Abstract:
  Machine learning decision systems are getting omnipresent in our lives. From
dating apps to rating loan seekers, algorithms affect both our well-being and
future. Typically, however, these systems are not infallible. Moreover, complex
predictive models are really eager to learn social biases present in historical
data that can lead to increasing discrimination. If we want to create models
responsibly then we need tools for in-depth validation of models also from the
perspective of potential discrimination. This article introduces an R package
fairmodels that helps to validate fairness and eliminate bias in classification
models in an easy and flexible fashion. The fairmodels package offers a
model-agnostic approach to bias detection, visualization and mitigation. The
implemented set of functions and fairness metrics enables model fairness
validation from different perspectives. The package includes a series of
methods for bias mitigation that aim to diminish the discrimination in the
model. The package is designed not only to examine a single model, but also to
facilitate comparisons between multiple models.


Abstract:
  Recent works for attributed network clustering utilize graph convolution to
obtain node embeddings and simultaneously perform clustering assignments on the
embedding space. It is effective since graph convolution combines the
structural and attributive information for node embedding learning. However, a
major limitation of such works is that the graph convolution only incorporates
the attribute information from the local neighborhood of nodes but fails to
exploit the mutual affinities between nodes and attributes. In this regard, we
propose a variational co-embedding learning model for attributed network
clustering (VCLANC). VCLANC is composed of dual variational auto-encoders to
simultaneously embed nodes and attributes. Relying on this, the mutual affinity
information between nodes and attributes could be reconstructed from the
embedding space and served as extra self-supervised knowledge for
representation learning. At the same time, trainable Gaussian mixture model is
used as priors to infer the node clustering assignments. To strengthen the
performance of the inferred clusters, we use a mutual distance loss on the
centers of the Gaussian priors and a clustering assignment hardening loss on
the node embeddings. Experimental results on four real-world attributed network
datasets demonstrate the effectiveness of the proposed VCLANC for attributed
network clustering.


Abstract:
  Let $G$ be a simple algebraic group over an algebraically closed field
$\mathbb{F}$ of characteristic $p\geq h$, the Coxeter number of $G$. We observe
an easy `recursion formula' for computing the Jantzen sum formula of a Weyl
module with $p$-regular highest weight. We also discuss a `duality formula'
that relates the Jantzen sum formula to Andersen's sum formula for tilting
filtrations and we give two different representation theoretic explanations of
the recursion formula. As a corollary, we also obtain an upper bound on the
length of the Jantzen filtration of a Weyl module with $p$-regular highest
weight in terms of the length of the Jantzen filtration of a Weyl module with
highest weight in an adjacent alcove.


Abstract:
  Let $A/F$ be an abelian variety over a field. Does there exist a smooth
projective $F$-variety $X$, such that $A$ is isomorphic to the automorphism
group scheme of $X/F$? We show that the answer is positive, if and only if $A$
has only finitely many automorphisms, over an algebraic closure of $F$. When
$F=\mathbb C$, this result is due to Lombardo and Maffei. When $F$ is
algebraically closed, it was obtained independently by Blanc and Brion.


Abstract:
  We present novel realizations of Higgs inflation within Supergravity which
are largely tied to the existence of a pole of order two in the kinetic term of
the inflaton field. This pole arises due to the selected Kaehler potentials
which parameterize the (SU(1,1)/U(1))^2 or SU(2,1)/(SU(2)xU(1)) manifolds with
scalar curvatures R_{(11)^2}=-4/N or R_{21}=-3/N respectively. The associated
superpotential includes, in addition to the Higgs superfields, a stabilizer
superfield, respects the gauge and an R symmetries and contains the first
allowed nonrenormalizable term. If the coefficient of this term is almost equal
to that of the renormalizable terms within about 10^-5 and N=1, the
inflationary observables can be done compatible with the present data and the
scale M of gauge-symmetry breaking may assume its value within MSSM. Increasing
M beyond this value, though, inflation may be attained with less tuning.
Modifications to the Kaehler potentials associated with the manifolds above
allow for inflation, realized with just renormalizable terms, resulting to
higher tensor-to-scalar ratios as N approaches its maximum at N=40.


Abstract:
  We develop a unified approach to proving $L^p-L^q$ boundedness of spectral
projectors, the resolvent of the Laplace-Beltrami operator and its derivative
on $\mathbb{H}^d.$ In the case of spectral projectors, and when $p$ and $q$ are
in duality, the dependence of the implicit constant on $p$ is shown to be
sharp. We also give partial results on the question of $L^p-L^q$ boundedness of
the Fourier extension operator. As an application, we prove smoothing estimates
for the free Schr\"{o}dinger equation on $\mathbb{H}^d$ and a limiting
absorption principle for the electromagnetic Schr\"{o}dinger equation with
small potentials.


Abstract:
  In this paper, we propose an effective method for fast and accurate scene
parsing called Bidirectional Alignment Network (BiAlignNet). Previously, one
representative work BiSeNet~\cite{bisenet} uses two different paths (Context
Path and Spatial Path) to achieve balanced learning of semantics and details,
respectively. However, the relationship between the two paths is not well
explored. We argue that both paths can benefit each other in a complementary
way. Motivated by this, we propose a novel network by aligning two-path
information into each other through a learned flow field. To avoid the noise
and semantic gaps, we introduce a Gated Flow Alignment Module to align both
features in a bidirectional way. Moreover, to make the Spatial Path learn more
detailed information, we present an edge-guided hard pixel mining loss to
supervise the aligned learning process. Our method achieves 80.1\% and 78.5\%
mIoU in validation and test set of Cityscapes while running at 30 FPS with full
resolution inputs. Code and models will be available at
\url{https://github.com/jojacola/BiAlignNet}.


Abstract:
  This paper studies a multi-Intelligent Reflecting Surfaces (IRSs)-assisted
wireless network consisting of multiple base stations (BSs) serving a set of
mobile users. We focus on the IRS-BS association problem in which multiple BSs
compete with each other for controlling the phase shifts of a limited number of
IRSs to maximize the long-term downlink data rate for the associated users. We
propose MDLBI, a Multi-agent Deep Reinforcement Learning-based BS-IRS
association scheme that optimizes the BS-IRS association as well as the
phase-shift of each IRS when being associated with different BSs. MDLBI does
not require information exchanging among BSs. Simulation results show that
MDLBI achieves significant performance improvement and is scalable for large
networking systems.


Abstract:
  We report an infinite number of orthonormal wave functions bases for the
quantum problem of a free particle in presence of an applied external magnetic
field. Each set of orthonormal wave functions (basis) is labeled by an integer
$p$, which is the number of magnetic fluxons trapped in the unit cell. These
bases are suitable to describe particles whose probability density is periodic
and defines a lattice in position space. The present bases of orthonormal wave
functions unveils fractional effects since the number of particles in the unit
cell is independent of the number of trapped fluxons. For a single particle
under $p$ fluxes in the unit cell, and confined to the lowest Landau level, the
probability density vanishes in $p$ points, thus each zero is associated to a
fraction $1/p$ of the particle. Remarkably the case of $n+1$ filled Landau
levels, hence with a total of $N=(n+1)p$ fermions, $n$ being the highest filled
Landau level, the density displays an egg-box pattern with $p^2$ maxima
(minima) which means that a $(n+1)/p$ fraction of flux is associated to every
one of these maxima (minima). We also consider the case of particles
interacting through the magnetic field energy created by their own motion and
find an attractive interaction among them in case they are confined to the
lowest Landau level ($n=0$). The well-known de Haas-van Alphen oscillations are
retrieved within the present orthonormal basis of wave functions thus providing
evidence of its correctness.


Abstract:
  Learning from heterogeneous data poses challenges such as combining data from
various sources and of different types. Meanwhile, heterogeneous data are often
associated with missingness in real-world applications due to heterogeneity and
noise of input sources. In this work, we propose the variational selective
autoencoder (VSAE), a general framework to learn representations from
partially-observed heterogeneous data. VSAE learns the latent dependencies in
heterogeneous data by modeling the joint distribution of observed data,
unobserved data, and the imputation mask which represents how the data are
missing. It results in a unified model for various downstream tasks including
data generation and imputation. Evaluation on both low-dimensional and
high-dimensional heterogeneous datasets for these two tasks shows improvement
over state-of-the-art models.


Abstract:
  This paper presents simulations of the metastable helium (He*) observations
of WASP-107b, so far the highest signal-to-noise ratio detection that is
confirmed by three different instruments. We employ full 3D hydrodynamics
coupled with co-evolving non-equilibrium thermochemistry and ray-tracing
radiation, predicting mass loss rates, temperature profiles, and synthetic He*
line profiles and light curves from first principles. We found that a stellar
wind stronger than solar is demanded by the observed heavily blueshifted line
profile and asymmetric transit light curve. Contrary to previous beliefs, we
argue that radiation pressure can be important for Ly$\alpha$ observations but
{\it not} He*. We found WASP-107b is losing mass at a rate of $\dot{M} \simeq
1.0\times 10^{-9}~M_\oplus~{\rm yr}^{-1}$. Although $\dot{M}$ varies by $<1~\%$
given constant wind and irradiation from the host, shear instabilities still
emerge from wind impacts, producing $\sim 10~\%$ fluctuations of He* transit
depths over hour-long timescales. The common assumption that He* transit depth
indicates the fluctuation of $\dot{M}$ is problematic. The trailing tail is
more susceptible than planet adjacency to the shear instabilities, thus the
line profile is more variable in the blue-shifted wing, while the transit light
curve is more variable after mid-transit. We stress the synergy between
Ly$\alpha$ (higher altitudes, lower density) and He* (lower altitudes, higher
density) transit observations, particularly simultaneous ones, yield better
understanding of planetary outflows and stellar wind properties.


Abstract:
  In this paper, we reformulate conjectural formulas for the arithmetic
intersection numbers of special cycles on unitary Shimura varieties with
minuscule parahoric level structure in terms of weighted counting of lattices
containing special homomorphisms.


Abstract:
  In 1909 Einstein described the thermalization of a mirror within a blackbody
cavity by collisions with thermal photons. While the time to thermalize the
motion of even a microscale or nanoscale object is so long that it is not
feasible, we show that it is using the high intensity light from an amplified
thermal light source with a well-defined chemical potential. We predict damping
of the center-of mass motion due to this effect on times scales of seconds for
small optomechanical systems, such as levitated nanoparticles, allowing
experimental observation.


