Abstract:
  The area of computing with uncertainty considers problems where some
information about the input elements is uncertain, but can be obtained using
queries. For example, instead of the weight of an element, we may be given an
interval that is guaranteed to contain the weight, and a query can be performed
to reveal the weight. While previous work has considered models where queries
are asked either sequentially (adaptive model) or all at once (non-adaptive
model), and the goal is to minimize the number of queries that are needed to
solve the given problem, we propose and study a new model where $k$ queries can
be made in parallel in each round, and the goal is to minimize the number of
query rounds. We use competitive analysis and present upper and lower bounds on
the number of query rounds required by any algorithm in comparison with the
optimal number of query rounds. Given a set of uncertain elements and a family
of $m$ subsets of that set, we present an algorithm for determining the value
of the minimum of each of the subsets that requires at most $(2+\varepsilon)
\cdot \mathrm{opt}_k+\mathrm{O}\left(\frac{1}{\varepsilon} \cdot \lg m\right)$
rounds for every $0<\varepsilon<1$, where $\mathrm{opt}_k$ is the optimal
number of rounds, as well as nearly matching lower bounds. For the problem of
determining the $i$-th smallest value and identifying all elements with that
value in a set of uncertain elements, we give a $2$-round-competitive
algorithm. We also show that the problem of sorting a family of sets of
uncertain elements admits a $2$-round-competitive algorithm and this is the
best possible.


Abstract:
  Non-Abelian excitations are an interesting feature of many fractional quantum
Hall phases, including those phases described by the Moore-Read (or Pfaffian)
wave function. However, the detection of the non-Abelian quasiparticles is
challenging. Here, we consider a system described by the Moore-Read wave
function, and assume that impurity particles bind to its quasiholes. Then, the
angular momentum of the impurities, reflected also by the impurity density,
provides a useful witness of the physics of the non-Abelian excitations. By
demanding that the impurities are constrained to the lowest Landau level, we
are able to write down the corresponding many-body wave function describing
both the Moore-Read liquid and the impurities. Through Monte Carlo sampling we
determine the impurity angular momentum, and we show that it suggests a
quantum-statistical parameter $\alpha = a\nu -b +P/2$ for the quasiholes, where
$\alpha$ ranges from $0$ for bosons to $1$ for fermions. A reasonable agreement
with the Monte Carlo results is obtained for $a=1/4$, $b=1/8$ and $P=0,1$
depending on the parity of the particle number in the Moore-Read liquid. This
parity-dependence of the angular momentum serves as an unambiguous
demonstration of the non-Abelian nature of the excitations. In addition to the
studies of excitations in the Moore-Read liquid, we also apply our scheme to
Laughlin liquids, for which we focus on interacting bosonic impurities. With
this, the impurities themselves form Laughlin states, which allows for a study
of hierarchical fractional quantum Hall states.


Abstract:
  From the Lytchak's result for polar foliations on an irreducible simply
connected symmetric space $G/K$ of compact type and rank greater than one, we
can derive that there exists no equifocal submanifold with non-flat section
whose codimension is greater than two in the symmetric space $G/K$. In the
first-half part of this paper, we give a new proof of this non-existence
theorem. The recipi of our new proof is as follows. Suppose that there exists
an equifocal submanifold $M$ with non-flat section whose codimension is greater
than two in an irreducible symmertric space $G/K$ of compact type and rank
greater than one. We introduce the notion of a slice topology of $G/K$
associated to $M$. We consider the universal covering $\pi:\widehat{G/K}\to
G/K$ of the slice topological space $G/K$ and give $\widehat{G/K}$ the manifold
structure and the Riemannian metric such that $\pi$ is a Riemannian submersion
onto the symmetric space $G/K$. First we show that a simplicial decomposition
of the Riemannian manifold $\widehat{G/K}$ gives an irreducible topological
Tits building of spherical type and rank greater than two. By applying
Burns-Spatzier's theorem to this topological Tits building, we show that the
Riemannian manifold $\widehat{G/K}$ is homothetic to the unit sphere.
Furthermore, from this fact, we show that $G/K$ is isometric to a sphere, a
complex projective space or a quaternionic projective space. This contradicts
that $G/K$ is of rank greater than one. This is the recipi of our proof. In the
second-half part, we estimate the codimension of $M$ from above by using the
multiplicities of the roots of the root system of $G/K$. As its result, we can
show that there exists no equifocal submanifold with non-flat section in some
irreducible simply connected symmetric spaces of compact type.


Abstract:
  The entropy produced when a quantum system is driven away from equilibrium
can be decomposed in two parts, one related with populations and the other with
quantum coherences. The latter is usually based on the so-called relative
entropy of coherence, a widely used quantifier in quantum resource theories. In
this paper we argue that, despite satisfying fluctuation theorems and having a
clear resource-theoretic interpretation, this splitting has shortcomings.
First, it predicts that at low temperatures the entropy production will always
be dominated by the classical term, irrespective of the quantum nature of the
process. Second, for infinitesimal quenches, the radius of convergence diverges
exponentially as the temperature decreases, rendering the functions
non-analytic. Motivated by this, we provide here a complementary approach,
where the entropy production is split in a way such that the contributions from
populations and coherences are written in terms of a thermal state of a
specially dephased Hamiltonian. The physical interpretation of our proposal is
discussed in detail. We also contrast the two approaches by studying work
protocols in a transverse field Ising chain, and a macrospin of varying
dimension.


Abstract:
  The segmentation of data into stationary stretches also known as multiple
change point problem is important for many applications in time series analysis
as well as signal processing. Based on strong invariance principles, we analyse
data segmentation methodology using moving sum (MOSUM) statistics for a class
of regime-switching multivariate processes where each switch results in a
change in the drift. In particular, this framework includes the data
segmentation of multivariate partial sum, integrated diffusion and renewal
processes even if the distance between change points is sublinear. We study the
asymptotic behaviour of the corresponding change point estimators, show
consistency and derive the corresponding localisation rates which are minimax
optimal in a variety of situations including an unbounded number of changes in
Wiener processes with drift. Furthermore, we derive the limit distribution of
the change point estimators for local changes - a result that can in principle
be used to derive confidence intervals for the change points.


Abstract:
  We introduce a notion of compatibility for families
$(\mathcal{F}_{\ell})_{\ell}$ of bounded constructible $\ell$-adic complexes of
\'etale sheaves on schemes. For schemes of finite type over a field, this
notion is preserved by the usual six functors. We prove that the compatibility
of a family is preserved by the nearby cycles functor and by the linearized
$\varepsilon$-factors introduced recently by the author. We establish
independence of $\ell$ for the characteristic cycles and characteristic
$\varepsilon$-cycles of compatible families.


Abstract:
  Models of chemical enrichment and inhomogeneity in high-redshift galaxies are
challenging to constrain observationally. In this work, we discuss a novel
approach to probe chemical inhomogeneities within long Gamma-Ray Burst (GRB)
host galaxies, by comparing the absorption metallicity, Z_abs, from the GRB
afterglow (which probes the environment along the line of sight) with the
emission-line metallicity, Z_emiss, measured via slit spectroscopy. Using the
IllustrisTNG simulation, the theoretical relationship between these metallicity
metrics is explored for a range of GRB formation models, varying the GRB
progenitor metallicity threshold. For galaxies with fixed Z_emiss, the median
value of Z_abs depends strongly on the GRB progenitor threshold metallicity,
with Z_abs significantly lower than Z_emiss for high metallicity hosts.
Conversely, at fixed Z_abs, the median value of Z_emiss depends primarily on
the metallicity distribution of galaxies in IllustrisTNG and their chemical
inhomogeneities, offering a GRB-model-independent way to constrain these
processes observationally. Currently, only one host galaxy has data for both
absorption and emission metallicities (GRB121014A). We re-analyse the emission
spectrum and compare the inferred metallicity Z_emiss to a recent Bayesian
determination of Z_abs, finding $\log(Z_{\rm emiss}/Z_{\odot}) = \log(Z_{\rm
abs}/Z_{\odot}) +0.35^{+ 0.14}_{- 0.25}$, within ~2 standard deviations of
predictions from the IllustrisTNG simulation. Future observations with the
James Webb Space Telescope will be able to measure Z_emiss for 4 other GRB
hosts with known Z_abs values, using ~2 hour observations. While small, the
sample will provide preliminary constraints on the Z_abs-Z_emiss relation to
test chemical enrichment schemes in cosmological simulations.


Abstract:
  The plethora of photometric data collected by the Kepler space telescope has
promoted the detection of tens of thousands of stellar rotation periods.
However, these periods are not found to an equal extent among different
spectral types. Interestingly, early G-type stars with near-solar rotation
periods are strongly underrepresented among those stars with known rotation
periods. In this study we investigate whether the small number of such stars
can be explained by difficulties in the period determination from photometric
time series. For that purpose, we generate model light curves of early G-type
stars with solar rotation periods for different inclination angles,
metallicities and (magnitude-dependent) noise levels. We find that the
detectability is determined by the predominant type of activity (i.e. spot or
faculae domination) on the surface, which defines the degree of irregularity of
the light curve, and further depends on the level of photometric noise. These
two effects significantly complicate the period detection and explain the lack
of solar-like stars with known near-solar rotation periods. We conclude that
the rotation periods of the majority of solar-like stars with near-solar
rotation periods remain undetected to date. Finally, we promote the use of new
techniques to recover more periods of near-solar rotators.


Abstract:
  Smart Contracts are software programs that are deployed and executed within a
blockchain infrastructure. Due to their immutable nature, directly resulting
from the specific characteristics of the deploying infrastructure, smart
contracts must be thoroughly tested before their release. Testing is one of the
main activities that can help to improve the reliability of a smart contract,
so as to possibly prevent considerable loss of valuable assets. It is therefore
important to provide the testers with tools that permit them to assess the
activity they performed. Mutation testing is a powerful approach for assessing
the fault-detection capability of a test suite. In this paper, we propose SuMo,
a novel mutation testing tool for Ethereum Smart Contracts. SuMo implements a
set of 44 mutation operators that were designed starting from the latest
Solidity documentation, and from well-known mutation testing tools. These allow
to simulate a wide variety of faults that can be made by smart contract
developers. The set of operators was designed to limit the generation of
stillborn mutants, which slow down the mutation testing process and limit the
usability of the tool. We report a first evaluation of SuMo on open-source
projects for which test suites were available. The results we got are
encouraging, and they suggest that SuMo can effectively help developers to
deliver more reliable smart contracts.


