Abstract:
  Multi-agent Markov Decision Processes (MMDPs) arise in a variety of
applications including target tracking, control of multi-robot swarms, and
multiplayer games. A key challenge in MMDPs occurs when the state and action
spaces grow exponentially in the number of agents, making computation of an
optimal policy computationally intractable for medium- to large-scale problems.
One property that has been exploited to mitigate this complexity is transition
independence, in which each agent's transition probabilities are independent of
the states and actions of other agents. Transition independence enables
factorization of the MMDP and computation of local agent policies but does not
hold for arbitrary MMDPs. In this paper, we propose an approximate transition
dependence property, called $\delta$-transition dependence and develop a metric
for quantifying how far an MMDP deviates from transition independence. Our
definition of $\delta$-transition dependence recovers transition independence
as a special case when $\delta$ is zero. We develop a polynomial time algorithm
in the number of agents that achieves a provable bound on the global optimum
when the reward functions are monotone increasing and submodular in the agent
actions. We evaluate our approach on two case studies, namely, multi-robot
control and multi-agent patrolling example.


Abstract:
  We report on the follow-up $XMM-Newton$ observation of the persistent X-ray
pulsar CXOU J225355.1+624336, discovered with the CATS@BAR project on archival
$Chandra$ data. The source was detected at $f_{\rm X}$(0.5-10 keV) = 3.4$\times
10^{-12}$ erg cm$^{-2}$ s$^{-1}$, a flux level which is fully consistent with
the previous observations performed with $ROSAT$, $Swift$, and $Chandra$. The
measured pulse period $P$ = 46.753(3) s, compared with the previous
measurements, implies a constant spin down at an average rate $\dot P =
5.3\times 10^{-10}$ s s$^{-1}$. The pulse profile is energy dependent, showing
three peaks at low energy and a less structured profile above about 3.5 keV.
The pulsed fraction slightly increases with energy. We described the
time-averaged EPIC spectrum with four different emission models: a partially
covered power law, a cut-off power law, and a power law with an additional
thermal component (either a black body or a collisionally ionized gas). In all
cases we obtained equally good fits, so it was not possible to prefer or reject
any emission model on the statistical basis. However, we disfavour the presence
of the thermal components, since their modeled X-ray flux, resulting from a
region larger than the neutron star surface, would largely dominate the X-ray
emission from the pulsar. The phase-resolved spectral analysis showed that a
simple flux variation cannot explain the source variability and proved that it
is characterized by a spectral variability along the pulse phase. The results
of the $XMM-Newton$ observation confirmed that CXOU J225355.1+624336 is a BeXB
with a low-luminosity ($L_{\rm X} \sim 10^{34-35}$ erg s$^{-1}$), a limited
variability, and a constant spin down. Therefore, they reinforce the source
classification as a persistent BeXB.


Abstract:
  Let us consider a Gaussian probability on a Banach space. We prove the
existence of an intermediate Banach space between the space where the Gaussian
measure lives and its RKHS. Such a space has full probability and a compact
embedding. This extends what happens with Wiener measure, where the
intermediate space can be chosen as a space of H\"older paths. From this result
it is very simple to deduce a result of exponential tightness for Gaussian
probabilities.


Abstract:
  Laser cooling of matter through anti-Stokes photoluminescence, where the
emitted frequency of light exceeds that of the impinging laser by virtue of
absorption of thermal vibrational energy, has been successfully realized in
condensed media, and in particular with rare earth doped systems achieving
sub-100K solid state optical refrigeration. Studies suggest that laser cooling
in semiconductors has the potential of achieving temperatures down to ~10K and
that its direct integration can usher unique high-performance nanostructured
semiconductor devices. While laser cooling of nanostructured II-VI
semiconductors has been reported recently, laser cooling of indirect bandgap
semiconductors such as group IV silicon and germanium remains a major
challenge. Here we report on the anomalous observation of dominant anti-Stokes
photoluminescence in germanium nanocrystals. We attribute this result to the
confluence of ultra-high purity nanocrystal germanium, generation of high
density of electron-hole plasma, the inherent degeneracy of longitudinal and
transverse optical phonons in non-polar indirect bandgap semiconductors, and
commensurate spatial confinement effects. At high laser intensities, laser
cooling with lattice temperature as low as ~50K is inferred.


Abstract:
  Major scandals in corporate history have urged the need for regulatory
compliance, where organizations need to ensure that their controls (processes)
comply with relevant laws, regulations, and policies. However, keeping track of
the constantly changing legislation is difficult, thus organizations are
increasingly adopting Regulatory Technology (RegTech) to facilitate the
process. To this end, we introduce regulatory information retrieval (REG-IR),
an application of document-to-document information retrieval (DOC2DOC IR),
where the query is an entire document making the task more challenging than
traditional IR where the queries are short. Furthermore, we compile and release
two datasets based on the relationships between EU directives and UK
legislation. We experiment on these datasets using a typical two-step pipeline
approach comprising a pre-fetcher and a neural re-ranker. Experimenting with
various pre-fetchers from BM25 to k nearest neighbors over representations from
several BERT models, we show that fine-tuning a BERT model on an in-domain
classification task produces the best representations for IR. We also show that
neural re-rankers under-perform due to contradicting supervision, i.e., similar
query-document pairs with opposite labels. Thus, they are biased towards the
pre-fetcher's score. Interestingly, applying a date filter further improves the
performance, showcasing the importance of the time dimension.


Abstract:
  First person action recognition is an increasingly researched topic because
of the growing popularity of wearable cameras. This is bringing to light
cross-domain issues that are yet to be addressed in this context. Indeed, the
information extracted from learned representations suffers from an intrinsic
environmental bias. This strongly affects the ability to generalize to unseen
scenarios, limiting the application of current methods in real settings where
trimmed labeled data are not available during training. In this work, we
propose to leverage over the intrinsic complementary nature of audio-visual
signals to learn a representation that works well on data seen during training,
while being able to generalize across different domains. To this end, we
introduce an audio-visual loss that aligns the contributions from the two
modalities by acting on the magnitude of their feature norm representations.
This new loss, plugged into a minimal multi-modal action recognition
architecture, leads to strong results in cross-domain first person action
recognition, as demonstrated by extensive experiments on the popular
EPIC-Kitchens dataset.


Abstract:
  Accurate prediction of pedestrian crossing behaviors by autonomous vehicles
can significantly improve traffic safety. Existing approaches often model
pedestrian behaviors using trajectories or poses but do not offer a deeper
semantic interpretation of a person's actions or how actions influence a
pedestrian's intention to cross in the future. In this work, we follow the
neuroscience and psychological literature to define pedestrian crossing
behavior as a combination of an unobserved inner will (a probabilistic
representation of binary intent of crossing vs. not crossing) and a set of
multi-class actions (e.g., walking, standing, etc.). Intent generates actions,
and the future actions in turn reflect the intent. We present a novel
multi-task network that predicts future pedestrian actions and uses predicted
future action as a prior to detect the present intent and action of the
pedestrian. We also designed an attention relation network to incorporate
external environmental contexts thus further improve intent and action
detection performance. We evaluated our approach on two naturalistic driving
datasets, PIE and JAAD, and extensive experiments show significantly improved
and more explainable results for both intent detection and action prediction
over state-of-the-art approaches. Our code is available at:
https://github.com/umautobots/pedestrian_intent_action_detection.


Abstract:
  Let $\Delta$ denote a non-degenerate $k$-simplex in $\mathbb{R}^k$. The set
$\text{Sim}(\Delta)$ of simplices in $\mathbb{R}^k$ similar to $\Delta$ is
diffeomorphic to $O(k)\times [0,\infty)\times \mathbb{R}^k$, where the factor
in $O(k)$ is a matrix called the {\em pose}. Among $(k-1)$-spheres smoothly
embedded in $\mathbb{R}^k$ and isotopic to the identity, there is a dense
family of spheres, for which the subset of $\text{Sim}(\Delta)$ of simplices
inscribed in each embedded sphere contains a similar simplex of every pose
$U\in O(k)$. Further, the intersection of $\text{Sim}(\Delta)$ with the
configuration space of $k+1$ distinct points on an embedded sphere is a
manifold whose top homology class maps to the top class in $O(k)$ via the pose
map. This gives a high dimensional generalization of classical results on
inscribing families of triangles in plane curves. We use techniques established
in our previous paper on the square-peg problem where we viewed inscribed
simplices in spheres as transverse intersections of submanifolds of
compactified configuration spaces.


Abstract:
  We propose an approach that links density functional theory (DFT) and
molecular dynamics (MD) simulation to study fluid behavior in nanopores in
contact with bulk (macropores). It consists of two principal steps. First, the
theoretical calculation of fluid composition and density distribution in
nanopore under specified thermodynamic conditions using DFT. Second, MD
simulation of the confined system with obtained characteristics. Thus, we
investigate an open system in a grand canonical ensemble. This method allows us
to investigate both structural and dynamic properties of confined fluid at
given bulk conditions and do not require computationally expensive simulation
of bulk reservoir. In this work, we obtain equilibrium density profiles of pure
methane, ethane and carbon dioxide and their binary mixtures in slitlike
nanopores with carbon walls. Good agreement of structures obtained by theory
and simulation confirms the applicability of the proposed method.


Abstract:
  Brown dwarfs with well-determined ages, luminosities, and masses provide rare
but valuable tests of low-temperature atmospheric and evolutionary models. We
present the discovery and dynamical mass measurement of a substellar companion
to HD 47127, an old ($\approx$7-10 Gyr) G5 main sequence star with a mass
similar to the Sun. Radial velocities of the host star with the Harlan J. Smith
Telescope uncovered a low-amplitude acceleration of 1.93 $\pm$ 0.08 m s$^{-1}$
yr$^{-1}$ based on 20 years of monitoring. We subsequently recovered a faint
($\Delta H$=13.14 $\pm$ 0.15 mag) co-moving companion at 1.95$''$ (52 AU) with
follow-up Keck/NIRC2 adaptive optics imaging. The radial acceleration of HD
47127 together with its tangential acceleration from Hipparcos and Gaia EDR3
astrometry provide a direct measurement of the three-dimensional acceleration
vector of the host star, enabling a dynamical mass constraint for HD 47127 B
(67.5-177 $M_\mathrm{Jup}$ at 95% confidence) despite the small fractional
orbital coverage of the observations. The absolute $H$-band magnitude of HD
47127 B is fainter than the benchmark T dwarfs HD 19467 B and Gl 229 B but
brighter than Gl 758 B and HD 4113 C, suggesting a late-T spectral type.
Altogether the mass limits for HD 47127 B from its dynamical mass and the
substellar boundary imply a range of 67-78 $M_\mathrm{Jup}$ assuming it is
single, although a preference for high masses of $\approx$100 $M_\mathrm{Jup}$
from dynamical constraints hints at the possibility that HD 47127 B could
itself be a binary pair of brown dwarfs or that another massive companion
resides closer in. Regardless, HD 47127 B will be an excellent target for more
refined orbital and atmospheric characterization in the future.


