Abstract:
  The widespread dissemination of forged images generated by Deepfake
techniques has posed a serious threat to the trustworthiness of digital
information. This demands effective approaches that can detect perceptually
convincing Deepfakes generated by advanced manipulation techniques. Most
existing approaches combat Deepfakes with deep neural networks by mapping the
input image to a binary prediction without capturing the consistency among
different pixels. In this paper, we aim to capture the subtle manipulation
artifacts at different scales for Deepfake detection. We achieve this with
transformer models, which have recently demonstrated superior performance in
modeling dependencies between pixels for a variety of recognition tasks in
computer vision. In particular, we introduce a Multi-modal Multi-scale
TRansformer (M2TR), which uses a multi-scale transformer that operates on
patches of different sizes to detect the local inconsistency at different
spatial levels. To improve the detection results and enhance the robustness of
our method to image compression, M2TR also takes frequency information, which
is further combined with RGB features using a cross modality fusion module.
Developing and evaluating Deepfake detection methods requires large-scale
datasets. However, we observe that samples in existing benchmarks contain
severe artifacts and lack diversity. This motivates us to introduce a
high-quality Deepfake dataset, SR-DF, which consists of 4,000 DeepFake videos
generated by state-of-the-art face swapping and facial reenactment methods. On
three Deepfake datasets, we conduct extensive experiments to verify the
effectiveness of the proposed method, which outperforms state-of-the-art
Deepfake detection methods.


Abstract:
  JUNO is a 20-kton liquid scintillator detector aiming to determine the
neutrino mass ordering, precisely measure the oscillation parameters, detect
the astrophysical neutrinos and search for exotic physics. It is designed to
reach an energy resolution of 3% at 1 MeV with the highest ever PMT coverage,
using two types of 20 inch phototubes: MCP-PMT from NNVT and dynode-PMT from
Hamamatsu. In this article, the gain and charge response of the MCP and dynode
PMTs are investigated with the study of JUNO Central Detector prototype. The
linearity of the MCP-PMT charge output is measured too to check the effect of a
long tail on its charge spectrum.


Abstract:
  The high dynamics and heterogeneous interactions in the complicated urban
systems have raised the issue of uncertainty quantification in spatiotemporal
human mobility, to support critical decision-makings in risk-aware web
applications such as urban event prediction where fluctuations are of
significant interests. Given the fact that uncertainty quantifies the potential
variations around prediction results, traditional learning schemes always lack
uncertainty labels, and conventional uncertainty quantification approaches
mostly rely upon statistical estimations with Bayesian Neural Networks or
ensemble methods. However, they have never involved any spatiotemporal
evolution of uncertainties under various contexts, and also have kept suffering
from the poor efficiency of statistical uncertainty estimation while training
models with multiple times. To provide high-quality uncertainty quantification
for spatiotemporal forecasting, we propose an uncertainty learning mechanism to
simultaneously estimate internal data quality and quantify external uncertainty
regarding various contextual interactions. To address the issue of lacking
labels of uncertainty, we propose a hierarchical data turbulence scheme where
we can actively inject controllable uncertainty for guidance, and hence provide
insights to both uncertainty quantification and weak supervised learning.
Finally, we re-calibrate and boost the prediction performance by devising a
gated-based bridge to adaptively leverage the learned uncertainty into
predictions. Extensive experiments on three real-world spatiotemporal mobility
sets have corroborated the superiority of our proposed model in terms of both
forecasting and uncertainty quantification.


Abstract:
  Recent advances in the areas of multimodal machine learning and artificial
intelligence (AI) have led to the development of challenging tasks at the
intersection of Computer Vision, Natural Language Processing, and Embodied AI.
Whereas many approaches and previous survey pursuits have characterised one or
two of these dimensions, there has not been a holistic analysis at the center
of all three. Moreover, even when combinations of these topics are considered,
more focus is placed on describing, e.g., current architectural methods, as
opposed to also illustrating high-level challenges and opportunities for the
field. In this survey paper, we discuss Embodied Vision-Language Planning
(EVLP) tasks, a family of prominent embodied navigation and manipulation
problems that jointly use computer vision and natural language. We propose a
taxonomy to unify these tasks and provide an in-depth analysis and comparison
of the new and current algorithmic approaches, metrics, simulated environments,
as well as the datasets used for EVLP tasks. Finally, we present the core
challenges that we believe new EVLP works should seek to address, and we
advocate for task construction that enables model generalizability and furthers
real-world deployment.


Abstract:
  We discuss a model of a $n$-person, non-cooperative stochastic game, inspired
by the discrete version of the red-and-black gambling problem introduced by
Dubins and Savage in 1965. Our main theorem generalizes a result of Pontiggia
from 2007 which provides conditions upon which bold strategies for all players
form a Nash equilibrium. Our tool is a functional inequality, which is
introduced and discussed in the present paper. It allows us to avoid
restrictive assumptions of super-multiplicativity and super-additivity, which
appear in Pontiggia' and other author works. We terminate the paper with some
examples which in particular show that our approach leads to a essentially
larger class of probability functions than existed in the literature so far.


Abstract:
  With increasing distributed energy resoures (DERs) integration, the strategic
behavior of a DER aggregator in electricity markets will significantly affect
the secure operation of the distribution system. In this paper, the
interactions among the DER aggregator, energy and reserve markets, and
distribution system are investigated through a single-leader-multi-follower
Stackelberg game model with the DER aggregator as the leader and the
independent system operator and distribution system operator as the followers.
To guarantee the operation security of the distribution system, security check
problems under three different scenarios are involved in the follower level,
which is linearized using a mixed-integer linearized power flow model. Then,
using the strong duality theorem, the proposed model is converted into a
bi-level mixed-integer linear (BMILP) programming model with only mixed-integer
linear follower-level problems. Next, an accelerated relaxation-based bi-level
reformulation and decomposition algorithm is proposed to solve the BMILP
problem. Finally, case studies are carried out on a constructed integrated
transmission and distribution (T&D) system and a practical integrated T&D
system to verify the effectiveness of the proposed model and algorithm. The
simulation results indicate that the available downward reserve of the DER
aggregator will decrease with the security limitation of the distribution
system.


Abstract:
  We report lowest-order series expansions for primary matrix functions of
quantum states based on a perturbation theory for functions of linear
operators. Our theory enables efficient computation of functions of perturbed
quantum states that assume only knowledge of the eigenspectrum of the zeroth
order state and the density matrix elements of a zero-trace, Hermitian
perturbation operator, not requiring analysis of the full state or the
perturbation term. We develop theories for two classes of quantum state
perturbations, perturbations that preserve the vector support of the original
state and perturbations that extend the support beyond the support of the
original state. We highlight relevant features of the two situations, in
particular the fact that functions and measures of perturbed quantum states
with preserved support can be elegantly and efficiently represented using
Fr\'echet derivatives. We apply our perturbation theories to find simple
expressions for four of the most important quantities in quantum information
theory that are commonly computed from density matrices: the Von Neumann
entropy, the quantum relative entropy, the quantum Chernoff bound, and the
quantum fidelity.


Abstract:
  The baryon acoustic oscillation feature can be used as a standard
cosmological ruler. In practice, for sub-percent level accuracy on the distance
scale, it must be standardized. The physical reason why is understood, so we
use this to develop an algorithm which improves the estimated scale. The
algorithm exploits the fact that, over the range of scales where the initial
correlation function is well-fit by a polynomial, the leading order effects
which distort the length of the ruler can be accounted for analytically. Tests
of the method in numerical simulations show that it provides simple and fast
reconstruction of the full shape of the BAO feature, as well as sub-percent
determination of the linear point in the correlation function of biased tracers
with minimal assumptions about the underlying cosmological model or the nature
of the observed tracers. Our results also suggest that, for least squares
estimators of the correlation function, half-integer generalized Laguerre
functions are a particularly useful choice.


Abstract:
  In this paper, we introduce a challenging global large-scale ship database
(called GLSD), designed specifically for ship detection tasks. The designed
GLSD database includes a total of 140,616 annotated instances from 100,729
images. Based on the collected images, we propose 13 categories that widely
exists in international routes. These categories include sailing boat, fishing
boat, passenger ship, war ship, general cargo ship, container ship, bulk cargo
carrier, barge, ore carrier, speed boat, canoe, oil carrier, and tug. The
motivations of developing GLSD include the following: 1) providing a refined
ship detection database; 2) providing the worldwide researchers of ship
detection and exhaustive label information (bounding box and ship class label)
in one uniform global database; and 3) providing a large-scale ship database
with geographic information (port and country information) that benefits
multi-modal analysis. In addition, we discuss the evaluation protocols given
image characteristics in GLSD and analyze the performance of selected
state-of-the-art object detection algorithms on GSLD, providing baselines for
future studies. More information regarding the designed GLSD can be found at
https://github.com/jiaming-wang/GLSD.


Abstract:
  We study stability of metric approximations of countable groups with respect
to groups endowed with ultrametrics, the main case study being a $p$-adic
analogue of Ulam stability, where we take $\mathrm{GL}_n(\mathbb{Z}_p)$ as
approximating groups instead of $\mathrm{U}(n)$. For finitely presented groups,
the ultrametric nature implies equivalence of the pointwise and uniform
stability problems, and the profinite one implies that the corresponding
approximation property is equivalent to residual finiteness. Moreover, a group
is uniformly stable if and only if its largest residually finite quotient is.
We provide several examples of uniformly stable groups: these include finite
groups, virtually free groups, some groups acting on rooted trees, and certain
lamplighter and (Generalized) Baumslag--Solitar groups.


Abstract:
  Relying on the local orientation of nanostructures, Pancharatnam-Berry
metasurfaces are currently enabling a new generation of polarization-sensitive
optical devices. A systematical mesoscopic description of topological
metasurfaces is developed, providing a deeper understanding of the physical
mechanisms leading to the polarization-dependent breaking of translational
symmetry in contrast with propagation phase effects. These theoretical results,
along with interferometric experiments, contribute to the development of a
solid theoretical framework for arbitrary polarization-dependent metasurfaces.


