property under mild assumptions. Several numerical experiments
illustrate the accuracy, convergence, and complexity scalability of pWGD with
respect to parameter dimension, sample size, and processor cores.


Abstract:
  In this paper, we investigate the computational intelligibility of Boolean
classifiers, characterized by their ability to answer XAI queries in polynomial
time. The classifiers under consideration are decision trees, DNF formulae,
decision lists, decision rules, tree ensembles, and Boolean neural nets. Using
9 XAI queries, including both explanation queries and verification queries, we
show the existence of large intelligibility gap between the families of
classifiers. On the one hand, all the 9 XAI queries are tractable for decision
trees. On the other hand, none of them is tractable for DNF formulae, decision
lists, random forests, boosted decision trees, Boolean multilayer perceptrons,
and binarized neural networks.


Abstract:
  An approach that extends equilibrium thermodynamics principles to
out-of-equilibrium systems is based on the local equilibrium hypothesis.
However, the validity of the a priori assumption of local equilibrium has been
questioned due to the lack of sufficient experimental evidence. In this paper,
we present experimental results obtained from a pure thermodynamic study of the
non-turbulent Rayleigh-B\'enard convection at steady-state to verify the
validity of the local equilibrium hypothesis. A non-turbulent Rayleigh-B\'enard
convection at steady-state is an excellent `model thermodynamic system' in
which local measurements provide no insights about the spatial heterogeneity
present in the macroscopic thermodynamic landscape. Indeed, the onset of
convection leads to the emergence of spatially stable hot and cold domains. Our
results indicate that these domains while break spatial symmetry
macroscopically, preserves it locally that exhibit room temperature
equilibrium-like statistics. Furthermore, the role of the emergent heat flux is
investigated and a linear relationship is observed between the heat flux and
the external driving force following the onset of thermal convection. Finally,
theoretical and conceptual implications of these results are discussed which
opens up new avenues in the study non-equilibrium steady-states, especially in
complex, soft, and active-matter systems.


Abstract:
  Graphical languages are symmetric monoidal categories presented by generators
and equations. The string diagrams notation allows to transform numerous axioms
into low dimension topological rules we are comfortable with as three
dimensional space citizens. This aspect is often referred to by the Only
Topology Matters paradigm (OTM). However OTM remains quite informal and its
exact meaning in terms of rewriting rules is ambiguous. In this paper we define
three precise aspects of the OTM paradigm, namely flexsymmetry, flexcyclicity
and flexibility of Frobenius algebras. We investigate how this new framework
can simplify the presentation of known graphical languages based on Frobenius
algebras.


Abstract:
  We show that there exist K\"ahler-Einstein metrics on two exceptional
Pasquier's two-orbits varieties. As an application, we will provide a new
example of K-unstable Fano manifold with Picard number one.


Abstract:
  In this letter, we investigate the changes in the quantum vacuum energy
density of a massless scalar field inside a Casimir cavity that orbits a
wormhole, by considering the cosmological model with an isotropic form of the
Morris-Thorne wormhole, embedded in the FLRW universe. In this sense, we
examine the effects of its global curvature and scale factor in an instant of
the cosmic history, besides the influences of the local geometry as well as of
inertial forces, on the Casimirenergy density. We also study the behavior of
this quantity when each plate is fixed without rotation at the opposite sides
of the wormhole throat, at zero and finite temperatures, taking into account
the effective distance between the plates through the wormhole throat.


Abstract:
  Determination of the neutrino mass ordering (NMO) is one of the biggest
priorities in the intensity frontier of high energy particle physics. To
accomplish that goal a lot of efforts are being put together with the
atmospheric, solar, reactor, and accelerator neutrinos. In the standard
3-flavor framework, NMO is defined to be normal if $m_1<m_2<m_3$, and inverted
if $m_3<m_1<m_2$, where $m_1$, $m_2$, and $m_3$ are the masses of the three
neutrino mass eigenstates $\nu_1$, $\nu_2$, and $\nu_3$ respectively.
Interestingly, two long-baseline experiments T2K and NO$\nu$A are playing a
leading role in this direction and provide a $\sim2.4\sigma$ indication in
favor of normal ordering (NO) which we find in this work. In addition, we
examine how the situation looks like in presence of non-standard interactions
(NSI) of neutrinos with a special focus on the non-diagonal flavor changing
type $\varepsilon_{e\tau}$ and $\varepsilon_{e\mu}$. We find that the present
indication of NO in the standard 3-flavor framework gets completely vanished in
the presence of NSI of the flavor changing type involving the $e-\tau$ flavors.


