title: An Adaptive Finite Element DtN Method for Maxwell's Equations

abstract:
  This paper is concerned with a numerical solution to the scattering of a
time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in
three dimensions. The electromagnetic wave propagation is modeled by a boundary
value problem of Maxwell's equations in the exterior domain of the obstacle.
Based on the Dirichlet-to-Neumann (DtN) operator, which is defined by an
infinite series, an exact transparent boundary condition is introduced and the
scattering problem is reduced equivalently into a bounded domain. An a
posteriori error estimate based adaptive finite element DtN method is developed
to solve the discrete variational problem, where the DtN operator is truncated
into a sum of finitely many terms. The a posteriori error estimate takes into
account both the finite element approximation error and the truncation error of
the DtN operator. The latter is shown to decay exponentially with respect to
the truncation parameter. Numerical experiments are presented to illustrate the
effectiveness of the proposed method.


title: Optimal convex domains for the first curl eigenvalue

abstract:
  We prove that there exists a bounded convex domain $\Omega \subset
\mathbf{R}^3$ of fixed volume that minimizes the first positive curl eigenvalue
among all other bounded convex domains of the same volume. We show that this
optimal domain cannot be analytic, and that it cannot be stably convex if it is
sufficiently smooth (e.g., of class $C^{1,1}$). Existence results for uniformly
H\"older optimal domains in a box (that is, contained in a fixed bounded domain
$D \subset \mathbf{R}^3$) are also presented.


title:
Chiral plasma instability and inverse cascade from nonequilibrium
  left-handed neutrinos in core-collapse supernovae

abstract:
  We show that the back reaction of left-handed neutrinos out of equilibrium on
the matter sector induces an electric current proportional to a magnetic field
even without a chiral imbalance for electrons in core-collapse supernovae. We
derive the transport coefficient of this effect based on the recently
formulated chiral radiation transport theory for neutrinos. This chiral
electric current generates a strong magnetic field via the so-called chiral
plasma instability, which could provide a new mechanism for the strong and
stable magnetic field of magnetars. We also numerically study the physical
origin of the inverse cascade of the magnetic energy in the
magnetohydrodynamics including this current. Our results indicate that
incorporating the chiral effects of neutrinos would drastically modify the
hydrodynamic evolutions of supernovae, which may also be relevant to the
explosion dynamics.


title:
Spatio-Temporal Outdoor Lighting Aggregation on Image Sequences using
  Transformer Networks

abstract:
  In this work, we focus on outdoor lighting estimation by aggregating
individual noisy estimates from images, exploiting the rich image information
from wide-angle cameras and/or temporal image sequences. Photographs inherently
encode information about the scene's lighting in the form of shading and
shadows. Recovering the lighting is an inverse rendering problem and as that
ill-posed. Recent work based on deep neural networks has shown promising
results for single image lighting estimation, but suffers from robustness. We
tackle this problem by combining lighting estimates from several image views
sampled in the angular and temporal domain of an image sequence. For this task,
we introduce a transformer architecture that is trained in an end-2-end fashion
without any statistical post-processing as required by previous work. Thereby,
we propose a positional encoding that takes into account the camera calibration
and ego-motion estimation to globally register the individual estimates when
computing attention between visual words. We show that our method leads to
improved lighting estimation while requiring less hyper-parameters compared to
the state-of-the-art.


title:
Leveraging Self-Sovereign Identity, Blockchain, and Zero-Knowledge Proof
  to Build a Privacy-Preserving Vaccination Pass

abstract:
  The current humanitarian health crisis popularized the debate on data
privacy. At the same time, several cities, states, and even countries put the
mandatory presentation of health pass to access services into practice. In this
article, we explore the concepts of self-sovereign identity, blockchain, and
zero-knowledge proofs to propose a solution to the problem of presenting proof
of vaccination. This solution allows users to prove that they are vaccinated
for different pathogens without revealing their identity. The architecture is
loosely coupled, allowing components to be exchanged, which we discuss when we
present the implementation of a working prototype.


title: Convective mesoscale turbulence at very low Prandtl numbers

abstract:
  Horizontally extended turbulent convection, termed mesoscale convection in
natural systems, remains a challenge to investigate in both experiments and
simulations. This is particularly so for very low molecular Prandtl numbers as
in stellar convection and in Earth's outer core. The present study reports
three-dimensional direct numerical simulations of turbulent Rayleigh-B\'{e}nard
convection in square boxes of side $L$ and height $H$ with the aspect ratio
$\Gamma =L/H$ of 25, for Prandtl numbers $10^{-3}\le Pr \le 7$ and Rayleigh
numbers $10^5 \le Ra \le 10^7$, obtained by massively parallel computations on
grids of up to $5.36\times 10^{11}$ points. The low end of this $Pr$-range
cannot be accessed in controlled laboratory measurements. We report essential
properties of the flow and their trends with Rayleigh and Prandtl numbers, in
particular the global transport of momentum and heat -- the latter decomposed
into convective and diffusive contributions -- across the convection layer,
mean vertical profiles of the temperature, temperature fluctuations, and the
kinetic energy and thermal dissipation rates. We also explore the degree to
which the turbulence in the bulk of the convection layer resembles classical
homogeneous and isotropic turbulence in terms of spectra, increment moments,
and dissipative anomaly. Finally, we show that a characteristic scale on the
order of the mesoscale seems to saturate to a wavelength of $\lambda\gtrsim 3H$
for $Pr\lesssim 0.005$. We briefly discuss possible implications of these
results for the development of subgrid scale parameterization of turbulent
convection.


title:
A time-causal and time-recursive scale-covariant scale-space
  representation of temporal signals and past time

abstract:
  This article presents an overview of a theory for performing temporal
smoothing on temporal signals in such a way that: (i) temporally smoothed
signals at coarser temporal scales are guaranteed to constitute simplifications
of corresponding temporally smoothed signals at any finer temporal scale
(including the original signal) and (ii) the temporal smoothing process is both
time-causal and time-recursive, in the sense that it does not require access to
future information and can be performed with no other temporal memory buffer of
the past than the resulting smoothed temporal scale-space representations
themselves.
  For specific subsets of parameter settings for the classes of linear and
shift-invariant temporal smoothing operators that obey this property, it is
shown how temporal scale covariance can be additionally obtained, guaranteeing
that if the temporal input signal is rescaled by a uniform scaling factor, then
also the resulting temporal scale-space representations of the rescaled
temporal signal will constitute mere rescalings of the temporal scale-space
representations of the original input signal, complemented by a shift along the
temporal scale dimension. The resulting time-causal limit kernel that obeys
this property constitutes a canonical temporal kernel for processing temporal
signal in real-time scenarios when the regular Gaussian kernel cannot be used
because of its non-causal access to information from the future and we cannot
additionally require the temporal smoothing process to comprise a complementary
memory of the past beyond the information contained in the temporal smoothing
process itself, which in this way also serves as a multi-scale temporal memory
of the past.
  This theory is generally applicable for both: (i) modelling continuous
temporal phenomena over multiple temporal scales and (ii) digital processing of
measured temporal signals in real time.


title: Hedonic Diversity Games: A Complexity Picture with More than Two Colors

abstract:
  Hedonic diversity games are a variant of the classical Hedonic games designed
to better model a variety of questions concerning diversity and fairness.
Previous works mainly targeted the case with two diversity classes (represented
as colors in the model) and provided some initial complexity-theoretic and
existential results concerning Nash and individually stable outcomes. Here, we
design new algorithms accompanied with lower bounds which provide a complete
parameterized-complexity picture for computing Nash and individually stable
outcomes with respect to the most natural parameterizations of the problem.
Crucially, our results hold for general Hedonic diversity games where the
number of colors is not necessarily restricted to two, and show that -- apart
from two trivial cases -- a necessary condition for tractability in this
setting is that the number of colors is bounded by the parameter. Moreover, for
the special case of two colors we resolve an open question asked in previous
work (Boehmer and Elkind, AAAI 2020).


title: Simulation of in-ice cosmic ray air shower induced particle cascades

abstract:
  We present detailed microscopic simulations of high-energy cosmic-ray air
showers penetrating high-altitude ice layers that can be found at the polar
regions. We use a combination of the CORSIKA Monte Carlo code and the Geant4
simulation toolkit, and focus on the particle cascade that develops in the ice
to describe its most prominent features. We discuss the impact of the ice layer
on the total number of particles in function of depth of the air shower, and we
give a general parameterization of the charge distribution in the cascade front
in function of Xmax of the cosmic ray air shower, which can be used for
analytical and semi-analytical calculations of the expected Askaryan radio
emission of the in-ice particle cascade. We show that the core of the cosmic
ray air shower dominates during the propagation in ice, therefore creating an
in-ice particle cascade strongly resembling a neutrino-induced particle
cascade. Finally, we present the results of microscopic simulations of the
Askaryan radio emission of the in-ice particle cascade, showing that the
emission is dominated by the shower core, and discuss the feasibility of
detecting the plasma created by the particle cascade in the ice using RADAR
echo techniques.


title: Molecule Generation for Drug Design: a Graph Learning Perspective

abstract:
  Machine learning has revolutionized many fields, and graph learning is
recently receiving increasing attention. From the application perspective, one
of the emerging and attractive areas is aiding the design and discovery of
molecules, especially in drug industry. In this survey, we provide an overview
of the state-of-the-art molecule (and mostly for de novo drug) design and
discovery aiding methods whose methodology involves (deep) graph learning.
Specifically, we propose to categorize these methods into three groups: i) all
at once, ii) fragment-based and iii) node-by-node. We further present some
representative public datasets and summarize commonly utilized evaluation
metrics for generation and optimization, respectively. Finally, we discuss
challenges and directions for future research, from the drug design
perspective.


title: Laser-written vapor cells for chip-scale atomic sensing and spectroscopy

abstract:
  We report the fabrication of alkali-metal vapor cells using femtosecond laser
machining. This laser-written vapor-cell (LWVC) technology allows
arbitrarily-shaped 3D interior volumes and has potential for integration with
photonic structures and optical components. We use nonevaporable getters both
to dispense rubidium and to absorb buffer gas. This enables us to produce cells
with sub-atmospheric buffer gas pressures without vacuum apparatus. We
demonstrate sub-Doppler saturated absorption spectroscopy and single beam
optical magnetometry with a single LWVC. The LWVC technology may find
application in miniaturized atomic quantum sensors and frequency references.