Abstract:
  Near-field radiative heat transfer (NFHT) research currently suffers from an
imbalance between numerous theoretical studies, as opposed to experimental
reports that remain, in proportion, relatively scarce. Existing experimental
platforms all rely on unique custom-built devices on which it is difficult to
integrate new materials and structures for studying the breadth of
theoretically proposed phenomena. Here we show high-resolution NFHT
measurements using, as our sensing element, silicon nitride (SiN) freestanding
nanomembranes$-$a widely available platform routinely used in materials and
cavity optomechanics research. We measure NFHT by tracking the high mechanical
quality (Q) factor ($>2\times10^6$) resonance of a membrane placed in the
near-field of a hemispherical hot object. We find that high Q-factor enables a
temperature resolution ($1.2\times10^{-6} \ \mathrm{K}$) that is unparalleled
in previous NFHT experiments. Results are in good agreement with a custom-built
model combining heat transport in nanomembranes and the effect of non-uniform
stress/temperature on the resonator eigenmodes.


Abstract:
  Despite the fact that it is publicly available, collecting and processing the
full bitcoin blockchain data is not trivial. Its mere size, history, and other
features indeed raise quite specific challenges, that we address in this paper.
The strengths of our approach are the following: it relies on very basic and
standard tools, which makes the procedure reliable and easily reproducible; it
is a purely lossless procedure ensuring that we catch and preserve all existing
data; it provides additional indexing that makes it easy to further process the
whole data and select appropriate subsets of it. We present our procedure in
details and illustrate its added value on large-scale use cases, like address
clustering. We provide an implementation online, as well as the obtained
dataset.


Abstract:
  A bi-unitary connection in subfactor theory of Jones producing a subfactor of
finite depth gives a 4-tensor appearing in a recent work of
Bultinck-Mariena-Williamson-Sahinoglu-Haegemana-Verstraete on 2-dimensional
topological order and anyons. In their work, they have a special projection
called a projector matrix product operator. We prove that the range of this
projection of length k is naturally identified with the k-th higher relative
commutant of the subfactor arising from the bi-unitary connection. This gives a
further connection between 2-dimensional topological order and subfactor
theory.


Abstract:
  In the cold dark matter scenario, galactic dark matter halos are populated
with a large number of smaller subhalos. Previous work has shown that dark
matter annihilations in subhalos can generate a distinctive, non-Poisson signal
in the gamma-ray photon counts probability distribution function (PDF). Here we
show that the gamma-ray PDF also carries information about the velocity
dependence of the dark matter annihilation cross section. After calculating the
PDF assuming $s$-wave and Sommerfeld-enhanced annihilation, we perform a mock
data analysis to illustrate how current and future observations can constrain
the microphysics of the dark matter annihilation. We find that, with current
Fermi data, and assuming a dark matter annihilation cross section roughly at
the limit of current bounds from annihilation in dwarf spheroidal galaxies, one
can potentially distinguish the non-Poissonian fluctuations expected from dark
matter annihilation in subhalos from Poisson sources, as well as from dark
matter models with an incorrect velocity-dependence. We explore how robust
these results are to assumptions about the modeling of astrophysical
backgrounds. We also point out a four-parameter degeneracy between the velocity
dependence of the dark matter annihilation, the minimum subhalo mass, the power
law index of the subhalo mass function, and the normalization of the dark
matter signal. This degeneracy can be broken with priors from N-body
simulations or from observational constraints on the subhalo mass function.


Abstract:
  For certain types of quadratic forms lying in the n-th power of the
fundamental ideal, we compute upper bounds and where possible exact values for
the minimal number of general n-fold Pfister forms, that are needed to write
the Witt class of that given form as the sum of the Witt classes of those
n-fold Pfister forms. We restrict ourselves mostly to the case of so called
rigid fields, i.e. fields in which binary anisotropic forms represent at most 2
square classes.


Abstract:
  We classify compact manifolds of dimension three equipped with a path
structure and a fixed contact form (which we refer to as a strict path
structure) under the hypothesis that their automorphism group is non-compact.
We use a Cartan connection associated to the structure and show that its
curvature is constant.


Abstract:
  We present the results of a single dish survey toward 95 VeLLOs in optically
thick (HCN 1-0) and thin ($\rm N_2H^+$ 1-0) lines performed for the purpose of
understanding the physical processes of inward motions in the envelopes of the
VeLLOs and characterizing their true nature. The normalized velocity
differences ($\delta V_{HCN}$) between the peak velocities of the two lines
were derived for 41 VeLLOs detected in both lines. The $\delta V$ distribution
of these VeLLOs is found to be significantly skewed to the blue, indicating the
dominance of infalling motions in their envelopes. The infall speeds were
derived for 15 infall candidates by using the HILL5 radiative transfer model.
The speeds were in the range of 0.03 $\rm km~s^{-1}$ to 0.3 $\rm km~s^{-1}$,
with a median value of 0.16 $\rm km~s^{-1}$, being consistent with the
gravitational free-fall speeds from pressure-free envelopes. The mass infall
rates calculated from the infall speeds are mostly of the order of $10^{-6}
M_{\odot}~yr^{-1}$ with a median value of $\rm 3.4 \pm 1.5 \times 10^{-6}
M_{\odot}~yr^{-1}$. These are found to be also consistent with the values
predicted with the inside-out collapse model and show a fairly good correlation
with the internal luminosities of the VeLLOs. This again indicates that the
infall motions observed toward the VeLLOs are likely to be due to the
gravitational infall motions in their envelopes. Our study suggests that most
of the VeLLOs are potentially faint protostars while two of the VeLLOs could
possibly be proto-brown dwarf candidates.


Abstract:
  We address the problem of universal domain adaptation (UDA) in ordinal
regression (OR), which attempts to solve classification problems in which
labels are not independent, but follow a natural order. We show that the UDA
techniques developed for classification and based on the clustering assumption,
under-perform in OR settings. We propose a method that complements the OR
classifier with an auxiliary task of order learning, which plays the double
role of discriminating between common and private instances, and expanding
class labels to the private target images via ranking. Combined with
adversarial domain discrimination, our model is able to address the closed set,
partial and open set configurations. We evaluate our method on three face age
estimation datasets, and show that it outperforms the baseline methods.


Abstract:
  Perhaps surprisingly sewerage infrastructure is one of the most costly
infrastructures in modern society. Sewer pipes are manually inspected to
determine whether the pipes are defective. However, this process is limited by
the number of qualified inspectors and the time it takes to inspect a pipe.
Automatization of this process is therefore of high interest. So far, the
success of computer vision approaches for sewer defect classification has been
limited when compared to the success in other fields mainly due to the lack of
public datasets. To this end, in this work we present a large novel and
publicly available multi-label classification dataset for image-based sewer
defect classification called Sewer-ML.
  The Sewer-ML dataset consists of 1.3 million images annotated by professional
sewer inspectors from three different utility companies across nine years.
Together with the dataset, we also present a benchmark algorithm and a novel
metric for assessing performance. The benchmark algorithm is a result of
evaluating 12 state-of-the-art algorithms, six from the sewer defect
classification domain and six from the multi-label classification domain, and
combining the best performing algorithms. The novel metric is a
class-importance weighted F2 score, $\text{F}2_{\text{CIW}}$, reflecting the
economic impact of each class, used together with the normal pipe F1 score,
$\text{F}1_{\text{Normal}}$. The benchmark algorithm achieves an
$\text{F}2_{\text{CIW}}$ score of 55.11% and $\text{F}1_{\text{Normal}}$ score
of 90.94%, leaving ample room for improvement on the Sewer-ML dataset. The
code, models, and dataset are available at the project page
https://vap.aau.dk/sewer-ml/


Abstract:
  Quantitative magneto-optical imaging of a type-II superconductor thin film
cooled under zero, homogeneous, and inhomogeneous applied magnetic fields,
indicates that the latter procedure leads to an enhancement of the screening
capacity. Such an observation is corroborated by both B-independent and
B-dependent critical state model analyses. Furthermore, repulsive (attractive)
vortex-(anti)vortex interactions were found to have a decisive role in the
shielding ability, with initial states prepared with vortices resulting in a
shorter magnetic flux front penetration depth than those prepared with
antivortices. The proposed strategy could be implemented to boost the
performance of thin superconducting devices.


Abstract:
  We consider the problem of generalization in reinforcement learning where
visual aspects of the observations might differ, e.g. when there are different
backgrounds or change in contrast, brightness, etc. We assume that our agent
has access to only a few of the MDPs from the MDP distribution during training.
The performance of the agent is then reported on new unknown test domains drawn
from the distribution (e.g. unseen backgrounds). For this "zero-shot RL" task,
we enforce invariance of the learned representations to visual domains via a
domain adversarial optimization process. We empirically show that this approach
allows achieving a significant generalization improvement to new unseen
domains.


Abstract:
  Let $C$ be a hyperelliptic curve of genus $g>1$ over an algebraically closed
field $K$ of characteristic zero and $O$ one of the $(2g+2)$ Weierstrass points
in $C(K)$. Let $J$ be the jacobian of $C$, which is a $g$-dimensional abelian
variety over $K$. Let us consider the canonical embedding of $C$ into $J$ that
sends $O$ to the zero of the group law on $J$. This embedding allows us to
identify $C(K)$ with a certain subset of the commutative group $J(K)$.
  A special case of the famous theorem of Raynaud (Manin--Mumford conjecture)
asserts that the set of torsion points in $C(K)$ is finite. It is well known
that the points of order 2 in $C(K)$ are exactly the "remaining" $(2g+1)$
Weierstrass points. One of the authors proved that there are no torsion points
of order $n$ in $C(K)$ if $3\le n\le 2g$. So, it is natural to study torsion
points of order $2g+1$ (notice that the number of such points in $C(K)$ is
always even). Recently, the authors proved that there are infinitely many (for
a given $g$) mutually nonisomorphic pairs $C,O)$ such that $C(K)$ contains at
least four points of order $2g+1$.
  In the present paper we prove that (for a given $g$) there are at most
finitely many (up to a isomorphism) pairs $(C,O)$ such that $C(K)$ contains at
least six points of order $2g+1$.


