Abstract:
  We experimentally investigate the effect of electron temperature on transport
in the two-dimensional Dirac surface states of the three-dimensional
topological insulator HgTe. We find that around the minimal conductivity point,
where both electrons and holes are present, heating the carriers with a DC
current results in a non-monotonic differential resistance of narrow channels.
We show that the observed initial increase in resistance can be attributed to
electron-hole scattering, while the decrease follows naturally from the change
in Fermi energy of the charge carriers. Both effects are governed dominantly by
a van Hove singularity in the bulk valence band. The results demonstrate the
importance of interband electron-hole scattering in the transport properties of
topological insulators.


Abstract:
  In this work, we present a program in the computational environment,
GeoGebra, that enables a graphical study of Newton's Method. Using this
computational device, we will analyze Newton's Method convergence applied to
various examples of real functions. Then, it will be given a guide to the
construction of the program in GeoGebra.


Abstract:
  In recent paper Fakkousy et al. show that the 3D H\'{e}non-Heiles system with
Hamiltonian $ H = \frac{1}{2} (p_1 ^2 + p_2 ^2 + p_3 ^2) +\frac{1}{2} (A q_1 ^2
+ C q_2 ^2 + B q_3 ^2) + (\alpha q_1 ^2 + \gamma q_2 ^2)q_3 +
\frac{\beta}{3}q_3 ^3 $ is integrable in sense of Liouville when $\alpha =
\gamma, \frac{\alpha}{\beta} = 1, A = B = C$; or $\alpha = \gamma,
\frac{\alpha}{\beta} = \frac{1}{6}, A = C$, $B$-arbitrary; or $\alpha = \gamma,
\frac{\alpha}{\beta} = \frac{1}{16}, A = C, \frac{A}{B} = \frac{1}{16}$ (and of
course, when $\alpha=\gamma=0$, in which case the Hamiltonian is separable). It
is known that the second case remains integrable for $A, C, B$ arbitrary. Using
Morales-Ramis theory, we prove that there are no other cases of integrability
for this system.


Abstract:
  We derive novel explicit formulas for the inverses of truncated block
Toeplitz matrices that correspond to a multivariate minimal stationary process.
The main ingredients of the formulas are the Fourier coefficients of the phase
function attached to the spectral density of the process. The derivation of the
formulas is based on a recently developed finite prediction theory applied to
the dual process of the stationary process. We illustrate the usefulness of the
formulas by two applications. The first one is a strong convergence result for
solutions of general block Toeplitz systems for a multivariate short-memory
process. The second application is closed-form formulas for the inverses of
truncated block Toeplitz matrices corresponding to a multivariate ARMA process.
The significance of the latter is that they provide us with a linear-time
algorithm to compute the solutions of corresponding block Toeplitz systems.


Abstract:
  In this article, we consider mixed local and nonlocal Sobolev
$(q,p)$-inequalities with extremal in the case $0<q<1<p<\infty$. We prove that
the extremal of such inequalities is unique up to a multiplicative constant
that is associated with a singular elliptic problem involving the mixed local
and nonlocal $p$-Laplace operator. Moreover, it is proved that the mixed
Sobolev inequalities are necessary and sufficient condition for the existence
of weak solutions of such singular problems. As a consequence, a relation
between the singular $p$-Laplace and mixed local and nonlocal $p$-Laplace
equation is established. Finally, we investigate the existence, uniqueness,
regularity and symmetry properties of weak solutions for such problems.


Abstract:
  Let $A$ be a Noetherian local ring with the maximal ideal $\mathfrak{m}$ and
$I$ be an $\mathfrak{m}$-primary ideal in $A$. In this paper, we study a
boundary condition of an inequality on Hilbert coefficients of an
$I$-admissible filtration $\mathcal{I}$. When $A$ is a Buchsbaum local ring,
the above equality forces Buchsbaumness on the associated graded ring of
filtration. Our result provides a positive resolution of a question of Corso in
a general set up of filtration.


Abstract:
  Three dimensional (3D) resource reuse is an important design requirement for
the prospective 6G wireless communication systems. Hence, we propose a
cooperative 3D beamformer for use in 3D space. Explicitly, we harness multiple
base station antennas for joint zero forcing transmit pre-coding for beaming
the transmit signals in specific 3D directions. The technique advocated is
judiciously configured for use in both cell-based and cell-free wireless
architectures. We evaluated the performance of the proposed scheme using the
novel metric of Volumetric Spectral Efficiency (VSE). We also characterized the
performance of the scheme in terms of its spectral efficiency (SE) and Bit
Error Rate (BER) through extensive simulation studies.


Abstract:
  Recent information extraction approaches have relied on training deep neural
models. However, such models can easily overfit noisy labels and suffer from
performance degradation. While it is very costly to filter noisy labels in
large learning resources, recent studies show that such labels take more
training steps to be memorized and are more frequently forgotten than clean
labels, therefore are identifiable in training. Motivated by such properties,
we propose a simple co-regularization framework for entity-centric information
extraction, which consists of several neural models with identical structures
but different parameter initialization. These models are jointly optimized with
the task-specific losses and are regularized to generate similar predictions
based on an agreement loss, which prevents overfitting on noisy labels.
Extensive experiments on two widely used but noisy benchmarks for information
extraction, TACRED and CoNLL03, demonstrate the effectiveness of our framework.
We release our code to the community for future research.


Abstract:
  Gene genealogies are frequently studied by measuring properties such as their
height ($H$), length ($L$), sum of external branches ($E$), sum of internal
branches ($I$), and mean of their two basal branches ($B$), and the coalescence
times that contribute to the other genealogical features ($T$). These tree
properties and their relationships can provide insight into the effects of
population-genetic processes on genealogies and genetic sequences. Here, under
the coalescent model, we study the 15 correlations among pairs of features of
genealogical trees: $H_n$, $L_n$, $E_n$, $I_n$, $B_n$, and $T_k$ for a sample
of size $n$, with $2 \leq k \leq n$. We report high correlations among $H_n$,
$L_n$, $I_n,$ and $B_n$, with all pairwise correlations of these quantities
having values greater than or equal to $\sqrt{6} [6 \zeta(3) + 6 - \pi^2] / (
\pi \sqrt{18 + 9\pi^2 - \pi^4}) \approx 0.84930$ in the limit as $n \rightarrow
\infty$. Although $E_n$ has an expectation of 2 for all $n$ and $H_n$ has
expectation 2 in the limit as $n \rightarrow \infty$, their limiting
correlation is 0. The results contribute toward understanding features of the
shapes of coalescent trees.


Abstract:
  The discrete phase space and continuous time representation of relativistic
quantum mechanics is further investigated here as a continuation of paper I
[1]. The main mathematical construct used here will be that of an area-filling
Peano curve. We show that the limit of a sequence of a class of Peano curves is
a Peano circle denoted as $\bar{S}^{1}_{n}$, a circle of radius $\sqrt{2n+1}$
where $n \in \{0,1,\cdots\}$. We interpret this two-dimensional Peano circle in
our framework as a phase cell inside our two-dimensional discrete phase plane.
We postulate that a first quantized Planck oscillator, being very light, and
small beyond current experimental detection, occupies this phase cell
$\bar{S}^{1}_{n}$. The time evolution of this Peano circle sweeps out a
two-dimensional vertical cylinder analogous to the world-sheet of string
theory. Extending this to three dimensional space, we introduce a
$(2+2+2)$-dimensional phase space hyper-tori $\bar{S}^{1}_{n^1} \times
\bar{S}^{1}_{n^2} \times \bar{S}^{1}_{n^3}$ as the appropriate phase cell in
the physical dimensional discrete phase space. A geometric interpretation of
this structure in state space is given in terms of product fibre bundles. We
also study free scalar Bosons in the background $[(2+2+2)+1]$-dimensional
discrete phase space and continuous time state space using the relativistic
partial difference-differential Klein-Gordon equation. The second quantized
field quantas of this system can cohabit with the tiny Planck oscillators
inside the $\bar{S}^{1}_{n^1} \times \bar{S}^{1}_{n^2} \times
\bar{S}^{1}_{n^3}$ phase cells for eternity. Finally, a generalized free second
quantized Klein-Gordon equation in a higher $[(2+2+2)N+1]$-dimensional discrete
state space is explored. The resulting discrete phase space dimension is
compared to the significant spatial dimensions of some of the popular models of
string theory.


Abstract:
  Fluctuation-dissipation relations (FDRs) and time-reversal symmetry (TRS),
two pillars of statistical mechanics, are both broken in generic
driven-dissipative systems. These systems rather lead to non-equilibrium steady
states far from thermal equilibrium. Driven-dissipative Ising-type models,
however, are widely believed to exhibit effective thermal critical behavior
near their phase transitions. Contrary to this picture, we show that both the
FDR and TRS are broken even macroscopically at, or near, criticality. This is
shown by inspecting different observables, both even and odd operators under
time-reversal transformation, that overlap with the order parameter.
Remarkably, however, a modified form of the FDR as well as TRS still holds, but
with drastic consequences for the correlation and response functions as well as
the Onsager reciprocity relations. Finally, we find that, at criticality, TRS
remains broken even in the weakly-dissipative limit.


Abstract:
  Batch policy optimization considers leveraging existing data for policy
construction before interacting with an environment. Although interest in this
problem has grown significantly in recent years, its theoretical foundations
remain under-developed. To advance the understanding of this problem, we
provide three results that characterize the limits and possibilities of batch
policy optimization in the finite-armed stochastic bandit setting. First, we
introduce a class of confidence-adjusted index algorithms that unifies
optimistic and pessimistic principles in a common framework, which enables a
general analysis. For this family, we show that any confidence-adjusted index
algorithm is minimax optimal, whether it be optimistic, pessimistic or neutral.
Our analysis reveals that instance-dependent optimality, commonly used to
establish optimality of on-line stochastic bandit algorithms, cannot be
achieved by any algorithm in the batch setting. In particular, for any
algorithm that performs optimally in some environment, there exists another
environment where the same algorithm suffers arbitrarily larger regret.
Therefore, to establish a framework for distinguishing algorithms, we introduce
a new weighted-minimax criterion that considers the inherent difficulty of
optimal value prediction. We demonstrate how this criterion can be used to
justify commonly used pessimistic principles for batch policy optimization.