Abstract:
  In this chapter, we derive and analyse models for consensus dynamics on
hypergraphs. As we discuss, unless there are nonlinear node interaction
functions, it is always possible to rewrite the system in terms of a new
network of effective pairwise node interactions, regardless of the initially
underlying multi-way interaction structure. We thus focus on dynamics based on
a certain class of non-linear interaction functions, which can model different
sociological phenomena such as peer pressure and stubbornness. Unlike for
linear consensus dynamics on networks, we show how our nonlinear model dynamics
can cause shifts away from the average system state. We examine how these
shifts are influenced by the distribution of the initial states, the underlying
hypergraph structure and different forms of non-linear scaling of the node
interaction function.


Abstract:
  Transformers are state-of-the-art models for a variety of sequence modeling
tasks. At their core is an attention function which models pairwise
interactions between the inputs at every timestep. While attention is powerful,
it does not scale efficiently to long sequences due to its quadratic time and
space complexity in the sequence length. We propose RFA, a linear time and
space attention that uses random feature methods to approximate the softmax
function, and explore its application in transformers. RFA can be used as a
drop-in replacement for conventional softmax attention and offers a
straightforward way of learning with recency bias through an optional gating
mechanism. Experiments on language modeling and machine translation demonstrate
that RFA achieves similar or better performance compared to strong transformer
baselines. In the machine translation experiment, RFA decodes twice as fast as
a vanilla transformer. Compared to existing efficient transformer variants, RFA
is competitive in terms of both accuracy and efficiency on three long text
classification datasets. Our analysis shows that RFA's efficiency gains are
especially notable on long sequences, suggesting that RFA will be particularly
useful in tasks that require working with large inputs, fast decoding speed, or
low memory footprints.


Abstract:
  We analyze the connections between the non-Markovianity degree of the most
general phase-damping qubit maps and their legitimate mixtures. Using the
results for image non-increasing dynamical maps, we formulate the necessary and
sufficient conditions for the Pauli maps to satisfy specific divisibility
criteria. Next, we examine how the non-Markovianity properties for (in general
noninvertible) Pauli dynamical maps influence the properties of their convex
combinations. Our results are illustrated with instructive examples. For
P-divisible maps, we propose a legitimate time-local generator whose all
decoherence rates are temporarily infinite.


Abstract:
  In this paper we attempt to examine the possibility of construction of a
traversable wormhole on the Randall-Sundrum braneworld with ordinary matter
employing the Kuchowicz potential as one of the metric potentials. In this
scenario, the wormhole shape function is obtained and studied, along with
validity of Null Energy Condition (NEC) and the junction conditions at the
surface of the wormhole are used to obtain a few of the model parameters. The
investigation, besides giving an estimate for the bulk equation of state
parameter, draws important constraints on the brane tension which is a novel
attempt in this aspect and very interestingly the constraints imposed by a
physically plausible traversable wormhole is in high confirmity with those
drawn from more general space-times or space-time independent situations
involved in fundamental physics. Also, we go on to claim that the possible
existence of a wormhole may very well indicate that we live on a three-brane
universe.


Abstract:
  We consider a numerical scheme for the approximation of a system that couples
the evolution of a two--dimensional hypersurface to a reaction--diffusion
equation on the surface. The surfaces are assumed to be graphs and evolve
according to forced mean curvature flow. The method uses continuous, piecewise
linear finite elements in space and a backward Euler scheme in time. Assuming
the existence of a smooth solution we prove optimal error bounds both in
$L^\infty(L^2)$ and in $L^2(H^1)$. We present several numerical experiments
that confirm our theoretical findings and apply the method in order to simulate
diffusion induced grain boundary motion.


Abstract:
  This paper presents a new prescribed performance control scheme for the
attitude tracking of the three degree-of-freedom (3-DOF) helicopter system with
lumped disturbances under mechanical constraints. First, a novel prescribed
performance function is defined to guarantee that the tracking error
performance has a small overshoot in the transient process and converges to an
arbitrary small region within a predetermined time in the steady-state process
without knowing the initial tracking error in advance. Then, based on the novel
prescribed performance function, an error transformation combined with the
smooth finite-time control method we proposed before is employed to drive the
elevation and pitch angles to track given desired trajectories with guaranteed
tracking performance. The theoretical analysis of finite-time Lyapunov
stability indicates that the closed-loop system is fast finite-time uniformly
ultimately boundedness. Finally, comparative experiment results illustrate the
effectiveness and superiority of the proposed control scheme.


Abstract:
  One of the challenges in many-body physics is determining the effects of
phonons on strongly correlated electrons. The difficulty arises from strong
correlations at differing energy scales -- for band metals, Migdal-Eliashberg
theory accurately determines electron-phonon coupling effects due to the
absence of vertex corrections -- but strongly correlated electrons require a
more complex description and the standard Migdal-Eliashberg approach does not
necessarily apply. In this work, we solve for the atomic limit Green's function
of the Holstein-Hubbard model with both time-dependent electron-electron and
electron-phonon couplings. We then examine the photoemission spectra (PES) of
this model in and out of equilibrium. Next we use similar methods to exactly
solve an extended version of the Hatsugai-Komoto model, and examine its
behavior in and out of equilibrium. These calculations lead us to propose using
the first moment of the photoemission spectra to signal non-equilibrium changes
in electron-electron and electron-phonon couplings.


Abstract:
  The paper treats pseudodifferential operators $P=Op(p(\xi ))$ with
homogeneous complex symbol $p(\xi )$ of order $2a>0$, generalizing the
fractional Laplacian $(-\Delta )^a$ but lacking its symmetries, and taken to
act on the halfspace $R^n_+$. The operators are seen to satisfy a principal
$\mu $-transmission condition relative to $R^n_+$, but generally not the full
$\mu $-transmission condition satisfied by $(-\Delta )^a$ and related operators
(with $\mu =a$). However, $P$ acts well on the so-called $\mu $-transmission
spaces over $R^n_+$ (defined in earlier works), and when $P$ moreover is
strongly elliptic, these spaces are the solution spaces for the homogeneous
Dirichlet problem for $P$, leading to regularity results with a factor $x_n^\mu
$ (in a limited range of Sobolev spaces). The information is then shown to be
sufficient to establish an integration by parts formula over $R^n_+$ for $P$
acting on such functions. The formulation in Sobolev spaces, and the results on
strongly elliptic operators going beyond operators with real kernels, are new.
  Furthermore, large solutions with nonzero Dirichlet traces are described, and
a halfways Green's formula is established, for this new class of operators.
  Since the principal $\mu $-transmission condition has weaker requirements
than the full $\mu $-transmission condition assumed in earlier papers, new
arguments were needed, relying on work of Vishik and Eskin instead of the
Boutet de Monvel theory. The results cover the case of nonsymmetric operators
with real kernel that were only partially treated in a preceding paper.


Abstract:
  Representing complex 3D objects as simple geometric primitives, known as
shape abstraction, is important for geometric modeling, structural analysis,
and shape synthesis. In this paper, we propose an unsupervised shape
abstraction method to map a point cloud into a compact cuboid representation.
We jointly predict cuboid allocation as part segmentation and cuboid shapes and
enforce the consistency between the segmentation and shape abstraction for
self-learning. For the cuboid abstraction task, we transform the input point
cloud into a set of parametric cuboids using a variational auto-encoder
network. The segmentation network allocates each point into a cuboid
considering the point-cuboid affinity. Without manual annotations of parts in
point clouds, we design four novel losses to jointly supervise the two branches
in terms of geometric similarity and cuboid compactness. We evaluate our method
on multiple shape collections and demonstrate its superiority over existing
shape abstraction methods. Moreover, based on our network architecture and
learned representations, our approach supports various applications including
structured shape generation, shape interpolation, and structural shape
clustering.


Abstract:
  Grammatical Evolution (GE) is one of the most popular Genetic Programming
(GP) variants, and it has been used with success in several problem domains.
Since the original proposal, many enhancements have been proposed to GE in
order to address some of its main issues and improve its performance.
  In this paper we propose Probabilistic Grammatical Evolution (PGE), which
introduces a new genotypic representation and new mapping mechanism for GE.
Specifically, we resort to a Probabilistic Context-Free Grammar (PCFG) where
its probabilities are adapted during the evolutionary process, taking into
account the productions chosen to construct the fittest individual. The
genotype is a list of real values, where each value represents the likelihood
of selecting a derivation rule. We evaluate the performance of PGE in two
regression problems and compare it with GE and Structured Grammatical Evolution
(SGE).
  The results show that PGE has a a better performance than GE, with
statistically significant differences, and achieved similar performance when
comparing with SGE.


Abstract:
  We analyze internal device physics, performance limitations, and optimization
options for a unique laser design with multiple active regions separated by
tunnel junctions, featuring surprisingly wide quantum wells. Contrary to common
assumptions, these quantum wells are revealed to allow for perfect screening of
the strong built-in polarization field, while optical gain is provided by
higher quantum levels. However, internal absorption, low p-cladding
conductivity, and self-heating are shown to strongly limit the laser
performance.


