Abstract:
  We study the impact of maximal zeros of the Dirac mass matrix on neutrino
phenomenology and dark matter within the framework of an inverse seesaw ISS
$(2,3)$. ISS $(2,3)$ is obtained by adding two right handed neutrinos and three
gauge singlets sterile fermions to the standard model leading to an extra
sterile state in the keV range. The model is more predictive because of the
presence of fewer numbers of right handed neutrinos than the conventional
inverse seesaw. Moreover, texture zeros in the structures of the mass matrices
involved in the model can reduce the free parameters. We extensively study the
effect of different textures of Dirac mass matrix on sterile neutrino dark
matter phenomenology. Our study also includes the implications of these texture
zero mass matrices on low energy phenomena like neutrinoless double beta decay
(0$\nu\beta\beta$). The zero textures highly constrain the parameter space of
the model. Based on the allowed cosmological ranges of the relic abundance,
decay rates, and dark matter mixing with the active neutrinos, we study the
viability of the different textures within the framework.


Abstract:
  Proteins typically undergo conformational dynamics on the microsecond to
millisecond timescale as they perform their function, which is much faster than
the time-resolution of cryo-electron microscopy and has thus prevented
real-time observations. Here, we propose a novel approach for microsecond
time-resolved cryo-electron microscopy that involves rapidly melting a cryo
specimen in situ with a laser beam. The sample remains liquid for the duration
of the laser pulse, offering a tunable time window in which the dynamics of
embedded particles can be induced in their native liquid environment. After the
laser pulse, the sample vitrifies in just a few microseconds, trapping
particles in their transient configurations, so that they can subsequently be
characterized with conventional cryo-electron microscopy. We demonstrate that
our melting and revitrification approach is viable and affords microsecond time
resolution. As a proof of principle, we study the disassembly of particles
after they incur structural damage and trap them in partially unraveled
configurations.


Abstract:
  Independent deeply learned matrix analysis (IDLMA) is one of the
state-of-the-art supervised multichannel audio source separation methods. It
blindly estimates the demixing filters on the basis of source independence,
using the source model estimated by the deep neural network (DNN). However,
since the ratios of the source to interferer signals vary widely among
time-frequency (TF) slots, it is difficult to obtain reliable estimated power
spectrograms of sources at all TF slots. In this paper, we propose an IDLMA
extension, empirical Bayesian IDLMA (EB-IDLMA), by introducing a prior
distribution of source power spectrograms and treating the source power
spectrograms as latent random variables. This treatment allows us to implicitly
consider the reliability of the estimated source power spectrograms for the
estimation of demixing filters through the hyperparameters of the prior
distribution estimated by the DNN. Experimental evaluations show the
effectiveness of EB-IDLMA and the importance of introducing the reliability of
the estimated source power spectrograms.


Abstract:
  We provide a formal definition for a class of algorithms known as "particle
methods". Particle methods are used in scientific computing. They include
popular simulation methods, such as Discrete Element Methods (DEM), Molecular
Dynamics (MD), Particle Strength Exchange (PSE), and Smoothed Particle
Hydrodynamics (SPH), but also particle-based image processing methods,
point-based computer graphics, and computational optimization algorithms using
point samples. All of these rest on a common concept, which we here formally
define. The presented definition of particle methods makes it possible to
distinguish what formally constitutes a particle method, and what not. It also
enables us to define different sub-classes of particle methods that differ with
respect to their computational complexity and power. Our definition is purely
formal, independent of any application. After stating the definition, we
therefore illustrate how several well-known particle methods can be formalized
in our framework, and we show how the formal definition can be used to
formulate novel particle methods for non-canonical problems.


Abstract:
  This paper presents a novel Generative Neural Network Architecture for
modelling the inverse function of an Artificial Neural Network (ANN) either
completely or partially. Modelling the complete inverse function of an ANN
involves generating the values of all features that corresponds to a desired
output. On the other hand, partially modelling the inverse function means
generating the values of a subset of features and fixing the remaining feature
values. The feature set generation is a critical step for artificial neural
networks, useful in several practical applications in engineering and science.
The proposed Oracle Guided Generative Neural Network, dubbed as OGGN, is
flexible to handle a variety of feature generation problems. In general, an ANN
is able to predict the target values based on given feature vectors. The OGGN
architecture enables to generate feature vectors given the predetermined target
values of an ANN. When generated feature vectors are fed to the forward ANN,
the target value predicted by ANN will be close to the predetermined target
values. Therefore, the OGGN architecture is able to map, inverse function of
the function represented by forward ANN. Besides, there is another important
contribution of this work. This paper also introduces a new class of functions,
defined as constraint functions. The constraint functions enable a neural
network to investigate a given local space for a longer period of time. Thus,
enabling to find a local optimum of the loss function apart from just being
able to find the global optimum. OGGN can also be adapted to solve a system of
polynomial equations in many variables. The experiments on synthetic datasets
validate the effectiveness of OGGN on various use cases.


Abstract:
  While artificial intelligence has been applied to control players' decisions
in board games for over half a century, little attention is given to games with
no player competition. Pandemic is an exemplar collaborative board game where
all players coordinate to overcome challenges posed by events occurring during
the game's progression. This paper proposes an artificial agent which controls
all players' actions and balances chances of winning versus risk of losing in
this highly stochastic environment. The agent applies a Rolling Horizon
Evolutionary Algorithm on an abstraction of the game-state that lowers the
branching factor and simulates the game's stochasticity. Results show that the
proposed algorithm can find winning strategies more consistently in different
games of varying difficulty. The impact of a number of state evaluation metrics
is explored, balancing between optimistic strategies that favor winning and
pessimistic strategies that guard against losing.


Abstract:
  We present the first statistical analysis of kinematically-resolved,
spatially-extended Ly$\alpha$ emission around $z = 2-3$ galaxies in the Keck
Baryonic Structure Survey (KBSS) using the Keck Cosmic Web Imager (KCWI). Our
sample of 59 star-forming galaxies ($z_\mathrm{med} = 2.29$) comprises the
subset with typical KCWI integration times of ~5 hours and with existing
imaging data from the Hubble Space Telescope and/or adaptive optics-assisted
integral field spectroscopy. The high resolution images were used to evaluate
the azimuthal dependence of the diffuse Ly$\alpha$ emission with respect to the
stellar continuum within projected galactocentric distances of $\lesssim 30$
proper kpc. We introduce cylindrically-projected 2D spectra (CP2D) that map the
averaged Ly$\alpha$ spectral profile over a specified range of azimuthal angle,
as a function of impact parameter around galaxies. The averaged CP2D spectrum
of all galaxies shows clear signatures of Ly$\alpha$ resonant scattering by
outflowing gas. We stacked the CP2D spectra of individual galaxies over ranges
of azimuthal angle with respect to their major axes. The extended Ly$\alpha$
emission along the galaxy principal axes are statistically indistinguishable,
with residual asymmetry of $\le$ 2% ($\sim 2 \sigma$) of the integrated
Ly$\alpha$ emission. The symmetry implies that the Ly$\alpha$ scattering medium
is dominated by outflows in all directions within 30 kpc. Meanwhile, we find
that the blueshifted component of Ly$\alpha$ emission is marginally stronger
along galaxy minor axes for galaxies with relatively weak Ly$\alpha$ emission.
We speculate that this weak directional dependence of Ly$\alpha$ emission
becomes discernible only when the Ly$\alpha$ escape fraction is low. These
discoveries highlight the need for similar analyses in simulations with
Ly$\alpha$ radiative transfer modeling.


Abstract:
  Black holes in general relativity are commonly believed to evolve towards a
Schwarzschild state as they gradually lose angular momentum and electrical
charge under Hawking evaporation. However, when Kim and Wen applied quantum
information theory to Hawking evaporation and argued that Hawking particles
with maximum mutual information could dominate the emission process, they found
that charged black holes tend towards extremality. In view of some evidence
pointing towards extremal black holes being effectively singular, this would
violate the cosmic censorship conjecture. In this work, we clarified the
difference between the two models -- they pertain to two different regimes. By
taking into account the discreteness of the charge-to-mass ratio of finite
species of charged particles, we also obtained a clearer picture of the end
state of Hawking evaporation. We found that in agreement with the weak gravity
conjecture, if there is no particle with charge-to-mass ratio q/m>1, stable
remnant states are formed, though they are non-extremal. Furthermore, and more
surprisingly, we show that extremality can be reached if there exists a
particle with q/m<1, even in the presence of other particles with q/m>1. This
may explain why there is no charged particle with q/m<1 in the Standard Model
of particle physics. Cosmic censorship could thus play a bigger role in
fundamental physics than previously thought.


Abstract:
  We introduce the active audio-visual source separation problem, where an
agent must move intelligently in order to better isolate the sounds coming from
an object of interest in its environment. The agent hears multiple audio
sources simultaneously (e.g., a person speaking down the hall in a noisy
household) and it must use its eyes and ears to automatically separate out the
sounds originating from a target object within a limited time budget. Towards
this goal, we introduce a reinforcement learning approach that trains movement
policies controlling the agent's camera and microphone placement over time,
guided by the improvement in predicted audio separation quality. We demonstrate
our approach in scenarios motivated by both augmented reality (system is
already co-located with the target object) and mobile robotics (agent begins
arbitrarily far from the target object). Using state-of-the-art realistic
audio-visual simulations in 3D environments, we demonstrate our model's ability
to find minimal movement sequences with maximal payoff for audio source
separation. Project: http://vision.cs.utexas.edu/projects/move2hear.


Abstract:
  Deep learning based face recognition has achieved significant progress in
recent years. Yet, the practical model production and further research of deep
face recognition are in great need of corresponding public support. For
example, the production of face representation network desires a modular
training scheme to consider the proper choice from various candidates of
state-of-the-art backbone and training supervision subject to the real-world
face recognition demand; for performance analysis and comparison, the standard
and automatic evaluation with a bunch of models on multiple benchmarks will be
a desired tool as well; besides, a public groundwork is welcomed for deploying
the face recognition in the shape of holistic pipeline. Furthermore, there are
some newly-emerged challenges, such as the masked face recognition caused by
the recent world-wide COVID-19 pandemic, which draws increasing attention in
practical applications. A feasible and elegant solution is to build an
easy-to-use unified framework to meet the above demands. To this end, we
introduce a novel open-source framework, named FaceX-Zoo, which is oriented to
the research-development community of face recognition. Resorting to the highly
modular and scalable design, FaceX-Zoo provides a training module with various
supervisory heads and backbones towards state-of-the-art face recognition, as
well as a standardized evaluation module which enables to evaluate the models
in most of the popular benchmarks just by editing a simple configuration. Also,
a simple yet fully functional face SDK is provided for the validation and
primary application of the trained models. Rather than including as many as
possible of the prior techniques, we enable FaceX-Zoo to easily upgrade and
extend along with the development of face related domains. The source code and
models are available at https://github.com/JDAI-CV/FaceX-Zoo.