Abstract:
  We prove that with high probability maximum sizes of induced forests in dense
binomial random graphs are concentrated in two consecutive values.


Abstract:
  We compute the variance asymptotics for the number of real zeros of
trigonometric polynomials with random dependent Gaussian coefficients and show
that under mild conditions, the asymptotic behavior is the same as in the
independent framework. In fact our proof goes beyond this framework and makes
explicit the variance asymptotics of various models of random Gaussian
polynomials. Though we use the Kac--Rice formula, we do not use the explicit
closed formula for the second moment of the number of zeros, but we rather rely
on intrinsic properties of the Kac--Rice density.


Abstract:
  Automatic Speech Recognition (ASR) systems generalize poorly on accented
speech. The phonetic and linguistic variability of accents present hard
challenges for ASR systems today in both data collection and modeling
strategies. The resulting bias in ASR performance across accents comes at a
cost to both users and providers of ASR.
  We present a survey of current promising approaches to accented speech
recognition and highlight the key challenges in the space. Approaches mostly
focus on single model generalization and accent feature engineering. Among the
challenges, lack of a standard benchmark makes research and comparison
especially difficult.


Abstract:
  In recent years, many different approaches have been proposed to quantify the
performances of soccer players. Since player performances are challenging to
quantify directly due to the low-scoring nature of soccer, most approaches
estimate the expected impact of the players' on-the-ball actions on the
scoreline. While effective, these approaches are yet to be widely embraced by
soccer practitioners. The soccer analytics community has primarily focused on
improving the accuracy of the models, while the explainability of the produced
metrics is often much more important to practitioners.
  To help bridge the gap between scientists and practitioners, we introduce an
explainable Generalized Additive Model that estimates the expected value for
shots. Unlike existing models, our model leverages features corresponding to
widespread soccer concepts. To this end, we represent the locations of shots by
fuzzily assigning the shots to designated zones on the pitch that practitioners
are familiar with. Our experimental evaluation shows that our model is as
accurate as existing models, while being easier to explain to soccer
practitioners.


Abstract:
  Along the rapid development of deep learning techniques in generative models,
it is becoming an urgent issue to combine machine intelligence with human
intelligence to solve the practical applications. Motivated by this
methodology, this work aims to adjust the machine generated character fonts
with the effort of human workers in the perception study. Although numerous
fonts are available online for public usage, it is difficult and challenging to
generate and explore a font to meet the preferences for common users. To solve
the specific issue, we propose the perceptual manifold of fonts to visualize
the perceptual adjustment in the latent space of a generative model of fonts.
In our framework, we adopt the variational autoencoder network for the font
generation. Then, we conduct a perceptual study on the generated fonts from the
multi-dimensional latent space of the generative model. After we obtained the
distribution data of specific preferences, we utilize manifold learning
approach to visualize the font distribution. In contrast to the conventional
user interface in our user study, the proposed font-exploring user interface is
efficient and helpful in the designated user preference.


Abstract:
  Arcades of flare loops form as a consequence of magnetic reconnection
powering solar flares and eruptions. We analyse the morphology and evolution of
flare arcades that formed during five well-known eruptive flares. We show that
the arcades have a common saddle-like shape. The saddles occur despite the fact
that the flares were of different classes (C to X), occurred in different
magnetic environments, and were observed in various projections. The saddles
are related to the presence of longer, relatively-higher, and inclined flare
loops, consistently observed at the ends of the arcades, which we term
`cantles'. Our observations indicate that cantles typically join straight
portions of flare ribbons with hooked extensions of the conjugate ribbons. The
origin of the cantles is investigated in stereoscopic observations of the 2011
May 9 eruptive flare carried out by the Atmospheric Imaging Assembly (AIA) and
Extreme Ultraviolet Imager (EUVI). The mutual separation of the instruments led
to ideal observational conditions allowing for simultaneous analysis of the
evolving cantle and the underlying ribbon hook. Based on our analysis we
suggest that the formation of one of the cantles can be explained by magnetic
reconnection between the erupting structure and its overlying arcades. We
propose that the morphology of flare arcades can provide information about the
reconnection geometries in which the individual flare loops originate.


Abstract:
  Our understanding of strong gravity near supermassive compact objects has
recently improved thanks to the measurements made by the Event Horizon
Telescope (EHT). We use here the M87* shadow size to infer constraints on the
physical charges of a large variety of nonrotating or rotating black holes. For
example, we show that the quality of the measurements is already sufficient to
rule out that M87* is a highly charged dilaton black hole. Similarly, when
considering black holes with two physical and independent charges, we are able
to exclude considerable regions of the space of parameters for the
doubly-charged dilaton and the Sen black holes.


Abstract:
  Medical imaging deep learning models are often large and complex, requiring
specialized hardware to train and evaluate these models. To address such
issues, we propose the PocketNet paradigm to reduce the size of deep learning
models by throttling the growth of the number of channels in convolutional
neural networks. We demonstrate that, for a range of segmentation and
classification tasks, PocketNet architectures produce results comparable to
that of conventional neural networks while reducing the number of parameters by
multiple orders of magnitude, using up to 90% less GPU memory, and speeding up
training times by up to 40%, thereby allowing such models to be trained and
deployed in resource-constrained settings.


Abstract:
  We study the behavior of the tail of a measure $\mu^{\boxtimes t}$, where
$\boxtimes t$ is the $t$-fold free multiplicative convolution power for $t\geq
1$. We focus on the case where $\mu$ is a probability measure on the positive
half-line with a regularly varying tail i.e. of the form $x^{-\alpha} L(x)$,
where $L$ is slowly varying. We obtain a phase transition in the behavior of
the tail of $\mu^{\boxplus t}$ between regimes $\alpha<1$ and $\alpha>1$. Our
main tool is a description of the regularly varying tails of $\mu$ in terms of
the behavior of the corresponding $S$-transform at $0^-$. We also describe the
tails of $\boxtimes$ infinitely divisible measures in terms of the tails of
corresponding L\'evy measure, treat symmetric measures with regularly varying
tails and prove the free analog of the Breiman lemma.


Abstract:
  Motivated by the need of {\em social distancing} during a pandemic, we
consider an approach to schedule the visitors of a facility (e.g., a general
store). Our algorithms take input from the citizens and schedule the store's
discrete time-slots based on their importance to visit the facility. Naturally,
the formulation applies to several similar problems. We consider {\em
indivisible} job requests that take single or multiple slots to complete. The
salient properties of our approach are: it (a)~ensures social distancing by
ensuring a maximum population in a given time-slot at the facility, (b)~aims to
prioritize individuals based on the importance of the jobs, (c)~maintains
truthfulness of the reported importance by adding a {\em cooling-off} period
after their allocated time-slot, during which the individual cannot re-access
the same facility, (d)~guarantees voluntary participation of the citizens, and
yet (e)~is computationally tractable. The mechanisms we propose are prior-free.
We show that the problem becomes NP-complete for indivisible multi-slot
demands, and provide a polynomial-time mechanism that is truthful, individually
rational, and approximately optimal. Experiments with data collected from a
store show that visitors with more important (single-slot) jobs are allocated
more preferred slots, which comes at the cost of a longer cooling-off period
and significantly reduces social congestion. For the multi-slot jobs, our
mechanism yields reasonable approximation while reducing the computation time
significantly.


Abstract:
  Customization is a general trend in software engineering, demanding systems
that support variable stakeholder requirements. Two opposing strategies are
commonly used to create variants: software clone & own and software
configuration with an integrated platform. Organizations often start with the
former, which is cheap, agile, and supports quick innovation, but does not
scale. The latter scales by establishing an integrated platform that shares
software assets between variants, but requires high up-front investments or
risky migration processes. So, could we have a method that allows an easy
transition or even combine the benefits of both strategies? We propose a method
and tool that supports a truly incremental development of variant-rich systems,
exploiting a spectrum between both opposing strategies. We design, formalize,
and prototype the variability-management framework virtual platform. It bridges
clone & own and platform-oriented development. Relying on
programming-language-independent conceptual structures representing software
assets, it offers operators for engineering and evolving a system, comprising:
traditional, asset-oriented operators and novel, feature-oriented operators for
incrementally adopting concepts of an integrated platform. The operators record
meta-data that is exploited by other operators to support the transition. Among
others, they eliminate expensive feature-location effort or the need to trace
clones. Our evaluation simulates the evolution of a real-world, clone-based
system, measuring its costs and benefits.


Abstract:
  The Kronecker product-based algorithm for context-free path querying (CFPQ)
was proposed by Orachev et al. (2020). We reduce this algorithm to operations
over Boolean matrices and extend it with the mechanism to extract all paths of
interest. We also prove $O(n^3/\log{n})$ time complexity of the proposed
algorithm, where n is a number of vertices of the input graph. Thus, we provide
the alternative way to construct a slightly subcubic algorithm for CFPQ which
is based on linear algebra and incremental transitive closure (a classic
graph-theoretic problem), as opposed to the algorithm with the same complexity
proposed by Chaudhuri (2008). Our evaluation shows that our algorithm is a good
candidate to be the universal algorithm for both regular and context-free path
querying.


Abstract:
  We estimate the black hole spin parameter in GRS 1915+105 using the
continuum-fitting method with revised mass and inclination constraints based on
the very long baseline interferometric parallax measurement of the distance to
this source. We fit Rossi X-ray Timing Explorer observations selected to be
accretion disk-dominated spectral states as described in McClinotck et al.
(2006) and Middleton et al. (2006), which previously gave discrepant spin
estimates with this method. We find that, using the new system parameters, the
spin in both datasets increased, providing a best-fit spin of $a_*=0.86$ for
the Middleton et al. data and a poor fit for the McClintock et al. dataset,
which becomes pegged at the BHSPEC model limit of $a_*=0.99$. We explore the
impact of the uncertainties in the system parameters, showing that the best-fit
spin ranges from $a_*= 0.4$ to 0.99 for the Middleton et al. dataset and allows
reasonable fits to the McClintock et al. dataset with near maximal spin for
system distances greater than $\sim 10$ kpc. We discuss the uncertainties and
implications of these estimates.