title:
Pinpointing Anomaly Events in Logs from Stability Testing -- N-Grams vs.
  Deep-Learning

abstract:
  As stability testing execution logs can be very long, software engineers need
help in locating anomalous events. We develop and evaluate two models for
scoring individual log-events for anomalousness, namely an N-Gram model and a
Deep Learning model with LSTM (Long short-term memory). Both are trained on
normal log sequences only. We evaluate the models with long log sequences of
Android stability testing in our company case and with short log sequences from
HDFS (Hadoop Distributed File System) public dataset. We evaluate next event
prediction accuracy and computational efficiency. The LSTM model is more
accurate in stability testing logs (0.848 vs 0.865), whereas in HDFS logs the
N-Gram is slightly more accurate (0.904 vs 0.900). The N-Gram model has far
superior computational efficiency compared to the Deep model (4 to 13 seconds
vs 16 minutes to nearly 4 hours), making it the preferred choice for our case
company. Scoring individual log events for anomalousness seems like a good aid
for root cause analysis of failing test cases, and our case company plans to
add it to its online services. Despite the recent surge in using deep learning
in software system anomaly detection, we found limited benefits in doing so.
However, future work should consider whether our finding holds with different
LSTM-model hyper-parameters, other datasets, and with other deep-learning
approaches that promise better accuracy and computational efficiency than LSTM
based models.


title: On the Significance of Knowing the Arrival Order in Prophet Inequality

abstract:
  In a prophet inequality problem, $n$ boxes arrive online, each containing
some value that is drawn independently from a known distribution. Upon the
arrival of a box, its value is realized, and an online algorithm decides,
immediately and irrevocably, whether to accept it or proceed to the next box.
Clearly, an online algorithm that knows the arrival order may be more powerful
than an online algorithm that is unaware of the order. Despite the growing
interest in the role of the arrival order on the performance of online
algorithms, the effect of knowledge of the order has been overlooked thus far.
  Our goal in this paper is to quantify the loss due to unknown order. We
define the order competitive ratio as the worst-case ratio between the
performance of the best order-unaware and the best order-aware algorithms. We
study the order competitive ratio for two objective functions, namely (i)
max-expectation: maximizing the expected accepted value, and (ii)
max-probability: maximizing the probability of accepting the box with the
largest value. For the max-expectation objective, we're golden: we give a
deterministic order-unaware algorithm that achieves an order competitive ratio
of the inverse of the golden ratio (i.e., $1/\phi \approx 0.618$). For the
max-probability objective, we give a deterministic order-unaware algorithm that
achieves an order competitive ratio of $\ln \frac{1}{\lambda} \approx 0.806$
(where $\lambda$ is the unique solution to $\frac{x}{1-x}= \ln \frac{1}{x}$).
Both results are tight. Our algorithms are inevitably adaptive and go beyond
single-threshold algorithms.


title: Planar Tur\'an numbers of cubic graphs and disjoint union of cycles

abstract:
  The planar Tur\'an number of a graph $H$, denoted $ex_{_\mathcal{P}}(n,H)$,
is the maximum number of edges in a planar graph on $n$ vertices without
containing $H$ as a subgraph. This notion was introduced by Dowden in 2016 and
has attracted quite some attention since then; those work mainly focus on
finding $ex_{_\mathcal{P}}(n,H)$ when $H$ is a cycle or Theta graph or $H$ has
maximum degree at least four. In this paper, we study $ex_{_\mathcal{P}}(n,H)$
when $H$ is a cubic graph or disjoint union of cycles or $H=K_{s, t}$.


title: Indirect search of Heavy Neutral Leptons using the DUNE Near Detector

abstract:
  We evaluate the potential of the DUNE Near Detector (DUNEND) for establishing
bounds for heavy neutral leptons in the region of masses below 500 MeV. These
bounds are obtained from the deficit of muon and electron charged current
events expected at the LArTPC of DUNEND. The latter happens because the active
neutrinos produced from the decays of the heavy ones do not hit the detector.
As a result, we get limits of $|U_{\mu4}|^2 < 6 \times10^{-5}$ and $|U_{e4}|^2
< 9\times10^{-5}$ for masses below 10 MeV, for five years per each mode
(neutrino/antineutrino). These limits, within the region of masses below 7-8
MeV, are better than those that can be achieved by DUNE direct searches,
improving from 1 to 3 orders of magnitude the current experimental constraints
for masses under 2.5 MeV.


title: Archetypal Factorization and Gluon Poles in semi-exclusive reactions

abstract:
  Within the archetypal factorization procedure, we study the gluon pole
contributions manifesting in the nucleon-lepton hard processes of hadron
production. We prove the dominant role of gluon pole contributions in the
processes of such kind. We analyse the different sources of complexity
associated with the gluon pole functions. As a practical application, we derive
a new single spin asymmetry related directly to the gluon poles which can be
studied experimentally.


title: $\mathbb{Q}$-curves and the Lebesgue-Nagell equation

abstract:
  In this paper, we consider the equation \[ x^2 - q^{2k+1} = y^n, \qquad q
\nmid x, \quad 2 \mid y, \] for integers $x,q,k,y$ and $n$, with $k \geq 0$ and
$n \geq 3$. We extend work of the first and third-named authors by finding all
solutions in the cases $q= 41$ and $q = 97$. We do this by constructing a
Frey-Hellegouarch $\mathbb{Q}$-curve defined over the real quadratic field
$K=\mathbb{Q}(\sqrt{q})$, and using the modular method with multi-Frey
techniques.


title: Unified products for Zinbiel 2-algebras

abstract:
  The extending structures problem for Zinbiel 2-algebras is studied. We
introduce the concept of unified products for Zinbiel 2-algebras. Some special
cases of unified products such as crossed product and matched pair of Zinbiel
2-algebras are investigated. It is proved that the extending problem for
Zinbiel 2-algebras can be classified by some non-abelian cohomology theory.


title:
A practical DMPs Implementation for Skill Creation and Teleoperation
  with Assistive Manipulators

abstract:
  Assistive robotic manipulators are becoming increasingly important for people
with disabilities. Teleoperating the manipulator in mundane tasks is part of
their daily lives. Instead of steering the robot through all actions, applying
self-recorded motion skills could greatly facilitate repetitive tasks. Dynamic
Movement Primitives (DMP) are a powerful method for skill learning. For this
use case, however, they need a simple heuristic to specify where to start and
stop a skill without additional sensors. This paper provides the concept of
local, global, and hybrid skills that form a modular basis for composing
single-handed tasks with ease. A focus is on presenting the necessary
mathematical details to support custom implementations with assistive robot
arms. Experiments validate the developed methods for scratching an itchy spot,
sorting objects on a desk, and feeding a piggy bank with coins. The paper is
accompanied by an open-source implementation at
https://github.com/fzi-forschungszentrum-informatik/ArNe


title: Improving AoI via Learning-based Distributed MAC in Wireless Networks

abstract:
  In this work, we consider a remote monitoring scenario in which multiple
sensors share a wireless channel to deliver their status updates to a process
monitor via an access point (AP). Moreover, we consider that the sensors
randomly arrive and depart from the network as they become active and inactive.
The goal of the sensors is to devise a medium access strategy to collectively
minimize the long-term mean network \ac{AoI} of their respective processes at
the remote monitor. For this purpose, we propose specific modifications to
ALOHA-QT algorithm, a distributed medium access algorithm that employs a policy
tree (PT) and reinforcement learning (RL) to achieve high throughput. We
provide the upper bound on the mean network Age of Information (AoI) for the
proposed algorithm along with pointers for selecting its key parameter. The
results reveal that the proposed algorithm reduces mean network \ac{AoI} by
more than 50 percent for state of the art stationary randomized policies while
successfully adjusting to a changing number of active users in the network. The
algorithm needs less memory and computation than ALOHA-QT while performing
better in terms of AoI.


title: History Data Driven Distributed Consensus in Networks

abstract:
  The association of weights in a distributed consensus protocol quantify the
trust that an agent has on its neighbors in a network. An important problem in
such networked systems is the uncertainty in the estimation of trust between
neighboring agents, coupled with the losses arising from mistakenly associating
wrong amounts of trust with different neighboring agents. We introduce a
probabilistic approach which uses the historical data collected in the network,
to determine the level of trust between each agent. Specifically, using the
finite history of the shared data between neighbors, we obtain a configuration
which represents the confidence estimate of every neighboring agent's
trustworthiness. Finally, we propose a History-Data-Driven (HDD) distributed
consensus protocol which translates the computed configuration data into
weights to be used in the consensus update. The approach using the historical
data in the context of a distributed consensus setting marks the novel
contribution of our paper.


title: Crossed modules for Hom-Leibniz-Rinehart algebras

abstract:
  In this paper, we introduce the notion of crossed module for
Hom-Leibniz-Rinehart algebras and cat$^1$-Hom-Leibniz-Rinehart algebras. A
detailed study on its construction from the Hom-actions and semi-direct
products is given. We prove that there is a one-to-one correspondence between
crossed modules of Hom-Leibniz-Rinehart algebras and
cat$^1$-Hom-Leibniz-Rinehart algebras. Finally, categorical properties of
Hom-Leibniz-Rinehart crossed modules are investigated.


title:
A multivariate extension of the Misspecification-Resistant Information
  Criterion

abstract:
  The Misspecification-Resistant Information Criterion (MRIC) proposed in
[H.-L. Hsu, C.-K. Ing, H. Tong: On model selection from a finite family of
possibly misspecified time series models. The Annals of Statistics. 47 (2),
1061--1087 (2019)] is a model selection criterion for univariate parametric
time series that enjoys both the property of consistency and asymptotic
efficiency. In this article we extend the MRIC to the case where the response
is a multivariate time series and the predictor is univariate. The extension
requires novel derivations based upon random matrix theory. We obtain an
asymptotic expression for the mean squared prediction error matrix, the
vectorial MRIC and prove the consistency of its method-of-moments estimator.
Moreover, we prove its asymptotic efficiency. Finally, we show with an example
that, in presence of misspecification, the vectorial MRIC identifies the best
predictive model whereas traditional information criteria like AIC or BIC fail
to achieve the task.