Abstract:
  The current Siamese network based on region proposal network (RPN) has
attracted great attention in visual tracking due to its excellent accuracy and
high efficiency. However, the design of the RPN involves the selection of the
number, scale, and aspect ratios of anchor boxes, which will affect the
applicability and convenience of the model. Furthermore, these anchor boxes
require complicated calculations, such as calculating their
intersection-over-union (IoU) with ground truth bounding boxes.Due to the
problems related to anchor boxes, we propose a simple yet effective anchor-free
tracker (named Siamese corner networks, SiamCorners), which is end-to-end
trained offline on large-scale image pairs. Specifically, we introduce a
modified corner pooling layer to convert the bounding box estimate of the
target into a pair of corner predictions (the bottom-right and the top-left
corners). By tracking a target as a pair of corners, we avoid the need to
design the anchor boxes. This will make the entire tracking algorithm more
flexible and simple than anchorbased trackers. In our network design, we
further introduce a layer-wise feature aggregation strategy that enables the
corner pooling module to predict multiple corners for a tracking target in deep
networks. We then introduce a new penalty term that is used to select an
optimal tracking box in these candidate corners. Finally, SiamCorners achieves
experimental results that are comparable to the state-of-art tracker while
maintaining a high running speed. In particular, SiamCorners achieves a 53.7%
AUC on NFS30 and a 61.4% AUC on UAV123, while still running at 42 frames per
second (FPS).


Abstract:
  Information exchange is a crucial component of many real-world multi-agent
systems. However, the communication between the agents involves two major
challenges: the limited bandwidth, and the shared communication medium between
the agents, which restricts the number of agents that can simultaneously
exchange information. While both of these issues need to be addressed in
practice, the impact of the latter problem on the performance of the
multi-agent systems has often been neglected. This becomes even more important
when the agents' information or observations have different importance, in
which case the agents require different priorities for accessing the medium and
sharing their information. Representing the agents' priorities by fairness
weights and normalizing each agent's share by the assigned fairness weight, the
goal can be expressed as equalizing the agents' normalized shares of the
communication medium. To achieve this goal, we adopt a queueing theoretic
approach and propose a distributed fair scheduling algorithm for providing
weighted fairness in single-hop networks. Our proposed algorithm guarantees an
upper-bound on the normalized share disparity among any pair of agents. This
can particularly improve the short-term fairness, which is important in
real-time applications. Moreover, our scheduling algorithm adjusts itself
dynamically to achieve a high throughput at the same time. The simulation
results validate our claims and comparisons with the existing methods show our
algorithm's superiority in providing short-term fairness, while achieving a
high throughput.


Abstract:
  We show that quantum state tomography with perfect knowledge of the
measurement apparatus proves to be, in some instances, inferior to strategies
discarding all information about the measurement at hand, as in the case of
data pattern tomography. In those scenarios, the larger uncertainty about the
measurement is traded for the smaller uncertainty about the reconstructed
signal. This effect is more pronounced for minimal or nearly minimal
informationally complete measurement settings, which are of utmost practical
importance.


Abstract:
  This letter gives a credit to a pioneering paper that is almost unknown to
scientific community. On the basis of Transmission Electron Microscopy images
and X-ray Ray Diffraction patterns of carbon multi-layer tubular crystals the
authors suggested a model of nanotube structure formation and hypothesis on
various chirality of carbon nanotubes.


Abstract:
  Subspace-valued functions arise in a wide range of problems, including
parametric reduced order modeling (PROM). In PROM, each parameter point can be
associated with a subspace, which is used for Petrov-Galerkin projections of
large system matrices. Previous efforts to approximate such functions use
interpolations on manifolds, which can be inaccurate and slow. To tackle this,
we propose a novel Bayesian nonparametric model for subspace prediction: the
Gaussian Process Subspace regression (GPS) model. This method is extrinsic and
intrinsic at the same time: with multivariate Gaussian distributions on the
Euclidean space, it induces a joint probability model on the Grassmann
manifold, the set of fixed-dimensional subspaces. The GPS adopts a simple yet
general correlation structure, and a principled approach for model selection.
Its predictive distribution admits an analytical form, which allows for
efficient subspace prediction over the parameter space. For PROM, the GPS
provides a probabilistic prediction at a new parameter point that retains the
accuracy of local reduced models, at a computational complexity that does not
depend on system dimension, and thus is suitable for online computation. We
give four numerical examples to compare our method to subspace interpolation,
as well as two methods that interpolate local reduced models. Overall, GPS is
the most data efficient, more computationally efficient than subspace
interpolation, and gives smooth predictions with uncertainty quantification.