Abstract:
  A report and examination of a Remote Work experience during the Covid-19
pandemic encompassing a 14-hour time difference from the primary work location.
Advantages and disadvantages of a globally distributed work experience as
compared to an aligned time zone are explored. Logistical aspects of the
arrangement are provided as well as the management support, peer reaction, and
relative productivity. Recommendations are also provided on how to improve
future geographically diverse team arrangements.
  [Keywords: Global Software Development, Offshore Development, Software
Engineering, IT Management, Remote Work, Remote Office Design, Distributed
Communications, Collaboration Technology, Team Management, Research,
Development, Productivity]


Abstract:
  The effect of protoplanetary differentiation on the fate of life essential
volatiles like nitrogen and carbon and its subsequent effect on the dynamics of
planetary growth is unknown. Because the dissolution of nitrogen in magma
oceans depends on its partial pressure and oxygen fugacity, it is an ideal
proxy to track volatile redistribution in protoplanets as a function of their
sizes and growth zones. Using high pressure and high temperature experiments in
graphite undersaturated conditions, here we show that the iron loving character
of nitrogen is an order of magnitude higher than previous estimates across a
wide range of oxygen fugacity. The experimental data combined with metal,
silicate and atmosphere fractionation models suggest that asteroid sized
protoplanets, and planetary embryos that grew from them, were nitrogen
depleted. However, protoplanets that grew to planetary embryo size before
undergoing differentiation had nitrogen rich cores and nitrogen poor silicate
reservoirs. Bulk silicate reservoirs of large Earth like planets attained
nitrogen from the cores of latter type of planetary embryos. Therefore, to
satisfy the volatile budgets of Earth like planets during the main stage of
their growth, the timescales of planetary embryo accretion had to be shorter
than their differentiation timescales, that is, Moon to Mars sized planetary
embryos grew rapidly within 1 to 2 million years of the Solar System formation.


Abstract:
  Intelligent reflecting/refracting surface (IRS) has recently emerged as a
promising solution to reconfigure wireless propagation environment for
enhancing the communication performance. In this paper, we study a new
IRS-aided high-mobility communication system by employing the intelligent
refracting surface with a high-speed vehicle to aid its passenger's
communication with a remote base station (BS). Due to the environment's random
scattering and vehicle's high mobility, a rapidly time-varying channel is
typically resulted between the static BS and fast-moving IRS/user, which
renders the channel estimation for IRS with a large number of elements more
challenging. In order to reap the high IRS passive beamforming gain with low
channel training overhead, we propose a new and efficient transmission protocol
to achieve both IRS channel estimation and refraction optimization for data
transmission. Specifically, by exploiting the quasi-static channel between the
IRS and user both moving at the same high speed as well as the line-of-sight
(LoS) dominant channel between the BS and IRS, the user first estimates the LoS
component of the cascaded BS-IRS-user channel, based on which IRS passive
refraction is designed to maximize the corresponding IRS-refracted channel
gain. Then, the user estimates the resultant IRS-refracted channel as well as
the non-IRS-refracted channel for setting an additional common phase shift at
all IRS refracting elements so as to align these two channels for maximizing
the overall channel gain for data transmission. Simulation results show
significant performance improvement of the proposed design as compared to
various benchmark schemes. The proposed on-vehicle IRS system is further
compared with a baseline scheme of deploying fixed intelligent reflecting
surfaces on the roadside to assist high-speed vehicular communications, which
achieves significant rate improvement.


Abstract:
  Home automation Internet of Things (IoT) systems have recently become a
target for several types of attacks. In this paper, we present an
authentication and key agreement protocol for a home automation network based
on the ZigBee standard, which connects together a central controller and
several end devices. Our scheme performs mutual authentication between end
devices and the controller, which is followed by device-to-device
communication. The scheme achieves confidentiality, message integrity,
anonymity, unlinkability, forward and backward secrecy, and availability. Our
scheme uses only simple hash and XOR computations and symmetric key encryption,
and hence is resource-efficient. We show using a detailed security analysis and
numerical results that our proposed scheme provides better security and
anonymity, and is more efficient in terms of computation time, communication
cost, and storage cost than schemes proposed in prior works.


Abstract:
  The characteristic microstructure of Sm(Co,Fe,Cu,Zr)$_z$ alloys with SmCo$_5$
cell walls in Sm$_2$Co$_{17}$ cells, all intersected by Zr-rich platelets,
makes them some of the best performing high-temperature permanent magnets.
Plentiful research has been performed to tailor the microstructure at the
nanoscale, but due to its complexity many questions remain unanswered about the
effect of the individual phases on the magnetic performance at different
temperatures. Here, we explore this mechanism effect for three different
Sm(Co,Fe,Cu,Zr)$_z$ alloys by deploying high-resolution magnetic imaging via
in-situ transmission electron microscopy and three-dimensional chemical
analysis using atom probe tomography. We show that their microstructures differ
in terms of SmCo$_5$ cell-wall and Z-phase size and density, as well as the Cu
concentration in the cell walls, and demonstrate how these features influence
the magnetic domain size and density and thus form different magnetic textures.
Moreover, we illustrate that the dominant coercivity mechanism at room
temperature is domain-wall pinning and show that magnets with a denser
cell-wall network, a steeper Cu gradient across the cell-wall boundary, and
thinner Z-phase platelets have a higher coercivity. We also show that the
coercivity mechanism at high temperatures is domain-wall nucleation at the cell
walls. Increasing the Cu concentration inside the cell walls decreases the
transition temperature between pinning and nucleation, significantly decreasing
the coercivity with increasing temperature. We therefore provide a detailed
explanation of how the microstructure on the atomic to nanoscale directly
affects the magnetic performance and provide detailed guidelines for an
improved design of Sm(Co,Fe,Cu,Zr)$_z$ magnets.


Abstract:
  The graphene superlattice equation, a modified sine-Gordon equation, governs
the propagation of solitary electromagnetic waves in a graphene superlattice.
This equation has kink solutions without explicit analytical expression,
requiring the use of quadrature methods. The inelastic collision of kinks and
antikinks with the same but opposite speed is studied numerically for the first
time; after their interaction they escape to infinity when its speed is either
larger than a critical value or it is inside a series of resonance windows;
otherwise, they form a breather-like state that slowly decays by radiating
energy. Here, the fractal structure of these resonance windows is characterized
by using a multi-index notation and their main features are compared with the
predictions of the resonant energy exchange theory showing good agreement. Our
results can be interpreted as new evidence in favour of this theory.


Abstract:
  Quantum technology has made tremendous strides over the past two decades with
remarkable advances in materials engineering, circuit design and dynamic
operation. In particular, the integration of different quantum modules has
benefited from hybrid quantum systems, which provide an important pathway for
harnessing the different natural advantages of complementary quantum systems
and for engineering new functionalities. This review focuses on the current
frontiers with respect to utilizing magnetic excitatons or magnons for novel
quantum functionality. Magnons are the fundamental excitations of magnetically
ordered solid-state materials and provide great tunability and flexibility for
interacting with various quantum modules for integration in diverse quantum
systems. The concomitant rich variety of physics and material selections enable
exploration of novel quantum phenomena in materials science and engineering. In
addition, the relative ease of generating strong coupling and forming hybrid
dynamic systems with other excitations makes hybrid magnonics a unique platform
for quantum engineering. We start our discussion with circuit-based hybrid
magnonic systems, which are coupled with microwave photons and acoustic
phonons. Subsequently, we are focusing on the recent progress of magnon-magnon
coupling within confined magnetic systems. Next we highlight new opportunities
for understanding the interactions between magnons and nitrogen-vacancy centers
for quantum sensing and implementing quantum interconnects. Lastly, we focus on
the spin excitations and magnon spectra of novel quantum materials investigated
with advanced optical characterization.


Abstract:
  We perform micro-rheological experiments with a colloidal bead driven through
a viscoelastic worm-like micellar fluid and observe two distinctive shear
thinning regimes, each of them displaying a Newtonian-like plateau. The shear
thinning behavior at larger velocities is in qualitative agreement with
macroscopic rheological experiments. The second process, observed at
Weissenberg numbers as small as a few percent, appears to have no analog in
macro rheological findings. A simple model introduced earlier captures the
observed behavior, and implies that the two shear thinning processes correspond
to two different length scales in the fluid. This model also reproduces
oscillations which have been observed in this system previously. While the
system under macro-shear seems to be near equilibrium for shear rates in the
regime of the intermediate Newtonian-like plateau, the one under micro-shear is
thus still far from it. The analysis suggests the existence of a length scale
of a few micrometres, the nature of which remains elusive.


Abstract:
  We present some transversality results for a category of Fr\'{e}chet
manifolds, the so-called $MC^k$-Fr\'{e}chet manifolds. In this context, we
apply the obtained transversality results to construct the degree of nonlinear
Fredholm mappings by virtue of which we prove a rank theorem, an invariance of
domain theorem and a Bursuk-Ulam type theorem.


Abstract:
  In this paper we present a novel class of convolutional codes and investigate
its use in a variant of the McEliece cryptosystem that possesses several
interesting properties, including a reduction of the public key for a given
security level. In contrast to the classical McEliece cryptosystems, where
block codes are used, we propose the use of a convolutional encoder to be part
of the public key. The secret key is constituted by a Generalized Reed-Solomon
encoder and two Laurent polynomial matrices that contain large parts that are
generated completely at random. Instead of multiplying on the right the GRS
encoder by a permutation matrix, it is multiplied by a polynomial matrix with
columns having weight zero or at least two. In this setting the message is a
sequence of messages instead of a single block message and the errors are added
randomly throughout the sequence. We conclude the paper studying its security
and presenting several examples.