Abstract:
  In this paper, we present SANTA, a scalable framework to automatically
normalize E-commerce attribute values (e.g. "Win 10 Pro") to a fixed set of
pre-defined canonical values (e.g. "Windows 10"). Earlier works on attribute
normalization focused on fuzzy string matching (also referred as syntactic
matching in this paper). In this work, we first perform an extensive study of
nine syntactic matching algorithms and establish that 'cosine' similarity leads
to best results, showing 2.7% improvement over commonly used Jaccard index.
Next, we argue that string similarity alone is not sufficient for attribute
normalization as many surface forms require going beyond syntactic matching
(e.g. "720p" and "HD" are synonyms). While semantic techniques like
unsupervised embeddings (e.g. word2vec/fastText) have shown good results in
word similarity tasks, we observed that they perform poorly to distinguish
between close canonical forms, as these close forms often occur in similar
contexts. We propose to learn token embeddings using a twin network with
triplet loss. We propose an embedding learning task leveraging raw attribute
values and product titles to learn these embeddings in a self-supervised
fashion. We show that providing supervision using our proposed task improves
over both syntactic and unsupervised embeddings based techniques for attribute
normalization. Experiments on a real-world attribute normalization dataset of
50 attributes show that the embeddings trained using our proposed approach
obtain 2.3% improvement over best string matching and 19.3% improvement over
best unsupervised embeddings.


Abstract:
  When a deep learning model is deployed in the wild, it can encounter test
data drawn from distributions different from the training data distribution and
suffer drop in performance. For safe deployment, it is essential to estimate
the accuracy of the pre-trained model on the test data. However, the labels for
the test inputs are usually not immediately available in practice, and
obtaining them can be expensive. This observation leads to two challenging
tasks: (1) unsupervised accuracy estimation, which aims to estimate the
accuracy of a pre-trained classifier on a set of unlabeled test inputs; (2)
error detection, which aims to identify mis-classified test inputs. In this
paper, we propose a principled and practically effective framework that
simultaneously addresses the two tasks. The proposed framework iteratively
learns an ensemble of models to identify mis-classified data points and
performs self-training to improve the ensemble with the identified points.
Theoretical analysis demonstrates that our framework enjoys provable guarantees
for both accuracy estimation and error detection under mild conditions readily
satisfied by practical deep learning models. Along with the framework, we
proposed and experimented with two instantiations and achieved state-of-the-art
results on 59 tasks. For example, on iWildCam, one instantiation reduces the
estimation error for unsupervised accuracy estimation by at least 70% and
improves the F1 score for error detection by at least 4.7% compared to existing
methods.


Abstract:
  This short note revisit information metric, underlining that it is a pseudo
metric on manifolds of observables (random variables), rather than as usual on
probability laws. Geodesics are characterized in terms of their boundaries and
conditional independence condition. Pythagorean theorem is given, providing in
special case potentially interesting natural integer triplets. This metric is
computed for illustration on Diabetes dataset using infotopo package.


Abstract:
  Biomedical entity linking is the task of identifying mentions of biomedical
concepts in text documents and mapping them to canonical entities in a target
thesaurus. Recent advancements in entity linking using BERT-based models follow
a retrieve and rerank paradigm, where the candidate entities are first selected
using a retriever model, and then the retrieved candidates are ranked by a
reranker model. While this paradigm produces state-of-the-art results, they are
slow both at training and test time as they can process only one mention at a
time. To mitigate these issues, we propose a BERT-based dual encoder model that
resolves multiple mentions in a document in one shot. We show that our proposed
model is multiple times faster than existing BERT-based models while being
competitive in accuracy for biomedical entity linking. Additionally, we modify
our dual encoder model for end-to-end biomedical entity linking that performs
both mention span detection and entity disambiguation and out-performs two
recently proposed models.


Abstract:
  Spiking Neural Networks (SNNs) have been attached great importance due to
their biological plausibility and high energy-efficiency on neuromorphic chips.
As these chips are usually resource-constrained, the compression of SNNs is
thus crucial along the road of practical use of SNNs. Most existing methods
directly apply pruning approaches in artificial neural networks (ANNs) to SNNs,
which ignore the difference between ANNs and SNNs, thus limiting the
performance of the pruned SNNs. Besides, these methods are only suitable for
shallow SNNs. In this paper, inspired by synaptogenesis and synapse elimination
in the neural system, we propose gradient rewiring (Grad R), a joint learning
algorithm of connectivity and weight for SNNs, that enables us to seamlessly
optimize network structure without retraining. Our key innovation is to
redefine the gradient to a new synaptic parameter, allowing better exploration
of network structures by taking full advantage of the competition between
pruning and regrowth of connections. The experimental results show that the
proposed method achieves minimal loss of SNNs' performance on MNIST and
CIFAR-10 dataset so far. Moreover, it reaches a $\sim$3.5% accuracy loss under
unprecedented 0.73% connectivity, which reveals remarkable structure refining
capability in SNNs. Our work suggests that there exists extremely high
redundancy in deep SNNs. Our codes are available at
https://github.com/Yanqi-Chen/Gradient-Rewiring.


Abstract:
  We propose and analyze computationally a new fictitious domain method, based
on higher order space-time finite element discretizations, for the simulation
of the nonstationary, incompressible Navier-Stokes equations on evolving
domains. The physical domain is embedded into a fixed computational mesh such
that arbitrary intersections of the moving domain's boundaries with the
background mesh occur. The potential of such cut finite element techniques for
higher order space-time finite element methods has rarely been studied in the
literature so far and deserves further elucidation. The key ingredients of the
approach are the weak formulation of Dirichlet boundary conditions by Nitsche's
method, the flexible and efficient integration over all types of intersections
of cells by moving boundaries and the spatial extension of the discrete
physical quantities to the entire computational background mesh including
fictitious (ghost) subdomains of fluid flow. Thereby, an expensive remeshing
and adaptation of the sparse matrix data structure are avoided and the
computations are accelerated. To prevent spurious oscillations caused by
irregular intersections of mesh cells, a penalization, defining also implicitly
the extension to ghost domains, is added. These techniques are embedded in an
arbitrary order, discontinuous Galerkin discretization of the time variable and
an inf-sup stable discretization of the spatial variables. The parallel
implementation of the matrix assembly is described. The optimal order
convergence properties of the algorithm are illustrated in a numerical
experiment for an evolving domain. The well-known 2d benchmark of flow around a
cylinder as well as flow around moving obstacles with arising cut cells and
fictitious domains are considered further.


Abstract:
  Laser-plasma accelerators (LPAs) outperform current radiofrequency technology
in acceleration strength by orders of magnitude. Yet, enabling them to deliver
competitive beam quality for demanding applications, particularly in terms of
energy spread and stability, remains a major challenge. In this Letter, we
propose to combine bunch decompression and active plasma dechirping for
drastically improving the energy profile and stability of beams from LPAs.
Start-to-end simulations demonstrate the efficacy of such post-acceleration
phase-space manipulations and the potential to reduce current state-of-the-art
energy spread and jitter from $1\%$ to $0.10\%$ and $0.024\%$, respectively,
closing the beam-quality gap to conventional acceleration schemes.


Abstract:
  Understanding how massive stars die as supernovae is a crucial question in
modern astrophysics. Supernovae are powerful stellar explosions and key drivers
in the cosmic baryonic cycles by injecting their explosion energy and heavy
elements to the interstellar medium that forms new stars. After decades of
effort, astrophysicists have built up a stand model for the explosion mechanism
of massive stars. However, this model is challenged by new kinds of stellar
explosions discovered in the recent transit surveys. In particular, the new
population called superluminous supernovae, which are a hundred times brighter
than typical supernovae, is revolutionizing our understanding of supernovae.
New studies suggest the superluminous supernovae are associated with the
unusual demise of very massive stars and their extreme supernovae powered by
the radioactive isotopes or compact objects formed after the explosion.
Studying these supernovae fills a gap of knowledge between the death of massive
stars and their explosions; furthermore, we may apply their intense luminosity
to light up the distant universe. This paper aims to provide a timely review of
superluminous supernovae physics, focusing on the latest development of their
theoretical models.


Abstract:
  Learning classifiers that are robust to adversarial examples has received a
great deal of recent attention. A major drawback of the standard robust
learning framework is there is an artificial robustness radius $r$ that applies
to all inputs. This ignores the fact that data may be highly heterogeneous, in
which case it is plausible that robustness regions should be larger in some
regions of data, and smaller in others. In this paper, we address this
limitation by proposing a new limit classifier, called the neighborhood optimal
classifier, that extends the Bayes optimal classifier outside its support by
using the label of the closest in-support point. We then argue that this
classifier maximizes the size of its robustness regions subject to the
constraint of having accuracy equal to the Bayes optimal. We then present
sufficient conditions under which general non-parametric methods that can be
represented as weight functions converge towards this limit, and show that both
nearest neighbors and kernel classifiers satisfy them under certain conditions.


Abstract:
  In this paper we settle the two-dimensional case of a conjecture involving
unknown semialgebraic functions with specified smoothness. More precisely, we
prove the following result: Let $\mathcal{H}$ be a semialgebraic bundle with
respect to $C^m_{loc}\left( \mathbb{R}^{2},\mathbb{R}^{D}\right) .$ If
$\mathcal{H}$ has a section, then it has a semialgebraic section.


Abstract:
  This note is devoted to the study of Hyt\"{o}nen's extrapolation theorem of
compactness on weighted Lebesgue spaces. Two criteria of compactness of linear
operators in the two-weight setting are obtained. As applications, we obtain
two-weight compactness of commutators of Calder\'{o}n--Zygmund operators,
fractional integrals and bilinear Calder\'{o}n--Zygmund operators.


