title: Modifying the Dyson Series for Unstable Particles and Resonances

abstract:
  In this work, we introduce a modification of the Dyson series based on the
perturbative unitarity as a starting point. The presented approach
systematically avoids singularities and double-counting related to the presence
of unstable particles as intermediate states and, at the same time, it does not
rely on a specific choice of the renormalization scheme.


title:
Rings and arcs around evolved stars -- III. Physical conditions of the
  ring-like structures in the planetary nebula IC 4406 revealed by MUSE

abstract:
  We present the analysis of Very Large Telescope (VLT) Multi Unit
Spectroscopic Explorer (MUSE) observations of the planetary nebula (PN) IC
4406. MUSE images in key emission lines are used to unveil the presence of at
least 5 ring-like structures North and South of the main nebula of IC 4406.
MUSE spectra are extracted from the rings to unambiguously assess for the first
time in a PN their physical conditions, electron density (ne) and temperature
(Te). The rings are found to have similar Te than the rim of the main nebula,
but smaller ne. Ratios between different ionic species suggest that the rings
of IC 4406 have a lower ionization state than the main cavity, in contrast to
what was suggested for the rings in NGC6543, the Cat's Eye Nebula.


title: Low-Degree Multicalibration

abstract:
  Introduced as a notion of algorithmic fairness, multicalibration has proved
to be a powerful and versatile concept with implications far beyond its
original intent. This stringent notion -- that predictions be well-calibrated
across a rich class of intersecting subpopulations -- provides its strong
guarantees at a cost: the computational and sample complexity of learning
multicalibrated predictors are high, and grow exponentially with the number of
class labels. In contrast, the relaxed notion of multiaccuracy can be achieved
more efficiently, yet many of the most desirable properties of multicalibration
cannot be guaranteed assuming multiaccuracy alone. This tension raises a key
question: Can we learn predictors with multicalibration-style guarantees at a
cost commensurate with multiaccuracy?
  In this work, we define and initiate the study of Low-Degree
Multicalibration. Low-Degree Multicalibration defines a hierarchy of
increasingly-powerful multi-group fairness notions that spans multiaccuracy and
the original formulation of multicalibration at the extremes. Our main
technical contribution demonstrates that key properties of multicalibration,
related to fairness and accuracy, actually manifest as low-degree properties.
Importantly, we show that low-degree multicalibration can be significantly more
efficient than full multicalibration. In the multi-class setting, the sample
complexity to achieve low-degree multicalibration improves exponentially (in
the number of classes) over full multicalibration. Our work presents compelling
evidence that low-degree multicalibration represents a sweet spot, pairing
computational and sample efficiency with strong fairness and accuracy
guarantees.


title:
Recommendations in a Multi-Domain Setting: Adapting for Customization,
  Scalability and Real-Time Performance

abstract:
  In this industry talk at ECIR'2022, we illustrate how to build a modern
recommender system that can serve recommendations in real-time for a diverse
set of application domains. Specifically, we present our system architecture
that utilizes popular recommendation algorithms from the literature such as
Collaborative Filtering, Content-based Filtering as well as various neural
embedding approaches (e.g., Doc2Vec, Autoencoders, etc.). We showcase the
applicability of our system architecture using two real-world use-cases, namely
providing recommendations for the domains of (i) job marketplaces, and (ii)
entrepreneurial start-up founding. We strongly believe that our experiences
from both research- and industry-oriented settings should be of interest for
practitioners in the field of real-time multi-domain recommender systems.


title:
Accurate Metallicities for Very Metal-Poor Stars from the Ca~II Infrared
  Triplet

abstract:
  The Ca~II H \& K lines are among the few features available to infer the
metallicity of extremely metal-poor stars from medium-resolution spectroscopy.
Unfortunately, these lines can overlap with absorption produced in the
intervening interstellar medium, introducing systematic errors in the derived
metallicities. The strength of the Ca~II infrared triplet lines can also be
measured at extremely low metallicities, and it is not affected by interstellar
absorption, but suffers significant departures from Local Thermodynamical
Equilibrium (LTE). We investigate the feasibility of adopting the Ca~II
infrared triplet as a metallicity indicator in extremely metal-poor stars using
state-of-the art Non-LTE models including the most recent atomic data. We find
that the triplet lines exhibit Non-LTE abundance corrections that can exceed
0.5\,dex. When interstellar absorption affecting the Ca~II resonance lines is
accounted for using high-resolution observations, the agreement between Non-LTE
abundances for the triplet and those for the resonance lines, with only minor
departures from LTE, is excellent. Non-LTE effects strengthen the Ca~II IR
triplet lines, facilitating measurements at very low metallicities, compared
with LTE estimates, down to $\rm [Fe/H]=-6.0$. This result has important
implications for the discovery of primitive stars in our Galaxy and others,
since instruments are most sensitive at red/near-infrared wavelengths, and tens
of millions of spectra covering the Ca~II IR triplet will soon become available
from the Gaia, DESI, WEAVE, and PFS missions.


title:
Lefschetz properties of some codimension three Artinian Gorenstein
  algebras

abstract:
  Codimension two Artinian algebras $A$ have the strong and weak Lefschetz
properties provided the characteristic is zero or greater than the socle
degree. It is open to what extent such results might extend to codimension
three AG algebras - the most promising results so far have concerned the weak
Lefschetz property for such algebras. We here show that every standard-graded
codimension three Artinian Gorenstein algebra $A$ having low maximum value of
the Hilbert function - at most six - has the strong Lefschetz property,
provided that the characteristic is zero. When the characteristic is greater
than the socle degree of $A$, we show that $A$ is almost strong Lefschetz. This
quite modest result is nevertheless arguably the most encompassing so far
concerning the strong Lefschetz property for graded codimension three AG
algebras.


title: Finite System Size Correction to NLO Scattering in $\phi^4$ Theory

abstract:
  We compute $2\rightarrow2$ scattering in massive $\phi^4$ theory on $\mathbb
R^{1,m}\times T^n$ to NLO. We perform the calculations using "denominator
regularization" instead of the usual dimensional regularization, which allows
for asymmetric configurations of the $T^n$. We give a transparent derivation of
and equation for the analytic continuation of the generalized Epstein zeta
function. We show that the Optical Theorem is satisfied and generalize a
conjecture by Hardy on square counting functions. We comment on the
implications.


title: The Diffuse Gamma-Ray Flux from Clusters of Galaxies

abstract:
  The origin of the diffuse gamma-ray background (DGRB) detected by EGRET and
Fermi-LAT, the one that remains after subtracting all individual sources from
the observed gamma-ray sky, is unknown. The DGRB possibly encompasses
contributions from different source populations such as star-forming galaxies,
starburst galaxies, active galactic nuclei, gamma-ray bursts, or galaxy
clusters. Here, we combine cosmological magnetohydrodynamical simulations of
clusters of galaxies with the propagation of CRs using Monte Carlo simulations,
in the redshift range $z\leq 5.0$, and find that the integrated gamma-ray flux
from clusters can contribute up to $100\%$ of the DGRB flux observed by
Fermi-LAT above $100$~GeV, for CR spectral indices $\alpha = 1.5 - 2.5$ and
energy cutoffs $E_{\text{max}} = 10^{16} - 10^{17}$~eV. The flux is dominated
by clusters with masses $10^{13}< M/M_{\odot} < 10^{15}$ and redshift $ z \leq
0.3$. Our results also predict the potential observation of high-energy gamma
rays from clusters by experiments like HAWC, LHAASO, and even the upcoming CTA.


title:
TAE: A Semi-supervised Controllable Behavior-aware Trajectory Generator
  and Predictor

abstract:
  Trajectory generation and prediction are two interwoven tasks that play
important roles in planner evaluation and decision making for intelligent
vehicles. Most existing methods focus on one of the two and are optimized to
directly output the final generated/predicted trajectories, which only contain
limited information for critical scenario augmentation and safe planning. In
this work, we propose a novel behavior-aware Trajectory Autoencoder (TAE) that
explicitly models drivers' behavior such as aggressiveness and intention in the
latent space, using semi-supervised adversarial autoencoder and domain
knowledge in transportation. Our model addresses trajectory generation and
prediction in a unified architecture and benefits both tasks: the model can
generate diverse, controllable and realistic trajectories to enhance planner
optimization in safety-critical and long-tailed scenarios, and it can provide
prediction of critical behavior in addition to the final trajectories for
decision making. Experimental results demonstrate that our method achieves
promising performance on both trajectory generation and prediction.


title:
Viscosity in water from first-principles and deep-neural-network
  simulations

abstract:
  We report on an extensive study of the viscosity of liquid water at
near-ambient conditions, performed within the Green-Kubo theory of linear
response and equilibrium ab initio molecular dynamics (AIMD), based on
density-functional theory (DFT). In order to cope with the long simulation
times necessary to achieve an acceptable statistical accuracy just above
melting, our ab initio approach is enhanced with deep-neural-network potentials
(NNP) force fields, trained and validated on extensive DFT data. This approach
is first validated against AIMD results for the viscosity, obtained by using
the PBE exchange-correlation functional and paying careful attention to crucial
aspects of the statistical data analysis that are often overlooked. We then
train a second NNP to a dataset generated from the SCAN-DFT functional, which
is known to describe significantly better than PBE the H-bonding features of
different phases of water. Close to melting, the viscosity depends very
sensitively on temperature. Once the error resulting from the imperfect
prediction of the melting line is offset by referring the simulated temperature
to the theoretical melting one, our SCAN DFT predictions of the shear viscosity
of water are in very good agreement with experiments.


title: Interactive Visualization of Protein RINs using NetworKit in the Cloud

abstract:
  Network analysis has been applied in diverse application domains. In this
paper, we consider an example from protein dynamics, specifically residue
interaction networks (RINs). In this context, we use NetworKit -- an
established package for network analysis -- to build a cloud-based environment
that enables domain scientists to run their visualization and analysis
workflows on large compute servers, without requiring extensive programming
and/or system administration knowledge. To demonstrate the versatility of this
approach, we use it to build a custom Jupyter-based widget for RIN
visualization. In contrast to existing RIN visualization approaches, our widget
can easily be customized through simple modifications of Python code, while
both supporting a good feature set and providing near real-time speed. It is
also easily integrated into analysis pipelines (e.g., that use Python to feed
RIN data into downstream machine learning tasks).


