title:
Deterministic n-person shortest path and terminal games on symmetric
  digraphs have Nash equilibria in pure stationary strategies

abstract:
  We prove that a deterministic n-person shortest path game has a Nash
equlibrium in pure and stationary strategies, provided that the game is
symmetric (that is (u,v) is a move whenever (v,u) is, apart from moves entering
terminal vertices) and the length of every move is positive for each player.
Both conditions are essential, though it remains an open problem whether there
exists a NE-free 2-person non-symmetric game with positive lengths. We provide
examples for NE-free 2-person symmetric games that are not positive. We also
consider the special case of terminal games (shortest path games in which only
terminal moves have nonzero length, possibly negative) and prove that symmetric
n-person terminal games always have Nash equilibria in pure and stationary
strategies. Furthermore, we prove that a symmetric 2-person terminal game has a
uniform (sub-game perfect) Nash equilibrium, provided any infinite play is
worse than any of the terminals for both players.


title: Rough or crumpled: Phases in kinetic growth with surface relaxation

abstract:
  We show that generic kinetic growth processes with surface relaxations can
exhibit a new crumpled phase with short-range orientational order at dimensions
$d<4$. A sufficiently strong spatially non-local part of the chemical potential
associated with the particle current above a threshold in the system can
trigger this crumpling. The system can also be in a perturbatively accessible
rough phase with long range orientational order but short range positional
order at $d<4$ with known scaling exponents. Intriguingly, in $d>4$ we argue
that there is no crumpling transition; instead, there is a roughening
transition from a smooth to a rough phase for large enough non-local particle
current. Experimental and theoretical implications of these results are
discussed.


title: Bounds on the Twin-Width of Product Graphs

abstract:
  Twin-width is a graph width parameter recently introduced by Bonnet, Kim,
Thomass\'{e} & Watrigant. Given two graphs $G$ and $H$ and a graph product
$\star$, we address the question: is the twin-width of $G\star H$ bounded by a
function of the twin-widths of $G$ and $H$ and their maximum degrees? It is
known that a bound of this type holds for strong products (Bonnet, Geniet, Kim,
Thomass\'{e} & Watrigant; SODA 2021).
  We show that bounds of the same form hold for Cartesian, tensor/direct,
rooted, replacement, and zig-zag products. For the lexicographical product we
prove that the twin-width of the product of two graphs is exactly the maximum
of the twin-widths of the individual graphs. In contrast, for the modular
product we show that no bound can hold. In addition, we provide examples
showing many of our bounds are tight, and give improved bounds for certain
classes of graphs.


title:
Single Gaussian Process Method for Arbitrary Tokamak Regimes with a
  Statistical Analysis

abstract:
  Gaussian Process Regression (GPR) is a Bayesian method for inferring profiles
based on input data. The technique is increasing in popularity in the fusion
community due to its many advantages over traditional fitting techniques
including intrinsic uncertainty quantification and robustness to over-fitting.
This work investigates the use of a new method, the change-point method, for
handling the varying length scales found in different tokamak regimes. The use
of the Student's t-distribution for the Bayesian likelihood probability is also
investigated and shown to be advantageous in providing good fits in profiles
with many outliers. To compare different methods, synthetic data generated from
analytic profiles is used to create a database enabling a quantitative
statistical comparison of which methods perform the best. Using a full Bayesian
approach with the change-point method, Mat\'ern kernel for the prior
probability, and Student's t-distribution for the likelihood is shown to give
the best results.


title: Short-answer scoring with ensembles of pretrained language models

abstract:
  We investigate the effectiveness of ensembles of pretrained transformer-based
language models on short answer questions using the Kaggle Automated Short
Answer Scoring dataset. We fine-tune a collection of popular small, base, and
large pretrained transformer-based language models, and train one feature-base
model on the dataset with the aim of testing ensembles of these models. We used
an early stopping mechanism and hyperparameter optimization in training. We
observe that generally that the larger models perform slightly better, however,
they still fall short of state-of-the-art results one their own. Once we
consider ensembles of models, there are ensembles of a number of large networks
that do produce state-of-the-art results, however, these ensembles are too
large to realistically be put in a production environment.


title:
Bayesian Target-Vector Optimization for Efficient Parameter
  Reconstruction

abstract:
  Parameter reconstructions are indispensable in metrology. Here, on wants to
explain $K$ experimental measurements by fitting to them a parameterized model
of the measurement process. The model parameters are regularly determined by
least-square methods, i.e., by minimizing the sum of the squared residuals
between the $K$ model predictions and the $K$ experimental observations,
$\chi^2$. The model functions often involve computationally demanding numerical
simulations. Bayesian optimization methods are specifically suited for
minimizing expensive model functions. However, in contrast to least-square
methods such as the Levenberg-Marquardt algorithm, they only take the value of
$\chi^2$ into account, and neglect the $K$ individual model outputs. We
introduce a Bayesian target-vector optimization scheme that considers all $K$
contributions of the model function and that is specifically suited for
parameter reconstruction problems which are often based on hundreds of
observations. Its performance is compared to established methods for an optical
metrology reconstruction problem and two synthetic least-squares problems. The
proposed method outperforms established optimization methods. It also enables
to determine accurate uncertainty estimates with very few observations of the
actual model function by using Markov chain Monte Carlo sampling on a trained
surrogate model.


title: Easily generating and absorbing waves using machine learning

abstract:
  High-order wave-making theories are becoming available but are limited to
certain ranges of waves and wavemaker types in their applicability.
Alternatively, machine learning can be considered to find nonlinear functional
relationships. Therefore, this paper proposes a simple and universal framework
for generating and absorbing waves based on machine learning. This framework
trains neural networks to establish the transfer function between the
free-surface elevation on the wavemaker and the wavemaker velocity.
Significantly, penalty term and data augmentation techniques based on
wave-making mechanisms are introduced to increase the generalization ability of
neural networks, rather than pure data-driven. Therefore, once the target wave
profiles in front of the wavemaker are given, it can realize generating waves
and absorbing reflected waves at the same time. Taking piston and plunger
wavemakers as examples, an in-house numerical solver is applied to simulate
both wave generation and absorption. The simulated wave profiles and wave
orbital velocities are validated with analytical solutions, showing that the
proposed framework is effective at eliminating the re-reflection wave. Then,
the validation for generating the solitary wave and the New-year wave is
performed, indicating that the generated waves agree quite well with the
desired wave elevation. The proposed framework can facilitate the wavemaker
design in the future, and no complex theoretical derivation is required.


title: A Machian reformulation of Quantum Mechanics

abstract:
  The widely known but also somewhat esoteric Mach principle envisages a fully
relational formulation of physical theories without any reference to a concept
of `absolute space'. When applied to classical mechanics, under the guise of an
extended symmetry group, this procedure is known to lead to an equation of
motion with inertial-like forces that are sourced by the mass distribution of
the system itself. In this paper we follow a similar procedure and reformulate
the Schr\"odinger equation of non-relativistic quantum mechanics in a fully
Machian way. Just like its classical counterpart, the resulting quantum theory
is fully relational in the positions and momenta of the bodies comprising a
given physical system, leaving no room for the notion of absolute space.


title: Transitions in Dynamic Map Labeling

abstract:
  The labeling of point features on a map is a well-studied topic. In a static
setting, the goal is to find a non-overlapping label placement for (a subset
of) point features. In a dynamic setting, the set of point features and their
corresponding labels changes, and the labeling has to adapt to such changes. To
aid the user in tracking these changes, we can use morphs, here called
transitions, to indicate how a labeling changes. Such transitions have not
gained much attention yet, and we investigate different types of transitions
for labelings of points, most notably consecutive transitions and simultaneous
transitions. We give (tight) bounds on the number of overlaps that can occur
during these transitions. When each label has a (non-negative) weight
associated to it, and each overlap imposes a penalty proportional to the weight
of the overlapping labels, we show that it is NP-complete to decide whether the
penalty during a simultaneous transition has weight at most $k$.


title: On generalized nefness and bigness in adjunction theory

abstract:
  We investigate effectiveness and ampleness of adjoint divisors of the form
$aL+bK_X$, where $L$ is a suitably positive line bundle on a smooth projective
variety $X$ and $a,b$ are positive integers.


title: Pathwise Blowup of space-time fractional SPDEs

abstract:
  The finite time blowup in the almost sure sense of a class of space-time
fractional stochastic partial differential equations is discussed. Both the
cases of white noise and colored noise are considered. The sufficient and
necessary condition between the blowup and Osgood condition is obtained when
the spatial domain is bounded. And the sufficient condition for the blowup is
obtained when the spatial domain is the whole space. The results in this paper
could be regarded as extensions to some results in Foondun and Nualart, 2021.


title:
On the H\"older regularity for obstacle problems to porous medium type
  equations

abstract:
  We show that signed weak solutions to parabolic obstacle problems with porous
medium type structure are locally H\"older continuous, provided that the
obstacle is H\"older continuous.


title:
Pessimistic Bootstrapping for Uncertainty-Driven Offline Reinforcement
  Learning

abstract:
  Offline Reinforcement Learning (RL) aims to learn policies from previously
collected datasets without exploring the environment. Directly applying
off-policy algorithms to offline RL usually fails due to the extrapolation
error caused by the out-of-distribution (OOD) actions. Previous methods tackle
such problem by penalizing the Q-values of OOD actions or constraining the
trained policy to be close to the behavior policy. Nevertheless, such methods
typically prevent the generalization of value functions beyond the offline data
and also lack precise characterization of OOD data. In this paper, we propose
Pessimistic Bootstrapping for offline RL (PBRL), a purely uncertainty-driven
offline algorithm without explicit policy constraints. Specifically, PBRL
conducts uncertainty quantification via the disagreement of bootstrapped
Q-functions, and performs pessimistic updates by penalizing the value function
based on the estimated uncertainty. To tackle the extrapolating error, we
further propose a novel OOD sampling method. We show that such OOD sampling and
pessimistic bootstrapping yields provable uncertainty quantifier in linear
MDPs, thus providing the theoretical underpinning for PBRL. Extensive
experiments on D4RL benchmark show that PBRL has better performance compared to
the state-of-the-art algorithms.