Abstract:
  Online class-incremental continual learning (CL) studies the problem of
learning new classes continually from an online non-stationary data stream,
intending to adapt to new data while mitigating catastrophic forgetting. While
memory replay has shown promising results, the recency bias in online learning
caused by the commonly used Softmax classifier remains an unsolved challenge.
Although the Nearest-Class-Mean (NCM) classifier is significantly undervalued
in the CL community, we demonstrate that it is a simple yet effective
substitute for the Softmax classifier. It addresses the recency bias and avoids
structural changes in the fully-connected layer for new classes. Moreover, we
observe considerable and consistent performance gains when replacing the
Softmax classifier with the NCM classifier for several state-of-the-art replay
methods. To leverage the NCM classifier more effectively, data embeddings
belonging to the same class should be clustered and well-separated from those
with a different class label. To this end, we contribute Supervised Contrastive
Replay (SCR), which explicitly encourages samples from the same class to
cluster tightly in embedding space while pushing those of different classes
further apart during replay-based training. Overall, we observe that our
proposed SCR substantially reduces catastrophic forgetting and outperforms
state-of-the-art CL methods by a significant margin on a variety of datasets.


Abstract:
  The conventional federated learning (FedL) architecture distributes machine
learning (ML) across worker devices by having them train local models that are
periodically aggregated by a server. FedL ignores two important characteristics
of contemporary wireless networks, however: (i) the network may contain
heterogeneous communication/computation resources, while (ii) there may be
significant overlaps in devices' local data distributions. In this work, we
develop a novel optimization methodology that jointly accounts for these
factors via intelligent device sampling complemented by device-to-device (D2D)
offloading. Our optimization aims to select the best combination of sampled
nodes and data offloading configuration to maximize FedL training accuracy
subject to realistic constraints on the network topology and device
capabilities. Theoretical analysis of the D2D offloading subproblem leads to
new FedL convergence bounds and an efficient sequential convex optimizer. Using
this result, we develop a sampling methodology based on graph convolutional
networks (GCNs) which learns the relationship between network attributes,
sampled nodes, and resulting offloading that maximizes FedL accuracy. Through
evaluation on real-world datasets and network measurements from our IoT
testbed, we find that our methodology while sampling less than 5% of all
devices outperforms conventional FedL substantially both in terms of trained
model accuracy and required resource utilization.


Abstract:
  Bayesian computation plays an important role in modern machine learning and
statistics to reason about uncertainty. A key computational challenge in
Bayesian inference is to develop efficient techniques to approximate, or draw
samples from posterior distributions. Stein variational gradient decent (SVGD)
has been shown to be a powerful approximate inference algorithm for this issue.
However, the vanilla SVGD requires calculating the gradient of the target
density and cannot be applied when the gradient is unavailable or too expensive
to evaluate. In this paper we explore one way to address this challenge by the
construction of a local surrogate for the target distribution in which the
gradient can be obtained in a much more computationally feasible manner. More
specifically, we approximate the forward model using a deep neural network
(DNN) which is trained on a carefully chosen training set, which also
determines the quality of the surrogate. To this end, we propose a general
adaptation procedure to refine the local approximation online without
destroying the convergence of the resulting SVGD. This significantly reduces
the computational cost of SVGD and leads to a suite of algorithms that are
straightforward to implement. The new algorithm is illustrated on a set of
challenging Bayesian inverse problems, and numerical experiments demonstrate a
clear improvement in performance and applicability of standard SVGD.


Abstract:
  We determine a characterization of all 2-slices of equivariant spectra over
the Klein four-group $C_2\times C_2$. We then describe all slices of integral
suspensions of the equivariant Eilenberg-MacLane spectrum
$H\underline{\mathbb{Z}}$ for the constant Mackey functor over $C_2\times C_2$.


Abstract:
  Beam stripping losses of H- ion beams by interactions with residual gas and
electromagnetic fields are evaluated. These processes play an important role in
compact cyclotrons where the beam is produced on an internal ion source, and
they operate under high magnetic field. The implementation of stripping
interactions into the beam dynamics code OPAL provides an adequate framework to
estimate the stripping losses for compact cyclotrons such as AMIT. The analysis
is focused on optimizing the high energy beam current delivered to the target.
The optimization is performed by adjusting parameters of the ion source to
regulate the vacuum level inside the accelerator and minimize the beam
stripping losses.


Abstract:
  In the manuscript, we report evidence on broad \oiii components apparently
obscured in Type-2 AGN under the framework of the Unified model, after checking
properties of broad \oiii emissions in large samples of Type-1 and Type-2 AGN
in SDSS DR12. We can well confirm the statistically lower flux ratios of the
broad to the core \oiii components in Type-2 AGN than in Type-1 AGN, which can
be naturally explained by stronger obscured broad \oiii components by central
dust torus in Type-2 AGN, unless the Unified model for AGN was not appropriate
to the narrow emission lines. The results provide further evidence to support
broad \oiii components coming from emission regions nearer to central BHs, and
also indicate the core \oiii component as the better indicator for central
activities in Type-2 AGN, due to few effects of obscuration on the core \oiii
component. Considering the broad \oiii components as signs of central outflows,
the results provide evidence for strong central outflows being preferentially
obscured in Type-2 AGN. Furthermore, the obscured broad \oiii component can be
applied to explain the different flux ratios of \oiiihb between Type-1 and
Type-2 AGN in the BPT diagram.


Abstract:
  We present the collective excitation spectrum analysis of binary
Bose-Einstein condensates (BECs) with spin-orbit (SO) and Rabi couplings in a
quasi-two-dimensional system. In particular, we investigate the role of SO and
Rabi coupling strengths in determining the dynamical stability of the coupled
BECs using Bogoliubov-de Gennes (BdG) theory. Using the eigenergy of BdG
spectrum, we confirm the existence of phonon, roton, and maxon modes with weak
repulsive intra- and inter-species contact interactions. The depth of the
minimum corresponding to the roton mode depends strongly on the coupling
strength. We find that the increase of the SO coupling leads to instability,
while the increase in the Rabi coupling stabilizes the system. Also the
eigenvectors of BdG spectrum indicates the presence of density like mode in the
stable regime and spin like modes in unstable regimes. A phase diagram
demonstrating the stability regime in the plane of SO and Rabi coupling
strengths is obtained. Finally, we complement the observation of the excitation
spectrum with the direct numerical simulation results of coupled
Gross-Pitaevskii equations.


Abstract:
  The Ashtekar-Streubel fluxes give a proposed definition of the angular
momentum emitted by an isolated gravitationally radiating system. This was
based on identifying a "phase space of radiative modes," independent of any
internal degrees of freedom, and using the Hamiltonian functions conjugate to
the action of the Bondi-Metzner-Sachs (BMS) group as the energy-momentum,
supermomentum and angular momentum. However, there are some difficulties in
formulating this phase space so as to get the proper degrees of freedom. I
consider how to address this point, and also to identify circumstances in which
the radiative modes are sufficiently decoupled that they can be assigned their
own angular momentum. Two different phase spaces are considered. One, which
seems to reflect what previous workers have done (it leads to the usual
formulas for the Ashtekar-Streubel fluxes), is mathematically simpler, but this
has unwanted degrees of freedom and is difficult to interpret physically. The
second is a quotient of the first; it is better justified (at least in terms of
degrees of freedom), and plausibly decouples the radiative angular momentum
from internal modes (at least for systems which ultimately become stationary).
The symplectic form for this quotient, and the corresponding angular momentum
flux, involve highly non-local correlations. Both phase spaces are shown to
have Poisson brackets implementing the BMS algebra. For both phase spaces, for
axisymmetric space-times vacuum near null infinity, there can be no
gravitational radiation of angular momentum about the axis of symmetry,
although matter can carry off angular momentum in such cases.


Abstract:
  The emergence of the modern gig economy introduces a new set of employment
considerations for firms and laborers that include various trade-offs. With a
game-theoretical approach, we examine the influences of technology, policy and
markets on firm and worker preferences for gig labor. Theoretically, we present
a new extension to the replicator equation and model oscillating dynamics in
two-player asymmetric bi-matrix games with time-evolving environments,
introducing concepts of the attractor arc, trapping zone and escape. We
demonstrate how changing market conditions result in distinct evolutionary
patterns for gig-labor preferences across high and low skill work-forces, which
we explain through their differing sensitivities to market-driven consumer
demand and financial incentives among other considerations. Informing tensions
regarding the future of this new employment category, we present a novel payoff
framework to analyze the role of technology on the growth of the gig economy.
Finally, we explore regulatory implications within the gig economy,
demonstrating how intervals of lenient and strict policy alter firm and worker
sensitivities between gig and employee labor strategies.


Abstract:
  We study the Closest Pair Problem in Hamming metric, which asks to find the
pair with the smallest Hamming distance in a collection of binary vectors. We
give a new randomized algorithm for the problem on uniformly random input
outperforming previous approaches whenever the dimension of input points is
small compared to the dataset size. For moderate to large dimensions, our
algorithm matches the time complexity of the previously best-known locality
sensitive hashing based algorithms. Technically our algorithm follows similar
design principles as Dubiner (IEEE Trans. Inf. Theory 2010) and May-Ozerov
(Eurocrypt 2015). Besides improving the time complexity in the aforementioned
areas, we significantly simplify the analysis of these previous works. We give
a modular analysis, which allows us to investigate the performance of the
algorithm also on non-uniform input distributions. Furthermore, we give a proof
of concept implementation of our algorithm which performs well in comparison to
a quadratic search baseline. This is the first step towards answering an open
question raised by May and Ozerov regarding the practicability of algorithms
following these design principles.


Abstract:
  Predicting the answer to a product-related question is an emerging field of
research that recently attracted a lot of attention. Answering subjective and
opinion-based questions is most challenging due to the dependency on
customer-generated content. Previous works mostly focused on review-aware
answer prediction; however, these approaches fail for new or unpopular
products, having no (or only a few) reviews at hand. In this work, we propose a
novel and complementary approach for predicting the answer for such questions,
based on the answers for similar questions asked on similar products. We
measure the contextual similarity between products based on the answers they
provide for the same question. A mixture-of-expert framework is used to predict
the answer by aggregating the answers from contextually similar products.
Empirical results demonstrate that our model outperforms strong baselines on
some segments of questions, namely those that have roughly ten or more similar
resolved questions in the corpus. We additionally publish two large-scale
datasets used in this work, one is of similar product question pairs, and the
second is of product question-answer pairs.