title:
Bound state of a He-3 atom at the interface of crystal and superfluid
  He-4

abstract:
  The bound state of a He-3 atom at the interface between coexisting
crystalline and superfluid phases of He-4 is studied theoretically by means of
first principle Quantum Monte Carlo simulations. We consider both the case of a
solid/superfluid He-4 interface, as well as that of a few solid layers of He-4
forming on an attractive substrate. It is observed that the He-3 bound state is
sharply localized in a well-defined, quasi-2D layer of He-4 in the region
intermediate between the solid and the liquid. The layer in which the He-3 atom
resides displays an intriguing interplay of atomic localization and
quantum-mechanical exchanges; is not necessarily the first "non-solid" layer,
as suggested in previous studies, and it is affected by the attractive strength
of the substrate.


title: Self-supervised Transformer for Deepfake Detection

abstract:
  The fast evolution and widespread of deepfake techniques in real-world
scenarios require stronger generalization abilities of face forgery detectors.
Some works capture the features that are unrelated to method-specific
artifacts, such as clues of blending boundary, accumulated up-sampling, to
strengthen the generalization ability. However, the effectiveness of these
methods can be easily corrupted by post-processing operations such as
compression. Inspired by transfer learning, neural networks pre-trained on
other large-scale face-related tasks may provide useful features for deepfake
detection. For example, lip movement has been proved to be a kind of robust and
good-transferring highlevel semantic feature, which can be learned from the
lipreading task. However, the existing method pre-trains the lip feature
extraction model in a supervised manner, which requires plenty of human
resources in data annotation and increases the difficulty of obtaining training
data. In this paper, we propose a self-supervised transformer based
audio-visual contrastive learning method. The proposed method learns mouth
motion representations by encouraging the paired video and audio
representations to be close while unpaired ones to be diverse. After
pre-training with our method, the model will then be partially fine-tuned for
deepfake detection task. Extensive experiments show that our self-supervised
method performs comparably or even better than the supervised pre-training
counterpart.


title:
Semilinear elliptic Schr\"odinger equations with singular potentials and
  absorption terms

abstract:
  Let $\Omega \subset \mathbb{R}^N$ ($N \geq 3$) be a $C^2$ bounded domain and
$\Sigma \subset \Omega$ be a compact, $C^2$ submanifold without boundary, of
dimension $k$ with $0\leq k < N-2$. Put $L_\mu = \Delta + \mu d_\Sigma^{-2}$ in
$\Omega \setminus \Sigma$, where $d_\Sigma(x) = \mathrm{dist}(x,\Sigma)$ and
$\mu$ is a parameter. We investigate the boundary value problem (P) $-L_\mu u +
g(u) = \tau$ in $\Omega \setminus \Sigma$ with condition $u=\nu$ on $\partial
\Omega \cup \Sigma$, where $g: \mathbb{R} \to \mathbb{R}$ is a nondecreasing,
continuous function, and $\tau$ and $\nu$ are positive measures. The complex
interplay between the competing effects of the inverse-square potential
$d_\Sigma^{-2}$, the absorption term $g(u)$ and the measure data $\tau,\nu$
discloses different scenarios in which problem (P) is solvable. We provide
sharp conditions on the growth of $g$ for the existence of solutions. When $g$
is a power function, namely $g(u)=|u|^{p-1}u$ with $p>1$, we show that problem
(P) admits several critical exponents in the sense that singular solutions
exist in the subcritical cases (i.e. $p$ is smaller than a critical exponent)
and singularities are removable in the supercritical cases (i.e. $p$ is greater
than a critical exponent). Finally, we establish various necessary and
sufficient conditions expressed in terms of appropriate capacities for the
solvability of (P).


title:
Generating gravitational waveform libraries of exotic compact binaries
  with deep learning

abstract:
  Current gravitational wave (GW) detections rely on the existence of libraries
of theoretical waveforms. Consequently, finding new physics with GWs requires
libraries of non-standard models, which are computationally demanding. We
discuss how deep learning frameworks can be used to generate new waveforms
"learned" from a simulation dataset obtained, say, from numerical relativity
simulations. Concretely, we use the WaveGAN architecture of a generative
adversarial network (GAN). As a proof of concept we provide this neural network
(NN) with a sample of ($>500$) waveforms from the collisions of exotic compact
objects (Proca stars), obtained from numerical relativity simulations. Dividing
the sample into a training and a validation set, we show that after a
sufficiently large number of training epochs the NN can produce from 12\% to
25\% of the synthetic waveforms with an overlapping match of at least 95\% with
the ones from the validation set. We also demonstrate that a NN can be used to
predict the overlapping match score, with 90\% of accuracy, of new synthetic
samples. These are encouraging results for using GANs for data augmentation and
interpolation in the context of GWs, to cover the full parameter space of, say,
exotic compact binaries, without the need of intensive numerical relativity
simulations.


title: A duality theorem for the ic-resurgence of edge ideals

abstract:
  The aim of this work is to use linear programming and polyhedral geometry to
prove a duality formula for the ic-resurgence of edge ideals. We show that the
ic-resurgence of the edge ideal $I$ of a clutter $\mathcal{C}$ is equal to the
ic-resurgence of the edge ideal $I^\vee$ of the blocker $\mathcal{C}^\vee$ of
$\mathcal{C}$. We study the linear programs and the associated polyhedra that
have been used to compute the ic-resurgence of squarefree monomial ideals. If
$\mathcal{C}$ is a connected non-bipartite graph with a perfect matching or
$\mathcal{C}$ is the clutter of bases of certain uniform matroids, we compute a
formula for the ic-resurgence of $I$.


title: Truncated moment problems on positive-dimensional algebraic varieties

abstract:
  This manuscript transfers the main aspects of Prony's method from
finitely-supported measures to the classes of signed or non-negative measures
supported on algebraic varieties of any dimension. In particular, we show that
the Zariski closure of the support of these measures is determined by finitely
many moments and can be computed from the kernel of certain moment matrices.


title:
First joint observation by the underground gravitational-wave detector,
  KAGRA, with GEO600

abstract:
  We report the results of the first joint observation of the KAGRA detector
with GEO600. KAGRA is a cryogenic and underground gravitational-wave detector
consisting of a laser interferometer with three-kilometer arms, and located in
Kamioka, Gifu, Japan. GEO600 is a British--German laser interferometer with 600
m arms, and located near Hannover, Germany. GEO600 and KAGRA performed a joint
observing run from April 7 to 20, 2020. We present the results of the joint
analysis of the GEO--KAGRA data for transient gravitational-wave signals,
including the coalescence of neutron-star binaries and generic unmodeled
transients. We also perform dedicated searches for binary coalescence signals
and generic transients associated with gamma-ray burst events observed during
the joint run. No gravitational-wave events were identified. We evaluate the
minimum detectable amplitude for various types of transient signals and the
spacetime volume for which the network is sensitive to binary neutron-star
coalescences. We also place lower limits on the distances to the gamma-ray
bursts analysed based on the non-detection of an associated gravitational-wave
signal for several signal models, including binary coalescences. These analyses
demonstrate the feasibility and utility of KAGRA as a member of the global
gravitational-wave detector network.


title:
Stochastic Approximation for Estimating the Price of Stability in
  Stochastic Nash Games

abstract:
  The goal in this paper is to estimate the Price of Stability (PoS) for
stochastic Nash games using stochastic approximation (SA) schemes. PoS is
amongst the most popular metrics in game theory and provides an avenue for
estimating the efficiency of Nash games. In particular, knowing the value of
PoS can help significantly with designing efficient networked systems,
including transportation networks and power market mechanisms. Motivated by the
lack of efficient methods for estimating PoS, first we consider stochastic
optimization problems with a nonsmooth and merely convex objective function and
a merely monotone stochastic variational inequality (SVI) constraint. This
problem appears in the numerator of the PoS. We develop a randomized
block-coordinate stochastic extra-(sub)gradient method where we employ a novel
iterative penalization scheme to account for the mapping of the SVI in each of
the two gradient updates of the algorithm. We obtain an iteration complexity of
the order $\epsilon^{-4}$ that appears to be best known result for this class
of constrained stochastic optimization problems. Second, we develop an SA-based
algorithm to estimate the PoS. In particular, combining the proposed
extra-(sub)gradient-based method with a variance reduction technique, we derive
a confidence interval with lower and upper errors of the order
$\frac{1}{\sqrt{k}}$ and $\frac{1}{\sqrt[4]{k}}$, respectively. Such guarantees
appear to be new for estimating the PoS. To validate our theoretical findings,
we provide some preliminary simulation results on a stochastic Nash Cournot
competition over a network.


title:
Implicit Definitions with Differential Equations for KeYmaera X (System
  Description)

abstract:
  Definition packages in theorem provers provide users with means of defining
and organizing concepts of interest. This system description presents a new
definition package for the hybrid systems theorem prover KeYmaera X based on
differential dynamic logic (dL). The package adds KeYmaera X support for
user-defined smooth functions whose graphs can be implicitly characterized by
dL formulas. Notably, this makes it possible to implicitly characterize
functions, such as the exponential and trigonometric functions, as solutions of
differential equations and then prove properties of those functions using dL's
differential equation reasoning principles. Trustworthiness of the package is
achieved by minimally extending KeYmaera X's soundness-critical kernel with a
single axiom scheme that expands function occurrences with their implicit
characterization. Users are provided with a high-level interface for defining
functions and non-soundness-critical tactics that automate low-level reasoning
over implicit characterizations in hybrid system proofs.


title: Nematic spectral signatures of the Hund's metal

abstract:
  We show, by means of dynamical mean-field theory calculations, that the
experimental fingerprints of the nematic order in iron-based superconductors
are intrinsically connected with the electronic correlations in the Hund's
correlated metallic state and they can not be accessed via a renormalized
quasiparticle picture. In particular, our results show that: (i) in a metal in
which correlations are dominated by the Hund's coupling the nematic ordering
does not produce a rigid energy shift in the photoemission spectra, but a much
richer spectral weight redistribution which mirrors the experimental results;
(ii) the nematic ordering is characterized by an orbital-selective coherence
induced by the Hund's physics in agreement with the experimental picture.