Abstract:
  Systems of interacting agents can often be modeled as contextual games, where
the context encodes additional information, beyond the control of any agent
(e.g. weather for traffic and fiscal policy for market economies). In such
systems, the most likely outcome is given by a Nash equilibrium. In many
practical settings, only game equilibria are observed, while the optimal
parameters for a game model are unknown. This work introduces Nash Fixed Point
Networks (N-FPNs), a class of implicit-depth neural networks that output Nash
equilibria of contextual games. The N-FPN architecture fuses data-driven
modeling with provided constraints. Given equilibrium observations of a
contextual game, N-FPN parameters are learnt to predict equilibria outcomes
given only the context. We present an end-to-end training scheme for N-FPNs
that is simple and memory efficient to implement with existing
autodifferentiation tools. N-FPNs also exploit a novel constraint decoupling
scheme to avoid costly projections. Provided numerical examples show the
efficacy of N-FPNs on atomic and non-atomic games (e.g. traffic routing).


Abstract:
  The Weisfeiler--Leman algorithm is a ubiquitous tool for the Graph
Isomorphism Problem with various characterisations in e.g. descriptive
complexity and convex optimisation. It is known that graphs that are not
distinguished by the two-dimensional variant have cospectral adjacency
matrices. We tackle a converse problem by proposing a set of matrices called
Generalised Laplacians that characterises the expressiveness of WL in terms of
spectra. As an application to random walks, we show using Generalised
Laplacians that the edge colours produced by 2-WL determine commute distances.


Abstract:
  An all-electric unmanned aerial system with both VTOL and Fixed wing
capabilities is designed and optimized for long range surveillance and relief
operations. The UAV is equipped with onboard computers and sensors and is
capable of carrying 1kg of relief payload upto 100 Km. The entire low fidelity
design process -- from concept to render -- is carried out using completely
open source tools, libraries and in-house code. The challenges faced and
primary differences are discussed parallelly. A comparison with commercial
codes and programs is also done in some areas to give an overview of key
capabilities and caveats.


Abstract:
  We show that for $\gamma<\sqrt{4/3}$, it is possible to define the Levy area
of a planar Brownian motion with the Liouville measure of intermittency
parameter $\gamma$ as the underlying area measure. We also consider the case of
smoother curves, and study some properties of the integration map thus defined.


Abstract:
  In the pursuit of a deeper understanding of a model's behaviour, there is
recent impetus for developing suites of probes aimed at diagnosing models
beyond simple metrics like accuracy or BLEU. This paper takes a step back and
asks an important and timely question: how reliable are these diagnostics in
providing insight into models and training setups? We critically examine three
recent diagnostic tests for pre-trained language models, and find that
likelihood-based and representation-based model diagnostics are not yet as
reliable as previously assumed. Based on our empirical findings, we also
formulate recommendations for practitioners and researchers.


Abstract:
  Source independent quantum random number generators (SI-QRNG) are
cryptographic protocols which attempt to extract random strings from quantum
sources where the source is under the control of an adversary while the
measurement devices are fully characterized. This represents a middle-ground
between fully-trusted and full-device independence, allowing for fast
bit-generation rates with current-day technology, while also providing a strong
security guarantee. In this paper we analyze an SI-QRNG protocol based on
quantum walks and develop a new proof technique to show security.


Abstract:
  We consider learning the structures of Gaussian latent tree models with
vector observations when a subset of them are arbitrarily corrupted. First, we
present the sample complexities of Recursive Grouping (RG) and Chow-Liu
Recursive Grouping (CLRG) without the assumption that the effective depth is
bounded in the number of observed nodes, significantly generalizing the results
in Choi et al. (2011). We show that Chow-Liu initialization in CLRG greatly
reduces the sample complexity of RG from being exponential in the diameter of
the tree to only logarithmic in the diameter for the hidden Markov model (HMM).
Second, we robustify RG, CLRG, Neighbor Joining (NJ) and Spectral NJ (SNJ) by
using the truncated inner product. These robustified algorithms can tolerate a
number of corruptions up to the square root of the number of clean samples.
Finally, we derive the first known instance-dependent impossibility result for
structure learning of latent trees. The optimalities of the robust version of
CLRG and NJ are verified by comparing their sample complexities and the
impossibility result.


Abstract:
  One of the promising applications of early quantum computers is the
simulation of quantum systems. Variational methods for near-term quantum
computers, such as the variational quantum eigensolver (VQE), are a promising
approach to finding ground states of quantum systems relevant in physics,
chemistry, and materials science. These approaches, however, are constrained by
the effects of noise as well as the limited quantum resources of near-term
quantum hardware, motivating the need for quantum error mitigation techniques
to reduce the effects of noise. Here we introduce $\textit{neural error
mitigation}$, a novel method that uses neural networks to improve estimates of
ground states and ground-state observables obtained using VQE on near-term
quantum computers. To demonstrate our method's versatility, we apply neural
error mitigation to finding the ground states of H$_2$ and LiH molecular
Hamiltonians, as well as the lattice Schwinger model. Our results show that
neural error mitigation improves the numerical and experimental VQE computation
to yield low-energy errors, low infidelities, and accurate estimations of
more-complex observables like order parameters and entanglement entropy,
without requiring additional quantum resources. Additionally, neural error
mitigation is agnostic to both the quantum hardware and the particular noise
channel, making it a versatile tool for quantum simulation. Applying quantum
many-body machine learning techniques to error mitigation, our method is a
promising strategy for extending the reach of near-term quantum computers to
solve complex quantum simulation problems.


Abstract:
  Contextual information has been shown to be powerful for semantic
segmentation. This work proposes a novel Context-based Tandem Network (CTNet)
by interactively exploring the spatial contextual information and the channel
contextual information, which can discover the semantic context for semantic
segmentation. Specifically, the Spatial Contextual Module (SCM) is leveraged to
uncover the spatial contextual dependency between pixels by exploring the
correlation between pixels and categories. Meanwhile, the Channel Contextual
Module (CCM) is introduced to learn the semantic features including the
semantic feature maps and class-specific features by modeling the long-term
semantic dependence between channels. The learned semantic features are
utilized as the prior knowledge to guide the learning of SCM, which can make
SCM obtain more accurate long-range spatial dependency. Finally, to further
improve the performance of the learned representations for semantic
segmentation, the results of the two context modules are adaptively integrated
to achieve better results. Extensive experiments are conducted on three
widely-used datasets, i.e., PASCAL-Context, ADE20K and PASCAL VOC2012. The
results demonstrate the superior performance of the proposed CTNet by
comparison with several state-of-the-art methods.


Abstract:
  Predictive business process monitoring is concerned with the prediction how a
running process instance will unfold up to its completion at runtime. Most of
the proposed approaches rely on a wide number of different machine learning
(ML) techniques. In the last years numerous comparative studies, reviews, and
benchmarks of such approaches where published and revealed that they can be
successfully applied for different prediction targets. ML techniques require a
qualitatively and quantitatively sufficient data set. However, there are many
situations in business process management (BPM) where only a quantitatively
insufficient data set is available. The problem of insufficient data in the
context of BPM is still neglected. Hence, none of the comparative studies or
benchmarks investigates the performance of predictive business process
monitoring techniques in environments with small data sets. In this paper an
evaluation framework for comparing existing approaches with regard to their
suitability for small data sets is developed and exemplarily applied to
state-of-the-art approaches in predictive business process monitoring.


Abstract:
  Neural Module Networks (NMNs) aim at Visual Question Answering (VQA) via
composition of modules that tackle a sub-task. NMNs are a promising strategy to
achieve systematic generalization, i.e. overcoming biasing factors in the
training distribution. However, the aspects of NMNs that facilitate systematic
generalization are not fully understood. In this paper, we demonstrate that the
stage and the degree at which modularity is defined has large influence on
systematic generalization. In a series of experiments on three VQA datasets
(MNIST with multiple attributes, SQOOP, and CLEVR-CoGenT), our results reveal
that tuning the degree of modularity in the network, especially at the image
encoder stage, reaches substantially higher systematic generalization. These
findings lead to new NMN architectures that outperform previous ones in terms
of systematic generalization.


Abstract:
  For a generalized holomorphic vector bundle, we introduce the Atiyah class,
which is the obstruction of the existence of generalized holomorphic
connections on this bundle. Similar to the holomorphic case, such Atiyah
classes can be defined by three approaches: the $\rm{\check{C}}$ech cohomology,
the extension class of the first jet bundle as well as the Lie pair.


Abstract:
  Kreck's modified surgery theory reduces the classification of closed,
connected 4-manifolds, up to connect sum with some number of copies of
$S^2\times S^2$, to a series of bordism questions. We implement this in the
case of unorientable 4-manifolds M and show that for some choices of
fundamental groups, the computations simplify considerably. We use this to
solve some cases in which $\pi_1(M)$ is finite of order 2 mod 4: under an
assumption on cohomology, there are nine stable diffeomorphism classes for
which M is pin$^+$, one stable diffeomorphism class for which M is pin$^-$, and
four stable diffeomorphism classes for which M is neither. We also determine
the corresponding stable homeomorphism classes.


Abstract:
  Information Causality is a physical principle which states that the amount of
randomly accessible data over a classical communication channel cannot exceed
its capacity, even if the sender and the receiver have access to a source of
nonlocal correlations. This principle can be used to bound the nonlocality of
quantum mechanics without resorting to its full formalism, with a notable
example of reproducing the Tsirelson's bound of the Clauser-Horne-Shimony-Holt
inequality. Despite being promising, the latter result found little
generalization to other Bell inequalities because of the limitations imposed by
the process of concatenation, in which several nonsignaling resources are put
together to produce tighter bounds. In this work, we show that concatenation
can be successfully replaced by limits on the communication channel capacity.
It allows us to re-derive and, in some cases, significantly improve all the
previously known results in a simpler manner and apply the Information
Causality principle to previously unapproachable Bell scenarios.


Abstract:
  To obtain the Dirichlet series for complex powers of the Riemann zeta
function, we define and study the basic properties of a sequence of polynomials
that, used as coefficients of the respective terms of the Dirichlet series of
the Riemann zeta function in the half plane $x > 1$, produces the required
exponential function. Unlike the method described in ([4], p.~278), which
requires more advanced knowledge of the relationships between Dirichlet series
and multiplicative arithmetic functions, our approach only needs mathematical
induction on the total number of prime divisors of $n$, the Dirichlet product
and the use of an analytic property characteristic of the exponential function
in the complex plane.


