title:
Semi-Data-Aided Channel Estimation for MIMO Systems via Reinforcement
  Learning

abstract:
  Data-aided channel estimation is a promising solution to improve channel
estimation accuracy by exploiting data symbols as pilot signals for updating an
initial channel estimate. In this paper, we propose a semi-data-aided channel
estimator for multiple-input multiple-output communication systems. Our
strategy is to leverage reinforcement learning (RL) for selecting reliable
detected symbols among the symbols in the first part of transmitted data block.
This strategy facilitates an update of the channel estimate before the end of
data block transmission and therefore achieves a significant reduction in
communication latency compared to conventional data-aided channel estimation
approaches. Towards this end, we first define a Markov decision process (MDP)
which sequentially decides whether to use each detected symbol as an additional
pilot signal. We then develop an RL algorithm to efficiently find the best
policy of the MDP based on a Monte Carlo tree search approach. In this
algorithm, we exploit the a-posteriori probability for approximating both the
optimal future actions and the corresponding state transitions of the MDP and
derive a closed-form expression for the best policy. Simulation results
demonstrate that the proposed channel estimator effectively mitigates both
channel estimation error and detection performance loss caused by insufficient
pilot signals.


title:
Quantum uncertainties in sequential measurements under prediction and
  retrodiction

abstract:
  In sequential measurements, we consider the prediction is as an inference of
the subsequent observational data from the prior measurements, while the
retrodiction is as an inference of the prior observational data from the
subsequent measurements. We theoretically study the impact of the quantum
backaction (QBA) in the sequential measurements on the inferred observational
data from the prediction and retrodiction. The QBA of the prediction behaves
like the disturbance caused by prior measurements affecting subsequent
measurements, whereas the QBA of the retrodiction behaves through the
disturbance caused by the subsequent measurements affecting the prior
measurements. In particular, we consider the sequential measurements of two
observables A and B, one after another, i.e., A first and B later, and then we
theoretically formulate the quantum uncertainties in the value of these
observables (for both prediction and retrodiction) as figures of merit for the
disturbances. These results are illustrated in spin systems, where we present
the dependence of the uncertainty in subsequent measurement on the prior
measurement and vice versa. We further find a hint for beyond the stronger
uncertainty relation. The work is finally extended to N-sequential
measurements.


title: Combinatorial refinement on circulant graphs

abstract:
  The combinatorial refinement techniques have proven to be an efficient
approach to isomorphism testing for particular classes of graphs. If the number
of refinement rounds is small, this puts the corresponding isomorphism problem
in a low-complexity class. We investigate the round complexity of the
2-dimensional Weisfeiler-Leman algorithm on circulant graphs, i.e. on Cayley
graphs of the cyclic group $\mathbb{Z}_n$, and prove that the number of rounds
until stabilization is bounded by $\mathcal{O}(d(n)\log n)$, where $d(n)$ is
the number of divisors of $n$. As a particular consequence, isomorphism can be
tested in NC for connected circulant graphs of order $p^\ell$ with $p$ an odd
prime, $\ell>3$ and vertex degree $\Delta$ smaller than $p$.
  We also show that the color refinement method (also known as the
1-dimensional Weisfeiler-Leman algorithm) computes a canonical labeling for
every non-trivial circulant graph with a prime number of vertices after
individualization of two appropriately chosen vertices. Thus, the canonical
labeling problem for this class of graphs has at most the same complexity as
color refinement, which results in a time bound of $\mathcal{O}(\Delta n\log
n)$. Moreover, this provides a first example where a sophisticated approach to
isomorphism testing put forward by Tinhofer has a real practical meaning.


title:
Stochastic parameter-shift rule for quantum metrology with general
  Hamiltonians

abstract:
  Recently, quantum metrology with multiplicative Hamiltonians has been
proposed in the variational quantum algorithms, from which the estimation
precision can be adaptively optimized via the variational circuits. For systems
with general Hamiltonians, however, still lack these variational schemes. In
this work, we introduce a quantum-circuit-based approach for studying quantum
metrology with general Hamiltonians. We introduce the stochastic
parameter-shift rule for the derivatives of the evolved quantum state under the
parameterized gates in the circuit, whereby the quantum Fisher information can
be obtained. Here the parameters are those we wish to estimate. We find that
under the family of the parameterized gates, our scheme can be executed in
universal quantum computers. Moreover, in the examples of the magnetic field
estimation, we show the consistency between the results obtained from the
stochastic parameter-shift rule and the exact results while the standard
parameter-shift rule slightly deviates from the exact ones. Our work sheds new
light for studying quantum metrology with general Hamiltonians using quantum
circuit algorithms.


title:
Exploring terra incognita in the phase diagram of strongly interacting
  matter -- Experiments at FAIR and NICA

abstract:
  The fundamental properties of dense nuclear matter, as it exists in the core
of massive stellar objects, are still largely unknown. The investigation of the
high-density equation of state (EOS), which determines mass and radii of
neutron stars and the dynamics of neutron star mergers, is in the focus of
astronomical observations and of laboratory experiments with heavy-ion
collisions. Moreover, the microscopic degrees-of-freedom of strongly
interacting matter at high baryon densities are also unknown. While
Quantum-Chromo-Dynamics (QCD) calculations on the lattice find a smooth chiral
crossover between hadronic matter and the quark-gluon plasma for high
temperatures at zero baryon chemical potential, effective models predict a 1st
order chiral transition with a critical endpoint for matter at large baryon
chemical potentials. Up to date, experimental data both on the high-density EOS
and on a possible phase transition in dense baryonic matter are very scarce. In
order to explore this terra incognita, dedicated experimental programs are
planned at future heavy-ion research centres: the CBM experiment at FAIR, and
the MPD and BM@N experiments at NICA. The research programs and the layout of
these experiments will be presented. The future results of these laboratory
experiments will complement astronomical observations concerning the EOS, and,
in addition, will shed light on the microscopic degrees of freedom of QCD
matter at neutron star core densities.


title: Learning-Based Approaches for Graph Problems: A Survey

abstract:
  Over the years, many graph problems specifically those in NP-complete are
studied by a wide range of researchers. Some famous examples include graph
colouring, travelling salesman problem and subgraph isomorphism. Most of these
problems are typically addressed by exact algorithms, approximate algorithms
and heuristics. There are however some drawback for each of these methods.
Recent studies have employed learning-based frameworks such as machine learning
techniques in solving these problems, given that they are useful in discovering
new patterns in structured data that can be represented using graphs. This
research direction has successfully attracted a considerable amount of
attention. In this survey, we provide a systematic review mainly on classic
graph problems in which learning-based approaches have been proposed in
addressing the problems. We discuss the overview of each framework, and provide
analyses based on the design and performance of the framework. Some potential
research questions are also suggested. Ultimately, this survey gives a clearer
insight and can be used as a stepping stone to the research community in
studying problems in this field.


title:
Correlation Functions in Random Fully Connected Neural Networks at
  Finite Width

abstract:
  This article considers fully connected neural networks with Gaussian random
weights and biases and $L$ hidden layers, each of width proportional to a large
parameter $n$. For polynomially bounded non-linearities we give sharp estimates
in powers of $1/n$ for the joint correlation functions of the network output
and its derivatives. Moreover, we obtain exact layerwise recursions for these
correlation functions and solve a number of special cases for classes of
non-linearities including $\mathrm{ReLU}$ and $\tanh$. We find in both cases
that the depth-to-width ratio $L/n$ plays the role of an effective network
depth, controlling both the scale of fluctuations at individual neurons and the
size of inter-neuron correlations. We use this to study a somewhat simplified
version of the so-called exploding and vanishing gradient problem, proving that
this particular variant occurs if and only if $L/n$ is large. Several of the
key ideas in this article were first developed at a physics level of rigor in a
recent monograph with Roberts and Yaida.


title:
Emergence of Autocatalytic Sets in a Simple Model of Technological
  Evolution

abstract:
  Two alternative views of an economy are combined and studied. The first view
is that of technological evolution as a process of combinatorial innovation.
Recently a simple mathematical model (TAP) was introduced to study such a
combinatorial process. The second view is that of a network of production
functions forming an autocatalytic set. Autocatalytic (RAF) sets have been
studied extensively in the context of chemical reaction networks.
  Here, we combine the two models (TAP and RAF) and show that they are
compatible. In particular, it is shown that production function networks
resulting from the combinatorial TAP model have a high probability of
containing autocatalytic (RAF) sets. We also study the size distribution and
robustness of such "economic autocatalytic sets", and compare our results with
those from the chemical context. These initial results strongly support earlier
claims that the economy can indeed be seen as an autocatalytic set.


title:
Non-abelian extensions of Rota-Baxter Lie algebras and inducibility of
  automorphisms

abstract:
  A Rota-Baxter Lie algebra $\mathfrak{g}_T$ is a Lie algebra $\mathfrak{g}$
equipped with a Rota-Baxter operator $T : \mathfrak{g} \rightarrow
\mathfrak{g}$. In this paper, we consider non-abelian extensions of a
Rota-Baxter Lie algebra $\mathfrak{g}_T$ by another Rota-Baxter Lie algebra
$\mathfrak{h}_S.$ We define the non-abelian cohomology $H^2_{nab}
(\mathfrak{g}_T, \mathfrak{h}_S)$ which classifies {equivalence classes of}
such extensions. Given a non-abelian extension $$ 0 \rightarrow \mathfrak{h}_S
\xrightarrow{i} \mathfrak{e}_U \xrightarrow{p} \mathfrak{g}_T \rightarrow 0$$
of Rota-Baxter Lie algebras, we also show that the obstruction for a pair of
Rota-Baxter automorphisms in $\mathrm{Aut}(\mathfrak{h}_S ) \times
\mathrm{Aut}(\mathfrak{g}_T)$ to be induced by an automorphism in
$\mathrm{Aut}(\mathfrak{e}_U)$ lies in the cohomology group $H^2_{{nab}}
(\mathfrak{g}_T, \mathfrak{h}_S)$. As a byproduct, we obtain the Wells
short-exact sequence in the context of Rota-Baxter Lie algebras.