title:
Faster change of order algorithm for Gr\"obner bases under shape and
  stability assumptions

abstract:
  Solving polynomial systems whose solution set is finite is usually done in
two main steps: compute a Gr\"obner basis for the degree reverse lexicographic
order, and perform a change of order to find the lexicographic Gr\"obner basis.
The second step is generally considered as better understood, in terms of
algorithms and complexity. Yet, after two decades of progress on the first
step, it turns out that the change of order now takes a large part of the
solving time for many instances, including those that are generic or reached
after applying a random change of variables.
  Like the fastest known change of order algorithms, this work focuses on the
latter situation, where the ideal defined by the system satisfies structural
properties. First, the ideal has a shape lexicographic Gr\"obner basis. Second,
the set of leading terms with respect to the degree reverse lexicographic order
has a stability property; in particular, the multiplication matrix of the
smallest variable is computed for free from the input Gr\"obner basis.
  The current fastest algorithms rely on the sparsity of this multiplication
matrix to find its minimal polynomial efficiently using Wiedemann's approach.
This paper starts from the observation that this sparsity is a consequence of
an algebraic structure, which can be exploited to represent the matrix
concisely as a univariate polynomial matrix. We show that the Hermite normal
form of that matrix yields the sought lexicographic Gr\"obner basis, under
assumptions which cover the shape position case. This leads to an improved
complexity bound for the second step. The practical benefit is also confirmed
via implementations based on the state-of-the-art software libraries msolve and
PML.


title: Hallmarks of Majorana mode leaking into a hybrid double quantum dot

abstract:
  We investigate the spectral and transport properties of a double quantum dot
laterally attached to a topological superconducting nanowire, hosting the
Majorana zero-energy modes. Specifically, we consider a geometry, in which the
outer quantum dot is embedded between the external normal and superconducting
leads, forming a circuit. First, we derive analytical expressions for the bound
states in the case of an uncorrelated system and discuss their signatures in
the tunneling spectroscopy. Then, we explore the case of strongly correlated
quantum dots by performing the numerical renormalization group calculations,
focusing on the interplay and relationship between the leaking Majorana mode
and the Kondo states on both quantum dots. Finally, we discuss feasible means
to experimentally probe the in-gap quasiparticles by using the Andreev
spectroscopy based on the particle-to-hole scattering mechanism.


title:
Topology-Level Reactivity in Distributed Reactive Programs: Reactive
  Acquaintance Management using Flocks

abstract:
  Reactive programming is a popular paradigm to program event-driven
applications, and it is often proposed as a paradigm to write distributed
applications. One such type of application is *prosumer* applications, which
are distributed applications that both produce and consume many events. We
analyse the problems that occur when using a reactive programming language or
framework to implement prosumer applications. We find that the assumption of an
open network, which means prosumers of various types spontaneously join and
leave the network, can cause a lot of code complexity or run-time inefficiency.
At the basis of these issues lies *acquaintance management*: the ability to
discover prosumers as they join and leave the network, and correctly
maintaining this state throughout the reactive program. Most existing reactive
programming languages and frameworks have limited support for managing
acquaintances, resulting in accidental complexity of the code or inefficient
computations.
  In this paper we present acquaintance management for reactive programs.
First, we design an *acquaintance discovery* mechanism to create a *flock* that
automatically discovers prosumers on the network. An important aspect of flocks
is their integration with reactive programs, such that a reactive program can
correctly and efficiently maintain its state. To this end we design an
*acquaintance maintenance* mechanism: a new type of operator for functional
reactive programming languages that we call `deploy-*`. The `deploy-*` operator
enables correct and efficient reactions to time-varying collections of
discovered prosumers. The proposed mechanisms are implemented in a reactive
programming language called Stella, which serves as a linguistic vehicle to
demonstrate the ideas of our approach. Our implementation of acquaintance
management results in computationally efficient and idiomatic reactive code.
  We evaluate our approach quantitatively via benchmarks that show that our
implementation is efficient: computations will efficiently update whenever a
new prosumer is discovered, or a connected prosumer is dropped. To evaluate the
distributed capabilities of our prototype implementation, we implement a
use-case that simulates the bike-sharing infrastructure of Brussels, and we run
it on a Raspberry Pi cluster computer. We consider our work to be an important
step to use functional reactive programming to build distributed systems for
open networks, in other words, distributed reactive programs that involve many
prosumer devices and sensors that spontaneously join and leave the network.


title: Figuring and Drawing: A Visual Approach to Principled Programming

abstract:
  A standing challenge in undergraduate Computer Science curricula is the
teaching and learning of computer programming. Through this paper which is an
essay about programming, we aim to contribute to the plethora of existing
pedagogies, approaches and philosophies, by discussing a specific feature of
our approach in teaching principled programming to undergraduate students, in
their first semester of studies, namely the utilization of pictures, both
text-based and raster-based graphics. Although the given course has evolved
substantially over the thirty years of its delivery regarding the programming
languages (Miranda, C, C++, Java) and paradigms (functional, imperative,
object-oriented, combination of procedural and object-oriented) used, the
discussed visual feature has been maintained and steadily strengthened.
  We list abstraction, problem decomposition and synthesis, information hiding,
reusability, modularity and extensibility as key principles of problem solving
and algorithmic thinking. These principles are closely aligned with the
advocated computational thinking techniques of problem decomposition, pattern
recognition, pattern generalization and algorithm design. We aim for our
students to familiarize themselves with all the above principles through
practical problem solving. Our ongoing inquiry has been whether the problem
domain of pictures is contributing valuably towards this aim. Moreover, an
added-value is that students get a glimpse of computational complexity in a
visual, empirical way.
  The presented work is not related to visual programming, since the students
write their programs textually and not graphically; it's the output of their
programs which is in visual form. Our approach though is loosely related to the
classical paradigm of turtle graphics. However, our focus is Computer Science
majors, who should be able to design and build turtles and other objects and
not just use them. Indeed, the programming principles course helps them to do
both and also to appreciate the multitude of algorithmic ways for producing the
same visual output. Currently the given programming principles are approached
both from a procedural, process-based and an object-oriented, concept-based
perspective and the course uses the Java language. Through the presented
example problems, we aim to show the appropriateness of the visual domain of
pictures for supporting the learning of principled programming. The problem
domain of pictures is abundantly rich with potential examples to draw from.
Moreover, as reported in the literature, female students may show higher
interest towards visual problem domains in programming classes, in relation to
other problem domains. We plan to investigate this conjecture in the context of
our broader aim to encourage more females to follow university studies in
computer science; in this paper only a cursory finding is presented, that bears
some relation to what is reported in the literature.


title:
United Monoids: Finding Simplicial Sets and Labelled Algebraic Graphs in
  Trees

abstract:
  Graphs and various graph-like combinatorial structures, such as preorders and
hypergraphs, are ubiquitous in programming. This paper focuses on representing
graphs in a purely functional programming language like Haskell. There are
several existing approaches; one of the most recently developed ones is the
"algebraic graphs" approach (2017). It uses an algebraic data type to represent
graphs and has attracted users, including from industry, due to its emphasis on
equational reasoning and making a common class of bugs impossible by
eliminating internal invariants.
  The previous formulation of algebraic graphs did not support edge labels,
which was a serious practical limitation. In this paper, we redesign the main
algebraic data type and remove this limitation. We follow a fairly standard
approach of parameterising a data structure with a semiring of edge labels. The
new formulation is both more general and simpler: the two operations for
composing graphs used in the previous work can now be obtained from a single
operation by fixing the semiring parameter to zero and one, respectively.
  By instantiating the new data type with different semirings, and working out
laws for interpreting the resulting expression trees, we discover an unusual
algebraic structure, which we call "united monoids", that is, a pair of monoids
whose unit elements coincide. We believe that it is worth studying united
monoids in their full generality, going beyond the graphs which prompted their
discovery. To that end, we characterise united monoids with a minimal set of
axioms, prove a few basic theorems, and discuss several notable examples.
  We validate the presented approach by implementing it in the open-source
*algebraic-graphs* library. Our theoretical contributions are supported by
proofs that are included in the paper and have also been machine-checked in
Agda. By extending algebraic graphs with support for edge labels, we make them
suitable for a much larger class of possible applications. By studying united
monoids, we provide a theoretical foundation for further research in this area.


title: Debootstrapping without Archeology: Stacked Implementations in Camlboot

abstract:
  Context: It is common for programming languages that their reference
implementation is implemented in the language itself. This requires a
"bootstrap": a copy of a previous version of the implementation is provided
along with the sources, to be able to run the implementation itself. Those
bootstrap files are opaque binaries; they could contain bugs, or even malicious
changes that could reproduce themselves when running the source version of the
language implementation -- this is called the "trusting trust attack". For this
reason, a collective project called Bootstrappable was launched in 2016 to
remove those bootstraps, providing alternative build paths that do not rely on
opaque binaries.
  Inquiry: Debootstrapping generally combines a mix of two approaches. The
"archaeological" approach works by locating old versions of systems, or legacy
alternative implementations, that do not need the bootstrap, and by preserving
or restoring the ability to run them. The "tailored" approach re-implements a
new, non-bootstrapped implementation of the system to debootstrap. Currently,
the "tailored" approach is dominant for low-level system components (C,
coreutils), and the "archaeological" approach is dominant among the few
higher-level languages that were debootstrapped.
  Approach: We advocate for the benefits of "tailored" debootstrapping
implementations of high-level languages. The new implementation needs not be
production-ready, it suffices that it is able to run the reference
implementation correctly. We argue that this is feasible with a reasonable
development effort, with several side benefits besides debootstrapping.
  Knowledge: We propose a specific design of composing/stacking several
implementations: a reference interpreter for the language of interest,
implemented in a small subset of the language, and a compiler for this small
subset (in another language). Developing a reference interpreter is valuable
independently of debootstrapping: it may help clarify the language semantics,
and can be reused for other purposes such as differential testing of the other
implementations.
  Grounding: We present Camlboot, our project to debootstrap the OCaml
compiler, version 4.07. Once we converged on this final design, the last
version of Camlboot took about a person-month of implementation effort,
demonstrating feasibility. Using diverse double-compilation, we were able to
prove the absence of trusting trust attack in the existing bootstrap of the
standard OCaml implementation.
  Importance: To our knowledge, this document is the first scholarly discussion
of "tailored" debootstrapping for high-level programming languages.
Debootstrapping is an interesting problem which recently grew an active
community of free software contributors, but so far the interactions with the
programming-language research community have been minimal. We share our
experience on Camlboot, trying to highlight aspects that are of interest to
other language designers and implementors; we hope to foster stronger ties
between the Bootstrappable project and relevant academic communities. In
particular, the debootstrapping experience has been an interesting reflection
on OCaml design and implementation, and we hope that other language
implementors would find it equally valuable.