Abstract:
  Adversarial robustness has become a topic of growing interest in machine
learning since it was observed that neural networks tend to be brittle. We
propose an information-geometric formulation of adversarial defense and
introduce FIRE, a new Fisher-Rao regularization for the categorical
cross-entropy loss, which is based on the geodesic distance between natural and
perturbed input features. Based on the information-geometric properties of the
class of softmax distributions, we derive an explicit characterization of the
Fisher-Rao Distance (FRD) for the binary and multiclass cases, and draw some
interesting properties as well as connections with standard regularization
metrics. Furthermore, for a simple linear and Gaussian model, we show that all
Pareto-optimal points in the accuracy-robustness region can be reached by FIRE
while other state-of-the-art methods fail. Empirically, we evaluate the
performance of various classifiers trained with the proposed loss on standard
datasets, showing up to 2\% of improvements in terms of robustness while
reducing the training time by 20\% over the best-performing methods.


Abstract:
  Deep learning (DL) relies on massive amounts of labeled data, and improving
its labeled sample-efficiency remains one of the most important problems since
its advent. Semi-supervised learning (SSL) leverages unlabeled data that are
more accessible than their labeled counterparts. Active learning (AL) selects
unlabeled instances to be annotated by a human-in-the-loop in hopes of better
performance with less labeled data. Given the accessible pool of unlabeled data
in pool-based AL, it seems natural to use SSL when training and AL to update
the labeled set; however, algorithms designed for their combination remain
limited. In this work, we first prove that convergence of gradient descent on
sufficiently wide ReLU networks can be expressed in terms of their Gram matrix'
eigen-spectrum. Equipped with a few theoretical insights, we propose
convergence rate control (CRC), an AL algorithm that selects unlabeled data to
improve the problem conditioning upon inclusion to the labeled set, by
formulating an acquisition step in terms of improving training dynamics.
Extensive experiments show that SSL algorithms coupled with CRC can achieve
high performance using very few labeled data.


Abstract:
  An $\ell$-facial edge-coloring of a plane graph is a coloring of its edges
such that any two edges at distance at most $\ell$ on a boundary walk of any
face receive distinct colors. It is the edge-coloring variant of the
$\ell$-facial vertex coloring, which arose as a generalization of the
well-known cyclic coloring. It is conjectured that at most $3\ell + 1$ colors
suffice for an $\ell$-facial edge-coloring of any plane graph. The conjecture
has only been confirmed for $\ell \le 2$, and in this paper, we prove its
validity for $\ell = 3$.


Abstract:
  Despite the increasing interest, the research field which studies the
concepts of work and heat at quantum level has suffered from two main
drawbacks: first, the difficulty to properly define and measure the work, heat
and internal energy variation in a quantum system and, second, the lack of
experiments. Here, we report a full characterization of the dissipated heat,
work and internal energy variation in a two-level quantum system interacting
with an engineered environment. We use the IBMQ quantum computer to implement
the driven system's dynamics in a dissipative environment. The experimental
data allow us to construct quasi-probability distribution functions from which
we recover the correct averages of work, heat and internal energy variation in
the dissipative processes. Interestingly, by increasing the environment
coupling strength, we observe a reduction of the pure quantum features of the
energy exchange processes that we interpret as the emergence of the classical
limit. This makes the present approach a privileged tool to study, understand
and exploit quantum effects in energy exchanges.


Abstract:
  Many machine learning tasks involve subpopulation shift where the testing
data distribution is a subpopulation of the training distribution. For such
settings, a line of recent work has proposed the use of a variant of empirical
risk minimization(ERM) known as distributionally robust optimization (DRO). In
this work, we apply DRO to real, large-scale tasks with subpopulation shift,
and observe that DRO performs relatively poorly, and moreover has severe
instability. We identify one direct cause of this phenomenon: sensitivity of
DRO to outliers in the datasets. To resolve this issue, we propose the
framework of DORO, for Distributional and Outlier Robust Optimization. At the
core of this approach is a refined risk function which prevents DRO from
overfitting to potential outliers. We instantiate DORO for the Cressie-Read
family of R\'enyi divergence, and delve into two specific instances of this
family: CVaR and $\chi^2$-DRO. We theoretically prove the effectiveness of the
proposed method, and empirically show that DORO improves the performance and
stability of DRO with experiments on large modern datasets, thereby positively
addressing the open question raised by Hashimoto et al., 2018.


Abstract:
  We study two-sided reputational bargaining with opportunities to issue an
ultimatum -- threats to force dispute resolution. Each player is either a
justified type, who never concedes and issues an ultimatum whenever an
opportunity arrives, or an unjustified type, who can concede, wait, or bluff
with an ultimatum. In equilibrium, the presence of ultimatum opportunities can
harm or benefit a player by decelerating or accelerating reputation building.
When only one player can issue an ultimatum, equilibrium play is unique. The
hazard rate of dispute resolution is discontinuous and piecewise monotonic in
time. As the probabilities of being justified vanish, agreement is immediate
and efficient, and if the set of justifiable demands is rich, payoffs modify
Abreu and Gul (2000), with the discount rate replaced by the ultimatum
opportunity arrival rate if the former is smaller. When both players' ultimatum
opportunities arrive sufficiently fast, there may exist multiple equilibria in
which their reputations do not build up and negotiation lasts forever.


Abstract:
  Overparametrized interpolating models have drawn increasing attention from
machine learning. Some recent studies suggest that regularized interpolating
models can generalize well. This phenomenon seemingly contradicts the
conventional wisdom that interpolation tends to overfit the data and performs
poorly on test data. Further, it appears to defy the bias-variance trade-off.
As one of the shortcomings of the existing theory, the classical notion of
model degrees of freedom fails to explain the intrinsic difference among the
interpolating models since it focuses on estimation of in-sample prediction
error. This motivates an alternative measure of model complexity which can
differentiate those interpolating models and take different test points into
account. In particular, we propose a measure with a proper adjustment based on
the squared covariance between the predictions and observations. Our analysis
with least squares method reveals some interesting properties of the measure,
which can reconcile the "double descent" phenomenon with the classical theory.
This opens doors to an extended definition of model degrees of freedom in
modern predictive settings.


Abstract:
  Solving for detailed chemical kinetics remains one of the major bottlenecks
for computational fluid dynamics simulations of reacting flows using a
finite-rate-chemistry approach. This has motivated the use of fully connected
artificial neural networks to predict stiff chemical source terms as functions
of the thermochemical state of the combustion system. However, due to the
nonlinearities and multi-scale nature of combustion, the predicted solution
often diverges from the true solution when these deep learning models are
coupled with a computational fluid dynamics solver. This is because these
approaches minimize the error during training without guaranteeing successful
integration with ordinary differential equation solvers. In the present work, a
novel neural ordinary differential equations approach to modeling chemical
kinetics, termed as ChemNODE, is developed. In this deep learning framework,
the chemical source terms predicted by the neural networks are integrated
during training, and by computing the required derivatives, the neural network
weights are adjusted accordingly to minimize the difference between the
predicted and ground-truth solution. A proof-of-concept study is performed with
ChemNODE for homogeneous autoignition of hydrogen-air mixture over a range of
composition and thermodynamic conditions. It is shown that ChemNODE accurately
captures the correct physical behavior and reproduces the results obtained
using the full chemical kinetic mechanism at a fraction of the computational
cost.


Abstract:
  Graphics Processing Units (GPUs) have been widely used to accelerate
artificial intelligence, physics simulation, medical imaging, and information
visualization applications. To improve GPU performance, GPU hardware designers
need to identify performance issues by inspecting a huge amount of
simulator-generated traces. Visualizing the execution traces can reduce the
cognitive burden of users and facilitate making sense of behaviors of GPU
hardware components. In this paper, we first formalize the process of GPU
performance analysis and characterize the design requirements of visualizing
execution traces based on a survey study and interviews with GPU hardware
designers. We contribute data and task abstraction for GPU performance
analysis. Based on our task analysis, we propose Daisen, a framework that
supports data collection from GPU simulators and provides visualization of the
simulator-generated GPU execution traces. Daisen features a data abstraction
and trace format that can record simulator-generated GPU execution traces.
Daisen also includes a web-based visualization tool that helps GPU hardware
designers examine GPU execution traces, identify performance bottlenecks, and
verify performance improvement. Our qualitative evaluation with GPU hardware
designers demonstrates that the design of Daisen reflects the typical workflow
of GPU hardware designers. Using Daisen, participants were able to effectively
identify potential performance bottlenecks and opportunities for performance
improvement. The open-sourced implementation of Daisen can be found at
gitlab.com/akita/vis. Supplemental materials including a demo video, survey
questions, evaluation study guide, and post-study evaluation survey are
available at osf.io/j5ghq.


Abstract:
  A set of boundary conditions called the Transpiration-Resistance Model (TRM)
are investigated in altering near-wall turbulence. The TRM has been previously
proposed by \citet{Lacis2020} as a means of representing the net effect of
surface micro-textures on their overlying bulk flows. It encompasses
conventional Navier-slip boundary conditions relating the streamwise and
spanwise velocities to their respective shears through the slip lengths
$\ell_x$ and $\ell_z$. In addition, it features a transpiration condition
accounting for the changes induced in the wall-normal velocity by expressing it
in terms of variations of the wall-parallel velocity shears through the
transpiration lengths $m_x$ and $m_z$. Greater levels of drag increase occur
when more transpiration takes place at the boundary plane, with turbulent
transpiration being predominately coupled to the spanwise shear component for
canonical near-wall turbulence. The TRM can reproduce the effect of a
homogeneous and structured roughness up to ${k^+}\,{\approx18}$. In this
transitionally rough flow regime, the transpiration lengths of the TRM must be
empirically determined. The \emph{transpiration factor} is defined as the
product between the slip and transpiration lengths, i.e. $(m\ell)_{x,z}$. This
factor contains the compound effect of the wall-parallel velocity occurring at
the boundary plane and increased permeability, both of which lead to the
transport of momentum in the wall-normal direction. A linear relation between
the transpiration factor and the roughness function is observed for regularly
textured surfaces in the transitionally rough regime of turbulence. The
relations obtained between the transpiration factor and the roughness function
show that such effective flow quantities can be suitable measures for
characterizing rough surfaces in this flow regime.