Abstract:
  We generalize to the ${\rm RCD}(0,N)$ setting a family of monotonicity
formulas by Colding and Minicozzi for positive harmonic functions in Riemannian
manifolds with non-negative Ricci curvature. Rigidity and almost rigidity
statements are also proven, the second appearing to be new even in the smooth
setting. Motivated by the recent work in [AFM] we also introduce the notion of
electrostatic potential in ${\rm RCD}$ spaces, which also satisfies our
monotonicity formulas. Our arguments are mainly based on new estimates for
harmonic functions in ${\rm RCD}(K,N)$ spaces and on a new functional version
of the `(almost) outer volume cone implies (almost) outer metric cone' theorem.


Abstract:
  The epidemic threshold of a social system is the ratio of infection and
recovery rate above which a disease spreading in it becomes an epidemic. In the
absence of pharmaceutical interventions (i.e. vaccines), the only way to
control a given disease is to move this threshold by non-pharmaceutical
interventions like social distancing, past the epidemic threshold corresponding
to the disease, thereby tipping the system from epidemic into a non-epidemic
regime. Modeling the disease as a spreading process on a social graph, social
distancing can be modeled by removing some of the graphs links. It has been
conjectured that the largest eigenvalue of the adjacency matrix of the
resulting graph corresponds to the systems epidemic threshold. Here we use a
Markov chain Monte Carlo (MCMC) method to study those link removals that do
well at reducing the largest eigenvalue of the adjacency matrix. The MCMC
method generates samples from the relative canonical network ensemble with a
defined expectation value of $\lambda_{max}$. We call this the
"well-controlling network ensemble" (WCNE) and compare its structure to
randomly thinned networks with the same link density. We observe that networks
in the WCNE tend to be more homogeneous in the degree distribution and use this
insight to define two ad-hoc removal strategies, which also substantially
reduce the largest eigenvalue. A targeted removal of 80\% of links can be as
effective as a random removal of 90\%, leaving individuals with twice as many
contacts.


Abstract:
  We prove new Fourier restriction estimates to the unit sphere $S^{d-1}$ on
the class of $O(d-k)\times O(k)$-symmetric functions, for every $d\geq 4$ and
$2\leq k\leq d-2$. As an application, we establish the existence of maximizers
for the endpoint Tomas--Stein inequality within that class. Moreover, we
construct examples showing that the range of Lebesgue exponents in our
estimates is sharp in the Tomas--Stein regime.


Abstract:
  This paper studies the formation stabilization problem of asynchronous
nonlinear multi-agent systems (MAS) subject to parametric uncertainties,
external disturbances and bounded time-varying communication delays. A
self-triggered min-max distributed model predictive control (DMPC) approach is
proposed to handle these practical issues. At triggering instants, each agent
solves a local min-max optimization problem based on local system states and
predicted system states of neighbors, determines its next triggering instant
and broadcasts its predicted state trajectory to its neighbors. As a result,
the communication load is greatly alleviated while retaining robustness and
comparable control performance compared to periodic algorithms. In order to
handle time-varying delays, a novel consistency constraint is incorporated into
each local optimization problem to restrict the deviation between the newest
predicted states and previously broadcast predicted states. Consequently, each
agent can utilize previously predicted states of its neighbors to achieve
cooperation in the presence of time-varying delays and asynchronous
communication induced by the distributed triggered scheduler. The recursive
feasibility of the proposed algorithm and the closed-loop stability of MAS at
triggering time instants are proven. Finally, numerical simulations are
conducted to verify the efficiency of the proposed control method.


Abstract:
  Causal induction, i.e., identifying unobservable mechanisms that lead to the
observable relations among variables, has played a pivotal role in modern
scientific discovery, especially in scenarios with only sparse and limited
data. Humans, even young toddlers, can induce causal relationships surprisingly
well in various settings despite its notorious difficulty. However, in contrast
to the commonplace trait of human cognition is the lack of a diagnostic
benchmark to measure causal induction for modern Artificial Intelligence (AI)
systems. Therefore, in this work, we introduce the Abstract Causal REasoning
(ACRE) dataset for systematic evaluation of current vision systems in causal
induction. Motivated by the stream of research on causal discovery in Blicket
experiments, we query a visual reasoning system with the following four types
of questions in either an independent scenario or an interventional scenario:
direct, indirect, screening-off, and backward-blocking, intentionally going
beyond the simple strategy of inducing causal relationships by covariation. By
analyzing visual reasoning architectures on this testbed, we notice that pure
neural models tend towards an associative strategy under their chance-level
performance, whereas neuro-symbolic combinations struggle in backward-blocking
reasoning. These deficiencies call for future research in models with a more
comprehensive capability of causal induction.


Abstract:
  The benzene radical anion, well-known in organic chemistry as the first
intermediate in the Birch reduction of benzene in liquid ammonia, exhibits
intriguing properties from the point of view of quantum chemistry. Notably, it
has the character of a metastable shape resonance in the gas phase, while
measurements in solution find it to be experimentally detectable and stable. In
this light, our previous calculations performed in bulk liquid ammonia
explicitly reveal that solvation leads to stabilization. Here, we focus on the
transition of the benzene radical anion from an unstable gas-phase ion to a
fully solvated bound species by explicit ionization calculations of the radical
anion solvated in molecular clusters of increasing size. The computational cost
of the largest systems is mitigated by combining density functional theory with
auxiliary methods including effective fragment potentials or approximating the
bulk by polarizable continuum models. Using this methodology, we obtain the
cluster size dependence of the vertical binding energy of the benzene radical
anion converging to the value of $-$2.3 eV at a modest computational cost.


Abstract:
  We study the numerical range of the Weighted Composition Operator over the
Mittag-Leffler space of entire functions.


Abstract:
  We address the worst-user bottleneck of wireless coded caching, which is
known to severely diminish cache-aided multicasting gains due to the
fundamental worst-channel limitation of multicasting transmission. We consider
the quasi-static Rayleigh fading Broadcast Channel, for which we first show
that the effective coded caching gain of the XOR-based standard coded-caching
scheme completely vanishes in the low-SNR regime. Then, we reveal that this
collapse is not intrinsic to coded caching. We do so by presenting a novel
scheme that can fully recover the coded caching gains by capitalizing on one
aspect that has to date remained unexploited: the shared side information
brought about by the effectively unavoidable file-size constraint. As a
consequence, the worst-user effect is dramatically ameliorated, as it is
substituted by a much more subtle worst-group-of-users effect, where the
suggested grouping is fixed, and it is decided before the channel or the
demands are known. In some cases, the theoretical gains are completely
recovered, and this is done without any user selection technique. We analyze
the achievable rate performance of the proposed scheme and derive insightful
performance approximations which prove to be very precise.


Abstract:
  Node copying is an important mechanism for network formation, yet most models
assume uniform copying rules. Motivated by observations of heterogeneous
triadic closure in real networks, we introduce the concept of a hidden network
model - a generative two-layer model in which an observed network evolves
according to the structure of an underlying hidden layer - and apply the
framework to a model of heterogeneous copying. Framed in a social context,
these two layers represent a node's inner social circle, and wider social
circle, such that the model can bias copying probabilities towards, or against,
a node's inner circle of friends. Comparing the case of extreme inner circle
bias to an equivalent model with uniform copying, we find that heterogeneous
copying suppresses the power-law degree distributions commonly seen in copying
models, and results in networks with much higher clustering than even the most
optimum scenario for uniform copying. Similarly large clustering values are
found in real collaboration networks, lending empirical support to the
mechanism.


Abstract:
  Synthesis of new elements at the upper border of the charts of nuclei and
investigation of their decay properties and nuclear structure has been one of
the main research topics in low energy nuclear physics since more than five
decades. Main items are the quest for the heaviest nuclei that can exist and
the verification of the theoretical predicted spherical proton and neutron
shells at Z = 114, 120 or 126 and N = 172 or 184. The scope of the present
paper is to illustrate some technical and physical aspects in investigation of
the heaviest nuclei ('superheavy nuclei') and to critical discuss some selected
results, which from a strict scientific point of view are not completely clear
so far, making partly also suggestions for alternatively interpretations. A
complete review of the whole field of superheavy element research, however, is
out of the scope of this paper.


Abstract:
  We present DistillFlow, a knowledge distillation approach to learning optical
flow. DistillFlow trains multiple teacher models and a student model, where
challenging transformations are applied to the input of the student model to
generate hallucinated occlusions as well as less confident predictions. Then, a
self-supervised learning framework is constructed: confident predictions from
teacher models are served as annotations to guide the student model to learn
optical flow for those less confident predictions. The self-supervised learning
framework enables us to effectively learn optical flow from unlabeled data, not
only for non-occluded pixels, but also for occluded pixels. DistillFlow
achieves state-of-the-art unsupervised learning performance on both KITTI and
Sintel datasets. Our self-supervised pre-trained model also provides an
excellent initialization for supervised fine-tuning, suggesting an alternate
training paradigm in contrast to current supervised learning methods that
highly rely on pre-training on synthetic data. At the time of writing, our
fine-tuned models ranked 1st among all monocular methods on the KITTI 2015
benchmark, and outperform all published methods on the Sintel Final benchmark.
More importantly, we demonstrate the generalization capability of DistillFlow
in three aspects: framework generalization, correspondence generalization and
cross-dataset generalization.


Abstract:
  The Central Molecular Zone (CMZ) is a ring-like structure sitting at the
center of the Milky Way. Using the 870 $\mu$m continuum map from the APEX
Telescope Large Area Survey of the Galaxy (ATLASGAL), we study the anisotropy
of the density structure of the gas in the Central Molecular Zone (CMZ) using
the 2D correlation function. To quantify the spatial anisotropy, we define the
critical angle $\theta_{\rm half}$, as well as the anisotropy parameter
$A\equiv \frac{\pi}{4\theta_{\rm half}}-1$. We find that the density structure
is strongly anisotropic at the large scale (~ 100 pc), and the degree of
spatial anisotropy decreases with the decreasing scale. At the scale of ~ 10
pc, the structure is still mildly anisotropic. In our analyses, we provide a
quantitative description of the anisotropic density structure of gas in the
CMZ, and the formalism can be applied to different regions to study their
differences.


