Abstract:
  In this study, we investigate the cyclotron resonance effect in the
first-order AC current, magnetic ratchet effect, and second harmonic generation
in phosphorene in the presence of a steady tilted magnetic field and under THz
laser radiation. We establish that various cyclotron resonances exist in the
deduced currents based on the angular frequency of the incoming light. These
resonances are dependent on the $\omega_{c_{+}}$ value, a function of the
carrier charge, the perpendicular magnetic field, and the effective masses
along the armchair or zigzag edges. We discuss the direction and the magnitude
of the deduced currents for various radiation polarizations. We compare the
results with a zero perpendicular magnetic field. Cyclotron resonance for the
first order AC current occurs at $\omega= \pm \omega_{c_{+}}$. The deduced
current declines if the perpendicular magnetic field is zero. Meanwhile, for
the ratchet current, cyclotron resonances occur at $\omega= \pm
\omega_{c_{+}}$, $\omega= \pm 2\omega_{c_{+}}$, and radiation helicity affects
the deduced current for circularly polarized light. Cyclotron resonance for the
second harmonic generation current occurs at $\omega= \pm \omega_{c_{+}}$,
$\omega= \pm 2 \omega_{c_{+}}$ and $\omega= \pm \omega_{c_{+}}/2 $ and the
current is stronger compared to the case with no perpendicular magnetic field.
As the magnetic field rotates in the plane of anisotropic phosphorene, separate
directions are predicted for the second harmonic generation--related current.
It is noteworthy that the magnitude of the ratchet and second harmonic
generation current are within the same range and comparable to the magnetic
ratchet current in monolayer graphene, $\mu A / cm$.


Abstract:
  We consider the strongly connected components (SCCs) of a uniform directed
graph on $n$ vertices with i.i.d. in- and out-degree pairs distributed as
$(D^-,D^+)$, with $\mathbb E[D^+]=\mathbb E[D^-]=\mu$. We condition on equal
total in- and out-degree. A phase transition for the emergence of a giant SCC
is known to occur at the critical value $\mathbb E[D^-D^+] = \mu$. We study the
model at this critical value and, additionally, require that $\mathbb
E[(D^-)^i(D^+)^j]<\infty$ for all $i+j\leq 3$, and for $(i,j)=(1,3)$ and
$(i,j)=(3,1)$. We show that, under these conditions, the SCCs ranked by
decreasing number of edges with distances rescaled by $n^{-1/3}$ converge in
distribution to a sequence of finite strongly connected directed multigraphs
with edge lengths, and that these are either $3$-regular or loops. The limit
objects lie in a $3$-parameter family, which contains the scaling limit of the
SCCs in the directed Erd\H{o}s-R\'enyi model at criticality as found by
Goldschmidt and Stephenson (2019). This is the first universality result for
the scaling limit of a critical directed graph model and the first quantitative
result on the directed configuration model at criticality. As a trivial
consequence, the largest SCCs at criticality contain $\Theta(n^{1/3})$ vertices
and edges in probability, and the diameter of the directed graph at criticality
is $\Omega(n^{1/3})$ in probability. We use a metric on the space of weighted
multigraphs in which two multigraphs are close if there are compatible
isomorphisms between their vertex and edge sets which roughly preserve the edge
lengths. We use the product topology on the sequence of multigraphs. Our method
of proof involves a depth-first exploration of the directed graph, resulting in
a spanning forest with additional identifications, of which we study the limit
under rescaling.


Abstract:
  Multidimensional scaling in networks allows for the discovery of latent
information about their structure by embedding nodes in some feature space.
Ideological scaling for users in social networks such as Twitter is an example,
but similar settings can include diverse applications in other networks and
even media platforms or e-commerce. A growing literature of ideology scaling
methods in social networks restricts the scaling procedure to nodes that
provide interpretability of the feature space: on Twitter, it is common to
consider the sub-network of parliamentarians and their followers. This allows
to interpret inferred latent features as indices for ideology-related concepts
inspecting the position of members of parliament. While effective in inferring
meaningful features, this is generally restrained to these sub-networks,
limiting interesting applications such as country-wide measurement of
polarization and its evolution. We propose two methods to propagate ideological
features beyond these sub-networks: one based on homophily (linked users have
similar ideology), and the other on structural similarity (nodes with similar
neighborhoods have similar ideologies). In our methods, we leverage the concept
of neighborhood ideological coherence as a parameter for propagation. Using
Twitter data, we produce an ideological scaling for 370K users, and analyze the
two families of propagation methods on a population of 6.5M users. We find
that, when coherence is considered, the ideology of a user is better estimated
from those with similar neighborhoods, than from their immediate neighbors.