Abstract:
  The CHIME/FRB Project has recently released its first catalog of fast radio
bursts (FRBs), containing 492 unique sources. We present results from angular
cross-correlations of CHIME/FRB sources with galaxy catalogs. We find a
statistically significant ($p$-value $\sim 10^{-4}$, accounting for
look-elsewhere factors) cross-correlation between CHIME FRBs and galaxies in
the redshift range $0.3 \lesssim z \lesssim 0.5$, in three photometric galaxy
surveys: WISE$\times$SCOS, DESI-BGS, and DESI-LRG. The level of
cross-correlation is consistent with an order-one fraction of the CHIME FRBs
being in the same dark matter halos as survey galaxies in this redshift range.
We find statistical evidence for a population of FRBs with large host
dispersion measure ($\sim 400$ pc cm$^{-3}$), and show that this can plausibly
arise from gas in large halos ($M \sim 10^{14} M_\odot$), for FRBs near the
halo center ($r \lesssim 100$ kpc). These results will improve in future
CHIME/FRB catalogs, with more FRBs and better angular resolution.


Abstract:
  3D object detection with a single image is an essential and challenging task
for autonomous driving. Recently, keypoint-based monocular 3D object detection
has made tremendous progress and achieved great speed-accuracy trade-off.
However, there still exists a huge gap with LIDAR-based methods in terms of
accuracy. To improve their performance without sacrificing efficiency, we
propose a sort of lightweight feature pyramid network called Lite-FPN to
achieve multi-scale feature fusion in an effective and efficient way, which can
boost the multi-scale detection capability of keypoint-based detectors.
Besides, the misalignment between classification score and localization
precision is further relieved by introducing a novel regression loss named
attention loss. With the proposed loss, predictions with high confidence but
poor localization are treated with more attention during the training phase.
Comparative experiments based on several state-of-the-art keypoint-based
detectors on the KITTI dataset show that our proposed methods manage to achieve
significant improvements in both accuracy and frame rate. The code and
pretrained models will be released at
\url{https://github.com/yanglei18/Lite-FPN}.


Abstract:
  Extracting information from documents usually relies on natural language
processing methods working on one-dimensional sequences of text. In some cases,
for example, for the extraction of key information from semi-structured
documents, such as invoice-documents, spatial and formatting information of
text are crucial to understand the contextual meaning. Convolutional neural
networks are already common in computer vision models to process and extract
relationships in multidimensional data. Therefore, natural language processing
models have already been combined with computer vision models in the past, to
benefit from e.g. positional information and to improve performance of these
key information extraction models. Existing models were either trained on
unpublished data sets or on an annotated collection of receipts, which did not
focus on PDF-like documents. Hence, in this research project a template-based
document generator was created to compare state-of-the-art models for
information extraction. An existing information extraction model "Chargrid"
(Katti et al., 2019) was reconstructed and the impact of a bounding box
regression decoder, as well as the impact of an NLP pre-processing step was
evaluated for information extraction from documents. The results have shown
that NLP based pre-processing is beneficial for model performance. However, the
use of a bounding box regression decoder increases the model performance only
for fields that do not follow a rectangular shape.


Abstract:
  In this paper, we provide (i) a rigorous general theory to elicit conditions
on (tail-dependent) heavy-tailed cyber-risk distributions under which a risk
management firm might find it (non)sustainable to provide aggregate cyber-risk
coverage services for smart societies, and (ii)a real-data driven numerical
study to validate claims made in theory assuming boundedly rational cyber-risk
managers, alongside providing ideas to boost markets that aggregate dependent
cyber-risks with heavy-tails.To the best of our knowledge, this is the only
complete general theory till date on the feasibility of aggregate cyber-risk
management.


Abstract:
  The discovery of pulsars is of great significance in the field of physics and
astronomy. As the astronomical equipment produces a large amount of pulsar
data, an algorithm for automatically identifying pulsars becomes urgent. We
propose a deep learning framework for pulsar recognition. In response to the
extreme imbalance between positive and negative examples and the hard negative
sample issue presented in the HTRU Medlat Training Data,there are two coping
strategies in our framework: the smart under-sampling and the improved loss
function. We also apply the early-fusion strategy to integrate features
obtained from different attributes before classification to improve the
performance. To our best knowledge,this is the first study that integrates
these strategies and techniques together in pulsar recognition. The experiment
results show that our framework outperforms previous works with the respect to
either the training time or F1 score. We can not only speed up the training
time by 10X compared with the state-of-the-art work, but also get a competitive
result in terms of F1 score.


Abstract:
  Quantum coherence and quantum correlations are studied in the strongly
interacting system composed of two qubits and an oscillator with the presence
of a parametric medium. To analytically solve the system, we employ the
adiabatic approximation approach. It assumes each qubit's characteristic
frequency is substantially lower than the oscillator frequency. To validate our
approximation, a good agreement between the calculated energy spectrum of the
Hamiltonian with its numerical result is presented. The time evolution of the
reduced density matrices of the two-qubit and the oscillator subsystems are
computed from the tripartite initial state. Starting with a factorized
two-qubit initial state, the quasi-periodicity in the revival and collapse
phenomenon that occurs in the two-qubit population inversion is studied. Based
on the measure of relative entropy of coherence, we investigate the quantum
coherence and its explicit dependence on the parametric term both for the
two-qubit and the individual qubit subsystems by adopting different choices of
the initial states. Similarly, the existence of quantum correlations is
demonstrated by studying the geometric discord and concurrence. Besides, by
numerically minimizing the Hilbert-Schmidt distance, the dynamically produced
near maximally entangled states are reconstructed. The reconstructed states are
observed to be nearly pure generalized Bell states. Furthermore, utilizing the
oscillator density matrix, the quadrature variance and phase-space distribution
of the associated Husimi $Q$-function are computed in the minimum entropy
regime and conclude that the obtained nearly pure evolved state is a squeezed
coherent state.


Abstract:
  It is an open question to give a combinatorial interpretation of the Falk
invariant of a hyperplane arrangement, i.e. the third rank of successive
quotients in the lower central series of the fundamental group of the
arrangement. In this article, we give a combinatorial formula for this
invariant in the case of hyperplane arrangements that are complete lift
representation of certain gain graphs. As a corollary, we compute the Falk
invariant for the cone of the braid, Shi, Linial and semiorder arrangements.


Abstract:
  We discuss compatibility between various quantum aspects of bosonic fields,
relevant for quantum optics and quantum thermodynamics, and the mesoscopic
formalism of reduced state of the field (RSF). In particular, we derive exact
conditions under which Gaussian and Bogoliubov-type evolutions can be cast into
the RSF framework. In that regard, special emphasis is put on Gaussian thermal
operations. To strengthen the link between the RSF formalism and the notion of
classicality for bosonic quantum fields, we prove that RSF contains no
information about entanglement in two-mode Gaussian states. For the same
purpose, we show that the entropic characterisation of RSF by means of the von
Neumann entropy is qualitatively the same as its description based on the Wehrl
entropy. Our findings help bridge the conceptual gap between quantum and
classical mechanics.


Abstract:
  Many machine learning techniques incorporate identity-preserving
transformations into their models to generalize their performance to previously
unseen data. These transformations are typically selected from a set of
functions that are known to maintain the identity of an input when applied
(e.g., rotation, translation, flipping, and scaling). However, there are many
natural variations that cannot be labeled for supervision or defined through
examination of the data. As suggested by the manifold hypothesis, many of these
natural variations live on or near a low-dimensional, nonlinear manifold.
Several techniques represent manifold variations through a set of learned Lie
group operators that define directions of motion on the manifold. However
theses approaches are limited because they require transformation labels when
training their models and they lack a method for determining which regions of
the manifold are appropriate for applying each specific operator. We address
these limitations by introducing a learning strategy that does not require
transformation labels and developing a method that learns the local regions
where each operator is likely to be used while preserving the identity of
inputs. Experiments on MNIST and Fashion MNIST highlight our model's ability to
learn identity-preserving transformations on multi-class datasets.
Additionally, we train on CelebA to showcase our model's ability to learn
semantically meaningful transformations on complex datasets in an unsupervised
manner.


Abstract:
  We study the fundamental design automation problem of equivalence checking in
the NISQ (Noisy Intermediate-Scale Quantum) computing realm where quantum noise
is present inevitably. The notion of approximate equivalence of (possibly
noisy) quantum circuits is defined based on the Jamiolkowski fidelity which
measures the average distance between output states of two super-operators when
the input is chosen at random. By employing tensor network contraction, we
present two algorithms, aiming at different situations where the number of
noises varies, for computing the fidelity between an ideal quantum circuit and
its noisy implementation. The effectiveness of our algorithms is demonstrated
by experimenting on benchmarks of real NISQ circuits. When compared with the
state-of-the-art implementation incorporated in Qiskit, experimental results
show that the proposed algorithms outperform in both efficiency and
scalability.


Abstract:
  In this article we consider the length functional defined on the space of
immersed planar curves. The $L^2(ds)$ Riemannian metric gives rise to the curve
shortening flow as the gradient flow of the length functional. Motivated by the
triviality of the metric topology in this space, we consider the gradient flow
of the length functional with respect to the $H^1(ds)$-metric. Circles with
radius $r_0$ shrink with $r(t) = \sqrt{W(e^{c-2t})}$ under the flow, where $W$
is the Lambert $W$ function and $c = r_0^2 + \log r_0^2$. We conduct a thorough
study of this flow, giving existence of eternal solutions and convergence for
general initial data, preservation of regularity in various spaces, qualitative
properties of the flow after an appropriate rescaling, and numerical
simulations.


Abstract:
  Relational knowledge bases (KBs) are commonly used to represent world
knowledge in machines. However, while advantageous for their high degree of
precision and interpretability, KBs are usually organized according to
manually-defined schemas, which limit their expressiveness and require
significant human efforts to engineer and maintain. In this review, we take a
natural language processing perspective to these limitations, examining how
they may be addressed in part by training deep contextual language models (LMs)
to internalize and express relational knowledge in more flexible forms. We
propose to organize knowledge representation strategies in LMs by the level of
KB supervision provided, from no KB supervision at all to entity- and
relation-level supervision. Our contributions are threefold: (1) We provide a
high-level, extensible taxonomy for knowledge representation in LMs; (2) Within
our taxonomy, we highlight notable models, evaluation tasks, and findings, in
order to provide an up-to-date review of current knowledge representation
capabilities in LMs; and (3) We suggest future research directions that build
upon the complementary aspects of LMs and KBs as knowledge representations.