Abstract:
  The lower the distortion of an estimator, the more the distribution of its
outputs generally deviates from the distribution of the signals it attempts to
estimate. This phenomenon, known as the perception-distortion tradeoff, has
captured significant attention in image restoration, where it implies that
fidelity to ground truth images comes at the expense of perceptual quality
(deviation from statistics of natural images). However, despite the increasing
popularity of performing comparisons on the perception-distortion plane, there
remains an important open question: what is the minimal distortion that can be
achieved under a given perception constraint? In this paper, we derive a closed
form expression for this distortion-perception (DP) function for the mean
squared-error (MSE) distortion and the Wasserstein-2 perception index. We prove
that the DP function is always quadratic, regardless of the underlying
distribution. This stems from the fact that estimators on the DP curve form a
geodesic in Wasserstein space. In the Gaussian setting, we further provide a
closed form expression for such estimators. For general distributions, we show
how these estimators can be constructed from the estimators at the two extremes
of the tradeoff: The global MSE minimizer, and a minimizer of the MSE under a
perfect perceptual quality constraint. The latter can be obtained as a
stochastic transformation of the former.


Abstract:
  Recently, coordinated attack campaigns started to become more widespread on
the Internet. In May 2017, WannaCry infected more than 300,000 machines in 150
countries in a few days and had a large impact on critical infrastructure.
Existing threat sharing platforms cannot easily adapt to emerging attack
patterns. At the same time, enterprises started to adopt machine learning-based
threat detection tools in their local networks. In this paper, we pose the
question: \emph{What information can defenders share across multiple networks
to help machine learning-based threat detection adapt to new coordinated
attacks?} We propose three information sharing methods across two networks, and
show how the shared information can be used in a machine-learning
network-traffic model to significantly improve its ability of detecting evasive
self-propagating malware.


Abstract:
  We describe a technique for self consistently characterizing both the quantum
state of a single qubit system, and the positive-operator-valued measure (POVM)
that describes measurements on the system. The method works with only ten
measurements. We assume that a series of unitary transformations performed on
the quantum state are fully known, while making minimal assumptions about both
the density operator of the state and the POVM. The technique returns
maximum-likely estimates of both the density operator and the POVM. To
experimentally demonstrate the method, we perform reconstructions of over 300
state-measurement pairs and compare them to their expected density operators
and POVMs. We find that 95% of the reconstructed POVMs have fidelities of 0.98
or greater, and 92% of the density operators have fidelities that are 0.98 or
greater.


Abstract:
  The fine structure of the exciton spectrum, containing optically allowed
(bright) and forbidden (dark) exciton states, determines the radiation
efficiency in nanostructures. We study time-resolved micro-photoluminescence in
MoS$_2$ monolayers and bilayers, both unstrained and compressively strained, in
a wide temperature range (10-300 K) to distinguish between exciton states
optically allowed and forbidden, both in spin and momentum, as well as to
estimate their characteristic decay times and contributions to the total
radiation intensity. The decay times were found to either increase or decrease
with increasing temperature, indicating the lowest bright or lowest dark state,
respectively. Our results unambiguously show that, in an unstrained monolayer,
the spin-allowed state is the lowest for a series of A excitons (1.9 eV) with
the dark state being < 2 meV higher, and that the splitting energy can increase
several times at compression. In contrast, in the indirect exciton series in
bilayers (1.5 eV), the spin-forbidden state is the lowest, being about 3 meV
below the bright one. The strong effect of strain on the exciton spectrum can
explain the large scatter among the published data and must be taken into
account to realize the desired optical properties of 2D MoS$_2$.


Abstract:
  Since reward functions are hard to specify, recent work has focused on
learning policies from human feedback. However, such approaches are impeded by
the expense of acquiring such feedback. Recent work proposed that agents have
access to a source of information that is effectively free: in any environment
that humans have acted in, the state will already be optimized for human
preferences, and thus an agent can extract information about what humans want
from the state. Such learning is possible in principle, but requires simulating
all possible past trajectories that could have led to the observed state. This
is feasible in gridworlds, but how do we scale it to complex tasks? In this
work, we show that by combining a learned feature encoder with learned inverse
models, we can enable agents to simulate human actions backwards in time to
infer what they must have done. The resulting algorithm is able to reproduce a
specific skill in MuJoCo environments given a single state sampled from the
optimal policy for that skill.


Abstract:
  Direct observations of gravitational waves at frequencies around deci-Hertz
will play a crucial role in fully exploiting the potential of multi-messenger
astronomy. In this chapter, we discuss the detection landscape for the next
several decades of the deci-Hertz gravitational-wave spectrum. We provide an
overview of the experimental frontiers being considered to probe this
challenging regime and the astrophysics and fundamental goals accessible
towards them. This includes interferometric observatories in space with
heliocentric and geocentric satellites, cubesats, lunar-based experiments and
atom intereferometry. A major focus of this chapter is towards the technology
behind DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) and
its scientific pathfinder mission concept B-DECIGO.


Abstract:
  We introduce the GANformer, a novel and efficient type of transformer, and
explore it for the task of visual generative modeling. The network employs a
bipartite structure that enables long-range interactions across the image,
while maintaining computation of linear efficiency, that can readily scale to
high-resolution synthesis. It iteratively propagates information from a set of
latent variables to the evolving visual features and vice versa, to support the
refinement of each in light of the other and encourage the emergence of
compositional representations of objects and scenes. In contrast to the classic
transformer architecture, it utilizes multiplicative integration that allows
flexible region-based modulation, and can thus be seen as a generalization of
the successful StyleGAN network. We demonstrate the model's strength and
robustness through a careful evaluation over a range of datasets, from
simulated multi-object environments to rich real-world indoor and outdoor
scenes, showing it achieves state-of-the-art results in terms of image quality
and diversity, while enjoying fast learning and better data-efficiency. Further
qualitative and quantitative experiments offer us an insight into the model's
inner workings, revealing improved interpretability and stronger
disentanglement, and illustrating the benefits and efficacy of our approach. An
implementation of the model is available at
https://github.com/dorarad/gansformer.


Abstract:
  We prove that the $f$-divergences between univariate Cauchy distributions are
all symmetric, and can be expressed as strictly increasing scalar functions of
the symmetric chi-squared divergence. We report the corresponding scalar
functions for the total variation distance, the Kullback-Leibler divergence,
the squared Hellinger divergence, and the Jensen-Shannon divergence among
others. Next, we give conditions to expand the $f$-divergences as converging
infinite series of higher-order power chi divergences, and illustrate the
criterion for converging Taylor series expressing the $f$-divergences between
Cauchy distributions. We then show that the symmetric property of
$f$-divergences holds for multivariate location-scale families with prescribed
matrix scales provided that the standard density is even which includes the
cases of the multivariate normal and Cauchy families. However, the
$f$-divergences between multivariate Cauchy densities with different scale
matrices are shown asymmetric. Finally, we present several metrizations of
$f$-divergences between univariate Cauchy distributions and further report
geometric embedding properties of the Kullback-Leibler divergence.


Abstract:
  Quantum cascade lasers (QCLs) represent a fascinating accomplishment of
quantum engineering and enable the direct generation of terahertz (THz)
frequency radiation from an electrically-biased semiconductor heterostructure.
Their large spectral bandwidth, high output powers and quantum-limited
linewidths have facilitated the realization of THz pulses by active
mode-locking and passive generation of optical frequency combs (FCs) through
intracavity four-wave-mixing, albeit over a restricted operational regime.
Here, we conceive an integrated architecture for the generation of high power
(10 mW) THz FCs comprising an ultrafast THz polaritonic reflector, exploiting
intersubband cavity polaritons, and a broad bandwidth (2.3-3.8 THz)
heterogeneous THz QCL. Quantum cascade lasers (QCLs) represent a fascinating
accomplishment of quantum engineering and enable the direct generation of
terahertz (THz) frequency radiation from an electrically-biased semiconductor
heterostructure. By tuning the group delay dispersion in an integrated
geometry, through the exploitation of light induced bleaching of the
intersubband-based THz polaritons, we demonstrate spectral reshaping of the QCL
emission and stable FC operation over an operational dynamic range of up to
38%, characterized by a single and narrow (down to 700 Hz) intermode beatnote.
Our concept provides design guidelines for a new generation of compact,
cost-effective, electrically driven chip-scale FC sources based on ultrafast
polariton dynamics, paving the way towards the generation of mode locked THz
micro-lasers that will strongly impact a broad range of applications in
ultrafast sciences, data storage, high-speed communication and spectroscopy.


Abstract:
  Recently there has been a renaissance in identifiability results in deep
generative models, not least for non-linear ICA. For i.i.d. data, prior works
have assumed access to a sufficiently-informative auxiliary set of
observations, denoted $\mathbf{u}$. We show here how identifiability can be
obtained in the absence of this side-information. Previous methods have had to
make strong assumptions in order to obtain identifiable models. Here we obtain
empirically identifiable models under a much looser set of constraints. In
particular, we focus on generative models which perform clustering in their
latent space -- a model structure which matches previous identifiable models,
but with the learnt clustering providing a synthetic form of auxiliary
information. We evaluate our proposals, including via statistical tests, and
find that the learned clusterings function effectively: deep generative models
with latent clusterings are empirically identifiable, to the same degree as
models which rely on side information.


Abstract:
  In search of the ferromagnetic insulators for spintronic device applications,
we have studied the electronic, optical, and magnetic properties
ofLa2CrNiO6(LCNO) using the first principle density functional theory (DFT)and
monte carlo simulation technique. Firstly, we have adopted the sol-gel method
for preparation of LCNO and refined the X-ray diffracted value using the
fullprof suite under the Rietveld mechanism. The obtained orthorhombic Pbnm and
cubic Fm-3m space groups are used as the input of the DFT calculations. Both
the structures have shown the half metallicity and insult-ing bandgap towards
the majority and minority spin direction respectively. From the magnetic moment
calculations, we have seen the low spin state ofNi3+and the double exchange
(DE) interaction is responsible for the ferro-magneticity of LCNO. The optical
dielectric constant is 10 and the refractive index is 3.2 for orthorhombic
structure. The transition temperature (TC) is determined to 110 K from MCS
study, which has well agreed with experimental value (111 K). The RCP value is
determined to 12 J/Kg with a 5 tesla applied field, which is good for
magnetocaloric applications.