Abstract:
  Positivity and Perron-Frobenius theory provide an elegant framework for the
convergence analysis of linear consensus algorithms. Here we consider a
generalization of these ideas to the analysis of nonlinear consensus algorithms
on the circle and establish tools for the design of consensus protocols that
monotonically converge to target formations on the circle.


Abstract:
  One of the advantages of kinetic inductance detectors is their intrinsic
frequency domain multiplexing capability. However, fabrication imperfections
usually give rise to resonance frequency deviations, which create frequency
collision and limit the array yield. Here we study the resonance frequency
deviation of a 4-inch kilo-pixel lumped-element kinetic inductance detector
(LEKID) array using optical mapping. Using the measured resonator dimensions
and film thickness, the fractional deviation can be explained within $\pm
25\times 10^{-3}$, whereas the residual deviation is due to variation of
electric film properties. Using the capacitor trimming technique, the
fractional deviation is decreased by a factor of 14. The yield of the trimming
process is found to be 97%. The mapping yield, measured under a 110~K
background, is improved from 69% to 76%, which can be further improved to 81%
after updating our readout system. With the improvement in yield, the capacitor
trimming technique may benefit future large-format LEKID arrays.


Abstract:
  For a gambler with side information, Kelly betting gives the optimal log
growth rate of the gambler's fortune, which is closely related to the mutual
information between the correct winner and the noisy side information. We show
conditions under which optimal Kelly betting can be implemented using
single-letter codes. We show that single-letter coding is optimal for a wide
variety of systems; for example, all systems with diagonal reward matrices
admit optimal single-letter codes. We also show that important classes of
systems do not admit optimal single-letter codes for Kelly betting, such as
when the side information is passed through a Z channel. Our results are
important to situations where the computational complexity of the gambler is
constrained, and may lead to new insights into the fitness value of information
for biological systems.


Abstract:
  Electro-optical control of on-chip photonic devices is an essential tool for
efficient integrated photonics. Lithium niobate on insulator (LNOI) is an
emerging platform for on-chip photonics due to its large electro-optic
coefficient and high nonlinearity [1]. Integrating quantum emitters into LNOI
would extend their versatile use in classic photonics to quantum computing and
communication [2, 3]. Here, we incorporate single rare-earth ions (REI) quantum
emitters in electro-optical tunable lithium niobite (LN) thin films and
demonstrate control of LN microcavities coupled to REI over a frequency range
of 160 GHz with 5 \mus switching speed. Dynamical control of the cavities
enables the modulation of the Purcell enhancement of the REIs with short time
constants. Using the Purcell enhancement, we show evidence of detecting single
Yb3+ ions in LN cavities. Coupling quantum emitters in fast tunable photonic
devices is an efficient method to shape the waveform of the emitter [4]. It
also offers a platform to encode quantum information in the integration of a
spectral-temporal-spatial domain to achieve high levels of channel
multiplexing, as well as an approach to generate deterministic single-photon
sources [5, 6].


Abstract:
  The performances of Low Gain Avalanche diode (LGAD) sensors from a neutron
irradiation campaign with fluences of 0.8 x 10^15, 15 x 10^15 and 2.5 x 10^15
neq/cm2 are reported in this article. These LGAD sensors are developed by the
Institute of High Energy Physics, Chinese Academy of Sciences and the Novel
Device Laboratory for the High Granularity Timing Detector of the High
Luminosity Large Hadron Collider. The timing resolution and collected charge of
the LGAD sensors were measured with electrons from a beta source. After
irradiation with a fluence of 2.5 x 10^15 neq/cm2, the collected charge
decreases from 40 fC to 7 fC, the signal-to-noise ratio deteriorates from 48 to
12, and the timing resolution increases from 29 ps to 39 ps.


Abstract:
  Attention mechanisms have shown promising results in sequence modeling tasks
that require long-term memory. Recent work investigated mechanisms to reduce
the computational cost of preserving and storing memories. However, not all
content in the past is equally important to remember. We propose Expire-Span, a
method that learns to retain the most important information and expire the
irrelevant information. This forgetting of memories enables Transformers to
scale to attend over tens of thousands of previous timesteps efficiently, as
not all states from previous timesteps are preserved. We demonstrate that
Expire-Span can help models identify and retain critical information and show
it can achieve strong performance on reinforcement learning tasks specifically
designed to challenge this functionality. Next, we show that Expire-Span can
scale to memories that are tens of thousands in size, setting a new state of
the art on incredibly long context tasks such as character-level language
modeling and a frame-by-frame moving objects task. Finally, we analyze the
efficiency of Expire-Span compared to existing approaches and demonstrate that
it trains faster and uses less memory.