Abstract:
  Scheduling computational tasks represented by directed acyclic graphs (DAGs)
is challenging because of its complexity. Conventional scheduling algorithms
rely heavily on simple heuristics such as shortest job first (SJF) and critical
path (CP), and are often lacking in scheduling quality. In this paper, we
present a novel learning-based approach to scheduling DAG tasks. The algorithm
employs a reinforcement learning agent to iteratively add directed edges to the
DAG, one at a time, to enforce ordering (i.e., priorities of execution and
resource allocation) of "tricky" job nodes. By doing so, the original DAG
scheduling problem is dramatically reduced to a much simpler proxy problem, on
which heuristic scheduling algorithms such as SJF and CP can be efficiently
improved. Our approach can be easily applied to any existing heuristic
scheduling algorithms. On the benchmark dataset of TPC-H, we show that our
learning based approach can significantly improve over popular heuristic
algorithms and consistently achieves the best performance among several methods
under a variety of settings.


Abstract:
  The fused deposition modeling is one of the most rapidly developing 3D
printing techniques, with numerous applications, also in the field of applied
electrochemistry. Here, utilization of conductive polylactic acid (C-PLA) for
3D printouts is the most promising, due to its biodegradability, commercial
availability, and ease of processing. To use C-PLA as an electrode material, an
activation process must be performed, removing the polymer matrix and
uncovering the electroactive filler. The most popular chemical or
electrochemical activation routes are done in solvents. In this manuscript, we
present a novel, alternative approach towards C-PLA activation with Nd:YAG
(lambda = 1064 nm) laser ablation. We present and discuss the activation
efficiency based on various laser source operating conditions, and the gas
matrix. The XPS, contact angle, and Raman analyses were performed for
evaluation of the surface chemistry and to discuss the mechanism of the
activation process. The ablation process carried out in the inert gas matrix
(helium) delivers a highly electroactive C-PLA electrode surface, while the
resultant charge transfer process is hindered when activated in the air. This
is due to thermally induced oxide layers formation. The electroanalytical
performance of laser-treated C-PLA in He atmosphere was confirmed through
caffeine detection, offering detection limits of 0.49 and 0.40 microM (S/N = 3)
based on CV and DPV studies, respectively.


Abstract:
  Supernova properties in radio strongly depend on their circumstellar
environment and they are an important probe to investigate the mass loss of
supernova progenitors. Recently, core-collapse supernova observations in radio
have been assembled and the rise time and peak luminosity distribution of
core-collapse supernovae at 8.4 GHz has been estimated. In this paper, we
constrain the mass-loss prescriptions for red supergiants by using the rise
time and peak luminosity distribution of Type II supernovae in radio. We take
the de Jager and van Loon mass-loss rates for red supergiants, calculate the
rise time and peak luminosity distribution based on them, and compare the
results with the observed distribution. We found that the de Jager mass-loss
rate explains the widely spread radio rise time and peak luminosity
distribution of Type II supernovae well, while the van Loon mass-loss rate
predicts a relatively narrow range for the rise time and peak luminosity. We
conclude that the mass-loss prescriptions of red supergiants should have strong
dependence on the luminosity as in the de Jager mass-loss rate to reproduce the
widely spread distribution of the rise time and peak luminosity in radio
observed in Type II supernovae.


Abstract:
  gComm is a step towards developing a robust platform to foster research in
grounded language acquisition in a more challenging and realistic setting. It
comprises a 2-d grid environment with a set of agents (a stationary speaker and
a mobile listener connected via a communication channel) exposed to a
continuous array of tasks in a partially observable setting. The key to solving
these tasks lies in agents developing linguistic abilities and utilizing them
for efficiently exploring the environment. The speaker and listener have access
to information provided in different modalities, i.e. the speaker's input is a
natural language instruction that contains the target and task specifications
and the listener's input is its grid-view. Each must rely on the other to
complete the assigned task, however, the only way they can achieve the same, is
to develop and use some form of communication. gComm provides several tools for
studying different forms of communication and assessing their generalization.