Abstract:
  We consider singular quasilinear stochastic partial differential equations
(SPDEs) studied in \cite{FHSX}, which are defined in paracontrolled sense. The
main aim of the present article is to establish the global-in-time solvability
for a particular class of SPDEs with origin in particle systems and, under a
certain additional condition on the noise, prove the convergence of the
solutions to stationary solutions as $t\to\infty$. We apply the method of
energy inequality and Poincar\'e inequality. It is essential that the
Poincar\'e constant can be taken uniformly in an approximating sequence of the
noise. We also use the continuity of the solutions in the enhanced noise,
initial values and coefficients of the equation, which we prove in this article
for general SPDEs discussed in \cite{FHSX} except that in the enhanced noise.
Moreover, we apply the initial layer property of improving regularity of the
solutions in a short time.


Abstract:
  Ultraluminous X-ray sources (ULXs) were identified as a separate class of
objects in 2000 based on data from the Chandra X-Ray Observatory. These are
unique objects: their X-ray luminosities exceed the Eddington limit for a
typical stellar-mass black hole. For a long time, the nature of ULXs remained
unclear. However, the gradual accumulation of data, new results of X-ray and
optical spectroscopy, and the study of the structure and energy of nebulae
surrounding ULXs led to the understanding that most of the ultraluminous X-ray
sources must be supercritical accretion disks like SS 433. The discovery of
neutron stars in a number of objects only increased the confidence of the
scientific community in the conclusions obtained, since the presence of neutron
stars in such systems clearly indicates a supercritical accretion regime. In
this review, we systematize the main facts about the observational
manifestations of ULXs and SS 433 in the X-ray and optical ranges and discuss
their explanation from the point of view of the supercritical accretion theory.


Abstract:
  We investigate the impact of geometric constriction on the viscous flow of
electron liquid through quantum point contacts. We provide analysis on the
electric potential distribution given the setup of a slit configuration and use
the method of conformal mapping to obtain analytical results. The potential
profile can be tested and contrasted experimentally with the scanning tunneling
potentiometry technique. We discuss intricate physics that underlies the Gurzhi
effect, i.e., the enhancement of conductivity in the viscous flow, and compare
results for different boundary conditions. In addition, we calculate the
temperature dependence of the momentum relaxation time as a result of impurity
assisted quasiballistic interference effects and discuss various correlational
corrections that lead to the violation of Matthiessen's rule in the
hydrodynamic regime. We caution that spatially inhomogeneous profiles of
current in the Gurzhi crossover between Ohmic and Stokes flows might also
appear in the nonhydrodynamic limit where nonlocality plays an important role.
This conclusion is corroborated by calculation of dispersive conductivity in
the weakly impure limit.


Abstract:
  The MultiplicitySequence package for Macaulay2 computes the multiplicity
sequence of a graded ideal in a standard graded ring over a field, as well as
several invariants of monomial ideals related to integral dependence. We
discuss two strategies implemented for computing multiplicity sequences: one
via the bivariate Hilbert polynomial, and the other via the technique of
general elements.


Abstract:
  Within the framework of the $s$-$d(f)$ exchange model in the mean-field
approximation for square, simple cubic, body-centered and face-centered cubic
lattices, the formation of a ferromagnetic, spiral, and commensurate
antiferromagnetic order is investigated. The possibility of the formation of
inhomogeneous states (magnetic phase separation), which necessarily arises
during first-order phase transitions in the electron filling parameter, is
taken into account. The saturation of the antiferromagnetic and spiral states
is studied depending on the parameters of the model. The results obtained
include a rich variety of magnetic structures and phase transitions, allowing
the interpretation of magnetic properties of semiconducting and metallic
systems containing magnetic atoms.


Abstract:
  The paper follows an operadic approach to provide a bialgebraic description
of substitution for Lie-Butcher series. We first show how the well-known
bialgebraic description for substitution in Butcher's $B$-series can be
obtained from the pre-Lie operad. We then apply the same construction to the
post-Lie operad to arrive at a bialgebra $\mathcal{Q}$. By considering a module
over the post-Lie operad, we get a cointeraction between $\mathcal{Q}$ and the
Hopf algebra $\mathcal{H}_N$ that describes composition for Lie-Butcher series.
We use this coaction to describe substitution for Lie-Butcher series.


Abstract:
  We study the dynamics of proppants carried by fluid driven into an evolving
penny-shaped fracture. The behaviour of the slurry flow is investigated in two
phases: pressurised injection and elastic closure. During injection the slurry
is modelled using a frictional rheology that takes into account the
shear-induced migration and jamming of the proppants. Making pragmatic
assumptions of negligible toughness and cross-fracture fluid slip, we find
self-similar solutions supporting a range of proppant concentration profiles.
In particular, we define an effective viscosity, which equates the fracture
evolution of a slurry flow with a given proppant volume fraction, to a
Newtonian flow with a particular viscosity. Using this framework, we are able
to make predictions about the geometry of the growing fracture and the
significance of tip screen-out. In the closure phase, proppants are modelled as
incompressible and radially immobile within the narrowing fracture. The effects
of proppant concentration on the geometry of the residual propped fracture are
explored in full. The results have important applications to industrial
fracking and geological dike formation by hot, intruding magma.


Abstract:
  The structure of an RNA molecule plays a significant role in its biological
function. Predicting structure given a one dimensional sequence of RNA
nucleotide bases is a difficult and important problem. Many computer programs
(known as in silico) are available for predicting 2-dimensional (secondary)
structures however 3-dimensional (tertiary) structure prediction is much more
difficult mainly due to the far greater number of feasible solutions and fewer
experimental data on the thermodynamic energies of 3D structures. It is also
challenging to verify the most likely three dimensional structure even with the
availability of sophisticated x-ray crystallography and nuclear magnetic
resonance imaging technologies. In this paper we develop three dimensional RNA
folding predictions by adding penalty and reward parameters to a previous two
dimensional approach based on Quadratic Unconstrained Binary Optimization
(QUBO) models. These parameters provide flexibility in the amount of three
dimensional folding allowed. We address the problem of multiple near-optimal
structures via a new weighted similarity structure measure and illustrate
folding pathways via progressively improving local optimal solutions. The
problems are solved via a new commercial QUBO solver AlphaQUBO (Meta-Analytics,
2020) that solves problems having hundreds of thousands of binary variables.


Abstract:
  We propose a novel method to detect cosmic magnification signals by
cross-correlating foreground convergence fields constructed from galaxy shear
measurements with background galaxy positional distributions, namely
shear-number density correlation. We apply it to the Hyper Suprime-Cam Subaru
Strategic Program (HSC-SSP) survey data. With 27 non-independent data points
and their full covariance, $\chi_0^2\approx 34.1$ and $\chi_T^2\approx 24.0$
with respect to the null and the cosmological model with the parameters from
HSC shear correlation analyses in Hamana et al. 2020 (arXiv:1906.06041),
respectively. The Bayes factor of the two is $\log_{10}B_{T0}\approx 2.2$
assuming equal model probabilities of null and HSC cosmology, showing a clear
detection of the magnification signals. Theoretically, the ratio of the
shear-number density and shear-shear correlations can provide a constraint on
the effective multiplicative shear bias $\bar m$ using internal data
themselves. We demonstrate the idea with the signals from our HSC-SSP mock
simulations and rescaling the statistical uncertainties to a survey of
$15000\deg^2$. For two-bin analyses with background galaxies brighter than
$m_{lim}=23$, the combined analyses lead to a forecasted constraint of
$\sigma(\bar m) \sim 0.032$, $2.3$ times tighter than that of using the
shear-shear correlation alone. Correspondingly, $\sigma(S_8)$ with
$S_8=\sigma_8(\Omega_\mathrm{m}/0.3)^{0.5}$ is tightened by $\sim 2.1$ times.
Importantly, the joint constraint on $\bar m$ is nearly independent of
cosmological parameters. Our studies therefore point to the importance of
including the shear-number density correlation in weak lensing analyses, which
can provide valuable consistency tests of observational data, and thus to
solidify the derived cosmological constraints.


Abstract:
  A {\it $k$-uniform hypergraph} $\mathcal{H}=(V, E)$ consists of a set $V$ of
vertices and a set $E$ of hyperedges ($k$-hyperedges), which is a family of
$k$-subsets of $V$. A {\it forbidden $k$-homogeneous (or forbidden
$k$-hypergraph)} access structure $\mathcal{A}$ is represented by a $k$-uniform
hypergraph $\mathcal{H}=(V, E)$ and has the following property: a set of
vertices (participants) can reconstruct the secret value from their shares in
the secret sharing scheme if they are connected by a $k$-hyperedge or their
size is at least $k+1$. A forbidden $k$-homogeneous access structure has been
studied by many authors under the terminology of $k$-uniform access structures.
In this paper, we provide efficient constructions on the total share size of
linear secret sharing schemes for sparse and dense $k$-uniform access
structures for a constant $k$ using the hypergraph decomposition technique and
the monotone span programs.


Abstract:
  The goal of entity matching in knowledge graphs is to identify entities that
refer to the same real-world objects using some similarity metric. The result
of entity matching can be seen as a set of entity pairs interpreted as the
same-as relation. However, the identified set of pairs may fail to satisfy some
structural properties, in particular transitivity, that are expected from the
same-as relation. In this work, we show that an ad-hoc enforcement of
transitivity, i.e. taking the transitive closure, on the identified set of
entity pairs may decrease precision dramatically. We therefore propose a
methodology that starts with a given similarity measure, generates a set of
entity pairs that are identified as referring to the same real-world objects,
and applies the cluster editing algorithm to enforce transitivity without
adding many spurious links, leading to overall improved performance.