Abstract:
  Respiratory ailments such as asthma, chronic obstructive pulmonary disease
(COPD), pneumonia, and lung cancer are life-threatening. Respiration rate (RR)
is a vital indicator of the wellness of a patient. Continuous monitoring of RR
can provide early indication and thereby save lives. However, a real-time
continuous RR monitoring facility is only available at the intensive care unit
(ICU) due to the size and cost of the equipment. Recent researches have
proposed Photoplethysmogram (PPG) and/ Electrocardiogram (ECG) signals for RR
estimation however, the usage of ECG is limited due to the unavailability of it
in wearable devices. Due to the advent of wearable smartwatches with built-in
PPG sensors, it is now being considered for continuous monitoring of RR. This
paper describes a novel approach to RR estimation using machine learning (ML)
models with the PPG signal features. Feature selection algorithms were used to
reduce computational complexity and the chance of overfitting. The best ML
model and the best feature selection algorithm combination was fine-tuned to
optimize its performance using hyperparameter optimization. Gaussian Process
Regression (GPR) with fitrgp feature selection algorithm outperformed all other
combinations and exhibits a root mean squared error (RMSE), mean absolute error
(MAE), and two-standard deviation (2SD) of 2.57, 1.91, and 5.13 breaths per
minute, respectively. This ML model based RR estimation can be embedded in
wearable devices for real-time continuous monitoring of the patient.


Abstract:
  Single particle tracking has found broad applications in the life and
physical sciences, enabling the observation and characterisation of nano- and
microscopic motion. Fluorescence-based approaches are ideally suited for
high-background environments, such as tracking lipids or proteins in or on
cells, due to superior background rejection. Scattering-based detection is
preferable when localisation precision and imaging speed are paramount due to
the in principle infinite photon budget. Here, we show that micromirror-based
total internal reflection dark field microscopy enables background suppression
previously only reported for interferometric scattering microscopy, resulting
in nm localisation precision at 6 $\mu$s exposure time for 20 nm gold
nanoparticles with a 25 x 25 $\mu$m$^{2}$ field of view. We demonstrate the
capabilities of our implementation by characterizing sub-nm deterministic flows
of 20 nm gold nanoparticles at liquid-liquid interfaces. Our results approach
the optimal combination of background suppression, localisation precision and
temporal resolution achievable with pure scattering-based imaging and tracking
of nanoparticles at regular interfaces.


Abstract:
  We study the chaotic behavior of multidimensional Hamiltonian systems in the
presence of nonlinearity and disorder. It is known that any localized initial
excitation in a large enough linear disordered system spreads for a finite
amount of time and then halts forever. This phenomenon is called Anderson
localization (AL). What happens to AL when nonlinearity is introduced is an
interesting question which has been considered in several studies over the past
decades. However, the characteristics and the asymptotic fate of such
evolutions still remain an issue of intense debate due to their computational
difficulty, especially in systems of more than one spatial dimension. As the
spreading of initially localized wave packets is a non-equilibrium
thermalization process related to the ergodic and chaotic properties of the
system, in our work we investigate the properties of chaos studying the
behavior of observables related to the system's tangent dynamics. In
particular, we consider the disordered discrete nonlinear Schr\"odinger (DDNLS)
equation of one (1D) and two (2D) spatial dimensions. We present detailed
computations of the time evolution of the system's maximum Lyapunov exponent
(MLE--$\Lambda$), and the related deviation vector distribution (DVD). We find
that although the systems' MLE decreases in time following a power law
$t^{\alpha_\Lambda}$ with $\alpha_\Lambda <0$ for both the weak and strong
chaos regimes, no crossover to the behavior $\Lambda \propto t^{-1}$ (which is
indicative of regular motion) is observed. In addition, the analysis of the
DVDs reveals the existence of random fluctuations of chaotic hotspots with
increasing amplitudes inside the excited part of the wave packet, which assist
in homogenizing chaos and contribute to the thermalization of more lattice
sites.