Abstract:
  This paper investigates the problem of computing the equilibrium of
competitive games, which is often modeled as a constrained saddle-point
optimization problem with probability simplex constraints. Despite recent
efforts in understanding the last-iterate convergence of extragradient methods
in the unconstrained setting, the theoretical underpinnings of these methods in
the constrained settings, especially those using multiplicative updates, remain
highly inadequate, even when the objective function is bilinear. Motivated by
the algorithmic role of entropy regularization in single-agent reinforcement
learning and game theory, we develop provably efficient extragradient methods
to find the quantal response equilibrium (QRE) -- which are solutions to
zero-sum two-player matrix games with entropy regularization -- at a linear
rate. The proposed algorithms can be implemented in a decentralized manner,
where each player executes symmetric and multiplicative updates iteratively
using its own payoff without observing the opponent's actions directly. In
addition, by controlling the knob of entropy regularization, the proposed
algorithms can locate an approximate Nash equilibrium of the unregularized
matrix game at a sublinear rate without assuming the Nash equilibrium to be
unique. Our methods also lead to efficient policy extragradient algorithms for
solving (entropy-regularized) zero-sum Markov games at similar rates. All of
our convergence rates are nearly dimension-free, which are independent of the
size of the state and action spaces up to logarithm factors, highlighting the
positive role of entropy regularization for accelerating convergence.


Abstract:
  SARAS is an ongoing experiment aiming to detect the redshifted global 21-cm
signal expected from Cosmic Dawn (CD) and the Epoch of Reionization (EoR).
Standard cosmological models predict the signal to be present in the redshift
range $z \sim $6--35, corresponding to a frequency range 40--200~MHz, as a
spectral distortion of amplitude 20--200~mK in the 3~K cosmic microwave
background. Since the signal might span multiple octaves in frequency, and this
frequency range is dominated by strong terrestrial Radio Frequency Interference
(RFI) and astrophysical foregrounds of Galactic and Extragalactic origin that
are several orders of magnitude greater in brightness temperature, design of a
radiometer for measurement of this faint signal is a challenging task. It is
critical that the instrumental systematics do not result in additive or
multiplicative confusing spectral structures in the measured sky spectrum and
thus preclude detection of the weak 21-cm signal. Here we present the system
design of the SARAS~3 version of the receiver. New features in the evolved
design include Dicke switching, double differencing and optical isolation for
improved accuracy in calibration and rejection of additive and multiplicative
systematics. We derive and present the measurement equations for the SARAS~3
receiver configuration and calibration scheme, and provide results of
laboratory tests performed using various precision terminations that qualify
the performance of the radiometer receiver for the science goal.


Abstract:
  In 1989, Burnett conjectured that, under appropriate assumptions, the limit
of highly oscillatory solutions to the Einstein vacuum equations is a solution
of the Einstein--massless Vlasov system. In a recent breakthrough, Huneau--Luk
(arXiv:1907.10743) gave a proof of the conjecture in U(1)-symmetry and elliptic
gauge. They also require control on up to fourth order derivatives of the
metric components. In this paper, we give a streamlined proof of a stronger
result and, in the spirit of Burnett's original conjecture, we remove the need
for control on higher derivatives. Our methods also apply to general wave map
equations.


Abstract:
  People are often reluctant to sell a house, or shares of stock, below the
price at which they originally bought it. While this is generally not
consistent with rational utility maximization, it does reflect two strong
empirical regularities that are central to the behavioral science of human
decision-making: a tendency to evaluate outcomes relative to a reference point
determined by context (in this case the original purchase price), and the
phenomenon of loss aversion in which people are particularly prone to avoid
outcomes below the reference point. Here we explore the implications of
reference points and loss aversion in optimal stopping problems, where people
evaluate a sequence of options in one pass, either accepting the option and
stopping the search or giving up on the option forever. The best option seen so
far sets a reference point that shifts as the search progresses, and a biased
decision-maker's utility incurs an additional penalty when they accept a later
option that is below this reference point.
  We formulate and study a behaviorally well-motivated version of the optimal
stopping problem that incorporates these notions of reference dependence and
loss aversion. We obtain tight bounds on the performance of a biased agent in
this model relative to the best option obtainable in retrospect (a type of
prophet inequality for biased agents), as well as tight bounds on the ratio
between the performance of a biased agent and the performance of a rational
one. We further establish basic monotonicity results, and show an exponential
gap between the performance of a biased agent in a stopping problem with
respect to a worst-case versus a random order. As part of this, we establish
fundamental differences between optimal stopping problems for rational versus
biased agents, and these differences inform our analysis.


Abstract:
  With the advent of Artificial Intelligence (AI)-empowered communications,
industry, academia, and standardization organizations are progressing on the
definition of mechanisms and procedures to address the increasing complexity of
future 5G and beyond communications. In this context, the International
Telecommunication Union (ITU) organized the first AI for 5G Challenge to bring
industry and academia together to introduce and solve representative problems
related to the application of Machine Learning (ML) to networks. In this paper,
we present the results gathered from Problem Statement~13 (PS-013), organized
by Universitat Pompeu Fabra (UPF), which primary goal was predicting the
performance of next-generation Wireless Local Area Networks (WLANs) applying
Channel Bonding (CB) techniques. In particular, we overview the ML models
proposed by participants (including Artificial Neural Networks, Graph Neural
Networks, Random Forest regression, and gradient boosting) and analyze their
performance on an open dataset generated using the IEEE 802.11ax-oriented
Komondor network simulator. The accuracy achieved by the proposed methods
demonstrates the suitability of ML for predicting the performance of WLANs.
Moreover, we discuss the importance of abstracting WLAN interactions to achieve
better results, and we argue that there is certainly room for improvement in
throughput prediction through ML.


Abstract:
  We present a conjectual hook formula concerning the number of the standard
tableaux on "cylindric" skew diagrams. Our formula can be seen as an extension
of Naruse's hook formula for skew diagrams. Moreover, we prove our conjecture
in some special cases.


Abstract:
  We consider the problem of teaching via demonstrations in sequential
decision-making settings. In particular, we study how to design a personalized
curriculum over demonstrations to speed up the learner's convergence. We
provide a unified curriculum strategy for two popular learner models: Maximum
Causal Entropy Inverse Reinforcement Learning (MaxEnt-IRL) and Cross-Entropy
Behavioral Cloning (CrossEnt-BC). Our unified strategy induces a ranking over
demonstrations based on a notion of difficulty scores computed w.r.t. the
teacher's optimal policy and the learner's current policy. Compared to the
state of the art, our strategy doesn't require access to the learner's internal
dynamics and still enjoys similar convergence guarantees under mild technical
conditions. Furthermore, we adapt our curriculum strategy to the setting where
no teacher agent is present using task-specific difficulty scores. Experiments
on a synthetic car driving environment and navigation-based environments
demonstrate the effectiveness of our curriculum strategy.


Abstract:
  A detailed study of the morphology of lenticular galaxies is an important way
to understand how this type of galaxy formed and evolves over time. Decomposing
a galaxy into its components (disc, bulge, bar, ...) allows recovering the
colour gradients present in each system, its star formation history, and its
assembly history. We use GALFITM to perform a multi-wavelength structural
decomposition of the closest lenticular galaxy, NGC 3115, resulting in the
description of its stellar light into several main components: a bulge, a thin
disc, a thick disc and also evidence of a bar. We report the finding of central
bluer stellar populations in the bulge, as compared to the colour of the galaxy
outskirts, indicating either the presence of an Active Galactic Nucleus (AGN)
and/or recent star formation activity. From the spectral energy distribution
results, we show that the galaxy has a low luminosity AGN component, but even
excluding the effect of the nuclear activity, the bulge is still bluer than the
outer-regions of the galaxy, revealing a recent episode of star formation.
Based on all of the derived properties, we propose a scenario for the formation
of NGC 3115 consisting of an initial gas-rich merger, followed by accretions
and feedback that quench the galaxy, until a recent encounter with the
companion KK084 that reignited the star formation in the bulge, provoked a core
displacement in NGC 3115 and generated spiral-like features. This result is
consistent with the two-phase formation scenario, proposed in previous studies
of this galaxy.


Abstract:
  In 2001, Leo Breiman wrote of a divide between "data modeling" and
"algorithmic modeling" cultures. Twenty years later this division feels far
more ephemeral, both in terms of assigning individuals to camps, and in terms
of intellectual boundaries. We argue that this is largely due to the "data
modelers" incorporating algorithmic methods into their toolbox, particularly
driven by recent developments in the statistical understanding of Breiman's own
Random Forest methods. While this can be simplistically described as "Breiman
won", these same developments also expose the limitations of the
prediction-first philosophy that he espoused, making careful statistical
analysis all the more important. This paper outlines these exciting recent
developments in the random forest literature which, in our view, occurred as a
result of a necessary blending of the two ways of thinking Breiman originally
described. We also ask what areas statistics and statisticians might currently
overlook.


Abstract:
  Let $\varphi:\Sigma_1\longrightarrow \mathbb{P}^2$ be a blow up at a point on
$\mathbb{P}^2$. Let $C$ be the proper transform of a smooth plane curve of
degree $d\geq 4$ by $\varphi$, and let $P$ be a point on $C$. Let
$\pi:\tilde{C}\longrightarrow C$ be a double covering branched along the
reduced divisor on $C$ obtained as the intersection of $C$ and a reduced
divisor in $|-2K_{\Sigma_1}|$ containing $P$. In this paper, we investigate the
Weierstrass semigroup $H(\tilde{P})$ at the ramification point $\tilde{P}$ of
$\pi$ over $P$, in the case where the intersection multiplicity at $\varphi(P)$
of $\varphi(C)$ and the tangent line at $\varphi(P)$ of $\varphi(C)$ is $d-1$.


Abstract:
  The origin and nature of ultra-high-energy cosmic rays (UHECRs) remain an
open question in astroparticle physics. Motivated by the need for an
unprecedented aperture for further advancements, the Fluorescence detector
Array of Single-pixel Telescopes (FAST) is a prospective next-generation,
ground-based UHECR observatory that aims to cover a huge area by deploying a
large array of low-cost fluorescence detectors. The full-scale FAST prototype
consists of four 20 cm photomultiplier tubes at the focus of a segmented mirror
1.6 m in diameter. Over the last five years, three prototypes have been
installed at the Telescope Array Experiment in Utah, USA, and one prototype at
the Pierre Auger Observatory in Mendoza, Argentina, commencing remote
observation of UHECRs in both hemispheres. We report on the latest results of
these FAST prototypes, including telescope calibrations, atmospheric
monitoring, ongoing electronics upgrades, development of sophisticated
reconstruction methods, and UHECR detections.