title:
Model of hybrid star with baryonic and strange quark matter in
  Tolman-Kuchowicz spacetime

abstract:
  The purpose of our present work is to investigate some new features of a
static anisotropic relativistic hybrid compact star composed of strange quark
matter (SQM) in the inner core and normal baryonic matter distribution in the
crust. Here we apply the simplest form of the phenomenological MIT bag model
equation of state $p_q = \frac{1}{3}(\rho_q - 4B_g)$ to correlate the density
and pressure of strange quark matter within the stellar interior, whereas
radial pressure and matter density due to baryonic matter are connected by the
simple linear equation of state $p_r = \alpha \rho - \beta$. In order to obtain
the solution of the Einstein field equations, we have used the Tolman-Kuchowicz
{\em ansatz} [Tolman, Phys Rev 55:364, 1939; Kuchowicz, Acta Phys Pol 33:541,
1968] and further derivation of the arbitrary constants from some physical
conditions. Here, we examine our proposed model graphically and analytically in
detail for physically plausible conditions. In particular, for this
investigation, we have reported on the compact object Her $X-1$ [Mass=$(0.98
\pm 0.12)M_{\odot}$; Radius= $8.1_{-0.41}^{+0.41}$ km] in our paper as a
strange quark star candidate. In order to check the physical validity and
stability of our suggested model, we have performed various physical tests both
analytically and graphically, namely, dynamical equilibrium of applied forces,
energy conditions, compactness factor, and surface redshift etc. Finally, we
have found that our present model meets all the necessary physical requirements
for a realistic model and can be studied for strange quark stars (SQS).


title:
Hydrogen burning of $^{29}$Si and its impact on presolar stardust grains
  from classical novae

abstract:
  Presolar stardust grains found in primitive meteorites are believed to retain
the isotopic composition of stellar outflows at the time of grain condensation.
Therefore, laboratory measurements of their isotopic ratios represent sensitive
probes for investigating open questions related to stellar evolution, stellar
explosions, nucleosynthesis, mixing mechanisms, dust formation, and galactic
chemical evolution. For a few selected presolar grains, classical novae have
been discussed as a potential source. For SiC, silicate, and graphite presolar
grains, the association is based on the observation of small
$N(^{12}$C)/$N(^{13}$C) and $N(^{14}$N)/$N(^{15}$N) number abundance ratios
compared to solar values, and abundance excesses in $^{30}$Si relative to
$^{29}$Si, as previously predicted by models of classical novae. We report on a
direct measurement of the $^{29}$Si(p,$\gamma$)$^{30}$P reaction, which
strongly impacts simulated $\delta ^{29}$Si values from classical novae. Our
new experimental $^{29}$Si(p,$\gamma$)$^{30}$P thermonuclear reaction rate
differs from previous results by up to 50\% in the classical nova temperature
range ($T$ $=$ $100$ $-$ $400$~MK), while the rate uncertainty is reduced by up
to a factor of $3$. Using our new reaction rate in Monte Carlo reaction network
and hydrodynamic simulations of classical novae, we estimate $\delta ^{29}$Si
values with much reduced uncertainties. Our results establish $\delta ^{29}$Si
values measured in presolar grains as a sensitive probe for assessing their
classical nova paternity. We also demonstrate that $\delta ^{30}$Si values from
nova simulations are presently not a useful diagnostic tool unless the large
uncertainty of the $^{30}$P(p,$\gamma$)$^{31}$S reaction rate can be
significantly reduced.


title: Spin-density-wave order controlled by uniaxial stress in CeAuSb$_2$

abstract:
  The tetragonal heavy fermion compound CeAuSb$_2$ (space group $P4/nmm$)
exhibits incommensurate spin density wave (SDW) order below $T_{N}\approx6.5~K$
with the propagation vector $\mathbf{q}_A = (\delta_A,\delta_A,1/2)$. The
application uniaxial stress along the [010] direction induces a sudden change
in the resistivity ratio $\rho_a/\rho_b$ at a compressive strain of $\epsilon
\approx -0.5$\%. Here we use neutron scattering to show that the uniaxial
stress induces a first-order transition to a SDW state with a different
propagation vector $(0,\delta_B,1/2)$ with $\delta_B=0.25$. The magnetic
structure of the new (B) phase consists of Ce layers with ordered moments
alternating with layers with zero moment stacked along the $c$-axis. The
ordered layers have an up-up-down-down configuration along the $b$-axis. This
is an unusual situation in which the loss of spatial inversion is driven by
itinerant magnetic order. We argue that the change in SDW wavevector leads to a
concomitant Fermi surface reconstruction, similar to other materials where a
SDW can be controlled by uniaxial stress or magnetic field such as
Sr$_3$Ru$_2$O$_7$.


title: Monitoring hyperproperties with circuits

abstract:
  This paper presents an extension of the safety fragment of Hennessy-Milner
Logic with recursion over sets of traces, in the spirit of Hyper-LTL. It then
introduces a novel monitoring setup that employs circuit-like structures to
combine verdicts from regular monitors. The main contribution of this study is
the monitors and their semantics themselves, as well as a monitor-synthesis
procedure from formulae in the logic that yields `circuit-like monitors' of
this type that are sound and violation complete over a finite set of infinite
traces.


title:
SporTran: a code to estimate transport coefficients from the cepstral
  analysis of (multivariate) current time series

abstract:
  SporTran is a Python utility designed to estimate generic transport
coefficients in extended systems, based on the Green-Kubo theory of linear
response and the recently introduced cepstral analysis of the current time
series generated by molecular dynamics simulations. SporTran can be applied to
univariate as well as multivariate time series. Cepstral analysis requires
minimum discretion from the user, in that it weakly depends on two parameters,
one of which is automatically estimated by a statistical model-selection
criterion that univocally determine the resulting accuracy. In order to
facilitate the optimal refinement of these parameters, SporTran features an
easy-to-use graphical user interface. A command-line interface and a Python
API, easy to embed in complex data-analysis workflows, are also provided.


title:
GAMEOPT: Optimal Real-time Multi-Agent Planning and Control for Dynamic
  Intersections

abstract:
  We propose GameOpt: a novel hybrid approach to cooperative intersection
control for dynamic, multi-lane, unsignalized intersections. Safely navigating
these complex and accident prone intersections requires simultaneous trajectory
planning and negotiation among drivers. GameOpt is a hybrid formulation that
first uses an auction mechanism to generate a priority entrance sequence for
every agent, followed by an optimization-based trajectory planner that computes
velocity controls that satisfy the priority sequence. This coupling operates at
real-time speeds of less than 10 milliseconds in high density traffic of more
than 10,000 vehicles/hr, 100 times faster than other fully optimization-based
methods, while providing guarantees in terms of fairness, safety, and
efficiency. Tested on the SUMO simulator, our algorithm improves throughput by
at least 25%, time taken to reach the goal by 75%, and fuel consumption by 33%
compared to auction-based approaches and signaled approaches using
traffic-lights and stop signs.


title: Hydrodynamic signatures and spectral properties of the quantum vortex

abstract:
  We characterize the low-lying excitations of a quantum vortex in a
quasi-two-dimensional Bose-Einstein condensate (BEC) using the standard
definition of the density of states (DOS) and a modified version that is
sensitive to complementary aspects of the excitation's spectrum. The latter
proves to be particularly relevant to studying the polaronic state realized
when an impurity is embedded in a quantum vortex. We establish that the
impurity becomes sensitive to the transversal fluctuations of the vortex, via
its remnant kelvon mode, and to the phase fluctuations of the BEC
Nambu-Goldstone mode. The presence of the vortex yields an anomalous excitation
spectrum with a finite energy gap and non-linear DOS at low energies. We find
that the high sensitivity of the kelvon mode to external potentials provides a
channel of quantum-level control over impurities trapped in a vortex. This
extra control channel may be of practical use for the proposal of using
vortex-trapped impurities as qubit units for quantum information processing.


title: Comment on "Does the weak trace show the past of a quantum particle?"

abstract:
  In the paper "Does the weak trace show the past of a quantum particle?"
[arXiv:2109.14060v2], it is argued that null weak values of the spatial
projectors are inadequate to infer the presence of a quantum particle at an
intermediate time between preparation and detection. This conclusion relies on
two arguments - (i) the role of the disturbance induced by a weak measurement,
and (ii) classical-like features like continuous paths that must purportedly be
associated with a quantum particle presence. Here we first show that (i) arises
from a misunderstanding of null weak values by putting forward a simple
counter-example that highlights that the relevant quantities to examine are the
vanishing amplitudes, not the wavefunction. Then we briefly argue that
enforcing classical pre-conditions in order to account for quantum properties
during unitary evolution is unlikely to lead to a consistent understanding of
quantum phenomena.


title:
Shisha: Online scheduling of CNN pipelines on heterogeneous
  architectures

abstract:
  Chiplets have become a common methodology in modern chip design. Chiplets
improve yield and enable heterogeneity at the level of cores, memory subsystem
and the interconnect. Convolutional Neural Networks (CNNs) have high
computational, bandwidth and memory capacity requirements owing to the
increasingly large amount of weights. Thus to exploit chiplet-based
architectures, CNNs must be optimized in terms of scheduling and workload
distribution among computing resources. We propose Shisha, an online approach
to generate and schedule parallel CNN pipelines on chiplet architectures.
Shisha targets heterogeneity in compute performance and memory bandwidth and
tunes the pipeline schedule through a fast online exploration technique. We
compare Shisha with Simulated Annealing, Hill Climbing and Pipe-Search. On
average, the convergence time is improved by ~35x in Shisha compared to other
exploration algorithms. Despite the quick exploration, Shisha's solution is
often better than that of other heuristic exploration algorithms.


title: Information break of time symmetry in the macroscopic limit

abstract:
  The evident contrast between the time symmetry of fundamental microscopic
laws and the time asymmetry of macroscopic processes is a challenging physical
problem. The observation of unitary evolution of a general physical system by
an idealized observer whose recording and processing information is time
neutral is studied in a full information context. In the macroscopic limit, a
contradiction between observations and predictions done at different times
appears. It implies that the observer cannot read records performed at times
when the entropy of the system is larger.