title:
Task2Dial: A Novel Task and Dataset for Commonsense enhanced Task-based
  Dialogue Grounded in Documents

abstract:
  This paper proposes a novel task on commonsense-enhanced task-based dialogue
grounded in documents and describes the Task2Dial dataset, a novel dataset of
document-grounded task-based dialogues, where an Information Giver (IG)
provides instructions (by consulting a document) to an Information Follower
(IF), so that the latter can successfully complete the task. In this unique
setting, the IF can ask clarification questions which may not be grounded in
the underlying document and require commonsense knowledge to be answered. The
Task2Dial dataset poses new challenges: (1) its human reference texts show more
lexical richness and variation than other document-grounded dialogue datasets;
(2) generating from this set requires paraphrasing as instructional responses
might have been modified from the underlying document; (3) requires commonsense
knowledge, since questions might not necessarily be grounded in the document;
(4) generating requires planning based on context, as task steps need to be
provided in order. The Task2Dial dataset contains dialogues with an average
$18.15$ number of turns and 19.79 tokens per turn, as compared to 12.94 and 12
respectively in existing datasets. As such, learning from this dataset promises
more natural, varied and less template-like system utterances.


title:
In Rain or Shine: Understanding and Overcoming Dataset Bias for
  Improving Robustness Against Weather Corruptions for Autonomous Vehicles

abstract:
  Several popular computer vision (CV) datasets, specifically employed for
Object Detection (OD) in autonomous driving tasks exhibit biases due to a range
of factors including weather and lighting conditions. These biases may impair a
model's generalizability, rendering it ineffective for OD in novel and unseen
datasets. Especially, in autonomous driving, it may prove extremely high risk
and unsafe for the vehicle and its surroundings. This work focuses on
understanding these datasets better by identifying such "good-weather" bias.
Methods to mitigate such bias which allows the OD models to perform better and
improve the robustness are also demonstrated. A simple yet effective OD
framework for studying bias mitigation is proposed. Using this framework, the
performance on popular datasets is analyzed and a significant difference in
model performance is observed. Additionally, a knowledge transfer technique and
a synthetic image corruption technique are proposed to mitigate the identified
bias. Finally, using the DAWN dataset, the findings are validated on the OD
task, demonstrating the effectiveness of our techniques in mitigating
real-world "good-weather" bias. The experiments show that the proposed
techniques outperform baseline methods by averaged fourfold improvement.


title:
Numerical analysis of processes for the formation of moonlets confining
  the arcs of Neptune

abstract:
  The arcs of Neptune - Fraternit\'e, Egalit\'e, Libert\'e, and Courage - are
four incomplete rings immersed in the Adams ring. A recent confinement model
for the arcs proposes that the structures are azimuthally confined by four
co-orbital moonlets. In this work, we intend to approach some points related to
the dynamics of co-orbital moonlets and suggest a model for their formation. We
study the equilibrium configurations for 1+N co-orbital satellites under the
42:43 Lindblad resonance with Galatea. We obtained three distinct
configurations with 1+3 and 1+4 moonlets able to confine and reproduce the
location of the arcs. The moonlets' formation is analysed by the disruption of
an ancient body at a Lagrangian point of a moon. The disruption fragments
spread out in horseshoe orbits and collide to form moonlets, which reach an
equilibrium configuration due to a non-conservative effect. In such a scenario,
the arcs likely formed through a mixture of different processes, with impacts
between disruption outcomes and meteoroid impacts with the moonlets being
possibilities.


title:
Learning Linear Representations of Nonlinear Dynamics Using Deep
  Learning

abstract:
  The vast majority of systems of practical interest are characterised by
nonlinear dynamics. This renders the control and optimization of such systems a
complex task due to their nonlinear behaviour. Additionally, standard methods
such as linearizing around a fixed point may not be an effective strategy for
many systems, thus requiring an alternative approach. For this reason, we
propose a new deep learning framework to discover a transformation of a
nonlinear dynamical system to an equivalent higher dimensional linear
representation. We demonstrate that the resulting learned linear representation
accurately captures the dynamics of the original system for a wider range of
conditions than standard linearization. As a result of this, we show that the
learned linear model can subsequently be used for the successful control of the
original system. We demonstrate this by applying the proposed framework to two
examples; one from the literature and a more complex example in the form of a
Continuous Stirred Tank Reactor (CSTR).


title:
Forward and backward mapping of image to 2D vector field using fiber
  bundle color space

abstract:
  We introduce the concept of a fiber bundle color space, which acts according
to the psychophysiological rules of trichromacy perception of colors by a
human. The image resides in the fiber bundle base space and the fiber color
space contains color vectors. Further we propose the decomposition of color
vectors into spectral and achromatic parts. A homomorphism of a color image and
constructed two-dimensional vector field is demonstrated that allows us to
apply well-known advanced methods of vector analysis to a color image, i.e.
ultimately give new numerical characteristics of the image. Appropriate image
to vector field forward mapping is constructed. The proposed backward mapping
algorithm converts a two-dimensional vector field to color image. The type of
image filter is described using sequential forward and backward mapping
algorithms. An example of the color image formation on the base of
two-dimensional magnetic vector field scattered by a typical pipe line defect
is given.


title:
Temperature dependence of the single photon source efficiency based on
  QD-cQED

abstract:
  We study a photonic circuit consisting of a quantum dot, QD, coupled to a
photon cavity over a wide range of temperature up to room temperature. A key
component of such a system is presented here in the form of a Purcell-enhanced
single-photon source based on Cavity Quantum Electrodynamics, cQED. We use a
real set of pure dephasing data extracted from experimental measurements of
InGaAs QD to calculate the effective QD-cavity coupling strength, the Purcell
factor, and the single photon efficiency emerged from the QD-cavity system in
the cases without and with detuning. In the non-detuned system, the effective
coupling strength between the QD and the resonator decreases with increasing
temperature, results in a decrease in efficiency. However, when the temperature
of the QD-cavity system increases under Purcell effect conditions, the detuned
QD-cavity system induces spontaneous emission rate enhancement. As a result, we
found that the increase in efficiency can be obtained under a certain
condition, when the maximum effective coupling strength and the Purcell factor
are related to the spontaneous emission and the pure dephasing rates.
Additionally, the influences of the pumping mechanism on the efficiency of the
QD-system were examined and showed that the pumping process can be used to
further increase in efficiency. Our results can be advantageous for advanced
quantum optics applications once temperature is taken into account.


title:
A Weak Galerkin Mixed Finite Element Method for second order elliptic
  equations on 2D Curved Domains

abstract:
  This article concerns the weak Galerkin mixed finite element method (WG-MFEM)
for second order elliptic equations on 2D domains with curved boundary. The
Neumann boundary condition is considered since it becomes the essential
boundary condition in this case. It is well-known that the discrepancy between
the curved physical domain and the polygonal approximation domain leads to a
loss of accuracy for discretization with polynomial order $\alpha>1$. The
purpose of this paper is two-fold. First, we present a detailed error analysis
of the original WG-MFEM for solving problems on curved domains, which exhibits
an $O(h^{1/2})$ convergence for all $\alpha\ge 1$. It is a little surprising to
see that even the lowest-order WG-MFEM ($\alpha=1$) experiences a loss of
accuracy. This is different from known results for the finite element method
(FEM) or the mixed FEM, and appears to be a combined effect of the WG-MFEM
design and the fact that the outward normal vector on the polygonal
approximation domain is different from the one on the curved domain. Second, we
propose a remedy to bring the approximation rate back to optimal by employing
two techniques. One is a specially designed boundary correction technique. The
other is to take full advantage of the nice feature that weak Galerkin
discretization can be defined on polygonal meshes, which allows the curved
boundary to be better approximated by multiple short edges without increasing
the total number of mesh elements. Rigorous analysis shows that a combination
of the above two techniques renders optimal convergence for all $\alpha$.
Numerical results further confirm this conclusion.


title: Period-doubling Continued Fractions are Algebraic in Characteristic $2$

abstract:
  Considering an arbitrary pair of distinct and non constant polynomials, $a$
and $b$ in $\mathbb{F}_2[t]$, we build a continued fraction in
$\mathbb{F}_2((1/t))$ whose partial quotients are only equal to $a$ or $b$. In
a previous work of the first author and Han (to appear in Acta Arithmetica),
the authors considered two cases where the sequence of partial quotients
represents in each case a famous and basic $2$-automatic sequence, both defined
in a similar way by morphisms. They could prove the algebraicity of the
corresponding continued fractions for several pairs $(a,b)$ in the first case
(the Prouhet-Thue-Morse sequence) and gave the proof for a particular pair for
the second case (the period-doubling sequence). Recently Bugeaud and Han
(arXiv:2203.02213) proved the algebraicity for an arbitrary pair in the first
case. Here we give a short proof for an arbitrary pair in the second case.


title: On the high-energy protons regular acceleration in the Fermi Bubbles

abstract:
  We propose the model of the global structure of the electromagnetic fields in
the Fermi bubbles (FBs), which makes possible the proton regular acceleration
up to ultra-high energies. The poloidal and the toroidal magnetic fields, as
well as the radial electric field, turn to have a structure similar to fields
that exist in jets ejected out from active galactic nuclei (AGN). A powerful
source of relativistic particles observed in the centre of the Galaxy and
associated with the rotating supermassive black hole (SMBH) Sgr A* can energize
the FB and keeps its active for a long time. The absence of accretion onto a BH
and thus the absence of a relativistic jet does not mean that there is no loss
of rotational energy of BH. In the case of FB, the energy lost by BH can keep
the FB activity. The regular FBs structure could be formed by inheritance from
a relativistic jet that presumably existed in the active past of the Galaxy $
10^7 $ years ago, or by processes near the Galaxy centre existing during the
entire life cycle of the Galaxy. The acceleration of protons in electromagnetic
fields of FB are found up to energies $ E_{max} \simeq 10^{17} $ eV, which
explains the observed radiation of FB in the gamma range, as well as the
emission of high-energy neutrinos.


title:
Large time behavior of solutions to the Cauchy problem for the
  BBM-Burgers equation

abstract:
  We consider the large time behavior of the solutions to the Cauchy problem
for the BBM-Burgers equation. We prove that the solution to this problem goes
to the self-similar solution to the Burgers equation called the nonlinear
diffusion wave. Moreover, we construct the appropriate second asymptotic
profiles of the solutions depending on the initial data. Based on that
discussion, we investigate the effect of the initial data on the large time
behavior of the solution, and derive the optimal asymptotic rate to the
nonlinear diffusion wave. Especially, the important point of this study is that
the second asymptotic profiles of the solutions with slowly decaying data,
whose case has not been studied, are obtained.