Abstract:
  We present EgoACO, a deep neural architecture for video action recognition
that learns to pool action-context-object descriptors from frame level features
by leveraging the verb-noun structure of action labels in egocentric video
datasets. The core component of EgoACO is class activation pooling (CAP), a
differentiable pooling operation that combines ideas from bilinear pooling for
fine-grained recognition and from feature learning for discriminative
localization. CAP uses self-attention with a dictionary of learnable weights to
pool from the most relevant feature regions. Through CAP, EgoACO learns to
decode object and scene context descriptors from video frame features. For
temporal modeling in EgoACO, we design a recurrent version of class activation
pooling termed Long Short-Term Attention (LSTA). LSTA extends convolutional
gated LSTM with built-in spatial attention and a re-designed output gate.
Action, object and context descriptors are fused by a multi-head prediction
that accounts for the inter-dependencies between noun-verb-action structured
labels in egocentric video datasets. EgoACO features built-in visual
explanations, helping learning and interpretation. Results on the two largest
egocentric action recognition datasets currently available, EPIC-KITCHENS and
EGTEA, show that by explicitly decoding action-context-object descriptors,
EgoACO achieves state-of-the-art recognition performance.


Abstract:
  The Euclid satellite, to be launched by ESA in 2022, will be a major
instrument for cosmology for the next decades. \Euclid\ is composed of two
instruments: the Visible (VIS) instrument and the Near Infrared Spectromete and
Photometer (NISP). In this work we estimate the implications of correlated
readout noise in the NISP detectors for the final in-flight flux measurements.
Considering the multiple accumulated (MACC) readout mode, for which the UTR (Up
The Ramp) exposure frames are averaged in groups, we derive an analytical
expression for the noise covariance matrix between groups in the presence of
correlated noise. We also characterize the correlated readout noise properties
in the NISP engineering grade detectors using long dark integrations. For this
purpose, we assume a $(1/f)^{\, \alpha}$-like noise model and fit the model
parameters to the data, obtaining typical values of $\sigma =
19.7^{+1.1}_{-0.8}$ e$^{-} \rm{Hz}^{-0.5}$, $f_{\rm{knee}} =
(5.2^{+1.8}_{-1.3}) \times 10^{-3} \, \rm{Hz}$ and $\alpha = 1.24
^{+0.26}_{-0.21}$. Furthermore, via realistic simulations and using a maximum
likelihood flux estimator we derive the bias between the input flux and the
recovered one. We find that using our analytical expression for the covariance
matrix of the correlated readout noise we diminish this bias by up to a factor
of four with respect to the white noise approximation for the covariance
matrix. Finally, we conclude that the final bias on the in-flight NISP flux
measurements should still be negligible even in the white noise approximation,
which is taken as a baseline for the Euclid\on-board processing


Abstract:
  Based on the quantum master equation approach, the nonlinear electric
conductivity of graphene is investigated under static electric fields for
various chemical potential shifts. The simulation results show that, as the
field strength increases, the effective conductivity is firstly suppressed,
reflecting the depletion of effective carriers due to the large displacement in
the Brillouin zone caused by the strong field. Then, as the field strength
exceeds $1$~MV/m, the effective conductivity increases, overcoming the carrier
depletion via the Landau--Zener tunneling process. Based on the nonlinear
behavior of the conductivity, the charge transport induced by few-cycle THz
pulses is studied to elucidate the ultrafast control of electric current in
matter.


Abstract:
  In the early 1990's, Billera and Sturmfels introduced the monotone path
polytope (MPP), a special case of the general theory of fiber polytopes that
associates a polytope to a pair $(P,\varphi)$ of a polytope $P$ and linear
functional $\varphi$. In that same paper, they showed that MPPs of simplices
and hyper-cubes are combinatorial cubes and permutahedra respectively. Their
work has lead to many developments in combinatorics. Here we investigate the
monotone paths for generic orientations of cross-polytopes. We show the face
lattice of its MPP is isomorphic to the lattice of intervals in the sign poset
from oriented matroid theory. We look at its $f$-vector, its realizations, and
facets.


Abstract:
  Liquid metal electrodes are one of the key components of different electrical
energy storage technologies. The understanding of transport phenomena in liquid
electrodes is mandatory in order to ensure efficient operation. In the present
study we focus our attention on the positive electrode of the Li||Bi liquid
metal battery. Starting from a real experimental setup, we numerically
investigate the charge transfer in a molten salt electrolyte and the mass
transport in the positive electrode. The two phenomena are tightly coupled,
because the current distribution influences the concentration field in the
positive electrode. The cell is studied during charging when compositional
convection becomes apparent. First results of compositional convection from a
non-uniform current distribution are presented, highlighting its capability to
affect the flow in the positive electrode and the cell performance.


Abstract:
  The data transfer capacity of a communication channel is limited by the
Shannon-Hartley theorem and scales as $\text{log}_2(1 + \text{SNR})$ for a
single channel with the power signal-to-noise ratio (SNR). We implement an
array of atom-optical receivers in a single-input-multi-output (SIMO)
configuration by using spatially distributed probe light beams. The data
capacity of the distributed receiver configuration is observed to scale as
$\text{log}_2(1 + N\times\text{SNR})$ for an array consisting of $N$ receivers.
Our result is independent on the modulation frequency, and we show that such
enhancement of the bandwidth cannot be obtained by a single receiver with a
similar level of combined optical power. We investigate both theoretically and
experimentally the origins of the single channel capacity limit for our
implementation.


Abstract:
  Several large-scale machine learning tasks, such as data summarization, can
be approached by maximizing functions that satisfy submodularity. These
optimization problems often involve complex side constraints, imposed by the
underlying application. In this paper, we develop an algorithm with
poly-logarithmic adaptivity for non-monotone submodular maximization under
general side constraints. The adaptive complexity of a problem is the minimal
number of sequential rounds required to achieve the objective.
  Our algorithm is suitable to maximize a non-monotone submodular function
under a $p$-system side constraint, and it achieves a $(p +
O(\sqrt{p}))$-approximation for this problem, after only poly-logarithmic
adaptive rounds and polynomial queries to the valuation oracle function.
Furthermore, our algorithm achieves a $(p + O(1))$-approximation when the given
side constraint is a $p$-extendible system.
  This algorithm yields an exponential speed-up, with respect to the
adaptivity, over any other known constant-factor approximation algorithm for
this problem. It also competes with previous known results in terms of the
query complexity. We perform various experiments on various real-world
applications. We find that, in comparison with commonly used heuristics, our
algorithm performs better on these instances.


Abstract:
  The effect on dynamo action of an anisotropic electrical conductivity
conjugated to an anisotropic magnetic permeability is considered. Not only is
the dynamo fully axisymmetric, but it requires only a simple differential
rotation, which twice challenges the well-established dynamo theory. Stability
analysis is conducted entirely analytically, leading to an explicit expression
of the dynamo threshold. The results show a competition between the anisotropy
of electrical conductivity and that of magnetic permeability, the dynamo effect
becoming impossible if the two anisotropies are identical. For isotropic
electrical conductivity, Cowling's neutral point argument does imply the
absence of an azimuthal component of current density, but does not prevent the
dynamo effect as long as the magnetic permeability is anisotropic.


Abstract:
  Adaptive Moment Estimation (ADAM) is a very popular training algorithm for
deep neural networks and belongs to the family of adaptive gradient descent
optimizers. However to the best of the authors knowledge no complete
convergence analysis exists for ADAM. The contribution of this paper is a
method for the local convergence analysis in batch mode for a deterministic
fixed training set, which gives necessary conditions for the hyperparameters of
the ADAM algorithm. Due to the local nature of the arguments the objective
function can be non-convex but must be at least twice continuously
differentiable. Then we apply this procedure to other adaptive gradient descent
algorithms and show for most of them local convergence with hyperparameter
bounds.


Abstract:
  Plasmons in two-dimensional (2D) materials beyond graphene have recently
gained much attention. However, the experimental investigation is limited due
to the lack of suitable materials. Here, we experimentally demonstrate
localized plasmons in a correlated 2D charge-density-wave (CDW) material:
2H-TaSe2. The plasmon resonance can cover a broad spectral range from the
terahertz (40 {\mu}m) to the telecom (1.55 {\mu}m) region, which is further
tunable by changing thickness and dielectric environments. The plasmon
dispersion flattens at large wave vectors, resulted from the universal
screening effect of interband transitions. More interestingly, anomalous
temperature dependence of plasmon resonances associated with CDW excitations is
observed. In the CDW phase, the plasmon peak close to the CDW excitation
frequency becomes wider and asymmetric, mimicking two coupled oscillators. Our
study not only reveals the universal role of the intrinsic screening on 2D
plasmons, but also opens an avenue for tunable plasmons in 2D correlated
materials.


Abstract:
  Boron-doped diamond granular thin films are known to exhibit
superconductivity with an optimal critical temperature of Tc = 7.2K. Here we
report the measured complex surface impedance of Boron-doped diamond films in
the microwave frequency range using a resonant technique. Experimentally
measured inductance values are in good agreement with estimates obtained from
the normal state sheet resistance of the material. The magnetic penetration
depth temperature dependence is consistent with that of a fully-gapped s-wave
superconductor. Boron-doped diamond films should find application where high
kinetic inductance is needed, such as microwave kinetic inductance detectors
and quantum impedance devices.


Abstract:
  Preferential attachment, homophily and, their consequences such as the glass
ceiling effect have been well-studied in the context of undirected networks.
However, the lack of an intuitive, theoretically tractable model of a directed,
bi-populated~(i.e.,~containing two groups) network with variable levels of
preferential attachment, homophily and growth dynamics~(e.g.,~the rate at which
new nodes join, whether the new nodes mostly follow existing nodes or the
existing nodes follow them, etc.) has largely prevented such consequences from
being explored in the context of directed networks, where they more naturally
occur due to the asymmetry of links. To this end, we present a rigorous
theoretical analysis of the \emph{Directed Mixed Preferential Attachment} model
and, use it to analyze the glass ceiling effect in directed networks. More
specifically, we derive the closed-form expressions for the power-law exponents
of the in- and out- degree distributions of each group~(minority and majority)
and, compare them with each other to obtain insights. In particular, our
results yield answers to questions such as: \emph{when does the minority group
have a heavier out-degree (or in-degree) distribution compared to the majority
group? what effect does frequent addition of edges between existing nodes have
on the in- and out- degree distributions of the majority and minority groups?}.
Such insights shed light on the interplay between the structure~(i.e., the in-
and out- degree distributions of the two groups) and dynamics~(characterized
collectively by the homophily, preferential attachment, group sizes and growth
dynamics) of various real-world networks. Finally, we utilize the obtained
analytical results to characterize the conditions under which the glass ceiling
effect emerge in a directed network. Our analytical results are supported by
detailed numerical results.