Abstract:
  Autonomous driving highly depends on capable sensors to perceive the
environment and to deliver reliable information to the vehicles' control
systems. To increase its robustness, a diversified set of sensors is used,
including radar sensors. Radar is a vital contribution of sensory information,
providing high resolution range as well as velocity measurements. The increased
use of radar sensors in road traffic introduces new challenges. As the so far
unregulated frequency band becomes increasingly crowded, radar sensors suffer
from mutual interference between multiple radar sensors. This interference must
be mitigated in order to ensure a high and consistent detection sensitivity. In
this paper, we propose the use of Complex-Valued Convolutional Neural Networks
(CVCNNs) to address the issue of mutual interference between radar sensors. We
extend previously developed methods to the complex domain in order to process
radar data according to its physical characteristics. This not only increases
data efficiency, but also improves the conservation of phase information during
filtering, which is crucial for further processing, such as angle estimation.
Our experiments show, that the use of CVCNNs increases data efficiency, speeds
up network training and substantially improves the conservation of phase
information during interference removal.


Abstract:
  Using a total of $5.25~{\rm fb}^{-1}$ of $e^{+}e^{-}$ collision data with
center-of-mass energies from 4.236 to 4.600 GeV, we report the first
observation of the process $e^{+}e^{-}\to \eta\psi(2S)$ with a statistical
significance of $5\sigma$. The data sets were collected by the BESIII detector
operating at the BEPCII storage ring. We measure the yield of events integrated
over center-of-mass energies and also present the energy dependence of the
measured cross section.


Abstract:
  The ongoing trend of moving data and computation to the cloud is met with
concerns regarding privacy and protection of intellectual property. Cloud
Service Providers (CSP) must be fully trusted to not tamper with or disclose
processed data, hampering adoption of cloud services for many sensitive or
critical applications. As a result, CSPs and CPU manufacturers are rushing to
find solutions for secure outsourced computation in the Cloud. While enclaves,
like Intel SGX, are strongly limited in terms of throughput and size, AMD's
Secure Encrypted Virtualization (SEV) offers hardware support for transparently
protecting code and data of entire VMs, thus removing the performance, memory
and software adaption barriers of enclaves. Through attestation of boot code
integrity and means for securely transferring secrets into an encrypted VM,
CSPs are effectively removed from the list of trusted entities. There have been
several attacks on the security of SEV, by abusing I/O channels to encrypt and
decrypt data, or by moving encrypted code blocks at runtime. Yet, none of these
attacks have targeted the attestation protocol, the core of the secure
computing environment created by SEV. We show that the current attestation
mechanism of Zen 1 and Zen 2 architectures has a significant flaw, allowing us
to manipulate the loaded code without affecting the attestation outcome. An
attacker may abuse this weakness to inject arbitrary code at startup -- and
thus take control over the entire VM execution, without any indication to the
VM's owner. Our attack primitives allow the attacker to do extensive
modifications to the bootloader and the operating system, like injecting spy
code or extracting secret data. We present a full end-to-end attack, from the
initial exploit to leaking the key of the encrypted disk image during boot,
giving the attacker unthrottled access to all of the VM's persistent data.


Abstract:
  We prove the well-posedness of entropy solutions for a wide class of nonlocal
transport equations with nonlinear mobility in one spatial dimension. The
solution is obtained as the limit of approximations constructed via a
deterministic system of interacting particles that exhibits a gradient flow
structure. At the same time, we expose a rigorous gradient flow structure for
this class of equations in terms of an Energy-Dissipation balance, which we
obtain via the asymptotic convergence of functionals.


Abstract:
  In autonomous microgrids frequency regulation (FR) is a critical issue,
especially with a high level of penetration of the photovoltaic (PV)
generation. In this study, a novel virtual synchronous generator (VSG) control
for PV generation was introduced to provide frequency support without energy
storage. PV generation reserve a part of the active power in accordance with
the pre-defined power versus voltage curve. Based on the similarities of the
synchronous generator power-angle characteristic curve and the PV array
characteristic curve, PV voltage Vpv can be analogized to the power angle
{\delta}. An emulated governor (droop control) and the swing equation control
is designed and applied to the DC-DC converter. PV voltage deviation is
subsequently generated and the pre-defined power versus voltage curve is
modified to provide the primary frequency and inertia support. A simulation
model of an autonomous microgrid with PV, storage, and diesel generator was
built. The feasibility and effectiveness of the proposed VSG strategy are
examined under different operating conditions.