title:
Improved Robust Price Bounds for Multi-Asset Derivatives under
  Market-Implied Dependence Information

abstract:
  We show how inter-asset dependence information derived from observed market
prices of liquidly traded options can lead to improved model-free price bounds
for multi-asset derivatives. Depending on the type of the observed liquidly
traded option, we either extract correlation information or we derive
restrictions on the set of admissible copulas that capture the inter-asset
dependencies. To compute the resultant price bounds for some multi-asset
options of interest, we apply a modified martingale optimal transport approach.
In particular, we derive an adjusted pricing-hedging duality. Several examples
based on simulated and real market data illustrate the improvement of the
obtained price bounds and thus provide evidence for the relevance and
tractability of our approach.


title:
Conductor Properties and Coil Technology for a Bi2212 Dipole Insert for
  20 Tesla Hybrid Accelerator Magnets

abstract:
  A dipole insert based on a 2-layer cos-theta coil with stress management and
Bi2212 superconducting strand and cable is being developed at Fermilab as part
of the US-MDP effort. The ultimate goal of this task is to develop coil
technology and an approach to manage azimuthal and radial strains of high
temperature superconductor inserts when integrated within Nb3Sn outserts as a
hybrid magnet system. This note reviews conductor properties and possible coil
technologies.


title: Relatively hyperbolic metric bundles and Cannon-Thurston map

abstract:
  Given a metric (graph) bundle $X$ over $B$ where all the fibres are strongly
relatively hyperbolic and nonelementary we show that, under certain conditions,
$X$ is strongly hyperbolic relative to a collection of maximal cone-subbundles
of horosphere-like spaces. Further, given a coarsely Lipschitz qi embedding $i:
A\to B$, we show that the pullback $Y$ is strongly relatively hyperbolic and
the map $Y\to X$ admits a Cannon-Thurston (CT) map. As an application, we prove
a group-theoretic analogue of this result for a relatively hyperbolic extension
of groups.


title: Precoloring extension of Vizing's Theorem for multigraphs

abstract:
  Let $G$ be a graph with maximum degree $\Delta(G)$ and maximum multiplicity
$\mu(G)$. Vizing and Gupta, independently, proved in the 1960s that the
chromatic index of $G$ is at most $\Delta(G)+\mu(G)$. The distance between two
edges $e$ and $f$ in $G$ is the length of a shortest path connecting an
endvertex of $e$ and an endvertex of $f$. A distance-$t$ matching is a set of
edges having pairwise distance at least $t$. Edwards et al. proposed the
following conjecture: For any graph $G$, using the palette $\{1, \dots,
\Delta(G)+\mu(G)\}$, any precoloring on a distance-$2$ matching can be extended
to a proper edge coloring of $G$. Gir\~{a}o and Kang verified this conjecture
for distance-$9$ matchings. In this paper, we improve the required distance
from $9$ to $3$ for multigraphs $G$ with $\mu(G) \ge 2$.


title:
Data Cards: Purposeful and Transparent Dataset Documentation for
  Responsible AI

abstract:
  As research and industry moves towards large-scale models capable of numerous
downstream tasks, the complexity of understanding multi-modal datasets that
give nuance to models rapidly increases. A clear and thorough understanding of
a dataset's origins, development, intent, ethical considerations and evolution
becomes a necessary step for the responsible and informed deployment of models,
especially those in people-facing contexts and high-risk domains. However, the
burden of this understanding often falls on the intelligibility, conciseness,
and comprehensiveness of the documentation. It requires consistency and
comparability across the documentation of all datasets involved, and as such
documentation must be treated as a user-centric product in and of itself. In
this paper, we propose Data Cards for fostering transparent, purposeful and
human-centered documentation of datasets within the practical contexts of
industry and research. Data Cards are structured summaries of essential facts
about various aspects of ML datasets needed by stakeholders across a dataset's
lifecycle for responsible AI development. These summaries provide explanations
of processes and rationales that shape the data and consequently the models,
such as upstream sources, data collection and annotation methods; training and
evaluation methods, intended use; or decisions affecting model performance. We
also present frameworks that ground Data Cards in real-world utility and
human-centricity. Using two case studies, we report on desirable
characteristics that support adoption across domains, organizational
structures, and audience groups. Finally, we present lessons learned from
deploying over 20 Data Cards.


title:
On Angles in Higher Order Brillouin Tessellations and Related Tilings in
  the Plane

abstract:
  For a locally finite set in $\mathbb{R}^2$, the order-$k$ Brillouin
tessellations form an infinite sequence of convex face-to-face tilings of the
plane. If the set is coarsely dense and generic, then the corresponding
infinite sequences of minimum and maximum angles are both monotonic in $k$. As
an example, a stationary Poisson point process in $\mathbb{R}^2$ is locally
finite, coarsely dense, and generic with probability one. For such a set, the
distribution of angles in the Voronoi tessellations, Delaunay mosaics, and
Brillouin tessellations are independent of the order and can be derived from
the formula for angles in order-$1$ Delaunay mosaics given by Miles in 1970.


title: Brillouin Zones of Integer Lattices and Their Perturbations

abstract:
  The $k$-th Brillouin zone of a point in a locally finite set in
$\mathbb{R}^d$ is the region in which the point is the $k$-closest in the set.
If the set is a lattice, the $k$-th Brillouin zones of different points are
translates of each other, which tile space. Depending on the value of $k$, they
express medium- or long-range order in the set. We study fundamental geometric
and combinatorial properties of Brillouin zones, focusing on the integer
lattice and its perturbations. Our results include the stability of a Brillouin
zone under perturbations, a linear upper bound on the number of chambers in a
zone for lattices in $\mathbb{R}^2$, and the convergence of the maximum volume
of a chamber to zero for the integer lattice.


title:
Absence of isolated critical points with nonstandard critical exponents
  in the four-dimensional regularization of Lovelock gravity

abstract:
  Hyperbolic vacuum black holes in Lovelock gravity theories of odd order $N$
are known to have the so-called isolated critical points with nonstandard
critical exponents (as $\alpha = 0$, $\beta = 1$, $\gamma = N-1$, and $\delta =
N$), different from those of mean-field critical exponents (with $\alpha = 0$,
$\beta = 1/2$, $\gamma = 1$, and $\delta = 3$). Motivated by this important
observation, here, we explore the consequences of taking the $D \to 4$ limit of
Lovelock gravity and the possibility of finding nonstandard critical exponents
associated with isolated critical points in four-dimensions by use of the
four-dimensional regularization, recently proposed by Glavan and Lin
\cite{Glavan2020}. It is shown that the regularized $4D$ Einstein-Lovelock
gravity theories of odd order $N > 3$ do not possess any physical isolated
critical point. In fact, the critical (inflection) points of equation of state
always occurs for the branch of black holes with negative entropy. The
situation is quite different for the case of the regularized $4D$
Einstein-Lovelock gravity with cubic curvature corrections ($N=3$). In this
case ($N=3$), although the entropy is non-negative and the equation of state of
hyperbolic vacuum black holes has a nonstandard Taylor expansion about its
inflection point, but there is no criticality associated with this special
point. At this point, the physical properties of the black hole system change
drastically, e.g., both the mass and entropy of the black hole vanishes,
meaning that there do not exist degrees of freedom in order for a phase
transition to occur. These results are in strong contrast to those findings in
Lovelock gravity.


title:
Modelling and Control of Production Systems based on Observed
  Inter-event Times: An Analytical and Empirical Investigation (Ph.D. Thesis)

abstract:
  Technological advances allow manufacturers to collect and access data from a
production system effectively. The objective of data collection is to deploy
the collected data in developing decision support systems for performance
evaluation, problem identification, and production control. The goal of this
dissertation is to investigate how the collected data can be used to evaluate
performance and optimize manufacturing systems, analytically and empirically.
In the first part of the thesis, I investigate how can the collected data from
the shop-floor be used in the efficient control and design of manufacturing
systems? To investigate the impact of possible dependency in the inter-event
times on the optimal control and performance measures of the system, a
manufacturing system that is controlled by using a single-threshold production
control policy is analyzed. It is shown that ignoring autocorrelation in
inter-arrival or service times leads to overestimation (underestimation) of the
optimal threshold level for negatively (positively) correlated processes. Then,
it is shown that the optimal control policy of a production/inventory system
with correlated inter-arrival and service times modeled as Markovian Arrival
Processes is a state-dependent threshold policy. In the second part of the
thesis, an exploratory data analysis is conducted by using a large industrial
dataset related to the flow of the products at a semiconductor wafer
fabrication. Then, the cycle times of the products are predicted using Machine
Learning methods, and the performance of different prediction algorithms is
assessed. The analytical and empirical results presented in this dissertation
show that effective use of collected data from a manufacturing system enables
controlling the system effectively and predicting its main performance measures
accurately.


title:
ES6D: A Computation Efficient and Symmetry-Aware 6D Pose Regression
  Framework

abstract:
  In this paper, a computation efficient regression framework is presented for
estimating the 6D pose of rigid objects from a single RGB-D image, which is
applicable to handling symmetric objects. This framework is designed in a
simple architecture that efficiently extracts point-wise features from RGB-D
data using a fully convolutional network, called XYZNet, and directly regresses
the 6D pose without any post refinement. In the case of symmetric object, one
object has multiple ground-truth poses, and this one-to-many relationship may
lead to estimation ambiguity. In order to solve this ambiguity problem, we
design a symmetry-invariant pose distance metric, called average (maximum)
grouped primitives distance or A(M)GPD. The proposed A(M)GPD loss can make the
regression network converge to the correct state, i.e., all minima in the
A(M)GPD loss surface are mapped to the correct poses. Extensive experiments on
YCB-Video and T-LESS datasets demonstrate the proposed framework's
substantially superior performance in top accuracy and low computational cost.


title: Faces: AI Blitz XIII Solutions

abstract:
  AI Blitz XIII Faces challenge hosted on www.aicrowd.com platform consisted of
five problems: Sentiment Classification, Age Prediction, Mask Prediction, Face
Recognition, and Face De-Blurring. Our team GLaDOS took second place. Here we
present our solutions and results. Code implementation:
https://github.com/ndrwmlnk/ai-blitz-xiii


title: Stratification and the smashing spectrum

abstract:
  We develop the theory of stratification for a rigidly-compactly generated
tensor-triangulated category from the standpoint of its smashing spectrum.
Prior to this, we give a smashing spectrum-correlated topological reformulation
of the telescope conjecture. Within the stratified context, we define a
comparison map connecting the homological spectrum to the smashing spectrum and
utilize it to provide an equivalent characterization of the telescope
conjecture in terms of properties of the homological spectrum and the
homological support. Additionally, we make a comparison with the Balmer-Favi
notion of stratification. Lastly, we study the map between smashing spectra
induced by a tensor-triangulated functor and prove a descent theorem for
stratification.