Abstract:
  A set of quadratic forms is simultaneously diagonalizable via congruence
(SDC) if there exists a basis under which each of the quadratic forms is
diagonal. This property appears naturally when analyzing quadratically
constrained quadratic programs (QCQPs) and has important implications in this
context. This paper extends the reach of the SDC property by studying two new
related but weaker notions of simultaneous diagonalizability. Specifically, we
say that a set of quadratic forms is almost SDC (ASDC) if it is the limit of
SDC sets and d-restricted SDC (d-RSDC) if it is the restriction of an SDC set
in up to d-many additional dimensions. Our main contributions are a complete
characterization of the ASDC pairs and the nonsingular ASDC triples, as well as
a sufficient condition for the 1-RSDC property for pairs of quadratic forms.
Surprisingly, we show that every singular pair is ASDC and that almost every
pair is 1-RSDC.
  We accompany our theoretical results with preliminary numerical experiments
applying the RSDC property to QCQPs with a single quadratic constraint.


Abstract:
  In order to increase the resilience of distribution systems against
high-impact low-probability (HILP) events, it is important to prioritize the
damaged assets so that the lost loads, especially critical and important loads,
can be restored faster. In addition, correctly predicting the number of repair
teams during critical times contributes to restoring the network to the initial
resilience level. For this reason, this paper discusses the prioritization of
electricity supply lines for evaluating the number of required repair teams. To
this end, the economic value of distribution system lines has been considered
as a criterion representing the sensitivity of the network to hurricanes. The
modeling is based on value, in which the load value, failure probability of the
poles, fragility curve, duration of line repair by the maintenance team, and
the topology factor have been considered. This is so that the significance of
the demand side, the failure extent and accessibility of the lines, the
importance of time, and the network configuration are considered. The results
provide a list of line priority for fault resolution, in which the topology
factor has a larger effect. The number of repair teams required to restore
critical and important loads is determined from this model. This modeling has
been tested on an IEEE 33-bus network. Keywords: Resilience, distribution
systems, asset evaluation, restoration prioritization, repair team


Abstract:
  We introduce Z-Sequence, a novel empirical model that utilises photometric
measurements of observed galaxies within a specified search radius to estimate
the photometric redshift of galaxy clusters. Z-Sequence itself is composed of a
machine learning ensemble based on the k-nearest neighbours algorithm. We
implement an automated feature selection strategy that iteratively determines
appropriate combinations of filters and colours to minimise photometric
redshift prediction error. We intend for Z-Sequence to be a standalone
technique but it can be combined with cluster finders that do not intrinsically
predict redshift, such as our own DEEP-CEE. In this proof-of-concept study we
train, fine-tune and test Z-Sequence on publicly available cluster catalogues
derived from the Sloan Digital Sky Survey. We determine the photometric
redshift prediction error of Z-Sequence via the median value of $|\Delta
z|/(1+z)$ (across a photometric redshift range of $0.05 \le \textit{z} \le
0.6$) to be $\sim0.01$ when applying a small search radius. The photometric
redshift prediction error for test samples increases by 30-50 per cent when the
search radius is enlarged, likely due to line-of-sight interloping galaxies.
Eventually, we aim to apply Z-Sequence to upcoming imaging surveys such as the
Legacy Survey of Space and Time to provide photometric redshift estimates for
large samples of as yet undiscovered and distant clusters.


Abstract:
  We give almost-linear-time algorithms for constructing sparsifiers with $n\
poly(\log n)$ edges that approximately preserve weighted $(\ell^{2}_2 +
\ell^{p}_p)$ flow or voltage objectives on graphs. For flow objectives, this is
the first sparsifier construction for such mixed objectives beyond unit
$\ell_p$ weights, and is based on expander decompositions. For voltage
objectives, we give the first sparsifier construction for these objectives,
which we build using graph spanners and leverage score sampling. Together with
the iterative refinement framework of [Adil et al, SODA 2019], and a new
multiplicative-weights based constant-approximation algorithm for
mixed-objective flows or voltages, we show how to find $(1+2^{-\text{poly}(\log
n)})$ approximations for weighted $\ell_p$-norm minimizing flows or voltages in
$p(m^{1+o(1)} + n^{4/3 + o(1)})$ time for $p=\omega(1),$ which is almost-linear
for graphs that are slightly dense ($m \ge n^{4/3 + o(1)}$).


Abstract:
  This paper proposes an approach to Dense Video Captioning (DVC) without
pairwise event-sentence annotation. First, we adopt the knowledge distilled
from relevant and well solved tasks to generate high-quality event proposals.
Then we incorporate contrastive loss and cycle-consistency loss typically
applied to cross-modal retrieval tasks to build semantic matching between the
proposals and sentences, which are eventually used to train the caption
generation module. In addition, the parameters of matching module are
initialized via pre-training based on annotated images to improve the matching
performance. Extensive experiments on ActivityNet-Caption dataset reveal the
significance of distillation-based event proposal generation and cross-modal
retrieval-based semantic matching to weakly supervised DVC, and demonstrate the
superiority of our method to existing state-of-the-art methods.


Abstract:
  We investigate Kapitsa pendulum-like effects in the magnetic moment dynamics
of a nanomagnet coupled to a Josephson junction under external periodic drive.
Generated by the Josephson junction and external drive, the magnetic field
plays the role of the oscillating force of the suspension point in the Kapitsa
pendulum. The high frequency oscillations change the orientation of magnetic
moment. The magnetic field of the quasiparticle current of the Josephson
junction determines the frequency dependence of the magnetic moment's
orientation. We obtain simple analytical formulas for the stable position of
magnetic moment, both under the external periodic drive and without it. The
influence of external periodic drive on the voltage of complete reorientation
have been demonstrated.


Abstract:
  Trans-Neptunian Objects (TNOs) in the scattered disk with 50 < a < 100 au are
thought to cluster near Neptune's n:1 resonances (e.g: 3:1, 4:1, and so on).
While these objects spend lengthy periods of time at large heliocentric
distances, if their perihelia remain less than around 40 au, their dynamical
evolution is still largely coupled to Neptune's. Conversely, around a dozen
extreme TNOs with a > 250 au and detached perihelia seem to exist in a regime
where they are too distant to be affected by the giant planets, and too close
for their dynamics to be governed by external forces. Recent work suggests that
the apparent alignment of these orbits in physical space is a signature of
gravitational shepherding by a distant massive planet. In this paper, we
investigate the evolution of TNOs in each of Neptune's n:1 resonances between
the 3:1 and 14:1. We conclude that both resonant and non-resonant objects
beyond the 12:1 near ~157 au are removed rather efficiently via perturbations
from the hypothetical Planet Nine. Additionally, we uncover a population of
simulated TNOs with a < 100 au, 40 < q < 45 au and low inclinations that
experience episodes of resonant interactions with both Neptune and Planet Nine.
Finally, we simulate the evolution of observed objects with a > 100 au and
identify several TNOs that are potentially locked in n:1 resonances with
Neptune; including the most distant known resonant candidates 2014 JW80 and
2014 OS394 that appear to be in the 10:1 and 11:1 resonances, respectively. Our
results suggest that the detection of similar remote objects might provide a
useful constraint on hypotheses invoking the existence of additional distant
planets.


Abstract:
  JUNO is a massive liquid scintillator detector with a primary scientific goal
of determining the neutrino mass ordering by studying the oscillated
anti-neutrino flux coming from two nuclear power plants at 53 km distance. The
expected signal anti-neutrino interaction rate is only 60 counts per day,
therefore a careful control of the background sources due to radioactivity is
critical. In particular, natural radioactivity present in all materials and in
the environment represents a serious issue that could impair the sensitivity of
the experiment if appropriate countermeasures were not foreseen. In this paper
we discuss the background reduction strategies undertaken by the JUNO
collaboration to reduce at minimum the impact of natural radioactivity. We
describe our efforts for an optimized experimental design, a careful material
screening and accurate detector production handling, and a constant control of
the expected results through a meticulous Monte Carlo simulation program. We
show that all these actions should allow us to keep the background count rate
safely below the target value of 10 Hz in the default fiducial volume, above an
energy threshold of 0.7 MeV.


Abstract:
  We prove an improved spectral large sieve inequality for the family of
$SL_3(\mathbb{Z})$ Hecke-Maass cusp forms. The method of proof uses duality and
its structure reveals unexpected connections to Heath-Brown's large sieve for
cubic characters.


Abstract:
  Backpropagation image saliency aims at explaining model predictions by
estimating model-centric importance of individual pixels in the input. However,
class-insensitivity of the earlier layers in a network only allows saliency
computation with low resolution activation maps of the deeper layers, resulting
in compromised image saliency. Remedifying this can lead to sanity failures. We
propose CAMERAS, a technique to compute high-fidelity backpropagation saliency
maps without requiring any external priors and preserving the map sanity. Our
method systematically performs multi-scale accumulation and fusion of the
activation maps and backpropagated gradients to compute precise saliency maps.
From accurate image saliency to articulation of relative importance of input
features for different models, and precise discrimination between model
perception of visually similar objects, our high-resolution mapping offers
multiple novel insights into the black-box deep visual models, which are
presented in the paper. We also demonstrate the utility of our saliency maps in
adversarial setup by drastically reducing the norm of attack signals by
focusing them on the precise regions identified by our maps. Our method also
inspires new evaluation metrics and a sanity check for this developing research
direction. Code is available here https://github.com/VisMIL/CAMERAS


Abstract:
  Despite advances in feature representation, leveraging geometric relations is
crucial for establishing reliable visual correspondences under large variations
of images. In this work we introduce a Hough transform perspective on
convolutional matching and propose an effective geometric matching algorithm,
dubbed Convolutional Hough Matching (CHM). The method distributes similarities
of candidate matches over a geometric transformation space and evaluate them in
a convolutional manner. We cast it into a trainable neural layer with a
semi-isotropic high-dimensional kernel, which learns non-rigid matching with a
small number of interpretable parameters. To validate the effect, we develop
the neural network with CHM layers that perform convolutional matching in the
space of translation and scaling. Our method sets a new state of the art on
standard benchmarks for semantic visual correspondence, proving its strong
robustness to challenging intra-class variations.