title:
Combining ozone and UV-light for energy efficient removal of SOx in
  low-temperature flue gas

abstract:
  The potential of a combined ozone O3 ultraviolet (UV) light reactor for
gas-phase oxidation of flue gas pollutants has been evaluated in this work. For
this, numerical simulations of a continuously stirred tank reactor (CSTR) have
been performed for the analysis of sulfur dioxide SO2 removal. Chemical
kinetics have been coupled with modeling of the radiation intensity
distribution produced by a UV lamp with five different radiation models. A grid
convergence study and an optimization of the number of discrete point light
sources employed for some of the radiation models was carried out. The effect
of residence time and reactor size on the removal of SO2 have also been
analyzed. Overall, results for the abatement of SO2 in an O3-UV reactor under
optimized conditions suggest that this approach is suitable for sustainable air
cleaning applications.


title: Mini-review: Expectations for supersymmetry from the string landscape

abstract:
  In this mini-review, we summarize a variety of findings pertaining to
consequences of the landscape of string theory for supersymmetry (SUSY)
phenomenology. The idea is to adopt the MSSM as the most parsimonious 4-d low
energy EFT after string compactification but where the scale of SUSY breaking
is as yet undetermined. A power-law landscape draw to large soft terms is
tempered by the requirement that the derived value of the weak scale lie within
the anthropic window of Agrawal {\it et al.} (ABDS). Such a set-up predicts a
light Higgs mass m_h~ 125 GeV with sparticles generally beyond LHC bounds. We
discuss consequences for LHC searches: light higgsinos, highly mixed TeV-scale
top squarks, same-sign diboson events and m_{\tg}~ 2-5 TeV. We expect dark
matter to consist of an axion/higgsino-like WIMP admixture.


title: Identifying Oscillations Injected by Inverter-Based Solar Energy Sources

abstract:
  Inverter-based solar energy sources are becoming widely integrated into
modern power systems. However, their impacts on the system in the frequency
domain are rarely investigated at a higher frequency range than conventional
electromechanical oscillations. This paper presents evidence of the emergence
of an oscillation mode injected by inverter-based solar energy sources in
Dominion Energy's service territory. This new mode was recognized from the
analysis of real-world ambient synchrophasor and point-of-wave data. The
analysis was performed by developing customized synchrophasor analysis tools
deployed on the PredictiveGrid^{TM} platform implemented at Dominion Energy.
Herein, we describe and illustrate the preliminary analysis results acquired
from spectrogram observations, power spectral density plots, and mode shape
estimation. The emergence and propagation of this new mode in Dominion Energy's
footprint is illustrated using a heatmap based on a proposed frequency
component energy metric, which helps to assess this oscillation's spread and
impact.


title:
The consistent behavior of negative Poissons ratio with interlayer
  interactions

abstract:
  Negative Poissons ratio (NPR) is of great interest due to the novel
applications in lots of fields. Films are the most commonly used form in
practical applications, which involves multiple layers. However, the effect of
interlayer interactions on the NPR is still unclear. In this study, based on
first principles calculations, we systematically investigate the effect of
interlayer interactions on the NPR by comparably studying single-layer
graphene, few-layer graphene, h-BN, and graphene-BN heterostructure. It is
found that they almost have the same geometry-strain response. Consequently,
the NPR in bilayer graphene, triple-layer graphene, and graphene-BN
heterostructure are consistent with that in single-layer graphene and h-BN. The
fundamental mechanism lies in that the response to strain of the orbital
coupling are consistent under the effect of interlayer interactions. The deep
understanding of the NPR with the effect of interlayer interactions as achieved
in this study is beneficial for the future design and development of
micro-/nanoscale electromechanical devices with novel functions based on
nanostructures.


title: Can LSTM outperform volatility-econometric models?

abstract:
  Volatility prediction for financial assets is one of the essential questions
for understanding financial risks and quadratic price variation. However,
although many novel deep learning models were recently proposed, they still
have a "hard time" surpassing strong econometric volatility models. Why is this
the case? The volatility prediction task is of non-trivial complexity due to
noise, market microstructure, heteroscedasticity, exogenous and asymmetric
effect of news, and the presence of different time scales, among others. In
this paper, we analyze the class of long short-term memory (LSTM) recurrent
neural networks for the task of volatility prediction and compare it with
strong volatility-econometric models.


title: The Boolean complexity of computing Chow forms

abstract:
  We consider the complexity of computing Chow forms and their generalization
to multiprojective spaces. We develop a deterministic algorithm using
resultants, and obtain a single exponential complexity upper bound. Earlier
computational results for Chow forms were in the arithmetic complexity model;
our result represents the first Boolean complexity bound. We also extend our
algorithm to multiprojective Chow forms and obtain the first computational
result in this setting. The motivation for our work comes from incidence
geometry where intriguing problems for computational algebraists remain open.


title:
Uniform stability in the Euclidean isoperimetric problem for the
  Allen--Cahn energy

abstract:
  We consider the isoperimetric problem defined on the whole $\mathbb{R}^n$ by
the Allen--Cahn energy functional. For non-degenerate double well potentials,
we prove sharp quantitative stability inequalities of quadratic type which are
uniform in the length scale of the phase transitions. We also derive a rigidity
theorem for critical points analogous to the classical Alexandrov's theorem for
constant mean curvature boundaries.


title:
Simple, reliable and noise-resilient continuous-variable quantum state
  tomography with convex optimization

abstract:
  Precise reconstruction of unknown quantum states from measurement data, a
process commonly called quantum state tomography, is a crucial component in the
development of quantum information processing technologies. Many different
tomography methods have been proposed over the years. Maximum likelihood
estimation is a prominent example, being the most popular method for a long
period of time. Recently, more advanced neural network methods have started to
emerge. Here, we go back to basics and present a method for continuous variable
state reconstruction that is both conceptually and practically simple, based on
convex optimization. Convex optimization has been used for process tomography
and qubit state tomography, but seems to have been overlooked for continuous
variable quantum state tomography. We demonstrate high-fidelity reconstruction
of an underlying state from data corrupted by thermal noise and imperfect
detection, for both homodyne and heterodyne measurements. A major advantage
over other methods is that convex optimization algorithms are guaranteed to
converge to the optimal solution.


title:
Amortised Likelihood-free Inference for Expensive Time-series Simulators
  with Signatured Ratio Estimation

abstract:
  Simulation models of complex dynamics in the natural and social sciences
commonly lack a tractable likelihood function, rendering traditional
likelihood-based statistical inference impossible. Recent advances in machine
learning have introduced novel algorithms for estimating otherwise intractable
likelihood functions using a likelihood ratio trick based on binary
classifiers. Consequently, efficient likelihood approximations can be obtained
whenever good probabilistic classifiers can be constructed. We propose a kernel
classifier for sequential data using path signatures based on the recently
introduced signature kernel. We demonstrate that the representative power of
signatures yields a highly performant classifier, even in the crucially
important case where sample numbers are low. In such scenarios, our approach
can outperform sophisticated neural networks for common posterior inference
tasks.


title:
Structure-preserving and helicity-conserving finite element
  approximations and preconditioning for the Hall MHD equations

abstract:
  We develop structure-preserving finite element methods for the
incompressible, resistive Hall magnetohydrodynamics (MHD) equations. These
equations incorporate the Hall current term in Ohm's law and provide a more
appropriate description of fully ionized plasmas than the standard MHD
equations on length scales close to or smaller than the ion skin depth. We
introduce a stationary discrete variational formulation of Hall MHD that
enforces the magnetic Gauss's law exactly (up to solver tolerances) and prove
the well-posedness and convergence of a Picard linearization. For the transient
problem, we present time discretizations that preserve the energy and magnetic
and hybrid helicity precisely in the ideal limit for two types of boundary
conditions. Additionally, we present an augmented Lagrangian preconditioning
technique for both the stationary and transient cases. We confirm our findings
with several numerical experiments.


title: Resonant Soft X-Ray Scattering on LaPt$_2$Si$_2$

abstract:
  X-ray absorption (XAS) and Resonant Inelastic X-ray Scattering (RIXS) spectra
of LaPt$_2$Si$_2$ single crystal at the Si L and La N edges are presented. The
data are interpreted in terms of density functional theory, showing that the Si
spectra can be described in terms of Si $s$ and $d$ local partial density of
states (LPDOS), and the La spectra are due to quasi-atomic local $4f$
excitations. Calculations show that Pt $d$-LPDOS dominates the occupied states,
and a sharp localized La $f$ state is found in the unoccupied states, in line
with the observations.


title:
A Deep Finite Difference Emulator for the Fast Simulation of Coupled
  Viscous Burgers' Equation

abstract:
  This work proposes a deep learning-based emulator for the efficient
computation of the coupled viscous Burgers' equation with random initial
conditions. In a departure from traditional data-driven deep learning
approaches, the proposed emulator does not require a classical numerical solver
to collect training data. Instead, it makes direct use of the problem's
physics. Specifically, the model emulates a second-order finite difference
solver, i.e., the Crank-Nicolson scheme in learning dynamics. A systematic case
study is conducted to examine the model's prediction performance,
generalization ability, and computational efficiency. The computed results are
graphically represented and compared to those of state-of-the-art numerical
solvers.


title:
Unphysical Discontinuities, Intruder States and Regularization in $GW$
  Methods

abstract:
  By recasting the non-linear frequency-dependent $GW$ quasiparticle equation
into a linear eigenvalue problem, we explain the appearance of multiple
solutions and unphysical discontinuities in various physical quantities
computed within the $GW$ approximation. Considering the $GW$ self-energy as an
effective Hamiltonian, it is shown that these issues are key signatures of
strong correlation in the $(N\pm1)$-electron states and can be directly related
to the intruder state problem. A simple and efficient regularization procedure
inspired by the similarity renormalization group is proposed to avoid such
issues and speed up convergence of partially self-consistent $GW$ calculations.

categories: physics.chem-ph cond-mat.mtrl-sci cond-mat.str-el nucl-th


title:
Optimal Second-Order Rates for Quantum Soft Covering and Privacy
  Amplification

abstract:
  We study quantum soft covering and privacy amplification against quantum side
information. The former task aims to approximate a quantum state by sampling
from a prior distribution and querying a quantum channel. The latter task aims
to extract uniform and independent randomness against quantum adversaries. For
both tasks, we use trace distance to measure the closeness between the
processed state and the ideal target state. We show that the minimal amount of
samples for achieving an $\varepsilon$-covering is given by the
$(1-\varepsilon)$-hypothesis testing information (with additional logarithmic
additive terms), while the maximal extractable randomness for an
$\varepsilon$-secret extractor is characterized by the conditional
$(1-\varepsilon)$-hypothesis testing entropy.
  When performing independent and identical repetitions of the tasks, our
one-shot characterizations lead to tight asymptotic expansions of the
above-mentioned operational quantities. We establish their second-order rates
given by the quantum mutual information variance and the quantum conditional
information variance, respectively. Moreover, our results extend to the
moderate deviation regime, which are the optimal asymptotic rates when the
trace distances vanish at sub-exponential speed. Our proof technique is direct
analysis of trace distance without smoothing.