Abstract:
  We use categorical methods to define a new flavor of Petri nets where
transitions can only fire a limited number of times, specified by a quantity
that we call mana. We do so with chemistry in mind, looking at ways of
modelling the behavior of chemical reactions that depend on enzymes to work. We
prove that such nets can be either obtained as a result of a comonadic
construction, or by enriching them with extra information encoded into a
functor. We then use a well-established categorical result to prove that the
two constructions are equivalent, and generalize them to the case where the
firing of some transitions can "regenerate" the mana of others. This allows us
to represent the action of catalysts and also of biochemical processes where
the byproducts of some chemical reaction are exactly the enzymes that another
reaction needs to work.


Abstract:
  Multidimensional packing problems generalize the classical packing problems
such as Bin Packing, Multiprocessor Scheduling by allowing the jobs to be
$d$-dimensional vectors. While the approximability of the scalar problems is
well understood, there has been a significant gap between the approximation
algorithms and the hardness results for the multidimensional variants. In this
paper, we close this gap by giving almost tight hardness results for these
problems.
  1. We show that Vector Bin Packing has no polynomial time $\Omega( \log d)$
factor asymptotic approximation algorithm when $d$ is a large constant,
assuming $\textsf{P}\neq \textsf{NP}$. This matches the $\ln d + O(1)$ factor
approximation algorithms (Chekuri, Khanna SICOMP 2004, Bansal, Caprara,
Sviridenko SICOMP 2009, Bansal, Eli\'{a}s, Khan SODA 2016) upto constants.
  2. We show that Vector Scheduling has no polynomial time algorithm with an
approximation ratio of $\Omega\left( (\log d)^{1-\epsilon}\right)$ when $d$ is
part of the input, assuming $\textsf{NP}\nsubseteq \textsf{ZPTIME}\left(
n^{(\log n)^{O(1)}}\right)$. This almost matches the $O\left( \frac{\log
d}{\log \log d}\right)$ factor algorithms(Harris, Srinivasan JACM 2019, Im,
Kell, Kulkarni, Panigrahi SICOMP 2019). We also show that the problem is
NP-hard to approximate within $(\log \log d)^{\omega(1)}$.
  3. We show that Vector Bin Covering is NP-hard to approximate within
$\Omega\left( \frac{\log d}{\log \log d}\right)$ when $d$ is part of the input,
almost matching the $O(\log d)$ factor algorithm (Alon et al., Algorithmica
1998).
  Previously, no hardness results that grow with $d$ were known for Vector
Scheduling and Vector Bin Covering when $d$ is part of the input and for Vector
Bin Packing when $d$ is a fixed constant.


Abstract:
  Regularizers helped deep neural networks prevent feature co-adaptations.
Dropout,as a commonly used regularization technique, stochastically disables
neuron ac-tivations during network optimization. However, such complete feature
disposal can affect the feature representation and network understanding.
Toward betterdescriptions of latent representations, we present DropGraph that
learns regularization function by constructing a stand-alone graph from the
backbone features. DropGraph first samples stochastic spatial feature vectors
and then incorporates graph reasoning methods to generate feature map
distortions. This add-on graph regularizes the network during training and can
be completely skipped during inference. We provide intuitions on the linkage
between graph reasoning andDropout with further discussions on how partial
graph reasoning method reduces feature correlations. To this end, we
extensively study the modeling of graphvertex dependencies and the utilization
of the graph for distorting backbone featuremaps. DropGraph was validated on
four tasks with a total of 7 different datasets.The experimental results show
that our method outperforms other state-of-the-art regularizers while leaving
the base model structure unmodified during inference.


Abstract:
  We extend the (continuous) multivariate Almkvist-Zeilberger algorithm in
order to apply it for instance to special Feynman integrals emerging in
renormalizable Quantum field Theories. We will consider multidimensional
integrals over hyperexponential integrands and try to find closed form
representations in terms of nested sums and products or iterated integrals. In
addition, if we fail to compute a closed form solution in full generality, we
may succeed in computing the first coefficients of the Laurent series
expansions of such integrals in terms of indefinite nested sums and products or
iterated integrals. In this article we present the corresponding methods and
algorithms. Our Mathematica package MultiIntegrate, can be considered as an
enhanced implementation of the (continuous) multivariate Almkvist Zeilberger
algorithm to compute recurrences or differential equations for hyperexponential
integrands and integrals. Together with the summation package Sigma and the
package HarmonicSums our package provides methods to compute closed form
representations (or coefficients of the Laurent series expansions) of
multidimensional integrals over hyperexponential integrands in terms of nested
sums or iterated integrals.


Abstract:
  A common optimization tool used in deep reinforcement learning is momentum,
which consists in accumulating and discounting past gradients, reapplying them
at each iteration. We argue that, unlike in supervised learning, momentum in
Temporal Difference (TD) learning accumulates gradients that become doubly
stale: not only does the gradient of the loss change due to parameter updates,
the loss itself changes due to bootstrapping. We first show that this
phenomenon exists, and then propose a first-order correction term to momentum.
We show that this correction term improves sample efficiency in policy
evaluation by correcting target value drift. An important insight of this work
is that deep RL methods are not always best served by directly importing
techniques from the supervised setting.


Abstract:
  We propose a system to capture nearly-synchronous frame streams from multiple
and moving handheld mobiles that is suitable for dynamic object 3D
reconstruction. Each mobile executes Simultaneous Localisation and Mapping
on-board to estimate its pose, and uses a wireless communication channel to
send or receive synchronisation triggers. Our system can harvest frames and
mobile poses in real time using a decentralised triggering strategy and a
data-relay architecture that can be deployed either at the Edge or in the
Cloud. We show the effectiveness of our system by employing it for 3D skeleton
and volumetric reconstructions. Our triggering strategy achieves equal
performance to that of an NTP-based synchronisation approach, but offers higher
flexibility, as it can be adjusted online based on application needs. We
created a challenging new dataset, namely 4DM, that involves six handheld
augmented reality mobiles recording an actor performing sports actions
outdoors. We validate our system on 4DM, analyse its strengths and limitations,
and compare its modules with alternative ones.


Abstract:
  Global 21cm experiments aim to measure the sky averaged HI absorption signal
from cosmic dawn and the epoch of reionisation. However, antenna chromaticity
coupling to bright foregrounds can introduce distortions into the observational
data of such experiments. We demonstrate a method for guiding the antenna
design of a global experiment through data analysis simulations. This is done
by performing simulated observations for a range of inserted 21cm signals, then
attempting to identify the signals with a data analysis pipeline. We
demonstrate this method on five antennae that were considered as potential
designs for the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH); a
conical log spiral antenna, an inverted conical sinuous antenna and polygonal-,
square- and elliptical-bladed dipoles. We find that the log spiral performs
significantly better than the other antennae tested, able to correctly and
confidently identify every inserted 21cm signal. In second place is the
polygonal dipole antenna, which was only unable to detect signals with both
very low amplitudes of 0.05K and low centre frequency of 80MHz. The conical
sinuous antenna was found to perform least accurately, only able to detect the
highest amplitude 21cm signals, and even then with biases. We also demonstrate
that, due to the non-trivial nature of chromatic distortion and the processes
of correcting for it, these are not the results that could have been expected
superficially from the extent of chromatic variation in each antenna.


Abstract:
  We investigate the time evolution and asymptotic behavior of a system of two
two-level atoms (qubits) interacting off-resonance with a single mode radiation
field. The two atoms are coupled to each other through dipole-dipole as well as
Ising interactions. An exact analytic solution for the system dynamics that
spans the entire phase space is provided. We focus on initial states that cause
the system to evolve to entanglement sudden death (ESD) between the two atoms.
We find that combining the Ising and dipole-dipole interactions is very
powerful in controlling the entanglement dynamics and ESD compared with either
one of them separately. Their effects on eliminating ESD may add up
constructively or destructively depending on the type of Ising interaction
(Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the
initial state of the system. The asymptotic behavior of the ESD is found to
depend substantially on the initial state of the system, where ESD can be
entirely eliminated by tuning the system parameters except in the case of an
initial correlated Bell state. Interestingly, the entanglement, atomic
population and quantum correlation between the two atoms and the field
synchronize and reach asymptotically quasi-steady dynamic states. Each one of
them ends up as a continuous irregular oscillation, where the collapse periods
vanish, with a limited amplitude and an approximately constant mean value that
depend on the initial state and the system parameters choice. This indicates an
asymptotic continuous exchange of energy (and strong quantum correlation)
between the atoms and the field takes place, accompanied by diminished ESD for
these chosen setups of the system. This system can be realized in spin states
of quantum dots or Rydberg atoms in optical cavities, and superconducting or
hybrid qubits in linear resonators.


Abstract:
  In a recent paper [1], it has been claimed that the outcomes of a quantum
coin toss which is idealized as an infinite binary sequence is 1-random. We
also defend the correctness of this claim and assert that the outcomes of
quantum measurements can be considered as an infinite 1-random or n-random
sequence. In this brief note we present our comments on this claim. We have
mostly positive but also some negative comments on the arguments of the paper
[1]. Furthermore, we speculate a logical-axiomatic study of nature which we
believe can intrinsically provide quantum mechanical probabilities based on
1(n)-randomness.


Abstract:
  This is the first part of a series of two papers aiming to construct a
categorification of the braiding on tensor products of Verma modules, and in
particular of the Lawrence--Krammer--Bigelow representations. \\ In this part,
we categorify all tensor products of Verma modules and integrable modules for
quantum $\mathfrak{sl_2}$. The categorification is given by derived categories
of dg versions of KLRW algebras which generalize both the tensor product
algebras of Webster, and the dg-algebras used by Lacabanne, the second author
and Vaz. We compute a basis for these dgKLRW algebras by using rewriting
methods modulo braid-like isotopy, which we develop in an Appendix.


Abstract:
  Let $R$ be a finite commutative ring with unity $1_R$ and $k \in R$.
Properties of one-sided $k$-orthogonal $n \times n$ matrices over $R$ are
presented. When $k$ is idempotent, these matrices form a semigroup structure.
Consequently new families of matrix semigroups over certain finite semi-local
rings are constructed. When $k=1_R$, the classical orthogonal group of degree
$n$ is obtained. It is proved that, if $R$ is a semi-local ring, then these
semigroups are isomorphic to a finite product of $k$-orthogonal semigroups over
fields. Finally, the antiorthogonal and self-orthogonal matrices that give rise
to leading-systematic self-dual or weakly self-dual linear codes are discussed.