title: On the discrete equation model for compressible multiphase fluid flows

abstract:
  The modeling of multi-phase flow is very challenging, given the range of
scales as well as the diversity of flow regimes that one encounters in this
context. We revisit the discrete equation method (DEM) for two-phase flow in
the absence of heat conduction and mass transfer. We analyze the resulting
probability coefficients and prove their local convexity, rigorously
establishing that our version of DEM can model different flow regimes ranging
from the disperse to stratified (or separated) flow. Moreover, we reformulate
the underlying mesoscopic model in terms of an one-parameter family of PDEs
that interpolates between different flow regimes. We also propose two sets of
procedures to enforce relaxation to equilibrium. We perform several numerical
tests to show the flexibility of the proposed formulation, as well as to
interpret different model components. The one-parameter family of PDEs provides
an unified framework for modeling mean quantities for a multiphase flow, while
at the same time identifying two key parameters that model the inherent
uncertainty in terms of the underlying microstructure.


title:
On Constrained Input Selections for Structured Systems: Polynomially
  Solvable Cases

abstract:
  This paper investigates two related optimal input selection problems for
structured systems. Given are an autonomous system and a set of inputs, where
whether an input can directly actuate a state variable is given a priori, and
each input has a non-negative cost. The problems are, selecting the minimum
cost of inputs, and selecting the inputs with the smallest possible cost with a
bound on their cardinality, all to ensure system structural controllability.
Those problems are known to be NP-hard in general. In this paper, instead of
finding approximation algorithms, we explore classes of systems on which those
problems are polynomially solvable. We show subject to the so-called source
strongly-connected component separated input constraint, which contains all the
currently known nontrivial polynomially solvable cases as special ones, those
problems can be solvable in polynomial time. We do this by first formulating
those problems as equivalent integer linear programmings (ILPs), and then
proving that the corresponding constraint matrices are totally unimodular. This
property allows us to solve those ILPs efficiently simply via their linear
programming (LP) relaxations, leading to a unifying algebraic method for these
problems with polynomial time complexity. A numerical example is given to
illustrate these results


title: On Pappus Configurations in Hall Planes

abstract:
  As the finite Hall planes are Non-Desarguesian, the Pappus Theorem does not
hold in them. In this paper we state and prove some weaker versions of Pappus's
Theorem in Hall planes.


title: Leptogenesis and light scalar dark matter in a $L_{\mu}-L_{\tau}$ model

abstract:
  We discuss the possibility of light scalar dark matter in a
$L_{\mu}-L_{\tau}$ model, in which the dark matter $\phi_{dm}$ carries
$U(1)_{L_{\mu}-L_{\tau}}$ charge but it is a singlet in the Standard Model. We
consider the case that the right-handed neutrinos not only generate baryon
asymmetry but also are related with dark matter production. We assume that dark
matter production mainly comes from scattering associated with a pair of
right-handed neutrinos while other related processes are highly suppressed due
to the tiny $U(1)_{L_{\mu}-L_{\tau}}$ charge of dark matter, and the dark
matter relic density are generated via freeze-in mechanism. A feasible
parameter space is considered and we found the correct dark matter relic
density can be obtained without influencing the result of leptogenesis, and the
allowed dark matter mass region is $[\rm 10^{-5}\ GeV,0.1\ GeV]$.


title:
Increased neuromodulation ability through EEG connectivity neurofeedback
  with simultaneous fMRI for emotion regulation

abstract:
  Emotion regulation plays a key role in human behavior and life. Neurofeedback
(NF) is a non-invasive self-brain training technique used for emotion
regulation to enhance brain function and treatment of mental disorders leading
to behavioral changes. Most neurofeedback studies were limited to using the
activity of a single brain region of fMRI data or the power of a single or two
EEG electrodes. In a novel study, we use the connectivity-based EEG
neurofeedback through retrieving positive autobiographical memories and
simultaneous fMRI to upregulate positive emotion. The feedback was calculated
based on the coherence of EEG electrodes rather than the power of single/two
electrodes. We demonstrated the efficiency of the connectivity-based
neurofeedback to traditional activity-based neurofeedback through several
experiments. The results confirmed the effectiveness of connectivity-based
neurofeedback to enhance brain activity/connectivity of deep brain regions with
key roles in emotion regulation e.g., amygdala, thalamus, and insula, and
increase EEG frontal asymmetry as a biomarker for emotion regulation or
treatment of mental disorders such as PTSD, anxiety, and depression. The
results of psychometric assessments before and after neurofeedback experiments
demonstrated that participants were able to increase positive and decrease
negative emotion using connectivity-based neurofeedback more than traditional
activity-based neurofeedback. The results suggest using the connectivity-based
neurofeedback for emotion regulation and alternative therapeutic approaches for
mental disorders with more effectiveness and higher volitional ability to
control brain and mental function.


title:
Covariance Representations, $L^p$-Poincar\'e Inequalities, Stein's
  Kernels and High Dimensional CLTs

abstract:
  We explore connections between covariance representations, Bismut-type
formulas and Stein's method. First, using the theory of closed symmetric forms,
we derive covariance representations for several well-known probability
measures on $\mathbb{R}^d$, $d \geq 1$. When strong gradient bounds are
available, these covariance representations immediately lead to $L^p$-$L^q$
covariance estimates, for all $p \in (1, +\infty)$ and $q = p/(p-1)$. Then, we
revisit the well-known $L^p$-Poincar\'e inequalities ($p \geq 2$) for the
standard Gaussian probability measure on $\mathbb{R}^d$ based on a covariance
representation. Moreover, for the nondegenerate symmetric $\alpha$-stable case,
$\alpha \in (1,2)$, we obtain $L^p$-Poincar\'e and pseudo-Poincar\'e
inequalities, for $p \in (1, \alpha)$, via a detailed analysis of the various
Bismut-type formulas at our disposal. Finally, using the construction of
Stein's kernels by closed forms techniques, we obtain quantitative
high-dimensional CLTs in $1$-Wasserstein distance when the limiting Gaussian
probability measure is anisotropic. The dependence on the parameters is
completely explicit and the rates of convergence are sharp.


abstract:
  Incorporating knowledge graph as side information has become a new trend in
recommendation systems. Recent studies regard items as entities of a knowledge
graph and leverage graph neural networks to assist item encoding, yet by
considering each relation type individually. However, relation types are often
too many and sometimes one relation type involves too few entities. We argue
that it is not efficient nor effective to use every relation type for item
encoding. In this paper, we propose a VRKG4Rec model (Virtual Relational
Knowledge Graphs for Recommendation), which explicitly distinguish the
influence of different relations for item representation learning. We first
construct virtual relational graphs (VRKGs) by an unsupervised learning scheme.
We also design a local weighted smoothing (LWS) mechanism for encoding nodes,
which iteratively updates a node embedding only depending on the embedding of
its own and its neighbors, but involve no additional training parameters. We
also employ the LWS mechanism on a user-item bipartite graph for user
representation learning, which utilizes encodings of items with relational
knowledge to help training representations of users. Experiment results on two
public datasets validate that our VRKG4Rec model outperforms the
state-of-the-art methods.


title: Breaking the De-Pois Poisoning Defense

abstract:
  Attacks on machine learning models have been, since their conception, a very
persistent and evasive issue resembling an endless cat-and-mouse game. One
major variant of such attacks is poisoning attacks which can indirectly
manipulate an ML model. It has been observed over the years that the majority
of proposed effective defense models are only effective when an attacker is not
aware of them being employed. In this paper, we show that the attack-agnostic
De-Pois defense is hardly an exception to that rule. In fact, we demonstrate
its vulnerability to the simplest White-Box and Black-Box attacks by an
attacker that knows the structure of the De-Pois defense model. In essence, the
De-Pois defense relies on a critic model that can be used to detect poisoned
data before passing it to the target model. In our work, we break this
poison-protection layer by replicating the critic model and then performing a
composed gradient-sign attack on both the critic and target models
simultaneously -- allowing us to bypass the critic firewall to poison the
target model.


title: Final bound-state formation effect on dark matter annihilation

abstract:
  If the annihilation products of dark matter (DM) are non-relativistic and
couples directly to a light force mediator, the non-perturbation effect like
final state bound state (FBS) formation and final state Sommerfeld (FSS) effect
must be considered. Non-relativistic region of final particles will appear when
there is small mass split between DM and products, so we study those effects in
the degenerate region of mass (including kinematics forbidden case) using two
specific models. We demonstrate that FBS effect will significantly modify the
DM relic abundance comparing to the standard perturbation calculation in some
mass split region. We emphasize that FBS effect is comparable to the FSS effect
in those mass split. The conservation angular momentum are subtle considering
FBS formation, in some cases there may be not $s$-wave, so we use two models
exhibit the different partial wave FBS effect contribution. We also show that
the FBS formation with vector boson emission process also contributes in DM
relic abundance, and first calculate the $p$-wave FSS effect in the specific
model.


title:
Study of $B_{(s)}^0 \to \phi\phi \to (K^+K^-)(K^+K^-)$ decays in the
  perturbative QCD approach

abstract:
  In this work, we make a detailed analysis on the penguin-dominant processes
$B_{(s)}^0 \to \phi\phi \to (K^+K^-)(K^+K^-)$ in the perturbative QCD (PQCD)
approach. In addition to the dominant $P$-wave resonance, the scalar background
$f_0(980) \to K^+K^-$ is also accounted for. We improve the Gegenbauer moments
in $KK$ two-meson distribution amplitudes by fitting the PQCD factorization
formulas to measured branching ratios of three-body and four-body $B$ decays.
We extract the branching ratios of two-body $B_{(s)}^0 \to \phi\phi$ decays
from the corresponding four-body decay modes and calculate the relevant
polarization fractions together with two relative phases
$\phi_{\parallel,\perp}$, which are consistent with the previous theoretical
predictions. The PQCD predictions for the "true" triple product asymmetries
(TPAs) are zero which are expected in the standard model due to the vanishing
weak phase difference, and support the current data reported by the CDF and
LHCb Collaborations. A large "fake" TPA $\mathcal{A}_\text{T-fake}^1=30.4\%$ of
the decay $B^0_s \to \phi\phi \to (K^+K^-)(K^+K^-)$ is predicted for the first
time, which indicates the presence of the significant final-state interactions.
The TPAs of the rare decay channel $B^0 \to \phi\phi\to (K^+K^-)(K^+K^-)$ are
also predicted and can be tested in the near future.