title:
Feynman's Sum-over-Paths method applied in wave optics and for
  calculating the quantum probability current

abstract:
  Based on the Sum-over-Paths approach of Richard Feynman, an integration
method for calculating wave phase vectors is derived. The diffraction and
interference patterns of various slit masks can be calculated from such phase
vectors. The results obtained match with those computed using the more complex
Fresnel integrals. Babinet's principle for phases is presented for the first
time. As an example, the diffraction pattern of a double slit can also be
calculated by subtracting the phase vectors of a smaller slit from those of a
larger one. This method is also demonstrated by using a diffraction calculation
tool when an obstacle is positioned behind a double slit. The approach of phase
vector integration is expanded to calculate the quantum probability current.
Based on the Hamilton-Jacobi -- and the stationary Schr\"odinger -- equation,
the quantum probability current is calculated and its continuity is shown. The
time-dependent differential equation of the probabilty current velocity is
numerically solved. For a large number of integrations it is statistically
shown that the distribution of the flux per area is consistent with the
probability density profile. This may raise the question of wether the
probability density or the probability current distribution is measured by an
interference experiment with particles. The quantum probability current is also
simulated for photons traversing an asymmetrical double slit and the special
results are discussed.


title:
Nonstationary multi-output Gaussian processes via harmonizable spectral
  mixtures

abstract:
  Kernel design for Multi-output Gaussian Processes (MOGP) has received
increased attention recently. In particular, the Multi-Output Spectral Mixture
kernel (MOSM) arXiv:1709.01298 approach has been praised as a general model in
the sense that it extends other approaches such as Linear Model of
Corregionalization, Intrinsic Corregionalization Model and Cross-Spectral
Mixture. MOSM relies on Cram\'er's theorem to parametrise the power spectral
densities (PSD) as a Gaussian mixture, thus, having a structural restriction:
by assuming the existence of a PSD, the method is only suited for multi-output
stationary applications. We develop a nonstationary extension of MOSM by
proposing the family of harmonizable kernels for MOGPs, a class of kernels that
contains both stationary and a vast majority of non-stationary processes. A
main contribution of the proposed harmonizable kernels is that they
automatically identify a possible nonstationary behaviour meaning that
practitioners do not need to choose between stationary or non-stationary
kernels. The proposed method is first validated on synthetic data with the
purpose of illustrating the key properties of our approach, and then compared
to existing MOGP methods on two real-world settings from finance and
electroencephalography.


title:
Majorana-Kondo competition in a cross-shaped double quantum
  dot-topological superconductor system

abstract:
  We examine the transport properties of a double quantum dot system coupled to
a topological superconducting nanowire hosting Majorana quasiparticles at its
ends, with the central quantum dot attached to the left and right leads. We
focus on the behavior of the local density of states and the linear
conductance, calculated with the aid of the numerical renormalization group
method, to describe the influence of the Majorana coupling on the
low-temperature transport properties induced by the Kondo correlations. In
particular, we show that the presence of Majorana quasiparticles in the system
affects both the spin-up and spin-down transport channels, affecting the energy
scales associated with the first-stage and second-stage Kondo temperatures,
respectively, and modifying the low-energy behavior of the system.


title: Qutrit metaplectic gates are a subset of Clifford+T

abstract:
  A popular universal gate set for quantum computing with qubits is Clifford+T,
as this can be readily implemented on many fault-tolerant architectures. For
qutrits, there is an equivalent T gate, that, like its qubit analogue, makes
Clifford+T approximately universal, is injectable by a magic state, and
supports magic state distillation. However, it was claimed that a better gate
set for qutrits might be Clifford+R, where R=diag(1,1,-1) is the metaplectic
gate, as certain protocols and gates could more easily be implemented using the
R gate than the T gate. In this paper we show that when we have at least two
qutrits, the qutrit Clifford+R unitaries form a strict subset of the Clifford+T
unitaries, by finding a direct decomposition of $R \otimes \mathbb{I}$ as a
Clifford+T circuit and proving that the T gate cannot be exactly synthesized in
Clifford+R. This shows that in fact the T gate is at least as powerful as the R
gate, up to a constant factor. Moreover, we additionally show that it is
impossible to find a single-qutrit Clifford+T decomposition of the R gate,
making our result tight.


title:
On the Secrecy Gain of Formally Unimodular Construction $\text{A}_4$
  Lattices

abstract:
  Lattice coding for the Gaussian wiretap channel is considered, where the goal
is to ensure reliable communication between two authorized parties while
preventing an eavesdropper from learning the transmitted messages. Recently, a
measure called secrecy gain was proposed as a design criterion to quantify the
secrecy-goodness of the applied lattice code. In this paper, the theta series
of the so-called formally unimodular lattices obtained by Construction
$\text{A}_4$ from codes over $\mathbb{Z}_4$ is derived, and we provide a
universal approach to determine their secrecy gains. Initial results indicate
that Construction $\text{A}_4$ lattices can achieve a higher secrecy gain than
the best-known formally unimodular lattices from the literature. Furthermore, a
new code construction of formally self-dual $\mathbb{Z}_4$-linear codes is
presented.


title:
Global Minimizers of a Large Class of Anisotropic Attractive-Repulsive
  Interaction Energies in 2D

abstract:
  We study a large family of Riesz-type singular interaction potentials with
anisotropy in two dimensions. Their associated global energy minimizers are
given by explicit formulas whose supports are determined by ellipses under
certain assumptions. More precisely, by parameterizing the strength of the
anisotropic part we characterize the sharp range in which these explicit
ellipse-supported configurations are the global minimizers based on linear
convexity arguments. Moreover, for certain anisotropic parts, we prove that for
large values of the parameter the global minimizer is only given by vertically
concentrated measures corresponding to one dimensional minimizers. We also show
that these ellipse-supported configurations generically do not collapse to a
vertically concentrated measure at the critical value for convexity, leading to
an interesting gap of the parameters in between. In this intermediate range, we
conclude by infinitesimal concavity that any superlevel set of any local
minimizer in a suitable sense does not have interior points. Furthermore, for
certain anisotropic parts, their support cannot contain any vertical segment
for a restricted range of parameters, and moreover the global minimizers are
expected to exhibit a zigzag behavior. All these results hold for the limiting
case of the logarithmic repulsive potential, extending and generalizing
previous results in the literature. Various examples of anisotropic parts
leading to even more complex behavior are numerically explored.


title: Dynamical origin of the Dwarf Planet Ceres

abstract:
  The Dwarf Planet Ceres revealed the presence of ammonia and other unique
properties compared to other asteroids in the main belt which suggests that it
was not formed in situ. We model the early dynamical evolution of the outer
Solar System to study possible dynamical mechanisms to implant a Ceres-sized
planetesimal in the asteroid belt from the trans-Saturnian region. We calculate
that the fraction of the population of Ceres-sized planetesimals that are
captured in the asteroid belt is in the range of 2.8e-5 to 1.2e-3 depending on
the initial location in the outer planetesimal disk. The captured bodies have a
70% probability to have a semimajor axis between 2.5 and 3 au, a 33%
probability to have an eccentricity smaller than 0.2 and a 45% probability to
have an orbital inclination smaller than 10 degrees. Assuming the existence of
3,600 Ceres-size planetesimals in the inner part of the trans-Saturnian disk,
consistent with the estimate of Nesvorny & Vokrouhlicky (2016) for the
trans-Neptunian disk, our estimated capture probability and a final 80%
depletion of the asteroid belt during the subsequent giant planet instability,
lead to capture 1 Ceres in the asteroid belt, with a probability of 15%, 34%,
and 51% to be located in the inner, middle and outer belt respectively.


title: Self-Kerr effect across the yellow $\mathrm{Cu_2O}$ Rydberg series

abstract:
  We investigate the nonlinear refraction induced by Rydberg excitons in
$\mathrm{Cu_2O}$. Using a high-precision interferometry imaging technique that
spatially resolves the nonlinear phase shift, we observe significant shifts at
extremely low laser intensity near each exciton resonance. From this, we derive
the nonlinear index $\mathrm{n_2}$, present the $\mathrm{n_2}$ spectrum for
$n\geq 5$ and report large $\mathrm{n_2}$ values of order $10^{-3}$ mm$^2$/mW.
Moreover, we observe a rapid saturation of the Kerr nonlinearity and find that
the saturation intensity $\mathrm{I_{sat}}$ decreases as $n^{-7}$. We explain
this with the Rydberg blockade mechanism, whereby giant Rydberg interactions
limit the exciton density, resulting in a maximum phase shift of 0.5 rad in our
setup.


title: Coulomb and Riesz gases: The known and the unknown

abstract:
  We review what is known, unknown and expected about the mathematical
properties of Coulomb and Riesz gases. Those describe infinite configurations
of points in $\mathbb{R}^d$ interacting with the Riesz potential $\pm |x|^{-s}$
(resp. $-\log|x|$ for $s=0$). Our presentation follows the standard point of
view of statistical mechanics, but we also mention how these systems arise in
other important situations (e.g. in random matrix theory). The main question
addressed in the article is how to properly define the associated infinite
point process and characterize it using some (renormalized) equilibrium
equation. This is largely open in the long range case $s<d$. For the
convenience of the reader we give the detail of what is known in the short
range case $s>d$. In the last part we discuss phase transitions and mention
what is expected on physical grounds.