Abstract:
  It turned out that the partial sums $g_n(z) = \sum_{k=0}^n \frac{(a_1)_k ...
(a_p)_k}{(b_1)_k ... (b_q)_k} \frac{z^k}{k!}$, of the generalized
hypergeometric series ${}_p F_q(a_1,...,a_p; b_1,...,b_q;z)$, with parameters
$a_j,b_l\in\mathbb{C}\backslash\{ 0,-1,-2,... \}$, are Sobolev orthogonal
polynomials. The corresponding monic polynomials $G_n(z)$ are polynomials of
$R_I$ type, and therefore they are related to biorthogonal rational functions.
Polynomials $g_n$ possess a differential equation (in $z$), and a recurrence
relation (in $n$). We study integral representations for $g_n$, and some other
their basic properties. Partial sums of arbitrary power series with non-zero
coefficients are shown to be also related to biorthogonal rational functions.
We obtain a relation of polynomials $g_n(z)$ to Jacobi-type pencils and their
associated polynomials.


Abstract:
  In this paper we demonstrate end-to-end precoded multi-user multiple-input
single-output (MU-MISO) communications over a live GEO satellite link. Precoded
communications enable full frequency reuse (FFR) schemes in satellite
communications (SATCOM) to achieve broader service availability and higher
spectrum efficiency than with the conventional four-color (4CR) and two-color
(2CR) reuse approaches. In this scope, we develop an over-the-air test-bed for
end-to-end precoding validations. We use an actual multi-beam satellite to
transmit and receive precoded signals using the DVB-S2X standard based gateway
and user terminals. The developed system is capable of end-to-end real-time
communications over the satellite link including channel measurements and
precompensation. It is shown, that by successfully canceling inter-user
interference in the actual satellite FFR link precoding brings gains in terms
of enhanced SINR and increased system goodput.


Abstract:
  This paper presents the Runge-Kutta-Legendre finite difference scheme,
allowing for an additional shift in its polynomial representation. A short
presentation of the stability region, comparatively to the
Runge-Kutta-Chebyshev scheme follows. We then explore the problem of pricing
American options with the Runge-Kutta-Legendre scheme under the one factor
Black-Scholes and the two factor Heston stochastic volatility models, as well
as the pricing of butterfly spread and digital options under the uncertain
volatility model, where a Hamilton-Jacobi-Bellman partial differential equation
needs to be solved. We explore the order of convergence in these problems, as
well as the option greeks stability, compared to the literature and popular
schemes such as Crank-Nicolson, with Rannacher time-stepping.


Abstract:
  The inductive biases of trained neural networks are difficult to understand
and, consequently, to adapt to new settings. We study the inductive biases of
linearizations of neural networks, which we show to be surprisingly good
summaries of the full network functions. Inspired by this finding, we propose a
technique for embedding these inductive biases into Gaussian processes through
a kernel designed from the Jacobian of the network. In this setting, domain
adaptation takes the form of interpretable posterior inference, with
accompanying uncertainty estimation. This inference is analytic and free of
local optima issues found in standard techniques such as fine-tuning neural
network weights to a new task. We develop significant computational speed-ups
based on matrix multiplies, including a novel implementation for scalable
Fisher vector products. Our experiments on both image classification and
regression demonstrate the promise and convenience of this framework for
transfer learning, compared to neural network fine-tuning. Code is available at
https://github.com/amzn/xfer/tree/master/finite_ntk.


Abstract:
  Classical graph modeling approaches such as Erd\H{o}s R\'{e}nyi (ER) random
graphs or Barab\'asi-Albert (BA) graphs, here referred to as stylized models,
aim to reproduce properties of real-world graphs in an interpretable way. While
useful, graph generation with stylized models requires domain knowledge and
iterative trial and error simulation. Previous work by Stoehr et al. (2019)
addresses these issues by learning the generation process from graph data,
using a disentanglement-focused deep autoencoding framework, more specifically,
a $\beta$-Variational Autoencoder ($\beta$-VAE). While they successfully
recover the generative parameters of ER graphs through the model's latent
variables, their model performs badly on sequentially generated graphs such as
BA graphs, due to their oversimplified decoder. We focus on recovering the
generative parameters of BA graphs by replacing their $\beta$-VAE decoder with
a sequential one. We first learn the generative BA parameters in a supervised
fashion using a Graph Neural Network (GNN) and a Random Forest Regressor, by
minimizing the squared loss between the true generative parameters and the
latent variables. Next, we train a $\beta$-VAE model, combining the GNN encoder
from the first stage with an LSTM-based decoder with a customized loss.


Abstract:
  We study theoretically the superconductor diodes, where the magnitude of the
critical current changes as the direction is reversed, in terms of a
generalized Ginzburg-Landau model with the higher-order terms in the momentum
of the order parameter. This theory is applied to Rashba spin-orbit coupled
systems, where analytical relations between the nonreciprocal critical currents
and the system parameters are achieved. Numerical calculations with mean-field
theory are also obtained to study broader parameter regions. These results
offer a rather general description and design principles of superconductor
diodes.


Abstract:
  Available algorithms for the initialization of volume fractions typically
utilize exact functions to model fluid interfaces, or they rely on
computationally costly intersections between volume meshes. Here, a new
algorithm is proposed that computes signed distances and volume fractions on
unstructured meshes from arbitrarily shaped surfaces, e.g. originating from
experimental data. The proposed algorithm calculates signed distances
geometrically near the fluid interface, approximated as a triangle surface
mesh, and propagates the inside/outside information by an approximate solution
of a Laplace equation. Volume fractions are computed based on signed distances,
using either geometrical intersections between cells of the unstructured mesh
and a sub-set of the surface mesh that represents the interface, or using a
polynomial approximation and adaptive mesh refinement. Although primarily
developed for multiphase flow simulations, the proposed algorithm can
potentially be used for other problems that require a phase-indicator:
inside/outside information with respect to an arbitrarily shaped surface on
arbitrarily unstructured meshes.


Abstract:
  In the paper, we use the equivalent formulation of a finite state mean field
game as a control problem with mixed constraints to study the dependence of
solutions to finite state mean field game on an initial distribution of
players. We introduce the concept of value multifunction of the mean field game
that is a mapping assigning to an initial time and an initial distribution a
set of expected outcomes of the representative player corresponding to
solutions of the mean field game. Using the control reformulation of the finite
state mean field game, we give the sufficient condition on a given
multifunction to be a value multifunction in the terms of the viability theory.
The maximal multifunction (i.e. the mapping assigning to an initial time and
distribution the whole set of values corresponding to solutions of the mean
field game) is characterized via the backward attainability set for the certain
control systems.


Abstract:
  Locating each node in a wireless sensor network is essential for starting the
monitoring job and sending information about the area. One method that has been
used in hard and inaccessible environments is randomly scattering each node in
the area. In order to reduce the cost of using GPS at each node, some nodes
should be equipped with GPS (anchors), Then using the belief propagation
algorithm, locate other nodes. The number of anchor nodes must be reduced since
they are expensive. Furthermore, the location of these nodes affects the
algorithm's performance. Using multi-objective optimization, an algorithm is
introduced in this paper that minimizes the estimated location error and the
number of anchor nodes. According to simulation results, This algorithm
proposes a set of solutions with less energy consumption and less error than
similar algorithms.


Abstract:
  We investigate in the framework of quantum noise theory how the striking
boundary-sensitivity recently discovered in the context of non-Hermitian (NH)
topological phases may be harnessed to devise novel quantum sensors.
Specifically, we study a quantum-optical setting of coupled modes arranged in
an array with broken ring geometry that would realize a NH topological phase in
the classical limit. Using methods from quantum-information theory of Gaussian
states, we show that a small coupling induced between the ends of the broken
ring may be detected with a precision that increases exponentially in the
number of coupled modes, e.g. by heterodyne detection of two output modes.
While this robust effect only relies on reaching a NH topological regime, we
identify a resonance phenomenon without direct classical counterpart that
provides an experimental knob for drastically enhancing the aforementioned
exponential growth. Our findings pave the way towards designing quantum NH
topological sensors (QUANTOS) that may observe with high precision any physical
observable that couples to the boundary conditions of the device.


Abstract:
  Optical vortex beams are profiled as helical wavefronts with a phase
singularity carrying an orbital angular momentum (OAM) associated with their
spatial distribution. The transverse intensity distribution of a conventional
optical vortex has a strong dependence on the carried topological charge.
However, perfect optical vortex (POV) beams have their transverse intensity
distribution independent of their charge. Such `size-invariant' POV beams have
found exciting applications in optical manipulation, imaging and communication.
In this article, we investigate the use of POV modes in the efficient
generation of high dimensional quantum states of light. We generate heralded
single photons carrying OAM using spontaneous parametric down-conversion (SPDC)
of POV beams. We show that the heralding efficiency of the SPDC single photons
generated with POV pump is greater than that with normal optical vortex beams.
The dimensionality of the two-photon OAM states is increased with POV modes in
the pump and projective measurements using Bessel-Gaussian vortex modes that
give POV, instead of the Laguerre-Gaussian modes.


Abstract:
  In this paper we consider some results obtained for graphs using minimal
vertex separators and generalized chordality and translate them to the context
of Geometric Group Theory. Using these new tools, we are able to give two new
characterizations for a group to be virtually free. Furthermore, we prove that
the Baumslag-Solitar group $BS(1,n)$ is $k$-chordal for some $k$ if and only if
$|n|<3$ and we give an application of generalized chordality to the study of
the word problem.


Abstract:
  In many real-world scenarios where extrinsic rewards to the agent are
extremely sparse, curiosity has emerged as a useful concept providing intrinsic
rewards that enable the agent to explore its environment and acquire
information to achieve its goals. Despite their strong performance on many
sparse-reward tasks, existing curiosity approaches rely on an overly holistic
view of state transitions, and do not allow for a structured understanding of
specific aspects of the environment. In this paper, we formulate curiosity
based on grounded question answering by encouraging the agent to ask questions
about the environment and be curious when the answers to these questions
change. We show that natural language questions encourage the agent to uncover
specific knowledge about their environment such as the physical properties of
objects as well as their spatial relationships with other objects, which serve
as valuable curiosity rewards to solve sparse-reward tasks more efficiently.