Abstract:
  This study investigates the origin and sustenance of self induced
oscillations of shock structures in a hypersonic flow over a double wedge
configuration. Previously, various researchers have considered the double wedge
flow configuration for inviscid flow with variations of different inflows as
well as geometric parameters such as inflow Mach number , wedge angles, and
wedge lengths. Few recently published articles reveal an unsteady flow physics
involved with the hypersonic viscous flow for double wedge configuration with
large second wedge angles. However, the reason for such self sustained flow
oscillations is not completely clear. The present work seeks out to investigate
the origin of such oscillations in a low enthalpy hypersonic flow with
different aft wedge angles and wedge length ratios.In the current study,
viscous flow over a double wedge at Mach 7 and fore wedge angle of 30{\deg} is
considered. An improved version of rhoCentralFoam solver in OpenFOAM is used to
investigate the double wedge flow over different grid resolutions in the
separation region and shock shock interaction region. This study corroborates
the observation from the previous literature with an improvement in the range
of parameters which results in a self sustained periodic oscillation. The
present study also suggests that the unsteadiness becomes possible when the
incidence shock is in the proximity of the aft wedge expansion corner as a
consequence of different wedge length ratios(L1/L2) or aft wedge angles
({\theta}2). Flow can still be steady at a large aft wedge angle if the
incidence shock is far ahead of the aft wedge expansion corner.


Abstract:
  Is a logicist bound to the claim that as a matter of analytic truth there is
an actual infinity of objects? If Hume's Principle is analytic then in the
standard setting the answer appears to be yes. Hodes's work pointed to a way
out by offering a modal picture in which only a potential infinity was posited.
However, this project was abandoned due to apparent failures of cross-world
predication. We re-explore this idea and discover that in the setting of the
potential infinite one can interpret first-order Peano arithmetic, but not
second-order Peano arithmetic. We conclude that in order for the logicist to
weaken the metaphysically loaded claim of necessary actual infinities, they
must also weaken the mathematics they recover.


Abstract:
  The general method of graph coarsening or graph reduction has been a
remarkably useful and ubiquitous tool in scientific computing and it is now
just starting to have a similar impact in machine learning. The goal of this
paper is to take a broad look into coarsening techniques that have been
successfully deployed in scientific computing and see how similar principles
are finding their way in more recent applications related to machine learning.
In scientific computing, coarsening plays a central role in algebraic multigrid
methods as well as the related class of multilevel incomplete LU
factorizations. In machine learning, graph coarsening goes under various names,
e.g., graph downsampling or graph reduction. Its goal in most cases is to
replace some original graph by one which has fewer nodes, but whose structure
and characteristics are similar to those of the original graph. As will be
seen, a common strategy in these methods is to rely on spectral properties to
define the coarse graph.


Abstract:
  Standard meta-learning for representation learning aims to find a common
representation to be shared across multiple tasks. The effectiveness of these
methods is often limited when the nuances of the tasks' distribution cannot be
captured by a single representation. In this work we overcome this issue by
inferring a conditioning function, mapping the tasks' side information (such as
the tasks' training dataset itself) into a representation tailored to the task
at hand. We study environments in which our conditional strategy outperforms
standard meta-learning, such as those in which tasks can be organized in
separate clusters according to the representation they share. We then propose a
meta-algorithm capable of leveraging this advantage in practice. In the
unconditional setting, our method yields a new estimator enjoying faster
learning rates and requiring less hyper-parameters to tune than current
state-of-the-art methods. Our results are supported by preliminary experiments.


Abstract:
  In their recent paper titled "Large Associative Memory Problem in
Neurobiology and Machine Learning" [arXiv:2008.06996] the authors gave a
biologically plausible microscopic theory from which one can recover many dense
associative memory models discussed in the literature. We show that the layers
of the recent "MLP-mixer" [arXiv:2105.01601] as well as the essentially
equivalent model in [arXiv:2105.02723] are amongst them.


Abstract:
  This paper presents a generic feature-based navigation framework for
autonomous vehicles using a soft constrained Particle Filter. Selected map
features, such as road and landmark locations, and vehicle states are used for
designing soft constraints. After obtaining features of mapped landmarks in
instance-based segmented images acquired from a monocular camera,
vehicle-to-landmark distances are predicted using Gaussian Process Regression
(GPR) models in a mixture of experts approach. Both mean and variance outputs
of GPR models are used for implementing adaptive constraints. Experimental
results confirm that the use of image segmentation features improves the
vehicle-to-landmark distance prediction notably, and that the proposed soft
constrained approach reliably localizes the vehicle even with reduced number of
landmarks and noisy observations.