categories: math-ph cond-mat.stat-mech math.MP math.PR


title:
Reversed Hardy-Littlewood-Sobolev inequality on Heisenberg group
  $\mathbb{H}^n$ and CR sphere $\mathbb{S}^{2n+1}$

abstract:
  This paper is mainly devoted to the study of the reversed
Hardy-Littlewood-Sobolev (HLS) inequality on Heisenberg group $\mathbb{H}^n$
and CR sphere $\mathbb{S}^{2n+1}$. First, we establish the roughly reversed HLS
inequality and give a explicitly lower bound for the sharp constant. Then, the
existence of the extremal functions with sharp constant is proved by
subcritical approach and some compactness techniques. Our method is
rearrangement free and can be applied to study the classical HLS inequality and
other similar inequalities.


title:
Existence and Uniqueness of Maximal Solutions to a 3D Navier-Stokes
  Equation with Stochastic Lie Transport

abstract:
  We present here a criterion to conclude that an abstract SPDE posseses a
unique maximal strong solution, which we apply to a three dimensional
Stochastic Navier-Stokes Equation. Inspired by the work of [Kato and Lai,1984]
in the deterministic setting, we provide a comparable result here in the
stochastic case whilst facilitating a variety of noise structures such as
additive, multiplicative and transport. In particular our criterion is designed
to fit viscous fluid dynamics models with Stochastic Advection by Lie Transport
(SALT) as introduced in [Holm,2015]. Our application to the Incompressible
Navier-Stokes equation matches the existence and uniqueness result of the
deterministic theory. This short work summarises the results and announces two
papers [Goodair et al, 2022] which give the full details for the abstract
well-posedness arguments and application to the Navier-Stokes Equation.


title:
COVID-19 Submodel for the NC MInD ABM Overview, Design Concepts, and
  Details Protocol

abstract:
  This Overview, Design Concepts, and Details (ODD) Protocol is an ODD
extension to an agent-based model (ABM) framework built for the North Carolina
Modeling Infectious Diseases Program (NC MInD). The model, NC MInD ABM, can be
used as a base model for various infectious disease simulations. In this
document, we describe a submodel specifically designed to simulate COVID-19
cases and hospitalizations within North Carolina. We describe in detail how
each piece of the submodel works and how it was created. We do not discuss
specific simulation scenarios or results. This information is reserved for
papers related to each use case of the submodel.


title:
Transfer and Marginalize: Explaining Away Label Noise with Privileged
  Information

abstract:
  Supervised learning datasets often have privileged information, in the form
of features which are available at training time but are not available at test
time e.g. the ID of the annotator that provided the label. We argue that
privileged information is useful for explaining away label noise, thereby
reducing the harmful impact of noisy labels. We develop a simple and efficient
method for supervised neural networks: it transfers via weight sharing the
knowledge learned with privileged information and approximately marginalizes
over privileged information at test time. Our method, TRAM (TRansfer and
Marginalize), has minimal training time overhead and has the same test time
cost as not using privileged information. TRAM performs strongly on CIFAR-10H,
ImageNet and Civil Comments benchmarks.


title: NLTE Effects on Kilonova Expansion Opacities

abstract:
  A binary neutron star merger produces a rapidly evolving transient known as a
kilonova (KN), which peaks a few days after merger. Modelling of KNe has often
been approached assuming local thermodynamic equilibrium (LTE) conditions in
the ejecta. We present the first analysis of non-local thermodynamic
equilibrium (NLTE) level populations, using the spectral synthesis code SUMO,
and compare these to LTE values. We investigate the importance of the radiation
field by conducting NLTE excitation calculations with and without radiative
transfer. Level populations, in particular higher lying ones, start to show
deviations from LTE a few days after merger. Excitation is lower in NLTE for
the majority of ions and states, and this tends to give lower expansion
opacities. While the difference is small for the first few days, it grows to
factors 2-10 after this. Our results are important both for demonstrating
validity of LTE expansion opacities for an initial phase (few days), while
highlighting the need for NLTE modelling during later phases. Considering also
NLTE ionisation, our results indicate that NLTE can give both higher or lower
opacities, depending on composition and wavelength, sometimes by orders of
magnitudes.


title: The sensitivity of $\mu\to e$ processes to $\tau$ flavour change

abstract:
  Transforming a $\mu$ to a $\tau$, then the $\tau$ to to an $e$, results in
$\mu \to e$. In an EFT framework, we explore the sensitivity of $\mu\to e$
observables to products of $(\mu\to \tau)\times (\tau \to e)$ interactions, and
show that the exceptional sensitivity of upcoming $\mu \to e$ experiments could
allow to probe parameter space beyond the reach of upcoming $\tau \to l$
searches in Higgs, $\tau$ and $B$ decays. We describe the $\tau \to l$
interactions as dimension six operators in the SM EFT, identify pairs of them
giving interesting contributions to $\mu \to e$ processes, and obtain the
anomalous dimensions mixing those pairs into dimension eight $\mu\to e$
operators. We find that $\mu \to e$ processes are sensitive to $\tau$
flavour-changing $B$ decays at rates comparable to current $B$ anomalies, but
cannot reduce rates -- as appropriate in many current $B$ anomalies -- because
they do not interfere with the SM.


title:
Beyond Vaccination Rates: A Synthetic Random Proxy Metric of Total
  SARS-CoV-2 Immunity Seroprevalence in the Community

abstract:
  Explicit knowledge of total community-level immune seroprevalence is critical
to developing policies to mitigate the social and clinical impact of
SARS-CoV-2. Publicly available vaccination data are frequently cited as a proxy
for population immunity, but this metric ignores the effects of
naturally-acquired immunity, which varies broadly throughout the country and
world. Without broad or random sampling of the population, accurate measurement
of persistent immunity post natural infection is generally unavailable. To
enable tracking of both naturally-acquired and vaccine-induced immunity, we set
up a synthetic random proxy based on routine hospital testing for estimating
total Immunoglobulin G (IgG) prevalence in the sampled community. Our approach
analyzes viral IgG testing data of asymptomatic patients who present for
elective procedures within a hospital system. We apply multilevel regression
and poststratification to adjust for demographic and geographic discrepancies
between the sample and the community population. We then apply state-based
vaccination data to categorize immune status as driven by natural infection or
by vaccine. We have validated the model using verified clinical metrics of
viral and symptomatic disease incidence to show the expected biological
correlation of these entities with the timing, rate, and magnitude of
seroprevalence. In mid-July 2021, the estimated immunity level was 74% with the
administered vaccination rate of 45% in the two counties. The metric improves
real-time understanding of immunity to COVID-19 as it evolves and the
coordination of policy responses to the disease, toward an inexpensive and
easily operational surveillance system that transcends the limits of
vaccination datasets alone.


title:
Stochastic Perturbations of Tabular Features for Non-Deterministic
  Inference with Automunge

abstract:
  Injecting gaussian noise into training features is well known to have
regularization properties. This paper considers noise injections to numeric or
categoric tabular features as passed to inference, which translates inference
to a non-deterministic outcome and may have relevance to fairness
considerations, adversarial example protection, or other use cases benefiting
from non-determinism. We offer the Automunge library for tabular preprocessing
as a resource for the practice, which includes options to integrate random
sampling or entropy seeding with the support of quantum circuits for an
improved randomness profile in comparison to pseudo random number generators.
Benchmarking shows that neural networks may demonstrate an improved performance
when a known noise profile is mitigated with corresponding injections to both
training and inference, and that gradient boosting appears to be robust to a
mild noise profile in inference, suggesting that stochastic perturbations could
be integrated into existing data pipelines for prior trained gradient boosting
models.


title: Convergence conditions for $p$--adic continued fractions

abstract:
  Continued fractions have been introduced in the field of $p$--adic numbers
$\mathbb{Q}_p$ by several authors. However, a standard definition is still
missing since all the proposed algorithms are not able to replicate all the
properties of continued fractions in $\mathbb{R}$. In particular, an analogue
of the Lagrange's Theorem is not yet proved for any attempt of generalizing
continued fractions in $\mathbb{Q}_p$. Thus, it is worth to study the
definition of new algorithms for $p$--adic continued fractions. The main
condition that a new method needs to fulfill is the convergence in $\mathbb
Q_p$ of the continued fractions. In this paper we study some convergence
conditions for continued fractions in $\mathbb{Q}_p$. These results allow to
define many new families of continued fractions whose convergence is
guaranteed. Then we provide some new algorithms exploiting the new convergence
condition and we prove that one of them terminates in a finite number of steps
when the input is rational, as it happens for real continued fractions.


title:
Data-Driven Enhanced Model Reduction for Bifurcating Models in
  Computational Fluid Dynamics

abstract:
  We investigate various data-driven methods to enhance projection-based model
reduction techniques with the aim of capturing bifurcating solutions. To show
the effectiveness of the data-driven enhancements, we focus on the
incompressible Navier-Stokes equations and different types of bifurcations. To
recover solutions past a Hopf bifurcation, we propose an approach that combines
proper orthogonal decomposition with Hankel dynamic mode decomposition. To
approximate solutions close to a pitchfork bifurcation, we combine localized
reduced models with artificial neural networks. Several numerical examples are
shown to demonstrate the feasibility of the presented approaches.


title:
Consistent mass formulae for the four-dimensional dyonic NUT-charged
  spacetimes

abstract:
  In our previous work, a novel idea that the NUT charge can be thought of as a
thermodynamical multi-hair has been advocated to describe perfectly the
thermodynamical character of the generic four-dimensional Taub-NUT spacetimes.
According to this scheme, the Komar mass M, the gravito-magnetic charge and/or
the dual (magnetic) mass N, together with a new secondary hair J_N=MN, namely,
a Kerr-like conserved angular momentum, enter into the standard forms of the
first law and Bekenstein-Smarr mass formula. Distinguished from other recent
attempts, our consistent thermodynamic differential and integral mass formulae
are both obtainable from a meaningful Christodoulou-Ruffini-type squared mass
formula of almost all of the four-dimensional NUT-charged spacetimes. As an
excellent consequence, the famous Bekenstein-Hawking one-quarter area-entropy
relation can be naturally restored not only in the Lorentzian sector and but
also in the Euclidian counterpart of the generic Taub-NUT-type spacetimes
without imposing any constraint condition. However, only purely
electric-charged cases in the four-dimensional Einstein-Maxwell gravity theory
with a NUT charge have been addressed there. In this paper, we shall follow the
simple, systematic way proposed in that article to further investigate the
dyonic NUT-charged case. It is shown that the standard thermodynamic relations
continue to hold true provided that no new secondary charge is added, however,
the so-obtained electrostatic and magneto-static potentials are not coincident
with those computed via the standard method. To rectify this inconsistence, a
simple strategy is provided by further introducing two additional secondary
hairs: Q_N=QN and P_N=PN, together with their thermodynamical conjugate
potentials, so that the first law and Bekenstein-Smarr mass formula are still
satisfied.