Abstract:
  This paper addresses the trajectory tracking problem of an autonomous
tractor-trailer system by using a fast distributed nonlinear model predictive
control algorithm in combination with nonlinear moving horizon estimation for
the state and parameter estimation in which constraints on the inputs and the
states can be incorporated. The proposed control algorithm is capable of
driving the tractor-trailer system to any desired trajectory ensuring high
control accuracy and robustness against environmental disturbances.


Abstract:
  We introduce FaDIV-Syn, a fast depth-independent method for novel view
synthesis. Related methods are often limited by their depth estimation stage,
where incorrect depth predictions can lead to large projection errors. To avoid
this issue, we efficiently warp input images into the target frame for a range
of assumed depth planes. The resulting plane sweep volume (PSV) is directly fed
into our network, which first estimates soft PSV masks in a self-supervised
manner, and then directly produces the novel output view. We therefore
side-step explicit depth estimation. This improves efficiency and performance
on transparent, reflective, thin, and feature-less scene parts. FaDIV-Syn can
perform both interpolation and extrapolation tasks and outperforms
state-of-the-art extrapolation methods on the large-scale RealEstate10k
dataset. In contrast to comparable methods, it achieves real-time performance
due to its lightweight architecture. We thoroughly evaluate ablations, such as
removing the Soft-Masking network, training from fewer examples as well as
generalization to higher resolutions and stronger depth discretization.


Abstract:
  The unique properties of blockchain enable central requirements of
distributed secure logging: Immutability, integrity, and availability.
Especially when providing transparency about data usages, a blockchain-based
secure log can be beneficial, as no trusted third party is required. Yet, with
data governed by privacy legislation such as the GDPR or CCPA, the core
advantage of immutability becomes a liability. After a rightful request, an
individual's personal data need to be rectified or deleted, which is impossible
in an immutable blockchain. To solve this issue, we exploit a legal property of
pseudonymized data: They are only regarded personal data if they can be
associated with an individual's identity. We make use of this fact by
presenting P3, a pseudonym provisioning system for secure usage logs including
a protocol for recording new usages. For each new block, a one-time transaction
pseudonym is generated. The pseudonym generation algorithm guarantees
unlinkability and enables proof of ownership. These properties enable
GDPR-compliant use of blockchain, as data subjects can exercise their legal
rights with regards to their personal data. The new-usage protocol ensures
non-repudiation, and therefore accountability and liability. Most importantly,
our approach does not require a trusted third party and is independent of the
utilized blockchain software.


Abstract:
  The spectrum of laser-plasma generated X-rays is very important, it
characterizes electron dynamics in plasma and is basic for applications.
However, the accuracies and efficiencies of existing methods to diagnose the
spectrum of laser-plasma based X-ray pulse are not very high, especially in the
range of several hundred keV. In this study, a new method based on electron
tracks detection to measure the spectrum of laser-plasma produced X-ray pulses
is proposed and demonstrated. Laser-plasma generated X-rays are scattered in a
multi-pixel silicon tracker. Energies and scattering directions of Compton
electrons can be extracted from the response of the detector, and then the
spectrum of X-rays can be reconstructed. Simulations indicate that the energy
resolution of this method is approximately 20% for X-rays from 200 to 550 keV
for a silicon-on-insulator pixel detector with 12 $\rm \mu$m pixel pitch and
500 $\rm \mu$m depletion region thickness. The results of a proof-of-principle
experiment based on a Timepix3 detector are also shown.


Abstract:
  We present spectroscopy of individual stars in 26 Magellanic Cloud (MC) star
clusters with the aim of estimating dynamical masses and $V$-band mass-to-light
($M/L_V$) ratios over a wide range in age and metallicity. We obtained 3137
high-resolution stellar spectra with M2FS on the \textit{Magellan}/Clay
Telescope. Combined with 239 published spectroscopic results of comparable
quality, we produced a final sample of 2787 stars with good quality spectra for
kinematic analysis in the target clusters. Line-of-sight velocities measured
from these spectra and stellar positions within each cluster were used in a
customized expectation-maximization (EM) technique to estimate cluster
membership probabilities. Using appropriate cluster structural parameters and
corresponding single-mass dynamical models, this technique ultimately provides
self-consistent total mass and $M/L_V$ estimates for each cluster. Mean
metallicities for the clusters were also obtained and tied to a scale based on
calcium IR triplet metallicites. We present trends of the cluster $M/L_V$
values with cluster age, mass and metallicity, and find that our results run
about 40 per cent on average lower than the predictions of a set of simple
stellar population (SSP) models. Modified SSP models that account for internal
and external dynamical effects greatly improve agreement with our results, as
can models that adopt a strongly bottom-light IMF. To the extent that dynamical
evolution must occur, a modified IMF is not required to match data and models.
In contrast, a bottom-heavy IMF is ruled out for our cluster sample as this
would lead to higher predicted $M/L_V$ values, significantly increasing the
discrepancy with our observations.


Abstract:
  Current vision systems are trained on huge datasets, and these datasets come
with costs: curation is expensive, they inherit human biases, and there are
concerns over privacy and usage rights. To counter these costs, interest has
surged in learning from cheaper data sources, such as unlabeled images. In this
paper we go a step further and ask if we can do away with real image datasets
entirely, instead learning from noise processes. We investigate a suite of
image generation models that produce images from simple random processes. These
are then used as training data for a visual representation learner with a
contrastive loss. We study two types of noise processes, statistical image
models and deep generative models under different random initializations. Our
findings show that it is important for the noise to capture certain structural
properties of real data but that good performance can be achieved even with
processes that are far from realistic. We also find that diversity is a key
property to learn good representations. Datasets, models, and code are
available at https://mbaradad.github.io/learning_with_noise.


Abstract:
  The detection of polylines is usually either bound to branchless polylines or
formulated in a recurrent way, prohibiting their use in real-time systems.
  We propose an approach that builds upon the idea of single shot object
detection. Reformulating the problem of polyline detection as a bottom-up
composition of small line segments allows to detect bounded, dashed and
continuous polylines with a single head. This has several major advantages over
previous methods. Not only is the method at 187 fps more than suited for
real-time applications with virtually any restriction on the shapes of the
detected polylines. By predicting multiple line segments for each cell, even
branching or crossing polylines can be detected.
  We evaluate our approach on three different applications for road marking,
lane border and center line detection. Hereby, we demonstrate the ability to
generalize to different domains as well as both implicit and explicit polyline
detection tasks.


Abstract:
  We develop the covariant phase space formalism allowing for non-vanishing
flux, anomalies and field dependence in the vector field generators. We
construct a charge bracket that generalizes the one introduced by Barnich and
Troessaert and includes contributions from the Lagrangian and its anomaly. This
bracket is uniquely determined by the choice of Lagrangian representative of
the theory. We then extend the notion of corner symmetry algebra to include the
surface translation symmetries and prove that the charge bracket provides a
canonical representation of the extended corner symmetry algebra. This
representation property is shown to be equivalent to the projection of the
gravitational equations of motion on the corner, providing us with an encoding
of the bulk dynamics in a locally holographic manner.


Abstract:
  We introduce Virasoro operators for any Landau-Ginzburg pair (W, G) where W
is a non-degenerate quasi-homogeneous polynomial and G is a certain group of
diagonal symmetries. We propose a conjecture that the total ancestor potential
of the FJRW theory of the pair (W, G) is annihilated by these Virasoro
operators. We prove the conjecture in various cases, including: (1) invertible
polynomials with the maximal group, (2) two-variable homogeneous Fermat
polynomials with the minimal group, (3) certain Calabi-Yau polynomials with
groups. We also discuss the connections among Virasoro constraints, mirror
symmetry of Landau-Ginzburg models, and Landau-Ginzburg/Calabi-Yau
correspondence.


Abstract:
  Although the unscented Kalman filter (UKF) is applicable to nonlinear
systems, it turns out that, for linear systems, UKF does not specialize to the
classical Kalman filter. This situation suggests that it may be advantageous to
modify UKF in such a way that, for linear systems, the Kalman filter is
recovered. The ultimate goal is thus to develop modifications of UKF that
specialize to the Kalman filter for linear systems and have improved accuracy
for nonlinear systems. With this motivation, this paper presents two
modifications of UKF that specialize to the Kalman filter for linear systems.
The first modification (EUKF-A) requires the Jacobian of the dynamics map,
whereas the second modification (EUKF-C) requires the Jacobian of the
measurement map. For various nonlinear examples, the accuracy of EUKF-A and
EUKF-C is compared to the accuracy of UKF.


Abstract:
  In this article we show why flying and rotating beer mats, CDs, or other flat
disks will eventually flip in the air and end up flying with backspin, thus,
making them unusable as frisbees. The crucial effect responsible for the
flipping is found to be the lift attacking not in the center of mass but
slightly offset to the forward edge. This induces a torque leading to a
precession towards backspin orientation. An effective theory is developed
providing an approximate solution for the disk's trajectory with a minimal set
of parameters. Our theoretical results are confronted with experimental results
obtained using a beer mat shooting apparatus and a high speed camera. Very good
agreement is found.


Abstract:
  Line intensity mapping (LIM) proposes to efficiently observe distant faint
galaxies and map the matter density field at high redshift. Building upon the
formalism in the companion paper, we first highlight the degeneracies between
cosmology and astrophysics in LIM. We discuss what can be constrained from
measurements of the mean intensity and redshift-space power spectra. With a
sufficient spectral resolution, the large-scale redshift-space distortions of
the 2-halo term can be measured, helping to break the degeneracy between bias
and mean intensity. With a higher spectral resolution, measuring the
small-scale redshift-space distortions disentangles the 1-halo and shot noise
terms. Cross-correlations with external galaxy catalogs or lensing surveys
further break degeneracies. We derive requirements for experiments similar to
SPHEREx, HETDEX, CDIM, COMAP and CONCERTO. We then revisit the question of the
optimality of the LIM observables, compared to galaxy detection, for
astrophysics and cosmology. We use a matched filter to compute the luminosity
detection threshold for individual sources. We show that LIM contains
information about galaxies too faint to detect, in the high-noise or
high-confusion regimes. We quantify the sparsity and clustering bias of the
detected sources and compare them to LIM, showing in which cases LIM is a
better tracer of the matter density. We extend previous work by answering these
questions as a function of Fourier scale, including for the first time the
effect of cosmic variance, pixel-to-pixel correlations, luminosity-dependent
clustering bias and redshift-space distortions.