title:
Hierarchical Frequency Control of Hybrid Power Plants Using Frequency
  Response Observer

abstract:
  Frequency control (FC) enables utility-scale grid-connected hybrid power
plants (HPPs) to operate in compliance with grid code requirements while to
capture value streams from provision of frequency control services (FCSs). In
this paper, a novel hierarchical FC approach is proposed to allow HPPs to
provide three types of FCSs, namely fast frequency response (FFR), frequency
containment response (FCR) and frequency restoration response (FRR). To
accommodate state-of-the-art fast FC, controllers for fast FCSs, such as FFR
and FCR, are implemented at asset controllers, while controllers for slow FCSs
like FRR are implemented at plant controllers or the HPP controller (HPPC).
Control counteraction issue, which arises across control hierarchy, is then
discussed. To solve this issue, an innovative frequency response observer
(FROB) is proposed. Inspired by the concept of disturbance observer (DOB), FROB
at plant controllers and the HPPC accurately estimates frequency response
initiated at asset controllers, and the obtained estimation is used for control
compensation at plant controllers and the HPPC to avoid control counteraction.
This scheme achieves robust performance even when there are system
uncertainties existing in HPPs, such as parameter uncertainty, unknown control
malfunction, and time-varying communication delays. The proposed approach is
implemented in a power system dynamic model in MATLAB/Simulink to highlight its
effectiveness and robustness.


title: Quantization of linearized gravity by Wick rotation in Gaussian time

abstract:
  We consider the problem of quantizing linearized Einstein equations. We
provide a rigorous construction applicable to a large class of Einstein
metrics. More precisely, we prove the existence of Hadamard states in the
harmonic gauge on analytic backgrounds of bounded geometry. This includes
examples such as Minkowski, de Sitter, Kerr-Kruskal and Schwarzschild-de Sitter
spacetimes. The states are constructed from Calder\'on projectors for an
elliptic boundary problem obtained by Wick rotation near a Cauchy surface. The
key ingredients of the proof are gauge transformations in the Wick-rotated
setting and various techniques from elliptic theory and microlocal analysis.


title:
pmuBAGE: The Benchmarking Assortment of Generated PMU Data for Power
  System Events -- Part I: Overview and Results

abstract:
  We present pmuGE (phasor measurement unit Generator of Events), one of the
first data-driven generative model for power system event data. We have trained
this model on thousands of actual events and created a dataset denoted pmuBAGE
(the Benchmarking Assortment of Generated PMU Events). The dataset consists of
almost 1000 instances of labeled event data to encourage benchmark evaluations
on phasor measurement unit (PMU) data analytics. The dataset is available
online for use by any researcher or practitioner in the field. PMU data are
challenging to obtain, especially those covering event periods. Nevertheless,
power system problems have recently seen phenomenal advancements via
data-driven machine learning solutions - solutions created by researchers who
were fortunate enough to obtain such PMU data. A highly accessible standard
benchmarking dataset would enable a drastic acceleration of the development of
successful machine learning techniques in this field. We propose a novel
learning method based on the Event Participation Decomposition of Power System
Events, which makes it possible to learn a generative model of PMU data during
system anomalies. The model can create highly realistic event data without
compromising the differential privacy of the PMUs used to train it. The dataset
is available online for any researcher to use at the pmuBAGE Github Repository
- https://github.com/NanpengYu/pmuBAGE.
  Part I - This is part I of a two part paper. In part I, we describe a high
level overview of pmuBAGE, its creation, and the experiments used to test it.
Part II will discuss the exact models used in its generation in far more
detail.


title: The Constrained Blaschke Functional for Spherical Curves

abstract:
  We study critical trajectories in the sphere for the Blaschke variational
problem with length constraint. For every Lagrange multiplier encoding the
conservation of the length during the variation, we show the existence of
infinitely many closed trajectories which depend on a pair of relative prime
natural numbers. A geometric description of these numbers and the relation with
the shape of the corresponding critical trajectories is also given.


title: Localizing the Vehicle's Antenna: an Open Problem in 6G Network Sensing

abstract:
  Millimeter Waves (mmW) and sub-THz frequencies are the candidate bands for
the upcoming Sixth Generation (6G) of communication systems. The use of
collimated beams at mmW/sub-THz to compensate for the increased path and
penetration loss arises the need for a seamless Beam Management (BM),
especially for high mobility scenarios such as the Vehicle-to-Infrastructure
(V2I) one. Recent research advances in Integrated Sensing and Communication
(ISAC) indicate that equipping the network infrastructure, e.g., the Base
Station (BS), with either a stand-alone radar or sensing capabilities using
optimized waveforms, represents the killer technology to facilitate the BM.
However, radio sensing should accurately localize the Vehicular Equipment
(VE)'s antenna, which is not guaranteed in general. Differently, employing side
information from VE's onboard positioning sensors might overcome this
limitation at the price of an increased control signaling between VE and BS.
This paper provides a pragmatic comparison between radar-assisted and
position-assisted BM for mmW V2I systems in a typical urban scenario in terms
of BM training time and beamforming gain loss due to a wrong BM decision.
Simulation results, supported by experimental evidence, show that the point
target approximation of a traveling VE does not hold in practical V2I scenarios
with radar-equipped BS. Therefore, the true antenna position has a residual
uncertainty that is independent of radar's resolution and implies 50\,\% more
BM training time on average. Moreover, there is not a winning technology for BM
between BS-mounted radar and VE's onboard positioning systems. They provide
complementary performance, depending on position, although outperforming blind
BM techniques compared to conventional blind methods. Thus, we propose to
optimally combine radar and positioning information in a multi-technology
integrated BM solution.


title: A sequence-to-sequence approach for document-level relation extraction

abstract:
  Motivated by the fact that many relations cross the sentence boundary, there
has been increasing interest in document-level relation extraction (DocRE).
DocRE requires integrating information within and across sentences, capturing
complex interactions between mentions of entities. Most existing methods are
pipeline-based, requiring entities as input. However, jointly learning to
extract entities and relations can improve performance and be more efficient
due to shared parameters and training steps. In this paper, we develop a
sequence-to-sequence approach, seq2rel, that can learn the subtasks of DocRE
(entity extraction, coreference resolution and relation extraction) end-to-end,
replacing a pipeline of task-specific components. Using a simple strategy we
call entity hinting, we compare our approach to existing pipeline-based methods
on several popular biomedical datasets, in some cases exceeding their
performance. We also report the first end-to-end results on these datasets for
future comparison. Finally, we demonstrate that, under our model, an end-to-end
approach outperforms a pipeline-based approach. Our code, data and trained
models are available at {\url{https://github.com/johngiorgi/seq2rel}}. An
online demo is available at
{\url{https://share.streamlit.io/johngiorgi/seq2rel/main/demo.py}}.


title:
Adversarially robust segmentation models learn perceptually-aligned
  gradients

abstract:
  The effects of adversarial training on semantic segmentation networks has not
been thoroughly explored. While previous work has shown that
adversarially-trained image classifiers can be used to perform image synthesis,
we have yet to understand how best to leverage an adversarially-trained
segmentation network to do the same. Using a simple optimizer, we demonstrate
that adversarially-trained semantic segmentation networks can be used to
perform image inpainting and generation. Our experiments demonstrate that
adversarially-trained segmentation networks are more robust and indeed exhibit
perceptually-aligned gradients which help in producing plausible image
inpaintings. We seek to place additional weight behind the hypothesis that
adversarially robust models exhibit gradients that are more
perceptually-aligned with human vision. Through image synthesis, we argue that
perceptually-aligned gradients promote a better understanding of a neural
network's learned representations and aid in making neural networks more
interpretable.


title:
Strong convergence rates of an explicit scheme for stochastic
  Cahn-Hilliard equation with additive noise

abstract:
  In this paper, we propose and analyze an explicit time-stepping scheme for a
spatial discretization of stochastic Cahn-Hilliard equation with additive
noise. The fully discrete approximation combines a spectral Galerkin method in
space with a tamed exponential Euler method in time. In contrast to implicit
schemes in the literature, the explicit scheme here is easily implementable and
produces significant improvement in the computational efficiency. It is shown
that the fully discrete approximation converges strongly to the exact solution,
with strong convergence rates identified. To the best of our knowledge, it is
the first result concerning an explicit scheme for the stochastic Cahn-Hilliard
equation. Numerical experiments are finally performed to confirm the
theoretical results.


title: Learning-Based Safe Motion Control of Vehicle Ski-Stunt Maneuvers

abstract:
  This paper presents a safety guaranteed control method for an autonomous
vehicle ski-stunt maneuver, that is, a vehicle moving with two one-side wheels.
To capture the vehicle dynamics precisely, a Gaussian process model is used as
additional correction to the nominal model that is obtained from physical
principles. We construct a probabilistic control barrier function (CBF) to
guarantee the planar motion safety. The CBF and the balance equilibrium
manifold are enforced as the constraints into a safety critical control form.
Under the proposed control method, the vehicle avoids the obstacle collision
and safely maintain the balance for autonomous ski-stunt maneuvers. We conduct
numerical simulation validation to demonstrate the control design. Preliminary
experiment results are also presented to confirm the learning-based motion
control using a scaled RC truck for autonomous ski-stunt maneuvers.


title: A Formal Privacy Framework for Partially Private Data

abstract:
  Despite its many useful theoretical properties, differential privacy (DP) has
one substantial blind spot: any release that non-trivially depends on
confidential data without additional privacy-preserving randomization fails to
satisfy DP. Such a restriction is rarely met in practice, as most data releases
under DP are actually "partially private" data (PPD). This poses a significant
barrier to accounting for privacy risk and utility under logistical constraints
imposed on data curators, especially those working with official statistics. In
this paper, we propose a privacy definition which accommodates PPD and prove it
maintains similar properties to standard DP. We derive optimal transport-based
mechanisms for releasing PPD that satisfy our definition and algorithms for
valid statistical inference using PPD, demonstrating their improved performance
over post-processing methods. Finally, we apply these methods to a case study
on US Census and CDC PPD to investigate private COVID-19 infection rates. In
doing so, we show how data curators can use our framework to overcome barriers
to operationalizing formal privacy while providing more transparency and
accountability to users.