title: Universal control of a six-qubit quantum processor in silicon

abstract:
  Future quantum computers capable of solving relevant problems will require a
large number of qubits that can be operated reliably. However, the requirements
of having a large qubit count and operating with high-fidelity are typically
conflicting. Spins in semiconductor quantum dots show long-term promise but
demonstrations so far use between one and four qubits and typically optimize
the fidelity of either single- or two-qubit operations, or initialization and
readout. Here we increase the number of qubits and simultaneously achieve
respectable fidelities for universal operation, state preparation and
measurement. We design, fabricate and operate a six-qubit processor with a
focus on careful Hamiltonian engineering, on a high level of abstraction to
program the quantum circuits and on efficient background calibration, all of
which are essential to achieve high fidelities on this extended system. State
preparation combines initialization by measurement and real-time feedback with
quantum-non-demolition measurements. These advances will allow for testing of
increasingly meaningful quantum protocols and constitute a major stepping stone
towards large-scale quantum computers.


title: Sketching Distances in Monotone Graph Classes

abstract:
  We study the problems of adjacency sketching, small-distance sketching, and
approximate distance threshold sketching for monotone classes of graphs. The
problem is to obtain randomized sketches of the vertices of any graph G in the
class, so that adjacency, exact distance thresholds, or approximate distance
thresholds of two vertices u, v can be decided (with high probability) from the
sketches of u and v, by a decoder that does not know the graph. The goal is to
determine when sketches of constant size exist.
  We show that, for monotone classes of graphs, there is a strict hierarchy:
approximate distance threshold sketches imply small-distance sketches, which
imply adjacency sketches, whereas the reverse implications are each false. The
existence of an adjacency sketch is equivalent to the condition of bounded
arboricity, while the existence of small-distance sketches is equivalent to the
condition of bounded expansion. Classes of constant expansion admit approximate
distance threshold sketches, while a monotone graph class can have arbitrarily
small non-constant expansion without admitting an approximate distance
threshold sketch.


title:
Cell-Free Massive MIMO in Virtualized CRAN: How to Minimize the Total
  Network Power?

abstract:
  Previous works on cell-free massive MIMO mostly consider physical-layer and
fronthaul transport aspects. How to deploy cell-free massive MIMO functionality
in a practical wireless system is an open problem. This paper proposes a new
cell-free architecture that can be implemented on top of a virtualized cloud
radio access network (V-CRAN). We aim to minimize the end-to-end power
consumption by jointly considering the radio, optical fronthaul, virtualized
cloud processing resources, and spectral efficiency requirements of the user
equipments. The considered optimization problem is cast in a mixed binary
second-order cone programming form and, thus, the global optimum can be found
using a branch-and-bound algorithm. The optimal power-efficient solution of our
proposed cell-free system is compared with conventional small-cell implemented
using V-CRAN, to determine the benefits of cell-free networking. The numerical
results demonstrate that cell-free massive MIMO increases the maximum rate
substantially, which can be provided with almost the same energy per bit. We
show that it is more power-efficient to activate cell-free massive MIMO already
at low spectral efficiencies (above 1 bit/s/Hz).


title: On heights of distributivity matrices

abstract:
  We construct a model in which there exists a distributivity matrix of regular
height $\lambda$ larger than $\mathfrak{h}$; both $\lambda = \mathfrak{c}$ and
$\lambda < \mathfrak{c}$ are possible. A distributivity matrix is a refining
system of mad families without common refinement. Of particular interest in our
proof is the preservation of $\mathcal{B}$-Canjarness.


title:
Traffic-Aware Dynamic Functional Split for 5G Cloud Radio Access
  Networks

abstract:
  As we are moving towards adopting virtualization technologies for next
generation mobile networks, 5G base station (called gNB) is segregated into a
Radio Unit (RU), a Distributed Unit (DU), and a Central Unit (CU) in order to
support Cloud based Radio Access Networks (C-RAN) where RU and DU are connected
through a fronthaul link while CU and DU are connected through a midhaul link.
Although virtualization of CU gives benefits of centralization to the
operators, there are other issues to be solved such as optimization of midhaul
bandwidth and computing resources at edge cloud and central cloud where the DUs
and CUs are deployed, respectively. In this paper, we propose a dynamic
functional split selection for the DUs in 5G C-RAN by adopting to traffic
heterogeneity where the midhaul bandwidth is limited. We proposed an
optimization problem that maximizes the centralization of the C-RAN system by
operating more number of DUs on split Option-7 by changing the channel
bandwidth of the DUs. The dynamical selection of split options among each CU-DU
pair gives 90% centralization over the static functional split for a given
midhaul bandwidth.


title:
Next-Level, Robotic Telescope-Based Observing Experiences to Boost STEM
  Enrollments and Majors on a National Scale

abstract:
  Funded by a $3M Department of Defense (DoD) National Defense Education
Program (NDEP) award, we are developing and deploying on a national scale a
follow-up curriculum to "Our Place In Space!", or OPIS!, in which approx. 3,500
survey-level astronomy students are using our global network of "Skynet"
robotic telescopes each year. The goal of this new curriculum, called
"Astrophotography of the Multi-Wavelength Universe!", or MWU!, is to boost the
number of these students who choose STEM majors. One semester in, our
participant program has begun, and participating educators have made good
progress on MWU!'s first two modules. Excellent progress has been made on the
software front, where we have developed new graphing, analysis, and modeling
tools in support of these, and upcoming, modules. On the hardware front,
preparation continues to expand Skynet to include a global network of
intermediate-sized, radio telescopes, capable of exploring the invisible
universe.


title:
Autoencoding Low-Resolution MRI for Semantically Smooth Interpolation of
  Anisotropic MRI

abstract:
  High-resolution medical images are beneficial for analysis but their
acquisition may not always be feasible. Alternatively, high-resolution images
can be created from low-resolution acquisitions using conventional upsampling
methods, but such methods cannot exploit high-level contextual information
contained in the images. Recently, better performing deep-learning based
super-resolution methods have been introduced. However, these methods are
limited by their supervised character, i.e. they require high-resolution
examples for training. Instead, we propose an unsupervised deep learning
semantic interpolation approach that synthesizes new intermediate slices from
encoded low-resolution examples. To achieve semantically smooth interpolation
in through-plane direction, the method exploits the latent space generated by
autoencoders. To generate new intermediate slices, latent space encodings of
two spatially adjacent slices are combined using their convex combination.
Subsequently, the combined encoding is decoded to an intermediate slice. To
constrain the model, a notion of semantic similarity is defined for a given
dataset. For this, a new loss is introduced that exploits the spatial
relationship between slices of the same volume. During training, an existing
in-between slice is generated using a convex combination of its neighboring
slice encodings. The method was trained and evaluated using publicly available
cardiac cine, neonatal brain and adult brain MRI scans. In all evaluations, the
new method produces significantly better results in terms of Structural
Similarity Index Measure and Peak Signal-to-Noise Ratio (p< 0.001 using
one-sided Wilcoxon signed-rank test) than a cubic B-spline interpolation
approach. Given the unsupervised nature of the method, high-resolution training
data is not required and hence, the method can be readily applied in clinical
settings.


title:
Reduced-Order Modeling of Thermal Dynamics in District Energy Networks
  using Spectral Clustering

abstract:
  Simulation of thermal dynamics in city-scale district energy grids often
becomes computationally prohibitive for long simulation runs. Current model
order reduction methods offer limited interpretability with regards to the
non-reduced system, and are not in general applicable for e.g., varying flow
rates, multiple producers, or changing flow directions. This article presents a
novel method based on graph theory that approximates the solution of an
optimization problem that minimizes the local truncation error for heat
transport in the grid. It is shown that the method can be used to reduce the
thermal dynamic model of a city-scale energy grid, resulting in a coarser
temporal and spatial resolution. The relative root mean square error was 2.3\%
for the temperature in the evaluation scenario, comparing the reduced-order
system with the non-reduced system at the instances of the coarser time-step.


title:
Strichartz estimates for equations with structured Lipschitz
  coefficients

abstract:
  Sharp Strichartz estimates are proved for Schr\"odinger and wave equations
with Lipschitz coefficients satisfying additional structural assumptions. We
use Phillips functional calculus as a substitute for Fourier inversion, which
shows how dispersive properties are inherited from the constant coefficient
case. Global Strichartz estimates follow provided that the derivatives of the
coefficients are integrable. The estimates extend to structured coefficients of
bounded variations. As applications we derive Strichartz estimates with
additional derivative loss for wave equations with H\"older-continuous
coefficients and solve nonlinear Schr\"odinger equations. Finally, we record
spectral multiplier estimates, which follow from the Strichartz estimates by
well-known means.


title: Is the relativistic Structure of Spacetime Ontic or Epistemic?

abstract:
  As repeatedly emphasized by Einstein our knowledge of the structure of space
and time is based entirely on inferences from observations of physical objects
and processes. At the most fundamental level these objects and processes are
described by quantum theory. However, the ontological status of the theoretical
entities employed by quantum theory is a matter of considerable debate.
Furthermore, the nonlocal correlations identified by Bell cannot readily be
explained within the standard relativistic framework. This suggests that we
should re-examine our understanding of spacetime.


title:
Soft Actor-Critic Deep Reinforcement Learning for Fault Tolerant Flight
  Control

abstract:
  Fault-tolerant flight control faces challenges, as developing a model-based
controller for each unexpected failure is unrealistic, and online learning
methods can handle limited system complexity due to their low sample
efficiency. In this research, a model-free coupled-dynamics flight controller
for a jet aircraft able to withstand multiple failure types is proposed. An
offline trained cascaded Soft Actor-Critic Deep Reinforcement Learning
controller is successful on highly coupled maneuvers, including a coordinated
40 degree bank climbing turn with a normalized Mean Absolute Error of 2.64%.
The controller is robust to six failure cases, including the rudder jammed at
-15 deg, the aileron effectiveness reduced by 70%, a structural failure, icing
and a backward c.g. shift as the response is stable and the climbing turn is
completed successfully. Robustness to biased sensor noise, atmospheric
disturbances, and to varying initial flight conditions and reference signal
shapes is also demonstrated.