Abstract:
  We present a comprehensive study of a model system of repulsive
self-propelled disks in two dimensions with ferromagnetic and nematic velocity
alignment interactions. We characterize the phase behavior of the system as a
function of the alignment and self-propulsion strength, featuring orientational
order for strong alignment and Motility-Induced Phase Separation (MIPS) at
moderate alignment but high enough self-propulsion. We derive a microscopic
theory for these systems yielding a close set of hydrodynamic equations from
which we perform a linear stability analysis of the homogenous disordered
state. This analysis predicts MIPS in the presence of aligning torques. The
nature of the continuum theory allows for an explicit quantitative comparison
with particle-based simulations, which consistently shows that ferromagnetic
alignment fosters phase separation, while nematic alignment does not alter
either the nature or the location of the instability responsible for it. In the
ferromagnetic case, such behavior is due to an increase of the imbalance of the
number of particle collisions along different orientations, giving rise to the
self-trapping of particles along their self-propulsion direction. On the
contrary, the anisotropy of the pair correlation function, which encodes this
self-trapping effect, is not significantly affected by nematic torques. Our
work shows the predictive power of such microscopic theories to describe
complex active matter systems with different interaction symmetries and sheds
light on the impact of velocity-alignment interactions in Motility-Induced
Phase Separation.


Abstract:
  Recently a new kind of quintessential inflation coming from the Lorentzian
distribution has been introduced in [1,2]. The model leads to a very simple
potential, which basically depends on two parameters, belonging to the class of
$\alpha$-attractors and depicting correctly the early and late time
accelerations of our universe. The potential emphasizes a {\it cosmological
seesaw mechanism} (CSSM) that produces a large inflationary vacuum energy in
one side of the potential and a very small value of dark energy on the right
hand side of the potential. {Here we show that the model agrees with the recent
observations and with the reheating constraints. Therefore the model gives a
reasonable scenario beyond the standard $\Lambda$CDM that includes the
inflationary epoch.}


Abstract:
  Exclusive electro-weak processes have peculiar features which make them
complementary to usually discussed deeply virtual electroproduction processes
such as deep virtual Compton scattering or meson production (and the
corresponding crossed reactions). They allow in particular single charmed meson
production, which we study in two different contexts : electroproduction at an
electron ion collider and neutrino-production at a medium energy neutrino
facility. We rely on the QCD collinear factorization framework where
generalized parton distributions allow physicists to perform a nucleon
tomography.


Abstract:
  The rules governing the essentially algebraic notion of a category with
families have been observed (independently) by Steve Awodey and Marcelo Fiore
to precisely match those of a representable natural transformation between
presheaves. This provides us with a natural, functorial description of
essentially algebraic objects which are used to model dependent type theory;
following Steve Awodey, we call them 'natural models'.
  We can view natural models from several different viewpoints, of which we
focus on three in this thesis. First, natural models are essentially algebraic,
meaning that they can be described by specifying operations between sorts,
subject to equational axioms; this allows us to assemble natural models into a
category with certain beneficial properties. Second, since natural models are
natural transformations between presheaves, they are morphisms in a locally
cartesian closed category, meaning that they can be regarded as polynomials.
Third, since natural models admit interpretations of dependent type theory, we
can use them to provide a functorial semantics.


Abstract:
  System behavior is often expressed by causal relations in requirements (e.g.,
If event 1, then event 2). Automatically extracting this embedded causal
knowledge supports not only reasoning about requirements dependencies, but also
various automated engineering tasks such as seamless derivation of test cases.
However, causality extraction from natural language is still an open research
challenge as existing approaches fail to extract causality with reasonable
performance. We understand causality extraction from requirements as a two-step
problem: First, we need to detect if requirements have causal properties or
not. Second, we need to understand and extract their causal relations. At
present, though, we lack knowledge about the form and complexity of causality
in requirements, which is necessary to develop a suitable approach addressing
these two problems. We conduct an exploratory case study with 14,983 sentences
from 53 requirements documents originating from 18 different domains and shed
light on the form and complexity of causality in requirements. Based on our
findings, we develop a tool-supported approach for causality detection (CiRA).
This constitutes a first step towards causality extraction from NL
requirements. We report on a case study and the resulting tool-supported
approach for causality detection in requirements. Our case study corroborates,
among other things, that causality is, in fact, a widely used linguistic
pattern to describe system behavior, as about a third of the analyzed sentences
are causal. We further demonstrate that our tool CiRA achieves a macro-F1 score
of 82 % on real word data and that it outperforms related approaches with an
average gain of 11.06 % in macro-Recall and 11.43 % in macro-Precision.
Finally, we disclose our open data sets as well as our tool to foster the
discourse on the automatic detection of causality in the RE community.