Abstract:
  We introduce a location statistic for distributions on non-linear geometric
spaces, the diffusion mean, serving both as an extension of and an alternative
to the Fr\'echet mean. The diffusion mean arises as the generalization of
Gaussian maximum likelihood analysis to non-linear spaces by maximizing the
likelihood of a Brownian motion. The diffusion mean depends on a time parameter
$t$, which admits the interpretation of the allowed variance of the mean. The
diffusion $t$-mean of a distribution $X$ is the most likely origin of a
Brownian motion at time $t$, given the end-point distribution $X$. We give a
detailed description of the asymptotic behavior of the diffusion estimator and
provide sufficient conditions for the diffusion estimator to be strongly
consistent. Furthermore, we present a smeary central limit theorem for
diffusion means and investigate properties of the diffusion mean for
distributions on the sphere $\mathcal{S}^n$. Experimentally, we consider
simulated data and data from magnetic pole reversals, all indicating similar or
improved convergence rate compared to the Fr\'echet mean. Here, we additionally
estimate $t$ and consider its effects on smeariness and uniqueness of the
diffusion mean for distributions on the sphere.


Abstract:
  Solar neutrino capture cross-section by 127I nucleus has been studied with
taking into account the influence of the resonance structure of the nuclear
strength function S(E). Three types of isobaric resonances: giant Gamow-Teller,
analog resonance and low-lying Gamow-Teller pigmy resonances has been
investigated on the framework of self-consistent theory of finite Fermi
systems. The calculations have been performed considering the resonance
structure of the charge-exchange strength function S(E). We analyze the effect
of each resonance on the energy dependence of the cross-section. It has been
shown that all high-lying resonances should be considered. Neutron emission
process for high energy nuclear excitation leads to formation 126Xe isotope. We
evaluate contribution from various sources of solar neutrinos to the
126Xe/127Xe isotopes ratio formed by energetic neutrinos. 126Xe/127Xe isotope
ratio could be an indicator of high-energy boron neutrinos in the solar
spectrum. We also discuss the uncertainties in the often used Fermi-functions
calculations.


Abstract:
  Coronal mass ejections (CMEs) and solar energetic particles (SEPs) are two
phenomena that can cause severe space weather effects throughout the
heliosphere. The evolution of CMEs, especially in terms of their magnetic
structure, and the configuration of the interplanetary magnetic field (IMF)
that influences the transport of SEPs are currently areas of active research.
These two aspects are not necessarily independent of each other, especially
during solar maximum when multiple eruptive events can occur close in time.
Accordingly, we present the analysis of a CME that erupted on 2012 May 11
(SOL2012-05-11) and an SEP event following an eruption that took place on 2012
May 17 (SOL2012-05-17). After observing the May 11 CME using remote-sensing
data from three viewpoints, we evaluate its propagation through interplanetary
space using several models. Then, we analyse in-situ measurements from five
predicted impact locations (Venus, Earth, the Spitzer Space Telescope, the Mars
Science Laboratory en route to Mars, and Mars) in order to search for CME
signatures. We find that all in-situ locations detect signatures of an SEP
event, which we trace back to the May 17 eruption. These findings suggest that
the May 11 CME provided a direct magnetic connectivity for the efficient
transport of SEPs. We discuss the space weather implications of CME evolution,
regarding in particular its magnetic structure, and CME-driven IMF
preconditioning that facilitates SEP transport. Finally, this work remarks the
importance of using data from multiple spacecraft, even those that do not
include space weather research as their primary objective.


Abstract:
  This paper discusses modern Auto Machine Learning (AutoML) tools from the
perspective of a person with little prior experience in Machine Learning (ML).
There are many AutoML tools both ready-to-use and under development, which are
created to simplify and democratize usage of ML technologies in everyday life.
Our position is that ML should be easy to use and available to a greater number
of people. Prior research has identified the need for intuitive AutoML tools.
This work seeks to understand how well AutoML tools have achieved that goal in
practice. We evaluate three AutoML Tools to evaluate the end-user experience
and system performance. We evaluate the tools by having them create models from
a competition dataset on banking data. We report on their performance and the
details of our experience. This process provides a unique understanding of the
state of the art of AutoML tools. Finally, we use these experiences to inform a
discussion on how future AutoML tools can improve the user experience for
neophytes of Machine Learning.


Abstract:
  It is shown that impulsive systems of nonlinear, time-varying and/or switched
form that allow a stable global state weak linearization are jointly
input-to-state stable (ISS) under small inputs and integral ISS (iISS). The
system is said to allow a global state weak linearization if its flow and jump
equations can be written as a (time-varying, switched) linear part plus a
(nonlinear) pertubation satisfying a bound of affine form on the state. This
bound reduces to a linear form under zero input but does not force the system
to be linear under zero input. The given results generalize and extend
previously existing ones in many directions: (a) no (dwell-time or other)
constraints are placed on the impulse-time sequence, (b) the system need not be
linear under zero input, (c) existence of a (common) Lyapunov function is not
required, (d) the perturbation bound need not be linear on the input.


Abstract:
  The holographic principle implies that quantum field theory overcounts the
number of independent degrees of freedom in quantum gravity. An argument due to
Cohen, Kaplan, and Nelson (CKN) suggests that the number of degrees of freedom
well-described by QFT is even smaller than required by holographic bounds, and
CKN interpreted this result as indicative of a correlation between the UV and
IR cutoffs on QFT. Here we consider an alternative interpretation in which the
QFT degrees of freedom are depleted as a function of scale. We use a simple
recipe to estimate the impact of depleted densities of states on precision
observables, including the Lamb shift and lepton $g-2$. Although these
observables are not sensitive to the level of depletion motivated by
gravitational considerations, the phenomenological exercises also provide an
interesting test of quantum field theory that is independent of underlying
quantum gravity assumptions. A depleted density of states can also render the
QFT vacuum energy UV-insensitive, reconciling the success of QFT in describing
ordinary particle physics processes and its apparent failure in predicting the
cosmological constant.


Abstract:
  Photo-induced phase-segregation in mixed halide perovskite MAPb(BrxI1-x)3 is
investigated in the full compositional range by correlative X-ray diffraction
and photo-luminescence experiments.


Abstract:
  We give a simple proof of a recent result due to Agostiniani, Fogagnolo and
Mazzieri.


Abstract:
  While recent computer vision algorithms achieve impressive performance on
many benchmarks, they lack robustness - presented with an image from a
different distribution, (e.g. weather or lighting conditions not considered
during training), they may produce an erroneous prediction. Therefore, it is
desired that such a model will be able to reliably predict its confidence
measure. In this work, uncertainty estimation for the task of semantic
segmentation is evaluated under a varying level of domain shift: in a
cross-dataset setting and when adapting a model trained on data from the
simulation. It was shown that simple color transformations already provide a
strong baseline, comparable to using more sophisticated style-transfer data
augmentation. Further, by constructing an ensemble consisting of models using
different backbones and/or augmentation methods, it was possible to improve
significantly model performance in terms of overall accuracy and uncertainty
estimation under the domain shift setting. The Expected Calibration Error (ECE)
on challenging GTA to Cityscapes adaptation was reduced from 4.05 to the
competitive value of 1.1. Further, an ensemble of models was utilized in the
self-training setting to improve the pseudo-labels generation, which resulted
in a significant gain in the final model accuracy, compared to the standard
fine-tuning (without ensemble).


Abstract:
  Comprehensive benchmarking of clustering algorithms is rendered difficult by
two key factors: (i)~the elusiveness of a unique mathematical definition of
this unsupervised learning approach and (ii)~dependencies between the
generating models or clustering criteria adopted by some clustering algorithms
and indices for internal cluster validation. Consequently, there is no
consensus regarding the best practice for rigorous benchmarking, and whether
this is possible at all outside the context of a given application. Here, we
argue that synthetic datasets must continue to play an important role in the
evaluation of clustering algorithms, but that this necessitates constructing
benchmarks that appropriately cover the diverse set of properties that impact
clustering algorithm performance. Through our framework, HAWKS, we demonstrate
the important role evolutionary algorithms play to support flexible generation
of such benchmarks, allowing simple modification and extension. We illustrate
two possible uses of our framework: (i)~the evolution of benchmark data
consistent with a set of hand-derived properties and (ii)~the generation of
datasets that tease out performance differences between a given pair of
algorithms. Our work has implications for the design of clustering benchmarks
that sufficiently challenge a broad range of algorithms, and for furthering
insight into the strengths and weaknesses of specific approaches.


Abstract:
  We construct a Floer type boundary operator for generalised Morse-Smale
dynamical systems on compact smooth manifolds by counting the number of
suitable flow lines between closed (both homoclinic and periodic) orbits and
isolated critical points. The same principle works for the discrete situation
of general combinatorial vector fields, defined by Forman, on CW complexes. We
can thus recover the $\mathbb{Z}_2$ homology of both smooth and discrete
structures directly from the flow lines (V-paths) of our vector field.


Abstract:
  We study the inverse random source problem for the time-space fractional
diffusion equation driven by fractional Brownian motion with Hurst index
$H\in(0,1)$. With the aid of a novel estimate, by using the operator approach
we propose regularity analyses for the direct problem. Then we provide a
reconstruction scheme for the source terms $f$ and $g$ up to the sign. Next,
combining the properties of Mittag-Leffler function, the complete uniqueness
and instability analyses are provided. It's worth mentioning that all the
analyses are unified for $H\in(0,1)$.


Abstract:
  This work introduces a novel epidemiological model that simultaneously
considers multiple viral strains, reinfections due to waning immunity response
over time and an optimal control formulation. This enables us to derive optimal
mitigation strategies over a prescribed time horizon under a more realistic
framework that does not imply perennial immunity and a single strain, although
these can also be derived as particular cases of our formulation. The model
also allows estimation of the number of infections over time in the absence of
mitigation strategies under any number of viral strains. We validate our
approach in the light of the COVID-19 epidemic and present a number of
experiments to shed light on the overall behaviour under one or two strains in
the absence of sufficient mitigation measures. We also derive optimal control
strategies for distinct mitigation costs and evaluate the effect of these costs
on the optimal mitigation measures over a two-year horizon. The results show
that relaxations in the mitigation measures cause a rapid increase in the
number of cases, which then demand more restrictive measures in the future.