title:
An interaction-based contagion model over temporal networks demonstrates
  that reducing temporal network density reduces total infection rate

abstract:
  Contacts' temporal ordering and dynamics, such as their order and timing, are
crucial for understanding the transmission of infectious diseases. Using
path-preserving temporal networks, we evaluate the effect of spatial pods
(social distancing pods) and temporal pods (meetings' rate reduction) on the
spread of the disease. We use our interaction-driven contagion model,
instantiated for COVID-19, over history-maintaining random temporal networks as
well as over real-world contacts. We find that temporal pods significantly
reduce the overall number of infected individuals and slow the spread of the
disease. This result is robust under changing initial conditions, such as
initial patients' numbers and locations. Social distancing (spatial) pods
perform well only at the initial phase of the disease, i.e., with a minimal
number of initial patients. Using real-life contact information and extending
our interaction-driven model to consider the exposures, we demonstrate the
beneficial effect of reducing the temporal density on overall infection rates.
We further show that slow-spreading pathogens spread almost as fast-spreading
pathogens in dense topologies. Our results show that given the same
transmission level, there is a decrease in the disease's rate and spread in
less dense networks. Thus, reducing the rate of encounters is more effective
than social distancing.


title: How Many Data Are Needed for Robust Learning?

abstract:
  We show that the sample complexity of robust interpolation problem could be
exponential in the input dimensionality and discover a phase transition
phenomenon when the data are in a unit ball. Robust interpolation refers to the
problem of interpolating $n$ noisy training data in $\R^d$ by a Lipschitz
function. Although this problem has been well understood when the covariates
are drawn from an isoperimetry distribution, much remains unknown concerning
its performance under generic or even the worst-case distributions. Our results
are two-fold: 1) too many data hurt robustness; we provide a tight and
universal Lipschitzness lower bound $\Omega(n^{1/d})$ of the interpolating
function for arbitrary data distributions. Our result disproves potential
existence of an $\mathcal{O}(1)$-Lipschitz function in the overparametrization
scenario when $n=\exp(\omega(d))$. 2) Small data hurt robustness:
$n=\exp(\Omega(d))$ is necessary for obtaining a good population error under
certain distributions by any $\mathcal{O}(1)$-Lipschitz learning algorithm.
Perhaps surprisingly, our results shed light on the curse of big data and the
blessing of dimensionality for robustness, and discover an intriguing
phenomenon of phase transition at $n=\exp(\Theta(d))$.


title: Finding Safe Zones of policies Markov Decision Processes

abstract:
  Given a policy, we define a SafeZone as a subset of states, such that most of
the policy's trajectories are confined to this subset. The quality of the
SafeZone is parameterized by the number of states and the escape probability,
i.e., the probability that a random trajectory will leave the subset. SafeZones
are especially interesting when they have a small number of states and low
escape probability. We study the complexity of finding optimal SafeZones, and
show that in general the problem is computationally hard. For this reason we
concentrate on computing approximate SafeZones. Our main result is a
bi-criteria approximation algorithm which gives a factor of almost $2$
approximation for both the escape probability and SafeZone size, using a
polynomial size sample complexity. We conclude the paper with an empirical
evaluation of our algorithm.


title: Quarter-wave Resonator Based Tunable Coupler for Xmon Qubits

abstract:
  We propose a scheme of tunable coupler based on quarter-wave resonator for
scalable quantum integrated circuits. The open end of the T-type resonator is
capacitively coupled to two Xmon qubits, while another end is an asymmetric
dc-SQUID which dominates the inductive energy of coupler resonator. The
dc-Current applied through the flux bias line could change the magnetic flux
inside the dc-SQUID, so the frequency of coupler resonator can be effectively
tuned and the qubit-qubit coupling can be totally switched off. As the increase
of junction asymmetry for the dc-SQUID, the coupling of SQUID's effective phase
difference and cavity modes become smaller at required working frequency regime
of coupler resonator, and this could reduce the descent of the resonator's
quality factor. The separation between two cross-capacitor can be larger with
help of transverses width of the T-shape resonator, and then the ZZ crosstalk
coupling can be effectively suppressed. The asymmetric dc-SQUID is about 5
millimeters away from the Xmon qubits and only needs a small current on the
flux bias line, which in principle creates less flux noises to superconducting
Xmon qubits.


title: Induced Disjoint Paths and Connected Subgraphs for $H$-Free Graphs

abstract:
  Paths $P_1,\ldots, P_k$ in a graph $G=(V,E)$ are mutually induced if any two
distinct $P_i$ and $P_j$ have neither common vertices nor adjacent vertices.
The Induced Disjoint Paths problem is to decide if a graph $G$ with $k$ pairs
of specified vertices $(s_i,t_i)$ contains $k$ mutually induced paths $P_i$
such that each $P_i$ starts from $s_i$ and ends at $t_i$. This is a classical
graph problem that is NP-complete even for $k=2$. We introduce a natural
generalization, Induced Disjoint Connected Subgraphs: instead of connecting
pairs of terminals, we must connect sets of terminals. We give almost-complete
dichotomies of the computational complexity of both problems for H-free graphs,
that is, graphs that do not contain some fixed graph H as an induced subgraph.
Finally, we give a complete classification of the complexity of the second
problem if the number k of terminal sets is fixed, that is, not part of the
input.


title: Emergent de Sitter Cosmology Near Black Hole Horizon

abstract:
  We propose an effective model for an exponentially expanding universe based
on 5D gravity where we assume there is a spherical brane in 5D spacetime.
Considering a 5D Schwarzschild black hole with its center on the brane we find
out the induced metric outside the black hole horizon on the brane is static de
Sitter. Solving for a homogeneous and isotropic fluid in the corresponding FLRW
coordinates we find the perturbative Friedmann equation and find the 4
dimensional gravitational constant. We find that the bulk fluid density inside
the brane which has the same equation of state as the fluid on the brane
contributes to the energy density in the Friedmann equation and therefore in
late time may be attributed to dark matter. Studying the stability of the setup
we observe that the brane becomes stabilized in the presence of matter on the
brane with a de Sitter length that is qualitatively of the order of
Schwarzschild radius of the universe. We study the semiclassical evaporation of
de Sitter spacetime in this framework. We also discuss effects other than black
hole evaporation that can alter de Sitter lifetime. In particular this model
can provide a lifetime compatible with Trans Planckian Censorship conjecture
for the current de Sitter phase.


title:
Riemannian optimization on unit sphere with $p$-norm and its
  applications

abstract:
  This paper deals with Riemannian optimization on the unit sphere in terms of
$p$-norm with general $p > 1$. As a Riemannian submanifold of the Euclidean
space, the geometry of the sphere with $p$-norm is investigated, and several
geometric tools used for Riemannian optimization, such as retractions and
vector transports, are proposed and analyzed. Applications to Riemannian
optimization on the sphere with nonnegative constraints and
$L_p$-regularization-related optimization are also discussed. As practical
examples, the former includes nonnegative principal component analysis and the
latter is closely related to the Lasso regression and box-constrained problems.
Numerical experiments verify that Riemannian optimization on the sphere with
$p$-norm has substantial potential for such applications, and the proposed
framework provides a theoretical basis for such optimization.


title:
A Dimensionality Reduction Method for Finding Least Favorable Priors
  with a Focus on Bregman Divergence

abstract:
  A common way of characterizing minimax estimators in point estimation is by
moving the problem into the Bayesian estimation domain and finding a least
favorable prior distribution. The Bayesian estimator induced by a least
favorable prior, under mild conditions, is then known to be minimax. However,
finding least favorable distributions can be challenging due to inherent
optimization over the space of probability distributions, which is
infinite-dimensional. This paper develops a dimensionality reduction method
that allows us to move the optimization to a finite-dimensional setting with an
explicit bound on the dimension. The benefit of this dimensionality reduction
is that it permits the use of popular algorithms such as projected gradient
ascent to find least favorable priors. Throughout the paper, in order to make
progress on the problem, we restrict ourselves to Bayesian risks induced by a
relatively large class of loss functions, namely Bregman divergences.


title: NysADMM: faster composite convex optimization via low-rank approximation

abstract:
  This paper develops a scalable new algorithm, called NysADMM, to minimize a
smooth convex loss function with a convex regularizer. NysADMM accelerates the
inexact Alternating Direction Method of Multipliers (ADMM) by constructing a
preconditioner for the ADMM subproblem from a randomized low-rank Nystr\"om
approximation. NysADMM comes with strong theoretical guarantees: it solves the
ADMM subproblem in a constant number of iterations when the rank of the
Nystr\"om approximation is the effective dimension of the subproblem
regularized Gram matrix. In practice, ranks much smaller than the effective
dimension can succeed, so NysADMM uses an adaptive strategy to choose the rank
that enjoys analogous guarantees. Numerical experiments on real-world datasets
demonstrate that NysADMM can solve important applications, such as the lasso,
logistic regression, and support vector machines, in half the time (or less)
required by standard solvers. The breadth of problems on which NysADMM beats
standard solvers is a surprise: it suggests that ADMM is a dominant paradigm
for numerical optimization across a wide range of statistical learning problems
that are usually solved with bespoke methods.


title:
Variational problems on Riemannian manifolds with constrained
  accelerations

abstract:
  We introduce variational problems on Riemannian manifolds with constrained
acceleration and derive necessary conditions for normal extremals in the
constrained variational problem. The problem consists on minimizing a
higher-order energy functional, among a set of admissible curves defined by a
constraint on the covariant acceleration. In addition, we use this framework to
address the elastic splines problem with obstacle avoidance in the presence of
this type of contraints.