Abstract:
  In this paper, we show that the (admissible) character stack, which is a
stack version of the character variety, is an open substack of the
Teichm\"uller stack of homogeneous spaces of SL(2,C). We show that the
tautological family over the representation variety, given by deforming the
holonomy, is always a complete family. This is a generalisation of the work of
E. Ghys about deformations of complex structures these homogeneous spaces.


Abstract:
  In this manuscript we demonstrate a method to reconstruct the wavefront of
focused beams from a measured diffraction pattern behind a diffracting mask in
real-time. The phase problem is solved by means of a neural network, which is
trained with simulated data and verified with experimental data. The neural
network allows live reconstructions within a few milliseconds, which previously
with iterative phase retrieval took several seconds, thus allowing the
adjustment of complex systems and correction by adaptive optics in real time.
The neural network additionally outperforms iterative phase retrieval with high
noise diffraction patterns.


Abstract:
  To realize high-accuracy classification of high spatial resolution (HSR)
images, this letter proposes a new multi-feature fusion-based scene
classification framework (MF2SCF) by fusing local, global, and color features
of HSR images. Specifically, we first extract the local features with the help
of image slicing and densely connected convolutional networks (DenseNet), where
the outputs of dense blocks in the fine-tuned DenseNet-121 model are jointly
averaged and concatenated to describe local features. Second, from the
perspective of complex networks (CN), we model a HSR image as an undirected
graph based on pixel distance, intensity, and gradient, and obtain a gray-scale
image (GSI), a gradient of image (GoI), and three CN-based feature images to
delineate global features. To make the global feature descriptor resist to the
impact of rotation and illumination, we apply uniform local binary patterns
(LBP) on GSI, GoI, and feature images, respectively, and generate the final
global feature representation by concatenating spatial histograms. Third, the
color features are determined based on the normalized HSV histogram, where HSV
stands for hue, saturation, and value, respectively. Finally, three feature
vectors are jointly concatenated for scene classification. Experiment results
show that MF2SCF significantly improves the classification accuracy compared
with state-of-the-art LBP-based methods and deep learning-based methods.


Abstract:
  In this paper we study quasilinear elliptic equations driven by the double
phase operator and a right-hand side which has the combined effect of a
singular and of a parametric term. Based on the fibering method by using the
Nehari manifold we are going to prove the existence of at least two weak
solutions for such problem when the parameter is sufficiently small.


Abstract:
  Deep learning has made significant impacts on multi-view stereo systems.
State-of-the-art approaches typically involve building a cost volume, followed
by multiple 3D convolution operations to recover the input image's pixel-wise
depth. While such end-to-end learning of plane-sweeping stereo advances public
benchmarks' accuracy, they are typically very slow to compute. We present
\ouralg, a highly efficient multi-view stereo algorithm that seamlessly
integrates multi-view constraints into single-view networks via an attention
mechanism. Since \ouralg only builds on 2D convolutions, it is at least
$2\times$ faster than all the notable counterparts. Moreover, our algorithm
produces precise depth estimations and 3D reconstructions, achieving
state-of-the-art results on challenging benchmarks ScanNet, SUN3D, RGBD, and
the classical DTU dataset. our algorithm also out-performs all other algorithms
in the setting of inexact camera poses. Our code is released at
\url{https://github.com/zhenpeiyang/MVS2D}


Abstract:
  We are interested in solutions of the nonlinear Klein-Gordon equation (NLKG)
in $\mathbb{R}^{1+d}$, $d\ge1$, which behave as a soliton or a sum of solitons
in large time. In the spirit of other articles focusing on the supercritical
generalized Korteweg-de Vries equations and on the nonlinear Schr{\"o}dinger
equations, we obtain an $N$-parameter family of solutions of (NLKG) which
converges exponentially fast to a sum of given (unstable) solitons. For $N =
1$, this family completely describes the set of solutions converging to the
soliton considered; for $N\ge 2$, we prove uniqueness in a class with explicit
algebraic rate of convergence.


Abstract:
  In this paper we completely solve the family of parametrised Thue equations
\[
  X(X-F_n Y)(X-2^n Y)-Y^3=\pm 1, \] where $F_n$ is the $n$-th Fibonacci number.
In particular, for any integer $n\geq 3$ the Thue equation has only the trivial
solutions $(\pm 1,0), (0,\mp 1), \mp(F_n,1), \mp(2^n,1)$.


Abstract:
  Indexing intervals is a fundamental problem, finding a wide range of
applications. Recent work on managing large collections of intervals in main
memory focused on overlap joins and temporal aggregation problems. In this
paper, we propose novel and efficient in-memory indexing techniques for
intervals, with a focus on interval range queries, which are a basic component
of many search and analysis tasks. First, we propose an optimized version of a
single-level (flat) domain-partitioning approach, which may have large space
requirements due to excessive replication. Then, we propose a hierarchical
partitioning approach, which assigns each interval to at most two partitions
per level and has controlled space requirements. Novel elements of our
techniques include the division of the intervals at each partition into groups
based on whether they begin inside or before the partition boundaries, reducing
the information stored at each partition to the absolutely necessary, and the
effective handling of data sparsity and skew. Experimental results on real and
synthetic interval sets of different characteristics show that our approaches
are typically one order of magnitude faster than the state-of-the-art.


Abstract:
  We propose a novel storage scheme for three-nucleon (3N) interaction matrix
elements relevant for the normal-ordered two-body approximation used
extensively in ab initio calculations of atomic nuclei. This scheme reduces the
required memory by approximately two orders of magnitude, which allows the
generation of 3N interaction matrix elements with the standard truncation of
$E_{\rm 3max}=28$, well beyond the previous limit of 18. We demonstrate that
this is sufficient to obtain the ground-state energy of $^{132}$Sn converged to
within a few MeV with respect to the $E_{\rm 3max}$ truncation.In addition, we
study the asymptotic convergence behavior and perform extrapolations to the
un-truncated limit. Finally, we investigate the impact of truncations made when
evolving free-space 3N interactions with the similarity renormalization group.
We find that the contribution of blocks with angular momentum $J_{\rm rel}>9/2$
to the ground-state energy is dominated by a basis-truncation artifact which
vanishes in the large-space limit, so these computationally expensive
components can be neglected. For the two sets of nuclear interactions employed
in this work, the resulting binding energy of $^{132}$Sn agrees with the
experimental value within theoretical uncertainties. This work enables
converged ab initio calculations of heavy nuclei.


Abstract:
  We show that the standard notion of entanglement is not defined for
gravitationally anomalous two-dimensional theories because they do not admit a
local tensor factorization of the Hilbert space into local Hilbert spaces.
Qualitatively, the modular flow cannot act consistently and unitarily in a
finite region, if there are different numbers of states with a given energy
traveling in the two opposite directions. We make this precise by decomposing
it into two observations: First, a two-dimensional CFT admits a consistent
quantization on a space with boundary only if it is not anomalous. Second, a
local tensor factorization always leads to a definition of consistent, unitary,
energy-preserving boundary condition. As a corollary we establish a
generalization of the Nielsen-Ninomiya theorem to all two-dimensional unitary
local QFTs: No continuum quantum field theory in two dimensions can admit a
lattice regulator unless its gravitational anomaly vanishes. We also show that
the conclusion can be generalized to six dimensions by dimensional reduction on
a four-manifold of nonvanishing signature. We advocate that these points be
used to reinterpret the gravitational anomaly
quantum-information-theoretically, as a fundamental obstruction to the
localization of quantum information.


Abstract:
  Thermal jitter (phase noise) from a free-running ring oscillator is a common,
easily implementable physical randomness source in True Random Number
Generators (TRNGs). We show how to evaluate entropy, autocorrelation, and bit
pattern distributions of ring oscillator noise sources, even with low jitter
levels or some bias. Entropy justification is required in NIST 800-90B and
AIS-31 testing and for applications such as the RISC-V entropy source
extension. Our numerical evaluation algorithms outperform Monte Carlo
simulations in speed and accuracy. We also propose a new lower bound estimation
formula for the entropy of ring oscillator sources which applies more generally
than previous ones.


Abstract:
  This paper applies t-SNE, a visualisation technique familiar from Deep Neural
Network research to argumentation graphs by applying it to the output of graph
embeddings generated using several different methods. It shows that such a
visualisation approach can work for argumentation and show interesting
structural properties of argumentation graphs, opening up paths for further
research in the area.


Abstract:
  The fracture stress of materials typically depends on the sample size and is
traditionally explained in terms of extreme value statistics. A recent work
reported results on the carrying capacity of long polyamide and polyester wires
and interpret the results in terms of a probabilistic argument known as the St.
Petersburg paradox. Here, we show that the same results can be better explained
in terms of extreme value statistics. We also discuss the relevance of rate
dependent effects.


Abstract:
  This paper proposes a model to explain the potential role of inter-group
conflicts in determining the rise and fall of signaling norms. In one
population, assortative matching according to types is sustained by signaling.
In the other population, individuals do not signal and they are randomly
matched. Types evolve within each population. At the same time, the two
populations may engage in conflicts. Due to assortative matching, high types
grow faster in the population with signaling, yet they bear the cost of
signaling, which lowers their population's fitness in the long run. We show
that the survival of the signaling population depends crucially on the timing
and the intensity of inter-group conflicts.


Abstract:
  For predicting the kinetics of nucleic acid reactions, continuous-time Markov
chains (CTMCs) are widely used. The rate of a reaction can be obtained through
the mean first passage time (MFPT) of its CTMC. However, a typical issue in
CTMCs is that the number of states could be large, making MFPT estimation
challenging, particularly for events that happen on a long time scale (rare
events). We propose the pathway elaboration method, a time-efficient
probabilistic truncation-based approach for detailed-balance CTMCs. It can be
used for estimating the MFPT for rare events in addition to rapidly evaluating
perturbed parameters without expensive recomputations. We demonstrate that
pathway elaboration is suitable for predicting nucleic acid kinetics by
conducting computational experiments on 267 measurements that cover a wide
range of rates for different types of reactions. We utilize pathway elaboration
to gain insight on the kinetics of two contrasting reactions, one being a rare
event. We then compare the performance of pathway elaboration with the
stochastic simulation algorithm (SSA) for MFPT estimation on 237 of the
reactions for which SSA is feasible. We further build truncated CTMCs with SSA
and transition path sampling (TPS) to compare with pathway elaboration.
Finally, we use pathway elaboration to rapidly evaluate perturbed model
parameters during optimization with respect to experimentally measured rates
for these 237 reactions. The testing error on the remaining 30 reactions, which
involved rare events and were not feasible to simulate with SSA, improved
comparably with the training error. Our framework and dataset are available at
https://github.com/ DNA-and-Natural-Algorithms-Group/PathwayElaboration.