title:
Synthetic solar cycle for active regions violating the Hale's polarity
  law

abstract:
  Long observational series for bipolar active regions (ARs) provide
significant information about the mutual transformation of the poloidal and
toroidal components of the global solar magnetic field. The direction of the
toroidal field determines the polarity of leading sunspots in ARs in accordance
with the Hale's polarity law. The vast majority of bipolar ARs obey this
regularity, whereas a few percent of ARs have the opposite sense of polarity
(anti-Hale ARs). However, the study of these ARs is hampered by their poor
statistics. The data for five 11-year cycles (16-18 and 23,24) were combined
here to compile a synthetic cycle of unique time length and latitudinal width.
The synthetic cycle comprises data for 14838 ARs and 367 of them are the
anti-Hale ARs. A specific routine to compile the synthetic cycle was
demonstrated. We found that, in general, anti-Hale ARs follow the solar cycle
and are spread throughout the time-latitude diagram evenly, which implies their
fundamental connection with the global dynamo mechanism and the toroidal flux
system. The increase in their number and percentage occurs in the second part
of the cycle, which is in favour of their contribution to the polar field
reversal. The excess in the anti-Hale ARs percentage at the edges of the
butterfly diagram and near an oncoming solar minimum (where the toroidal field
weakens) might be associated with strengthening of the influence of turbulent
convection and magnetic field fluctuations on the arising flux tubes. The
evidence of the misalignment between the magnetic and heliographic equators is
also found.


title:
Anisotropic superconductivity in ZrB$_{12}$ near critical Bogomolnyi
  point

abstract:
  The superconductors with the Ginzburg-Landau (G-L) parameter ($\kappa$)
$\sim1/\sqrt{2}$ exist near a critical Bogolomonyi (B) point where they show
inter-type domains between type-I and type-II superconductivity. While such
physics is well understood for isotropic superconductors, the experimental
investigation of the physics of anisotropic superconductors near a critical
B-point remains an unattained goal mainly due to the unavailability of model
material systems. Theoretically, such superconductors are expected to show
type-I or type-II behaviour for definite directions of an applied magnetic
field. Here, from directional point-contact Andreev reflection spectroscopy and
field-angle dependent ac magnetic susceptibility measurements, we show that
ZrB$_{12}$ is an anisotropic superconductor, and it exhibits field-direction
dependent type-I and type-II behaviour. These observations match remarkably
well with the theoretical expectations for an anisotropic superconductor near a
critical B-point. Therefore, our results project ZrB$_{12}$ as a model material
system where the physics of inter-type anisotropic superconductivity can be
explored experimentally.


title:
Machine learning models predict calculation outcomes with the
  transferability necessary for computational catalysis

abstract:
  Virtual high throughput screening (VHTS) and machine learning (ML) have
greatly accelerated the design of single-site transition-metal catalysts. VHTS
of catalysts, however, is often accompanied with high calculation failure rate
and wasted computational resources due to the difficulty of simultaneously
converging all mechanistically relevant reactive intermediates to expected
geometries and electronic states. We demonstrate a dynamic classifier approach,
i.e., a convolutional neural network that monitors geometry optimization on the
fly, and exploit its good performance and transferability for catalyst design.
We show that the dynamic classifier performs well on all reactive intermediates
in the representative catalytic cycle of the radical rebound mechanism for
methane-to-methanol despite being trained on only one reactive intermediate.
The dynamic classifier also generalizes to chemically distinct intermediates
and metal centers absent from the training data without loss of accuracy or
model confidence. We rationalize this superior model transferability to the use
of on-the-fly electronic structure and geometric information generated from
density functional theory calculations and the convolutional layer in the
dynamic classifier. Combined with model uncertainty quantification, the dynamic
classifier saves more than half of the computational resources that would have
been wasted on unsuccessful calculations for all reactive intermediates being
considered.


title: Deep Temporal Interpolation of Radar-based Precipitation

abstract:
  When providing the boundary conditions for hydrological flood models and
estimating the associated risk, interpolating precipitation at very high
temporal resolutions (e.g. 5 minutes) is essential not to miss the cause of
flooding in local regions. In this paper, we study optical flow-based
interpolation of globally available weather radar images from satellites. The
proposed approach uses deep neural networks for the interpolation of multiple
video frames, while terrain information is combined with temporarily
coarse-grained precipitation radar observation as inputs for self-supervised
training. An experiment with the Meteonet radar precipitation dataset for the
flood risk simulation in Aude, a department in Southern France (2018),
demonstrated the advantage of the proposed method over a linear interpolation
baseline, with up to 20% error reduction.


title: Black hole and wormhole solutions in Einstein-Maxwell-Scalar theory

abstract:
  We classified and studied the charged black hole and wormhole solutions in
the Einstein--Maxwell system in the presence of a massless, real scalar field.
The possible existence of charged black holes in general scalar--tensor
theories was studied in {Bronnikov et al, 1999;} black holes and wormholes
exist for a negative kinetic term for the scalar field. Using a conformal
transformation, the static, spherically symmetric possible structures in the
minimal coupled system are described. Besides wormholes and naked
singularities, only a restricted class of black hole exists, exhibiting a
horizon with an infinite surface and a timelike central singularity. The black
holes and wormholes defined in the Einstein frame have some specificities with
respect to the non-minimal coupling original frame, which are discussed in the
text.


title: Structure of sets with nearly maximal Favard length

abstract:
  Let $E \subset B(1) \subset \mathbb R^{2}$ be an $\mathcal{H}^{1}$ measurable
set with $\mathcal{H}^{1}(E) < \infty$, and let $L \subset \mathbb R^{2}$ be a
line segment with $\mathcal{H}^{1}(L) = \mathcal{H}^{1}(E)$. It is not hard to
see that $\mathrm{Fav}(E) \leq \mathrm{Fav}(L)$. We prove that in the case of
near equality, that is, $$ \mathrm{Fav}(E) \geq \mathrm{Fav}(L) - \delta, $$
the set $E$ can be covered by an $\epsilon$-Lipschitz graph, up to a set of
length $\epsilon$. The dependence between $\epsilon$ and $\delta$ is
polynomial: in fact, the conclusions hold with $\epsilon = C\delta^{1/70}$ for
an absolute constant $C > 0$.


title:
Total Stiefel Whitney classes for real representations of
  $\mathrm{GL}_n$ over $\mathbb{F}_q, \mathbb{R}$ and $\mathbb{C}$

abstract:
  We compute the total Stiefel Whitney class for a real representation $\pi$ of
$\mathrm{GL}_n(\mathbb{F}_q)$, where $q$ is odd in terms of character values of
$\pi$ on order $2$ diagonal elements. We also compute the total Stiefel Whitney
class of real representations of $\mathrm{GL}_n(\mathbb{R})$ and
$\mathrm{GL}_n(\mathbb{C})$.


title:
Operational interpretation of predictability in entanglement swapping
  from partially entangled pure states

abstract:
  Quantum complementarity and entanglement are fundamental features of Quantum
Mechanics. The purity of a bipartite quantum state $|\Psi\rangle_{AB}$ was
shown to imply in complete complementarity relations for the quanton $A$ or
$B$. These triality equalities involve quantum coherence $C(\rho_{A})$, the
wave aspect of a quanton, and quantum predictability $P(\rho_{A})$ and quantum
entanglement $E(|\Psi\rangle_{AB})$, the particle aspect of a quanton.
Recently, we reported a resource theory for quantum predictability, which
quantifies the "path" information from the knowledge of the quanton's density
matrix. In this article, we give an operational interpretation to
predictability in entanglement swapping from initially partially entangled
states. Entanglement swapping is an essential primitive for quantum
communication where one starts with two pairs of entangled qubits and makes a
Bell-basis measurement (BBM) on one qubit from each pair, ending up maximally
entangling the other two qubits, that possibly have never interacted directly.
Here we start by noticing that there is a plethora of partially entangled
states as well as maximally entangled states that can be obtained after a BBM.
Then, we show that the predictability of the pre-measurement one-qubit density
matrix is directly related to the probability of the partially entangled
component of the post-measurement state. Going even further, we analyze the
entanglement swapping for partially entangled states in the light of
complementarity relations and show that, in the cases where the entanglement
increases after the BBM, the predictability is consumed when compared to the
initially prepared state. Moreover, the triality relations will always remain
valid before and after the BBM, which means the we have a interplay between
predictability and entanglement before and after the BBM.


title: py-irt: A Scalable Item Response Theory Library for Python

abstract:
  py-irt is a Python library for fitting Bayesian Item Response Theory (IRT)
models. py-irt estimates latent traits of subjects and items, making it
appropriate for use in IRT tasks as well as ideal-point models. py-irt is built
on top of the Pyro and PyTorch frameworks and uses GPU-accelerated training to
scale to large data sets. Code, documentation, and examples can be found at
https://github.com/nd-ball/py-irt. py-irt can be installed from the GitHub page
or the Python Package Index (PyPI).


title:
Cesium-involved electron transfer and electron-electron interaction in
  high-pressure metallic CsPbI3

abstract:
  Electron-phonon coupling was believed to govern the carrier transport in
halide perovskites and related phases. Here we demonstrate that
electron-electron interaction plays a direct and prominent role in the
low-temperature electrical transport of compressed CsPbI3 and renders Fermi
liquid (FL)-like behavior. By compressing {\delta}-CsPbI3 to 80 GPa, an
insulator-to-metal transition occurs, concomitant with the completion of a
sluggish structural transition from the one-dimensional (1D) Pnma ({\delta})
phase to a 3D Pmn21 ({\epsilon}) phase. Deviation from FL behavior is observed
in CsPbI3 upon entering the metallic {\epsilon} phase, which progressively
evolves into a FL-like state at 186 GPa. First-principles density functional
theory calculations reveal that the enhanced electron-electron coupling is
related to the Cs-involved electron transfer and sudden increase of the 5d
state occupation of the high-pressure {\epsilon} phase. Our study presents a
promising strategy for tuning the electronic interaction in halide perovskites
for realizing intriguing electronic states.


title:
On Stretching, Bending, Shearing and Twisting of Actin Filaments II:
  Multi-Resolution Modelling

abstract:
  We present a multi-resolution methodology for modelling F-actin filaments. It
provides detailed microscopic information at the level of individual monomers
at a lower computational cost by replacing the monomer-based model in parts of
the simulated filament by a rod-based macroscopic model. In the monomer-based
description, G-actin is represented by ellipsoids bound at the surface in a
double helical configuration to form F-actin. The rod-based model is coarser,
in which F-actin is described using a Cosserat model, as seen in the preceding
paper [arXiv:2112.01480]. The multi-resolution methodology is illustrated using
three case studies, designed to test the properties of F-actin under
stretching, bending, shearing and twisting. The methodology is especially
suited for situations where filaments are subject to bending deformations. We
investigate the limitations of using the standard Cosserat model to capture the
complete torsional behaviour of F-actin, presenting its extensions which
account for curvature dependent rigidities and a twist-stretch coupling to
improve accuracy of the overall multi-resolution scheme.