Abstract:
  We provide sufficient conditions on the profile $\varphi$, on the sequence of
random variables $\varepsilon_j>0$ and on the sequence of random vectors
$y_j\in\mathbb{R}^n$ such that
$\mathscr{E}\left(\frac{1}{\varepsilon_j^n(\omega)}\int_{z\in\mathbb{R}^n}\varphi\left(\frac{|x-z-y_j(\omega)|}{\varepsilon_j(\omega)}\right)f(z)
dz\right)\longrightarrow f(x)$ when $j\to\infty$ for almost every
$x\in\mathbb{R}^n$, $f\in L^p(\mathbb{R}^n)$, $1\leq p\leq\infty$, where
$\mathscr{E}$ denotes the expectation, $\varepsilon_j$ tends to
$0\in\mathbb{R}$ in law and $y_j$ tends to $\mathbf{0}\in\mathbb{R}^n$ in law.


Abstract:
  Breast cancer is one of the most common cause of deaths among women.
Mammography is a widely used imaging modality that can be used for cancer
detection in its early stages. Deep learning is widely used for the detection
of cancerous masses in the images obtained via mammography. The need to improve
accuracy remains constant due to the sensitive nature of the datasets so we
introduce segmentation and wavelet transform to enhance the important features
in the image scans. Our proposed system aids the radiologist in the screening
phase of cancer detection by using a combination of segmentation and wavelet
transforms as pre-processing augmentation that leads to transfer learning in
neural networks. The proposed system with these pre-processing techniques
significantly increases the accuracy of detection on Mini-MIAS.


Abstract:
  The recent report of an association of the gravitational-wave (GW) binary
black hole (BBH) merger GW190521 with a flare in the Active Galactic Nuclei
(AGN) J124942.3+344929 has generated tremendous excitement. However, GW190521
has one of the largest localization volumes amongst all of the GW events
detected so far. The 90\% localization volume likely contains $7,400$
unobscured AGN brighter than $g \leq 20.5$ AB mag, and it results in a $\gtrsim
70\%$ probability of chance coincidence for an AGN flare consistent with the GW
event. We present a Bayesian formalism to estimate the confidence of an AGN
association by analyzing a population of BBH events with dedicated follow-up
observations. Depending on the fraction of BBH arising from AGNs, counterpart
searches of $\mathcal{O}(1)-\mathcal{O}(100)$ GW events are needed to establish
a confident association, and more than an order of magnitude more for searches
without followup (i.e, using only the locations of AGNs and GW events).
Follow-up campaigns of the top $\sim 5\%$ (based on volume localization and
binary mass) of BBH events with total rest frame mass $\ge 50~M_\odot$ are
expected to establish a confident association during the next LIGO/Virgo/KAGRA
observing run (O4), as long as the true value of the fraction of BBH giving
rise to AGN flares is $>0.1$. Our formalism allows us to jointly infer
cosmological parameters from a sample of BBH events that include chance
coincidence flares. Until the confidence of AGN associations is established,
the probability of chance coincidence must be taken into account to avoid
biasing astrophysical and cosmological constraints.


Abstract:
  The usage of environment sensor models for virtual testing is a promising
approach to reduce the testing effort of autonomous driving. However, in order
to deduce any statements regarding the performance of an autonomous driving
function based on simulation, the sensor model has to be validated to determine
the discrepancy between the synthetic and real sensor data. Since a certain
degree of divergence can be assumed to exist, the sufficient level of fidelity
must be determined, which poses a major challenge. In particular, a method for
quantifying the fidelity of a sensor model does not exist and the problem of
defining an appropriate metric remains. In this work, we train a neural network
to distinguish real and simulated radar sensor data with the purpose of
learning the latent features of real radar point clouds. Furthermore, we
propose the classifier's confidence score for the `real radar point cloud'
class as a metric to determine the degree of fidelity of synthetically
generated radar data. The presented approach is evaluated and it can be
demonstrated that the proposed deep evaluation metric outperforms conventional
metrics in terms of its capability to identify characteristic differences
between real and simulated radar data.


Abstract:
  We review and give detailed description for ${\rm gl}_{NM}$ Gaudin models
related to holomorphic vector bundles of rank $NM$ and degree $N$ over elliptic
curve with $n$ punctures. Then we introduce their generalizations constructed
by means of $R$-matrices satisfying the associative Yang-Baxter equation. A
natural extension of the obtained models to the Schlesinger systems is given as
well.


Abstract:
  Deep CNN-based methods have so far achieved the state of the art results in
multi-view 3D object reconstruction. Despite the considerable progress, the two
core modules of these methods - multi-view feature extraction and fusion, are
usually investigated separately, and the object relations in different views
are rarely explored. In this paper, inspired by the recent great success in
self-attention-based Transformer models, we reformulate the multi-view 3D
reconstruction as a sequence-to-sequence prediction problem and propose a new
framework named 3D Volume Transformer (VolT) for such a task. Unlike previous
CNN-based methods using a separate design, we unify the feature extraction and
view fusion in a single Transformer network. A natural advantage of our design
lies in the exploration of view-to-view relationships using self-attention
among multiple unordered inputs. On ShapeNet - a large-scale 3D reconstruction
benchmark dataset, our method achieves a new state-of-the-art accuracy in
multi-view reconstruction with fewer parameters ($70\%$ less) than other
CNN-based methods. Experimental results also suggest the strong scaling
capability of our method. Our code will be made publicly available.


Abstract:
  We construct, for any given positive integer $n$, Reeb flows on contact
integral homology 3-spheres which do not admit global surfaces of section with
fewer than $n$ boundary components. We use a connected sum operation for open
books to construct such a system. We prove that this property is stable with
respect to $C^{4+\epsilon}$-small perturbations of the Hamiltonian given on the
symplectization.


Abstract:
  We introduce S++, a simple, robust, and deployable framework for training a
neural network (NN) using private data from multiple sources, using
secret-shared secure function evaluation. In short, consider a virtual third
party to whom every data-holder sends their inputs, and which computes the
neural network: in our case, this virtual third party is actually a set of
servers which individually learn nothing, even with a malicious (but
non-colluding) adversary.
  Previous work in this area has been limited to just one specific activation
function: ReLU, rendering the approach impractical for many use-cases. For the
first time, we provide fast and verifiable protocols for all common activation
functions and optimize them for running in a secret-shared manner. The ability
to quickly, verifiably, and robustly compute exponentiation, softmax, sigmoid,
etc., allows us to use previously written NNs without modification, vastly
reducing developer effort and complexity of code. In recent times, ReLU has
been found to converge much faster and be more computationally efficient as
compared to non-linear functions like sigmoid or tanh. However, we argue that
it would be remiss not to extend the mechanism to non-linear functions such as
the logistic sigmoid, tanh, and softmax that are fundamental due to their
ability to express outputs as probabilities and their universal approximation
property. Their contribution in RNNs and a few recent advancements also makes
them more relevant.


Abstract:
  Beginning with the 'conventional' two-dimensional (2D) quantum wells (QWs)
based on III-V and II-VI semiconductors in the 1970s, to the recent
atomically-thin sheets of van der Waals materials such as 2D semiconducting
transition metal dichalcogenides (TMDCs) and 2D magnets, the research in 2D
materials is continuously evolving and providing new challenges. Magnetooptical
spectroscopy has played a significant role in this area of research, both from
fundamental physics and technological perspectives. A major challenge in 2D
semiconductors such as TMDCs is to understand their spin-valley-resolved
physics, and their implications in quantum computation and information
research. Since the discovery of valley Zeeman effects, deep insights into the
spin-valley physics of TMDCs and their heterostructures has emerged through
magnetooptical spectroscopy. In this perspective, we highlight the role of
magnetooptics in many milestones such as the discovery of interlayer excitons,
phase control between coherently-excited valleys, determination of
exciton-reduced masses, Bohr radii and binding energies, physics of the
optically-bright and dark excitons, trions, other many-body species such as
biexcitons and their phonon replicas in TMDC monolayers. The discussion
accompanies open questions, challenges and future prospects in the field
including comments on the magnetooptics of van der Waals heterostructures
involving TMDCs and 2D magnets.


Abstract:
  DA-type white dwarfs account for 80% of all white dwarfs and represent, for
most of them, the ultimate outcome of the typical evolution of
low-to-intermediate mass stars. Their internal chemical stratification is
strongly marked by passed, often uncertain, stellar evolution processes that
occurred during the helium (core and shell) burning phases, i.e., from the
horizontal branch through AGB and post-AGB stages. Pulsating white dwarfs, in
particular the "cool" DA-type ZZ Ceti variables, offer an outstanding
opportunity to dig into these stars by fully exploiting their asteroseismic
potential. With our most recent tools dedicated to that purpose, we show that a
complete cartography of the stratification of the main constituents of a white
dwarf can be inferred, leading in particular to strong constraints on the C/O
core structure produced by the processes mentioned above. This opens up the way
toward a systematic exploration of white-dwarf internal properties.


Abstract:
  In this paper we prove a direct geometric relation between Deligne--Lusztig
varieties and Springer fibres in type $\mathsf{A}$: For any rational unipotent
element, the Springer fibre cuts out a unique component of a specific
Deligne--Lusztig variety; moreover, this component forms an open dense subset
of a component of the Springer fibre. This boils down to a map from the
unipotent variety to the Weyl group, and combines several constructions with a
combinatorial flavour (like Weyr normal forms, Robinson--Schensted
correspondence, and Spaltenstein's and Steinberg's labellings); it also
provides a geometric interpretation of a classical dimension formula of
unipotent centralisers.


Abstract:
  We introduce a weakening of the notion of fusion 2-category given in
arXiv:1812.11933. Then, we establish a number of properties of (multi)fusion
2-categories. Finally, we describe the fusion rule of the fusion 2-categories
associated to certain pointed braided fusion categories.


Abstract:
  A heterogeneous graph consists of different vertices and edges types.
Learning on heterogeneous graphs typically employs meta-paths to deal with the
heterogeneity by reducing the graph to a homogeneous network, guide random
walks or capture semantics. These methods are however sensitive to the choice
of meta-paths, with suboptimal paths leading to poor performance. In this
paper, we propose an approach for learning on heterogeneous graphs without
using meta-paths. Specifically, we decompose a heterogeneous graph into
different homogeneous relation-type graphs, which are then combined to create
higher-order relation-type representations. These representations preserve the
heterogeneity of edges and retain their edge directions while capturing the
interaction of different vertex types multiple hops apart. This is then
complemented with attention mechanisms to distinguish the importance of the
relation-type based neighbors and the relation-types themselves. Experiments
demonstrate that our model generally outperforms other state-of-the-art
baselines in the vertex classification task on three commonly studied
heterogeneous graph datasets.