Abstract:
  We study an optimal control problem for a simple transportation model on a
path graph. We give a closed form solution for the optimal controller, which
can also account for planned disturbances using feed-forward. The optimal
controller is highly structured, which allows the controller to be implemented
using only local communication, conducted through two sweeps through the graph.


Abstract:
  We present the GeneScore, a concept of feature reduction for Machine Learning
analysis of biomedical data. Using expert knowledge, the GeneScore integrates
different molecular data types into a single score. We show that the GeneScore
is superior to a binary matrix in the classification of cancer entities from
SNV, Indel, CNV, gene fusion and gene expression data. The GeneScore is a
straightforward way to facilitate state-of-the-art analysis, while making use
of the available scientific knowledge on the nature of molecular data features
used.


Abstract:
  In their everyday life, the speech recognition performance of human listeners
is influenced by diverse factors, such as the acoustic environment, the talker
and listener positions, possibly impaired hearing, and optional hearing
devices. Prediction models come closer to considering all required factors
simultaneously to predict the individual speech recognition performance in
complex acoustic environments. While such predictions may still not be
sufficiently accurate for serious applications, they can already be performed
and demand an accessible representation. In this contribution, an interactive
representation of speech recognition performance is proposed, which focuses on
the listeners head orientation and the spatial dimensions of an acoustic scene.
A exemplary modeling toolchain, including an acoustic rendering model, a
hearing device model, and a listener model, was used to generate a data set for
demonstration purposes. Using the spatial speech recognition maps to explore
this data set demonstrated the suitability of the approach to observe possibly
relevant behavior. The proposed representation provides a suitable target to
compare and validate different modeling approaches in ecologically relevant
contexts. Eventually, it may serve as a tool to use validated prediction models
in the design of spaces and devices which take speech communication into
account.


Abstract:
  Let $K$ be an imaginary quadratic field with class number 1, in this paper we
obtain the functional equation of the $p$-adic $L$-function of: (1) a small
slope $p$-stabilisation of a Bianchi modular form, and (2) a critical slope
$p$-stabilisation of a Base change Bianchi modular form that is
$\Sigma$-smooth. To treat case (2) we use $p$-adic families of Bianchi modular
forms.


Abstract:
  For every prime number $p\geq 3$ and every integer $m\geq 1$, we prove the
existence of a continuous Galois representation $\rho: G_\mathbb{Q} \rightarrow
Gl_m(\mathbb{Z}_p)$ which has open image and is unramified outside
$\{p,\infty\}$ (resp. outside $\{2,p,\infty\}$) when $p\equiv 3$ mod $4$ (resp.
$p \equiv 1$ mod $4$).


Abstract:
  Low-dimensional node embeddings play a key role in analyzing graph datasets.
However, little work studies exactly what information is encoded by popular
embedding methods, and how this information correlates with performance in
downstream machine learning tasks. We tackle this question by studying whether
embeddings can be inverted to (approximately) recover the graph used to
generate them. Focusing on a variant of the popular DeepWalk method (Perozzi et
al., 2014; Qiu et al., 2018), we present algorithms for accurate embedding
inversion - i.e., from the low-dimensional embedding of a graph G, we can find
a graph H with a very similar embedding. We perform numerous experiments on
real-world networks, observing that significant information about G, such as
specific edges and bulk properties like triangle density, is often lost in H.
However, community structure is often preserved or even enhanced. Our findings
are a step towards a more rigorous understanding of exactly what information
embeddings encode about the input graph, and why this information is useful for
learning tasks.


Abstract:
  Here, we propose an original approach for human activity recognition (HAR)
with commercial IEEE 802.11ac (WiFi) devices, which generalizes across
different persons, days and environments. To achieve this, we devise a
technique to extract, clean and process the received phases from the channel
frequency response (CFR) of the WiFi channel, obtaining an estimate of the
Doppler shift at the receiver of the communication link. The Doppler shift
reveals the presence of moving scatterers in the environment, while not being
affected by (environment specific) static objects. The proposed HAR framework
is trained on data collected as a person performs four different activities and
is tested on unseen setups, to assess its performance as the person, the day
and/or the environment change with respect to those considered at training
time. In the worst case scenario, the proposed HAR technique reaches an average
accuracy higher than 95%, validating the effectiveness of the extracted Doppler
information, used in conjunction with a learning algorithm based on a neural
network, in recognizing human activities in a subject and environment
independent fashion.


Abstract:
  Good approximate eigenstates of a Hamiltionian operator which poesses a point
as well as a continuous spectrum have beeen obtained using the Lanczos
algorithm. Iterating with the bare Hamiltonian operator yields spurious
solutions which can easily be identified. The rms radius of the ground state
eigenvector, for example, is calculated using the bare operator.


Abstract:
  Frequency estimation is a fundamental problem in many areas. The well-known
A&M and its variant estimators have established an estimation framework by
iteratively interpolating the discrete Fourier transform (DFT) coefficients. In
general, those estimators require two DFT interpolations per iteration, have
uneven initial estimation performance against frequencies, and are incompetent
for small sample numbers due to low-order approximations involved. Exploiting
the iterative estimation framework of A&M, we unprecedentedly introduce the
Pad\'e approximation to frequency estimation, unveil some features about the
updating function used for refining the estimation in each iteration, and
develop a simple closed-form solution to solving the residual estimation error.
Extensive simulation results are provided, validating the superiority of the
new estimator over the state-the-art estimators in wide ranges of key
parameters.


Abstract:
  The pandemic by COVID-19 is causing a devastating effect on the health of
global population. There are several efforts to prevent the spread of the
virus. Among those efforts, cleaning and disinfecting public areas have become
important tasks. In order to contribute in this direction, this paper proposes
a coverage path planning algorithm for a spraying drone, a micro aerial vehicle
that has mounted a sprayer/sprinkler system, to disinfect areas. In contrast
with planners in the state-of-the-art, this proposal presents i) a new
sprayer/sprinkler model that fits a more realistic coverage volume to the drop
dispersion and ii) a planning algorithm that efficiently restricts the flight
to the region of interest avoiding potential collisions in bounded scenes. The
drone with the algorithm has been tested in several simulation scenes, showing
that the algorithm is effective and covers more areas with respect to other
approaches in the literature. Note that the proposal is not limited to
disinfection applications, but can be applied to other ones, such as painting
or precision agriculture.


Abstract:
  The combination of machine learning with control offers many opportunities,
in particular for robust control. However, due to strong safety and reliability
requirements in many real-world applications, providing rigorous statistical
and control-theoretic guarantees is of utmost importance, yet difficult to
achieve for learning-based control schemes. We present a general framework for
learning-enhanced robust control that allows for systematic integration of
prior engineering knowledge, is fully compatible with modern robust control and
still comes with rigorous and practically meaningful guarantees. Building on
the established Linear Fractional Representation and Integral Quadratic
Constraints framework, we integrate Gaussian Process Regression as a learning
component and state-of-the-art robust controller synthesis. In a concrete
robust control example, our approach is demonstrated to yield improved
performance with more data, while guarantees are maintained throughout.


Abstract:
  Thermal conduction in polymer nanocomposites depends on several parameters
including the thermal conductivity and geometrical features of the
nanoparticles, the particle loading, their degree of dispersion and formation
of a percolating networks. To enhance efficiency of thermal contact between
free-standing conductive nanoparticles were previously proposed. This work
report for the first time the investigation of molecular junctions within a
graphene polymer nanocomposite. Molecular dynamics simulations were conducted
to investigate the thermal transport efficiency of molecular junctions in
polymer tight contact, to quantify the contribution of molecular junctions when
graphene and the molecular junctions are surrounded by polydimethylsiloxane
(PDMS). A strong dependence of the thermal conductance in PDMS/graphene model
was found, with best performances obtained with short and conformationally
rigid molecular junctions.


Abstract:
  We consider adversarial training of deep neural networks through the lens of
Bayesian learning, and present a principled framework for adversarial training
of Bayesian Neural Networks (BNNs) with certifiable guarantees. We rely on
techniques from constraint relaxation of non-convex optimisation problems and
modify the standard cross-entropy error model to enforce posterior robustness
to worst-case perturbations in $\epsilon$-balls around input points. We
illustrate how the resulting framework can be combined with methods commonly
employed for approximate inference of BNNs. In an empirical investigation, we
demonstrate that the presented approach enables training of certifiably robust
models on MNIST, FashionMNIST and CIFAR-10 and can also be beneficial for
uncertainty calibration. Our method is the first to directly train certifiable
BNNs, thus facilitating their deployment in safety-critical applications.


Abstract:
  In this paper, we consider distributed Nash equilibrium seeking in monotone
and hypomonotone games. We first assume that each player has knowledge of the
opponents' decisions and propose a passivity-based modification of the standard
gradient-play dynamics, that we call "Heavy Anchor". We prove that Heavy Anchor
allows a relaxation of strict monotonicity of the pseudo-gradient, needed for
gradient-play dynamics, and can ensure exact asymptotic convergence in merely
monotone regimes. We extend these results to the setting where each player has
only partial information of the opponents' decisions. Each player maintains a
local decision variable and an auxiliary state estimate and communicates with
their neighbours to learn the opponents' actions. We modify Heavy Anchor via a
distributed Laplacian feedback and show how we can exploit
equilibrium-independent passivity properties to achieve convergence to a Nash
equilibrium in hypomonotone regimes.


Abstract:
  In this paper we find curves minimizing the elastic energy among curves whose
length is fixed and whose ends are pinned. Applying the shooting method, we can
identify all critical points explicitly and determine which curve is the global
minimizer. As a result we show that the critical points consist of wavelike
elasticae and the minimizers do not have any loops or interior inflection
points.