title: Fast and Succinct Population Protocols for Presburger Arithmetic

abstract:
  In their 2006 seminal paper in Distributed Computing, Angluin et al. present
a construction that, given any Presburger predicate as input, outputs a
leaderless population protocol that decides the predicate. The protocol for a
predicate of size $m$ (when expressed as a Boolean combination of threshold and
remainder predicates with coefficients in binary) runs in $\mathcal{O}(m \cdot
n^2 \log n)$ expected number of interactions, which is almost optimal in $n$.
However, the number of states of the protocol is exponential in $m$. Blondin et
al. described in STACS 2020 another construction that produces protocols with a
polynomial number of states, but exponential expected number of interactions.
We present a construction that produces protocols with $\mathcal{O}(m)$ states
that run in expected $\mathcal{O}(m^{7} \cdot n^2)$ interactions, optimal in
$n$, for all inputs of size $\Omega(m)$. For this we introduce population
computers, a carefully crafted generalization of population protocols easier to
program, and show that our computers for Presburger predicates can be
translated into fast and succinct population protocols.


title:
Joint IRS Location and Size Optimization in Multi-IRS Aided Two-Way
  Full-Duplex Communication Systems

abstract:
  Intelligent reflecting surfaces (IRSs) have emerged as a promising wireless
technology for the dynamic configuration and control of electromagnetic waves,
thus creating a smart (programmable) radio environment. In this context, we
study a multi-IRS assisted two-way communication system consisting of two users
that employ full-duplex (FD) technology. More specifically, we deal with the
joint IRS location and size (i.e., the number of reflecting elements)
optimization in order to minimize an upper bound of system outage probability
under various constraints, namely, minimum and maximum number of reflecting
elements per IRS, maximum number of installed IRSs, maximum total number of
reflecting elements (implicit bound on the signaling overhead) as well as
maximum total IRS installation cost. First, the problem is formulated as a
discrete optimization problem and, then, a theoretical proof of its NP-hardness
is given. Moreover, we provide a lower bound on the optimum value by solving a
linear-programming relaxation (LPR) problem. Subsequently, we design two
polynomial-time algorithms, a deterministic greedy algorithm and a randomized
approximation algorithm, based on the LPR solution. The former is a heuristic
method that always computes a feasible solution for which (a posteriori)
performance guarantee can be provided. The latter achieves an approximate
solution, using randomized rounding, with provable (a priori) probabilistic
guarantees on the performance. Furthermore, extensive numerical simulations
demonstrate the superiority of the proposed algorithms compared to the baseline
schemes. Finally, useful conclusions regarding the comparison between FD and
conventional half-duplex (HD) systems are also drawn.


title: Probing spin dynamics of 2D excitons with twisted light

abstract:
  We propose a mechanism of dark to bright exciton transitions in spin-valley
coupled twodimensional systems by transferring momentum of light into exciton
center of mass using optical vortex (OV) beams. By varying the dispersion of
light using the topological charge of OV beam, we demonstrate a unique approach
to control the intra-valley spin-flip scattering rate of excitons. From our
photoluminescence measurements, we demonstrate that the intravalley scattering
rate in W-based TMDs can be tuned externally by OV beams. Variation of
photoluminescence intensity with topological charges shows a crossover
temperature (> 150 K), indicating competitions among time scales involving
radiative recombination, spin-flip scattering, and thermal relaxations. Our
proposed technique utilizing a structured light beam can open up a new approach
to explore the physics of excitons in 2D systems.


title:
The Segment Number: Algorithms and Universal Lower Bounds for Some
  Classes of Planar Graphs

abstract:
  The segment number of a planar graph $G$ is the smallest number of line
segments needed for a planar straight-line drawing of $G$. Dujmovi\'c,
Eppstein, Suderman, and Wood [CGTA'07] introduced this measure for the visual
complexity of graphs. There are optimal algorithms for trees and worst-case
optimal algorithms for outerplanar graphs, 2-trees, and planar 3-trees. It is
known that every cubic triconnected planar $n$-vertex graph (except $K_4$) has
segment number $n/2+3$, which is the only known universal lower bound for a
meaningful class of planar graphs.
  We show that every triconnected planar 4-regular graph can be drawn using at
most $n+3$ segments. This bound is tight up to an additive constant, improves a
previous upper bound of $7n/4+2$ implied by a more general result of Dujmovi\'c
et al., and supplements the result for cubic graphs. We also give a simple
optimal algorithm for cactus graphs, generalizing the above-mentioned result
for trees. We prove the first linear universal lower bounds for outerpaths,
maximal outerplanar graphs, 2-trees, and planar 3-trees. This shows that the
existing algorithms for these graph classes are constant-factor approximations.
For maximal outerpaths, our bound is best possible and can be generalized to
circular arcs.


title:
On removable singular sets for solutions of higher order differential
  inequalities

abstract:
  We obtain conditions guaranteeing that weak solutions of the differential
inequality $$
  \sum_{|\alpha| = m}
  \partial^\alpha
  a_\alpha (x, u)
  \ge
  f (x)
  g (|u|)
  \quad
  \mbox{in } \Omega \setminus S, $$ has a removable singular set $S \subset
\Omega$, where $\Omega$ is a bounded domain and $a_\alpha$, $f$, and $g$ are
some functions.


title: Pricing options on flow forwards by neural networks in Hilbert space

abstract:
  We propose a new methodology for pricing options on flow forwards by applying
infinite-dimensional neural networks. We recast the pricing problem as an
optimization problem in a Hilbert space of real-valued function on the positive
real line, which is the state space for the term structure dynamics. This
optimization problem is solved by facilitating a novel feedforward neural
network architecture designed for approximating continuous functions on the
state space. The proposed neural net is built upon the basis of the Hilbert
space. We provide an extensive case study that shows excellent numerical
efficiency, with superior performance over that of a classical neural net
trained on sampling the term structure curves.


title: Deep Bayesian ICP Covariance Estimation

abstract:
  Covariance estimation for the Iterative Closest Point (ICP) point cloud
registration algorithm is essential for state estimation and sensor fusion
purposes. We argue that a major source of error for ICP is in the input data
itself, from the sensor noise to the scene geometry. Benefiting from recent
developments in deep learning for point clouds, we propose a data-driven
approach to learn an error model for ICP. We estimate covariances modeling
data-dependent heteroscedastic aleatoric uncertainty, and epistemic uncertainty
using a variational Bayesian approach. The system evaluation is performed on
LiDAR odometry on different datasets, highlighting good results in comparison
to the state of the art.


title: How to optimize an academic team when the outlier member is leaving?

abstract:
  An academic team is a highly-cohesive collaboration group of scholars, which
has been recognized as an effective way to improve scientific output in terms
of both quality and quantity. However, the high staff turnover brings about a
series of problems that may have negative influence on team performance. To
address this challenge, we first detect the tendency of the member who may
potentially leave. Here the outlierness is defined with respect to familiarity,
which is quantified by using collaboration intensity. It is assumed that if a
team member has a higher familiarity with scholars outside the team, then this
member might probably leave the team. To minimize the influence caused by the
leaving of such an outlier member, we propose an optimization solution to find
a proper candidate who can replace the outlier member. Based on random walk
with graph kernel, our solution involves familiarity matching, skill matching,
as well as structure matching. The proposed approach proves to be effective and
outperforms existing methods when applied to computer science academic teams.


title:
Neural network analysis of neutron and X-ray reflectivity data:
  automated analysis using mlreflect, experimental errors and feature
  engineering

abstract:
  This work demonstrates the Python package mlreflect which implements an
optimized pipeline for the automized analysis of reflectometry data using
machine learning. The package combines several training and data treatment
techniques discussed in previous publications. The predictions made by the
neural network are accurate and robust enough to serve as good starting
parameters for an optional subsequent least mean squares (LMS) fit of the data.
It is shown that for a large dataset of 242 reflectivity curves of various thin
films on silicon substrates, the pipeline reliably finds an LMS minimum very
close to a fit produced by a human researcher with the application of physical
knowledge and carefully chosen boundary conditions. Furthermore, the
differences between simulated and experimental data and their implications for
the training and performance of neural networks are discussed. The experimental
test set is used to determine the optimal noise level during training.
Furthermore, the extremely fast prediction times of the neural network are
leveraged to compensate for systematic errors by sampling slight variations of
the data.


title:
Stress overshoot, hysteresis and Bauschinger effect in sheared dense
  colloidal suspensions

abstract:
  The mechanical non-linear response of dense Brownian suspensions of polymer
gel particles is studied experimentally and by means of numerical simulations.
It is shown that the response to the application of a constant shear rate
depends on the previous history of the suspension. When the flow starts from a
suspension at rest, it exhibits an elastic response followed by a stress
overshoot and then a plastic flow regime. Conversely, after flow reversal, the
stress overshoot does not occur, and the apparent elastic modulus is reduced
while numerical simulations reveal that the anisotropy of the local
microstructure is delayed relative to the macroscopic stress.


title: Node polynomials for curves on surfaces

abstract:
  We complete the proof of a theorem we announced and partly proved in [Math.
Nachr., vol. 271 (2004), Thm. 2.5, p. 74]. The theorem concerns a family of
curves on a family of surfaces. It has two parts. The first was proved in
[Math. Nachr.]. It describes a natural cycle that enumerates the curves in the
family with precisely $r$ ordinary nodes. The second part is proved here. It
asserts that, for $r\le 8$, the class of this cycle is given by a computable
universal polynomial in the pushdowns to the parameter space of products of the
Chern classes of the family.


title:
Testing Granger Non-Causality in Panels with Cross-Sectional
  Dependencies

abstract:
  This paper proposes a new approach for testing Granger non-causality on panel
data. Instead of aggregating panel member statistics, we aggregate their
corresponding p-values and show that the resulting p-value approximately bounds
the type I error by the chosen significance level even if the panel members are
dependent. We compare our approach against the most widely used Granger
causality algorithm on panel data and show that our approach yields lower FDR
at the same power for large sample sizes and panels with cross-sectional
dependencies. Finally, we examine COVID-19 data about confirmed cases and
deaths measured in countries/regions worldwide and show that our approach is
able to discover the true causal relation between confirmed cases and deaths
while state-of-the-art approaches fail.