title: Stackelberg-Pareto Synthesis (Extended Version)

abstract:
  We study the framework of two-player Stackelberg games played on graphs in
which Player 0 announces a strategy and Player 1 responds rationally with a
strategy that is an optimal response. While it is usually assumed that Player 1
has a single objective, we consider here the new setting where he has several.
In this context, after responding with his strategy, Player 1 gets a payoff in
the form of a vector of Booleans corresponding to his satisfied objectives.
Rationality of Player 1 is encoded by the fact that his response must produce a
Pareto-optimal payoff given the strategy of Player 0. We study for several
kinds of $\omega$-regular objectives the Stackelberg-Pareto Synthesis problem
which asks whether Player 0 can announce a strategy which satisfies his
objective, whatever the rational response of Player 1. We show that this
problem is fixed-parameter tractable for games in which objectives are all
reachability, safety, B\"uchi, co-B\"uchi, Boolean B\"uchi, parity, Muller,
Streett or Rabin objectives. We also show that this problem is
NEXPTIME-complete except for the cases of B\"uchi objectives for which it is
NP-complete and co-B\"uchi objectives for which it is in NEXPTIME and NP-hard.
The problem is already NP-complete in the simple case of reachability
objectives and graphs that are trees.


title: Far-UVC Disinfection with Robotic Mobile Manipulator

abstract:
  The COVID-19 pandemic has demonstrated the need for a more effective and
efficient disinfection approach to combat infectious diseases. Ultraviolet
germicidal irradiation (UVGI) is a proven mean for disinfection and
sterilization and has been integrated into handheld devices and autonomous
mobile robots. Existing UVGI robots which are commonly equipped with uncovered
lamps that emit intense ultraviolet radiation suffer from: inability to be used
in human presence, shadowing of objects, and long disinfection time. These
robots also have a high operational cost. This paper introduces a
cost-effective germicidal system that utilizes UVGI to disinfect pathogens,
such as viruses, bacteria, and fungi, on high contact surfaces (e.g. doors and
tables). This system is composed of a team of 5-DOF mobile manipulators with
end-effectors that are equipped with far-UVC excimer lamps. The design of the
system is discussed with emphasis on path planning, coverage planning, and
scene understanding. Evaluations of the UVGI system using simulations and
irradiance models are also included.


title:
The role of haptic communication in dyadic collaborative object
  manipulation tasks

abstract:
  Intuitive and efficient physical human-robot collaboration relies on the
mutual observability of the human and the robot, i.e. the two entities being
able to interpret each other's intentions and actions. This is remedied by a
myriad of methods involving human sensing or intention decoding, as well as
human-robot turn-taking and sequential task planning. However, the physical
interaction establishes a rich channel of communication through forces, torques
and haptics in general, which is often overlooked in industrial implementations
of human-robot interaction. In this work, we investigate the role of haptics in
human collaborative physical tasks, to identify how to integrate physical
communication in human-robot teams. We present a task to balance a ball at a
target position on a board either bimanually by one participant, or dyadically
by two participants, with and without haptic information. The task requires
that the two sides coordinate with each other, in real-time, to balance the
ball at the target. We found that with training the completion time and number
of velocity peaks of the ball decreased, and that participants gradually became
consistent in their braking strategy. Moreover we found that the presence of
haptic information improved the performance (decreased completion time) and led
to an increase in overall cooperative movements. Overall, our results show that
humans can better coordinate with one another when haptic feedback is
available. These results also highlight the likely importance of haptic
communication in human-robot physical interaction, both as a tool to infer
human intentions and to make the robot behaviour interpretable to humans.


title:
Star discrepancy for new stratified random sampling I: optimal expected
  star discrepancy

abstract:
  We introduce a class of convex equivolume partitions. Expected star
discrepancy results are compared for stratified samples under these partitions,
including simple random samples. There are four main parts of our results.
First, among these newly designed partitions, there is one that minimizes the
expected star discrepancy, thus we partly answer an open question in [F.
Pausinger, S. Steinerberger, J. Complex. 2016]. Second, there are an infinite
number of such class of partitions, which generate point sets with smaller
expected discrepancy than classical jittered sampling for large sampling
number, leading to an open question in [M. Kiderlen, F. Pausinger, Monatsh.
Math. 2021] being solved. Third, we prove a strong partition principle and
generalize the expected star discrepancy under these partition models from
$L_2-$discrepancy to star discrepancy, hence an open question in [M. Kiderlen,
F. Pausinger, J. Complex. 2021] is answered. In the end, optimal expected star
discrepancy upper bound under this class of partitions is given, which is
better than using jittered sampling.


title:
ADVISE: ADaptive Feature Relevance and VISual Explanations for
  Convolutional Neural Networks

abstract:
  To equip Convolutional Neural Networks (CNNs) with explainability, it is
essential to interpret how opaque models take specific decisions, understand
what causes the errors, improve the architecture design, and identify unethical
biases in the classifiers. This paper introduces ADVISE, a new explainability
method that quantifies and leverages the relevance of each unit of the feature
map to provide better visual explanations. To this end, we propose using
adaptive bandwidth kernel density estimation to assign a relevance score to
each unit of the feature map with respect to the predicted class. We also
propose an evaluation protocol to quantitatively assess the visual
explainability of CNN models. We extensively evaluate our idea in the image
classification task using AlexNet, VGG16, ResNet50, and Xception pretrained on
ImageNet. We compare ADVISE with the state-of-the-art visual explainable
methods and show that the proposed method outperforms competing approaches in
quantifying feature-relevance and visual explainability while maintaining
competitive time complexity. Our experiments further show that ADVISE fulfils
the sensitivity and implementation independence axioms while passing the sanity
checks. The implementation is accessible for reproducibility purposes on
https://github.com/dehshibi/ADVISE.


title:
Effect of congestion avoidance due to congestion information provision
  on optimizing agent dynamics on an endogenous star network topology

abstract:
  The importance of fundamental research on network topologies is widely
acknowledged. This study aims to elucidate the effect of congestion avoidance
of agents given congestion information on optimizing traffic in a network
topology. We investigated stochastic traffic networks in a star topology with a
central node connected to isolated secondary nodes with different preferences.
Each agent at the central node selects a secondary node by referring to the
declining preferences based on the congestion rate of the secondary nodes. We
examined two scenarios: 1) Each agent can repeatedly visit the central and
secondary nodes. 2) Each agent can access each secondary node only once. For
1), we investigated the uniformity of the agent distribution in a stationary
state, and for 2), we measured the travel time for all agents visiting all
nodes. When agents repeatedly visit central and other nodes, the uniformity of
agent distribution has been found to show three types of nonlinear dependence
on the increase in nodes. We found that multivariate statistics describe these
characteristic dependences well, suggesting that the balance between the
equalization of network usage by avoiding congestion and the covariance caused
by mutual referral to congestion information determines the uniformity. We
discovered that congestion-avoidance linearizes the travel time, which
increases exponentially with the number of nodes, notwithstanding the degree of
reference to the congestion information. Consequently, we successfully
described the optimization effect of congestion-avoidance on the collective
dynamics of agents in star topologies. Our findings are useful in many areas of
network science.


title:
Fast and scalable quantum Monte Carlo simulations of electron-phonon
  models

abstract:
  We introduce methodologies for highly scalable quantum Monte Carlo
simulations of electron-phonon models, and report benchmark results for the
Holstein model on the square lattice. The determinant quantum Monte Carlo
(DQMC) method is a widely used tool for simulating simple electron-phonon
models at finite temperatures, but incurs a computational cost that scales
cubically with system size. Alternatively, near-linear scaling with system size
can be achieved with the hybrid Monte Carlo (HMC) method and an integral
representation of the Fermion determinant. Here, we introduce a collection of
methodologies that make such simulations even faster. To combat "stiffness"
arising from the bosonic action, we review how Fourier acceleration can be
combined with time-step splitting. To overcome phonon sampling barriers
associated with strongly-bound bipolaron formation, we design global Monte
Carlo updates that approximately respect particle-hole symmetry. To accelerate
the iterative linear solver, we introduce a preconditioner that becomes exact
in the adiabatic limit of infinite atomic mass. Finally, we demonstrate how
stochastic measurements can be accelerated using fast Fourier transforms. These
methods are all complementary and, combined, may produce multiple orders of
magnitude speedup, depending on model details.


title:
Andes_gym: A Versatile Environment for Deep Reinforcement Learning in
  Power Systems

abstract:
  This paper presents Andes_gym, a versatile and high-performance reinforcement
learning environment for power system studies. The environment leverages the
modeling and simulation capability of ANDES and the reinforcement learning (RL)
environment OpenAI Gym to enable the prototyping and demonstration of RL
algorithms for power systems. The architecture of the proposed software tool is
elaborated to provide the observation and action interfaces for RL algorithms.
An example is shown to rapidly prototype a load-frequency control algorithm
based on RL trained by available algorithms. The proposed environment is highly
generalized by supporting all the power system dynamic models available in
ANDES and numerous RL algorithms available for OpenAI Gym.


title: Paley Graphs and S\'ark\"ozy's Theorem In Function Fields

abstract:
  S\'ark\"ozy's theorem states that dense sets of integers must contain two
elements whose difference is a $k^{th}$ power. Following the polynomial method
breakthrough of Croot, Lev, and Pach, Green proved a strong quantitative
version of this result for $\mathbb{F}_{q}[T]$. In this paper we provide a
lower bound for S\'{a}rk\"{o}zy's theorem in function fields by adapting
Ruzsa's construction for the analogous problem in $\mathbb{Z}$. We construct a
set $A$ of polynomials of degree $<n$ such that $A$ does not contain a $k^{th}$
power difference with $|A|=q^{n-n/2k}$. Additionally, we prove a handful of
results concerning the independence number of generalized Paley Graphs,
including a generalization of a claim of Ruzsa, which helps with understanding
the limit of the method.