Abstract:
  This paper aims at using the functional renormalization group formalism to
study the equilibrium states of a stochastic process described by a
quench--disordered multilinear Langevin equation. Such an equation
characterizes the evolution of a time-dependent $N$-vector
$q(t)=\{q_1(t),\cdots q_N(t)\}$ and is traditionally encountered in the
dynamical description of glassy systems at and out of equilibrium through the
so-called Glauber model. From the connection between Langevin dynamics and
quantum mechanics in imaginary time, we are able to coarse-grain the path
integral of the problem in the Fourier modes, and to construct a
renormalization group flow for effective euclidean action. In the large
$N$-limit we are able to solve the flow equations for both matrix and tensor
disorder. The numerical solutions of the resulting exact flow equations are
then investigated using standard local potential approximation, taking into
account the quench disorder. In the case where the interaction is taken to be
matricial, for finite $N$ the flow equations are also solved. However, the case
of finite $N$ and taking into account the non-equilibrum process will be
considered in a companion investigation.


Abstract:
  Semi-discrete and fully discrete mixed finite element methods are considered
for Maxwell-model-based problems of wave propagation in linear viscoelastic
solid. This mixed finite element framework allows the use of a large class of
existing mixed conforming finite elements for elasticity in the spatial
discretization. In the fully discrete scheme, a Crank-Nicolson scheme is
adopted for the approximation of the temporal derivatives of stress and
velocity variables. Error estimates of the semi-discrete and fully discrete
schemes, as well as an unconditional stability result for the fully discrete
scheme, are derived. Numerical experiments are provided to verify the
theoretical results.


Abstract:
  A novel approach for electrochemical tuning of alcohol oxidase (AOx) and
alcohol dehydrogenase (ADH) biocatalysis towards butanol-1 oxidation by
incorporating enzymes in various designs of amperometric biosensors is
presented. The biosensors were developed by using commercial graphene
oxide-based screen-printed electrodes and varying enzyme producing strains,
encapsulation approaches (layer-by-layer (LbL) or one-step electrodeposition
(EcD)), layers composition and structure, operating conditions (applied
potential values) and introducing mediators (Meldola Blue and Prussian Blue) or
Pd-nanoparticles (Pd-NPs). Simultaneous analysis/screening of multiple crucial
system parameters during the enzyme engineering process allowed to identify
within a period of one month that four out of twelve proposed designs
demonstrated a good signal reproducibility and linear response (up to 14.6 mM
of butanol) under very low applied potentials (from -0.02 to -0.32 V). Their
mechanical stability was thoroughly investigated by multi-analytical techniques
prior to butanol determination in cell-free samples from an anaerobic butanol
fermentation. The EcD-based biosensor that incorporates ADH, NAD+, Pd-NPs and
Nafion showed no loss of enzyme activity after preparation and demonstrated
capabilities towards low potential (-0.12 V) detection of butanol-1 in
fermentation medium (4 mM) containing multiple electroactive species with
almost 15 times enhanced sensitivity (0.2282 $\mu$A/mM $\pm$ 0.05) when
compared to the LbL design. Furthermore, the ADH-Nafion bonding for the S.
cerevisiae strain was confirmed to be 3 times higher than for E. coli.


Abstract:
  Electronic states of a correlated material can be effectively modified by
structural variations delivered from a single-crystal substrate. In this
letter, we show that the CrN films grown on MgO (001) substrates have a (001)
orientation, whereas the CrN films on {\alpha}-Al2O3 (0001) substrates are
oriented along (111) direction parallel to the surface normal. Transport
properties of CrN films are remarkably different depending on crystallographic
orientations. The critical thickness for the metal-insulator transition (MIT)
in CrN 111 films is significantly larger than that of CrN 001 films. In
contrast to CrN 001 films without apparent defects, scanning transmission
electron microscopy results reveal that CrN 111 films exhibit strain-induced
structural defects, e. g. the periodic horizontal twinning domains, resulting
in an increased electron scattering facilitating an insulating state.
Understanding the key parameters that determine the electronic properties of
ultrathin conductive layers is highly desirable for future technological
applications.


Abstract:
  Statistical Hypothesis Testing (SHT) is a class of inference methods whereby
one makes use of empirical data to test a hypothesis and often emit a judgment
about whether to reject it or not. In this paper we focus on the logical aspect
of this strategy, which is largely independent of the adopted school of
thought, at least within the various frequentist approaches. We identify SHT as
taking the form of an unsound argument from Modus Tollens in classical logic,
and, in order to rescue SHT from this difficulty, we propose that it can
instead be grounded in t-norm based fuzzy logics. We reformulate the
frequentists' SHT logic by making use of a fuzzy extension of modus Tollens to
develop a model of truth valuation for its premises. Importantly, we show that
it is possible to preserve the soundness of Modus Tollens by exploring the
various conventions involved with constructing fuzzy negations and fuzzy
implications (namely, the S and R conventions). We find that under the S
convention, it is possible to conduct the Modus Tollens inference argument
using Zadeh's compositional extension and any possible t-norm. Under the R
convention we find that this is not necessarily the case, but that by mixing
R-implication with S-negation we can salvage the product t-norm, for example.
In conclusion, we have shown that fuzzy logic is a legitimate framework to
discuss and address the difficulties plaguing frequentist interpretations of
SHT.


Abstract:
  We present the first version of a system for interactive generation of
theatre play scripts. The system is based on a vanilla GPT-2 model with several
adjustments, targeting specific issues we encountered in practice. We also list
other issues we encountered but plan to only solve in a future version of the
system. The presented system was used to generate a theatre play script planned
for premiere in February 2021.


Abstract:
  We consider the revenue maximization problem in social advertising, where a
social network platform owner needs to select seed users for a group of
advertisers, each with a payment budget, such that the total expected revenue
that the owner gains from the advertisers by propagating their ads in the
network is maximized. Previous studies on this problem show that it is
intractable and present approximation algorithms. We revisit this problem from
a fresh perspective and develop novel efficient approximation algorithms, both
under the setting where an exact influence oracle is assumed and under one
where this assumption is relaxed. Our approximation ratios significantly
improve upon the previous ones. Furthermore, we empirically show, using
extensive experiments on four datasets, that our algorithms considerably
outperform the existing methods on both the solution quality and computation
efficiency.


Abstract:
  A spectral-energy distribution (SED) model for Type Ia supernovae (SNe Ia) is
a critical tool for measuring precise and accurate distances across a large
redshift range and constraining cosmological parameters. We present an improved
model framework, SALT3, which has several advantages over current models
including the leading SALT2 model (SALT2.4). While SALT3 has a similar
philosophy, it differs from SALT2 by having improved estimation of
uncertainties, better separation of color and light-curve stretch, and a
publicly available training code. We present the application of our training
method on a cross-calibrated compilation of 1083 SNe with 1207 spectra. Our
compilation is $2.5\times$ larger than the SALT2 training sample and has
greatly reduced calibration uncertainties. The resulting trained SALT3.K21
model has an extended wavelength range $2000$-$11000$ angstroms (1800 angstroms
redder) and reduced uncertainties compared to SALT2, enabling accurate use of
low-$z$ $I$ and $iz$ photometric bands. Including these previously discarded
bands, SALT3.K21 reduces the Hubble scatter of the low-z Foundation and CfA3
samples by 15% and 10%, respectively. To check for potential systematic
uncertainties we compare distances of low ($0.01<z<0.2$) and high ($0.4<z<0.6$)
redshift SNe in the training compilation, finding an insignificant $2\pm14$
mmag shift between SALT2.4 and SALT3.K21. While the SALT3.K21 model was trained
on optical data, our method can be used to build a model for rest-frame NIR
samples from the Roman Space Telescope. Our open-source training code, public
training data, model, and documentation are available at
https://saltshaker.readthedocs.io/en/latest/, and the model is integrated into
the sncosmo and SNANA software packages.


Abstract:
  We all know that in the dense anisotropic interior of the star,
neutrino-neutrino forward-scattering can lead to fast collective neutrino
oscillations, which has striking consequences on flavor dependent neutrino
emission and can be crucial for the evolution of a supernova and its neutrino
signal. The flavor evolution of such dense neutrino system is governed by a
large number of coupled nonlinear partial differential equations which are
almost always very difficult to solve. Although the triggering, initial linear
growth and the condition for fast oscillations to occur are understood by
"Linear stability analysis" but this fails to answer an important question:
"what is the impact of fast flavor conversion on observable neutrino fluxes or
the supernova explosion mechanism?". This is a significantly harder problem
that requires understanding the nature of the final state solution in the
nonlinear regime. Moving towards this direction we present one of the first
numerical as well as an analytical study of the coupled flavor evolution of a
non-stationary and inhomogeneous dense neutrino system in the nonlinear regime
considering one spatial dimension and a spectrum of velocity modes. This work
gives a clear picture of the final state flavor dynamics of such systems
specifying its dependence on space-time coordinates, phase space variables as
well as the lepton asymmetry and thus can have significant implications for the
supernova astrophysics as well as its associated neutrino phenomenology even
for the most realistic scenario.


Abstract:
  Coherent quantum phase slips are expected to lead to a blockade of dc
conduction in sufficiently narrow superconducting nanowires below a certain
critical voltage. We present measurements of NbN nanowires in which not only is
a critical voltage observed, but also in which this critical voltage may be
tuned using a side-gate electrode. The critical voltage varies periodically as
the applied gate voltage is varied. While the observations are qualitatively as
expected for quantum interference between coherent quantum phase slip elements,
the period of the tuning is orders of magnitude larger than expected on the
basis of simple capacitance considerations. Furthermore, two significant abrupt
changes in the period of the variations during measurements of one nanowire are
observed, an observation which constrains detailed explanations for the
behaviour. The plausibility of an explanation assuming that the behaviour
arises from granular Josephson junctions in the nanowire is also considered.