title:
Spontaneous Lorentz symmetry breaking and one-loop effective action in
  the metric-affine bumblebee gravity

abstract:
  In this contribution, we study the metric-affine bumblebee model coupled to
fermions. Proceeding in a manner different from [1, 2], we find the exact
result for the fermionic determinant in the Einstein frame, including all
orders in the non-minimal coupling $\xi$. We demonstrate that the axial
contributions are at least of second order in the perturbative expansion of
$\xi$. Furthermore, we compute the one-loop effective potential within the weak
field approximation.


title: Nonstationary Dual Averaging and Online Fair Allocation

abstract:
  We consider the problem of fairly allocating items to a set of individuals,
when the items are arriving online. A central solution concept in fair
allocation is competitive equilibrium: every individual is endowed with a
budget of faux currency, and the resulting competitive equilibrium is used to
allocate. For the online fair allocation context, the PACE algorithm of Gao et
al. [2021] leverages the dual averaging algorithm to approximate competitive
equilibria. The authors show that, when items arrive i.i.d, the algorithm
asymptotically achieves the fairness and efficiency guarantees of the offline
competitive equilibrium allocation. However, real-world data is typically not
stationary. One could instead model the data as adversarial, but this is often
too pessimistic in practice. Motivated by this consideration, we study an
online fair allocation setting with nonstationary item arrivals. To address
this setting, we first develop new online learning results for the dual
averaging algorithm under nonstationary input models. We show that the dual
averaging iterates converge in mean square to both the underlying optimal
solution of the ``true'' stochastic optimization problem as well as the
``hindsight'' optimal solution of the finite-sum problem given by the sample
path. Our results apply to several nonstationary input models: adversarial
corruption, ergodic input, and block-independent (including periodic) input.
Here, the bound on the mean square error depends on a nonstationarity measure
of the input. We recover the classical bound when the input data is i.i.d. We
then show that our dual averaging results imply that the PACE algorithm for
online fair allocation simultaneously achieves ``best of both worlds''
guarantees against any of these input models. Finally, we conduct numerical
experiments which show strong empirical performance against nonstationary
inputs.


title:
Next-to-next-to-leading-order QCD corrections to $J/\psi+\chi_{c0,1,2}$
  production at $B$ factory

abstract:
  We compute the next-to-next-to-leading-order (NNLO) perturbative corrections
to the exclusive channels $e^+e^-\to J/\psi+\chi_{cJ}$ ($J=0,1,2$) at
$\sqrt{s}=10.58$ GeV within the nonrelativistic QCD (NRQCD) factorization
framework. The validity of NRQCD factorization at ${\cal O}(\alpha_s^2)$ has
been confirmed for these double-charmonium exclusive production processes. We
analyze the impact of the NNLO perturbative corrections on the polarized and
unpolarized cross sections, as well as the $J/\psi$ angular distributions,
which largely reduce the renormalization scale dependence but lower the NLO
NRQCD predictions to some extent for $\chi_{c0,1}$. With high numerical
accuracy, our NNLO predictions for $\sigma(J/\psi+\chi_{c1,2})$ are compatible
with the upper limit of the \texttt{Belle} measurement. Although the finest
prediction for $\sigma(J/\psi+\chi_{c0})$ is consistent with both
\texttt{Belle} and \texttt{BaBar} measurements within uncertainties, there
still exists serious tension between the predicted and the measured profiles
for the $J/\psi$ angular distribution. Regarding the bright observation
prospect of the $e^+e^-\to J/\psi+\chi_{c1,2}$ channels in \texttt{Belle 2}
experiment, it is interesting to compare the future measurements with our NNLO
predictions. The more accurate measurement of $e^+e^-\to J/\psi+\chi_{0}$ at
\texttt{Belle 2} will also help to clarify the long-standing puzzle of $J/\psi$
angular distribution.


title: Image Classification on Small Datasets via Masked Feature Mixing

abstract:
  Deep convolutional neural networks require large amounts of labeled data
samples. For many real-world applications, this is a major limitation which is
commonly treated by augmentation methods. In this work, we address the problem
of learning deep neural networks on small datasets. Our proposed architecture
called ChimeraMix learns a data augmentation by generating compositions of
instances. The generative model encodes images in pairs, combines the features
guided by a mask, and creates new samples. For evaluation, all methods are
trained from scratch without any additional data. Several experiments on
benchmark datasets, e.g. ciFAIR-10, STL-10, and ciFAIR-100, demonstrate the
superior performance of ChimeraMix compared to current state-of-the-art methods
for classification on small datasets.


title: Minimally globally rigid graphs

abstract:
  A graph $G = (V,E)$ is globally rigid in $\mathbb{R}^d$ if for any generic
placement $p : V \rightarrow \mathbb{R}^d$ of the vertices, the edge lengths
$\left\lVert p(u) - p(v)\right\rVert, uv \in E$ uniquely determine $p$, up to
congruence. In this paper we consider minimally globally rigid graphs, in which
the deletion of an arbitrary edge destroys global rigidity. We prove that if
$G=(V,E)$ is minimally globally rigid in $\mathbb{R}^d$ on at least $d+2$
vertices, then $|E|\leq (d+1)|V|-\binom{d+2}{2}$. This implies that the minimum
degree of $G$ is at most $2d+1$. We also show that the only graph in which the
upper bound on the number of edges is attained is the complete graph $K_{d+2}$.
It follows that every minimally globally rigid graph in $\mathbb{R}^d$ on at
least $d+3$ vertices is flexible in $\mathbb{R}^{d+1}$.
  As a counterpart to our main result on the sparsity of minimally globally
rigid graphs, we show that in two dimensions, dense graphs always contain
non-trivial globally rigid subgraphs. More precisely, if some graph $G=(V,E)$
satisfies $|E|\geq 5|V|$, then $G$ contains a globally rigid subgraph on at
least seven vertices in $\mathbb{R}^2$. If the well-known ``sufficient
connectivity conjecture'' is true, then this result also extends to higher
dimensions.
  Finally, we discuss a conjectured strengthening of our main result, which
states that if a pair of vertices $\{u,v\}$ is linked in $G$ in
$\mathbb{R}^{d+1}$, then $\{u,v\}$ is globally linked in $G$ in $\mathbb{R}^d$.
We prove this conjecture in the $d=1,2$ cases, along with a variety of related
results.


title:
Measurement of Energy Spectrum and Elemental Composition of PeV Cosmic
  Rays: Open Problems and Prospects

abstract:
  Cosmic rays represent one of the most important energy transformation
processes of the universe. They bring information about the surrounding
universe, our galaxy, and very probably also the extragalactic space, at least
at the highest observed energies. More than one century after their discovery,
we have no definitive models yet about the origin, acceleration and propagation
processes of the radiation. The main reason is that there are still significant
discrepancies among the results obtained by different experiments located at
ground level, probably due to unknown systematic uncertainties affecting the
measurements. In this document, we will focus on the detection of galactic
cosmic rays from ground with air shower arrays up to 10$^{18}$ eV. The aim of
this paper is to discuss the conflicting results in the 10$^{15}$ eV energy
range and the perspectives to clarify the origin of the so-called `knee' in the
all-particle energy spectrum, crucial to give a solid basis for models up to
the end of the cosmic ray spectrum. We will provide elements useful to
understand the basic techniques used in reconstructing primary particle
characteristics (energy, mass, and arrival direction) from the ground, and to
show why indirect measurements are difficult and results are still conflicting.


title: On discrimination between classes of distribution tails

abstract:
  We propose the test for distinguishing between two classes of distribution
tails using only the largest order statistics of the sample and state its
consistency. We do not assume belonging the corresponding distribution
functions to any maximum domain of attraction.


title:
Awakening City: Traces of the Circadian Rhythm within the Mobile Phone
  Network Data

abstract:
  In this study, Call Detail Records (CDR), covering Budapest, Hungary has been
processed to analyze the circadian rhythm of the subscribers. An indicator,
called wake-up time, is introduced to describe a behavior of a group of
subscribers. It is defined as the time, when the mobile phone activity of a
group rises in the morning. Its counterpart is the time, when the activity
falls in the evening. Inhabitant and area-based aggregation are also presented.
The former is to consider the people who live in an area, the latter uses the
transit activity in an area to describe the behavior of a part of the city. The
opening hours of the malls and the nightlife of the party district was used to
demonstrate this application, as real-life examples. The proposed approach was
also used to estimate the working hours of the workplaces. The findings are in
a good agreement with practice in Hungary, and also support the workplace
detection method. Negative correlation was found between wake-up time and
mobility indicators (Entropy, Radius of Gyration): On workdays, people wake up
earlier and travel more, on holidays it is quite the contrary. The wake-up time
was evaluated in different socioeconomic classes, using housing prices and
mobile phones prices, as well. It was found that lower socioeconomic groups
tend to wake up earlier.


title:
Optical Writing and Electro-Optic Imaging of Reversible Space Charges in
  Semi-Insulating CdTe Diodes

abstract:
  Deep levels control the space charge in electrically compensated
semi-insulating materials. They limit the performance of radiation detectors
but their interaction with free carriers can be favorably exploited in these
devices to manipulate the spatial distribution of the electric field by optical
beams. By using semi-insulating CdTe diodes as a case study, our results show
that optical doping functionalities are achieved. As such, a highly stable,
flux-dependent, reversible and spatially localized space charge is induced by a
line-shaped optical beam focused on the cathode contact area. Real-time
non-invasive imaging of the electric field is obtained through the Pockels
effect. A simple and convenient method to retrieve the two-dimensional electric
field components is presented. Numerical simulations involving just one deep
level responsible for the electrical compensation confirm the experimental
findings and help to identify the underlying mechanism and critical parameters
enabling the optical writing functionalities.


title:
Learning about treatment effects in a new target population under
  transportability assumptions for relative effect measures

abstract:
  Epidemiologists and applied statisticians often believe that relative effect
measures conditional on covariates, such as risk ratios and mean ratios, are
``transportable'' across populations. Here, we examine the identification of
causal effects in a target population using an assumption that conditional
relative effect measures (e.g., conditional risk ratios or mean ratios) are
transportable from a trial to the target population. We show that
transportability for relative effect measures is largely incompatible with
transportability for difference effect measures, unless the treatment has no
effect on average or one is willing to make even stronger transportability
assumptions, which imply the transportability of both relative and difference
effect measures. We then describe how marginal causal estimands in a target
population can be identified under the assumption of transportability of
relative effect measures, when we are interested in the effectiveness of a new
experimental treatment in a target population where the only treatment in use
is the control treatment evaluated in the trial. We extend these results to
consider cases where the control treatment evaluated in the trial is only one
of the treatments in use in the target population, under an additional partial
exchangeability assumption in the target population (i.e., a partial assumption
of no unmeasured confounding in the target population). We also develop
identification results that allow for the covariates needed for
transportability of relative effect measures to be only a small subset of the
covariates needed to control confounding in the target population. Last, we
propose estimators that can be easily implemented in standard statistical
software.