Abstract:
  We examine the effect of the decoherence-induced reduction of correlation
length on a one-dimensional scattering problem by solving numerically the
evolution equation for the Wigner function with decoherence proposed in [L.
Barletti, G. Frosali and E. Giovannini, Journal of Computational and
Theoretical Transport 47, 209 (2018)]. The numerical solution is achieved by
the Splitting-Scheme algorithm. Three cases are examined, corresponding to a
reflection-dominated regime, a transmission-dominated regime and an
intermediate one. The dynamic evolution of the Wigner function is followed
until the separation process of the reflected and of the transmitted packets is
complete and it is observed for three different values of the correlation
length. The outcomes show a broadening and flattening of the Wigner function
which becomes progressively more pronounced as the correlation length is
decreased. This results in a reduced reflection at low energies and in a
reduced transmission at high energies.


Abstract:
  Given a graph $G=(V,E)$ with a weight $w_v$ associated with each vertex $v\in
V$, the maximum weighted induced forest problem (MWIF) consists of encountering
a maximum weighted subset $V'\subseteq V$ of the vertices such that $V'$
induces a forest. This NP-hard problem is known to be equivalent to the minimum
weighted feedback vertex set problem, which has applicability in a variety of
domains. The closely related maximum weighted induced tree problem (MWIT), on
the other hand, requires that the subset $V'\subseteq V$ induces a tree. We
propose two new integer programming formulations with an exponential number of
constraints and branch-and-cut procedures for MWIF. Computational experiments
using benchmark instances are performed comparing several formulations,
including the newly proposed approaches and those available in the literature,
when solved by a standard commercial mixed integer programming solver. More
specifically, five formulations are compared, two compact (i.e., with a
polynomial number of variables and constraints) ones and the three others with
an exponential number of constraints. The experiments show that a new
formulation for the problem based on directed cutset inequalities for
eliminating cycles (DCUT) offers stronger linear relaxation bounds earlier in
the search process. The results also indicate that the other new formulation,
denoted tree with cycle elimination (TCYC), outperforms those available in the
literature when it comes to the average times for proving optimality for the
small instances, especially the more challenging ones. Additionally, this
formulation can achieve much lower average times for solving the larger random
instances that can be optimally solved. Furthermore, we show how the
formulations for MWIF can be easily extended for MWIT. Such extension allowed
us to compare the optimal solution values of the two problems.


Abstract:
  This work is about the semantic segmentation of skin lesion boundary and
their attributes using Image-to-Image Translation with Conditional Adversarial
Nets. Melanoma is a type of skin cancer that can be cured if detected in time.
Segmentation into dermoscopic images is an essential procedure for
computer-assisted diagnosis due to its existing artifacts typical of skin
images. To alleviate the image annotation process, we propose to use a modified
Pix2Pix network. The discriminator network learns the mapping from a dermal
image as an input and a mask image of six channels as an output. Likewise, the
discriminative network output called PatchGAN is varied for one channel and six
output channels. The photos used come from the 2018 ISIC Challenge, where 500
photographs are used with their respective semantic map, divided into 75% for
training and 35% for testing. Obtaining for 100 training epochs high Jaccard
indices for all attributes of the segmentation map.


Abstract:
  Intelligent reflecting surfaces (IRSs) have been introduced into wireless
communications systems due to their great potential to smartly customize and
reconfigure radio propagation environments in a cost-effective manner. Despite
the promising advantages of IRSs, academic research on IRSs is still in its
infancy. In particular, the design and analysis of IRS-assisted wireless
communication systems critically depend on an accurate and tractable modeling
of the IRS. In this article, we first present and compare three IRS models,
namely the conventional independent diffusive scatterer-based model,
physics-based model, and impedance network-based model, in terms of their
accuracy, tractability, and hardware complexity. Besides, a new framework based
on partitioning the IRS into tiles and employing codebooks of transmission
modes is introduced to enable scalable IRS optimization. Then, we investigate
the impact of the three considered IRS models on system design, where several
crucial technical challenges for the efficient design of IRS-assisted wireless
systems are identified and the corresponding solutions are unraveled.
Furthermore, to illustrate the properties of the considered models and the
efficiency of the proposed solution concepts, IRS-assisted secure wireless
systems and simultaneous wireless information and power transfer (SWIPT)
systems are studied in more detail. Finally, several promising future research
directions for IRS-assisted wireless systems are highlighted.


Abstract:
  In several domains it is crucial to store and manipulate data whose origin
needs to be completely traceable to guarantee the consistency, trustworthiness
and reliability on the data itself typically for ethical and legal reasons. It
is also important to guarantee that such properties are also carried further
when such data is composed and processed into new data. In this article we
present the main requirements and theorethical problems that arise by the
design of a system supporting data with such capabilities. We present an
architecture for implementing a system as well as a prototype developed in
Pharo.


Abstract:
  The Local Group is a unique environment in which to study the astrophysics of
galaxy formation. The proximity of the Milky Way and M31 causes a large
fraction of the low-mass halo population to interact with more massive dark
matter haloes, which increases their concentrations and strips them of gas and
other material. Some low-mass haloes pass through the haloes of the Milky Way
or M31 and are either ejected into the field or exchanged between the two
primary hosts. We use high resolution gas-dynamical simulations to describe a
new class of field halo that passed through the haloes of both the Milky Way
and M31 at early times and is almost twice as concentrated as isolated field
haloes. These 'Hermeian' haloes are distributed anisotropically at greater
distances from the Local Group barycentre than the primary haloes and appear to
cluster close to the Milky Way and M31 in projection. We show that some
Hermeian haloes can host galaxies that are promising targets for indirect dark
matter searches and are competitive with signals from other dwarf galaxies.
Hermeian galaxies in the Local Group should be detectable by forthcoming
wide-field imaging surveys.


Abstract:
  We investigate the $I=1$ $\pi \pi$ interaction using the HAL QCD method in
lattice QCD. We employ the (2+1)-flavor gauge configurations on $32^3 \times
64$ lattice at the lattice spacing $a \approx 0.0907$ fm and $m_{\pi} \approx
411$ MeV, in which the $\rho$ meson appears as a resonance state. We find that
all-to-all propagators necessary in this calculation can be obtained with
reasonable precision by a combination of three techniques, the one-end trick,
the sequential propagator, and the covariant approximation averaging (CAA). The
non-local $I=1$ $\pi \pi$ potential is determined at the
next-to-next-to-leading order (N$^2$LO) of the derivative expansion for the
first time, and the resonance parameters of the $\rho$ meson are extracted. The
obtained $\rho$ meson mass is found to be consistent with the value in the
literature, while the value of the coupling $g_{\rho \pi \pi}$ turns out to be
somewhat larger. The latter observation is most likely attributed to the lack
of low-energy information in our lattice setup with the center-of-mass frame.
Such a limitation may appear in other P-wave resonant systems and we discuss
possible improvement in future. With this caution in mind, we positively
conclude that we can reasonably extract the N$^2$LO potential and resonance
parameters even in the system requiring the all-to-all propagators in the HAL
QCD method, which opens up new possibilities for the study of resonances in
lattice QCD.


Abstract:
  Biomolecular electrostatics is key in protein function and the chemical
processes affecting it.Implicit-solvent models expressed by the
Poisson-Boltzmann (PB) equation can provide insights with less computational
power than full atomistic models, making large-system studies -- at the scale
of viruses, for example -- accessible to more researchers. This paper presents
a high-productivity and high-performance computational workflow combining
Exafmm, a fast multipole method (FMM) library, and Bempp, a Galerkin boundary
element method (BEM) package. It integrates an easy-to-use Python interface
with well-optimized computational kernels that are written in compiled
languages. Researchers can run PB simulations interactively via Jupyter
notebooks, enabling faster prototyping and analyzing. We provide results that
showcase the capability of the software, confirm correctness, and evaluate its
performance with problem sizes between 8,000 and 2 million boundary elements. A
study comparing two variants of the boundary integral formulation in regards to
algebraic conditioning showcases the power of this interactive computing
platform to give useful answers with just a few lines of code. As a form of
solution verification, mesh refinement studies with a spherical geometry as
well as with a real biological structure (5PTI) confirm convergence at the
expected $1/N$ rate, for $N$ boundary elements. Performance results include
timings, breakdowns, and computational complexity. Exafmm offers evaluation
speeds of just a few seconds for tens of millions of points, and
$\mathcal{O}(N)$ scaling. This allowed computing the solvation free energy of a
Zika virus, represented by 1.6 million atoms and 10 million boundary elements,
at 80-min runtime on a single compute node (dual 20-core Intel Xeon Gold 6148).
All results in the paper are presented with utmost care for reproducibility.


Abstract:
  The convergence theory for the gradient sampling algorithm is extended to
directionally Lipschitz functions. Although directionally Lipschitz functions
are not necessarily locally Lipschitz, they are almost everywhere
differentiable and well approximated by gradients and so are a natural
candidate for the application of the gradient sampling algorithm. The main
obstacle to this extension is the potential unboundedness or emptiness of the
Clarke subdifferential at points of interest. The convergence analysis we
present provides one path to addressing these issues. In particular, we recover
the usual convergence theory when the function is locally Lipschitz. Moreover,
if the algorithm does not drive a certain measure of criticality to zero, then
the iterates must converge to a point at which either the Clarke
subdifferential is empty or the direction of steepest descent is degenerate in
the sense that it does lie in the interior of the domain of the regular
subderivative.


Abstract:
  Telescope Array (TA) is the largest ultrahigh energy cosmic-ray (UHECR)
observatory in the Northern Hemisphere. It explores the origin of UHECRs by
measuring their energy spectrum, arrival-direction distribution, and mass
composition using a surface detector (SD) array covering approximately 700
km$^2$ and fluorescence detector (FD) stations. TA has found evidence for a
cluster of cosmic rays with energies greater than 57 EeV. In order to confirm
this evidence with more data, it is necessary to increase the data collection
rate.We have begun building an expansion of TA that we call TAx4. In this
paper, we explain the motivation, design, technical features, and expected
performance of the TAx4 SD. We also present TAx4's current status and examples
of the data that have already been collected.