Abstract:
  One of the paramount advantages of multi-level cache-enabled (MLCE) networks
is pushing contents proximity to the network edge and proactively caching them
at multiple transmitters (i.e., small base-stations (SBSs), unmanned aerial
vehicles (UAVs), and cache-enabled device-to-device (CE-D2D) users). As such,
the fronthaul congestion between a core network and a large number of
transmitters is alleviated. For this objective, we exploit network coding (NC)
to schedule a set of users to the same transmitter. Focusing on this, we
consider the throughput maximization problem that optimizes jointly the
network-coded user scheduling and power allocation, subject to fronthaul
capacity, transmit power, and NC constraints. Given the intractability of the
problem, we decouple it into two separate subproblems. In the first subproblem,
we consider the network-coded user scheduling problem for the given power
allocation, while in the second subproblem, we use the NC resulting user
schedule to optimize the power levels. We design an innovative
\textit{two-layered rate-aware NC (RA-IDNC)} graph to solve the first
subproblem and evaluate the second subproblem using an iterative function
evaluation (IFE) approach. Simulation results are presented to depict the
throughput gain of the proposed approach over the existing solutions.


Abstract:
  Latent alignment objectives such as CTC and AXE significantly improve
non-autoregressive machine translation models. Can they improve autoregressive
models as well? We explore the possibility of training autoregressive machine
translation models with latent alignment objectives, and observe that, in
practice, this approach results in degenerate models. We provide a theoretical
explanation for these empirical results, and prove that latent alignment
objectives are incompatible with teacher forcing.


Abstract:
  Graph convolutional networks (GCNs) are widely used in graph-based
applications such as graph classification and segmentation. However, current
GCNs have limitations on implementation such as network architectures due to
their irregular inputs. In contrast, convolutional neural networks (CNNs) are
capable of extracting rich features from large-scale input data, but they do
not support general graph inputs. To bridge the gap between GCNs and CNNs, in
this paper we study the problem of how to effectively and efficiently map
general graphs to 2D grids that CNNs can be directly applied to, while
preserving graph topology as much as possible. We therefore propose two novel
graph-to-grid mapping schemes, namely, {\em graph-preserving grid layout
(GPGL)} and its extension {\em Hierarchical GPGL (H-GPGL)} for computational
efficiency. We formulate the GPGL problem as integer programming and further
propose an approximate yet efficient solver based on a penalized Kamada-Kawai
method, a well-known optimization algorithm in 2D graph drawing. We propose a
novel vertex separation penalty that encourages graph vertices to lay on the
grid without any overlap. Along with this image representation, even extra 2D
maxpooling layers contribute to the PointNet, a widely applied point-based
neural network. We demonstrate the empirical success of GPGL on general graph
classification with small graphs and H-GPGL on 3D point cloud segmentation with
large graphs, based on 2D CNNs including VGG16, ResNet50 and multi-scale maxout
(MSM) CNN.


Abstract:
  The input of almost every machine learning algorithm targeting the properties
of matter at the atomic scale involves a transformation of the list of
Cartesian atomic coordinates into a more symmetric representation. Many of
these most popular representations can be seen as an expansion of the
symmetrized correlations of the atom density, and differ mainly by the choice
of basis. Here we discuss how to build an adaptive, optimal numerical basis
that is chosen to represent most efficiently the structural diversity of the
dataset at hand. For each training dataset, this optimal basis is unique, and
can be computed at no additional cost with respect to the primitive basis by
approximating it with splines. We demonstrate that this construction yields
representations that are accurate and computationally efficient, presenting
examples that involve both molecular and condensed-phase machine-learning
models.