title:
IOTLB-SC: An Accelerator-Independent Leakage Source in Modern Cloud
  Systems

abstract:
  Recent research in micro-architectural attacks has uncovered a variety of
vulnerabilities on shared compute devices like CPUs and GPUs which pose a
substantial thread to cloud service providers and customers alike. Cloud
service providers have therefore moved towards flexible systems that prioritize
re-arrangeable hardware components that are not shared between users to
minimize attack surfaces while retaining scalability. In this work, we show
that for the sake of system security it is necessary to consider not only the
security of the processors and peripherals of a system but also the security of
the subsystems that connect them. In particular, we investigate the
side-channel leakage potential of the I/O translation look-aside buffer (IOTLB)
used in I/O memory management units (IOMMUs) to cache address translations. To
exploit the IOTLB, we design a hardware module deployed to an FPGA to help us
perform precise timing measurements. For the first time, we prove that the
IOTLB is the source of a timing-based side-channel leakage and use it to create
two covert channels from CPU to peripheral and between peripherals. While the
first channel easily achieves an error rate of only 30%, the latter proved to
be very reliable as nearly no errors occur. We present a close look at web
fingerprints collected through this side-channel, and we examine the I/O
operation of a GPU-accelerated SQL database. We then discuss several methods to
remedy the observed side-channel leakages, including application design
techniques, peripheral layout within existing systems, and micro-architectural
features that could harden future IOMMUs.


title:
On continious billiard and quasigeodesic flows characterizing alcoves
  and isosceles tetrahedra

abstract:
  We characterize fundamental domains of affine reflection groups as those
polyhedral convex bodies which support a continuous billiard dynamics. We
interpret this characterization in the broader context of Alexandrov geometry
and prove an analogous characterization for isosceles tetrahedra in terms of
continuous quasigeodesic flows. Moreover, we show that for general convex
bodies the billiard dynamics is continuous if the boundary is sufficiently
regular. In particular, billiard trajectories converge to geodesics on the
boundary in this case. Our proof of the latter continuity statement is partly
based on Alexandrov geometry methods that we discuss resp. establish first.


title:
Fast methods to track grain coagulation and ionization. II. Extension to
  thermal ionization

abstract:
  Thermal ionization is a critical process at temperatures T > 10 3 K,
particularly during star formation. An increase in ionization leads to a
decrease in nonideal magnetohydrodynamics (MHD) resistivities, which has a
significant impact on protoplanetary disks and protostar formation. We
developed an extension of the fast computational ionization method presented in
our recent paper to include thermal ionization. The model can be used to
inexpensively calculate the density of ions and electrons and the electric
charge of each size of grains for an arbitrary size distribution. This tool
should be particularly useful for the self-consistent calculation of nonideal
MHD resistivities in multidimensional simulations, especially of protostellar
collapse and protoplanetary disks.


title: Asymptotic cones of snowflake groups and the strong shortcut property

abstract:
  We exhibit an infinite family of snowflake groups all of whose asymptotic
cones are simply connected. Our groups have neither polynomial growth nor
quadratic Dehn function, the two usual sources of this phenomenon. We further
show that each of our groups has an asymptotic cone containing an isometrically
embedded circle or, equivalently, has a Cayley graph that is not strongly
shortcut. These are the first examples of groups whose asymptotic cones contain
`metrically nontrivial' loops but no topologically nontrivial ones.


title: Dyck paths with catastrophes modulo the positions of a given pattern

abstract:
  For any pattern $p$ of length at most two, we provide generating functions
and asymptotic approximations for the number of $p$-equivalence classes of Dyck
paths with catastrophes, where two paths of the same length are $p$-equivalent
whenever the positions of the occurrences of the pattern $p$ are the same.


title:
Absorptive filters for quantum circuits: Efficient fabrication and
  cryogenic power handling

abstract:
  We present an efficient fabrication method for absorptive microwave filters
based on Eccosorb CR-124. Filters are fabricated from readily available parts
and their cut-off frequency can be set by their length. They exhibit desirable
properties such as a very large and deep stop band with rejection beyond 120 dB
at least up to 40 GHz, more than 10 dB return loss in both the pass and the
stop band as well as an error-function shaped step response without overshoot.
Measurements at very low temperature show that the filters thermalize on a time
scale of the order of 100 s and that they can absorb power as high as 100 nW
with their noise temperature staying remarkably cool, below 100 mK. These
properties make the filters ideal for cryogenic filtering and filtering of IF
port signals of mixers.


title:
A Complete Criterion for Value of Information in Soluble Influence
  Diagrams

abstract:
  Influence diagrams have recently been used to analyse the safety and fairness
properties of AI systems. A key building block for this analysis is a graphical
criterion for value of information (VoI). This paper establishes the first
complete graphical criterion for VoI in influence diagrams with multiple
decisions. Along the way, we establish two important techniques for proving
properties of multi-decision influence diagrams: ID homomorphisms are
structure-preserving transformations of influence diagrams, while a Tree of
Systems is collection of paths that captures how information and control can
flow in an influence diagram.


title: Canonical metrics on holomorphic fibre bundles

abstract:
  In this article we completely describe the existence of canonical metrics,
known as optimal symplectic connections, on isotrivial K\"ahler fibrations. In
this setting an optimal symplectic connection is induced from a
Hermite--Einstein connection on the holomorphic principal bundle of relative
automorphisms, and the Hitchin--Kobayashi correspondence asserts the existence
of such a connection precisely when the principal bundle is polystable.
Combined with results of Dervan and Sektnan this generates many new examples of
cscK metrics on the total space of holomorphic fibre bundles. Our results
indicate that in general the optimal symplectic connection equation should be
viewed as a generalisation of the Hermite--Einstein equation to holomorphic
fibrations where the complex structure of the fibres varies.


title: Production of $P_{c}$(4312) state in electron-proton collisions

abstract:
  We study the cross sections for the electro-production of $P_c(4312)$
particle, a recently discovered pentaquark state, in electron-proton collisions
assuming possible quantum numbers to be $J^{P}=\frac{1}{2}^\pm,
\frac{3}{2}^\pm$. $\sqrt{s}$ is set to the energy of the future Electron Ion
Collider at Brookhaven National Laboratory, in order to asses the possibility
of the measurement in this facility. One can discriminate the spin of
$P_c(4312)$ by comparing the pseudorapidity distribution in two different
polarization configurations for proton and electron beams. Furthermore, the
parity of $P_c(4312)$ can be discerned by analyzing the decay angle in the $P_c
\rightarrow p +J/\psi$ channel. As the multiplicity of $P_c$ production in our
calculation is large, the EIC can be considered as a future facility for
precision measurement of heavy pentaquarks.


title:
Mirror Descent Strikes Again: Optimal Stochastic Convex Optimization
  under Infinite Noise Variance

abstract:
  We study stochastic convex optimization under infinite noise variance.
Specifically, when the stochastic gradient is unbiased and has uniformly
bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the
convergence rate of the Stochastic Mirror Descent algorithm with a particular
class of uniformly convex mirror maps, in terms of the number of iterations,
dimensionality and related geometric parameters of the optimization problem.
Interestingly this algorithm does not require any explicit gradient clipping or
normalization, which have been extensively used in several recent empirical and
theoretical works. We complement our convergence results with
information-theoretic lower bounds showing that no other algorithm using only
stochastic first-order oracles can achieve improved rates. Our results have
several interesting consequences for devising online/streaming stochastic
approximation algorithms for problems arising in robust statistics and machine
learning.


title: Fusion of Probability Density Functions

abstract:
  Fusing probabilistic information is a fundamental task in signal and data
processing with relevance to many fields of technology and science. In this
work, we investigate the fusion of multiple probability density functions
(pdfs) of a continuous random variable or vector. Although the case of
continuous random variables and the problem of pdf fusion frequently arise in
multisensor signal processing, statistical inference, and machine learning, a
universally accepted method for pdf fusion does not exist. The diversity of
approaches, perspectives, and solutions related to pdf fusion motivates a
unified presentation of the theory and methodology of the field. We discuss
three different approaches to fusing pdfs. In the axiomatic approach, the
fusion rule is defined indirectly by a set of properties (axioms). In the
optimization approach, it is the result of minimizing an objective function
that involves an information-theoretic divergence or a distance measure. In the
supra-Bayesian approach, the fusion center interprets the pdfs to be fused as
random observations. Our work is partly a survey, reviewing in a structured and
coherent fashion many of the concepts and methods that have been developed in
the literature. In addition, we present new results for each of the three
approaches. Our original contributions include new fusion rules, axioms, and
axiomatic and optimization-based characterizations; a new formulation of
supra-Bayesian fusion in terms of finite-dimensional parametrizations; and a
study of supra-Bayesian fusion of posterior pdfs for linear Gaussian models.


title: Lattice path matroids and quotients

abstract:
  We characterize the quotients among lattice path matroids (LPMs) in terms of
their diagrams. This characterization allows us to show that ordering LPMs by
quotients yields a graded poset, whose rank polynomial has the Narayana numbers
as coefficients.
  Furthermore, we study full lattice path flag matroids and show that --
contrary to arbitrary positroid flag matroids -- they correspond to points in
the nonnegative flag variety. At the basis of this result lies an
identification of certain intervals of the strong Bruhat order with lattice
path flag matroids.
  A recent conjecture of Mcalmon, Oh, and Xiang states a characterization of
quotients of positroids. We use our results to prove this conjecture in the
case of LPMs.