Abstract:
  We propose a method to establish time reversal symmetry violation at future
neutrino oscillation experiments in a largely model-independent way. We
introduce a general parametrization of flavour transition probabilities which
holds under weak assumptions and covers a large class of new-physics scenarios.
This can be used to search for the presence of T-odd components in the
transition probabilities by comparing data at different baselines but at the
same neutrino energies. We show that this test can be performed already with
experiments at three different baselines and might be feasible with experiments
under preparation/consideration.


Abstract:
  We present the $360^\circ$ catalogue of physical properties of Hi-GAL compact
sources, detected between 70 and 500 $\mu$m. This release not only completes
the analogous catalogue previously produced by the Hi-GAL collaboration for
$-71^\circ \lesssim \ell \lesssim 67^\circ$, but also meaningfully improves it
thanks to a new set of heliocentric distances, 120808 in total. About a third
of the 150223 entries are located in the newly added portion of the Galactic
plane. A first classification based on detection at 70 $\mu$m as a signature of
ongoing star-forming activity distinguishes between protostellar sources
(23~per cent of the total) and starless sources, with the latter further
classified as gravitationally bound (pre-stellar) or unbound. The integral of
the spectral energy distribution, including ancillary photometry from
$\lambda=21$ to 1100 $\mu$m, gives the source luminosity and other bolometric
quantities, while a modified black body fitted to data for $\lambda \geq 160\,
\mu$m yields mass and temperature. All tabulated clump properties are then
derived using photometry and heliocentric distance, where possible. Statistics
of these quantities are discussed with respect to both source Galactic location
and evolutionary stage. No strong differences in the distributions of
evolutionary indicators are found between the inner and outer Galaxy. However,
masses and densities in the inner Galaxy are on average significantly larger,
resulting in a higher number of clumps that are candidates to host massive star
formation. Median behaviour of distance-independent parameters tracing source
evolutionary status is examined as a function of the Galactocentric radius,
showing no clear evidence of correlation with spiral arm positions.


Abstract:
  In this third paper of a series on the precision of obtaining ages of stellar
populations using the full spectrum fitting technique, we examine the precision
of this technique in deriving possible age spreads within a star cluster. We
test how well an internal age spread can be resolved as a function of cluster
age, population mass fraction, and signal-to-noise (S/N) ratio. For this test,
the two ages (Age (SSP1) and Age (SSP2)) are free parameters along with the
mass fraction of SSP1. We perform the analysis on 118,800 mock star clusters
covering all ages in the range 6.8 < log (age/yr) < 10.2, with mass fractions
from 10% to 90% for two age gaps (0.2 dex and 0.5 dex). Random noise is added
to the model spectra to achieve S/N ratios between 50 to 100 per wavelength
pixel. We find that the mean of the derived Age (SSP1) generally matches the
real Age (SSP1) to within 0.1 dex up to ages around log (age/yr) = 9.5. The
precision decreases for log (age/yr) > 9.6 for any mass fraction or S/N, due to
the similarity of SED shapes for those ages. In terms of the recovery of age
spreads, we find that the derived age spreads are often larger than the real
ones, especially for log(age/yr) < 8.0 and high mass fractions of SSP1.
Increasing the age gap in the mock clusters improves the derived parameters,
but Age (SSP2) is still overestimated for the younger ages.


Abstract:
  The basic idea here is that observation (or one's experience) is fundamental
and the `atomic world' is postulated as the source of such observation. Once
this source has been inferred to exist one may attempt to explicitly derive its
structure in such a way that the observation itself can be reproduced. And so
here is a purely quantum mechanical model of observation coupled to its
supposed source, and the observation itself is realised as a projection of this
quantum system.


Abstract:
  It goes back to Ahlfors that a real algebraic curve admits a real-fibered
morphism to the projective line if and only if the real part of the curve
disconnects its complex part. Inspired by this result, we are interested in
characterising real algebraic varieties of dimension $n$ admitting real-fibered
morphisms to the $n$-dimensional projective space. We present a criterion to
classify real-fibered morphisms that arise as finite surjective linear
projections from an embedded variety which relies on topological linking
numbers. We address special attention to real algebraic surfaces. We classify
all real-fibered morphisms from real del Pezzo surfaces to the projective plane
and determine which such morphisms arise as the composition of a projective
embedding with a linear projection. Furthermore, we give some insights in the
case of real conic bundles.


Abstract:
  A low loss propagating electromagnetic wave is shown to exist at a gradual
interface between two lossy conductive media. The electromagnetic frequency
range of this phenomenon may span from UV optics to RF range. In particular, it
is demonstrated that such a surface wave may be guided by a seafloor-seawater
interface and it may be used in radio communication and imaging underwater.
Similar surface waves may also be guided by various tissue boundaries inside a
human body. For example, such surface wave solutions may exist at planar
interfaces between skull bones and grey matter inside a human head at 6 GHz.


Abstract:
  Dual-phase noble-gas time projection chambers (TPCs) have improved the
sensitivities for dark matter direct search in past decades. The capability of
TPCs to reconstruct 3-D vertexes of keV scale recoilings is one of the most
advantageous features. In this work, we develop two horizontal position
reconstruction algorithms for the PandaX-II dark matter search experiment using
the dual-phase liquid xenon TPC. Both algorithms are optimized by the
$^{83m}$Kr calibration events and use photon distribution of ionization signals
among photomultiplier tubes to infer the positions. According to the events
coming from the gate electrode, the uncertainties in the horizontal positions
are 3.4 mm (3.9 mm) in the analytical (simulation-based) algorithm for an
ionization signal with several thousand photon electrons in the center of the
TPC


Abstract:
  The present paper deals with the control problems governed by fractional
non-instantaneous impulsive functional evolution equations with state-dependent
delay involving Caputo fractional derivatives in Banach spaces. The main
objective of this work is to formulate sufficient conditions for the
approximate controllability of the considered system in separable reflexive
Banach spaces. We have exploited the resolvent operator technique and
Schauder's fixed point theorem in the proofs to achieve this goal. The
approximate controllability of linear system is discussed in detail, which
lacks in the existing literature. We also provide an example to illustrate the
efficiency of the developed results. Moreover, we point out some shortcomings
of the existing works in the context of characterization of mild solution and
phase space, and approximate controllability of fractional order impulsive
systems in Banach spaces.


Abstract:
  Belief propagation (BP) decoding of low-density parity-check (LDPC) codes
with various dynamic decoding schedules have been proposed to improve the
efficiency of the conventional flooding schedule. As the ultimate goal of an
ideal LDPC code decoder is to have correct bit decisions, a dynamic decoding
schedule should be variable node (VN)-centric and be able to find the VNs with
probable incorrect decisions and having a good chance to be corrected if chosen
for update. We propose a novel and effective metric called conditional
innovation (CI) which serves this design goal well. To make the most of dynamic
scheduling which produces high-reliability bit decisions, we limit our search
for the candidate VNs to those related to the latest updated nodes only.
  Based on the CI metric and the new search guideline separately or in
combination, we develop several highly efficient decoding schedules. To reduce
decoding latency, we introduce multi-edge updating versions which offer extra
latency-performance tradeoffs. Numerical results show that both single-edge and
multi-edge algorithms provide better decoding performance against most dynamic
schedules and the CI-based algorithms are particularly impressive at the first
few decoding iterations.


Abstract:
  Complex systems like human mobility exhibit a wide range of collective
dynamics. Ride-sharing, the combination of multiple similar trips into one, is
a particularly prominent example due to the complex interplay between the
requests and the vehicle fleet. Several contributions have analyzed the
dynamics of the routing and the service efficiency of ride-sharing fleets.
Here, we adopt a complementary perspective and study the adoption of
ride-sharing from the perspective of its users. Collective interactions of the
users to avoid detours in shared rides give rise to spontaneous symmetry
breaking, pattern formation dynamics, and bistability, potentially limiting the
adoption of ride-sharing. Our results may provide a framework to understand
real-world adoption patterns of ride-sharing in complex urban settings and
(re)design ride-sharing services and incentives to promote sustainable shared
mobility.


Abstract:
  We investigate the breakdown of magneto-hydrodynamics at low temperature
($T$) with black holes whose extremal geometry is AdS$_2\times$R$^2$. The
breakdown is identified by the equilibration scales ($\omega_{\text{eq}},
k_{\text{eq}}$) defined as the collision point between the diffusive
hydrodynamic mode and the longest-lived non-hydrodynamic mode. We show
($\omega_{\text{eq}}, k_{\text{eq}}$) at low $T$ is determined by the diffusion
constant $D$ and the scaling dimension $\Delta(0)$ of an infra-red operator:
$\omega_{\text{eq}} = 2\pi T \Delta(0), \, k_{\text{eq}}^2 =
\omega_{\text{eq}}/D$, where $\Delta(0)=1$ in the presence of magnetic fields.
For the purpose of comparison, we have analytically shown $\Delta(0)=2$ for the
axion model independent of the translational symmetry breaking pattern
(explicit or spontaneous), which is complementary to previous numerical
results. Our results support the conjectured universal upper bound of the
energy diffusion $D \,\le\, \omega_{\text{eq}}/k_{\text{eq}}^2 \,:=\,
v_{\text{eq}}^2 \, \tau_{\text{eq}}$ where $v_{\text{eq}}:=
\omega_{\text{eq}}/k_{\text{eq}}$ and
$\tau_{\text{eq}}:=\omega_{\text{eq}}^{-1}$ are the velocity and the timescale
associated to equilibration, implying that the breakdown of hydrodynamics sets
the upper bound of the diffusion constant $D$ at low $T$.


Abstract:
  In this paper, we study a new generalization of the Lorentz cone, called the
Monotone Extended Second Order Cone (MESOC). We investigate basic properties of
MESOC including computation of its Lyapunov rank and proving its reducibility.
Moreover, we show that in an ambient space, a cylinder is an isotonic
projection set with respect to MESOC. We also examine a Nonlinear
Complementarity Problem on a cylinder, which is equivalent to a suitable Mixed
Complementarity Problem and provide a computational example illustrating
applicability of MESOC.