title:
Providing Insights for Open-Response Surveys via End-to-End
  Context-Aware Clustering

abstract:
  Teachers often conduct surveys in order to collect data from a predefined
group of students to gain insights into topics of interest. When analyzing
surveys with open-ended textual responses, it is extremely time-consuming,
labor-intensive, and difficult to manually process all the responses into an
insightful and comprehensive report. In the analysis step, traditionally, the
teacher has to read each of the responses and decide on how to group them in
order to extract insightful information. Even though it is possible to group
the responses only using certain keywords, such an approach would be limited
since it not only fails to account for embedded contexts but also cannot detect
polysemous words or phrases and semantics that are not expressible in single
words. In this work, we present a novel end-to-end context-aware framework that
extracts, aggregates, and abbreviates embedded semantic patterns in
open-response survey data. Our framework relies on a pre-trained natural
language model in order to encode the textual data into semantic vectors. The
encoded vectors then get clustered either into an optimally tuned number of
groups or into a set of groups with pre-specified titles. In the former case,
the clusters are then further analyzed to extract a representative set of
keywords or summary sentences that serve as the labels of the clusters. In our
framework, for the designated clusters, we finally provide context-aware
wordclouds that demonstrate the semantically prominent keywords within each
group. Honoring user privacy, we have successfully built the on-device
implementation of our framework suitable for real-time analysis on mobile
devices and have tested it on a synthetic dataset. Our framework reduces the
costs at-scale by automating the process of extracting the most insightful
information pieces from survey data.


title:
Dynamic Coupling Strategy for Interdependent Network Systems Against
  Cascading Failures

abstract:
  Cascading failures are a common phenomenon in complex networked systems where
failures at only a few nodes may trigger a process of sequential failure. We
applied a flow redistribution model to investigate the robustness against
cascading failures in modern systems carrying flows/loads (i.e. power grid,
transportation system, etc.) that contain multiple interdependent networks. In
such a system, the coupling coefficients between networks, which determine how
much flows/loads are redistributed between networks, are a key factor
determining the robustness to cascading failures. We derive recursive
expressions to characterize the evolution of such a system under dynamic
network coupling. Using these expressions, we enhance the robustness of
interdependent network systems by dynamically adjusting the coupling
coefficients based on current system situations, minimizing the subsequent
failures. The analytical and simulation results show a significant improvement
in robustness compared to prior work, which considers only fixed coupling
coefficients. Our proposed Step-wise Optimization (SWO) method not only shows
good performance against cascading failures, but also offers better
computational complexity, scalability to multiple networks, and flexibility to
different attack types. We show in simulation that SWO provides robustness
against cascading failures for multiple different network topologies.


title: Half Wavelet Attention on M-Net+ for Low-Light Image Enhancement

abstract:
  Low-Light Image Enhancement is a computer vision task which intensifies the
dark images to appropriate brightness. It can also be seen as an ill-posed
problem in image restoration domain. With the success of deep neural networks,
the convolutional neural networks surpass the traditional algorithm-based
methods and become the mainstream in the computer vision area. To advance the
performance of enhancement algorithms, we propose an image enhancement network
(HWMNet) based on an improved hierarchical model: M-Net+. Specifically, we use
a half wavelet attention block on M-Net+ to enrich the features from wavelet
domain. Furthermore, our HWMNet has competitive performance results on two
image enhancement datasets in terms of quantitative metrics and visual quality.
The source code and pretrained model are available at
https://github.com/FanChiMao/HWMNet.


title: Sparse matrix multiplication in the low-bandwidth model

abstract:
  We study matrix multiplication in the low-bandwidth model: There are $n$
computers, and we need to compute the product of two $n \times n$ matrices.
Initially computer $i$ knows row $i$ of each input matrix. In one communication
round each computer can send and receive one $O(\log n)$-bit message.
Eventually computer $i$ has to output row $i$ of the product matrix.
  We seek to understand the complexity of this problem in the uniformly sparse
case: each row and column of each input matrix has at most $d$ non-zeros and in
the product matrix we only need to know the values of at most $d$ elements in
each row or column. This is exactly the setting that we have, e.g., when we
apply matrix multiplication for triangle detection in graphs of maximum degree
$d$. We focus on the supported setting: the structure of the matrices is known
in advance; only the numerical values of nonzero elements are unknown.
  There is a trivial algorithm that solves the problem in $O(d^2)$ rounds, but
for a large $d$, better algorithms are known to exist; in the moderately dense
regime the problem can be solved in $O(dn^{1/3})$ communication rounds, and for
very large $d$, the dominant solution is the fast matrix multiplication
algorithm using $O(n^{1.158})$ communication rounds (for matrix multiplication
over rings).
  In this work we show that it is possible to overcome quadratic barrier for
all values of $d$: we present an algorithm that solves the problem in
$O(d^{1.907})$ rounds for rings and $O(d^{1.927})$ rounds for semirings,
independent of $n$.


title: Pareto Frontier Approximation Network (PA-Net) to Solve Bi-objective TSP

abstract:
  Travelling salesperson problem (TSP) is a classic resource allocation problem
used to find an optimal order of doing a set of tasks while minimizing (or
maximizing) an associated objective function. It is widely used in robotics for
applications such as planning, scheduling etc. In this work, we solve TSP for
two objectives using reinforcement learning. Often in multi objective
optimization problems, the associated objective functions can be conflicting in
nature. In such cases, the optimality is defined in terms of Pareto optimality.
A set of these Pareto Optimal solutions in the objective space form a Pareto
front (or frontier). Each solution has its own trade off. In this work, we
present PA-Net, a network that generates good approximations of the Pareto
front for the bi-objective travelling salesperson problem (BTSP). Firstly, BTSP
is converted into a constrained optimization problem. We then train our network
to solve this constrained problem using the Lagrangian relaxation and policy
gradient. With PA-Net we are able to generate good quality Pareto fronts with
fast inference times. Finally, we present the application of PA-Net to find
optimal visiting order in a robotic navigation task/coverage planning.


title:
STEADY: Simultaneous State Estimation and Dynamics Learning from
  Indirect Observations

abstract:
  Accurate kinodynamic models play a crucial role in many robotics applications
such as off-road navigation and high-speed driving. Many state-of-the-art
approaches in learning stochastic kinodynamic models, however, require precise
measurements of robot states as labeled input/output examples, which can be
hard to obtain in outdoor settings due to limited sensor capabilities and the
absence of ground truth. In this work, we propose a new technique for learning
neural stochastic kinodynamic models from noisy and indirect observations by
performing simultaneous state estimation and dynamics learning. The proposed
technique iteratively improves the kinodynamic model in an
expectation-maximization loop, where the E Step samples posterior state
trajectories using particle filtering, and the M Step updates the dynamics to
be more consistent with the sampled trajectories via stochastic gradient
ascent. We evaluate our approach on both simulation and real-world benchmarks
and compare it with several baseline techniques. Our approach not only achieves
significantly higher accuracy but is also more robust to observation noise,
thereby showing promise for boosting the performance of many other robotics
applications.


title: BGG sequences with weak regularity and applications

abstract:
  We investigate some Bernstein-Gelfand-Gelfand (BGG) complexes on bounded
Lipschitz domains in $\mathbb{R}^n$ consisting of Sobolev spaces. In
particular, we compute the cohomology of the conformal deformation complex and
the conformal Hessian complex in the Sobolev setting. The machinery does not
require algebraic injectivity/surjectivity conditions between the input spaces,
and allows multiple input complexes. As applications, we establish a conformal
Korn inequality in two space dimensions with the Cauchy-Riemann operator and an
additional third order operator with a background in M\"obius geometry. We show
that the linear Cosserat elasticity model is a Hodge-Laplacian problem of a
twisted de-Rham complex. From this cohomological perspective, we propose
potential generalizations of continuum models with microstructures.

categories: math.NA cs.NA math.AP math.DG math.FA math.RT


title: Frames of iterations and vector-valued model spaces

abstract:
  Let T be a bounded operator on a Hilbert space H, and F = {f_j: j in J} an at
most countable set of vectors in H. In this note, we characterize the pairs {T,
F} such that {T^n f: f in F, n in I} form a frame of H, for the cases of I =
N_0 and I = Z. The characterization for unilateral iterations gives a
similarity with the compression of the shift acting on model spaces of the
Hardy space of analytic functions defined on the unit disk with values in
$l^2(J). This generalizes recent work for iterations of a single function. In
the case of bilateral iterations, the characterization is by the bilateral
shift acting on doubly invariant subspaces of L^2(T,l^2(J)).
  Furthermore, we characterize the frames of iterations for vector-valued model
operators when J is finite in terms of Toeplitz and multiplication operators in
the unilateral and bilateral case, respectively. Finally, we study the problem
of finding the minimal number of orbits that produce a frame in this context.


title: Evolving Curricula with Regret-Based Environment Design

abstract:
  It remains a significant challenge to train generally capable agents with
reinforcement learning (RL). A promising avenue for improving the robustness of
RL agents is through the use of curricula. One such class of methods frames
environment design as a game between a student and a teacher, using
regret-based objectives to produce environment instantiations (or levels) at
the frontier of the student agent's capabilities. These methods benefit from
their generality, with theoretical guarantees at equilibrium, yet they often
struggle to find effective levels in challenging design spaces. By contrast,
evolutionary approaches seek to incrementally alter environment complexity,
resulting in potentially open-ended learning, but often rely on domain-specific
heuristics and vast amounts of computational resources. In this paper we
propose to harness the power of evolution in a principled, regret-based
curriculum. Our approach, which we call Adversarially Compounding Complexity by
Editing Levels (ACCEL), seeks to constantly produce levels at the frontier of
an agent's capabilities, resulting in curricula that start simple but become
increasingly complex. ACCEL maintains the theoretical benefits of prior
regret-based methods, while providing significant empirical gains in a diverse
set of environments. An interactive version of the paper is available at
accelagent.github.io.


title: An Analysis of Ensemble Sampling

abstract:
  Ensemble sampling serves as a practical approximation to Thompson sampling
when maintaining an exact posterior distribution over model parameters is
computationally intractable. In this paper, we establish a Bayesian regret
bound that ensures desirable behavior when ensemble sampling is applied to the
linear bandit problem. This represents the first rigorous regret analysis of
ensemble sampling and is made possible by leveraging information-theoretic
concepts and novel analytic techniques that may prove useful beyond the scope
of this paper.


title: Supervised Hebbian learning: toward eXplainable AI

abstract:
  In neural network's Literature, {\em Hebbian learning} traditionally refers
to the procedure by which the Hopfield model and its generalizations {\em
store} archetypes (i.e., definite patterns that are experienced just once to
form the synaptic matrix). However, the term {\em learning} in Machine Learning
refers to the ability of the machine to extract features from the supplied
dataset (e.g., made of blurred examples of these archetypes), in order to make
its own representation of the unavailable archetypes. Here we prove that, if we
feed the Hopfield model with blurred examples, we can define both {\em
supervised} and {\em unsupervised} learning protocols by which the network can
possibly infer the archetypes and we detect the correct control parameters
(including the dataset size and its quality) to depict a phase diagram for the
system performance. We also prove that, for random, structureless datasets, the
Hopfield model equipped with a supervised learning rule is equivalent to a
restricted Boltzmann machine and this suggests an optimal training routine; the
robustness of results is also checked numerically for structured datasets. This
work contributes to pave a solid way toward eXplainable AI (XAI).