Abstract:
  This paper initiates a discussion of mechanism design when the participating
agents exhibit preferences that deviate from expected utility theory (EUT). In
particular, we consider mechanism design for systems where the agents are
modeled as having cumulative prospect theory (CPT) preferences, which is a
generalization of EUT preferences. We point out some of the key modifications
needed in the theory of mechanism design that arise from agents having CPT
preferences and some of the shortcomings of the classical mechanism design
framework. In particular, we show that the revelation principle, which has
traditionally played a fundamental role in mechanism design, does not continue
to hold under CPT. We develop an appropriate framework that we call mediated
mechanism design which allows us to recover the revelation principle for CPT
agents. We conclude with some interesting directions for future work.


Abstract:
  We study the Becker-D\"oring bubblelator, a variant of the Becker-D\"oring
coagulation-fragmentation system that models the growth of clusters by gain or
loss of monomers. Motivated by models of gas evolution oscillators from
physical chemistry, we incorporate injection of monomers and depletion of large
clusters. For a wide range of physical rates, the Becker-D\"oring system itself
exhibits a dynamic phase transition as mass density increases past a critical
value. We connect the Becker-D\"oring bubblelator to a transport equation
coupled with an integrodifferential equation for excess monomer density by
formal asymptotics in the near-critical regime. For suitable
injection/depletion rates, we argue that time-periodic solutions appear via a
Hopf bifurcation. Numerics confirm that the generation and removal of large
clusters can become desynchronized, leading to temporal oscillations associated
with bursts of large-cluster nucleation.


Abstract:
  Graph convolutional neural networks (GCNs) generalize tradition convolutional
neural networks (CNNs) from low-dimensional regular graphs (e.g., image) to
high dimensional irregular graphs (e.g., text documents on word embeddings).
Due to inevitable faulty data collection instruments, deceptive data
manipulation, or other system errors, the data might be error-contaminated.
Even a small amount of error such as noise can compromise the ability of GCNs
and render them inadmissible to a large extent. The key challenge is how to
effectively and efficiently employ GCNs in the presence of erroneous data. In
this paper, we propose a novel Robust Graph Convolutional Neural Networks for
possible erroneous single-view or multi-view data where data may come from
multiple sources. By incorporating an extra layers via Autoencoders into
traditional graph convolutional networks, we characterize and handle typical
error models explicitly. Experimental results on various real-world datasets
demonstrate the superiority of the proposed model over the baseline methods and
its robustness against different types of error.


Abstract:
  Top-K SpMV is a key component of similarity-search on sparse embeddings. This
sparse workload does not perform well on general-purpose NUMA systems that
employ traditional caching strategies. Instead, modern FPGA accelerator cards
have a few tricks up their sleeve. We introduce a Top-K SpMV FPGA design that
leverages reduced precision and a novel packet-wise CSR matrix compression,
enabling custom data layouts and delivering bandwidth efficiency often
unreachable even in architectures with higher peak bandwidth. With HBM-based
boards, we are 100x faster than a multi-threaded CPU implementation and 2x
faster than a GPU with 20% higher bandwidth, with 14.2x higher
power-efficiency.


Abstract:
  To extract the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{ub}|$, we
have re-analyzed all the available inputs (data and theory) on the $B\to\pi
l\nu$ decays including the newly available inputs on the form-factors from
light cone sum rule (LCSR) approach. We have reproduced and compared the
results with the procedure taken up by the Heavy Flavor Averaging Group
(HFLAV), while commenting on the effect of outliers on the fits. After removing
the outliers and creating a comparable group of data-sets, we mention a few
scenarios in the extraction of $|V_{ub}|$. In all those scenarios, the
extracted values of $|V_{ub}|$ are higher than that obtained by HFLAV. Our best
results for $|V_{ub}|^{exc.}$ are $(3.88 \pm 0.13)\times 10^{-3}$ and $(3.87
\pm 0.13)\times 10^{-3}$ in frequentist and Bayesian approaches, respectively,
which are consistent with that extracted from inclusive decays $|V_{ub}|^{inc}$
within $1~\sigma$ confidence interval.


Abstract:
  Lithium metal has been an attractive candidate as a next generation anode
material. Despite its popularity, stability issues of lithium in the liquid
electrolyte and the formation of lithium whiskers have kept it from practical
use. Three-dimensional (3D) current collectors have been proposed as an
effective method to mitigate whiskers growth. Although extensive research
efforts have been done, the effects of three key parameters of the 3D current
collectors, namely the surface area, the tortuosity factor, and the surface
chemistry, on the performance of lithium metal batteries remain elusive.
Herein, we quantitatively studied the role of these three parameters by
synthesizing four types of porous copper networks with different sizes of
well-structured micro-channels. X-ray microscale computed tomography (micro-CT)
allowed us to assess the surface area, the pore size and the tortuosity factor
of the porous copper materials. A metallic Zn coating was also applied to study
the influence of surface chemistry on the performance of the 3D current
collectors. The effects of these parameters on the performance were studied in
detail through Scanning Electron Microscopy (SEM) and Titration Gas
Chromatography (TGC). Stochastic simulations further allowed us to interpret
the role of the tortuosity factor in lithiation. By understanding these
effects, the optimal range of the key parameters is found for the porous copper
anodes and their performance is predicted. Using these parameters to inform the
design of porous copper anodes for Li deposition, Coulombic efficiencies (CE)
of up to 99.56% are achieved, thus paving the way for the design of effective
3D current collector systems.


Abstract:
  This position paper summarizes a recently developed research program focused
on inference in the context of data centric science and engineering
applications, and forecasts its trajectory forward over the next decade. Often
one endeavours in this context to learn complex systems in order to make more
informed predictions and high stakes decisions under uncertainty. Some key
challenges which must be met in this context are robustness, generalizability,
and interpretability. The Bayesian framework addresses these three challenges
elegantly, while bringing with it a fourth, undesirable feature: it is
typically far more expensive than its deterministic counterparts. In the 21st
century, and increasingly over the past decade, a growing number of methods
have emerged which allow one to leverage cheap low-fidelity models in order to
precondition algorithms for performing inference with more expensive models and
make Bayesian inference tractable in the context of high-dimensional and
expensive models. Notable examples are multilevel Monte Carlo (MLMC),
multi-index Monte Carlo (MIMC), and their randomized counterparts (rMLMC),
which are able to provably achieve a dimension-independent (including
$\infty-$dimension) canonical complexity rate with respect to mean squared
error (MSE) of $1/$MSE. Some parallelizability is typically lost in an
inference context, but recently this has been largely recovered via novel
double randomization approaches. Such an approach delivers i.i.d. samples of
quantities of interest which are unbiased with respect to the infinite
resolution target distribution. Over the coming decade, this family of
algorithms has the potential to transform data centric science and engineering,
as well as classical machine learning applications such as deep learning, by
scaling up and scaling out fully Bayesian inference.


Abstract:
  We present a study on magnetotransport in films of the topological Dirac
semimetal Cd$_{3}$As$_{2}$ doped with Sb grown by molecular beam epitaxy. In
our weak antilocalization analysis, we find a significant enhancement of the
spin-orbit scattering rate, indicating that Sb doping leads to a strong
increase of the pristine band-inversion energy. We discuss possible origins of
this large enhancement by comparing Sb-doped Cd$_{3}$As$_{2}$ with other
compound semiconductors. Sb-doped Cd$_{3}$As$_{2}$ will be a suitable system
for further investigations and functionalization of topological Dirac
semimetals.


Abstract:
  Ultra-reliable low latency communications (URLLC) arose to serve industrial
IoT (IIoT) use cases within the 5G. Currently, it has inherent limitations to
support future services. Based on state-of-the-art research and practical
deployment experience, in this article, we introduce and advocate for three
variants: broadband, scalable and extreme URLLC. We discuss use cases and key
performance indicators and identify technology enablers for the new service
modes. We bring practical considerations from the IIoT testbed and provide an
outlook toward some new research directions.


Abstract:
  The design of algorithms that leverage machine learning alongside
combinatorial optimization techniques is a young but thriving area of
operations research. If trends emerge, the literature has still not converged
on the proper way of combining these two techniques or on the predictor
architectures that should be used. We focus on operations research problems for
which no efficient algorithms are known, but that are variants of classic
problems for which ones efficient algorithm exist. Elaborating on recent
contributions that suggest using a machine learning predictor to approximate
the variant by the classic problem, we introduce the notion of structured
approximation of an operations research problem by another. We provide a
generic learning algorithm to fit these approximations. This algorithm requires
only instances of the variant in the training set, unlike previous learning
algorithms that also require the solution of these instances. Using tools from
statistical learning theory, we prove a result showing the convergence speed of
the estimator, and deduce an approximation ratio guarantee on the performance
of the algorithm obtained for the variant. Numerical experiments on a single
machine scheduling and a stochastic vehicle scheduling problem from the
literature show that our learning algorithm is competitive with algorithms that
have access to optimal solutions, leading to state-of-the-art algorithms for
the variant considered.


Abstract:
  Spatial reasoning on multi-view line drawings by state-of-the-art supervised
deep networks is recently shown with puzzling low performances on the SPARE3D
dataset. To study the reason behind the low performance and to further our
understandings of these tasks, we design controlled experiments on both input
data and network designs. Guided by the hindsight from these experiment
results, we propose a simple contrastive learning approach along with other
network modifications to improve the baseline performance. Our approach uses a
self-supervised binary classification network to compare the line drawing
differences between various views of any two similar 3D objects. It enables
deep networks to effectively learn detail-sensitive yet view-invariant line
drawing representations of 3D objects. Experiments show that our method could
significantly increase the baseline performance in SPARE3D, while some popular
self-supervised learning methods cannot.