Abstract:
  The exceptional region of the parameter space (ERPS) of the two Higgs doublet
model (2HDM) is defined to be the parameter regime where the scalar potential
takes on a very special form. In the standard parameterization of the 2HDM
scalar potential with squared mass parameters $m_{11}^2$, $m_{22}^2$,
$m_{12}^2$, and dimensionless couplings, $\lambda_1$, $\lambda_2$,
$\ldots,\lambda_7$, the ERPS corresponds to $\lambda_1=\lambda_2$,
$\lambda_7=-\lambda_6$, $m_{11}^2=m_{22}^2$ and $m_{12}^2=0$, corresponding to
a scalar potential with an enhanced generalized CP symmetry called GCP2. Many
special features persist if $\lambda_1=\lambda_2$ and $\lambda_7=-\lambda_6$
are retained while allowing for $m_{11}^2\neq m_{22}^2$ and/or $m_{12}^2\neq
0$, corresponding to a scalar potential with a softly-broken GCP2 symmetry,
which we designate as the ERPS4. In this paper, we examine many of the special
features of the ERPS4, as well as even more specialized cases within the ERPS4
framework in which additional constraints on the scalar potential parameters
are imposed. By surveying the landscape of the ERPS4, we complete the
classification of 2HDM scalar potentials that exhibit an exact Higgs alignment
(where the tree-level couplings of one neutral scalar coincide with those of
the Standard Model Higgs boson), due to a residual symmetry that is unbroken in
the vacuum. One surprising aspect of the ERPS4 is the possibility that the
scalar sector is CP-conserving despite the presence of a complex parameter of
the scalar potential whose complex phase cannot be removed by separate
rephasings of the two scalar doublet fields. The significance of the ERPS4
regime for custodial symmetry is also discussed, and the cases where a
custodial symmetric 2HDM scalar potential preserves an exact Higgs alignment
are elucidated.


Abstract:
  Network slicing (NS) and multi-access edge computing (MEC) are new paradigms
which play key roles in 5G and beyond networks. NS allows network operators
(NOs) to divide the available network resources into multiple logical NSs for
providing dedicated virtual networks tailored to the specific service/business
requirements. MEC enables NOs to provide diverse ultra-low latency services for
supporting the needs of different industry verticals by moving computing
facilities to the network edge. NS can be constructed by instantiating a set of
virtual network functions (VNFs) on top of MEC cloud servers for provisioning
diverse latency-sensitive communication services (e.g., autonomous driving and
augmented reality) on demand at a lesser cost and time. However, VNFs, MEC
cloud servers, and communication links are subject to failures due to software
bugs, misconfiguration, overloading, hardware faults, cyber attacks, power
outage, and natural/man-made disaster. Failure of a critical network component
disrupts services abruptly and leads to users' dissatisfaction, which may
result in revenue loss for the NOs. In this paper, we present a novel approach
based on multi-connectivity in 5G networks to tackle this problem and our
proposed approach is resilient against i) failure of VNFs, ii) failure of local
servers within MEC, iii) failure of communication links, and iv) failure of an
entire MEC cloud facility in regional level. To this end, we formulate the
problem as a binary integer programming (BIP) model in order to optimally
deploy NSs with the minimum cost, and prove it is NP-hard. To overcome time
complexity, we propose an efficient genetic algorithm based heuristic to obtain
near-optimal solution in polynomial time. By extensive simulations, we show
that our proposed approach not only reduces resource wastage, but also improves
throughput while providing high resiliency against failures.


Abstract:
  The lack of guided exercises and practical opportunities to learn about
cybersecurity in a practical way makes it difficult for security experts to
improve their proficiency. Capture the Flag events and Cyber Ranges are ideal
for cybersecurity training. Thereby, the participants usually compete in teams
against each other, or have to defend themselves in a specific scenario. As
organizers of yearly events, we present a taxonomy for interactive cyber
training and education. The proposed taxonomy includes different factors of the
technical setup, audience, training environment, and training setup. By the
comprehensive taxonomy, different aspects of interactive training are
considered. This can help trainings to improve and to be established
successfully. The provided taxonomy is extendable and can be used in further
application areas as research on new security technologies.


Abstract:
  We consider a class of constrained multi-agent optimization problems where
the goal is to cooperatively minimize a sum of agent-specific nondifferentiable
merely convex functions. The constraint set is characterized as a variational
inequality (VI) problem where each agent is associated with a local monotone
mapping. We first discuss how the proposed formulation can be employed in
addressing several important classes of distributed optimization problems,
including those subject to complementarity constraints, nonlinear equality
constraints, and equilibrium constraints. Our main contributions are as
follows: (i) We develop an iteratively regularized incremental gradient method
where at each iteration, agents communicate over a cycle graph to update their
solution iterates using their local information about the objective and the
mapping. The proposed method is single-timescale in the sense that it does not
involve any excessive hard-to-project computation per iteration. (ii) We derive
non-asymptotic agent-wise convergence rates for the suboptimality of the global
objective function and infeasibility of the VI constraints measured by a
suitably defined dual gap function. (iii) To analyze the convergence rate in
the solution space, assuming the objective function is strongly convex and
smooth, we derive non-asymptotic agent-wise rates on an error metric that
relates the generated iterates with the Tikhonov trajectory. The proposed
method appears to be the first fully iterative scheme equipped with iteration
complexity that can address distributed optimization problems with VI
constraints. We provide preliminary numerical experiments for computing the
best equilibrium in a transportation network problem. We also compare the
performance of the proposed scheme with that of the existing incremental
gradient methods in addressing constrained finite-sum problems.


Abstract:
  Four different finite element level-set (FE-LS) formulations are compared for
the modeling of grain growth in the context of polycrystalline structures and,
moreover, two of them are presented for the first time using anisotropic grain
boundary (GB) energy and mobility. Mean values and distributions are compared
using the four formulations. First, we present the strong and weak formulations
for the different models and the crystallographic parameters used at the
mesoscopic scale. Second, some Grim Reaper analytical cases are presented and
compared with the simulation results, here the evolutions of individual
multiple junctions are followed. Additionally, large scale simulations are
presented. Anisotropic GB energy and mobility are respectively defined as
functions of the misorientation/inclination and disorientation. The evolution
of the disorientation distribution function (DDF) is computed and its evolution
is in accordance with prior works. We found that the formulation called
"Anisotropic" is the more physical one but it could be replaced at the
mesoscopic scale by an Isotropic formulation for simple microstructures
presenting an initial Mackenzie-type DDF.


Abstract:
  The effect of scattering of conduction electrons by dynamical spin
fluctuations on the thermopower in metals near a thermal phase transition into
an antiferromagnetic phase is considered. We are interested in a transition at
room temperature, as has been studied in a heterostructure involving layers of
IrMn. We show that the electrical resistivity exhibits a narrow but low peak at
the transition, which may be difficult to detect on top of the main
contributions induced by phonons and impurities. By contrast, the thermopower
is found to exhibit a prominent peak both as a function of temperature T for
fixed layer thickness tAFM and as a function of tAFM for fixed T: We conjecture
that the transition temperature Tc is a function of both tAFM and the Fermi
energy EF . Both dependencies give rise to a sharp peak of the thermopower as a
function of T or tAFM near the transition. The estimated magnitude of the peak
for the case of three-dimensional longitudinal spin fluctuations is in good
agreement with experiment.


Abstract:
  Issue trackers, such as Jira, have become the prevalent collaborative tools
in software engineering for managing issues, such as requirements, development
tasks, and software bugs. However, issue trackers inherently focus on the
life-cycle of single issues although issues have and express dependencies on
other issues that constitute an issue dependency network in a large complex
collaborative projects. The objective of this study is to develop supportive
solutions for the improved management of dependent issues in an issue tracker.
This study follows Design Science methodology, consisting of elicitation of
drawbacks, and construction and evaluation of a solution and system. The study
was carried out in the context of The Qt Company's Jira, which exemplifies an
actively used, almost two decade old issue tracker with over 100,000 issues.
The drawbacks capture how users operate with issue trackers to handle issue
information in large, collaborative and long-lived projects. The basis of the
solution is to keep issues and dependencies as separate objects and
automatically construct an issue graph. Dependency detection complements the
issue graph by proposing missing dependencies, and consistency check and
diagnosis identify incompatible issue priorities and release assignments.
Jira's plugin and service-based system architecture realizes the functional and
quality concerns of the system implementation. We show how to adopt the
supporting intelligent techniques of an issue tracker in a complex use context
and a large data-set. The solution takes into account integrated and holistic
system-view, practical applicability and utility, and the practical
characteristics, such as inherent incompleteness, of issue data.


Abstract:
  In a close look at the replica wormhole derivation of the island conjecture,
we note a discrepancy in the derived matrix eigenvalues in the limit where the
Hawking radiation entropy goes to zero. The small corrections to the density
matrix for the radiation infer that ${\rm tr}(\rho_\textsf{R}^2)$, equally a
sum over the eigenvalues squared, must be small ($\ll1$) at all times. This is
in contradiction with an ensemble dominated by a density matrix with an
eigenvalue close to unity. Also, the radiation entropy has been approximated by
the ensemble averaged entropy, as in a final state analysis. For
$\rho_\textsf{R}=\rho_\textsf{R}(\sigma)$ with $\sigma$ the set of variables
used in the average, the ensemble average is only an accurate estimate of the
entropy after $\sigma$ has been measured. At the formation of each Hawking
pair, there is a distribution over $\sigma$ that affects the entropy. Without a
real time determination of $\sigma$, the radiation entropy follows Hawking's
result during the evaporation. A question remains of how quickly such
determinations can be assumed to occur. A complete argument for that the
radiation entropy follows the Page curve should address this.