title: DN-DETR: Accelerate DETR Training by Introducing Query DeNoising

abstract:
  We present in this paper a novel denoising training method to speedup DETR
(DEtection TRansformer) training and offer a deepened understanding of the slow
convergence issue of DETR-like methods. We show that the slow convergence
results from the instability of bipartite graph matching which causes
inconsistent optimization goals in early training stages. To address this
issue, except for the Hungarian loss, our method additionally feeds
ground-truth bounding boxes with noises into Transformer decoder and trains the
model to reconstruct the original boxes, which effectively reduces the
bipartite graph matching difficulty and leads to a faster convergence. Our
method is universal and can be easily plugged into any DETR-like methods by
adding dozens of lines of code to achieve a remarkable improvement. As a
result, our DN-DETR results in a remarkable improvement ($+1.9$AP) under the
same setting and achieves the best result (AP $43.4$ and $48.6$ with $12$ and
$50$ epochs of training respectively) among DETR-like methods with ResNet-$50$
backbone. Compared with the baseline under the same setting, DN-DETR achieves
comparable performance with $50\%$ training epochs. Code is available at
\url{https://github.com/FengLi-ust/DN-DETR}.


title: Boson bunching is not maximized by indistinguishable particles

abstract:
  Boson bunching is amongst the most remarkable features of quantum physics. A
celebrated example in optics is the Hong-Ou-Mandel effect, where the bunching
of two photons arises from a destructive quantum interference between the
trajectories where they both either cross a beam splitter or are reflected.
This effect takes its roots in the indistinguishability of identical photons.
Hence, it is generally admitted -- and experimentally verified -- that bunching
vanishes as soon as photons can be distinguished, e.g., when they occupy
distinct time bins or have different polarizations. Here we disproof this
alleged straightforward link between indistinguishability and bunching by
exploiting a recent finding in the theory of matrix permanents. We exhibit a
family of optical circuits where the bunching of photons into two modes can be
significantly boosted by making them partially distinguishable via an
appropriate polarization pattern. This boosting effect is already visible in a
7-photon interferometric process, making the observation of this phenomenon
within reach of current photonic technology. This unexpected behavior questions
our understanding of multiparticle interference in the grey zone between
indistinguishable bosons and classical particles.


title:
An $L^p$-spectral multiplier theorem with sharp $p$-specific regularity
  bound on Heisenberg type groups

abstract:
  We prove an $L^p$-spectral multiplier theorem for sub-Laplacians on
Heisenberg type groups under the sharp regularity condition
$s>d\left(1/p-1/2\right)$, with $d$ being the topological dimension of the
underlying group. Our approach relies on restriction type estimates where the
multiplier is additionally truncated along the spectrum of the Laplacian on the
center of the group.


title:
Communicating over a Classical-Quantum MAC with State Information
  Distributed at Senders

abstract:
  We consider the problem of communicating over a classical-quantum (CQ)
multiple access channel with random classical states non-causally available at
the transmitter, referred to as a QMSTx. QMSTx is a classical-quantum multiple
access analogue of the channel considered by Gelfand and Pinsker in 1980. We
undertake a Shannon-theoretic study and focus on the problem of characterizing
inner bounds to the capacity region of a QMSTx. We propose a new coding scheme
based on \textit{union coset codes} - codes possessing algebraic properties and
derive a new inner bound that subsumes the inner based on IID random coding. We
identify examples for which the derived inner bound is strictly larger.


title:
Corrigendum to "Inverse Problems for abstract evolution equations II:
  higher order differentiability for viscoelasticity

abstract:
  In our paper [SIAM J.\ Appl.~Math.\ 79-6 (2019),
https://doi.org/10.1137/19M1269403] we considered full waveform inversion (FWI)
in the viscoelastic regime. FWI entails the nonlinear inverse problem of
recovering parameter functions of the viscoelastic wave equation from partial
measurements of reflected wave fields. We have obtained explicit analytic
expressions for the first and second order Fr\'echet derivatives and their
adjoints (adjoint wave equations) of the underlying parameter-to-solution map.
In the present manuscript we correct an error which occurred in a basic result
and thus affected several other statements, which we have also corrected.


title: Counterfactually Evaluating Explanations in Recommender Systems

abstract:
  Modern recommender systems face an increasing need to explain their
recommendations. Despite considerable progress in this area, evaluating the
quality of explanations remains a significant challenge for researchers and
practitioners. Prior work mainly conducts human study to evaluate explanation
quality, which is usually expensive, time-consuming, and prone to human bias.
In this paper, we propose an offline evaluation method that can be computed
without human involvement. To evaluate an explanation, our method quantifies
its counterfactual impact on the recommendation. To validate the effectiveness
of our method, we carry out an online user study. We show that, compared to
conventional methods, our method can produce evaluation scores more correlated
with the real human judgments, and therefore can serve as a better proxy for
human evaluation. In addition, we show that explanations with high evaluation
scores are considered better by humans. Our findings highlight the promising
direction of using the counterfactual approach as one possible way to evaluate
recommendation explanations.


title:
HighMMT: Towards Modality and Task Generalization for High-Modality
  Representation Learning

abstract:
  Learning multimodal representations involves discovering correspondences and
integrating information from multiple heterogeneous sources of data. While
recent research has begun to explore the design of more general-purpose
multimodal models (contrary to prior focus on domain and modality-specific
architectures), these methods are still largely focused on a small set of
modalities in the language, vision, and audio space. In order to accelerate
generalization towards diverse and understudied modalities, we investigate
methods for high-modality (a large set of diverse modalities) and
partially-observable (each task only defined on a small subset of modalities)
scenarios. To tackle these challenges, we design a general multimodal model
that enables multitask and transfer learning: multitask learning with shared
parameters enables stable parameter counts (addressing scalability), and
cross-modal transfer learning enables information sharing across modalities and
tasks (addressing partial observability). Our resulting model generalizes
across text, image, video, audio, time-series, sensors, tables, and set
modalities from different research areas, improves the tradeoff between
performance and efficiency, transfers to new modalities and tasks, and reveals
surprising insights on the nature of information sharing in multitask models.
We release our code and benchmarks which we hope will present a unified
platform for subsequent theoretical and empirical analysis:
https://github.com/pliang279/HighMMT.


title:
North Polar Spur/Loop I: gigantic outskirt of the Northern Fermi bubble
  or nearby hot gas cavity blown by supernovae?

abstract:
  Radio continuum, microwave and gamma-ray images of the Milky Way reveal a
conspicuous, loop-like structure that fills almost half of the northern
Galactic hemisphere, called Loop I. The interior of Loop I is shining in soft
X-rays, and its eastern base is a bright, elongated structure dubbed the North
Polar Spur (NPS). After 40 years of debates, two contradictory views of Loop
I/NPS are still defended: on the one hand, the NPS is a volume of expanding hot
gas that envelops and extends the northern Fermi Bubble (FB) known to be blown
by the Galactic center, and Loop I marks the shock front; on the other hand,
the NPS is a nearby cavity of hot gas blown by supernovae, Loop I is its shock
front and they are coincidentally located in the direction of the FB. To an
observer at the Sun, both structures can produce the same perspective view,
although the former has a size comparable to the Milky Way itself, and the
latter a diameter of a few hundreds parsecs. The energy involved varies by
3-4~orders of magnitude, and the solution has various important consequences. I
discuss recent results which have a connection with Loop I/NPS, overlooked or
used as arguments in the two opposite ways. They involve very different
spacecraft, from a 12 Kg Cubesat (HaloSat) to major space-borne observatories
(HST, Gaia, and Spektr-RG). I make use of 3D~maps of dust and a massive star
catalog. Considering all constraints, it is clear that there is no entirely
local or entirely distant scenario that is free from contradictions with some
of the data analyses or from improbable coincidences. I discuss a speculative
scenario, partially inspired by recent BF and Milky Way gas models, combining
near and far aspects and seeming to be able to meet the various constraints.
However, new data and models are needed to bring the controversy to a close and
we can still expect new episodes of this long story.


title:
Universal transport in periodically driven systems without long-lived
  quasiparticles

abstract:
  An intriguing regime of universal charge transport at high entropy density
has been proposed for periodically driven interacting one-dimensional systems
with Bloch bands separated by a large single-particle band gap. For weak
interactions, a simple picture based on well-defined Floquet quasiparticles
suggests that the system should host a quasisteady state current that depends
only on the populations of the system's Floquet-Bloch bands and their
associated quasienergy winding numbers. Here we show that such topological
transport persists into the strongly interacting regime where the
single-particle lifetime becomes shorter than the drive period. Analytically,
we show that the value of the current is insensitive to interaction-induced
band renormalizations and lifetime broadening when certain conditions are met
by the system's non-equilibrium distribution function. We show that these
conditions correspond to a quasisteady state. We support these predictions
through numerical simulation of a system of strongly interacting fermions in a
periodically-modulated chain of Sachdev-Ye-Kitaev dots. Our work establishes
universal transport at high entropy density as a robust far from equilibrium
topological phenomenon, which can be readily realized with cold atoms in
optical lattices.

categories: cond-mat.quant-gas cond-mat.mes-hall cond-mat.stat-mech cond-mat.str-el hep-th


title:
Determination of coupling patterns by parallel searches for $\mu^-\to
  e^+$ and $\mu^-\to e^-$ in muonic atoms

abstract:
  We investigate a possibility that the $\mu^-\to e^+$ conversion is discovered
prior to the $\mu^-\to e^-$ conversion, and its implications to the new physics
search. We focus on the specific model including the mixing of the $SU(2)_L$
doublet- and singlet-type scalar leptoquarks, which induces not only the lepton
flavor violation but also the lepton number violation. Such a structure is
motivated by R-parity violating (RPV) supersymmetric models, where a sbottom
mediates the conversion processes. We formulate the $\mu^-\to e^+$ rate in
analogy with the muon capture in a muonic atom, and numerically evaluate it
using several target nuclei. The lepton flavor universality test of pion decay
directly limits the $\mu^-\to e^+$ rate, and the maximally allowed $\mu^-\to
e^+$ branching ratio is $\sim 10^{-18}$ under the various bounds on RPV
parameters. We show that either $\mu^-\to e^-$ or $\mu^-\to e^+$ signals can be
discovered in near future experiments. This indicates that parallel searches
for these conversions will give us significant information on the pattern of
coupling constants.