Abstract:
  We have entered an era of a pandemic that has shaken the world with major
impact to medical systems, economics and agriculture. Prominent computational
and mathematical models have been unreliable due to the complexity of the
spread of infections. Moreover, lack of data collection and reporting makes any
such modelling attempts unreliable. Hence we need to re-look at the situation
with the latest data sources and most comprehensive forecasting models. Deep
learning models such as recurrent neural networks are well suited for modelling
temporal sequences. In this paper, prominent recurrent neural networks, in
particular \textit{long short term memory} (LSTMs) networks, bidirectional
LSTM, and encoder-decoder LSTM models for multi-step (short-term) forecasting
the spread of COVID-infections among selected states in India. We select states
with COVID-19 hotpots in terms of the rate of infections and compare with
states where infections have been contained or reached their peak and provide
two months ahead forecast that shows that cases will slowly decline. Our
results show that long-term forecasts are promising which motivates the
application of the method in other countries or areas. We note that although we
made some progress in forecasting, the challenges in modelling remain due to
data and difficulty in capturing factors such as population density, travel
logistics, and social aspects such culture and lifestyle.


Abstract:
  We measure the small-scale clustering of the Data Release 16 extended Baryon
Oscillation Spectroscopic Survey Luminous Red Galaxy sample, corrected for
fibre-collisions using Pairwise Inverse Probability weights, which give
unbiased clustering measurements on all scales. We fit to the monopole and
quadrupole moments and to the projected correlation function over the
separation range $7-60\,h^{-1}$Mpc with a model based on the Aemulus
cosmological emulator to measure the growth rate of cosmic structure,
parameterized by $f\sigma_8$. We obtain a measurement of
$f\sigma_8(z=0.737)=0.408\pm0.038$, which is $1.4\sigma$ lower than the value
expected from 2018 Planck data for a flat $\Lambda$CDM model, and is more
consistent with recent weak-lensing measurements. The level of precision
achieved is 1.7 times better than more standard measurements made using only
the large-scale modes of the same sample. We also fit to the data using the
full range of scales $0.1-60\,h^{-1}$Mpc modelled by the Aemulus cosmological
emulator and find a $4.5\sigma$ tension in the amplitude of the halo velocity
field with the Planck+$\Lambda$CDM model, driven by a mismatch on the
non-linear scales. This may not be cosmological in origin, and could be due to
a breakdown in the Halo Occupation Distribution model used in the emulator.
Finally, we perform a robust analysis of possible sources of systematics,
including the effects of redshift uncertainty and incompleteness due to target
selection that were not included in previous analyses fitting to clustering
measurements on small scales.


Abstract:
  We study the physical properties of four-dimensional, string-theoretical,
horizonless "fuzzball" geometries by imaging their shadows. Their
microstructure traps light rays straying near the would-be horizon on
long-lived, highly redshifted chaotic orbits. In fuzzballs sufficiently near
the scaling limit this creates a shadow much like that of a black hole, while
avoiding the paradoxes associated with an event horizon. Observations of the
shadow size and residual glow can potentially discriminate between fuzzballs
away from the scaling limit and alternative models of black compact objects.


Abstract:
  We introduce a simplified model of physiological coughing or sneezing, in the
form of a thin liquid layer subject to a rapid (30 m/s) air stream. The setup
is simulated using the Volume-Of-Fluid method with octree mesh adaptation, the
latter allowing grid sizes small enough to capture the Kolmogorov length scale.
The results confirm the trend to an intermediate distribution between a
Log-Normal and a Pareto distribution $P(d) \propto d^{-3.3}$ for the
distribution of droplet sizes in agreement with a previous re-analysis of
experimental results by one of the authors. The mechanism of atomisation does
not differ qualitatively from the multiphase mixing layer experiments and
simulations. No mechanism for a bimodal distribution, also sometimes observed,
is evidenced in these simulations.


Abstract:
  We show that the ring of modular forms with characters for the even
unimodular lattice of signature (2,18) is obtained from the invariant ring of
$\mathrm{Sym}(\mathrm{Sym}^8(V) \oplus \mathrm{Sym}^{12}(V))$ with respect to
the action of $\mathrm{SL}(V)$ by adding a Borcherds product of weight 132 with
one relation of weight 264, where $V$ is a 2-dimensional $\mathbb{C}$-vector
space. The proof is based on the study of the moduli space of elliptic K3
surfaces with a section.


Abstract:
  We present an overview of phase field modeling of active matter systems as a
tool for capturing various aspects of complex and active interfaces. We first
describe how interfaces between different phases are characterized in phase
field models and provide simple fundamental governing equations that describe
their evolution. For a simple model, we then show how physical properties of
the interface, such as surface tension and interface thickness, can be
recovered from these equations. We then explain how the phase field formulation
can be coupled to various active matter realizations and discuss three
particular examples of continuum biphasic active matter: active
nematic-isotropic interfaces, active matter in viscoelastic environments, and
active shells in fluid background. Finally, we describe how multiple phase
fields can be used to model active cellular monolayers and present a general
framework that can be applied to the study of tissue behaviour and collective
migration.


Abstract:
  The chiral magnetic effect with a fluctuating chiral imbalance is more
realistic in the evolution of quark-gluon plasma, which reflects the random
gluonic topological transition. Incorporating this dynamics, we calculate the
chiral magnetic current in response to space-time dependent axial gauge
potential and magnetic field in AdS/CFT correspondence. In contrast to
conventional treatment of constant axial chemical potential, the response
function here is the AVV three-point function of the $\mathcal{N}=4$ super
Yang-Mills at strong coupling. Through an iterative solution of the nonlinear
equations of motion in Schwarzschild-AdS$_5$ background, we are able to express
the AVV function in terms of two Heun functions and prove its UV/IR finiteness,
as expected for $\mathcal{N}=4$ super Yang-Mills theory. We found that the
dependence of the chiral magnetic current on a non-constant chiral imbalance is
non-local, different from hydrodynamic approximation, and demonstrates the
subtlety of the infrared limit discovered in field theoretic approach. We
expect our results enrich the understanding of the phenomenology of the chiral
magnetic effect in the context of relativistic heavy ion collisions.


Abstract:
  We re-examine the celebrated Doob--McKean identity that identifies a
conditioned one-dimensional Brownian motion as the radial part of a
3-dimensional Brownian motion or, equivalently, a Bessel-3 process, albeit now
in the analogous setting of isotropic $\alpha$-stable processes. We find a
natural analogue that matches the Brownian setting, with the role of the
Brownian motion replaced by that of the isotropic $\alpha$-stable process,
providing one interprets the components of the original identity in the right
way.


Abstract:
  In this paper, we consider Bayesian point estimation and predictive density
estimation in the binomial case. After presenting preliminary results on these
problems, we compare the risk functions of the Bayes estimators based on the
truncated and untruncated beta priors and obtain dominance conditions when the
probability parameter is less than or equal to a known constant. The case where
there are both a lower bound restriction and an upper bound restriction is also
treated. Then our problems are shown to be related to similar problems in the
Poisson case. Finally, numerical studies are presented.


Abstract:
  In this paper, we obtain a characterization of GVZ-groups in terms of
commutators and monolithic quotients. This characterization is based on
counting formulas due to Gallagher.


Abstract:
  Network traffic is growing at an outpaced speed globally. The modern network
infrastructure makes classic network intrusion detection methods inefficient to
classify an inflow of vast network traffic. This paper aims to present a modern
approach towards building a network intrusion detection system (NIDS) by using
various deep learning methods. To further improve our proposed scheme and make
it effective in real-world settings, we use deep transfer learning techniques
where we transfer the knowledge learned by our model in a source domain with
plentiful computational and data resources to a target domain with sparse
availability of both the resources. Our proposed method achieved 98.30%
classification accuracy score in the source domain and an improved 98.43%
classification accuracy score in the target domain with a boost in the
classification speed using UNSW-15 dataset. This study demonstrates that deep
transfer learning techniques make it possible to construct large deep learning
models to perform network classification, which can be deployed in the real
world target domains where they can maintain their classification performance
and improve their classification speed despite the limited accessibility of
resources.


Abstract:
  Efficient error-controlled lossy compressors are becoming critical to the
success of today's large-scale scientific applications because of the
ever-increasing volume of data produced by the applications. In the past
decade, many lossless and lossy compressors have been developed with distinct
design principles for different scientific datasets in largely diverse
scientific domains. In order to support researchers and users assessing and
comparing compressors in a fair and convenient way, we establish a standard
compression assessment benchmark -- Scientific Data Reduction Benchmark
(SDRBench). SDRBench contains a vast variety of real-world scientific datasets
across different domains, summarizes several critical compression quality
evaluation metrics, and integrates many state-of-the-art lossy and lossless
compressors. We demonstrate evaluation results using SDRBench and summarize six
valuable takeaways that are helpful to the in-depth understanding of lossy
compressors.


Abstract:
  The logistic linear mixed model (LLMM) is one of the most widely used
statistical models. Generally, Markov chain Monte Carlo algorithms are used to
explore the posterior densities associated with the Bayesian LLMMs. Polson,
Scott and Windle's (2013) Polya-Gamma data augmentation (DA) technique can be
used to construct full Gibbs (FG) samplers for the LLMMs. Here, we develop
efficient block Gibbs (BG) samplers for Bayesian LLMMs using the Polya-Gamma DA
method. We compare the FG and BG samplers in the context of a real data
example, as the correlation between the fixed effects and the random effects
changes as well as when the dimensions of the design matrices vary. These
numerical examples demonstrate superior performance of the BG samplers over the
FG samplers. We also derive conditions guaranteeing geometric ergodicity of the
BG Markov chain when the popular improper uniform prior is assigned on the
regression coefficients, and proper or improper priors are placed on the
variance parameters of the random effects. This theoretical result has
important practical implications as it justifies the use of asymptotically
valid Monte Carlo standard errors for Markov chain based estimates of the
posterior quantities.


Abstract:
  We consider bivariate polynomials over the skew field of quaternions, where
the indeterminates commute with all coefficients and with each other. We
analyze existence of univariate factorizations, that is, factorizations with
univariate linear factors. A necessary condition for existence of univariate
factorizations is factorization of the norm polynomial into a product of
univariate polynomials. This condition is, however, not sufficient. Our central
result states that univariate factorizations exist after multiplication with a
suitable univariate real polynomial as long as the necessary factorization
condition is fulfilled. We present an algorithm for computing this real
polynomial and a corresponding univariate factorization. If a univariate
factorization of the original polynomial exists, a suitable input of the
algorithm produces a constant multiplication factor, thus giving an a
posteriori condition for existence of univariate factorizations. Some
factorizations obtained in this way are of interest in mechanism science. We
present an example of a curious closed-loop mechanism with eight revolute
joints.