Abstract:
  We study the notion of a causal time-evolution of a conserved nonlocal
physical quantity in a globally hyperbolic spacetime $\mathcal{M}$. The role of
the `global time' is played by a chosen Cauchy temporal function $\mathcal{T}$,
whereas the instantaneous configurations of the nonlocal quantity are modeled
by probability measures $\mu_t$ supported on the corresponding time slices
$\mathcal{T}^{-1}(t)$. We show that the causality of such an evolution can be
expressed in three equivalent ways: (i) via the causal precedence relation
$\preceq$ extended to probability measures, (ii) with the help of a probability
measure $\sigma$ on the space of future-directed continuous causal curves
endowed with the compact-open topology and (iii) through a causal vector field
$X$ of $L^2_{\textrm{loc}}$-regularity, with which the map $t \mapsto \mu_t$
satisfies the continuity equation in the distributional sense. In the course of
the proof we find that the compact-open topology is sensitive to the
differential properties of the causal curves, being equal to a topology induced
from a suitable $H^1_{\textrm{loc}}$-Sobolev space. This enables us to
construct $X$ as a vector field in a sense `tangent' to $\sigma$. In addition,
we discuss the general covariance of descriptions (i)-(iii), unraveling the
geometrical, observer-independent notions behind them.


Abstract:
  In this paper, we generalize existing frameworks for
$\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broad
class of parametric linear time-invariant systems. To this end, we derive
first-order necessary ptimality conditions for a class of structured
reduced-order models, and then building on those, propose a
stability-preserving optimization-based method for computing locally
$\mathcal{H}_2\otimes\mathcal{L}_2$-optimal reduced-order models. We also make
a theoretical comparison to existing approaches in the literature, and in
numerical experiments, show how our new method, with reasonable computational
effort, produces stable optimized reduced-order models with significantly lower
approximation errors.


Abstract:
  Robots will be expected to manipulate a wide variety of objects in complex
and arbitrary ways as they become more widely used in human environments. As
such, the rearrangement of objects has been noted to be an important benchmark
for AI capabilities in recent years. We propose NeRP (Neural Rearrangement
Planning), a deep learning based approach for multi-step neural object
rearrangement planning which works with never-before-seen objects, that is
trained on simulation data, and generalizes to the real world. We compare NeRP
to several naive and model-based baselines, demonstrating that our approach is
measurably better and can efficiently arrange unseen objects in fewer steps and
with less planning time. Finally, we demonstrate it on several challenging
rearrangement problems in the real world.


Abstract:
  It is essential to explore the stability and activity of real-system
nanoparticles theoretically. While applications of theoretical methods for this
purpose can be found in literature, the expensive computational costs of
conventional theoretical methods hinder their massive applications to practical
materials design. With the recent development of neural network algorithms
along with the advancement of computer systems, neural network potentials have
emerged as a promising candidate for the description of a wide range of
materials, including metals and molecules, with a reasonable computational
time. In this study, we successfully validate a universal neural network
potential, PFP, for the description of monometallic Ru nanoparticles, PdRuCu
ternary alloy nanoparticles, and the NO adsorption on Rh nanoparticles against
first-principles calculations. We further conduct molecular dynamics
simulations on the NO-Rh system and challenge the PFP to describe a large,
supported Pt nanoparticle system.


Abstract:
  Very recently, the Tibet-AS$\gamma$ collaboration reported the detection of
$\gamma$ rays from the galactic disk in the energy range of 100 TeV -- 1 PeV.
Remarkably, many of these $\gamma$ rays were observed apart from known very
high energy (E$>$ 100 GeV) $\gamma$-ray sources. These results are best
understood if these diffuse $\gamma$ rays: 1) were produced by a conventional
rather than an exotic (i.e. dark matter decay or annihilation) process, 2) have
a hadronic rather than a leptonic origin, 3) were produced in impulsive rather
than stable sources or, alternatively, in optically thick sources. In addition
to that, the detection of the sub-PeV diffuse $\gamma$ rays implies a limit on
the flux of neutrinos from the Galactic disk and a lower limit on the rigidity
of the cutoff in the Galactic cosmic ray spectrum.


Abstract:
  We generalize to arbitrary categories of algebras the notion of an
NS-algebra. We do this by using a bimodule property, as we did for defining the
general notions of a dendriform and tridendriform algebra. We show that several
types of operators lead to NS-algebras: Nijenhuis operators, twisted
Rota-Baxter operators and relative Rota-Baxter operators of arbitrary weight.


Abstract:
  The concepts of blameworthiness and wrongness are of fundamental importance
in human moral life. But to what extent are humans disposed to blame
artificially intelligent agents, and to what extent will they judge their
actions to be morally wrong? To make progress on these questions, we adopted
two novel strategies. First, we break down attributions of blame and wrongness
into more basic judgments about the epistemic and conative state of the agent,
and the consequences of the agent's actions. In this way, we are able to
examine any differences between the way participants treat artificial agents in
terms of differences in these more basic judgments. our second strategy is to
compare attributions of blame and wrongness across human, artificial, and group
agents (corporations). Others have compared attributions of blame and wrongness
between human and artificial agents, but the addition of group agents is
significant because these agents seem to provide a clear middle-ground between
human agents (for whom the notions of blame and wrongness were created) and
artificial agents (for whom the question remains open).


Abstract:
  The discrimination of coherent states is a key task in optical communication
and quantum key distribution protocols. In this work, we use a
photon-number-resolving detector, the transition-edge sensor, to discriminate
binary-phase-shifted coherent states at a telecom wavelength. Owing to its
dynamic range and high efficiency, we achieve a bit error probability that
unconditionally exceeds the standard quantum limit (SQL) by up to 7.7 dB. The
improvement to the SQL persists for signals containing up to approximately
seven photons on average and is achieved in a single shot (i.e. without
measurement feedback), thus making our approach compatible with larger
bandwidths.


Abstract:
  This paper investigates the exotic phenomena exhibited by links of
disconnected surfaces with boundary that are properly embedded in the 4-ball.
Our main results provide two different constructions of exotic pairs of surface
links that are Brunnian, meaning that all proper sublinks of the surface are
trivial. We then modify these core constructions to vary the number of
components in the exotic links, the genera of the components, and the number of
components that must be removed before the surfaces become unlinked. Our
arguments extend two tools from 3-dimensional knot theory into the
4-dimensional setting: satellite operations, especially Bing doubling, and
covering links in branched covers.


Abstract:
  A linear layout of a graph typically consists of a total vertex order, and a
partition of the edges into sets of either non-crossing edges, called stacks,
or non-nested edges, called queues. The stack (queue) number of a graph is the
minimum number of required stacks (queues) in a linear layout. Mixed linear
layouts combine these layouts by allowing each set of edges to form either a
stack or a queue. In this work we initiate the study of the mixed page number
of a graph which corresponds to the minimum number of such sets.
  First, we study the edge density of graphs with bounded mixed page number.
Then, we focus on complete and complete bipartite graphs, for which we derive
lower and upper bounds on their mixed page number. Our findings indicate that
combining stacks and queues is more powerful in various ways compared to the
two traditional layouts.


Abstract:
  The continuous version of a fundamental result of Khinchin says that a
half-infinite torus line in the unit square $[0,1]^2$ exhibits superdensity,
which is a best form of time-quantitative density, if and only if the slope of
the geodesic is a badly approximable number. In this paper, we give a proof of
the extension of this result of Khinchin to the case when the unit torus
$[0,1]^2$ is replaced by a finite polysquare surface, or square tiled surface.
The argument is based on diophantine approximation and continued fractions,
traditional tools in number theory. In particular, we use the famous
$3$-distance theorem in diophantine approximation combined with an iterative
process. In short, this is a very number-theoretic study of a very
number-theoretic problem.
  This paper improves on an earlier result of the authors and Yang where it is
shown that badly approximable numbers that satisfy a quite severe technical
restriction on the digits of their continued fractions lead to superdense
geodesics. Here we overcome this technical impediment.
  This paper is self-contained, and the reader does not need any knowledge of
dynamical systems.


Abstract:
  Quantum computation represents an emerging framework to solve lattice gauge
theories (LGT) with arbitrary gauge groups, a general and long-standing problem
in computational physics. While quantum computers may encode LGT using only
polynomially increasing resources, a major openissue concerns the violation of
gauge-invariance during the dynamics and the search for groundstates. Here, we
propose a new class of parametrized quantum circuits that can represent states
belonging only to the physical sector of the total Hilbert space. This class of
circuits is compact yet flexible enough to be used as a variational ansatz to
study ground state properties, as well as representing states originating from
a real-time dynamics. Concerning the first application, the structure of the
wavefunction ansatz guarantees the preservation of physical constraints such as
the Gauss law along the entire optimization process, enabling reliable
variational calculations. As for the second application, this class of quantum
circuits can be used in combination with timedependent variational quantum
algorithms, thus drastically reducing the resource requirements to access
dynamical properties.


Abstract:
  We investigate the complexity of computing the Zariski closure of a finitely
generated group of matrices. The Zariski closure was previously shown to be
computable by Derksen, Jeandel, and Koiran, but the termination argument for
their algorithm appears not to yield any complexity bound. In this paper we
follow a different approach and obtain a bound on the degree of the polynomials
that define the closure. Our bound shows that the closure can be computed in
elementary time. We also obtain upper bounds on the length of chains of linear
algebraic groups, where all the groups are generated over a fixed number field.


Abstract:
  Echo State Networks (ESNs) are a special type of recurrent neural networks
(RNNs), in which the input and recurrent connections are traditionally
generated randomly, and only the output weights are trained. Despite the recent
success of ESNs in various tasks of audio, image and radar recognition, we
postulate that a purely random initialization is not the ideal way of
initializing ESNs. The aim of this work is to propose an unsupervised
initialization of the input connections using the K-Means algorithm on the
training data. We show that for a large variety of datasets this initialization
performs equivalently or superior than a randomly initialized ESN whilst
needing significantly less reservoir neurons. Furthermore, we discuss that this
approach provides the opportunity to estimate a suitable size of the reservoir
based on prior knowledge about the data.


Abstract:
  In this paper, we develop safe reinforcement-learning-based controllers for
systems tasked with accomplishing complex missions that can be expressed as
linear temporal logic specifications, similar to those required by
search-and-rescue missions. We decompose the original mission into a sequence
of tracking sub-problems under safety constraints. We impose the safety
conditions by utilizing barrier functions to map the constrained optimal
tracking problem in the physical space to an unconstrained one in the
transformed space. Furthermore, we develop policies that intermittently update
the control signal to solve the tracking sub-problems with reduced burden in
the communication and computation resources. Subsequently, an actor-critic
algorithm is utilized to solve the underlying Hamilton-Jacobi-Bellman
equations. Finally, we support our proposed framework with stability proofs and
showcase its efficacy via simulation results.