Abstract:
  Continual (or "incremental") learning approaches are employed when additional
knowledge or tasks need to be learned from subsequent batches or from streaming
data. However these approaches are typically adversary agnostic, i.e., they do
not consider the possibility of a malicious attack. In our prior work, we
explored the vulnerabilities of Elastic Weight Consolidation (EWC) to the
perceptible misinformation. We now explore the vulnerabilities of other
regularization-based as well as generative replay-based continual learning
algorithms, and also extend the attack to imperceptible misinformation. We show
that an intelligent adversary can take advantage of a continual learning
algorithm's capabilities of retaining existing knowledge over time, and force
it to learn and retain deliberately introduced misinformation. To demonstrate
this vulnerability, we inject backdoor attack samples into the training data.
These attack samples constitute the misinformation, allowing the attacker to
capture control of the model at test time. We evaluate the extent of this
vulnerability on both rotated and split benchmark variants of the MNIST dataset
under two important domain and class incremental learning scenarios. We show
that the adversary can create a "false memory" about any task by inserting
carefully-designed backdoor samples to the test instances of that task thereby
controlling the amount of forgetting of any task of its choosing. Perhaps most
importantly, we show this vulnerability to be very acute and damaging: the
model memory can be easily compromised with the addition of backdoor samples
into as little as 1\% of the training data, even when the misinformation is
imperceptible to human eye.


Abstract:
  Tidal range structures have been considered for large scale electricity
generation for their potential ability to produce reasonable predictable energy
without the emission of greenhouse gases. Once the main forcing components for
driving the tides have deterministic dynamics, the available energy in a given
tidal power plant has been estimated, through analytical and numerical
optimisation routines, as a mostly predictable event. This constraint imposes
state-of-art flexible operation methods to rely on tidal predictions
(concurrent with measured data and up to a multiple of half-tidal cycles into
the future) to infer best operational strategies for tidal lagoons, with the
additional cost of requiring to run optimisation routines for every new tide.
In this paper, we propose a novel optimised operation of tidal lagoons with
proximal policy optimisation through Unity ML-Agents. We compare this technique
with 6 different operation optimisation approaches (baselines) devised from the
literature, utilising the Swansea Bay Tidal Lagoon as a case study. We show
that our approach is successful in maximising energy generation through an
optimised operational policy of turbines and sluices, yielding competitive
results with state-of-the-art methods of optimisation, regardless of test data
used, requiring training once and performing real-time flexible control with
measured ocean data only.


Abstract:
  A two-dimensional inviscid incompressible fluid is governed by simple rules.
Yet, to characterise its long-time behaviour is a knotty problem. The fluid
evolves according to Euler's equations: a non-linear Hamiltonian system with
infinitely many conservation laws. In both experiments and numerical
simulations, coherent vortex structures, or blobs, emerge after an initial
stage. These formations dominate the large-scale dynamics, but small scales
also persist. Kraichnan describes in his classical work a forward cascade of
enstrophy into smaller scales, and a backward cascade of energy into larger
scales. Previous attempts to model Kraichnan's double cascade use filtering
techniques that enforce separation from the outset. Here we show that Euler's
equations posses an intrinsic, canonical splitting of the vorticity function.
The splitting is remarkable in four ways: (i) it is defined solely via the
Poisson bracket and the Hamiltonian, (ii) it characterises steady flows, (iii)
without imposition it yields a separation of scales, enabling the dynamics
behind Kraichnan's qualitative description, and (iv) it accounts for the
"broken line" in the power law for the energy spectrum, observed in both
experiments and numerical simulations. The splitting originates from Zeitlin's
truncated model of Euler's equations in combination with a standard
quantum-tool: the spectral decomposition of Hermitian matrices. In addition to
theoretical insight, the scale separation dynamics could be used for stochastic
model reduction, where small scales are modelled by multiplicative noise.


Abstract:
  We introduce a model of competing agents in a prophet setting, where rewards
arrive online, and decisions are made immediately and irrevocably. The rewards
are unknown from the outset, but they are drawn from a known probability
distribution. In the standard prophet setting, a single agent makes selection
decisions in an attempt to maximize her expected reward. The novelty of our
model is the introduction of a competition setting, where multiple agents
compete over the arriving rewards, and make online selection decisions
simultaneously, as rewards arrive. If a given reward is selected by more than a
single agent, ties are broken either randomly or by a fixed ranking of the
agents. The consideration of competition turns the prophet setting from an
online decision making scenario to a multi-agent game.
  For both random and ranked tie-breaking rules, we present simple threshold
strategies for the agents that give them high guarantees, independent of the
strategies taken by others. In particular, for random tie-breaking, every agent
can guarantee herself at least $\frac{1}{k+1}$ of the highest reward, and at
least $\frac{1}{2k}$ of the optimal social welfare. For ranked tie-breaking,
the $i$th ranked agent can guarantee herself at least a half of the $i$th
highest reward. We complement these results by matching upper bounds, even with
respect to equilibrium profiles. For ranked tie-breaking rule, we also show a
correspondence between the equilibrium of the $k$-agent game and the optimal
strategy of a single decision maker who can select up to $k$ rewards.


Abstract:
  Extremal clusters of stationary processes with long memory can be quite
intricate. For certain stationary infinitely divisible processes with
subexponential tails, including both power-like tails and certain lighter
tails, e.g. lognormal-like tails, such clusters may take the shape of stable
regenerative sets. In this paper we show that for semi-exponential tails, which
are even lighter, a new shape of extremal clusters arises. In this case each
stable regenerative set supports a random panoply of varying extremes.


Abstract:
  Metal-insulator-metal (MIM) nanogaps in canonical nanoparticle-on-mirror
geometry (NPoM) provide deep-subwavelength confinement of light with mode
volumes smaller than $V/V_0$ $<$ $10^{-6}$. However, access to these hotspots
is limited by the impendence mismatch between the high in-plane $k_{//}$ of
trapped light and free-space plane-waves, making the in- and out-coupling of
light difficult. Here, by constructing a nanoparticle-on-foil (NPoF) system
with thin metal films, we show the mixing of insulator-metal-insulator (IMI)
modes and MIM gap modes resulting in MIMI modes. This mixing provides
multi-channel access to the plasmonic nanocavity through light incident from
both sides of the metal film. The red-tuning and near-field strength of MIMI
modes for thinner foils is measured experimentally with white-light scattering
and surface-enhanced Raman scattering from individual NPoFs. We discuss further
the utility of NPoF systems since the geometry allows tightly confined light to
be accessed simply and through different ports.


Abstract:
  Inspired by the progress of the End-to-End approach [1], this paper
systematically studies the effects of Number of Filters of convolutional layers
on the model prediction accuracy of CNN+RNN (Convolutional Neural Networks
adding to Recurrent Neural Networks) for ASR Models (Automatic Speech
Recognition). Experimental results show that only when the CNN Number of
Filters exceeds a certain threshold value is adding CNN to RNN able to improve
the performance of the CNN+RNN speech recognition model, otherwise some
parameter ranges of CNN can render it useless to add the CNN to the RNN model.
Our results show a strong dependency of word accuracy on the Number of Filters
of convolutional layers. Based on the experimental results, the paper suggests
a possible hypothesis of Sound-2-Vector Embedding (Convolutional Embedding) to
explain the above observations.
  Based on this Embedding hypothesis and the optimization of parameters, the
paper develops an End-to-End speech recognition system which has a high word
accuracy but also has a light model-weight. The developed LVCSR (Large
Vocabulary Continuous Speech Recognition) model has achieved quite a high word
accuracy of 90.2% only by its Acoustic Model alone, without any assistance from
intermediate phonetic representation and any Language Model. Its acoustic model
contains only 4.4 million weight parameters, compared to the 35~68 million
acoustic-model weight parameters in DeepSpeech2 [2] (one of the top
state-of-the-art LVCSR models) which can achieve a word accuracy of 91.5%. The
light-weighted model is good for improving the transcribing computing
efficiency and also useful for mobile devices, Driverless Vehicles, etc. Our
model weight is reduced to ~10% the size of DeepSpeech2, but our model accuracy
remains close to that of DeepSpeech2. If combined with a Language Model, our
LVCSR system is able to achieve 91.5% word accuracy.


Abstract:
  Topological superconductivity can be engineered in semiconductors with strong
spin-orbit interaction coupled to a superconductor. Experimental advances in
this field have often been triggered by the development of new hybrid material
systems. Among these, two-dimensional electron gases (2DEGs) are of particular
interest due to their inherent design flexibility and scalability. Here we
discuss results on a 2D platform based on a ternary 2DEG (InSbAs) coupled to
in-situ grown Aluminum. The spin-orbit coupling in these 2DEGs can be tuned
with the As concentration, reaching values up to 400 meV$\unicode{xC5}$, thus
exceeding typical values measured in its binary constituents. In addition to a
large Land\'e g-factor $\sim$ 55 (comparable to InSb), we show that the clean
superconductor-semiconductor interface leads to a hard induced superconducting
gap. Using this new platform we demonstrate the basic operation of
phase-controllable Josephson junctions, superconducting islands and quasi-1D
systems, prototypical device geometries used to study Majorana zero modes.


Abstract:
  In the manuscript, we are interested in using kinetic theory to better
understand the time evolution of wealth distribution and their large scale
behavior such as the evolution of inequality (e.g. Gini index). We investigate
three type of dynamics denoted unbiased, poor-biased and rich-biased dynamics.
At the particle level, one agent is picked randomly based on its wealth and one
of its dollar is redistributed among the population. Proving the so-called
propagation of chaos, we identify the limit of each dynamics as the number of
individual approaches infinity using both coupling techniques [48] and
martingale-based approach [36]. Equipped with the limit equation, we identify
and prove the convergence to specific equilibrium for both the unbiased and
poor-biased dynamics. In the rich-biased dynamics however, we observe a more
complex behavior where a dispersive wave emerges. Although the dispersive wave
is vanishing in time, its also accumulates all the wealth leading to a Gini
approaching 1 (its maximum value). We characterize numerically the behavior of
dispersive wave but further analytic investigation is needed to derive such
dispersive wave directly from the dynamics.