Abstract:
  A complex manifold $X$ is \emph{weakly complete} if it admits a continuous
plurisubharmonic exhaustion function $\phi$. The minimal kernels $\Sigma_X^k, k
\in [0,\infty]$ (the loci where are all $\mathcal{C}^k$ plurisubharmonic
exhaustion functions fail to be strictly plurisubharmonic),introduced by
Slodkowski-Tomassini, and the Levi currents, introduced by Sibony, are both
concepts aimed at measuring how far $X$ is from being Stein. We compare these
notions, prove that all Levi currents are supported by all the $\Sigma_X^k$'s,
and give sufficient conditions for points in $\Sigma_X^k$ to be in the support
of some Levi current. When $X$ is a surface and $\phi$ can be chosen analytic,
building on previous work by the second author, Slodkowski, and Tomassini,we
prove the existence of a Levi current precisely supported on $\Sigma_X^\infty$,
and give a classification of Levi currents on $X$. In particular,unless $X$ is
a modification of a Stein space, every point in $X$ is in the support of some
Levi current.


Abstract:
  Modern engineering alloys have bespoke microstructures, where features such
as precipitates are used to control properties. In many Ni-based alloys,
carbo-nitride precipitates are introduced to strengthen and improve
performance. These precipitates can be distributed throughout the
microstructure and niobium rich carbides are often found at grain boundaries.
In this work, we used combined energy dispersive X-ray spectroscopy (EDS) and
electron backscatter diffraction (EBSD) to characterise the population of these
precipitates. Processing of the EDS signal is used to label the Mo/Nb-rich
precipitates, and their size and location are measured from maps using a
circular Hough transform. This label map is combined with the grain boundary
network (from EBSD analysis). Statistical analysis, using ANOVA testing,
reveals differences in chemistry between carbides found in Ni-rich matrix grain
interiors, on random high angle boundaries and on special boundaries ({\Sigma}3
and {\Sigma}9). These results are compared between wrought and power metallurgy
product forms. These distributions are discussed in the context of their
performance within demanding environments, such as reactor core internals.


Abstract:
  There are many different classifications of entanglement for multipartite
quantum systems, one of which is based on the number of unentangled particles.
In this paper, we mainly study the quantum states containing at most $k-1$
unentangled particles and provide several entanglement criteria based on
different forms of inequalities which can both identify quantum states
containing at most $k-1$ unentangled particles. We show that these criteria are
more effective for some states by concrete examples.


Abstract:
  Learning node representations that incorporate information from graph
structure benefits wide range of tasks on graph. The majority of existing graph
neural networks (GNNs) have limited power in capturing position information for
a given node. The idea of positioning nodes with selected anchors has been
exploited, yet mainly relying on explicit labeling of distance information.
Here we propose Graph Inference Representation (GIR), an anchor based GNN model
encoding path information related to pre-selected anchors for each node.
Abilities to get position-aware embeddings are theoretically and experimentally
investigated on GIR and its core variants. Further, the complementarity between
GIRs and typical GNNs is demonstrated. We show that GIRs get outperformed
results in position-aware scenarios, and performances on typical GNNs could be
improved by fusing GIR embeddings.


Abstract:
  Nonparametric feature selection in high-dimensional data is an important and
challenging problem in statistics and machine learning fields. Most of the
existing methods for feature selection focus on parametric or additive models
which may suffer from model misspecification. In this paper, we propose a new
framework to perform nonparametric feature selection for both regression and
classification problems. In this framework, we learn prediction functions
through empirical risk minimization over a reproducing kernel Hilbert space.
The space is generated by a novel tensor product kernel which depends on a set
of parameters that determine the importance of the features. Computationally,
we minimize the empirical risk with a penalty to estimate the prediction and
kernel parameters at the same time. The solution can be obtained by iteratively
solving convex optimization problems. We study the theoretical property of the
kernel feature space and prove both the oracle selection property and the
Fisher consistency of our proposed method. Finally, we demonstrate the superior
performance of our approach compared to existing methods via extensive
simulation studies and application to a microarray study of eye disease in
animals.


Abstract:
  Toxicity evaluation of chemical compounds has traditionally relied on animal
experiments;however, the demand for non-animal-based prediction methods for
toxicology of compounds is increasing worldwide. Our aim was to provide a
classification method for compounds based on \textit{in vitro} gene expression
profiles. The \textit{in vitro} gene expression data analyzed in the present
study was obtained from our previous study. The data concerned nine compounds
typically employed in chemical management.We used agglomerative hierarchical
clustering to classify the compounds;however, there was a statistical
difficulty to be overcome.We needed to properly extract RNAs for clustering
from more than 30,000 RNAs. In order to overcome this difficulty, we introduced
a combinatorial optimization problem with respect to both gene expression
levels and the correlation between gene expression profiles. Then, the
simulated annealing algorithm was used to obtain a good solution for the
problem. As a result, the nine compounds were divided into two groups using
1,000 extracted RNAs. Our proposed methodology enables read-across, one of the
frameworks for predicting toxicology, based on \textit{in vitro} gene
expression profiles.


Abstract:
  We report the discovery of the massive hot Jupiter NGTS-13b by the Next
Generation Transit Survey (NGTS). The V = 12.7 host star is likely in the
subgiant evolutionary phase with log g$_{*}$ = 4.04 $\pm$ 0.05, T$_{eff}$ =
5819 $\pm$ 73 K, M$_{*}$ = 1.30$^{+0.11}_{-0.18}$ M$_{\odot}$, and R$_{*}$ =
1.79 $\pm$ 0.06 R$_{\odot}$. NGTS detected a transiting planet with a period of
P = 4.12 days around the star, which was later validated with the Transiting
Exoplanet Survey Satellite (TESS; TIC 454069765). We confirm the planet using
radial velocities from the CORALIE spectrograph. Using NGTS and TESS full-frame
image photometry combined with CORALIE radial velocities we determine NGTS-13b
to have a radius of R$_{P}$ = 1.142 $\pm$ 0.046 R$_{Jup}$, mass of M$_{P}$ =
4.84 $\pm$ 0.44 M$_{Jup}$ and eccentricity e = 0.086 $\pm$ 0.034. Some previous
studies suggest that $\sim$4 M$_{Jup}$ may be a border between two separate
formation scenarios (e.g., core accretion and disk instability) and that
massive giant planets share similar formation mechanisms as lower-mass brown
dwarfs. NGTS-13b is just above 4 M$_{Jup}$ making it an important addition to
the statistical sample needed to understand the differences between various
classes of substellar companions. The high metallicity, [Fe/H] = 0.25 $\pm$
0.17, of NGTS-13 does not support previous suggestions that massive giants are
found preferentially around lower metallicity host stars, but NGTS-13b does
support findings that more massive and evolved hosts may have a higher
occurrence of close-in massive planets than lower-mass unevolved stars.


Abstract:
  Let $f:\, X\to Y$ be a semistable non-isotrivial family of $n$-folds over a
smooth projective curve with discriminant locus $S \subseteq Y$ and with
general fibre $F$ of general type. We show the strict Arakelov inequality
\[\frac{\mathrm{deg}\, f_*\omega_{X/Y}^\nu}{\mathrm{rank}\,
f_*\omega_{X/Y}^\nu} < {n\nu\over 2}\cdot\mathrm{deg}\,\Omega^1_Y(\log S),\]
for all $\nu\in \mathbb N$ such that the $\nu$-th pluricanonical linear system
$|\omega^\nu_F|$ is birational. This answers a question asked by M\"oller,
Viehweg and the third named author.


Abstract:
  Spin-to-orbit conversion of light is a dynamical optical phenomenon in
non-paraxial fields leading to various manifestations of the spin and orbital
Hall effect. However, effects of spin-orbit interaction (SOI) have not been
explored extensively for higher order Gaussian beams carrying no intrinsic
orbital angular momentum. Indeed, the SOI effects on such structured beams can
be directly visualized due to azimuthal rotation of their transverse intensity
profiles - a phenomenon we call the rotational Hall effect. In this paper, we
show that for an input circularly polarized (right/left) $HG_{10}$ mode, SOI
leads to a significant azimuthal rotation of the transverse intensity
distribution of both the orthogonal circularly polarized (left/right)
component, and the transverse component of the longitudinal field intensity
with respect to the input intensity profile. We validate our theoretical and
numerically simulated results experimentally by tightly focusing a circularly
polarized $HG_{10}$ beam in an optical tweezers configuration, and projecting
out the opposite circular polarization component and the transverse component
of the longitudinal field intensity at the output of the tweezers. We also
measure the rotational shift as a function of the refractive index contrast in
the path of the tightly focused light, and in general observe a proportional
increase. The enhanced spin-orbit conversion in these cases may lead to
interesting applications in inducing complex dynamics in optically trapped
birefringent particles using higher order Gaussian beams with no intrinsic
orbital angular momentum.


Abstract:
  The recent development of likelihood-free inference aims training a flexible
density estimator for the target posterior with a set of input-output pairs
from simulation. Given the diversity of simulation structures, it is difficult
to find a single unified inference method for each simulation model. This paper
proposes a universally applicable regularization technique, called
Posterior-Aided Regularization (PAR), which is applicable to learning the
density estimator, regardless of the model structure. Particularly, PAR solves
the mode collapse problem that arises as the output dimension of the simulation
increases. PAR resolves this posterior mode degeneracy through a mixture of 1)
the reverse KL divergence with the mode seeking property; and 2) the mutual
information for the high quality representation on likelihood. Because of the
estimation intractability of PAR, we provide a unified estimation method of PAR
to estimate both reverse KL term and mutual information term with a single
neural network. Afterwards, we theoretically prove the asymptotic convergence
of the regularized optimal solution to the unregularized optimal solution as
the regularization magnitude converges to zero. Additionally, we empirically
show that past sequential neural likelihood inferences in conjunction with PAR
present the statistically significant gains on diverse simulation tasks.