Abstract:
  Explaining the behavior of black box machine learning models through human
interpretable rules is an important research area. Recent work has focused on
explaining model behavior locally i.e. for specific predictions as well as
globally across the fields of vision, natural language, reinforcement learning
and data science. We present a novel model-agnostic approach that derives rules
to globally explain the behavior of classification models trained on numerical
and/or categorical data. Our approach builds on top of existing local model
explanation methods to extract conditions important for explaining model
behavior for specific instances followed by an evolutionary algorithm that
optimizes an information theory based fitness function to construct rules that
explain global model behavior. We show how our approach outperforms existing
approaches on a variety of datasets. Further, we introduce a parameter to
evaluate the quality of interpretation under the scenario of distributional
shift. This parameter evaluates how well the interpretation can predict model
behavior for previously unseen data distributions. We show how existing
approaches for interpreting models globally lack distributional robustness.
Finally, we show how the quality of the interpretation can be improved under
the scenario of distributional shift by adding out of distribution samples to
the dataset used to learn the interpretation and thereby, increase robustness.
All of the datasets used in our paper are open and publicly available. Our
approach has been deployed in a leading digital marketing suite of products.


Abstract:
  In this manuscript, working with a binary mechanical system, we examine the
effect of quantum gravity on the exceptional points of the system. On the one
side, we find that the exceedingly weak effect of quantum gravity can be sensed
via pushing the system towards a second-order exceptional point, where the
spectra of the non-Hermitian system exhibits non-analytic and even
discontinuous behavior. On the other side, the gravity perturbation will affect
the sensitivity of the system to deposition mass. In order to further enhance
the sensitivity of the system to quantum gravity, we extend the system to the
other one which has a higher-order (third-order) exceptional point. Our work
provides a feasible way to use exceptional points as a new tool to explore the
effect of quantum gravity.


Abstract:
  This paper develops a sparsity-inducing version of Bayesian Causal Forests, a
recently proposed nonparametric causal regression model that employs Bayesian
Additive Regression Trees and is specifically designed to estimate
heterogeneous treatment effects using observational data. The sparsity-inducing
component we introduce is motivated by empirical studies where not all the
available covariates are relevant, leading to different degrees of sparsity
underlying the surfaces of interest in the estimation of individual treatment
effects. The extended version presented in this work, which we name Shrinkage
Bayesian Causal Forest, is equipped with an additional pair of priors allowing
the model to adjust the weight of each covariate through the corresponding
number of splits in the tree ensemble. These priors improve the model's
adaptability to sparse data generating processes and allow to perform fully
Bayesian feature shrinkage in a framework for treatment effects estimation, and
thus to uncover the moderating factors driving heterogeneity. In addition, the
method allows prior knowledge about the relevant confounding covariates and the
relative magnitude of their impact on the outcome to be incorporated in the
model. We illustrate the performance of our method in simulated studies, in
comparison to Bayesian Causal Forest and other state-of-the-art models, to
demonstrate how it scales up with an increasing number of covariates and how it
handles strongly confounded scenarios. Finally, we also provide an example of
application using real-world data.


Abstract:
  3D object detection is a key component of many robotic applications such as
self-driving vehicles. While many approaches rely on expensive 3D sensors such
as LiDAR to produce accurate 3D estimates, methods that exploit stereo cameras
have recently shown promising results at a lower cost. Existing approaches
tackle this problem in two steps: first depth estimation from stereo images is
performed to produce a pseudo LiDAR point cloud, which is then used as input to
a 3D object detector. However, this approach is suboptimal due to the
representation mismatch, as the two tasks are optimized in two different metric
spaces. In this paper we propose a model that unifies these two tasks and
performs them in the same metric space. Specifically, we directly construct a
pseudo LiDAR feature volume (PLUME) in 3D space, which is then used to solve
both depth estimation and object detection tasks. Our approach achieves
state-of-the-art performance with much faster inference times when compared to
existing methods on the challenging KITTI benchmark.


Abstract:
  This report documents safety assurance argument templates to support the
deployment and operation of autonomous systems that include machine learning
(ML) components. The document presents example safety argument templates
covering: the development of safety requirements, hazard analysis, a safety
monitor architecture for an autonomous system including at least one ML
element, a component with ML and the adaptation and change of the system over
time. The report also presents generic templates for argument defeaters and
evidence confidence that can be used to strengthen, review, and adapt the
templates as necessary. This report is made available to get feedback on the
approach and on the templates. This work was sponsored by the UK Dstl under the
R-cloud framework.


Abstract:
  Integrating robots in complex everyday environments requires a multitude of
problems to be solved. One crucial feature among those is to equip robots with
a mechanism for teaching them a new task in an easy and natural way. When
teaching tasks that involve sequences of different skills, with varying order
and number of these skills, it is desirable to only demonstrate full task
executions instead of all individual skills. For this purpose, we propose a
novel approach that simultaneously learns to segment trajectories into
reoccurring patterns and the skills to reconstruct these patterns from
unlabelled demonstrations without further supervision. Moreover, the approach
learns a skill conditioning that can be used to understand possible sequences
of skills, a practical mechanism to be used in, for example,
human-robot-interactions for a more intelligent and adaptive robot behaviour.
The Bayesian and variational inference based approach is evaluated on synthetic
and real human demonstrations with varying complexities and dimensionality,
showing the successful learning of segmentations and skill libraries from
unlabelled data.


Abstract:
  The purpose of this work is to examine the structure of optimal dual fusion
frames and get more exibility in the use of dual fusion frames for erasures of
subspaces. We deal with optimal dual fusion frames with respect to different
definitions of duality and compare the advantages of these approaches. In
addition, we introduce a new concept so called partial optimal dual which
involves less time and computation for detecting optimal dual for erasures in
known locations. Then we study the relationship between local and global
optimal duals by partial optimal duals which leads to some applicable results.
In the sense that, we obtain an overcomplete frame and a family of associated
optimal duals by a given Riesz fusion basis. We present some examples to
exhibit the effect of error rate when dual fusion frames are applied in
reconstruction.


Abstract:
  By controlling quantum fluctuations via the Falk-Bruch inequality we give the
first rigorous argument for the existence of a spin-glass phase in the quantum
Sherrington-Kirkpatrick model with a transverse magnetic field if the
temperature and the field are sufficiently low. The argument also applies to
the generalization of the model with multi-spin interactions, sometimes dubbed
as transverse $p$-spin model.


Abstract:
  This paper presents a generic method for generating full facial 3D animation
from speech. Existing approaches to audio-driven facial animation exhibit
uncanny or static upper face animation, fail to produce accurate and plausible
co-articulation or rely on person-specific models that limit their scalability.
To improve upon existing models, we propose a generic audio-driven facial
animation approach that achieves highly realistic motion synthesis results for
the entire face. At the core of our approach is a categorical latent space for
facial animation that disentangles audio-correlated and audio-uncorrelated
information based on a novel cross-modality loss. Our approach ensures highly
accurate lip motion, while also synthesizing plausible animation of the parts
of the face that are uncorrelated to the audio signal, such as eye blinks and
eye brow motion. We demonstrate that our approach outperforms several baselines
and obtains state-of-the-art quality both qualitatively and quantitatively. A
perceptual user study demonstrates that our approach is deemed more realistic
than the current state-of-the-art in over 75% of cases. We recommend watching
the supplemental video before reading the paper:
https://research.fb.com/wp-content/uploads/2021/04/mesh_talk.mp4


Abstract:
  Surfaces inspired by nature and their replication find great interest in
science, technology, and medicine due to their unique functional properties.
This research aimed to develop an efficient laser milling technology using
single-pulse- and burst-modes of irradiation to replicate bio-inspired
structures over large areas at high speed. The ability to form the
trapezoidal-riblets inspired by shark skin at high production speeds while
maintaining the lowest possible surface roughness was demonstrated.


Abstract:
  Let $\alpha>0$, $\beta>\alpha$, and let $X_1,\ldots, X_q$ be
$\mathscr{C}^{\alpha}_{\mathrm{loc}}$ vector fields on a
$\mathscr{C}^{\alpha+1}$ manifold which span the tangent space at every point,
where $\mathscr{C}^{s}$ denotes the Zygmund-H\"older space of order $s$. We
give necessary and sufficient conditions for when there is a
$\mathscr{C}^{\beta+1}$ structure on the manifold, compatible with its
$\mathscr{C}^{\alpha+1}$ structure, with respect to which $X_1,\ldots, X_q$ are
$\mathscr{C}^{\beta}_{\mathrm{loc}}$. This strengthens previous results of the
first author which dealt with the setting $\alpha>1$, $\beta>\max\{ \alpha,
2\}$.


Abstract:
  We study scaling behavior of the disorder parameter, defined as the
expectation value of a symmetry transformation applied to a finite region, at
the deconfined quantum critical point in (2+1)$d$ in the $J$-$Q_3$ model via
large-scale quantum Monte Carlo simulations. We show that the disorder
parameter for U(1) spin rotation symmetry exhibits perimeter scaling with a
logarithmic correction associated with sharp corners of the region, as
generally expected for a conformally-invariant critical point. However, for
large rotation angle the universal coefficient of the logarithmic corner
correction becomes negative, which is not allowed in any unitary conformal
field theory. We also extract the current central charge from the small
rotation angle scaling, whose value is much smaller than that of the free
theory.


Abstract:
  We study an inverse problem for the fractional wave equation with a potential
by the measurement taking on arbitrary subsets of the exterior in the
space-time domain. We are interested in the issues of uniqueness and stability
estimate in the determination of the potential by the exterior
Dirichlet-to-Neumann map. The main tools are the qualitative and quantitative
unique continuation properties for the fractional Laplacian. For the stability,
we also prove that the log type stability estimate is optimal. The log type
estimate shows the striking difference between the inverse problems for the
fractional and classical wave equations in the stability issue. The results
hold for any spatial dimension $n\in \N$.