Abstract:
  The catch-up effect and the Matthew effect offer opposing characterizations
of globalization: the former predicts an eventual convergence as the poor can
grow faster than the rich due to free exchanges of complementary resources,
while the latter, a deepening inequality between the rich and the poor. To
understand these effects on the globalization of research, we conduct an
in-depth study based on scholarly and patent publications covering STEM
research from 218 countries/regions over the past four decades, covering more
than 55 million scholarly articles and 1.7 billion citations. Unique to this
investigation is the simultaneous examination of both the research output and
its impact in the same data set, using a novel machine learning based measure,
called saliency, to mitigate the intrinsic biases in quantifying the research
impact. The results show that the two effects are in fact co-occurring: there
are clear indications of convergence among the high income and upper middle
income countries across the STEM fields, but a widening gap is developing that
segregates the lower middle and low income regions from the higher income
regions. Furthermore, the rate of convergence varies notably among the STEM
sub-fields, with the highly strategic area of Artificial Intelligence (AI)
sandwiched between fields such as Medicine and Materials Science that occupy
the opposite ends of the spectrum. The data support the argument that a leading
explanation of the Matthew effect, namely, the preferential attachment theory,
can actually foster the catch-up effect when organizations from lower income
countries forge substantial research collaborations with those already
dominant. The data resoundingly show such collaborations benefit all parties
involved, and a case of role reversal can be seen in the Materials Science
field where the most advanced signs of convergence are observed.


Abstract:
  Employing the ultrafast control of electronic states of a semiconductor
quantum dot in a cavity, we introduce a novel approach to achieve on-demand
emission of single photons with almost perfect indistinguishability and photon
pairs with near ideal entanglement. Our scheme is based on optical excitation
off-resonant to a cavity mode followed by ultrafast control of the electronic
states using the time-dependent quantum-confined Stark effect, which then
allows for cavity-resonant emission. Our theoretical analysis takes into
account cavity-loss mechanisms, the Stark effect, and phonon-induced dephasing
allowing realistic predictions for finite temperatures.


Abstract:
  We show here how, using Euler's integration method and an associated function
bounding the error in function of time, one can generate structures closely
surrounding the invariant tori of dynamical systems. Such structures are
constructed from a finite number of balls of $\mathbb{R}^n$ and encompass the
deformations of the tori when small perturbations of the flow of the system
occur.


Abstract:
  We simulate neutrino-antineutrino oscillations caused by strong magnetic
fields in dense matter. With the strong magnetic fields and large neutrino
magnetic moments, Majorana neutrinos can reach flavor equilibrium. We find that
the flavor equilibration of neutrino-antineutrino oscillations is sensitive to
the values of the baryon density and the electron fraction inside the matter.
The neutrino-antineutrino oscillations are suppressed in the case of the large
baryon density in neutron (proton)-rich matter. On the other hand, the flavor
equilibration occurs when the electron fraction is close to $0.5$ even in the
large baryon density. From the simulations, we propose a necessary condition
for the equilibration of neutrino-antineutrino oscillations in dense matter. We
also study whether such necessary condition is satisfied near the proto-neutron
star by using results of neutrino hydrodynamic simulations of core-collapse
supernovae. In our explosion model, the flavor equilibration would be possible
if the magnetic field on the surface of the proto-neutron star is larger than
$10^{14}$ G which is the typical value of the magnetic fields of magnetars.


Abstract:
  The spiking neural network (SNN) has been attracting considerable attention
not only as a mathematical model for the brain, but also as an energy-efficient
information processing model for real-world applications. In particular, SNNs
based on temporal coding are expected to be much more efficient than those
based on rate coding, because the former requires substantially fewer spikes to
carry out tasks. As SNNs are continuous-state and continuous-time models, it is
favorable to implement them with analog VLSI circuits. However, the
construction of the entire system with continuous-time analog circuits would be
infeasible when the system size is very large. Therefore, mixed-signal circuits
must be employed, and the time discretization and quantization of the synaptic
weights are necessary. Moreover, the analog VLSI implementation of SNNs
exhibits non-idealities, such as the effects of noise and device mismatches, as
well as other constraints arising from the analog circuit operation. In this
study, we investigated the effects of the time discretization and/or weight
quantization on the performance of SNNs. Furthermore, we elucidated the effects
the lower bound of the membrane potentials and the temporal fluctuation of the
firing threshold. Finally, we propose an optimal approach for the mapping of
mathematical SNN models to analog circuits with discretized time.