Abstract:
  Contact tracing is a very effective way to control the COVID-19-like
pandemics. It aims to identify individuals who closely contacted an infected
person during the incubation period of the virus and notify them to quarantine.
However, the existing systems suffer from privacy, security, and efficiency
issues. To address these limitations, in this paper, we propose an efficient
and privacy-preserving Blockchain-based infection control system. Instead of
depending on a single authority to run the system, a group of health
authorities, that form a consortium Blockchain, run our system. Using
Blockchain technology not only secures our system against single point of
failure and denial of service attacks, but also brings transparency because all
transactions can be validated by different parties. Although contact tracing is
important, it is not enough to effectively control an infection. Thus, unlike
most of the existing systems that focus only on contact tracing, our system
consists of three integrated subsystems, including contact tracing, public
places access control, and safe-places recommendation. The access control
subsystem prevents infected people from visiting public places to prevent
spreading the virus, and the recommendation subsystem categorizes zones based
on the infection level so that people can avoid visiting contaminated zones.
Our analysis demonstrates that our system is secure and preserves the privacy
of the users against identification, social graph disclosure, and tracking
attacks, while thwarting false reporting (or panic) attacks. Moreover, our
extensive performance evaluations demonstrate the scalability of our system
(which is desirable in pandemics) due to its low communication, computation,
and storage overheads.


Abstract:
  Dynamics of the particle phase in a particle laden turbulent flow is highly
influenced by the fluctuating velocity and vorticity field of the fluid phase.
The present work mainly focuses on exploring the possibility of applying a
Langevin type of random torque model to predict the rotational dynamics of the
particle phase. Towards this objective, direct numerical simulations (DNS) have
been carried out for particle laden turbulent shear flow with Reynolds number,
$Re_\delta=750$ in presence of sub-Kolmogorov sized inertial particles (Stokes
number >>1). The inter-particle and wall-particle interactions have also been
considered to be elastic. From the particle equation of rotational motion, we
arrive at the expression where the fluctuating angular acceleration fluctuation
$\alpha'_i$ of the particle is expressed as the ratio of a linear combination
of fluctuating rotational velocities of particle $\omega'_i$ and fluid angular
velocity $\Omega'_i$ to the particle rotational relaxation time $\tau_r$. The
analysis was done using p.d.f plots and Jensen-Shannon Divergence based method
to assess the similarity of the particle net rotational acceleration
distribution $f(\alpha'_i)$, with (i) the distributions of particle
acceleration component arising from fluctuating fluid angular velocity computed
in the particle-Largrangian frame $f(\Omega'_i/\tau_r)_{pl}$, (ii) fluctuating
particle angular velocity $f(\omega'_i/\tau_r)_{pl}$, and (iii) the fluid
angular velocity $(\Omega'_i/\tau_r)_{e}$, computed in the fluid Eulerian
grids. The analysis leads to the conclusion that $f(\alpha'_i)$ can be modeled
with a Gaussian white noise using a pre-estimated strength which can be
calculated from the temporal correlation of $(\Omega'_i/\tau_r)_{e}$.


Abstract:
  The nebular phase of lanthanide-rich ejecta of a neutron star merger (NSM) is
studied by using a one-zone model, in which the atomic properties are
represented by a single species, neodymium (Nd). Under the assumption that
beta-decay of r-process nuclei is the heat and ionization source, we solve the
ionization and thermal balance of the ejecta under non-local thermodynamic
equilibrium. The atomic data including energy levels, radiative transition
rates, collision strengths, and recombination rate coefficients, are obtained
by using atomic structure codes, GRASP2K and HULLAC. We find that both
permitted and forbidden lines roughly equally contribute to the cooling rate of
Nd II and Nd III at the nebular temperatures. We show that the kinetic
temperature and ionization degree increase with time in the early stage of the
nebular phase while these quantities become approximately independent of time
after the thermalization break of the heating rate because the processes
relevant to the ionization and thermalization balance are attributed to
two-body collision between electrons and ions at later times. As a result, in
spite of the rapid decline of the luminosity, the shape of the emergent
spectrum does not change significantly with time after the break. We show that
the emission-line nebular spectrum of the pure Nd ejecta consists of a broad
structure from $0.5\,\mu m$ to $20\,\mu m$ with two distinct peaks around
$1\,\mu m$ and $10\,\mu m$.


Abstract:
  We present new approaches for solving constrained multicomponent nonlinear
Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an
artificial time and solve an extended damped second order dynamic system whose
stationary solution is the solution to the time-independent nonlinear
Schr\"odinger equation. Constraints are often considered by projection onto the
constraint set, here we include them explicitly into the dynamical system. We
show the applicability and efficiency of the methods on examples of relevance
in modern physics applications.


Abstract:
  This paper proposes an operational measure of non-stochastic information
leakage to formalize privacy against a brute-force guessing adversary. The
information is measured by non-probabilistic uncertainty of uncertain
variables, the non-stochastic counterparts of random variables. For $X$ that is
related to released data $Y$, the non-stochastic brute-force leakage is
measured by the complexity of exhaustively checking all the possibilities of
the private attribute $U$ of $X$ by an adversary. The complexity refers to the
number of trials to successfully guess $U$. Maximizing this leakage over all
possible private attributes $U$ gives rise to the maximal (i.e., worst-case)
non-stochastic brute-force guessing leakage. This is proved to be fully
determined by the minimal non-stochastic uncertainty of $X$ given $Y$, which
also determines the worst-case attribute $U$ indicating the highest privacy
risk if $Y$ is disclosed. The maximal non-stochastic brute-force guessing
leakage is shown to be proportional to the non-stochastic identifiability of
$X$ given $Y$ and upper bounds the existing maximin information. The latter
quantifies the information leakage when an adversary must perfectly guess $U$
in one-shot via $Y$. Experiments are used to demonstrate the tradeoff between
the maximal non-stochastic brute-force guessing leakage and the data utility
(measured by the maximum quantization error) and to illustrate the relationship
between maximin information and stochastic one-shot maximal leakage.


Abstract:
  Significance: Quantitative measurement of blood oxygen saturation (sO$_2$)
with photoacoustic (PA) imaging is one of the most sought after goals of
quantitative PA imaging research due to its wide range of biomedical
applications.
  Aim: A method for accurate and applicable real-time quantification of local
sO$_2$ with PA imaging.
  Approach: We combine multiple illumination (MI) sensing with learned spectral
decoloring (LSD); training on Monte Carlo simulations of spectrally colored
absorbed energy spectra, in order to apply the trained models to real PA
measurements. We validate our combined MI-LSD method on a highly reliable,
reproducible and easily scalable phantom model, based on copper and nickel
sulfate solutions.
  Results: With this sulfate model we see a consistently high estimation
accuracy using MI-LSD, with median absolute estimation errors of 2.5 to 4.5
percentage points. We further find fewer outliers in MI-LSD estimates compared
to LSD. Random forest regressors outperform previously reported neural network
approaches. Conclusions: Random forest based MI-LSD is a promising method for
accurate quantitative PA oximetry imaging.


Abstract:
  In the $SO(2,d)$ gauge theory formalism of AdS gravity established in
arXiv:1811.05286, the dynamics of bulk gravity is emergent from the vanishing
of the boundary covariant anomaly for the $SO(2,d)$ conservation law. Parallel
with the known results of chiral anomalies, we establish the descendent
structure of the holographic $SO(2,d)$ anomaly. The corresponding anomaly
characteristic class, bulk Chern-Simons like action as well as the boundary
effective action are constructed systematically. The anomalous conservation law
is presented both in terms of the covariant and consistent formalisms. Due to
the existence of the ruler field, not only the Bardeen-Zumino polynomial, but
also the covariant and consistent currents are explicitly constructed.


Abstract:
  We consider a method for estimating asymptotics of arithmetic functions in
the natural series in this paper. This question is closely related to the
distribution of prime numbers in natural numbers. Problems often arise even
with the definition of the asymptotics of the mean value of arithmetic
functions, and even more so in the determination of asymptotics of the moments
of higher orders. Therefore, the paper proposes a different from the
traditional, probabilistic approach based on the limiting distribution of
arithmetic functions. We will consider the general case of a method for
estimating asymptotics of the moments of additive arithmetic functions having a
limit distribution in the paper. Several assertions are proved about the
estimation of asymptotics of the moments of strongly additive arithmetic
functions, as well as additive functions of the class $H$ having a limit
distribution.


Abstract:
  We consider on the torus the scaling limit of stochastic 2D (inviscid) fluid
dynamical equations with transport noise to deterministic viscous equations.
Quantitative estimates on the convergence rates are provided by combining
analytic and probabilistic arguments, especially heat kernel properties and
maximal estimates for stochastic convolutions. Similar ideas are applied to the
stochastic 2D Keller-Segel model, yielding explicit choice of noise to ensure
that the blow-up probability is less than any given threshold. Our approach
also gives rise to some mixing property for stochastic linear transport
equations and dissipation enhancement in the viscous case.


Abstract:
  We consider the problem of discriminating quantum states, where the task is
to distinguish two different quantum states with a complete classical knowledge
about them, and the problem of classifying quantum states, where the task is to
distinguish two classes of quantum states where no prior classical information
is available but a finite number of physical copies of each classes are given.
In the case the quantum states are represented by coherent states of light, we
identify intermediate scenarios where partial prior information is available.
We evaluate an analytical expression for the minimum error when the quantum
states are opposite and a prior on the amplitudes is known. Such a threshold is
attained by complex POVM that involve highly non-linear optical procedure. A
suboptimal procedure that can be implemented with current technology is
presented that is based on a modification of the conventional Dolinar receiver.
We study and compare the performance of the scheme under different assumptions
on the prior information available.


Abstract:
  Recently LHCb declared a new structure $X(6900)$ in the final state
di-$J/\psi$ which is popularly regarded as a $cc$-$\bar c\bar c$ tetraquark
state. %popularly. Within the Bethe-Salpeter (B-S) frame we study the possible
$cc$-$\bar c\bar c$ bound states and the interaction between diquark ($cc$) and
antidiquark ($\bar c\bar c$). In this work $cc$ ($\bar c\bar c$) is treated as
a color anti-triplet (triplet) axial-vector so the quantum numbers of
$cc$-$\bar c\bar c$ bound state are $0^+$, $1^+$ and $2^+$. Learning from the
interaction in meson case and using the effective coupling we suggest the
interaction kernel for diquark and antidiquark system. Then we deduce the B-S
equations for different quantum numbers. Solving these equations numerically we
find the spectra of some excited states can be close to the mass of $X(6900)$
when we assign appropriate values for parameter $\kappa$ introduced in the
interaction (kernel).We also briefly calculate the spectra of $bb$-$\bar b\bar
b$ bound states. Future measurement of $bb$-$\bar b\bar b$ state will help us
to determine the exact form of effective interaction.