Abstract:
  Wearable data is a rich source of information that can provide deeper
understanding of links between human behaviours and human health. Existing
modelling approaches use wearable data summarized at subject level via scalar
summaries using regression techniques, temporal (time-of-day) curves using
functional data analysis (FDA), and distributions using distributional data
analysis (DDA). We propose to capture temporally local distributional
information in wearable data using subject-specific time-by-distribution (TD)
data objects. Specifically, we propose scalar on time-by-distribution
regression (SOTDR) to model associations between scalar response of interest
such as health outcomes or disease status and TD predictors. We show that TD
data objects can be parsimoniously represented via a collection of time-varying
L-moments that capture distributional changes over the time-of-day. The
proposed method is applied to the accelerometry study of mild Alzheimer's
disease (AD). Mild AD is found to be significantly associated with reduced
maximal level of physical activity, particularly during morning hours. It is
also demonstrated that TD predictors attain much stronger associations with
clinical cognitive scales of attention, verbal memory, and executive function
when compared to predictors summarized via scalar total activity counts,
temporal functional curves, and quantile functions. Taken together, the present
results suggest that the SOTDR analysis provides novel insights into cognitive
function and AD.


Abstract:
  When spin polarised electrons flow through a magnetic texture a transfer
torque is generated. We examine the effect of this torque on skyrmions and
skyrmion bags, skyrmionic structures of arbitrary integer topological degree,
in thin ferromagnetic films. Using micromagnetic simulations and analysis from
the well known Thiele equation we explore the potential for sorting or binning
skyrmions of varying degrees mechanically. We investigate the applicability of
the Thiele equation to problems of this nature and derive a theory of skyrmion
deflection ordered by topological degree.


Abstract:
  A key feature of intelligent behaviour is the ability to learn abstract
strategies that scale and transfer to unfamiliar problems. An abstract strategy
solves every sample from a problem class, no matter its representation or
complexity -- like algorithms in computer science. Neural networks are powerful
models for processing sensory data, discovering hidden patterns, and learning
complex functions, but they struggle to learn such iterative, sequential or
hierarchical algorithmic strategies. Extending neural networks with external
memories has increased their capacities in learning such strategies, but they
are still prone to data variations, struggle to learn scalable and transferable
solutions, and require massive training data. We present the Neural Harvard
Computer (NHC), a memory-augmented network based architecture, that employs
abstraction by decoupling algorithmic operations from data manipulations,
realized by splitting the information flow and separated modules. This
abstraction mechanism and evolutionary training enable the learning of robust
and scalable algorithmic solutions. On a diverse set of 11 algorithms with
varying complexities, we show that the NHC reliably learns algorithmic
solutions with strong generalization and abstraction: perfect generalization
and scaling to arbitrary task configurations and complexities far beyond seen
during training, and being independent of the data representation and the task
domain.


Abstract:
  Understanding the origin of life-essential volatiles like N in the Solar
System and beyond is critical to evaluate the potential habitability of rocky
planets. Whether the inner Solar System planets accreted these volatiles from
their inception or had an exogenous delivery from the outer Solar System is,
however, not well understood. Using previously published data of
nucleosynthetic anomalies of Ni, Mo, W and Ru in iron meteorites along with
their 15N-14N ratios, here we show that the earliest formed protoplanets in the
inner and outer protoplanetary disk accreted isotopically distinct N. While the
Sun and Jupiter captured N from nebular gas, concomitantly growing protoplanets
in the inner and outer disk possibly sourced their N from organics and/or dust
- with each reservoir having a different N isotopic composition. A distinct N
isotopic signature of the inner Solar System protoplanets coupled with their
rapid accretion suggests that non-nebular, isotopically processed N was
ubiquitous in their growth zone at 0-0.3 Myr after the formation of CAIs.
Because 15N-14N ratio of the bulk silicate Earth falls between that of inner
and outer Solar System reservoirs, we infer that N in the present-day rocky
planets represents a mixture of both inner and outer Solar System material.


Abstract:
  A Hilbert point in $H^p(\mathbb{T}^d)$, for $d\geq1$ and $1\leq p \leq
\infty$, is a nontrivial function $\varphi$ in $H^p(\mathbb{T}^d)$ such that
$\| \varphi \|_{H^p(\mathbb{T}^d)} \leq \|\varphi + f\|_{H^p(\mathbb{T}^d)}$
whenever $f$ is in $H^p(\mathbb{T}^d)$ and orthogonal to $\varphi$ in the usual
$L^2$ sense. When $p\neq 2$, $\varphi$ is a Hilbert point in $H^p(\mathbb{T})$
if and only if $\varphi$ is a nonzero multiple of an inner function. An inner
function on $\mathbb{T}^d$ is a Hilbert point in any of the spaces
$H^p(\mathbb{T}^d)$, but there are other Hilbert points as well when $d\geq 2$.
We investigate the case of $1$-homogeneous polynomials in depth and obtain as a
byproduct a new proof of the sharp Khintchin inequality for Steinhaus variables
in the range $2<p<\infty$. We also study briefly the dynamics of a certain
nonlinear projection operator that characterizes Hilbert points as its fixed
points. We exhibit an example of a function $\varphi$ that is a Hilbert point
in $H^p(\mathbb{T}^3)$ for $p=2, 4$, but not for any other $p$; this is
verified rigorously for $p>4$ but only numerically for $1\leq p<4$.


Abstract:
  To reduce Operation and Maintenance (O&M) costs on offshore wind farms,
wherein 80% of the O&M cost relates to deploying personnel, the offshore wind
sector looks to Robotics and Artificial Intelligence (RAI) for solutions.
Barriers to Beyond Visual Line of Sight (BVLOS) robotics include operational
safety compliance and resilience, inhibiting the commercialization of
autonomous services offshore. To address safety and resilience challenges we
propose a Symbiotic System Of Systems Approach (SSOSA), reflecting the
lifecycle learning and co-evolution with knowledge sharing for mutual gain of
robotic platforms and remote human operators. Our novel methodology enables the
run-time verification of safety, reliability and resilience during autonomous
missions. To achieve this, a Symbiotic Digital Architecture (SDA) was developed
to synchronize digital models of the robot, environment, infrastructure, and
integrate front-end analytics and bidirectional communication for autonomous
adaptive mission planning and situation reporting to a remote operator. A
reliability ontology for the deployed robot, based on our holistic
hierarchical-relational model, supports computationally efficient platform data
analysis. We demonstrate an asset inspection mission within a confined space
through Cooperative, Collaborative and Corroborative (C3) governance (internal
and external symbiosis) via decision-making processes and the associated
structures. We create a hyper enabled human interaction capability to analyze
the mission status, diagnostics of critical sub-systems within the robot to
provide automatic updates to our AI-driven run-time reliability ontology. This
enables faults to be translated into failure modes for decision-making during
the mission.


Abstract:
  The low temperature thermodynamics of correlated 1D fermionic models with
spin and charge degrees of freedom is obtained by exact diagonalization (ED) of
small systems and followed by density matrix renormalization group (DMRG)
calculations that target the lowest hundreds of states $\{E(N)\}$ at system
size $N$ instead of the ground state. Progressively larger $N$ reaches $T <
0.05t$ in correlated models with electron transfer $t$ between first neighbors
and bandwidth $4t$. The size dependence of the many-fermion basis is explicitly
included for arbitrary interactions by scaling the partition function. The
remaining size dependence is then entirely due to the energy spectrum
$\{E(N)\}$ of the model. The ED/DMRG method is applied to Hubbard and extended
Hubbard models, both gapped and gapless, with $N_e = N$ or $N/2$ electrons and
is validated against exact results for the magnetic susceptibility $\chi(T)$
and entropy $S(T)$ per site. Some limitations of the method are noted. Special
attention is given to the bond-order-wave phase of the extended Hubbard model
with competing interactions and low $T$ thermodynamics sensitive to small gaps.


Abstract:
  Confining dark sectors at the GeV scale can lead to novel collider signatures
including those termed emerging jets with large numbers of displaced vertices.
The triggers at the LHC experiments were not designed with this type of new
physics in mind, and triggering can be challenging, especially if the mediator
is relatively light and/or has quantum numbers such that additional jets are
not automatically produced in each event. We show that the efficiency and the
total event rate at current triggers can be significantly improved by
considering initial state radiation of the events, with the largest increase in
rate coming from simulation of two additional jets. We also explore possible
new triggers that employ hit counts in different tracker layers as input into a
machine learning algorithm. We show that these new triggers can have reasonably
low background rates, and that they are sensitive to a wide range of new
physics parameters even when trained on a single model.


Abstract:
  Sleep deprivation is a public health concern that significantly impacts one's
well-being and performance. Sleep is an intimate experience, and
state-of-the-art sleep monitoring solutions are highly-personalized to
individual users. With a motivation to expand sleep monitoring at a large-scale
and contribute sleep data to public health understanding, we present WiSleep, a
sleep monitoring and analytics platform using smartphone network connections
that are passively sensed from WiFi infrastructure. We propose an unsupervised
ensemble model of Bayesian change point detection to predict sleep and wake-up
times. Then, we validate our approach using ground truth from a user study in
campus dormitories and a private home. Our results find WiSleep outperforming
established methods for users with irregular sleep patterns while yielding
comparable accuracy for regular sleepers with an average 79.5\% accuracy. This
is comparable to client-side based methods, albeit utilizing only
coarse-grained information. Finally, we show that WiSleep can process data from
20,000 users on a single commodity server, allowing it to scale to large campus
populations with low server requirements.


Abstract:
  A systematic study of the compression creep properties of a
single-crystalline Co-base superalloy (Co-9Al-7.5W-2Ta) was conducted at 950
{\deg}C, 975 {\deg}C and 1000 {\deg}C to reveal the influence of temperature
and the resulting diffusion velocity of solutes like Al, W and Ta on the
deformation mechanisms. Two creep rate minima are observed at all temperatures
indicating that the deformation mechanisms causing these minima are quite
similar. Atom-probe tomography analysis reveals elemental segregation to
stacking faults, which had formed in the $\gamma\prime$ phase during creep.
Density-functional-theory calculations indicate segregation of W and Ta to the
stacking fault and an associated considerable reduction of the stacking fault
energy. Since solutes diffuse faster at a higher temperature, segregation can
take place more quickly. This results in a significantly faster softening of
the alloy, since cutting of the $\gamma\prime$ precipitate phase by partial
dislocations is facilitated through segregation already during the early stages
of creep. This is confirmed by transmission electron microscopy analysis.
Therefore, not only the smaller precipitate fraction at higher temperatures is
responsible for the worse creep properties, but also faster diffusion-assisted
shearing of the $\gamma\prime$ phase by partial dislocations. The understanding
of these mechanisms will help in future alloy development by offering new
design criteria.