Abstract:
  We construct the complementary short-range correlation relativistic
local-density-approximation functional to be used in relativistic
range-separated density-functional theory based on a Dirac-Coulomb Hamiltonian
in the no-pair approximation. For this, we perform relativistic
random-phase-approximation calculations of the correlation energy of the
relativistic homogeneous electron gas with a modified electron-electron
interaction, we study the high-density behavior, and fit the results to a
parametrized expression. The obtained functional should eventually be useful
for electronic-structure calculations of strongly correlated systems containing
heavy elements.


Abstract:
  We show that if the complement of a Donaldson hypersurface in a closed,
integral symplectic manifold has the homology of a subcritical Stein manifold,
then the hypersurface is of degree one. In particular, this demonstrates a
conjecture by Biran and Cieliebak on subcritical polarisations of symplectic
manifolds. Our proof is based on a simple homological argument using ideas of
Kulkarni-Wood.


Abstract:
  Density functional theory based computational study has been conducted in
order to investigate the effect of substitution of Cr and Co components by Si
on the structure, mechanical, electronic, and magnetic properties of the high
entropy alloy CrCoNiFe. It is found that the presence of a moderate
concentration of Si substitutes (up to 12.5 %) does not significantly reduce
the structural and mechanical stability of CrCoNiFe while it may modify its
electronic and magnetic properties. Based on that, Si is proposed as a cheap
and functional material for partial substitution of Cr or Co in CrCoNiFe.


Abstract:
  Argument mining systems often consider contextual information, i.e.
information outside of an argumentative discourse unit, when trained to
accomplish tasks such as argument component identification, classification, and
relation extraction. However, prior work has not carefully analyzed the utility
of different contextual properties in context-aware models. In this work, we
show how two different types of contextual information, local discourse context
and speaker context, can be incorporated into a computational model for
classifying argument components in multi-party classroom discussions. We find
that both context types can improve performance, although the improvements are
dependent on context size and position.


Abstract:
  The effect of a spatially uniform magnetic field on the shear rheology of a
dilute emulsion of monodispersed ferrofluid droplets, immersed in a
non-magnetizable immiscible fluid, is investigated using direct numerical
simulations. The direction of the applied magnetic field is normal to the shear
flow direction. The droplets extra stress tensor arising from the presence of
interfacial forces of magnetic nature is modeled on the basis of the seminal
work of G. K. Batchelor, J. Fluid Mech., 41.3 (1970) under the assumptions of a
linearly magnetizable ferrofluid phase and negligible inertia. The results show
that even relatively small magnetic fields can have significant consequences on
the rheological properties of the emulsion due to the magnetic forces that
contribute to deform and orient the droplets towards the direction of the
applied magnetic vector. In particular, we have observed an increase of the
effective (bulk) viscosity and a reversal of the sign of the two normal stress
differences with respect to the case without magnetic field for those
conditions where the magnetic force prevails over the shearing force.
Comparisons between the results of our model with a direct integration of the
viscous stress have provided an indication of its reliability to predict the
effective viscosity of the suspension. Moreover, this latter quantity has been
found to behave as a monotonic increasing function of the applied magnetic
field for constant shearing flows ("magneto-thickening" behaviour), which
allowed us to infer a simple constitutive equation describing the emulsion
viscosity.


Abstract:
  A good understanding of the confinement of energetic ions in non-axisymmetric
magnetic fields is key for the design of reactors based on the stellarator
concept. In this work, we develop a model that, based on the radially-local
bounce-averaged drift-kinetic equation, classifies orbits and succeeds in
predicting configuration-dependent aspects of the prompt losses of energetic
ions in stellarators. Such a model could in turn be employed in the
optimization stage of the design of new devices.


Abstract:
  State-of-the-art visual analytics techniques in application domains are often
designed by VA professionals over qualitative requirement collected from end
users. These VA techniques may not leverage users' domain knowledge about how
to achieve their analytical goals. In this position paper, we propose a
user-driven design process of VA applications centered around a new concept
called analytical representation (AR). AR features a formal abstraction of user
requirement and their desired analytical trails for certain VA application, and
is independent of the actual visualization design. A conceptual graph schema is
introduced to define the AR abstraction, which can be created manually or
constructed by semi-automated tools. Designing VA applications with AR provides
a shared opportunity for both optimal analysis blueprint from the perspective
of end users and optimal visualization/algorithm from the perspective of VA
designers. We demonstrate the usage of the design process in two case studies.


Abstract:
  The field of two-dimensional materials has been developing at an impressive
pace, with atomically thin crystals of an increasing number of different
compounds that have become available, together with techniques enabling their
assembly into functional heterostructures. The strategy to detect these
atomically thin crystals has however remained unchanged since the discovery of
graphene. Such an absence of evolution is starting to pose problems because for
many of the 2D materials of current interest the optical contrast provided by
the commonly used detection procedure is insufficient to identify the presence
of individual monolayers or to determine unambiguously the thickness of
atomically thin multilayers. Here we explore an alternative detection strategy,
in which the enhancement of optical contrast originates from the use of
optically inhomogeneous substrates, leading to diffusively reflected light.
Owing to its peculiar polarization properties and to its angular distribution,
diffusively reflected light allows a strong contrast enhancement to be achieved
through the implementation of suitable illumination-detection schemes. We
validate this conclusion by carrying out a detailed quantitative analysis of
optical contrast, which fully reproduces our experimental observations on over
60 WSe$_2$ mono-, bi-, and trilayers. We further validate the proposed strategy
by extending our analysis to atomically thin phosphorene, InSe, and graphene
crystals. Our conclusion is that the use of diffusively reflected light to
detect and identify atomically thin layers is an interesting alternative to the
common detection scheme based on Fabry-Perot interference, because it enables
atomically thin layers to be detected on substrates others than the commonly
used Si/SiO$_2$, and it may offer higher sensitivity depending on the specific
2D material considered.


Abstract:
  Panoptic segmentation presents a new challenge in exploiting the merits of
both detection and segmentation, with the aim of unifying instance segmentation
and semantic segmentation in a single framework. However, an efficient solution
for panoptic segmentation in the emerging domain of LiDAR point cloud is still
an open research problem and is very much under-explored. In this paper, we
present a fast and robust LiDAR point cloud panoptic segmentation framework,
referred to as Panoptic-PolarNet. We learn both semantic segmentation and
class-agnostic instance clustering in a single inference network using a polar
Bird's Eye View (BEV) representation, enabling us to circumvent the issue of
occlusion among instances in urban street scenes. To improve our network's
learnability, we also propose an adapted instance augmentation technique and a
novel adversarial point cloud pruning method. Our experiments show that
Panoptic-PolarNet outperforms the baseline methods on SemanticKITTI and
nuScenes datasets with an almost real-time inference speed. Panoptic-PolarNet
achieved 54.1% PQ in the public SemanticKITTI panoptic segmentation leaderboard
and leading performance for the validation set of nuScenes.


Abstract:
  Classical machine learning algorithms often assume that the data are drawn
i.i.d. from a stationary probability distribution. Recently, continual learning
emerged as a rapidly growing area of machine learning where this assumption is
relaxed, namely, where the data distribution is non-stationary, i.e., changes
over time. However, data distribution drifts may interfere with the learning
process and erase previously learned knowledge; thus, continual learning
algorithms must include specialized mechanisms to deal with such distribution
drifts. A distribution drift may change the class labels distribution, the
input distribution, or both. Moreover, distribution drifts might be abrupt or
gradual. In this paper, we aim to identify and categorize different types of
data distribution drifts and potential assumptions about them, to better
characterize various continual-learning scenarios. Moreover, we propose to use
the distribution drift framework to provide more precise definitions of several
terms commonly used in the continual learning field.


Abstract:
  Using elementary techniques from analytic perturbation theory of Hermitian
matrices, we devise a simple strategy to detect positive quantum capacities of
quantum channels and their complements. Several noteworthy examples, such as
the depolarizing and transpose-depolarizing channels (including the
Werner-Holevo channel), dephasing channels, generalized Pauli channels,
multi-level amplitude damping channels, and (conjugate) diagonal unitary
covariant channels, serve to aptly exhibit the utility of our method. Our main
result leads to simplified proofs of certain existing structure theorems for
the class of degradable quantum channels, and an extension of their
applicability to the larger class of more capable quantum channels.


Abstract:
  Convergence is a fundamental topic in analysis that is most commonly modelled
using topology. However, there are many natural convergences that are not given
by any topology; e.g., convergence almost everywhere of a sequence of
measurable functions and order convergence of nets in vector lattices. The
theory of convergence structures provides a framework for studying more general
modes of convergence. It also has one particularly striking feature: it is
formalized using the language of filters. This paper develops a general theory
of convergence in terms of nets. We show that it is equivalent to the
filter-based theory and present some translations between the two areas. In
particular, we provide a characterization of pretopological convergence
structures in terms of nets. We also use our results to unify certain topics in
vector lattices with general convergence theory.


Abstract:
  In this paper, we establish a general weighted Hardy type inequality for the
$% p-$Laplace operator with Robin boundary condition. We provide various
concrete examples to illustrate our results for different weights. Furthermore,
we present some Heisenberg-Pauli-Weyl type inequalities with boundary terms on
balls with radius $R$ at the origin in $\mathbb{R}^n$.


Abstract:
  Probabilistic model checking aims to prove whether a Markov decision process
(MDP) satisfies a temporal logic specification. The underlying methods rely on
an often unrealistic assumption that the MDP is precisely known. Consequently,
parametric MDPs (pMDPs) extend MDPs with transition probabilities that are
functions over unspecified parameters. The parameter synthesis problem is to
compute an instantiation of these unspecified parameters such that the
resulting MDP satisfies the temporal logic specification. We formulate the
parameter synthesis problem as a quadratically constrained quadratic program
(QCQP), which is nonconvex and is NP-hard to solve in general. We develop two
approaches that iteratively obtain locally optimal solutions. The first
approach exploits the so-called convex-concave procedure (CCP), and the second
approach utilizes a sequential convex programming (SCP) method. The techniques
improve the runtime and scalability by multiple orders of magnitude compared to
black-box CCP and SCP by merging ideas from convex optimization and
probabilistic model checking. We demonstrate the approaches on a satellite
collision avoidance problem with hundreds of thousands of states and tens of
thousands of parameters and their scalability on a wide range of commonly used
benchmarks.