title:
Is Cross-Attention Preferable to Self-Attention for Multi-Modal Emotion
  Recognition?

abstract:
  Humans express their emotions via facial expressions, voice intonation and
word choices. To infer the nature of the underlying emotion, recognition models
may use a single modality, such as vision, audio, and text, or a combination of
modalities. Generally, models that fuse complementary information from multiple
modalities outperform their uni-modal counterparts. However, a successful model
that fuses modalities requires components that can effectively aggregate
task-relevant information from each modality. As cross-modal attention is seen
as an effective mechanism for multi-modal fusion, in this paper we quantify the
gain that such a mechanism brings compared to the corresponding self-attention
mechanism. To this end, we implement and compare a cross-attention and a
self-attention model. In addition to attention, each model uses convolutional
layers for local feature extraction and recurrent layers for global sequential
modelling. We compare the models using different modality combinations for a
7-class emotion classification task using the IEMOCAP dataset. Experimental
results indicate that albeit both models improve upon the state-of-the-art in
terms of weighted and unweighted accuracy for tri- and bi-modal configurations,
their performance is generally statistically comparable. The code to replicate
the experiments is available at https://github.com/smartcameras/SelfCrossAttn


title:
Structure-aware combinatorial group testing: a new method for pandemic
  screening

abstract:
  Combinatorial group testing (CGT) is used to identify defective items from a
set of items by grouping them together and performing a small number of tests
on the groups. Recently, group testing has been used to design efficient
COVID-19 testing, so that resources are saved while still identifying all
infected individuals. Due to test waiting times, a focus is given to
non-adaptive CGT, where groups are designed a priori and all tests can be done
in parallel. The design of the groups can be done using Cover-Free Families
(CFFs). The main assumption behind CFFs is that a small number $d$ of positives
are randomly spread across a population of $n$ individuals. However, for
infectious diseases, it is reasonable to assume that infections show up in
clusters of individuals with high contact (children in the same classroom
within a school, households within a neighbourhood, students taking the same
courses within a university, people seating close to each other in a stadium).
The general structure of these communities can be modeled using hypergraphs,
where vertices are items to be tested and edges represent clusters containing
high contacts. We consider hypergraphs with non-overlapping edges and
overlapping edges (first two examples and last two examples, respectively). We
give constructions of what we call structure-aware CFF, which uses the
structure of the underlying hypergraph. We revisit old CFF constructions,
boosting the number of defectives they can identify by taking the hypergraph
structure into account. We also provide new constructions based on hypergraph
parameters.


title: Deep Movement Primitives: toward Breast Cancer Examination Robot

abstract:
  Breast cancer is the most common type of cancer worldwide. A robotic system
performing autonomous breast palpation can make a significant impact on the
related health sector worldwide. However, robot programming for breast
palpating with different geometries is very complex and unsolved. Robot
learning from demonstrations (LfD) reduces the programming time and cost.
However, the available LfD are lacking the modelling of the manipulation
path/trajectory as an explicit function of the visual sensory information. This
paper presents a novel approach to manipulation path/trajectory planning called
deep Movement Primitives that successfully generates the movements of a
manipulator to reach a breast phantom and perform the palpation. We show the
effectiveness of our approach by a series of real-robot experiments of reaching
and palpating a breast phantom. The experimental results indicate our approach
outperforms the state-of-the-art method.


title:
Informativity conditions for data-driven control based on input-state
  data and polyhedral cross-covariance noise bounds

abstract:
  Modeling and control of dynamical systems rely on measured data, which
contains information about the system. Finite data measurements typically lead
to a set of system models that are unfalsified, i.e., that explain the data.
The problem of data-informativity for stabilization or control with quadratic
performance is concerned with the existence of a controller that stabilizes all
unfalsified systems or achieves a desired quadratic performance. Recent results
in the literature provide informativity conditions for control based on
input-state data and ellipsoidal noise bounds, such as energy or magnitude
bounds. In this paper, we consider informativity of input-state data for
control where noise bounds are defined through the cross-covariance of the
noise with respect to an instrumental variable; bounds that were introduced
originally as a noise characterization in parameter bounding identification.
The considered cross-covariance bounds are defined by a finite number of
hyperplanes, which induce a (possibly unbounded) polyhedral set of unfalsified
systems. We provide informativity conditions for input-state data with
polyhedral cross-covariance bounds for stabilization and
$\mathcal{H}_2$/$\mathcal{H}_\infty$ control through vertex/half-space
representations of the polyhedral set of unfalsified systems.


title:
The VMC survey -- XLVII. Turbulence-Controlled Hierarchical Star
  Formation in the Large Magellanic Cloud

abstract:
  We perform a statistical clustering analysis of upper main-sequence stars in
the Large Magellanic Cloud (LMC) using data from the Visible and Infrared
Survey Telescope for Astronomy survey of the Magellanic Clouds. We map over
2500 young stellar structures at 15 significance levels across ~120 square
degrees centred on the LMC. The structures have sizes ranging from a few
parsecs to over 1 kpc. We find that the young structures follow power-law size
and mass distributions. From the perimeter-area relation, we derive a
perimeter-area dimension of 1.44+-0.20. From the mass-size relation and the
size distribution, we derive two-dimensional fractal dimensions of 1.50+-0.10
and 1.61+-0.20, respectively. We find that the surface density distribution is
well-represented by a lognormal distribution. We apply the Larson relation to
estimate the velocity dispersions and crossing times of these structures. Our
results indicate that the fractal nature of the young stellar structures has
been inherited from the gas clouds from which they form and that this
architecture is generated by supersonic turbulence. Our results also suggest
that star formation in the LMC is scale-free from 10 pc to 700 pc.


title: Using Lie derivatives with dual quaternions in robotics

abstract:
  We introduce the notion of the Lie derivative in the context of dual
quaternions that represent poses and twists. First we define the wrench in
terms of dual quaternions. Then we show how the Lie derivative helps understand
how actuators affect an end effector in parallel robots, and make it explicit
in the case of robot-driven parallel robots. We also show how to use Lie
derivatives with the Newton-Raphson Method to solve the forward kinematic
problem for over constrained parallel actuators. Finally, we derive the
equations of motion of the end effector in dual quaternion form, which include
the effect of inertia in the actuators. A large part of our methods is an
approximation of the normalization of a pure dual quaternion perturbation of
the identity, which shows that it is equal up to the second order to the
exponential of the pure dual quaternion.


title:
Quantification of Actual Road User Behavior on the Basis of Given
  Traffic Rules

abstract:
  Driving on roads is restricted by various traffic rules, aiming to ensure
safety for all traffic participants. However, human road users usually do not
adhere to these rules strictly, resulting in varying degrees of rule
conformity. Such deviations from given rules are key components of today's road
traffic. In autonomous driving, robotic agents can disturb traffic flow, when
rule deviations are not taken into account. In this paper, we present an
approach to derive the distribution of degrees of rule conformity from human
driving data. We demonstrate our method with the Waymo Open Motion dataset and
Safety Distance and Speed Limit rules.


title:
When Kinematics Dominates Mechanics: Locally Volume-Preserving
  Primitives for Model Reduction in Finite Elasticity

abstract:
  A new, and extremely fast, computational modeling paradigm is introduced here
for specific finite elasticity problems that arise in the context of soft
robotics. Whereas continuum mechanics is a very classical area of study, and
significant effort has been devoted to the development of intricate
constitutive models for finite elasticity, we show that in the kinds of
large-strain mechanics problems arising in soft robotics, many of the
parameters in constitutive models are irrelevant. For the most part, the
isochoric (locally volume-preserving) constraint dominates behavior, and this
can be built into closed-form kinematic deformation fields before even
considering other aspects of constitutive modeling. We therefore focus on
developing and applying primitive deformations that each observe this
constraint. It is shown that by composing a wide enough variety of such
deformations that the most common behaviors observed in soft robots can be
replicated. Case studies include an inflatable rubber chamber, a slender rubber
rod, and a rubber block subjected to different boundary conditions. We show
that this method is at least 50 times faster than the ABAQUS implementation of
the finite element method (FEM). Physical experiments and measurements show
that both our method and ABAQUS have approximately 10% error relative to
experimentally measured displacements, as well as to each other. Our method
provides a real-time alternative to FEM, and captures essential degrees of
freedom for use in feedback control systems.


title:
Enhanced Behavioral Cloning with Environmental Losses for Self-Driving
  Vehicles

abstract:
  Learned path planners have attracted research interest due to their ability
to model human driving behavior and rapid inference. Recent works on behavioral
cloning show that simple imitation of expert observations is not sufficient to
handle complex driving scenarios. Besides, predictions that land outside
drivable areas can lead to potentially dangerous situations. This paper
proposes a set of loss functions, namely Social loss and Road loss, which
account for modelling risky social interactions in path planning. These losses
act as a repulsive scalar field that surrounds non-drivable areas. Predictions
that land near these regions incur in a higher training cost, which is
minimized using backpropagation. This methodology provides additional
environment feedback to the traditional supervised learning set up. We
validated this approach on a large-scale urban driving dataset. The results
show the agent learns to imitate human driving while exhibiting better safety
metrics. Furthermore, the proposed methodology has positive effects on
inference without the need to artificially generate unsafe driving examples.
The explanability study suggests that the benefits obtained are associated with
a higher relevance of non-drivable areas in the agent's decisions compared to
classical behavioral cloning.


title:
Finite-time response of dynamo mean-field effects in magnetorotational
  turbulence

abstract:
  Accretion disc turbulence along with its effect on large-scale magnetic
fields plays an important role in understanding disc evolution in general, and
the launching of astrophysical jets in particular. Motivated by enabling a
comprehensive sub-grid description for global long-term simulations of
accretions discs, we aim to further characterize the transport coefficients
emerging in local simulations of magnetorotational disc turbulence. For the
current investigation, we leverage a time-dependent version of the test-field
method, which is sensitive to the turbulent electromotive force (EMF) generated
as a response to a set of pulsating background fields. We obtain Fourier
spectra of the transport coefficients as a function of oscillation frequency.
These are well approximated by a simple response function, describing a
finite-time build-up of the EMF as a result of a time-variable mean magnetic
field. For intermediate timescales (i.e., slightly above the orbital
frequency), we observe a significant phase lag of the EMF compared to the
causing field. Augmented with our previous result on a non-local closure
relation in space, and incorporated into a suitable mean-field description that
we briefly sketch out here, the new framework will allow to drop the
restrictive assumption of scale separation.