Abstract:
  The small GTPases Rac and Rho are known to regulate eukaryotic cell shape,
promoting front protrusion (Rac) or rear retraction (Rho) of the cell edge.
Such cell deformation changes the contact and adhesion of cell to the
extracellular matrix (ECM), while ECM signaling through integrin receptors also
affects GTPase activity. We develop and investigate a model for this three-way
feedback loop in 1D and 2D spatial domains, as well as in a fully deforming 2D
cell shape. The model consists of reaction-diffusion equations solved
numerically with open-source software, Morpheus, and with custom-built cellular
Potts model simulations. We find a variety of patterns and cell behaviors,
including persistent polarity, flipped front-back cell polarity oscillations,
and random protrusion-retraction. We show that the observed spatial patterns
depend on the cell shape, and vice versa. The cell stiffness and biophysical
properties also affect patterning, overall cell migration phenotypes.


Abstract:
  We study the propagation of a massless scalar wave in de Sitter spacetime
perturbed by an arbitrary central mass. By focusing on the late time limit,
this probes the portion of the scalar signal traveling inside the null cone.
Unlike in asymptotically flat spacetimes, the amplitude of the scalar field
detected by an observer at timelike infinity does not decay back to zero but
develops a spacetime constant shift - both at zeroth and first order in the
central mass M. This indicates that massless scalar field propagation in
asymptotically de Sitter spacetimes exhibits both linear and nonlinear
tail-induced memories. On the other hand, for sufficiently late retarded times,
the monopole portion of the scalar signal measured at null infinity is found to
be amplified relative to its timelike infinity counterpart, by its nonlinear
interactions with the gravitation field at first order in M.


Abstract:
  The helicity of a magnetic field is a fundamental property that is conserved
in ideal MHD. It can be explored in the stellar context by mapping large-scale
magnetic fields across stellar surfaces using Zeeman-Doppler imaging. A recent
study of 51 stars in the mass range 0.1-1.34 M$_\odot$ showed that the
photospheric magnetic helicity density follows a single power law when plotted
against the toroidal field energy, but splits into two branches when plotted
against the poloidal field energy. These two branches divide stars above and
below $\sim$ 0.5 M$_\odot$. We present here a novel method of visualising the
helicity density in terms of the linkage of the toroidal and poloidal fields
that are mapped across the stellar surface. This approach allows us to classify
the field linkages that provide the helicity density for stars of different
masses and rotation rates. We find that stars on the lower-mass branch tend to
have toroidal fields that are non-axisymmetric and so link through regions of
positive and negative poloidal field. A lower-mass star may have the same
helicity density as a higher-mass star, despite having a stronger poloidal
field. Lower-mass stars are therefore less efficient at generating large-scale
helicity.


Abstract:
  Fuzzy Dark Matter (FDM), consisting of ultralight bosons ($m_{\rm b} \sim
10^{-22}\ \rm eV$), is an intriguing alternative to Cold Dark Matter. Numerical
simulations that solve the Schr\"odinger-Poisson (SP) equation show that FDM
halos consist of a central solitonic core, which is the ground state of the SP
equation, surrounded by an envelope of interfering excited states. These
excited states also interfere with the soliton, causing it to oscillate and
execute a confined random walk with respect to the halo center of mass. Using
high-resolution numerical simulations of a $6.6 \times 10^9 M_{\odot}$ FDM halo
with $m_{\rm b} = 8 \times 10^{-23}\ \rm eV$ in isolation, we demonstrate that
the wobbling, oscillating soliton gravitationally perturbs nuclear objects,
such as supermassive black holes or dense star clusters, causing them to
diffuse outwards. In particular, we show that, on average, objects with mass
$\lesssim 0.3 \%$ of the soliton mass ($M_{\rm sol}$) are expelled from the
soliton in $\sim 3\ \rm Gyr$, after which they continue their outward diffusion
due to gravitational interactions with the soliton and the halo granules. More
massive objects ($\gtrsim 1 \% M_{\rm sol}$), while executing a random walk,
remain largely confined to the soliton due to dynamical friction. We also
present an effective treatment of the diffusion, based on kinetic theory, that
accurately reproduces the outward motion of low mass objects and briefly
discuss how the observed displacements of star clusters and active galactic
nuclei from the centers of their host galaxies can be used to constrain FDM.