Abstract:
  We formulate a plausible conjecture for the optimal Ehrhard-type inequality
for convex symmetric sets with respect to the Gaussian measure. Namely, letting
$J_{k-1}(s)=\int^s_0 t^{k-1} e^{-\frac{t^2}{2}}dt$ and
$c_{k-1}=J_{k-1}(+\infty)$, we conjecture that the function
$F:[0,1]\rightarrow\mathbb{R},$ given by $$F(a)= \sum_{k=1}^n 1_{a\in
E_k}\cdot(\beta_k J_{k-1}^{-1}(c_{k-1} a)+\alpha_k)$$ (with an appropriate
choice of a decomposition $[0,1]=\cup_{i} E_i$ and coefficients $\alpha_i,
\beta_i$) satisfies, for all symmetric convex sets $K$ and $L,$ and any
$\lambda\in[0,1]$, $$ F\left(\gamma(\lambda K+(1-\lambda)L)\right)\geq \lambda
F\left(\gamma(K)\right)+(1-\lambda) F\left(\gamma(L)\right). $$ We explain that
this conjecture is ``the most optimistic possible'', and is equivalent to the
fact that for any symmetric convex set $K,$ its \emph{Gaussian concavity power}
$p^s(K,\gamma)$ is greater than or equal to $p_s(RB^k_2\times
\mathbb{R}^{n-k},\gamma),$ for some $k\in \{1,...,n\}$. We call the sets
$RB^k_2\times \mathbb{R}^{n-k}$ round $k$-cylinders; they also appear as the
conjectured Gaussian isoperimetric minimizers for symmetric sets, see Heilman
\cite{Heilman}. In this manuscript, we make progress towards this question, and
prove certain inequality for which the round k-cylinders are the only equality
cases. As an auxiliary result on the way to the equality case characterization,
we characterize the equality cases in the ``convex set version'' of the
Brascamp-Lieb inequality, and moreover, obtain a quantitative stability version
in the case of the standard Gaussian measure; this may be of independent
interest.


Abstract:
  Federated learning (FL) is a distributed machine learning architecture that
leverages a large number of workers to jointly learn a model with decentralized
data. FL has received increasing attention in recent years thanks to its data
privacy protection, communication efficiency and a linear speedup for
convergence in training (i.e., convergence performance increases linearly with
respect to the number of workers). However, existing studies on linear speedup
for convergence are only limited to the assumptions of i.i.d. datasets across
workers and/or full worker participation, both of which rarely hold in
practice. So far, it remains an open question whether or not the linear speedup
for convergence is achievable under non-i.i.d. datasets with partial worker
participation in FL. In this paper, we show that the answer is affirmative.
Specifically, we show that the federated averaging (FedAvg) algorithm (with
two-sided learning rates) on non-i.i.d. datasets in non-convex settings
achieves a convergence rate $\mathcal{O}(\frac{1}{\sqrt{mKT}} + \frac{1}{T})$
for full worker participation and a convergence rate
$\mathcal{O}(\frac{\sqrt{K}}{\sqrt{nT}} + \frac{1}{T})$ for partial worker
participation, where $K$ is the number of local steps, $T$ is the number of
total communication rounds, $m$ is the total worker number and $n$ is the
worker number in one communication round if for partial worker participation.
Our results also reveal that the local steps in FL could help the convergence
and show that the maximum number of local steps can be improved to $T/m$ in
full worker participation. We conduct extensive experiments on MNIST and
CIFAR-10 to verify our theoretical results.


Abstract:
  We consider rather a general class of multi-level optimization problems,
where a convex objective function is to be minimized, subject to constraints to
optima of a nested convex optimization problem. As a special case, we consider
a trilevel optimization problem, where the objective of the two lower layers
consists of a sum of a smooth and a non-smooth term. Based on fixed-point
theory and related arguments, we present a natural first-order algorithm and
analyze its convergence and rates of convergence in several regimes of
parameters.


Abstract:
  The aim of this paper is to generalize results known for the symplectic
involutions on K3 surfaces to the order 3 symplectic automorphisms on K3
surfaces. In particular, we will explicitly describe the action induced on the
lattice $\Lambda_{K3}$, isometric to the second cohomology group of a K3
surface, by a symplectic automorphism of order 3; we exhibit the maps $\pi_*$
and $\pi^*$ induced in cohomology by the rational quotient map
$\pi:X\dashrightarrow Y$, where $X$ is a K3 surface admitting an order 3
symplectic automorphism $\sigma$ and $Y$ is the minimal resolution of the
quotient $X/\sigma$; we deduce the relation between the N\'eron--Severi group
of $X$ and the one of $Y$. Applying these results we describe explicit
geometric examples and generalize the Shioda--Inose structures, relating
Abelian surfaces admitting order 3 endomorphisms with certain specific K3
surfaces admitting particular order 3 symplectic automorphisms.