Abstract:
  To enhance adversarial robustness, adversarial training learns deep neural
networks on the adversarial variants generated by their natural data. However,
as the training progresses, the training data becomes less and less attackable,
undermining the robustness enhancement. A straightforward remedy is to
incorporate more training data, but sometimes incurring an unaffordable cost.
In this paper, to mitigate this issue, we propose the guided interpolation
framework (GIF): in each epoch, the GIF employs the previous epoch's meta
information to guide the data's interpolation. Compared with the vanilla mixup,
the GIF can provide a higher ratio of attackable data, which is beneficial to
the robustness enhancement; it meanwhile mitigates the model's linear behavior
between classes, where the linear behavior is favorable to generalization but
not to the robustness. As a result, the GIF encourages the model to predict
invariantly in the cluster of each class. Experiments demonstrate that the GIF
can indeed enhance adversarial robustness on various adversarial training
methods and various datasets.


Abstract:
  Purpose: to assess the efficacy of THEIA, an artificial intelligence for
screening diabetic retinopathy in a multi-center prospective study. To validate
the potential application of THEIA as clinical decision making assistant in a
national screening program. Methods: 902 patients were recruited from either an
urban large eye hospital, or a semi-rural optometrist led screening provider,
as they were attending their appointment as part of New Zealand Diabetic
Screening programme. These clinics used a variety of retinal cameras and a
range of operators. The de-identified images were then graded independently by
three senior retinal specialists, and final results were aggregated using New
Zealand grading scheme, which is then converted to referable\non-referable and
Healthy\mild\more than mild\vision threatening categories. Results: compared to
ground truth, THEIA achieved 100% sensitivity and [95.35%-97.44%] specificity,
and negative predictive value of 100%. THEIA also did not miss any patients
with more than mild or vision threatening disease. The level of agreement
between the clinicians and the aggregated results was (k value: 0.9881, 0.9557,
and 0.9175), and the level of agreement between THEIA and the aggregated labels
was (k value: 0.9515). Conclusion: Our multi-centre prospective trial showed
that THEIA does not miss referable disease when screening for diabetic
retinopathy and maculopathy. It also has a very high level of granularity in
reporting the disease level. Since THEIA is being tested on a variety of
cameras, operating in a range of clinics (rural\urban,
ophthalmologist-led\optometrist-led), we believe that it will be a suitable
addition to a public diabetic screening program.


Abstract:
  We present a map from the travelling salesman problem (TSP), a prototypical
NP-complete combinatorial optimisation task, to the ground state associated
with a system of many-qudits. Conventionally, the TSP is cast into a quadratic
unconstrained binary optimisation (QUBO) problem, that can be solved on an
Ising machine. The size of the corresponding physical system's Hilbert space is
$2^{N^2}$, where $N$ is the number of cities considered in the TSP. Our
proposal provides a many-qudit system with a Hilbert space of dimension
$2^{N\log_2N}$, which is considerably smaller than the dimension of the Hilbert
space of the system resulting from the usual QUBO map. This reduction can yield
a significant speedup in quantum and classical computers. We simulate and
validate our proposal using variational Monte Carlo with a neural quantum
state, solving the TSP in a linear layout for up to almost 100 cities.


Abstract:
  It is known in Hilbert space frame theory that a Bessel sequence can be
expanded to a frame. Contrary to Hilbert space situation, using a result of
Casazza and Christensen, we show that there are Banach spaces and approximate
Bessel sequences which can not be expanded to approximate Schauder frames. We
characterize Banach spaces in which one can expand approximate Bessel sequences
to approximate Schauder frames.


Abstract:
  This analysis presents the possibility for the search for Dark Matter (DM)
particles using events with a Z$^{\prime}$ heavy gauge boson and a large
missing transverse momentum at the Large Hadron Collider (LHC). We consider the
muonic decay of Z$^{\prime}$. The analyzed Monte Carlo samples were the Open
simulated files produced by the CMS collaboration for proton-proton collisions
correspond to an integrated luminosity of the LHC run-I with 19.7 fb$^{-1}$ at
$\sqrt{s} = $ 8 TeV. Two scenarios, one simplified benchmark scenario so called
Dark Higgs and the effective field theory (EFT) formalism, were used for
interpretations. Limits are set on both Z$^{\prime}$, dark matter masses and
the cutoff scale of the EFT.


Abstract:
  This paper proposes an accelerated method for approximately solving partially
observable Markov decision process (POMDP) problems offline. Our method
carefully combines two existing tools: Anderson acceleration (AA) and the fast
informed bound (FIB) method. Adopting AA, our method rapidly solves an
approximate Bellman equation with an efficient combination of previous solution
estimates. Furthermore, the use of FIB alleviates the scalability issue
inherent in POMDPs. We show the convergence of the overall algorithm to the
suboptimal solution obtained by FIB. We further consider a simulation-based
method and prove that the approximation error is bounded explicitly. The
performance of our algorithm is evaluated on several benchmark problems. The
results of our experiments demonstrate that the proposed algorithm converges
significantly faster without degrading the quality of the solution compared to
its standard counterpart.


Abstract:
  Today's mobile devices contain densely packaged system-on-chips (SoCs) with
multi-core, high-frequency CPUs and complex pipelines. In parallel,
sophisticated SoC-assisted security mechanisms have become commonplace for
protecting device data, such as trusted execution environments, full-disk and
file-based encryption. Both advancements have dramatically complicated the use
of conventional physical attacks, requiring the development of specialised
attacks. In this survey, we consolidate recent developments in physical fault
injections and side-channel attacks on modern mobile devices. In total, we
comprehensively survey over 50 fault injection and side-channel attack papers
published between 2009-2021. We evaluate the prevailing methods, compare
existing attacks using a common set of criteria, identify several challenges
and shortcomings, and suggest future directions of research.


Abstract:
  The neutronic properties of Molten Salt Reactor are different from that of
traditional solid-fuel reactors due to its nuclear fuel particularity. Based
upon MCNP code, the influence of the size and shape of fuel salt channel on
neutron physics of MSR cell was studied systematically in this work. The
results show that the infinite multiplication factors increases first and then
decreases with the change of graphite cell size under the condition of given
fuel volume fraction. In the case of the same FVF and average chord length,
when the average chord length is relatively small, the k values with different
fuel salt channel shapes are in good agreement; when the average chord length
is relatively large, the k values with different fuel salt channel shapes are
greatly different. In addition, some examples of practical application of this
work are illustrated in the end, including cell selection for the core and
thermal expansion displacement analysis of the cell.


Abstract:
  In this paper a variation of the classic vector quantization problem is
considered. In the standard formulation, a quantizer is designed to minimize
the distortion between input and output when the number of reconstruction
points is fixed. We consider, instead, the scenario in which the number of
comparators used in quantization is fixed. More precisely, we study the case in
which a vector quantizer of dimension d is comprised of k comparators, each
receiving a linear combination of the inputs and producing the output value
one/zero if this linear combination is above/below a certain threshold. In
reconstruction, the comparators' output is mapped to a reconstruction point,
chosen so as to minimize a chosen distortion measure between the quantizer
input and its reconstruction. The Comparison-Limited Vector Quantization (CLVQ)
problem is then defined as the problem of optimally designing the configuration
of the compactors and the choice of reconstruction points so as to minimize the
given distortion. In this paper, we design a numerical optimization algorithm
for the CLVQ problem. This algorithm leverages combinatorial geometrical
notions to describe the hyperplane arrangement induced by the configuration of
the comparators. It also relies on a genetic genetic meta heuristic to improve
the selection of the quantizer initialization and avoid local minima
encountered during optimization. We numerically evaluate the performance of our
algorithm in the case of input distributions following uniform and Gaussian
i.i.d. sources to be compressed under quadratic distortion and compare it to
the classic Linde-Buzo-Gray (LBG) algorithm.


Abstract:
  We study the general properties of the moduli spaces of SO(3) vortices over
orbifold Riemann surfaces and use these to characterize the solutions of the
SO(3) monopole equations on Seifert manifolds following in the footsteps of
Mrowka, Ozsv\'ath and Yu. We also study the solutions to the SO(3) monopole
equations on S1 x (Riemann Surface) in order to motivate the construction of a
version of monopole Floer homology, which we call framed monopole Floer
homology, in analogy with the construction given by Kronheimer and Mrowka for
the case of instanton Floer homology. Finally, the SO(3) vortex moduli spaces
provide a nice toy model for recent work due to Feehan and Leness regarding the
study of a natural Morse-Bott function on the moduli space of SO(3) monopoles
over Kahler manifolds. In particular, we compute the Morse-Bott indices of this
function.


Abstract:
  In medical and biological research, longitudinal data and survival data types
are commonly seen. Traditional statistical models mostly consider to deal with
either of the data types, such as linear mixed models for longitudinal data,
and the Cox models for survival data, while they do not adjust the association
between these two different data types. It is desirable to have a joint
modeling approach which accomadates both data types and the dependency between
them. In this paper, we extend traditional single-index models to a new joint
modeling approach, by replacing the single-index component to a varying
coefficient component to deal with longitudinal outcomes, and accomadate the
random censoring problem in survival analysis by nonparametric synthetic data
regression for the link function. Numerical experiments are conducted to
evaluate the finite sample performance.


Abstract:
  For a finitely generated group $G$ and collection of subgroups $\mathcal{P}$
we prove that the relative Dehn function of a pair $(G,\mathcal{P})$ is
invariant under quasi-isometry of pairs. Along the way we show quasi-isometries
of pairs preserve almost malnormality of the collection and fineness of the
associated coned off Cayley graphs. We also prove that for a cocompact simply
connected combinatorial $G$-$2$-complex $X$ with finite edge stabilisers, the
combinatorial Dehn function is well-defined if and only if the $1$-skeleton of
$X$ is fine.
  We also show that if $H$ is a hyperbolically embedded subgroup of a finitely
presented group $G$, then the relative Dehn function of the pair $(G, H)$ is
well-defined. In the appendix, it is shown that show that the Baumslag-Solitar
group $\mathrm{BS}(k,l)$ has a well-defined Dehn function with respect to the
cyclic subgroup generated by the stable letter if and only if neither $k$
divides $l$ nor $l$ divides $k$.