title:
Structural study and evaluation of thermoelectric properties of
  single-phase isocubanite (CuFe2S3) synthesized via an ultra-fast efficient
  microwave radiation technique

abstract:
  The current state-of-the-art thermoelectric materials are generally composed
of expensive, scarce, and toxic elements. In this respect, copper-based sulfide
compounds have emerged as viable alternatives. Herein, we report for the first
time the successful synthesis of single-phase cubic isocubanite CuFe2S3 using
mechanical-alloying combined with microwave-assisted synthesis. The isocubanite
phase synthesized via this ultra-fast out-of-equilibrium process exhibits a
maximum thermoelectric figure of merit, zTmax ~ 0.14 at 673 K. Besides the
thermoelectric properties, insights about the structure of isocubanite, based
on the refinement of X-ray diffraction data and first principles calculations,
are also investigated in detail. It confirms that the Cu-Fe cations in
synthetic isocubanite overwhelmingly occupy the 4d sites of the cubic structure
in an inherently disordered fashion.


title:
Towards 6G zero touch networks: The case of automated Cloud-RAN
  deployments

abstract:
  The arrival of 6G technologies shall massively increase the proliferation of
on-demand and ephemeral networks. Creating and removing customized networks on
the fly notably requires fully automation to guarantee commissioning-time
acceleration. In this paper, we address the deployment automation of an
end-to-end mobile network, with special focus on RAN units (referred to as
Cloud-RAN). The Cloud-RAN automation is especially challenging due to the
strong latency constraints expected in 6G as well as the required management of
physical antennas. To automatically instantiate a Cloud-RAN chain, we introduce
a Zero Touch Commissioning (ZTC) model which performs resource discovery while
looking for both antennas and computing capacity as near as possible to the
targeted coverage zone. We validate the ZTC model by a testbed which deploys,
configures and starts the network service without human intervention while
using Kubernetes-based infrastructures as well as open-source RAN and core
elements implementing the mobile network functions.


title:
Rethinking Pareto Frontier for Performance Evaluation of Deep Neural
  Networks

abstract:
  Recent efforts in deep learning show a considerable advancement in
redesigning deep learning models for low-resource and edge devices. The
performance optimization of deep learning models are conducted either manually
or through automatic architecture search, or a combination of both. The
throughput and power consumption of deep learning models strongly depend on the
target hardware. We propose to use a \emph{multi-dimensional} Pareto frontier
to re-define the efficiency measure using a multi-objective optimization, where
other variables such as power consumption, latency, and accuracy play a
relative role in defining a dominant model. Furthermore, a random version of
the multi-dimensional Pareto frontier is introduced to mitigate the uncertainty
of accuracy, latency, and throughput variations of deep learning models in
different experimental setups. These two breakthroughs provide an objective
benchmarking method for a wide range of deep learning models. We run our novel
multi-dimensional stochastic relative efficiency on a wide range of deep image
classification models trained ImageNet data. Thank to this new approach we
combine competing variables with stochastic nature simultaneously in a single
relative efficiency measure. This allows to rank deep models that run
efficiently on different computing hardware, and combines inference efficiency
with training efficiency objectively.


title:
Geometric Regularization from Overparameterization explains Double
  Descent and other findings

abstract:
  The volume of the distribution of possible weight configurations associated
with a loss value may be the source of implicit regularization from
overparameterization due to the phenomenon of contracting volume with
increasing dimensions for geometric figures demonstrated by hyperspheres. This
paper introduces geometric regularization and explores potential applicability
to several unexplained phenomenon including double descent, the differences
between wide and deep networks, the benefits of He initialization and retained
proximity in training, gradient confusion, fitness landscape properties, double
descent in other learning paradigms, and other findings for overparameterized
learning. Experiments are conducted by aggregating histograms of loss values
corresponding to randomly sampled initializations in small setups, which find
directional correlations in zero or central mode dominance from deviations in
width, depth, and initialization distributions. Double descent is likely due to
a regularization phase change when a training path reaches low enough loss that
the loss manifold volume contraction from a reduced range of potential weight
sets is amplified by an overparameterized geometry.


title: (2.5+1)D Spatio-Temporal Scene Graphs for Video Question Answering

abstract:
  Spatio-temporal scene-graph approaches to video-based reasoning tasks, such
as video question-answering (QA), typically construct such graphs for every
video frame. These approaches often ignore the fact that videos are essentially
sequences of 2D "views" of events happening in a 3D space, and that the
semantics of the 3D scene can thus be carried over from frame to frame.
Leveraging this insight, we propose a (2.5+1)D scene graph representation to
better capture the spatio-temporal information flows inside the videos.
Specifically, we first create a 2.5D (pseudo-3D) scene graph by transforming
every 2D frame to have an inferred 3D structure using an off-the-shelf 2D-to-3D
transformation module, following which we register the video frames into a
shared (2.5+1)D spatio-temporal space and ground each 2D scene graph within it.
Such a (2.5+1)D graph is then segregated into a static sub-graph and a dynamic
sub-graph, corresponding to whether the objects within them usually move in the
world. The nodes in the dynamic graph are enriched with motion features
capturing their interactions with other graph nodes. Next, for the video QA
task, we present a novel transformer-based reasoning pipeline that embeds the
(2.5+1)D graph into a spatio-temporal hierarchical latent space, where the
sub-graphs and their interactions are captured at varied granularity. To
demonstrate the effectiveness of our approach, we present experiments on the
NExT-QA and AVSD-QA datasets. Our results show that our proposed (2.5+1)D
representation leads to faster training and inference, while our hierarchical
model showcases superior performance on the video QA task versus the state of
the art.


title:
Exact time dependence of the cumulants of a tracer position in a dense
  lattice gas

abstract:
  We develop a general method to calculate the exact time dependence of the
cumulants of the position of a tracer particle in a dense lattice gas of
hardcore particles. More precisely, we calculate the cumulant generating
function associated with the position of a tagged particle at arbitrary time,
and at leading order in the density of vacancies on the lattice. In particular,
our approach gives access to the short-time dynamics of the cumulants of the
tracer position -- a regime in which few results are known. The generality of
our approach is demonstrated by showing that it goes beyond the case of a
symmetric 1D random walk, and covers the important situations of (i) a biased
tracer; (ii) comb-like structures; and (iii) $d$-dimensional situations.


title: The Haldane gap in the SU(3) [3 0 0] Heisenberg chain

abstract:
  We calculate the Haldane gap of the $\mathrm{SU}(3)$ spin $[3~0~0]$
Heisenberg model using variational uniform fully symmetric $\mathrm{SU}(3)$
matrix product states, and find that the minimal gap $\Delta /J = 0.0263 $ is
obtained in the $[2~1~0]$ sector at momentum $2\pi/3$. We also discuss the
symmetry protected topological order of the ground state, and determine the
full dispersion relation of the elementary excitations and the correlation
lengths of the system.


title:
Large anomalous Hall effect induced by weak ferromagnetism in the
  noncentrosymmetric antiferromagnet $\mathrm{Co}\mathrm{Nb}_3\mathrm{S}_6$

abstract:
  We study the mechanism of the exceptionally large anomalous Hall effect (AHE)
in the noncentrosymmetric antiferromagnet
$\mathrm{Co}\mathrm{Nb}_3\mathrm{S}_6$ by angle-resolved photoemission
spectroscopy (ARPES) and magnetotransport measurements. From ARPES measurements
of $\mathrm{Co}\mathrm{Nb}_3\mathrm{S}_6$ and its family compounds
($\mathrm{Fe}\mathrm{Nb}_3\mathrm{S}_6$ and
$\mathrm{Ni}\mathrm{Nb}_3\mathrm{S}_6$), we find a band dispersion unique to
the Co intercalation existing near the Fermi level. We further demonstrate that
a slight deficiency of sulfur in $\mathrm{Co}\mathrm{Nb}_3\mathrm{S}_6$
eliminates the ferromagnetism and the AHE simultaneously while hardly changing
the band structure, indicating that the weak ferromagnetism is responsible for
the emergence of the large AHE. Based on our results, we propose Weyl points
near the Fermi level to cause the large AHE.


title:
Unsupervised and supervised learning of interacting topological phases
  from single-particle correlation functions

abstract:
  The recent advances in machine learning algorithms have boosted the
application of these techniques to the field of condensed matter physics, in
order e.g. to classify the phases of matter at equilibrium or to predict the
real-time dynamics of a large class of physical models. Typically in these
works, a machine learning algorithm is trained and tested on data coming from
the same physical model. Here we demonstrate that unsupervised and supervised
machine learning techniques are able to predict phases of a non-exactly
solvable model when trained on data of a solvable model. In particular, we
employ a training set made by single-particle correlation functions of a
non-interacting quantum wire and by using principal component analysis, k-means
clustering, and convolutional neural networks we reconstruct the phase diagram
of an interacting superconductor. We show that both the principal component
analysis and the convolutional neural networks trained on the data of the
non-interacting model can identify the topological phases of the interacting
model with a high degree of accuracy. Our findings indicate that non-trivial
phases of matter emerging from the presence of interactions can be identified
by means of unsupervised and supervised techniques applied to data of
non-interacting systems.


title:
FinNet: Solving Time-Independent Differential Equations with Finite
  Difference Neural Network

abstract:
  In recent years, deep learning approaches for partial differential equations
have received much attention due to their mesh-freeness and other desirable
properties. However, most of the works so far concentrated on time-dependent
nonlinear differential equations. In this work, we analyze potential issues
with the well-known Physic Informed Neural Network for differential equations
that are not time-dependent. This analysis motivates us to introduce a novel
technique, namely FinNet, for solving differential equations by incorporating
finite difference into deep learning. Even though we use a mesh during the
training phase, the prediction phase is mesh-free. We illustrate the
effectiveness of our method through experiments on solving various equations.