Abstract:
  In the fields of statistics and unsupervised machine learning a fundamental
and well-studied problem is anomaly detection. Although anomalies are difficult
to define, many algorithms have been proposed. Underlying the approaches is the
nebulous understanding that anomalies are rare, unusual or inconsistent with
the majority of data. The present work gives a philosophical approach to
clearly define anomalies and to develop an algorithm for their efficient
detection with minimal user intervention. Inspired by the Gestalt School of
Psychology and the Helmholtz principle of human perception, the idea is to
assume anomalies are observations that are unexpected to occur with respect to
certain groupings made by the majority of the data. Thus, under appropriate
random variable modelling anomalies are directly found in a set of data under a
uniform and independent random assumption of the distribution of constituent
elements of the observations; anomalies correspond to those observations where
the expectation of occurrence of the elements in a given view is $<1$. Starting
from fundamental principles of human perception an unsupervised anomaly
detection algorithm is developed that is simple, real-time and parameter-free.
Experiments suggest it as the prime choice for univariate data and it shows
promising performance on the detection of global anomalies in multivariate
data.


Abstract:
  Bhargava, Hanke, and Shankar have recently shown that the asymptotic average
$2$-torsion subgroup size of the family of class groups of monogenized cubic
fields with positive and negative discriminants is $3/2$ and $2$, respectively.
In this paper, we provide strong computational evidence for these asymptotes.
We then develop a pair of novel conjectures that predicts, for $p$ prime, the
asymptotic average $p$-torsion subgroup size in class groups of monogenized
cubic fields.


Abstract:
  Purpose: We propose a general framework for quantifying predictive
uncertainties of dose-related quantities and leveraging this information in a
dose mimicking problem in the context of automated radiation therapy treatment
planning.
  Methods: A three-step pipeline, comprising feature extraction, dose statistic
prediction and dose mimicking, is employed. In particular, the features are
produced by a convolutional variational autoencoder and used as inputs in a
previously developed nonparametric Bayesian statistical method, estimating the
multivariate predictive distribution of a collection of predefined dose
statistics. Specially developed objective functions are then used to construct
a probabilistic dose mimicking problem based on the produced distributions,
creating deliverable treatment plans.
  Results: The numerical experiments are performed using a dataset of 94
retrospective treatment plans of prostate cancer patients. We show that the
features extracted by the variational autoencoder capture geometric information
of substantial relevance to the dose statistic prediction problem and are
related to dose statistics in a more regularized fashion than hand-crafted
features. The estimated predictive distributions are reasonable and outperforms
a non-input-dependent benchmark method, and the deliverable plans produced by
the probabilistic dose mimicking agree better with their clinical counterparts
than for a non-probabilistic formulation.
  Conclusions: We demonstrate that prediction of dose-related quantities may be
extended to include uncertainty estimation and that such probabilistic
information may be leveraged in a dose mimicking problem. The treatment plans
produced by the proposed pipeline resemble their original counterparts well,
illustrating the merits of a holistic approach to automated planning based on
probabilistic modeling.


Abstract:
  Let $T_D$ denote the first exit time of a Brownian motion from a domain $D$
in ${\mathbb R}^n$. Given domains $U,W \subseteq {\mathbb R}^n$ containing the
origin, we investigate the cases in which we are more likely to have fast exits
from $U$ than $W$, meaning ${\bf P}(T_U<t) > {\bf P}(T_W<t)$ for $t$ small. We
show that the primary factor in the probability of fast exits from domains is
the proximity of the closest regular part of the boundary to the origin. We
also prove a result on the complementary question of longs stays, meaning ${\bf
P}(T_U>t) > {\bf P}(T_W>t)$ for $t$ large. This result, which applies only in
two dimensions, shows that the unit disk has the lowest probability of long
stays amongst all Schlicht domains.


Abstract:
  The classification problem for simple $\mathfrak{sl}(2)$-modules leads in a
natural way to the study of the category of finite rank torsion free
$\mathfrak{sl}(2)$-modules and its subcategory of rational
$\mathfrak{sl}(2)$-modules. We prove that the rationalization functor induces
an identification between the isomorphism classes of simple modules of these
categories. This raises the question of what is the precise relationship
between other invariants associated with them. We give a complete solution to
this problem for the Grothendieck and Picard groups, obtaining along theway
several new results regarding these categories that are interesting in their
own right.


Abstract:
  We study the evolutionary and physical properties of evolved O stars in the
Small Magellanic Cloud (SMC), with a special focus on their surface abundances
to investigate the efficiency of rotational mixing as a function of age,
rotation and global metallicity. We analyse the UV + optical spectra of
thirteen SMC O-type giants and supergiants, using the stellar atmosphere code
CMFGEN to derive photospheric and wind properties. We compare the inferred
properties to theoretical predictions from evolution models. For a more
comprehensive analysis, we interpret the results together with those we
obtained for O-type dwarfs in a former study. Most dwarfs lie in the early
phases of the main-sequence. For a given initial mass, giants are farther along
the evolutionary tracks, confirming that they are more evolved than dwarfs.
Supergiants have higher initial masses and are located past the terminal age
main-sequence. We find no clear trend of a mass discrepancy, regardless of the
diagram that was used to estimate the evolutionary mass. CNO abundances are
consistent with nucleosynthesis from the CNO cycle. Comparisons to theoretical
predictions reveal that the initial mixture is important when the observed
trends in the N/C versus N/O diagram are to be reproduced. A trend for stronger
chemical evolution for more evolved objects is observed. More massive stars,
are on average, more chemically enriched at a given evolutionary phase,
qualitatively consistent with evolutionary models. Abundance ratios supports
the theoretical prediction that massive stars at low metallicity are more
chemically processed than their Galactic counterparts. Finally, models
including rotation generally reproduce the surface abundances and rotation
rates when different initial rotational velocities are considered.
Nevertheless, there are objects for which a stronger braking and/or more
efficient mixing is required.


Abstract:
  The moir\'e pattern observed in stacked non-commensurate crystal lattices,
such as hetero-bilayers of transition metal dichalcogenides, produces a
periodic modulation of their bandgap. Excitons subjected to this potential
landscape exhibit a band structure that gives rise to a quasi-particle dubbed
moir\'e exciton. In the case of MoS$_2$/WSe$_2$ hetero-bilayers, the moir\'e
trapping potential has honeycomb symmetry and, consequently, the moir\'e
exciton band structure is the same as that of a Dirac-Weyl fermion, whose mass
can be further tuned down to zero with a perpendicularly applied field. Here we
show that, analogously to other Dirac-like particles, moir\'e exciton exhibits
a trembling motion, also known as zitterbewegung, whose long timescales are
compatible with current experimental techniques for exciton dynamics. This
promotes the study of the dynamics of moir\'e excitons in van der Waals
heterostructures as an advantageous solid-state platform to probe
zitterbewegung, broadly tunable by gating and inter-layer twist angle.


Abstract:
  Gluons are strong interaction gauge fields which interact between quarks,
i.e. constituents of baryons and mesons. Interaction of matters is
phenomenologically described by gauge theory of strong, electromagnetic, weak
and gravitational interactions. In electro-weak theory, left handed leptons
${l}_L$ and neutrino ${\mathcal \nu}_L$, right handed leptons ${l}_R$ and left
handed quarks $u_L, d_L$ and right handed quarks $u_R, d_R$ follow $SU(2)\times
U(1)$ symmetry. Charge of leptons and quarks define hypercharge $Y$, and via
Higgs mechanism $SU(2)_L\times U(1)_Y$ symmetry forms $U(1)_{em}$ symmetry. In
order to describe Hadron dynamics properly, embedding of 4-dimensional space to
5-dimensional space was tried in lattice simulations, and in light front
holographic QCD (LFHQCD) approach in which conformally symmetric light-front
dynamics without ghost are embedded in $AdS_5$, and a parameter that fixes a
mass scale was chosen from the Principle of Maximum Conformality. Coulomb or
Landau gauge fixed Faddeev-Popov Yang-Mills field equation is known to have the
Gribov ambiguity, and tunneling between vacua between different topological
structures was proposed by van Baal and collaborators. The symmetry of three
colors can be assigned three vectors of quaternion ${\bf H}$, whose
multiplication on $2\times 2$ matrices of Dirac spinors on ${\bf S}^3$ induces
transformations. Instantons or sphalerons whose presence is expected from
conformal equivalence of ${\bf S}^3\times {\bf R}$ to ${\bf R}^4$ are reviewed.
An extension of the dynamics embedded in complex projective space is also
discussed.


Abstract:
  Controlling the perpendicular magnetic anisotropy (PMA) in thin films has
received considerable attention in recent years due to its technological
importance. PMA based devices usually involve heavy-metal
(oxide)/ferromagnetic-metal bilayers, where, thanks to interfacial spin-orbit
coupling (SOC), the in-plane (IP) stability of the magnetization is broken.
Here we show that in V/MgO/Fe(001) epitaxial junctions with competing in-plane
and out-of-plane (OOP) magnetic anisotropies, the SOC mediated interaction
between a ferromagnet (FM) and a superconductor (SC) enhances the effective PMA
below the superconducting transition. This produces a partial magnetization
reorientation without any applied field for all but the largest junctions,
where the IP anisotropy is more robust; for the smallest junctions there is a
reduction of the field required to induce a complete OOP transition
($H_\text{OOP}$) due to the stronger competition between the IP and OOP
anisotropies. Our results suggest that the degree of effective PMA could be
controlled by the junction lateral size in the presence of superconductivity
and an applied electric field. We also discuss how the $H_\text{OOP}$ field
could be affected by the interaction between magnetic stray fields and
superconducting vortices. Our experimental findings, supported by numerical
modelling of the ferromagnet-superconductor interaction, open pathways to
active control of magnetic anisotropy in the emerging dissipation-free
superconducting spin electronics.