Abstract:
  Magnetic Resonance Imaging (MRI) is a vital component of medical imaging.
When compared to other image modalities, it has advantages such as the absence
of radiation, superior soft tissue contrast, and complementary multiple
sequence information. However, one drawback of MRI is its comparatively slow
scanning and reconstruction compared to other image modalities, limiting its
usage in some clinical applications when imaging time is critical. Traditional
compressive sensing based MRI (CS-MRI) reconstruction can speed up MRI
acquisition, but suffers from a long iterative process and noise-induced
artefacts. Recently, Deep Neural Networks (DNNs) have been used in sparse MRI
reconstruction models to recreate relatively high-quality images from heavily
undersampled k-space data, allowing for much faster MRI scanning. However,
there are still some hurdles to tackle. For example, directly training DNNs
based on L1/L2 distance to the target fully sampled images could result in
blurry reconstruction because L1/L2 loss can only enforce overall image or
patch similarity and does not take into account local information such as
anatomical sharpness. It is also hard to preserve fine image details while
maintaining a natural appearance. More recently, Generative Adversarial
Networks (GAN) based methods are proposed to solve fast MRI with enhanced image
perceptual quality. The encoder obtains a latent space for the undersampling
image, and the image is reconstructed by the decoder using the GAN loss. In
this chapter, we review the GAN powered fast MRI methods with a comparative
study on various anatomical datasets to demonstrate the generalisability and
robustness of this kind of fast MRI while providing future perspectives.


Abstract:
  Diamond quantum thermometry exploits the optical and electrical spin
properties of colour defect centres in diamonds and, acts as a quantum sensing
method exhibiting ultrahigh precision and robustness. Compared to the existing
luminescent nanothermometry techniques, a diamond quantum thermometer can be
operated over a wide temperature range and a sensor spatial scale ranging from
nanometres to micrometres. Further, diamond quantum thermometry is employed in
several application, including electronics and biology, to explore these fields
with nanoscale temperature measurements. This review covers the operational
principles of diamond quantum thermometry for spin-based and all-optical
methods, material development of diamonds with a focus on thermometry, and
examples of applications in electrical and biological systems with demand-based
technological requirements.


Abstract:
  The SARS-CoV-2 virus and COVID-19 disease have posed unprecedented and
overwhelming demand, challenges and opportunities to domain, model and data
driven modeling. This paper provides a comprehensive review of the challenges,
tasks, methods, progress, gaps and opportunities in relation to modeling
COVID-19 problems, data and objectives. It constructs a research landscape of
COVID-19 modeling tasks and methods, and further categorizes, summarizes,
compares and discusses the related methods and progress of modeling COVID-19
epidemic transmission processes and dynamics, case identification and tracing,
infection diagnosis and medical treatments, non-pharmaceutical interventions
and their effects, drug and vaccine development, psychological, economic and
social influence and impact, and misinformation, etc. The modeling methods
involve mathematical and statistical models, domain-driven modeling by
epidemiological compartmental models, medical and biomedical analysis, AI and
data science in particular shallow and deep machine learning, simulation
modeling, social science methods, and hybrid modeling.


Abstract:
  In this paper, we investigate if we could make the self-training -- a simple
but popular framework -- work better for semi-supervised segmentation. Since
the core issue in semi-supervised setting lies in effective and efficient
utilization of unlabeled data, we notice that increasing the diversity and
hardness of unlabeled data is crucial to performance improvement. Being aware
of this fact, we propose to adopt the most plain self-training scheme coupled
with appropriate strong data augmentations on unlabeled data (namely ST) for
this task, which surprisingly outperforms previous methods under various
settings without any bells and whistles. Moreover, to alleviate the negative
impact of the wrongly pseudo labeled images, we further propose an advanced
self-training framework (namely ST++), that performs selective re-training via
selecting and prioritizing the more reliable unlabeled images. As a result, the
proposed ST++ boosts the performance of semi-supervised model significantly and
surpasses existing methods by a large margin on the Pascal VOC 2012 and
Cityscapes benchmark. Overall, we hope this straightforward and simple
framework will serve as a strong baseline or competitor for future works. Code
is available at https://github.com/LiheYoung/ST-PlusPlus.


Abstract:
  The terahertz current generated by a photoconductive device (PCD) saturates
as the power of the input optical pump is increased. This behavior is induced
by various screening effects that stem from the interactions between
electromagnetic (EM) fields and semiconductor carriers. In this work, these
screening effects are numerically analyzed for the first time using a
fully-coupled multiphysics approach. Unlike the previously developed simulation
frameworks, this approach rigorously models the nonlinear coupling between the
EM fields and the carriers and therefore is capable of accounting for the
screening effects. It is demonstrated that the results obtained using this
multiphysics approach and actual experiments are in excellent agreement. The
optical- and radiation-field screening effects are identified in the simulation
results and the optical-field screening is found to play a more dominant role
in the saturation of the PCD output under high optical pump power levels.


Abstract:
  Convolutional neural networks are very popular nowadays. Training neural
networks is not an easy task. Each convolution corresponds to a structured
transformation matrix. In order to help avoid the exploding/vanishing gradient
problem, it is desirable that the singular values of each transformation matrix
are not large/small in the training process. We propose three new
regularization terms for a convolutional kernel tensor to constrain the
singular values of each transformation matrix. We show how to carry out the
gradient type methods, which provides new insight about the training of
convolutional neural networks.


Abstract:
  We propose a data-driven model order reduction (MOR) technique for
parametrized partial differential equations that exhibit parameter-dependent
jump-discontinuities. Such problems have poor-approximability in a linear space
and therefore, are challenging for standard MOR techniques. We build upon the
methodology of approximating the map between the parameter domain and the
expansion coefficients of the reduced basis via regression. The online stage
queries the regression model for the expansion coefficients and recovers a
reduced approximation for the solution. We propose to apply this technique to a
transformed solution that results from composing the solution with a spatial
transform. Unlike the (untransformed) solution, it is sufficiently regular
along the parameter domain and thus, is well-approximable in a low-dimensional
linear space. To recover an approximation for the (untransformed) solution, we
propose an online efficient regression-based technique that approximates the
inverse of the spatial transform. Our method features a decoupled online and
offline stage, and benchmark problems involving hyperbolic and parabolic
equations demonstrate its effectiveness.


Abstract:
  We determine the irreducible components of Igusa varieties for Shimura
varieties of Hodge type and use that to determine the irreducible components of
central leaves. In particular, we show that the discrete Hecke-orbit conjecture
is false in general. Our method combines recent work of D'Addezio on monodromy
of compatible local systems with a generalisation of a method of Hida, using
the Honda-Tate theory for Shimura varieties of Hodge type developed by
Kisin-Madapusi Pera-Shin. We also determine the irreducible components of
Newton strata in Shimura varieties of Hodge type by combining our results with
recent work of Zhou-Zhu.


Abstract:
  Over-the-air computation (AirComp) has been recognized as a low-latency
solution for wireless sensor data fusion, where multiple sensors send their
measurement signals to a receiver simultaneously for computation. Most existing
work only considered performing AirComp over a single frequency channel.
However, for a sensor network with a massive number of nodes, a single
frequency channel may not be sufficient to accommodate the large number of
sensors, and the AirComp performance will be very limited. So it is highly
desirable to have more frequency channels for large-scale AirComp systems to
benefit from multi-channel diversity. In this letter, we propose an
$M$-frequency AirComp system, where each sensor selects a subset of the $M$
frequencies and broadcasts its signal over these channels under a certain power
constraint. We derive the optimal sensors' transmission and receiver's signal
processing methods separately, and develop an algorithm for joint design to
achieve the best AirComp performance. Numerical results show that increasing
one frequency channel can improve the AirComp performance by threefold compared
to the single-frequency case.


Abstract:
  Exceptional points are a ubiquitous concept widely present in
driven-dissipative coupled systems described by a non-Hermitian Hamiltonian. It
is characterized by the degeneracy of the Hamiltonian's eigenvalues and
coalescence of corresponding eigenvectors. Recent developments demonstrated
that exceptional points can play an important role in photonics. However, to
date, exceptional points have been extensively examined in the systems
supporting only a few optical modes, thereby leaving the observation of
collective (multimode) effects outside of the scope of study. In the present
paper, we analyze the role of exceptional points in nonlinear multimode
photonics. Specifically, we provide insights into complex nonlinear dynamics
arising in a continuous wave-driven pair of strongly coupled nonlinear
micro-resonators (i.e. a nonlinear photonic dimer) operating in the multimode
regime. Investigating this system, which is known to possess exceptional
points, we find two fundamentally different nonlinear regimes of operation
corresponding to effective parity-time symmetric and broken parity-time
symmetry states. We demonstrate that the photonic dimer can be critically
coupled to a bus waveguide, thereby, providing an efficient generation of the
dissipative Kerr solitons on both sides of the exceptional point. The
parity-time symmetric case, which corresponds to a pair of symmetrically split
resonances, has been recently shown to exhibit a variety of emergent phenomena
including gear soliton generation, symmetry breaking, and soliton hopping.
Dissipative solitons generation in the parity-time symmetry broken case -
leading to the dissipation splitting - up to now remains unexplored.


Abstract:
  Recent experiments suggest the possibility to tune superconductivity in
metallic nanowires by application of modest gate voltages. It is largely
debated whether the effect is due to an electric field at the superconductor
surface or small currents of high-energy electrons. We shed light on this
matter by studying the suppression of superconductivity in sample geometries
where the roles of electric field and electron-current flow can be clearly
separated. Our results show that suppression of superconductivity does not
depend on the presence or absence of an electric field at the surface of the
nanowire, but requires a current of high-energy electrons. The suppression is
most efficient when electrons are injected into the nanowire, but similar
results are obtained also when electrons are passed between two remote
electrodes at a distance $d$ to the nanowire (with $d$ in excess of
$1~\mathrm{\mu m}$). In the latter case, high-energy electrons decay into
phonons which propagate through the substrate and affect superconductivity in
the nanowire by generating quasiparticles. We show that this process involves a
non-thermal phonon distribution, with marked differences from the loss of
superconductivity due to Joule heating near the nanowire or an increase in the
bath temperature.