title:
Characterizing Urban Lifestyle Signatures Using Motif Properties in
  Network of Places

abstract:
  The lifestyles of urban dwellers could reveal important insights regarding
the dynamics and complexity of cities. Despite growing research on analysis of
lifestyle patterns in cities, little is known about the characteristics of
people's lifestyles patterns at urban scale. This limitation is primarily due
to challenges in characterizing lifestyle patterns when human movement data is
aggregated to protect the privacy of users. In this study, we model cities
based on aggregated human visitation data to construct a network of places. We
then examine the subgraph signatures in the networks of places to map and
characterize lifestyle patterns at city scale. Location-based data from Harris
County, Dallas County, New York County, and Broward County in the United States
were examined to reveal lifestyle signatures in cities. For the motif analysis,
two-node, three-node, and four-node motifs without location attributes were
extracted from human visitation networks. Second, homogenized nodes in motifs
were encoded with location categories from NAICS codes. Multiple statistical
measures, including network metrics and motif properties, were quantified to
characterize lifestyle signatures. The results show that: people's lifestyles
in urban environments can be well depicted and quantified based on distribution
and attributes of motifs in networks of places; motifs in networks of places
show stability in quantity and distance as well as periodicity on weekends and
weekdays indicating the stability of lifestyle patterns in cities; human
visitation networks and lifestyle patterns show similarities across different
metropolitan areas implying the universality of lifestyle signatures across
cities. The findings provide deeper insights into urban lifestyles signatures
in urban studies and provide important insights for data-informed urban
planning and management.


title:
Near-Infrared Spectroscopy Of The Nucleus Of Low-Activity Comet P/2016
  BA$_{14}$ During Its 2016 Close Approach

abstract:
  The Near-Earth Comet P/2016 BA$_{14}$ (PanSTARRS) is a slow-rotatating
nearly-dormant object, a likely dynamical twin of 252P/LINEAR, and was recently
shown to have a mid-infrared spectrum very dissimilar to other comets.
BA$_{14}$ also recently selected one of the back-up targets for the ESA's
\textit{Comet Interceptor}, so a clearer understanding of BA$_{14}$'s modern
properties would not just improve our understanding of how comets go dormant,
but could also aid planning for a potential spacecraft visit. We present
observations of BA$_{14}$ taken on two dates during its 2016 Earth close
approach with the NASA Infrared Telescope Facility, both of which are
consistent with direct observations of its nucleus. The reflectance spectrum of
BA$_{14}$ is similar to 67P/Churyumov-Gerasimenko, albeit highly
phase-reddened. Thermal emission contaminates the reflectance spectrum at
longer wavelengths, which we correct with a new Markov Chain Monte Carlo
thermal modeling code. The models suggest $BA_{14}$'s visible geometric albedo
is $p_V=0.01-0.03$, consistent with radar observations, its beaming parameter
is typical for NEOs observed in its geometry, and its reflectrance spectrum is
red and linear throughout H and K band. It appears very much like a "normal"
comet nucleus, despite its mid-infrared oddities. A slow loss of fine grains as
the object's activity diminished might help to reconcile some of the lines of
evidence, and we discuss other possibilities. A spacecraft flyby past BA$_{14}$
could get closer to the nucleus than with a more active target, and we
highlight some science questions that could be addressed with a visit to a
(nearly-)dormant comet.


title: Better Lattice Quantizers Constructed from Complex Integers

abstract:
  Real-valued lattices and complex-valued lattices are mutually convertible,
thus we can take advantages of algebraic integers to defined good lattice
quantizers in the real-valued domain. In this paper, we adopt complex integers
to define generalized checkerboard lattices, especially $\mathcal{E}_{m}$ and
$\mathcal{E}_{m}^+$ defined by Eisenstein integers. Using $\mathcal{E}_{m}^+$,
we report the best lattice quantizers in dimensions $14$, $18$, $20$, and $22$.
Their product lattices with integers $\mathbb{Z}$ also yield better quantizers
in dimensions $15$, $19$, $21$, and $23$. The Conway-Sloane type fast decoding
algorithms for $\mathcal{E}_{m}$ and $\mathcal{E}_{m}^+$ are given.


title: Harmonic forms on asymptotically AdS metrics

abstract:
  In this paper we study the rotationally invariant harmonic cohomology of a
2-parameter family of Einstein metrics $g$ which admits a cohomogeneity one
action of $SU (2) \times U (1) $ and has AdS asymptotics. Depending on the
parameters values, $g$ is either of NUT type, if the fixed-point locus of the
$U (1) $ action is 0-dimensional, or of bolt type, if it is 2-dimensional. We
find that if $g$ is of NUT type then the space of $SU (2) $-invariant harmonic
2-forms is 3-dimensional and consists entirely of self-dual forms; if $g$ is of
bolt type it is 4-dimensional. In both cases we explicitly determine a basis.
The pair $(g,F)$ for $F$ a self-dual harmonic 2-form is also a solution of the
bosonic sector of $4D $ supergravity. We determine for which choices it is a
supersymmetric solution and the amount of preserved supersymmetry.


title: Adaptive Stochastic MPC under Unknown Noise Distribution

abstract:
  In this paper, we address the stochastic MPC (SMPC) problem for linear
systems, subject to chance state constraints and hard input constraints, under
unknown noise distribution. First, we reformulate the chance state constraints
as deterministic constraints depending only on explicit noise statistics. Based
on these reformulated constraints, we design a distributionally robust and
robustly stable benchmark SMPC algorithm for the ideal setting of known noise
statistics. Then, we employ this benchmark controller to derive a novel
robustly stable adaptive SMPC scheme that learns the necessary noise statistics
online, while guaranteeing time-uniform satisfaction of the unknown
reformulated state constraints with high probability. The latter is achieved
through the use of confidence intervals which rely on the empirical noise
statistics and are valid uniformly over time. Moreover, control performance is
improved over time as more noise samples are gathered and better estimates of
the noise statistics are obtained, given the online adaptation of the estimated
reformulated constraints. Additionally, in tracking problems with multiple
successive targets our approach leads to an online-enlarged domain of
attraction compared to robust tube-based MPC. A numerical simulation of a DC-DC
converter is used to demonstrate the effectiveness of the developed
methodology.


title: Adjusting for Bias with Procedural Data

abstract:
  3D softwares are now capable of producing highly realistic images that look
nearly indistinguishable from the real images. This raises the question: can
real datasets be enhanced with 3D rendered data? We investigate this question.
In this paper we demonstrate the use of 3D rendered data, procedural, data for
the adjustment of bias in image datasets. We perform error analysis of images
of animals which shows that the misclassification of some animal breeds is
largely a data issue. We then create procedural images of the poorly classified
breeds and that model further trained on procedural data can better classify
poorly performing breeds on real data. We believe that this approach can be
used for the enhancement of visual data for any underrepresented group,
including rare diseases, or any data bias potentially improving the accuracy
and fairness of models. We find that the resulting representations rival or
even out-perform those learned directly from real data, but that good
performance requires care in the 3D rendered procedural data generation. 3D
image dataset can be viewed as a compressed and organized copy of a real
dataset, and we envision a future where more and more procedural data
proliferate while datasets become increasingly unwieldy, missing, or private.
This paper suggests several techniques for dealing with visual representation
learning in such a future.


title:
Large signal of $h \rightarrow \mu \tau$ within the constraints of $e_i
  \rightarrow e_j\gamma$ decays in the 3-3-1 model with neutral leptons

abstract:
  In the framework of the 3-3-1 model with neutral leptons, we have
investigated the lepton-flavor-violating sources based on the Higgs mass
spectrum which has two neutral Higgses identitied with corresponding ones in
the Two-Higgs-Doublet model (THDM). On the $13~\mathrm{TeV}$ scale of the LHC,
we point out the parameter space regions where the experimental limits of $e_i
\rightarrow e_j\gamma$ decays are satisfied. These regions depend heavily on
the mixing of exotic leptons but are predicted to have large $h^0_1\rightarrow
\mu \tau$ signals. We also show that $\mathrm{Br}(h^0_1\rightarrow \mu \tau)$
can reach a value of $10^{-4}$.


title:
Probability and Non-Probability Samples: Improving Regression Modeling
  by Using Data from Different Sources

abstract:
  Non-probability sampling, for example in the form of online panels, has
become a fast and cheap method to collect data. While reliable inference tools
are available for classical probability samples, non-probability samples can
yield strongly biased estimates since the selection mechanism is typically
unknown. We propose a general method how to improve statistical inference when
in addition to a probability sample data from other sources, which have to be
considered non-probability samples, are available. The method uses specifically
tailored regression residuals to enlarge the original data set by including
observations from other sources that can be considered as stemming from the
target population. Measures of accuracy of estimates are obtained by adapted
bootstrap techniques. It is demonstrated that the method can improve estimates
in a wide range of scenarios. For illustrative purposes, the proposed method is
applied to two data sets.


title:
Control of a qubit state by a soliton propagating through a Heisenberg
  spin chain

abstract:
  We demonstrate that nonlinear magnetic solitary excitations (solitons)
traveling through a Heisenberg spin chain may be used as a robust tool capable
of coherent control of the qubit's state. The physical problem is described by
a Hamiltonian involving the interaction between the soliton and the qubit. We
show that under certain conditions the generic Hamiltonian may be mapped on
that of a qubit two-level system with matrix elements depending on the soliton
parameters. We considered the action of a bright and a dark solitons depending
on the driving nonlinear wave function. We considered a local interaction
restricted the closest to the qubit spin in the chain. We computed the
expressions of the physical quantities of interest for all cases and analyzed
their behavior in some special limits.


title: Geometrical optics of large deviations of fractional Brownian motion

abstract:
  It has been shown recently that the optimal fluctuation method -- essentially
geometrical optics -- provides a valuable insight into large deviations of
Brownian motion. Here we extend the geometrical optics formalism to two-sided,
$-\infty<t<\infty$, fractional Brownian motion (fBM) on the line, which is
"pushed" to a large deviation regime by imposed constraints. We test the
formalism on three examples where exact solutions are available: the two- and
three-point probability distributions of the fBm and the distribution of the
area under the fBm on a specified time interval. Then we apply the formalsim to
several previously unsolved problems by evaluating large-deviation tails of the
following distributions: (i) of the first-passage time, (ii) of the maximum of,
and (iii) of the area under, fractional Brownian bridge and fractional Brownian
excursion, and (iv) of the first-passage area distribution of the fBm. An
intrinsic part of a geometrical optics calculation is determination of the
optimal path -- the most likely realization of the process which dominates the
probability distribution of the conditioned process. Due to the non-Markovian
nature of the fBm, the optimal paths of a fBm, subject to constraints on a
finite interval $0<t\leq T$, involve both the past $-\infty<t<0$ and the future
$T<t<\infty$.