title: Two Attacks On Proof-of-Stake GHOST/Ethereum

abstract:
  We present two attacks targeting the Proof-of-Stake (PoS) Ethereum consensus
protocol. The first attack suggests a fundamental conceptual incompatibility
between PoS and the Greedy Heaviest-Observed Sub-Tree (GHOST) fork choice
paradigm employed by PoS Ethereum. In a nutshell, PoS allows an adversary with
a vanishing amount of stake to produce an unlimited number of equivocating
blocks. While most equivocating blocks will be orphaned, such orphaned `uncle
blocks' still influence fork choice under the GHOST paradigm, bestowing upon
the adversary devastating control over the canonical chain. While the Latest
Message Driven (LMD) aspect of current PoS Ethereum prevents a straightforward
application of this attack, our second attack shows how LMD specifically can be
exploited to obtain a new variant of the balancing attack that overcomes a
recent protocol addition that was intended to mitigate balancing-type attacks.
Thus, in its current form, PoS Ethereum without and with LMD is vulnerable to
our first and second attack, respectively.


title:
A comparative study of 3D Cumulant and Central Moments lattice Boltzmann
  schemes with interpolated boundary conditions for the simulation of thermal
  flows in high Prandtl number regime

abstract:
  Thermal flows characterized by high Prandtl number are numerically
challenging as the transfer of momentum and heat occurs at different time
scales. To account for very low thermal conductivity and obey the
Courant-Friedrichs-Lewy condition, the numerical diffusion of the scheme has to
be reduced. As a consequence, the numerical artefacts are dominated by
dispersion errors commonly known as wiggles. In this study, we explore possible
remedies in the framework of the lattice Boltzmann method by applying novel
collision kernels, lattices with a large number of discrete velocities, namely
D3Q27, and second-order boundary conditions. For the first time, the
cumulant-based collision operator is utilised to simulate both the hydrodynamic
and the thermal field. Alternatively, the advected field is computed using the
central moments' collision operator. Different relaxation strategies have been
examined to account for additional degrees of freedom introduced by a
higher-order lattice. To validate the proposed kernels for a pure
advection-diffusion problem, the numerical simulations are compared against an
analytical solution of a Gaussian hill. The structure of the numerical
dispersion is shown by simulating advection and diffusion of a square indicator
function. Finally, a study of steady forced heat convection from a confined
cylinder is performed and compared against a FEM solution. It has been found,
that the relaxation scheme of the advected field must be adjusted to profit
from lattice with a larger number of discrete velocities. Obtained results show
clearly that it is not sufficient to assume that only the first-order central
moments/cumulants contribute to solving the macroscopic advection-diffusion
equation. In the case of central moments, the beneficial effect of the two
relaxation time approach is presented.


title:
Time-assisted energy reconstruction in a highly-granular hadronic
  calorimeter

abstract:
  The software compensation algorithms developed for the CALICE Analog Hadron
Calorimeter are extended to incorporate time information on the cell level, and
the performance is studied in GEANT4 simulations with a detector model of a
highly-granular SiPM-on-tile calorimeter. The addition of ns-level time
resolution is found to result in significant improvement of the energy
resolution for local software compensation, with further improvement possible
with better resolution. The high correlation of energy density and time
variables show that both provide sensitivity to correlated underlying shower
features, which limits the potential of timing information when used as a
global rather than a local variable.


title:
Protecting Celebrities from DeepFake with Identity Consistency
  Transformer

abstract:
  In this work we propose Identity Consistency Transformer, a novel face
forgery detection method that focuses on high-level semantics, specifically
identity information, and detecting a suspect face by finding identity
inconsistency in inner and outer face regions. The Identity Consistency
Transformer incorporates a consistency loss for identity consistency
determination. We show that Identity Consistency Transformer exhibits superior
generalization ability not only across different datasets but also across
various types of image degradation forms found in real-world applications
including deepfake videos. The Identity Consistency Transformer can be easily
enhanced with additional identity information when such information is
available, and for this reason it is especially well-suited for detecting face
forgeries involving celebrities. Code will be released at
\url{https://github.com/LightDXY/ICT_DeepFake}


title:
Mathematical aspects of Multiwell Deconvolution and its relation to
  Capacitance Resistance Model

abstract:
  The paper provides introduction into the mathematical aspects of Multiwell
Deconvolution (MDCV) and Capacitance Resistance Model (CRM) and connection
between them. Both methods are trying to train a model over the long-term
history of surface flowrates and bottomhole pressure readings and then predict
bottomhole and formation pressure in response to a given production/injection
flowrate scenario (called "rate control simulation") or alternatively may
predict flowrate and formation pressure in response to a given bottomhole
pressure scenario (called "pressure control simulation"). It has been shown
that CRM can be viewed as a partial case of MDCV with a specific type of a
drawdown and cross-well pressure transient responses which is not always met in
practice. The paper also explains limitations which are common for both methods
and specify additional limitations of CRM which MDCV can handle.


title: A $\mathbb{Z}_{2}$-Topological Index as a $\mathbb{Z}_{2}$-State Index

abstract:
  Within the setting of infinite dimensional self-dual $\mathrm{CAR}$
$C^{*}$-algebras describing fermions in the $\mathbb{Z}^{d}$-lattice, we depart
from the well-known Araki-Evans $\sigma(P_{1},P_{2})$ $\mathbb{Z}_{2}$-index
for quasi-free fermion states and rewrite it in terms of states, rather than in
terms of basis projections. Furthermore, we reformulate results which relate
equivalences of Fock representations with the index parity into results which
relate equivalences of GNS representations and the associated index parity.


title:
Colon Nuclei Instance Segmentation using a Probabilistic Two-Stage
  Detector

abstract:
  Cancer is one of the leading causes of death in the developed world. Cancer
diagnosis is performed through the microscopic analysis of a sample of
suspicious tissue. This process is time consuming and error prone, but Deep
Learning models could be helpful for pathologists during cancer diagnosis. We
propose to change the CenterNet2 object detection model to also perform
instance segmentation, which we call SegCenterNet2. We train SegCenterNet2 in
the CoNIC challenge dataset and show that it performs better than Mask R-CNN in
the competition metrics.


title:
Recent, rapid advancement in visual question answering architecture: a
  review

abstract:
  Understanding visual question answering is going to be crucial for numerous
human activities. However, it presents major challenges at the heart of the
artificial intelligence endeavor. This paper presents an update on the rapid
advancements in visual question answering using images that have occurred in
the last couple of years. Tremendous growth in research on improving visual
question answering system architecture has been published recently, showing the
importance of multimodal architectures. Several points on the benefits of
visual question answering are mentioned in the review paper by Manmadhan et al.
(2020), on which the present article builds, including subsequent updates in
the field.


title:
Benchmarking Robustness of Deep Learning Classifiers Using Two-Factor
  Perturbation

abstract:
  Accuracies of deep learning (DL) classifiers are often unstable in that they
may change significantly when retested on adversarial images, imperfect images,
or perturbed images. This paper adds to the fundamental body of work on
benchmarking the robustness of DL classifiers on defective images. To measure
robust DL classifiers, previous research reported on single-factor corruption.
We created comprehensive 69 benchmarking image sets, including a clean set,
sets with single factor perturbations, and sets with two-factor perturbation
conditions. The state-of-the-art two-factor perturbation includes (a) two
digital perturbations (salt & pepper noise and Gaussian noise) applied in both
sequences, and (b) one digital perturbation (salt & pepper noise) and a
geometric perturbation (rotation) applied in both sequences. Previous research
evaluating DL classifiers has often used top-1/top-5 accuracy. We innovate a
new two-dimensional, statistical matrix to evaluating robustness of DL
classifiers. Also, we introduce a new visualization tool, including minimum
accuracy, maximum accuracy, mean accuracies, and coefficient of variation (CV),
for benchmarking robustness of DL classifiers. Comparing with single factor
corruption, we first report that using two-factor perturbed images improves
both robustness and accuracy of DL classifiers. All source codes and related
image sets are shared on the Website at http://cslinux.semo.edu/david/data to
support future academic research and industry projects.


title:
Exploring Smoothness and Class-Separation for Semi-supervised Medical
  Image Segmentation

abstract:
  Semi-supervised segmentation remains challenging in medical imaging since the
amount of annotated medical data is often limited and there are many blurred
pixels near the adhesive edges or low-contrast regions. To address the issues,
we advocate to firstly constrain the consistency of samples with and without
strong perturbations to apply sufficient smoothness regularization and further
encourage the class-level separation to exploit the unlabeled ambiguous pixels
for the model training. Particularly, in this paper, we propose the SS-Net for
semi-supervised medical image segmentation tasks, via exploring the pixel-level
Smoothness and inter-class Separation at the same time. The pixel-level
smoothness forces the model to generate invariant results under adversarial
perturbations. Meanwhile, the inter-class separation constrains individual
class features should approach their corresponding high-quality prototypes, in
order to make each class distribution compact and separate different classes.
We evaluated our SS-Net against five recent methods on the public LA and ACDC
datasets. The experimental results under two semi-supervised settings
demonstrate the superiority of our proposed SS-Net, achieving new
state-of-the-art (SOTA) performance on both datasets. The codes will be
released.


title:
Self-Supervised Learning for Real-World Super-Resolution from Dual
  Zoomed Observations

abstract:
  In this paper, we consider two challenging issues in reference-based
super-resolution (RefSR), (i) how to choose a proper reference image, and (ii)
how to learn real-world RefSR in a self-supervised manner. Particularly, we
present a novel self-supervised learning approach for real-world image SR from
observations at dual camera zooms (SelfDZSR). For the first issue, the more
zoomed (telephoto) image can be naturally leveraged as the reference to guide
the SR of the lesser zoomed (short-focus) image. For the second issue, SelfDZSR
learns a deep network to obtain the SR result of short-focal image and with the
same resolution as the telephoto image. For this purpose, we take the telephoto
image instead of an additional high-resolution image as the supervision
information and select a patch from it as the reference to super-resolve the
corresponding short-focus image patch. To mitigate the effect of various
misalignment between the short-focus low-resolution (LR) image and telephoto
ground-truth (GT) image, we design a degradation model and map the GT to a
pseudo-LR image aligned with GT. Then the pseudo-LR and LR image can be fed
into the proposed adaptive spatial transformer networks (AdaSTN) to deform the
LR features. During testing, SelfDZSR can be directly deployed to super-solve
the whole short-focus image with the reference of telephoto image. Experiments
show that our method achieves better quantitative and qualitative performance
against state-of-the-arts. The code and pre-trained models will be publicly
available.