Abstract:
  We construct rogue wave solutions of a fifth-order nonlinear Schr\"odinger
equation on the Jacobian elliptic function background. By combining Darboux
transformation and the nonlinearization of spectral problem, we generate rogue
wave solution on two different periodic wave backgrounds. We analyze the
obtained solutions for different values of system parameter and point out
certain novel features of our results. We also compute instability growth rate
of both $dn$ and $cn$ periodic background waves for the considered system
through spectral stability problem. We show that instability growth rate
decreases (increases) for $dn$-$(cn)$ periodic waves when we vary the value of
the elliptic modulus parameter.


Abstract:
  There are rich synchronized audio and visual events in our daily life. Inside
the events, audio scenes are associated with the corresponding visual objects;
meanwhile, sounding objects can indicate and help to separate their individual
sounds in the audio track. Based on this observation, in this paper, we propose
a cyclic co-learning (CCoL) paradigm that can jointly learn sounding object
visual grounding and audio-visual sound separation in a unified framework.
Concretely, we can leverage grounded object-sound relations to improve the
results of sound separation. Meanwhile, benefiting from discriminative
information from separated sounds, we improve training example sampling for
sounding object grounding, which builds a co-learning cycle for the two tasks
and makes them mutually beneficial. Extensive experiments show that the
proposed framework outperforms the compared recent approaches on both tasks,
and they can benefit from each other with our cyclic co-learning.


Abstract:
  We study gradient-based regularization methods for neural networks. We mainly
focus on two regularization methods: the total variation and the Tikhonov
regularization. Applying these methods is equivalent to using neural networks
to solve some partial differential equations, mostly in high dimensions in
practical applications. In this work, we introduce a general framework to
analyze the generalization error of regularized networks. The error estimate
relies on two assumptions on the approximation error and the quadrature error.
Moreover, we conduct some experiments on the image classification tasks to show
that gradient-based methods can significantly improve the generalization
ability and adversarial robustness of neural networks. A graphical extension of
the gradient-based methods are also considered in the experiments.


Abstract:
  We present new conditions on the drift of the Morrey type with mixed norms
allowing us to obtain Aleksandrov type estimates of potentials of time
inhomogeneous diffusion processes in spaces with mixed norms and, for instance,
in $L_{d_{0}+1}$ with $d_{0}<d$.


Abstract:
  Maternal exposure to environmental chemicals during pregnancy can alter birth
and children's health outcomes. Research seeks to identify critical windows,
time periods when the exposures can change future health outcomes, and estimate
the exposure-response relationship. Existing statistical approaches focus on
estimation of the association between maternal exposure to a single
environmental chemical observed at high-temporal resolution, such as weekly
throughout pregnancy, and children's health outcomes. Extending to multiple
chemicals observed at high temporal resolution poses a dimensionality problem
and statistical methods are lacking. We propose a tree-based model for mixtures
of exposures that are observed at high temporal resolution. The proposed
approach uses an additive ensemble of structured tree-pairs that define
structured main effects and interactions between time-resolved predictors and
variable selection to select out of the model predictors not correlated with
the outcome. We apply our method in a simulation and the analysis of the
relationship between five exposures measured weekly throughout pregnancy and
resulting birth weight in a Denver, Colorado birth cohort. We identified
critical windows during which fine particulate matter, sulfur dioxide, and
temperature are negatively associated with birth weight and an interaction
between fine particulate matter and temperature. Software is made available in
the R package dlmtree.


Abstract:
  The general approach taken when training deep learning classifiers is to save
the parameters after every few iterations, train until either a human observer
or a simple metric-based heuristic decides the network isn't learning anymore,
and then backtrack and pick the saved parameters with the best validation
accuracy. Simple methods are used to determine if a neural network isn't
learning anymore because, as long as it's well after the optimal values are
found, the condition doesn't impact the final accuracy of the model. However
from a runtime perspective, this is of great significance to the many cases
where numerous neural networks are trained simultaneously (e.g. hyper-parameter
tuning). Motivated by this, we introduce a statistical significance test to
determine if a neural network has stopped learning. This stopping criterion
appears to represent a happy medium compared to other popular stopping
criterions, achieving comparable accuracy to the criterions that achieve the
highest final accuracies in 77% or fewer epochs, while the criterions which
stop sooner do so with an appreciable loss to final accuracy. Additionally, we
use this as the basis of a new learning rate scheduler, removing the need to
manually choose learning rate schedules and acting as a quasi-line search,
achieving superior or comparable empirical performance to existing methods.


Abstract:
  We study future coherent elastic neutrino-nucleus scattering (CE$\nu$NS)
modifications from a variety of possible models at the Coherent CAPTAIN Mills
(CCM) experiment at Los Alamos. We show that large regions of Non-Standard
Neutrino Interaction (NSI) parameter space will be excluded rapidly, and that
stringent new bounds on the gauge coupling in $Z'$ models will also be placed.
As a result, CCM will be able to rule out LMA-D solutions for a large class of
models with MeV-scale mediators.


Abstract:
  Our current understanding of interstellar carbon fractionation hinges on the
interpretation of astrochemical kinetic models. Yet, the various reactions
included carry large uncertainties in their (estimated) rate coefficients,
notably those involving C with C$_{2}$. In this work, we provide theoretical
thermal rate coefficients as a function of the temperature for all possible
gas-phase isotope-exchange reactions of
C+C$_{2}(X^{1}\Sigma_{g}^{+},a^{3}\Pi_{u})$. For this, we employ the
quasi-classical trajectory method, with the previously obtained potential
energy surfaces of C$_{3}$ dictating the forces between the colliding partners.
The calculated rate coefficients show a positive temperature dependence and are
markedly different from previous theoretical estimates. While the forward
reactions are fast and inherently exothermic owing to the lower zero-point
energy content of the products, the reverse processes have temperature
thresholds. For each reaction considered, analytic three-parameter
Arrhenius-Kooij formulas are provided that readily interpolate/extrapolate the
associated forward and backward rates. These forms can further be introduced in
astrochemical networks. Apart from the proper kinetic attributes, we also
provide equilibrium constants for these processes, thence confirming their
prominence in the overall C fractionation chemistry. In this respect, the
$^{13}$C + $^{12}$C$_{2}(X^{1}{\Sigma}^{+}_{g})$ and $^{13}$C +
$^{12}$C$_{2}(a^{3}{\Pi}_{u})$ reactions are found to be particularly
conspicuous, notably at the typical temperatures of dense molecular clouds. For
these reactions and considering both equilibrium and time-dependent chemistry,
theoretical $^{12}$C/$^{13}$C ratios as a function of the gas kinetic
temperature are also derived and shown to be consistent with available model
chemistry and observational data on C$_{2}$


Abstract:
  This paper addresses the problem of detecting multidimensional subspace
signals, which model range-spread targets, in noise of unknown covariance. It
is assumed that a primary channel of measurements, possibly consisting of
signal plus noise, is augmented with a secondary channel of measurements
containing only noise. The noises in these two channels share a common
covariance matrix, up to a scale, which may be known or unknown. The signal
model is a subspace model with variations: the subspace may be known or known
only by its dimension; consecutive visits to the subspace may be unconstrained
or they may be constrained by a prior distribution. As a consequence, there are
four general classes of detectors and, within each class, there is a detector
for the case where the scale between the primary and secondary channels is
known, and for the case where this scale is unknown. The generalized likelihood
ratio (GLR) based detectors derived in this paper, when organized with
previously published GLR detectors, comprise a unified theory of adaptive
subspace detection from primary and secondary channels of measurements.


Abstract:
  Recently, significant advancements have been made in face recognition
technologies using Deep Neural Networks. As a result, companies such as
Microsoft, Amazon, and Naver offer highly accurate commercial face recognition
web services for diverse applications to meet the end-user needs. Naturally,
however, such technologies are threatened persistently, as virtually any
individual can quickly implement impersonation attacks. In particular, these
attacks can be a significant threat for authentication and identification
services, which heavily rely on their underlying face recognition technologies'
accuracy and robustness. Despite its gravity, the issue regarding deepfake
abuse using commercial web APIs and their robustness has not yet been
thoroughly investigated. This work provides a measurement study on the
robustness of black-box commercial face recognition APIs against Deepfake
Impersonation (DI) attacks using celebrity recognition APIs as an example case
study. We use five deepfake datasets, two of which are created by us and
planned to be released. More specifically, we measure attack performance based
on two scenarios (targeted and non-targeted) and further analyze the differing
system behaviors using fidelity, confidence, and similarity metrics.
Accordingly, we demonstrate how vulnerable face recognition technologies from
popular companies are to DI attack, achieving maximum success rates of 78.0%
and 99.9% for targeted (i.e., precise match) and non-targeted (i.e., match with
any celebrity) attacks, respectively. Moreover, we propose practical defense
strategies to mitigate DI attacks, reducing the attack success rates to as low
as 0% and 0.02% for targeted and non-targeted attacks, respectively.


Abstract:
  It is shown that for the one-dimensional quantum quartic anharmonic
oscillator the numerical results obtained by Okun-Burke in Ref.2 are easily
reproduced and can be significantly improved in Lagrange Mesh Method (based on
non-uniform lattice).


Abstract:
  The total extragalactic $\gamma$-ray flux provides a powerful probe into the
origin and evolution of the highest energy processes in our universe. An
important component of this emission is the isotropic $\gamma$-ray background
(IGRB), composed of sources that cannot be individually resolved by current
experiments. Previous studies have determined that the IGRB can be dominated by
either misaligned active galactic nuclei (mAGN) or star-forming galaxies
(SFGs). However, these analyses are limited, because they have utilized binary
source classifications and examined only one source class at a time. We perform
the first combined joint-likelihood analysis that simultaneously correlates the
$\gamma$-ray luminosity of extragalactic objects with both star-formation and
mAGN activity. We find that SFGs produce 48$^{+33}_{-20}$\% of the total IGRB
at~1 GeV and 56$^{+40}_{-23}$\% of the total IGRB at 10 GeV. The contribution
of mAGN is more uncertain, but can also be significant. Future work to quantify
the radio and infrared properties of nearby galaxies could significantly
improve these constraints.


Abstract:
  In this paper, we derive an analytic characterization of the symmetric
extension of a Herglotz-Nevanlinna function in several variables. Here, the
main tools used are the so-called variable non-dependence property and the
symmetry formula satisfied by Herglotz-Nevanlinna function and Cauchy-type
functions. We also provide an extension of the Stieltjes inversion formula for
Cauchy-type functions.