Abstract:
  This book develops an effective theory approach to understanding deep neural
networks of practical relevance. Beginning from a first-principles
component-level picture of networks, we explain how to determine an accurate
description of the output of trained networks by solving layer-to-layer
iteration equations and nonlinear learning dynamics. A main result is that the
predictions of networks are described by nearly-Gaussian distributions, with
the depth-to-width aspect ratio of the network controlling the deviations from
the infinite-width Gaussian description. We explain how these effectively-deep
networks learn nontrivial representations from training and more broadly
analyze the mechanism of representation learning for nonlinear models. From a
nearly-kernel-methods perspective, we find that the dependence of such models'
predictions on the underlying learning algorithm can be expressed in a simple
and universal way. To obtain these results, we develop the notion of
representation group flow (RG flow) to characterize the propagation of signals
through the network. By tuning networks to criticality, we give a practical
solution to the exploding and vanishing gradient problem. We further explain
how RG flow leads to near-universal behavior and lets us categorize networks
built from different activation functions into universality classes.
Altogether, we show that the depth-to-width ratio governs the effective model
complexity of the ensemble of trained networks. By using information-theoretic
techniques, we estimate the optimal aspect ratio at which we expect the network
to be practically most useful and show how residual connections can be used to
push this scale to arbitrary depths. With these tools, we can learn in detail
about the inductive bias of architectures, hyperparameters, and optimizers.


Abstract:
  Programming efficiently heterogeneous systems is a major challenge, due to
the complexity of their architectures. Intel oneAPI, a new and powerful
standards-based unified programming model, built on top of SYCL, addresses
these issues. In this paper, oneAPI is provided with co-execution strategies to
run the same kernel between different devices, enabling the exploitation of
static and dynamic policies. On top of that, static and dynamic load-balancing
algorithms are integrated and analyzed.
  This work evaluates the performance and energy efficiency for a well-known
set of regular and irregular HPC benchmarks, using an integrated GPU and CPU.
Experimental results show that co-execution is worthwhile when using dynamic
algorithms, improving efficiency even more when using unified shared memory.


Abstract:
  Open Radio Access Network (ORAN) is being developed with an aim to
democratise access and lower the cost of future mobile data networks,
supporting network services with various QoS requirements, such as massive IoT
and URLLC. In ORAN, network functionality is dis-aggregated into remote units
(RUs), distributed units (DUs) and central units (CUs), which allows flexible
software on Commercial-Off-The-Shelf (COTS) deployments. Furthermore, the
mapping of variable RU requirements to local mobile edge computing centres for
future centralized processing would significantly reduce the power consumption
in cellular networks. In this paper, we study the RU-DU resource assignment
problem in an ORAN system, modelled as a 2D bin packing problem. A deep
reinforcement learning-based self-play approach is proposed to achieve
efficient RU-DU resource management, with AlphaGo Zero inspired neural
Monte-Carlo Tree Search (MCTS). Experiments on representative 2D bin packing
environment and real sites data show that the self-play learning strategy
achieves intelligent RU-DU resource assignment for different network
conditions.


Abstract:
  This paper presents a novel solution paradigm of general optimization under
both exogenous and endogenous uncertainties. This solution paradigm consists of
a probability distribution (PD)-free method of obtaining deterministic
equivalents and an innovative approach of scenario reduction. First, dislike
the existing methods that use scenarios sampled from pre-known PD functions,
the PD-free method uses historical measurements of uncertain variables as input
to convert the logical models into a type of deterministic equivalents called
General Scenario Program (GSP). Our contributions to the PD-free deterministic
equivalent construction reside in generalization (making it applicable to
general optimization under uncertainty rather than just chance-constrained
optimization) and extension (enabling it to the problems under endogenous
uncertainty via developing an iterative and a non-iterative frameworks).
Second, this paper reveals some unknown properties of the PD-free deterministic
equivalent construction, such as the characteristics of active scenarios and
repeated scenarios. Base on this discoveries, we propose a concept and methods
of strategic scenario selection which can effectively reduce the required
number of scenarios as demonstrated in both mathematical analysis and numerical
experiments. Numerical experiments are conducted on two typical smart grid
optimization problems under exogenous and endogenous uncertainties.