title:
Precise Stock Price Prediction for Optimized Portfolio Design Using an
  LSTM Model

abstract:
  Accurate prediction of future prices of stocks is a difficult task to
perform. Even more challenging is to design an optimized portfolio of stocks
with the identification of proper weights of allocation to achieve the
optimized values of return and risk. We present optimized portfolios based on
the seven sectors of the Indian economy. The past prices of the stocks are
extracted from the web from January 1, 2016, to December 31, 2020. Optimum
portfolios are designed on the selected seven sectors. An LSTM regression model
is also designed for predicting future stock prices. Five months after the
construction of the portfolios, i.e., on June 1, 2021, the actual and predicted
returns and risks of each portfolio are computed. The predicted and the actual
returns indicate the very high accuracy of the LSTM model.


title:
Hyperspectral Pixel Unmixing with Latent Dirichlet Variational
  Autoencoder

abstract:
  Hyperspectral pixel intensities result from a mixing of reflectances from
several materials. This paper develops a method of hyperspectral pixel {\it
unmixing} that aims to recover the "pure" spectral signal of each material
(hereafter referred to as {\it endmembers}) together with the mixing ratios
({\it abundances}) given the spectrum of a single pixel. The unmixing problem
is particularly relevant in the case of low-resolution hyperspectral images
captured in a remote sensing setting, where individual pixels can cover large
regions of the scene. Under the assumptions that (1) a multivariate Normal
distribution can represent the spectra of an endmember and (2) a Dirichlet
distribution can encode abundances of different endmembers, we develop a Latent
Dirichlet Variational Autoencoder for hyperspectral pixel unmixing. Our
approach achieves state-of-the-art results on standard benchmarks and on
synthetic data generated using United States Geological Survey spectral
library.


title:
Semilinear elliptic Schr\"odinger equations involving singular
  potentials and source terms

abstract:
  Let $\Omega \subset \mathbb{R}^N$ ($N>2$) be a $C^2$ bounded domain and
$\Sigma \subset \Omega$ be a compact, $C^2$ submanifold without boundary, of
dimension $k$ with $0\leq k < N-2$. Put $L_\mu = \Delta + \mu d_\Sigma^{-2}$ in
$\Omega \setminus \Sigma$, where $d_\Sigma(x) = \mathrm{dist}(x,\Sigma)$ and
$\mu$ is a parameter. We study the boundary value problem (P) $-L_\mu u = g(u)
+ \tau$ in $\Omega \setminus \Sigma$ with condition $u=\nu$ on $\partial \Omega
\cup \Sigma$, where $g: \mathbb{R} \to \mathbb{R}$ is a nondecreasing,
continuous function and $\tau$ and $\nu$ are positive measures. The interplay
between the inverse-square potential $d_\Sigma^{-2}$, the nature of the source
term $g(u)$ and the measure data $\tau,\nu$ yields substantial difficulties in
the research of the problem. We perform a deep analysis based on delicate
estimate on the Green kernel and Martin kernel and fine topologies induced by
appropriate capacities to establish various necessary and sufficient conditions
for the existence of a solution in different cases.


title:
Energetic cost of measurements using quantum, coherent, and thermal
  light

abstract:
  Quantum measurements are basic operations that play a critical role in the
study and application of quantum information. We study how the use of quantum,
coherent, and classical thermal states of light in a circuit quantum
electrodynamics setup impacts the performance of quantum measurements, by
comparing their respective measurement backaction and measurement signal to
noise ratio per photon. In the strong dispersive limit, we find that thermal
light is capable of performing quantum measurements with comparable efficiency
to coherent light, both being outperformed by single-photon light. We then
analyze the thermodynamic cost of each measurement scheme. We show that
single-photon light shows an advantage in terms of energy cost per information
gain, reaching the fundamental thermodynamic cost.


title:
Binary evolution, gravitational-wave mergers and explosive transients in
  multiple-populations gas-enriched globular-clusters

abstract:
  Most globular clusters (GCs) show evidence for multiple stellar populations,
suggesting the occurrence of several distinct star-formation episodes. The
large fraction of second population (2P) stars observed requires a very large
2P gaseous mass to have accumulated in the cluster core to form these stars.
Hence the first population of stars (1P) in the cluster core has had to become
embedded in 2P gas, just prior to the formation of later populations. Here we
explore the evolution of binaries in ambient 2P gaseous media of
multiple-population GCs. We mostly focus on black hole binaries and follow
their evolution as they evolve from wide binaries towards short periods through
interaction with ambient gas, followed by gravitational-wave (GW) dominated
inspiral and merger. We show this novel GW-merger channel could provide a major
contribution to the production of GW-sources. We consider various assumptions
and initial conditions and calculate the resulting gas-mediated change in the
population of binaries and the expected merger rates due to gas-catalyzed
GW-inspirals. For plausible conditions and assumptions, we find an expected GW
merger rate observable by aLIGO of the order of up to a few tens of
$\rm{Gpc^{-3} yr^{-1}}$, and an overall range for our various models of
$0.08-25.51 \ \rm{Gpc^{-3} yr^{-1}}$. Finally, our results suggest that the
conditions and binary properties in the early stage of GCs could be critically
affected by gas-interactions and may require a major revision in the current
modeling of the evolution of GCs.


title:
BPS and near-BPS black holes in $AdS_5$ and their spectrum in
  $\mathcal{N}=4$ SYM

abstract:
  We study quantum corrections in the gravitational path integral around nearly
$1/16$-BPS black holes in asymptotically $AdS_5 \times S^5$ space, dual to
heavy states in 4D $\mathcal{N}=4$ super Yang-Mills. The analysis provides a
gravitational explanation of why $1/16$-BPS black holes exhibit an exact
degeneracy at large $N$ and why all such states have the same charges,
confirming the belief that the superconformal index precisely counts the
entropy of extremal black holes. We show the presence of a gap of order
$N^{-2}$ between the $1/16$-BPS black holes and the lightest near-BPS black
holes within the same charge sector. This is the first example of such a gap
for black holes states within the context of $AdS_5$ holography. We also derive
the spectrum of near-BPS states that lie above this gap. Our computation relies
on finding the correct version of the $\mathcal{N}=2$ super-Schwarzian theory
which captures the breaking of the $SU(1, 1|1)$ symmetry when the black hole
has finite temperature and non-zero chemical potential. Finally, we comment on
possible stringy and non-perturbative corrections that can affect the black
hole spectrum.


title: The two classes of hybrid classical-quantum dynamics

abstract:
  Coupling between quantum and classical systems is consistent, provided the
evolution is linear in the state space, preserves the split of systems into
quantum and classical degrees of freedom, and preserves probabilities. The
evolution law must be a completely positive and norm preserving map. We prove
that if the dynamics is memoryless, there are two classes of these dynamics,
one which features finite sized jumps in the classical phase space and one
which is continuous. We find the most general form of each class of
classical-quantum master equation. This is achieved by applying the complete
positivity conditions using a generalized Cauchy-Schwartz inequality applicable
to classical-quantum systems. The key technical result is a generalisation of
the Pawula theorem.


title: Liouvillian Skin Effect in an Exactly Solvable Model

abstract:
  The interplay between dissipation, topology and sensitivity to boundary
conditions has recently attracted tremendous amounts of attention at the level
of effective non-Hermitian descriptions. Here we exactly solve a quantum
mechanical Lindblad master equation describing a dissipative topological
Su-Schrieffer-Heeger (SSH) chain of fermions for both open and periodic
boundary conditions. We find that the extreme sensitivity on the boundary
conditions associated with the non-Hermitian skin effect is directly reflected
in the rapidities governing the time evolution of the density matrix giving
rise to a {\it Liouvillian Skin Effect}. This leads to several intriguing
phenomena including boundary sensitive damping behavior, steady state currents
in finite periodic systems, and diverging relaxation times in the limit of
large systems. We illuminate how the role of topology in these systems differ
in the effective non-Hermitian Hamiltonian limit and the full master equation
framework.

categories: quant-ph cond-mat.mes-hall cond-mat.quant-gas physics.optics


title: Eccentricity Evolution in Gaseous Dynamical Friction

abstract:
  We analyse how drag forces modify the orbits of objects moving through
extended gaseous distributions. We consider how hydrodynamic (surface area)
drag forces and dynamical friction (gravitational) drag forces drive the
evolution of orbital eccentricity. While hydrodynamic drag forces cause
eccentric orbits to become more circular, dynamical friction drag can cause
orbits to become more eccentric. We develop a semi-analytic model that
accurately predicts these changes by comparing the total work and torque
applied to the orbit at periapse and apoapse. We use a toy model of a radial
power-law density profile, $\rho \propto r^{-\gamma}$, to determine that there
is a critical $\gamma = 3$ power index which separates the eccentricity
evolution: orbits become more eccentric for $\gamma < 3$ and circularize for
$\gamma > 3$. We apply these findings to the infall of a Jupiter-like planet
into the envelope of its host star. The hydrostatic envelopes of stars are
defined by steep density gradients near the limb and shallower gradients in the
interior. Under the influence of gaseous dynamical friction, an infalling
object's orbit will first decrease in eccentricity, then increase. The critical
separation that delineates these regimes is predicted by the local density
slope and is linearly dependent on polytropic index. More broadly, our findings
indicate that binary systems may routinely emerge from common envelope phases
with non-zero eccentricities that were excited by the dynamical friction forces
that drove their orbital tightening.


title: Quivers, Lattice Gauge Theories and Fractons

abstract:
  We argue that quiver gauge theories with $SU(N)$ gauge groups give rise to
lattice gauge theories with matter possessing fractonic properties, where the
lattice is the quiver itself. This idea extends a recent proposal by Razamat.
This class of theories exhibit a $\mathbb{Z}_N$ 1-form global symmetry that can
be used to classify their phases. The order parameter of this transition is the
expectation value of Wilson loops, which correspond to mesonic operators in the
underlying quiver gauge theory. We discuss how this perspective naturally fits
with the deconstruction of a higher dimensional theory.