title:
Spectral estimation for stoquastic Hamiltonians: a comparison between
  classical imaginary-time evolution and quantum real-time evolution

abstract:
  We present a classical Monte Carlo (MC) scheme which efficiently estimates an
imaginary-time, decaying signal for stoquastic (i.e. sign-problem-free) local
Hamiltonians. The decay rates in this signal correspond to Hamiltonian
eigenvalues (with associated eigenstates present in an initial state) and can
be classically extracted using a classical signal processing method like
ESPRIT. We compare the efficiency of this MC scheme to its quantum counterpart
in which one extracts eigenvalues of a general local Hamiltonian from a
real-time, oscillatory signal obtained through quantum phase estimation
circuits, again using the ESPRIT method. We prove that the ESPRIT method can
resolve S = poly(n) eigenvalues, assuming a 1/poly(n) gap between them, with
poly(n) quantum and classical effort through the quantum phase estimation
circuits. We prove that our Monte Carlo scheme plus the ESPRIT method can
resolve S = O(1) eigenvalues, assuming a 1/poly(n) gap between them, with
poly(n) purely classical effort for stoquastic Hamiltonians. These results thus
quantify some opportunities and limitations of classical Monte Carlo methods
for spectral estimation of stoquastic Hamiltonians. We numerically compare
these MC and QPE eigenvalue estimation schemes by implementing them for an
archetypal stoquastic Hamiltonian system: the transverse field Ising chain.


title: Symmetric Molecular Dynamics

abstract:
  We derive a formulation of molecular dynamics that generates only symmetric
configurations. We implement it for all 2D planar and 3D space groups. An atlas
of 2D Lennard-Jones crystals under all planar groups is created with symmetric
molecular dynamics.


title: On incorporating social speaker characteristics in synthetic speech

abstract:
  In our previous work, we derived the acoustic features, that contribute to
the perception of warmth and competence in synthetic speech. As an extension,
in our current work, we investigate the impact of the derived vocal features in
the generation of the desired characteristics. The acoustic features, spectral
flux, F1 mean and F2 mean and their convex combinations were explored for the
generation of higher warmth in female speech. The voiced slope, spectral flux,
and their convex combinations were investigated for the generation of higher
competence in female speech. We have employed a feature quantization approach
in the traditional end-to-end tacotron based speech synthesis model. The
listening tests have shown that the convex combination of acoustic features
displays higher Mean Opinion Scores of warmth and competence when compared to
that of individual features.


title: Optimal navigation of microswimmers in complex and noisy environments

abstract:
  We design new navigation strategies for travel time optimization of
microscopic self-propelled particles in complex and noisy environments. In
contrast to strategies relying on the results of optimal control theory, these
protocols allow for semi-autonomous navigation as they do not require control
over the microswimmer motion via external feedback loops. Although the
strategies we propose rely on simple principles, they show arrival time
statistics strikingly similar to those obtained from stochastic optimal control
theory, as well as performances that are robust to environmental changes and
strong fluctuations. These features, as well as their applicability to more
general optimization problems, make these strategies promising candidates for
the realization of optimized semi-autonomous navigation.


title: UrbanFlow: Designing Comfortable Outdoor Areas

abstract:
  Design decisions in urban planning have to be made with particular
carefulness as the resulting constraints are binding for the whole
architectural design that follows. In this context, investigating and
optimizing the airflow in urban environments is critical to design comfortable
outdoor areas as unwanted effects such as windy areas and the formation of heat
pockets have to be avoided. Our UrbanFlow framework enables interactive
architectural design allowing for decision making based on simulating urban
flow. Compared to real-time fluid flow simulation, enabling interactive
architecture design poses an even higher computational efficiency challenge as
evaluating a design by simulation usually requires hundreds of time steps. This
is addressed based on a highly efficient Eulerian fluid simulator in which we
incorporate a unified porosity model which is devised to encode digital urban
models containing objects such as buildings and trees. UrbanFlow is equipped
with an optimization routine enabling the direct computation of design
adaptations improving livability and comfort for given parameterized
architectural designs. To ensure convergence of the optimization process,
instead of the classical Navier-Stokes equations, the Reynolds-averaged
Navier-Stokes equations are solved as this can be done on a relatively coarse
grid and allows for the decoupling of the effects of turbulent eddies which are
taken into account using a separate turbulence model. As we demonstrate on a
real-world example taken from an ongoing architectural competition, this
results in a fast convergence of the optimization process which computes a
design adaptation avoiding heat pockets as well as uncomfortable windy areas.


title: An introduction to composition operators in Sobolev spaces

abstract:
  We propose a survey on composition operators in classical Sobolev spaces. We
mention results obtained in 2019, on the continuity of such operators.


title: Fitting an immersed submanifold to data via Sussmann's orbit theorem

abstract:
  This paper describes an approach for fitting an immersed submanifold of a
finite-dimensional Euclidean space to random samples. The reconstruction
mapping from the ambient space to the desired submanifold is implemented as a
composition of an encoder that maps each point to a tuple of (positive or
negative) times and a decoder given by a composition of flows along finitely
many vector fields starting from a fixed initial point. The encoder supplies
the times for the flows. The encoder-decoder map is obtained by empirical risk
minimization, and a high-probability bound is given on the excess risk relative
to the minimum expected reconstruction error over a given class of
encoder-decoder maps. The proposed approach makes fundamental use of Sussmann's
orbit theorem, which guarantees that the image of the reconstruction map is
indeed contained in an immersed submanifold.


title:
Learning-Augmented Mechanism Design: Leveraging Predictions for Facility
  Location

abstract:
  In this work we introduce an alternative model for the design and analysis of
strategyproof mechanisms that is motivated by the recent surge of work in
"learning-augmented algorithms". Aiming to complement the traditional approach
in computer science, which analyzes the performance of algorithms based on
worst-case instances, this line of work has focused on the design and analysis
of algorithms that are enhanced with machine-learned predictions regarding the
optimal solution. The algorithms can use the predictions as a guide to inform
their decisions, and the goal is to achieve much stronger performance
guarantees when these predictions are accurate (consistency), while also
maintaining near-optimal worst-case guarantees, even if these predictions are
very inaccurate (robustness). So far, these results have been limited to
algorithms, but in this work we argue that another fertile ground for this
framework is in mechanism design.
  We initiate the design and analysis of strategyproof mechanisms that are
augmented with predictions regarding the private information of the
participating agents. To exhibit the important benefits of this approach, we
revisit the canonical problem of facility location with strategic agents in the
two-dimensional Euclidean space. We study both the egalitarian and utilitarian
social cost functions, and we propose new strategyproof mechanisms that
leverage predictions to guarantee an optimal trade-off between consistency and
robustness guarantees. This provides the designer with a menu of mechanism
options to choose from, depending on her confidence regarding the prediction
accuracy. Furthermore, we also prove parameterized approximation results as a
function of the prediction error, showing that our mechanisms perform well even
when the predictions are not fully accurate.


title:
Solvability of the Gleason problem on a class of bounded pseudoconvex
  domains

abstract:
  We show that if a bounded pseudoconvex domain satisfies the solvability of
the bounded $\bar{\partial}$ problem, then the ideal of bounded holomorphic
functions vanishing at a point in the domain is finitely generated. We also
prove a smooth analog of the main result for bounded pseudoconvex domains with
a sufficiently smooth boundary and also consider the Bergman space case.


title:
Yet another Freiheitssatz: Mating finite groups with locally indicable
  ones

abstract:
  The main result includes as special cases on the one hand, the
Gerstenhaber--Rothaus theorem (1962) and its generalisation due to Nitsche and
Thom (2022) and, on the other hand, the Brodskii--Howie--Short theorem
(1980--1984) generalising Magnus's Freiheitssatz (1930).


title:
Masses and Thermodynamic Quantities of Quarkonia in Nonrelativistic
  Quark Model

abstract:
  The temperature dependent energy, mass and some of thermodynamic quantities
of charmonium and bottomonium have been calculated by solving the radial
Schr{\"{o}}dinger equation with the extended Cornell potential at finite
temperature using the Nikiforov-Uvarov method. Obtained results accord with
experimental data and theoretical results of the previous studies. We have
found the spectrum of quarkonia mass strictly decreases at high values of
temperature.


title:
Measurements of one-point statistics in 21 cm intensity maps via
  foreground avoidance strategy

abstract:
  Measurements of the one-point probability distribution function and
higher-order moments (variance, skewness, and kurtosis) of the high-redshift 21
cm fluctuations are among the most direct statistical probes of the
non-Gaussian nature of structure formation and evolution during reionization.
However, contamination from astrophysical foregrounds and instrument
systematics pose significant challenges in measuring these statistics in real
observations. In this work, we use forward modelling to investigate the
feasibility of measuring 21 cm one-point statistics through a foreground
avoidance strategy. Leveraging the well-known characteristic of foreground
contamination in which it occupies a wedge-shape region in k-space, we apply a
foreground wedge-cut filter that removes the contaminated modes from a mock
data set based on the Hydrogen Epoch of Reionization Array (HERA) instrument,
and measure the one-point statistics from the image-space representation of the
remaining non-contaminated modes. We experiment with wedge-cutting over
different frequency bandwidths and varying degrees of removal that correspond
to different assumptions on the extent of the foreground sources on the sky and
leakage from the Fourier Transform window function. We find that the centre of
the band is the least biased from wedge-cutting while the edges of the band are
unusable due to being highly down-weighted by the window function. Based on
this finding, we introduce a rolling filter method that allows reconstruction
of an optimal wedge-cut 21~cm intensity map over the full bandwidth using
outputs from wedge-cutting over multiple sub-bands. We perform Monte Carlo
simulations to show that HERA should be able to measure the rise in skewness
and kurtosis near the end of reionization with the rolling wedge-cut method if
foreground leakage from the Fourier transform window function can be
controlled.


title: An introduction to KMS weights I

abstract:
  The theory of KMS weights is based on a theorem of Combes and a theorem of
Kustermans. In applications to KMS states for flows on a unital C*-algebra the
relation to KMS weights of the stabilized algebra has proved useful and this
relation hinges on a theorem of Laca and Neshveyev. This text presents proofs
of these three fundamental results that require a minimum of prerequisites; in
particular, they do not depend on the modular theory of von Neumann algebras.