title:
Periodic temporal environmental variations induce coexistence in
  resource competition models

abstract:
  Natural ecosystems, in particular on the microbial scale, are inhabited by a
large number of species. The population size of each species is affected by
interactions of individuals with each other and by spatial and temporal changes
in environmental conditions, such as resource abundance. Here, we use a generic
population dynamics model to study how, and under what conditions, a periodic
temporal environmental variation can alter an ecosystem's composition and
biodiversity. We demonstrate that using time scale separation allows one to
qualitatively predict the long-term population dynamics of interacting species
in varying environments. We show that the notion of competitive exclusion, a
well-known principle that applies for constant environments, can be extended to
temporally varying environments if the time scale of environmental changes
(e.g., the circadian cycle of a host) is much faster than the time scale of
population growth (doubling time in bacteria). When these time scales are
similar, our analysis shows that a varying environment deters the system from
reaching a steady state, and coexistence between multiple species becomes
possible. Our results posit that biodiversity can in parts be attributed to
natural environmental variations.


title: Derived projectivizations of complexes

abstract:
  In this paper, we study the counterpart of Grothendieck's projectivization
construction in the context of derived algebraic geometry. Our main results are
as follows: First, we define the derived projectivization of a connective
complex, study its fundamental properties such as finiteness properties and
functorial behaviors, and provide explicit descriptions of their relative
cotangent complexes, We then focus on the derived projectivizations of
complexes of perfect-amplitude contained in $[0,1]$. In this case, we prove a
generalized Serre's theorem, a derived version of Beilinson's relations, and
establish semiorthogonal decompositions for their derived categories. Finally,
we show that many moduli problems fit into the framework of derived
projectivizations, such as moduli spaces that arise in Hecke correspondences.
We apply our results to these situations.


title: Spin-orbit enabled all-electrical readout of chiral spin-textures

abstract:
  Chirality and topology are intimately related fundamental concepts, which are
heavily explored to establish spin-textures as potential magnetic bits in
information technology. However, this ambition is inhibited since electrical
reading of chiral attributes is highly non-trivial with conventional current
perpendicular-to-plane (CPP) sensing devices. Here we demonstrate from
extensive first-principles simulations and multiple scattering expansion the
emergence of the chiral spin-mixing magnetoresistance (C-XMR) enabling highly
efficient all-electrical readout of the chirality and helicity of respectively
one- and two-dimensional magnetic states of matter. It is linear with
spin-orbit coupling in contrast to the quadratic dependence associated with the
newly unveiled non-local spin-mixing anisotropic MR (X-AMR). Such transport
effects are systematised on various non-collinear magnetic states --
spin-spirals and skyrmions -- and compared to the uncovered
spin-orbit-independent multi-site magnetoresistances. Owing to their simple
implementation in readily available reading devices, the proposed
magnetoresistances offer exciting and decisive ingredients to explore with
all-electrical means the rich physics of topological and chiral magnetic
objects.


title:
Confronting dark fermion with a doubly charged Higgs in the left-right
  symmetric model

abstract:
  We consider a fermionic dark matter (DM) in the left-right symmetric
framework by introducing a pair of vector-like (VL) doublets in the particle
spectrum. The stability of the DM is ensured through an unbroken
$\mathcal{Z}_2$ symmetry. We explore the parameter space of the model
compatible with the observed relic density and direct and indirect detection
cross sections. The presence of charged dark fermions opens up an interesting
possibility for the doubly charged Higgs signal at LHC and ILC. The signal for
the doubly charged scalar decaying into the dark sector is analyzed in
multilepton final states for a few representative parameter choices consistent
with DM observations.


title:
Funding Covid-19 research: Insights from an exploratory analysis using
  open data infrastructures

abstract:
  To analyse the outcomes of the funding they provide, it is essential for
funding agencies to be able to trace the publications resulting from their
funding. We study the open availability of funding data in Crossref, focusing
on funding data for publications that report research related to Covid-19. We
also present a comparison with the funding data available in two proprietary
bibliometric databases: Scopus and Web of Science. Our analysis reveals a
limited coverage of funding data in Crossref. It also shows problems related to
the quality of funding data, especially in Scopus. We offer recommendations for
improving the open availability of funding data in Crossref.


title:
Mass-energy threshold dynamics for the focusing NLS with a repulsive
  inverse-power potential

abstract:
  In this paper we study long time dynamics (i.e., scattering and blow-up) of
solutions for the focusing NLS with a repulsive inverse-power potential and
with initial data lying exactly at the mass-energy threshold, namely, when
$E_{V}(u_{0})M(u_{0})=E_{0}(Q)M(Q)$. Moreover, we prove failure of the uniform
space-time bounds at the mass-energy threshold.


title: Matching Theory and Barnette's Conjecture

abstract:
  Barnette's Conjecture claims that all cubic, 3-connected, planar, bipartite
graphs are Hamiltonian. We give a translation of this conjecture into the
matching-theoretic setting. This allows us to relax the requirement of
planarity to give the equivalent conjecture that all cubic, 3-connected,
Pfaffian, bipartite graphs are Hamiltonian.
  A graph, other than the path of length three, is a brace if it is bipartite
and any two disjoint edges are part of a perfect matching. Our perspective
allows us to observe that Barnette's Conjecture can be reduced to cubic, planar
braces. We show a similar reduction to braces for cubic, 3-connected, bipartite
graphs regarding four stronger versions of Hamiltonicity. Note that in these
cases we do not need planarity. As a practical application of these results, we
provide some supplements to a generation procedure for cubic, 3-connected,
planar, bipartite graphs discovered by Holton et al. [Hamiltonian Cycles in
Cubic 3-Connected Bipartite Planar Graphs, JCTB, 1985]. These allow us to check
whether a graph we generated is a brace.


title:
Nature and Energy Source of the Strong Waveforms Recorded during the
  2008 Wenchuan Earthquake

abstract:
  Earthquakes are indeed triggered by fault dislocations, but whether this
process alone can produce the actual earthquake energy released by the
mainshock has long been questioned. Therefore, exploring the true source of
energy that causes earthquakes after the first motion is necessary. Based on
analyses of the waveforms and ray paths at seismic stations close to the
epicenter, it is considered that strong earthquake vibrations may not be caused
by S-waves. It is also proposed that the reservoirs in sedimentary strata
contain large amounts of high-pressure fluids, whose pressures can be released
under certain conditions; this release of pressure may be an important
component of the main earthquake energy. When a natural fault ruptures and
penetrates a reservoir with a large area, the elastic energy produced by the
release of pressure can reach the energy released by an earthquake of magnitude
8.0. Artificial engineering activities can lead to small-scale fluid pressure
release phenomena, such as blowouts during drilling and earthquakes induced by
hydraulic fracturing. Much direct and indirect evidence, such as the
characteristics of seismic waves in the time and frequency domains recorded
during the Wenchuan earthquake, explosion phenomena observed on the ground and
cores obtained by scientific drilling, indicates the possibility of such energy
release. We propose that seismicity can be divided into three stages: the
microfracturing stage, in which there is fluid activity and can produce an
electrokinetic effect; the significant fracturing stage after the initial
movement; and the strong earthquake stage caused by fluid pressure release.


title: A posteriori error estimates for Darcy-Forchheimer's problem

abstract:
  This work deals with the a posteriori error estimates for the
Darcy-Forchheimer problem. We introduce the corresponding variational
formulation and discretize it by using the finite-element method. A posteriori
error estimate with two types of computable error indicators is showed. The
first one is linked to the linearization and the second one to the
discretization. Finally, numerical computations are performed to show the
effectiveness of the error indicators.


title: PRECISE localizations of repeating Fast Radio Bursts

abstract:
  Fast Radio Bursts (FRBs) are extremely luminous and brief signals (with
duration of milliseconds or even shorter) of extragalactic origin. Despite the
fact that hundreds of FRBs have been discovered to date, their nature still
remains unclear. Precise localizations of FRBs can unveil their host galaxies
and local environments -- and thus shed light on the physical processes that
led to the burst production. However, this has only been achieved for a few
FRBs to date. The European VLBI Network (EVN) is currently the only instrument
capable of localizing FRBs down to the milliarcsecond level. This level of
precision was critical to associate the first localized FRB, 20121102A, to a
star-forming region in a low-metallicity dwarf galaxy and physically related it
to a compact persistent radio source. Analogously, a second repeating FRB,
20180916B, was found to just outside the edge of a prominent star-forming
region of a nearby spiral galaxy. The PRECISE project (Pinpointing REpeating
ChIme Sources with EVN dishes), starting from 2019, has observed hundreds of
hours per year with a subset of EVN telescopes with the goal of localizing
repeating FRBs discovered by the CHIME/FRB Collaboration. The ultimate goal of
PRECISE is to disentangling the environments where FRBs can be produced. Here
we present the state of the art of the FRB field, the PRECISE project, and the
localizations achieved until now, which have unveiled a variety of environments
where FRBs can be found that challenges the current models.


title:
Cyclical Variational Bayes Monte Carlo for Efficient Multi-Modal
  Posterior Distributions Evaluation

abstract:
  Statistical model updating is frequently used in engineering to calculate the
uncertainty of some unknown latent parameters when a set of measurements on
observable quantities is given. Variational inference is an alternative
approach to sampling methods that has been developed by the machine learning
community to estimate posterior approximations through an optimization
approach. In this paper, the Variational Bayesian Monte Carlo (VBMC) method is
investigated with the purpose of dealing with statistical model updating
problems in engineering involving expensive-to-run models. This method combines
the active-sampling Bayesian quadrature with a Gaussian-process based
variational inference to yield a non-parametric estimation of the posterior
distribution of the identified parameters involving few runs of the
expensive-to-run model. VBMC can also be used for model selection as it
produces an estimation of the model's evidence lower bound. In this paper, a
variant of the VBMC algorithm is developed through the introduction of a
cyclical annealing schedule into the algorithm. The proposed cyclical VBMC
algorithm allows to deal effectively with multi-modal posteriors by having
multiple cycles of exploration and exploitation phases. Four numerical examples
are used to compare the standard VBMC algorithm, the monotonic VBMC, the
cyclical VBMC and the Transitional Ensemble Markov Chain Monte Carlo (TEMCMC).
Overall, it is found that the proposed cyclical VBMC approach yields accurate
results with a very reduced number of model runs compared to the state of the
art sampling technique TEMCMC. In the presence of potential multi-modal
problems, the proposed cyclical VBMC algorithm outperforms all the other
approaches in terms of accuracy of the resulting posterior.