Abstract:
  Purpose
  A Magnetic Resonance Imaging (MRI) exam typically consists of several
sequences that yield different image contrasts. Each sequence is parameterized
through multiple acquisition parameters that influence image contrast,
signal-to-noise ratio, acquisition time, and/or resolution. Depending on the
clinical indication, different contrasts are required by the radiologist to
make a diagnosis. As MR sequence acquisition is time consuming and acquired
images may be corrupted due to motion, a method to synthesize MR images with
adjustable contrast properties is required.
  Methods
  Therefore, we trained an image-to-image generative adversarial network
conditioned on the MR acquisition parameters repetition time and echo time. Our
approach is motivated by style transfer networks, whereas the "style" for an
image is explicitly given in our case, as it is determined by the MR
acquisition parameters our network is conditioned on.
  Results
  This enables us to synthesize MR images with adjustable image contrast. We
evaluated our approach on the fastMRI dataset, a large set of publicly
available MR knee images, and show that our method outperforms a benchmark
pix2pix approach in the translation of non-fat-saturated MR images to
fat-saturated images. Our approach yields a peak signal-to-noise ratio and
structural similarity of 24.48 and 0.66, surpassing the pix2pix benchmark model
significantly.
  Conclusion
  Our model is the first that enables fine-tuned contrast synthesis, which can
be used to synthesize missing MR contrasts or as a data augmentation technique
for AI training in MRI.


Abstract:
  In problem solving, understanding the problem that one seeks to solve is an
essential initial step. In this paper, we propose computational methods for
facilitating problem understanding through the task of recognizing the unknown
in specifications of long Math problems. We focus on the topic of Probability.
Our experimental results show that learning models yield strong results on the
task, a promising first step towards human interpretable, modular approaches to
understanding long Math problems.


Abstract:
  Cyber-Physical Systems (CPSs) play an increasingly significant role in many
critical applications. These valuable applications attract various
sophisticated attacks. This paper considers a stealthy estimation attack, which
aims to modify the state estimation of the CPSs. The intelligent attackers can
learn defense strategies and use clandestine attack strategies to avoid
detection. To address the issue, we design a Chi-square detector in a Digital
Twin (DT), which is an online digital model of the physical system. We use a
Signaling Game with Evidence (SGE) to find the optimal attack and defense
strategies. Our analytical results show that the proposed defense strategies
can mitigate the impact of the attack on the physical estimation and guarantee
the stability of the CPSs. Finally, we use an illustrative application to
evaluate the performance of the proposed framework.


Abstract:
  We study mixing times for the totally asymmetric simple exclusion process
(TASEP) on a segment of size $N$ with open boundaries. We focus on the maximal
current phase, and prove that the mixing time is of order $N^{3/2}$, up to
logarithmic corrections. In the triple point, where the TASEP with open
boundaries approaches the Uniform distribution on the state space, we show that
the mixing time is precisely of order $N^{3/2}$. This is conjectured to be the
correct order of the mixing time for a wide range of particle systems with
maximal current. Our arguments rely on a connection to last-passage
percolation, and recent results on moderate deviations of last-passage times.


Abstract:
  Although training data is essential for machine learning, railway companies
are facing difficulties in gathering adequate images of defective equipment due
to their proactive replacement of would be defective equipment. Nevertheless,
proactive replacement is indispensable for safe and undisturbed operation of
public transport. In this research, we have developed a model using CycleGAN to
generate artificial images of defective equipment instead of real images. By
adopting these generated images as training data, we verified that these images
are indistinguishable from real images and they play a vital role in enhancing
the accuracy of the defect detection models.


Abstract:
  Novel multimodal imaging methods are capable of generating extensive, super
high resolution datasets for preclinical research. Yet, a massive lack of
annotations prevents the broad use of deep learning to analyze such data. So
far, existing generative models fail to mitigate this problem because of
frequent labeling errors. In this paper, we introduce a novel generative method
which leverages real anatomical information to generate realistic image-label
pairs of tumours. We construct a dual-pathway generator, for the anatomical
image and label, trained in a cycle-consistent setup, constrained by an
independent, pretrained segmentor. The generated images yield significant
quantitative improvement compared to existing methods. To validate the quality
of synthesis, we train segmentation networks on a dataset augmented with the
synthetic data, substantially improving the segmentation over baseline.


Abstract:
  We present a benchmark database of public social media postings from the
United Kingdom related to the Covid-19 pandemic for academic research purposes,
along with some initial analysis, including a taxonomy of key themes organised
by keyword. This release supports the findings of a research study funded by
the Scottish Government Chief Scientist Office that aims to investigate social
sentiment in order to understand the response to public health measures
implemented during the pandemic.


Abstract:
  Federated learning is an appealing framework for analyzing sensitive data
from distributed health data networks. Under this framework, data partners at
local sites collaboratively build an analytical model under the orchestration
of a coordinating site, while keeping the data decentralized. While integrating
information from multiple sources may boost statistical efficiency, existing
federated learning methods mainly assume data across sites are homogeneous
samples of the global population, failing to properly account for the extra
variability across sites in estimation and inference. Drawing on a
multi-hospital electronic health records network, we develop an efficient and
interpretable tree-based ensemble of personalized treatment effect estimators
to join results across hospital sites, while actively modeling for the
heterogeneity in data sources through site partitioning. The efficiency of this
approach is demonstrated by a study of causal effects of oxygen saturation on
hospital mortality and backed up by comprehensive numerical results.


Abstract:
  Algorithmic recourse aims to provide actionable recommendations to
individuals to obtain a more favourable outcome from an automated
decision-making system. As it involves reasoning about interventions performed
in the physical world, recourse is fundamentally a causal problem. Existing
methods compute the effect of recourse actions using a causal model learnt from
data under the assumption of no hidden confounding and modelling assumptions
such as additive noise. Building on the seminal work of Balke and Pearl (1994),
we propose an alternative approach for discrete random variables which relaxes
these assumptions and allows for unobserved confounding and arbitrary
structural equations. The proposed approach only requires specification of the
causal graph and confounding structure and bounds the expected counterfactual
effect of recourse actions. If the lower bound is above a certain threshold,
i.e., on the other side of the decision boundary, recourse is guaranteed in
expectation.


Abstract:
  We consider the effect of a partial transpose on the limit $*$-distribution
of a Haar distributed random unitary matrix. If we fix, $b$, the number of
blocks, we show that the partial transpose can be decomposed into a sum of $b$
matrices which are asymptotically free and identically distributed. We then
consider the joint effect of different block decompositions and show that under
some mild assumptions we also get asymptotic freeness.


Abstract:
  Social media has become an essential part of the daily routines of children
and adolescents. Moreover, enormous efforts have been made to ensure the
psychological and emotional well-being of young users as well as their safety
when interacting with various social media platforms. In this paper, we
investigate the exposure of those users to inappropriate comments posted on
YouTube videos targeting this demographic. We collected a large-scale dataset
of approximately four million records and studied the presence of five
age-inappropriate categories and the amount of exposure to each category. Using
natural language processing and machine learning techniques, we constructed
ensemble classifiers that achieved high accuracy in detecting inappropriate
comments. Our results show a large percentage of worrisome comments with
inappropriate content: we found 11% of the comments on children's videos to be
toxic, highlighting the importance of monitoring comments, particularly on
children's platforms.


Abstract:
  We introduce environment predictive coding, a self-supervised approach to
learn environment-level representations for embodied agents. In contrast to
prior work on self-supervised learning for images, we aim to jointly encode a
series of images gathered by an agent as it moves about in 3D environments. We
learn these representations via a zone prediction task, where we intelligently
mask out portions of an agent's trajectory and predict them from the unmasked
portions, conditioned on the agent's camera poses. By learning such
representations on a collection of videos, we demonstrate successful transfer
to multiple downstream navigation-oriented tasks. Our experiments on the
photorealistic 3D environments of Gibson and Matterport3D show that our method
outperforms the state-of-the-art on challenging tasks with only a limited
budget of experience.


Abstract:
  The Besicovitch projection theorem states that if a subset $E$ of the plane
has finite length in the sense of Hausdorff measure and is purely unrectifiable
(so its intersection with any Lipschitz graph has zero length), then almost
every orthogonal projection of $E$ to a line will have zero measure. In other
words, the Favard length of a purely unrectifiable $1$-set vanishes. In this
article, we show that when linear projections are replaced by certain nonlinear
projections called curve projections, this result remains true. In fact, we go
further and use multiscale analysis to prove a quantitative version of this
Besicovitch nonlinear projection theorem. Roughly speaking, we show that if a
subset of the plane has finite length in the sense of Hausdorff and is nearly
purely unrectifiable, then its Favard curve length is very small. Our
techniques build on those of Tao, who in [Tao09] proves a quantification of the
original Besicovitch projection theorem.


Abstract:
  In this paper, we present a data-driven secondary controller for regulating
to some desired values several variables of interest in a power system, namely,
electrical frequency, voltage magnitudes at critical buses, and active power
flows through critical lines. The power generation system is based on
distributed energy resources (DERs) interfaced with either grid-forming (GFM)
or grid-following (GFL) inverters. The secondary controller is based on online
feedback optimization leveraging the learned sensitivities of the changes in
the system frequency, voltage magnitudes at critical buses, and active power
flows through critical lines to the changes in inverter active and reactive
power setpoints. To learn the sensitivities accurately from data, the feedback
optimization has a built-in mechanism for keeping the secondary control inputs
persistently exciting without degrading its performance. The feedback
optimization also utilizes the learned power-voltage characteristics of
photovoltaic (PV) arrays to compute DC-link voltage setpoints so as to allow
the PV arrays to track the power setpoints. To learn the power-voltage
characteristics, we separately execute a data-driven approach that fits a
concave polynomial to the collected power-voltage measurements by solving a
sum-of-squares (SoS) optimization. We showcase the secondary controller using
the modified IEEE-14 bus test system, in which conventional energy sources are
replaced with inverter-interfaced DERs.