Abstract:
  We deal with the construction of linear connections associated with second
order ordinary differential equations with and without first order constraints.
We use a novel method allowing glueing of submodule covariant derivatives to
produce new, closed form expressions for the Massa-Pagani connection and our
extension of it to the constrained case.


Abstract:
  Speaker segmentation consists in partitioning a conversation between one or
more speakers into speaker turns. Usually addressed as the late combination of
three sub-tasks (voice activity detection, speaker change detection, and
overlapped speech detection), we propose to train an end-to-end segmentation
model that does it directly. Inspired by the original end-to-end neural speaker
diarization approach (EEND), the task is modeled as a multi-label
classification problem using permutation-invariant training. The main
difference is that our model operates on short audio chunks (5 seconds) but at
a much higher temporal resolution (every 16ms). Experiments on multiple speaker
diarization datasets conclude that our model can be used with great success on
both voice activity detection and overlapped speech detection. Our proposed
model can also be used as a post-processing step, to detect and correctly
assign overlapped speech regions. Relative diarization error rate improvement
over the best considered baseline (VBx) reaches 17% on AMI, 13% on DIHARD 3,
and 13% on VoxConverse.


Abstract:
  Interpreting the environmental, behavioural and psychological data from
in-home sensory observations and measurements can provide valuable insights
into the health and well-being of individuals. Presents of neuropsychiatric and
psychological symptoms in people with dementia have a significant impact on
their well-being and disease prognosis. Agitation in people with dementia can
be due to many reasons such as pain or discomfort, medical reasons such as side
effects of a medicine, communication problems and environment. This paper
discusses a model for analysing the risk of agitation in people with dementia
and how in-home monitoring data can support them. We proposed a semi-supervised
model which combines a self-supervised learning model and a Bayesian ensemble
classification. We train and test the proposed model on a dataset from a
clinical study. The dataset was collected from sensors deployed in 96 homes of
patients with dementia. The proposed model outperforms the state-of-the-art
models in recall and f1-score values by 20%. The model also indicates better
generalisability compared to the baseline models.


Abstract:
  With the rise of the "big data" phenomenon in recent years, data is coming in
many different complex forms. One example of this is multi-way data that come
in the form of higher-order tensors such as coloured images and movie clips.
Although there has been a recent rise in models for looking at the simple case
of three-way data in the form of matrices, there is a relative paucity of
higher-order tensor variate methods. The most common tensor distribution in the
literature is the tensor variate normal distribution; however, its use can be
problematic if the data exhibit skewness or outliers. Herein, we develop four
skewed tensor variate distributions which to our knowledge are the first skewed
tensor distributions to be proposed in the literature, and are able to
parameterize both skewness and tail weight. Properties and parameter estimation
are discussed, and real and simulated data are used for illustration.


Abstract:
  We consider the additional entropy production (EP) incurred by a fixed
quantum or classical process on some initial state $\rho$, above the minimum EP
incurred by the same process on any initial state. We show that this additional
EP, which we term the "mismatch cost of $\rho$", has a universal
information-theoretic form: it is given by the contraction of the relative
entropy between $\rho$ and the least-dissipative initial state $\varphi$ over
time. We derive versions of this result for integrated EP incurred over the
course of a process, for trajectory-level fluctuating EP, and for instantaneous
EP rate. We also show that mismatch cost for fluctuating EP obeys an integral
fluctuation theorem. Our results demonstrate a fundamental relationship between
"thermodynamic irreversibility" (generation of EP) and "logical
irreversibility" (inability to know the initial state corresponding to a given
final state). We use this relationship to derive quantitative bounds on the
thermodynamics of quantum error correction and to propose a
thermodynamically-operationalized measure of the logical irreversibility of a
quantum channel. Our results hold for both finite and infinite dimensional
systems, and generalize beyond EP to many other thermodynamic costs, including
nonadiabatic EP, free energy loss, and entropy gain.


Abstract:
  We consider two-dimensional Schroedinger equations with honeycomb potentials
and slow time-periodic forcing of the form: $$i\psi_t (t,x) =
H^\varepsilon(t)\psi=\left(H^0+2i\varepsilon A (\varepsilon t) \cdot \nabla
\right)\psi,\quad H^0=-\Delta +V (x) .$$ The unforced Hamiltonian, $H^0$, is
known to generically have Dirac (conical) points in its band spectrum. The
evolution under $H^\varepsilon(t)$ of {\it band limited Dirac wave-packets}
(spectrally localized near the Dirac point) is well-approximated on large time
scales ($t\lesssim \varepsilon^{-2+}$) by an effective time-periodic Dirac
equation with a gap in its quasi-energy spectrum. This quasi-energy gap is
typical of many reduced models of time-periodic (Floquet) materials and plays a
role in conclusions drawn about the full system: conduction vs. insulation,
topological vs. non-topological bands. Much is unknown about nature of the
quasi-energy spectrum of original time-periodic Schroedinger equation, and it
is believed that no such quasi-energy gap occurs. In this paper, we explain how
to transfer quasi-energy gap information about the effective Dirac dynamics to
conclusions about the full Schroedinger dynamics. We introduce the notion of an
{\it effective quasi-energy gap}, and establish its existence in the
Schroedinger model. In the current setting, an effective quasi-energy gap is an
interval of quasi-energies which does not support modes with large spectral
projection onto band-limited Dirac wave-packets. The notion of effective
quasi-energy gap is a physically relevant relaxation of the strict notion of
quasi-energy spectral gap; if a system is tuned to drive or measure at momenta
and energies near the Dirac point of $H^0$, then the resulting modes in the
effective quasi-energy gap will only be weakly excited and detected.


Abstract:
  We prove that, for a Poisson vertex algebra V, the canonical injective
homomorphism of the variational cohomology of V to its classical cohomology is
an isomorphism, provided that V, viewed as a differential algebra, is an
algebra of differential polynomials in finitely many differential variables.
This theorem is one of the key ingredients in the computation of vertex algebra
cohomology. For its proof, we introduce the sesquilinear Hochschild and
Harrison cohomology complexes and prove a vanishing theorem for the symmetric
sesquilinear Harrison cohomology of the algebra of differential polynomials in
finitely many differential variables.


Abstract:
  We address the problem of analysing the complexity of concurrent programs
written in Pi-calculus. We are interested in parallel complexity, or span,
understood as the execution time in a model with maximal parallelism. A type
system for parallel complexity has been recently proposed by Baillot and
Ghyselen but it is too imprecise for non-linear channels and cannot analyse
some concurrent processes. Aiming for a more precise analysis, we design a type
system which builds on the concepts of sized types and usages. The new variant
of usages we define accounts for the various ways a channel is employed and
relies on time annotations to track under which conditions processes can
synchronize. We prove that a type derivation for a process provides an upper
bound on its parallel complexity.


Abstract:
  Deep neural networks are vulnerable to small input perturbations known as
adversarial attacks. Inspired by the fact that these adversaries are
constructed by iteratively minimizing the confidence of a network for the true
class label, we propose the anti-adversary layer, aimed at countering this
effect. In particular, our layer generates an input perturbation in the
opposite direction of the adversarial one and feeds the classifier a perturbed
version of the input. Our approach is training-free and theoretically
supported. We verify the effectiveness of our approach by combining our layer
with both nominally and robustly trained models and conduct large-scale
experiments from black-box to adaptive attacks on CIFAR10, CIFAR100, and
ImageNet. Our layer significantly enhances model robustness while coming at no
cost on clean accuracy.


Abstract:
  Coded caching is an emerging technique to reduce the data transmission load
during the peak-traffic times. In such a scheme, each file in the data center
or library is usually divided into a number of packets to pursue a low
broadcasting rate based on the designed placements at each user's cache.
However, the implementation complexity of this scheme increases as the number
of packets increases. It is crucial to design a scheme with a small
subpacketization level, while maintaining a relatively low transmission rate.
It is known that the design of caches in users (i.e., the placement phase) and
broadcasting (i.e., the delivery phase) can be unified in one matrix, namely
the placement delivery array (PDA). This paper proposes a novel PDA
construction by selecting proper orthogonal arrays (POAs), which generalizes
some known constructions but with a more flexible memory size. Based on the
proposed PDA construction, an effective transformation is further proposed to
enable a coded caching scheme to have a smaller subpacketization level.
Moreover, two new coded caching schemes with the coded placement are
considered. It is shown that the proposed schemes yield a lower
subpacketization level and transmission rate over some existing schemes.


Abstract:
  The Newcomb-Benford law, also known as the first-digit law, gives the
probability distribution associated with the first digit of a dataset, so that,
for example, the first significant digit has a probability of $30.1$ % of being
$1$ and $4.58$ % of being $9$. This law can be extended to the second and next
significant digits. This article presents an introduction to the discovery of
the law, its derivation from the scale invariance property, as well as some
applications and examples, are presented. Additionally, a simple model of a
Markov process inspired by scale invariance is proposed. Within this model, it
is proved that the probability distribution irreversibly converges to the
Newcomb-Benford law, in analogy to the irreversible evolution toward
equilibrium of physical systems in thermodynamics and statistical mechanics.


Abstract:
  Nature-inspired algorithms are commonly used for solving the various
optimization problems. In past few decades, various researchers have proposed a
large number of nature-inspired algorithms. Some of these algorithms have
proved to be very efficient as compared to other classical optimization
methods. A young researcher attempting to undertake or solve a problem using
nature-inspired algorithms is bogged down by a plethora of proposals that exist
today. Not every algorithm is suited for all kinds of problem. Some score over
others. In this paper, an attempt has been made to summarize various leading
research proposals that shall pave way for any new entrant to easily understand
the journey so far. Here, we classify the nature-inspired algorithms as natural
evolution based, swarm intelligence based, biological based, science based and
others. In this survey, widely acknowledged nature-inspired algorithms namely-
ACO, ABC, EAM, FA, FPA, GA, GSA, JAYA, PSO, SFLA, TLBO and WCA, have been
studied. The purpose of this review is to present an exhaustive analysis of
various nature-inspired algorithms based on its source of inspiration, basic
operators, control parameters, features, variants and area of application where
these algorithms have been successfully applied. It shall also assist in
identifying and short listing the methodologies that are best suited for the
problem.