title: A System for Interactive Examination of Learned Security Policies

abstract:
  We present a system for interactive examination of learned security policies.
It allows a user to traverse episodes of Markov decision processes in a
controlled manner and to track the actions triggered by security policies.
Similar to a software debugger, a user can continue or or halt an episode at
any time step and inspect parameters and probability distributions of interest.
The system enables insight into the structure of a given policy and in the
behavior of a policy in edge cases. We demonstrate the system with a network
intrusion use case. We examine the evolution of an IT infrastructure's state
and the actions prescribed by security policies while an attack occurs. The
policies for the demonstration have been obtained through a reinforcement
learning approach that includes a simulation system where policies are
incrementally learned and an emulation system that produces statistics that
drive the simulation runs.


title: Bayesian estimation of topological features of persistence diagrams

abstract:
  Persistent homology is a common technique in topological data analysis
providing geometrical and topological information about the sample space. All
this information, known as topological features, is summarized in persistence
diagrams, and the main interest is in identifying the most persisting ones
since they correspond to the Betti number values. Given the randomness inherent
in the sampling process, and the complex structure of the space where
persistence diagrams take values, estimation of Betti numbers is not
straightforward. The approach followed in this work makes use of features'
lifetimes and provides a full Bayesian clustering model, based on random
partitions, in order to estimate Betti numbers. A simulation study is also
presented.


title: Big line bundles on unitary modular varieties

abstract:
  We prove that unitary modular varieties are of general type if their
dimension $n> 196$ or the discriminant of the imaginary quadratic field is
sufficiently large, under the assumption that there exists at least one
non-zero cusp form of low weight and special unitary groups are principal. This
follows from the result that the line bundle, whose section is Hermitian
modular forms vanishing on branch divisors, on unitary modular varieties is
big, through the calculation of the Hirzebruch-Mumford volume. In particular,
for Hermitian lattices whose determinant is odd square-free, we find that the
associated special unitary groups are principal and there are only finitely
many ones whose corresponding varieties are not of general type, under the
existence of cusp forms. Consequently, we formulate and partially show the
finiteness of the number of Hermitian lattices admitting Hermitian reflective
modular forms, which is a unitary analog of the conjecture proposed by
Gritsenko-Nikulin for quadratic forms. Our study is motivated by the celebrated
work of Tai, Freitag, and Mumford on Siegel modular varieties and of Kond\={o},
Gritsenko-Hulek-Sankaran, and Ma on orthogonal modular varieties.


title: Bernstein algebras that are algebraic and the Kurosh problem

abstract:
  We study the class of Bernstein algebras that are algebraic, in the sense
that each element generates a finite-dimensional subalgebra. Every Bernstein
algebra has a maximal algebraic ideal, and the quotient algebra is a
zero-multiplication algebra. Several equivalent conditions for a Bernstein
algebra to be algebraic are given. In particular, known characterizations of
train Bernstein algebras in terms of nilpotency are generalized to the case of
locally train algebras. Along the way, we show that if a Banach Bernstein
algebra is algebraic (respectively, locally train), then it is of bounded
degree (respectively, train).
  Then we investigate the Kurosh problem for Bernstein algebras: whether a
finitely generated Bernstein algebra which is algebraic of bounded degree is
finite-dimensional. This problem turns out to have a closed link with a
question about associative algebras. In particular, when the barideal is nil,
the Kurosh problem asks whether a finitely generated Bernstein-train algebra is
finite-dimensional. We prove that the answer is positive for some specific
cases and for low degrees, and construct counter-examples in the general case.
  By results of Yagzhev, the Jacobian conjecture is equivalent to a certain
statement about Engel and nilpotence identities of multioperator algebras. We
show that the generalized Jacobian conjecture for quadratic mappings holds for
Bernstein algebras.


title: On dark radiation from string moduli decay to ALPs

abstract:
  We examine the issue of dark radiation (DR) from string moduli decay into
axion-like particles (ALPs). In KKLT-type models of moduli stabilization, the
axionlike phases of moduli fields are expected to decouple whilst in LVS-type
moduli stabilization some can remain light and may constitute dark radiation.
We evaluate modulus decay to Minimal Supersymmetric Standard Model (MSSM)
particles and dark radiation for more general compactifications. In spite of
tightening error bars on \Delta N_{eff}, we find only mild constraints on
modulus-ALP couplings due to the somewhat suppressed modulus branching fraction
to DR owing to the large number of MSSM decay modes. We anticipate that future
CMB experiments with greater precision on \Delta N_{eff} may still turn up
evidence for DR if the ALP associated with the lightest modulus field is indeed
light.


title:
Efficient and Accurate Candidate Generation for Grasp Pose Detection in
  SE(3)

abstract:
  Grasp detection of novel objects in unstructured environments is a key
capability in robotic manipulation. For 2D grasp detection problems where
grasps are assumed to lie in the plane, it is common to design a fully
convolutional neural network that predicts grasps over an entire image in one
step. However, this is not possible for grasp pose detection where grasp poses
are assumed to exist in SE(3). In this case, it is common to approach the
problem in two steps: grasp candidate generation and candidate classification.
Since grasp candidate classification is typically expensive, the problem
becomes one of efficiently identifying high quality candidate grasps. This
paper proposes a new grasp candidate generation method that significantly
outperforms major 3D grasp detection baselines. Supplementary material is
available at https://atenpas.github.io/psn/.


title:
Exact Privacy Guarantees for Markov Chain Implementations of the
  Exponential Mechanism with Artificial Atoms

abstract:
  Implementations of the exponential mechanism in differential privacy often
require sampling from intractable distributions. When approximate procedures
like Markov chain Monte Carlo (MCMC) are used, the end result incurs costs to
both privacy and accuracy. Existing work has examined these effects
asymptotically, but implementable finite sample results are needed in practice
so that users can specify privacy budgets in advance and implement samplers
with exact privacy guarantees. In this paper, we use tools from ergodic theory
and perfect simulation to design exact finite runtime sampling algorithms for
the exponential mechanism by introducing an intermediate modified target
distribution using artificial atoms. We propose an additional modification of
this sampling algorithm that maintains its $\epsilon$-DP guarantee and has
improved runtime at the cost of some utility. We then compare these methods in
scenarios where we can explicitly calculate a $\delta$ cost (as in $(\epsilon,
\delta)$-DP) incurred when using standard MCMC techniques. Much as there is a
well known trade-off between privacy and utility, we demonstrate that there is
also a trade-off between privacy guarantees and runtime.


title:
Evaluation of finite difference based asynchronous partial differential
  equations solver for reacting flows

abstract:
  Next-generation exascale machines with extreme levels of parallelism will
provide massive computing resources for large scale numerical simulations of
complex physical systems at unprecedented parameter ranges. However, novel
numerical methods, scalable algorithms and re-design of current state-of-the
art numerical solvers are required for scaling to these machines with minimal
overheads. One such approach for partial differential equations based solvers
involves computation of spatial derivatives with possibly delayed or
asynchronous data using high-order asynchrony-tolerant (AT) schemes to
facilitate mitigation of communication and synchronization bottlenecks without
affecting the numerical accuracy. In the present study, an effective
methodology of implementing temporal discretization using a multi-stage
Runge-Kutta method with AT schemes is presented. Together these schemes are
used to perform asynchronous simulations of canonical reacting flow problems,
demonstrated in one-dimension including auto-ignition of a premixture, premixed
flame propagation and non-premixed autoignition. Simulation results show that
the AT schemes incur very small numerical errors in all key quantities of
interest including stiff intermediate species despite delayed data at
processing element (PE) boundaries. For simulations of supersonic flows, the
degraded numerical accuracy of well-known shock-resolving WENO (weighted
essentially non-oscillatory) schemes when used with relaxed synchronization is
also discussed. To overcome this loss of accuracy, high-order AT-WENO schemes
are derived and tested on linear and non-linear equations. Finally the novel
AT-WENO schemes are demonstrated in the propagation of a detonation wave with
delays at PE boundaries.


title:
Control Co-design of a Hydrokinetic Turbine with Open-loop Optimal
  Control

abstract:
  This paper introduces a control co-design (CCD) framework to simultaneously
explore the physical parameters and control spaces for a hydro-kinetic turbine
(HKT) rotor optimization. The optimization formulation incorporates a coupled
dynamic-hydrodynamic model to maximize the rotor power efficiency for various
time-variant flow profiles. The open-loop optimal control is applied for
maximum power tracking, and the blade element momentum theory (BEMT) is used to
model the hydrodynamics. Case studies with different control constraints are
investigated for CCD. Sensitivity analyses were conducted with respect to
different flow profiles and initial geometries. Comparisons are made between
CCD and the sequential process, with physical design followed by a control
design process under the same conditions. The results demonstrate the benefits
of CCD and reveal that, with control constraints, CCD leads to increased energy
production compared to the design obtained from the sequential design process.


title:
Annular structures in perturbed low mass disc-shaped gaseous nebulae I :
  general and standard models

abstract:
  This is the first of two papers where we study analytical solutions of a
bidimensional low mass gaseous disc rotating around a central mass and
submitted to small radial perturbations. Hydrodynamics equations are solved for
the equilibrium and perturbed configurations. A wave-like equation for the gas
perturbed specific mass is deduced and solved analytically for several cases of
exponents of the power law distributions of the unperturbed specific mass and
sound speed. It is found that, first, the gas perturbed specific mass displays
exponentially spaced maxima, corresponding to zeros of the radial perturbed
velocity; second, the distance ratio of successive maxima of the perturbed
specific mass is a constant depending on disc characteristics and, following
the model, also on the perturbation's frequency; and, third, inward and outward
gas flows are induced from zones of minima toward zones of maxima of perturbed
specific mass, leading eventually to the possible formation of gaseous annular
structures in the disc. The results presented may be applied in various
astrophysical contexts to thin gaseous discs of negligible relative mass,
submitted to small radial perturbations.

categories: astro-ph.EP astro-ph.GA astro-ph.SR physics.flu-dyn


title:
Multiple Charged Meson Production in Exclusive $B_{c}$ Decays:
  $K+4\pi,$$KK+3\pi$, $7\pi$ Cases

abstract:
  Theoretical analysis of three exclusive decays, $B_{c}\to
J/\psi+\mathcal{R},$where $\mathcal{R}=K+4\pi,$$KK+3\pi$, or $7\pi$, is given.
Using the factorization method and the resonance approximation (methods proved
to be very useful in the analysis of some other similar decays), we have
obtained analytical expressions of the required amplitudes and created
distributions over some interesting mass combinations. Presented results could
be used for comparison with forthcoming experimental data and better
understanding of the nature of heavy quarkonia.