Abstract:
  We consider a wireless source localization network in which a target node
emits localization signals that are used by anchor nodes to estimate the target
node position. In addition to target and anchor nodes, there can also exist
eavesdropper nodes and jammer nodes which aim to estimate the position of the
target node and to degrade the accuracy of localization, respectively. We first
propose the problem of eavesdropper selection with the goal of optimally
placing a given number of eavesdropper nodes to a subset of possible positions
in the network to estimate the target node position as accurately as possible.
As the performance metric, the Cramer-Rao lower bound (CRLB) related to the
estimation of the target node position by eavesdropper nodes is derived, and
its convexity and monotonicity properties are investigated. By relaxing the
integer constraints, the eavesdropper selection problem is approximated by a
convex optimization problem and algorithms are proposed for eavesdropper
selection. Moreover, in the presence of parameter uncertainty, a robust version
of the eavesdropper selection problem is developed. Then, the problem of jammer
selection is proposed where the aim is to optimally place a given number of
jammer nodes to a subset of possible positions for degrading the localization
accuracy of the network as much as possible. A CRLB expression from the
literature is used as the performance metric, and its concavity and
monotonicity properties are derived. Also, a convex optimization problem and
its robust version are derived after relaxation. Moreover, the joint
eavesdropper and jammer selection problem is proposed with the goal of placing
certain numbers of eavesdropper and jammer nodes to a subset of possible
positions. Simulation results are presented to illustrate performance of the
proposed algorithms.


Abstract:
  We construct and analyze first- and second-order implicit-explicit (IMEX)
schemes based on the scalar auxiliary variable (SAV) approach for the
magneto-hydrodynamic equations. These schemes are linear, only require solving
a sequence of linear differential equations with constant coefficients at each
time step, and are unconditionally energy stable. We derive rigorous error
estimates for the velocity, pressure and magnetic field of the first-order
scheme in the two dimensional case without any condition on the time step.
Numerical examples are presented to validate the proposed schemes.


Abstract:
  For crystalline materials with long-range orders, the phonon modes involved
in the phonon-assisted radiation process are generally involving one or several
phonons with specific vibration frequencies 1-4. In some glassy material, the
phonon modes broaden in a short range 5-7. However, the locally distinct
chemical environments or mass disorder in high-entropy systems can induce an
anharmonic phonon-phonon coupling and composition disorder, which leads to
significant phonon broadening 8,9.The terminology of high-entropy comes from
the high configuration entropy larger than 1.5R (R is the gas constant), which
results from randomly distributed multiple nearly equal components in a crystal
lattice 10,11. Inspired by the high-entropy strategy, we deployed a
high-entropy glass system (HEGS) doped with neodymium ions, which exhibits a
complex structure with tetrahedral voids filled by different ions, including,
Li+, Zn2+, Si4+, P5+, S6+, etc. Phonon spectral broadening up to thousands of
wavenumbers in the HEGS allows strong wide-band absorption in both the
near-infrared and mid-infrared ranges and assists the system radiation, i.e.,
broadened phonon-assisted wide-band radiation (BPAWR). The subsequent
low-threshold self-absorption coherence modulation (SACM) was also observed in
the HEGS, modulated by changing excitation wavelengths, sample size, and doping
concentrations. The time delay of the BPAWR signal is up to 1.66 ns relative to
the zero-delay signal, while the time delay of the Raman process is typically
in the order of fs to ps, rarely up to 10 ps 12-15.The BPAWR-SACM can be
applied to realize signal amplification of the centered non-absorption band
when dual-wavelength lasers pump the HEGS sample, and signal amplification can
be up to 26.02 dB. The spectral characteristics of the BPAWR and the dynamics
of the energy distribution of the excited species are investigated in detail.


Abstract:
  Certification and quantification of correlations for multipartite states of
quantum systems appear to be a central task in quantum information theory. We
give here a unitary quantum-mechanical perspective of both entanglement and
Einstein-Podolsky-Rosen (EPR) steering of continuous-variable multimode states.
This originates in the Heisenberg uncertainty relations for the canonical
quadrature operators of the modes. Correlations of two-party $(N\, \text{vs}
\,1)$-mode states are examined by using the variances of a pair of suitable
EPR-like observables. It turns out that the uncertainty sum of these nonlocal
variables is bounded from below by local uncertainties and is strengthened
differently for separable states and for each one-way unsteerable ones. The
analysis of the minimal properly normalized sums of these variances yields
necessary conditions of separability and EPR unsteerability of $(N\, \text{vs}
\,1)$-mode states in both possible ways of steering. When the states and the
performed measurements are Gaussian, then these conditions are precisely the
previously-known criteria of separability and one-way unsteerability.


Abstract:
  We study identifying user clusters in contextual multi-armed bandits (MAB).
Contextual MAB is an effective tool for many real applications, such as content
recommendation and online advertisement. In practice, user dependency plays an
essential role in the user's actions, and thus the rewards. Clustering similar
users can improve the quality of reward estimation, which in turn leads to more
effective content recommendation and targeted advertising. Different from
traditional clustering settings, we cluster users based on the unknown bandit
parameters, which will be estimated incrementally. In particular, we define the
problem of cluster detection in contextual MAB, and propose a bandit algorithm,
LOCB, embedded with local clustering procedure. And, we provide theoretical
analysis about LOCB in terms of the correctness and efficiency of clustering
and its regret bound. Finally, we evaluate the proposed algorithm from various
aspects, which outperforms state-of-the-art baselines.


Abstract:
  We analyze the structure and stickiness in the chaotic components of generic
Hamiltonian systems with divided phase space. Following the method proposed
recently in Lozej and Robnik [Phys. Rev. E 98, 022220 (2018)], the sticky
regions are identified using the statistics of recurrence times of a single
chaotic orbit into cells dividing the phase space into a grid. We perform
extensive numerical studies of three example systems: the Chirikov standard
map, the family of Robnik billiards, and the family of lemon billiards. The
filling of the cells is compared to the random model of chaotic diffusion,
introduced in Robnik et al. [J. Phys. A: Math. Gen. 30, L803 (1997)] for the
description of transport in the phase spaces of ergodic systems. The model is
based on the assumption of completely uncorrelated cell visits because of the
strongly chaotic dynamics of the orbit and the distribution of recurrence times
is exponential. In generic systems the stickiness induces correlations in the
cell visits. The distribution of recurrence times exhibits a separation of
timescales because of the dynamical trapping. We model the recurrence time
distributions to cells inside sticky areas as a mixture of exponential
distributions with different decay times. We introduce the variable S, which is
the ratio between the standard deviation and the mean of the recurrence times
as a measure of stickiness. We use S to globally assess the distributions of
recurrence times. We find that in the bulk of the chaotic sea S=1, while S>1 in
areas of stickiness. We present the results in the form of animated grayscale
plots of the variable S in the largest chaotic component for the three example
systems, included as supplemental material to this paper.


Abstract:
  Within the framework of quantum molecular dynamics transport model, the
isospin and in-medium effects on the hyperon production in the reaction of
$^{197}$Au + $^{197}$Au are investigated thoroughly. A repulsive
hyperon-nucleon potential from the chiral effective field theory is implemented
into the model, which is related to the hyperon momentum and baryon density.
The correction on threshold energy of the elementary hyperon cross section is
taken into account. It is found that the $\Sigma$ yields are suppressed in the
domain of midrapidity and kinetic energy spectra with the potential. The
hyperons are emitted in the reaction plane because of the strangeness exchange
reaction and reabsorption process in nuclear medium. The
$\Sigma^{-}/\Sigma^{+}$ ratio depends on the stiffness of nuclear symmetry
energy, in particular in the high-energy region (above 500 MeV).


Abstract:
  We consider a biological network of the hippocampal dentate gyrus (DG). The
DG is a pre-processor for pattern separation which facilitates pattern storage
and retrieval in the CA3 area of the hippocampus. The main encoding cells in
the DG are the granule cells (GCs) which receive the input from the entorhinal
cortex (EC) and send their output to the CA3. The activation degree of GCs is
so low (~ 5%). This sparsity has been thought to enhance the pattern
separation. We investigate the dynamical origin for winner-take-all (WTA)
competition which leads to sparse activation of the GCs. The whole GCs are
grouped into lamellar clusters. In each GC cluster, there is one inhibitory (I)
basket cell (BC) along with excitatory (E) GCs. There are three kinds of
external inputs into the GCs; the direct excitatory EC input, the indirect
inhibitory EC input, mediated by the HIPP (hilar perforant path-associated)
cells, and the excitatory input from the hilar mossy cells (MCs). The firing
activities of the GCs are determined via competition between the external E and
I inputs. The E-I conductance ratio ${\cal{R}}_{\rm E-I}^{\rm (con)*}$ (given
by the time average of the external E to I conductances) may represents well
the degree of such external E-I input competition. GCs become active when their
$\cal{R}_{\rm E-I}^{\rm (con)*}$ is larger than a threshold ${\cal{R}}_{th}^*$,
and then the mean firing rates of the active GCs are strongly correlated with
$\cal{R}_{\rm E-I}^{\rm (con)*}$. In each GC cluster, the feedback inhibition
of the BC may select the winner GCs. GCs with larger $\cal{R}_{\rm E-I}^{\rm
(con)*}$ than the threshold ${\cal{R}}_{th}^*$ survive, and they become
winners; all the other GCs with smaller $\cal{R}_{\rm E-I}^{\rm (con)*}$ become
silent. The WTA competition occurs via competition between the firing activity
of the GCs and the feedback inhibition from the BC in each GC cluster.


Abstract:
  Narrow escape and narrow capture problems which describe the average times
required to stop the motion of a randomly travelling particle within a domain
have applications in various areas of science. While for general domains, it is
known how the escape time decreases with the increase of the trap sizes, for
some specific 2D and 3D domains, higher-order asymptotic formulas have been
established, providing the dependence of the escape time on the sizes and
locations of the traps. Such results allow the use of global optimization to
seek trap arrangements that minimize average escape times. In a recent paper,
the escape time expansion for a 2D elliptic domain was derived, providing the
dependence of the average MFPT on sizes and locations of small internal traps.
The goal of this work is to systematically seek global minima of MFPT for
$1\leq N\leq 50$ traps, and compare the corresponding putative optimal trap
arrangements for different values of the domain eccentricity.