Abstract:
  Speaker recognition deals with recognizing speakers by their speech. Most
speaker recognition systems are built upon two stages, the first stage extracts
low dimensional correlation embeddings from speech, and the second performs the
classification task. The robustness of a speaker recognition system mainly
depends on the extraction process of speech embeddings, which are primarily
pre-trained on a large-scale dataset. As the embedding systems are pre-trained,
the performance of speaker recognition models greatly depends on domain
adaptation policy, which may reduce if trained using inadequate data. This
paper introduces a speaker recognition strategy dealing with unlabeled data,
which generates clusterable embedding vectors from small fixed-size speech
frames. The unsupervised training strategy involves an assumption that a small
speech segment should include a single speaker. Depending on such a belief, a
pairwise constraint is constructed with noise augmentation policies, used to
train AutoEmbedder architecture that generates speaker embeddings. Without
relying on domain adaption policy, the process unsupervisely produces
clusterable speaker embeddings, termed unsupervised vectors (u-vectors). The
evaluation is concluded in two popular speaker recognition datasets for English
language, TIMIT, and LibriSpeech. Also, a Bengali dataset is included to
illustrate the diversity of the domain shifts for speaker recognition systems.
Finally, we conclude that the proposed approach achieves satisfactory
performance using pairwise architectures.


Abstract:
  We show that lenders face more uncertainty when assessing default risk of
historically under-served groups in US credit markets and that this information
disparity is a quantitatively important driver of inefficient and unequal
credit market outcomes. We first document that widely used credit scores are
statistically noisier indicators of default risk for historically under-served
groups. This noise emerges primarily through the explanatory power of the
underlying credit report data (e.g., thin credit files), not through issues
with model fit (e.g., the inability to include protected class in the scoring
model). Estimating a structural model of lending with heterogeneity in
information, we quantify the gains from addressing these information
disparities for the US mortgage market. We find that equalizing the precision
of credit scores can reduce disparities in approval rates and in credit
misallocation for disadvantaged groups by approximately half.


Abstract:
  Let $K = R$ or $C$. We study basic invariants of submanifolds of solutions
$\mathcal{M} = \{ y = Q(x,a,b)\} = \{b = P(a,x,y)\}$ in coordinates $x \in
K^{n\geqslant 1}$, $y \in K$, $a \in K^{m\geqslant 1}$, $b \in K$ under
split-diffeomorphisms $(x,y,a,b) \,\longmapsto\, \big(
f(x,y),\,g(x,y),\,\varphi(a,b),\,\psi(a,b) \big)$. Two Levi forms exist, and
have the same rank $r \leqslant \min (n,m)$. If $\mathcal{M}$ is
$k$-nondegenerate with respect to parameters and $l$-nondegenerate with respect
to variables, $\mbox{Aut}(\mathcal{M})$ is a local Lie group of dimension: \[
\dim\, \mbox{Aut} (\mathcal{M}) \,\,\leqslant\,\,
{\textstyle{\binom{n+1+2k+2l}{2k+2l}}}\,\, \min\, \big\{ (n+1),\, (m+1) \big\}.
\] Mainly, our goal is to set up foundational material addressed to CR
geometers. We focus on $n = m = 2$, assuming $r = 1$. In coordinates $(x,y,z,
a,b,c)$, a local equation is: \[ z \,=\, c + xa + \beta\,xxb +
\underline{\beta}\,yaa + c\,{\rm O}_{x,y,a,b}(2) + {\rm O}_{x,y,a,b,c}(4), \]
with $\beta$ and $\underline{\beta}$ representing the two $2$-nondegeneracy
invariants at $0$. The associated para-CR PDE system: \[ z_y \,=\,
\big(x,y,z,z_x,z_{xx}\big) \ \ \ \ \ \ \ \ \ \ \ \ \ \& \ \ \ \ \ \ \ \ \ \ \ \
\ z_{xxx} \,=\, H\big(x,y,z,z_x,z_{xx}\big), \] satisfies $F_{z_{xx}} \equiv 0$
from Levi degeneracy. We show in details that the hypothesis of
$2$-nondegeneracy with respect to variables is equivalent to $F_{z_x z_x} \neq
0$. This gives CR-geometric meaning to the first two para-CR relative
differential invariants encountered independently in arXiv:2003.08166 .


Abstract:
  We develop a statistical model for the testing of disease prevalence in a
population. The model assumes a binary test result, positive or negative, but
allows for biases in sample selection and both type I (false positive) and type
II (false negative) testing errors. Our model also incorporates multiple test
types and is able to distinguish between retesting and exclusion after testing.
Our quantitative framework allows us to directly interpret testing results as a
function of errors and biases. By applying our testing model to COVID-19
testing data and actual case data from specific jurisdictions, we are able to
estimate and provide uncertainty quantification of indices that are crucial in
a pandemic, such as disease prevalence and fatality ratios.


Abstract:
  In this paper, the problem on formation and construction of a
multidimensional shock wave is studied for the first order conservation law
$\partial_t u+\partial_x F(u)+\partial_y G(u)=0$ with smooth initial data
$u_0(x,y)$. It is well-known that the smooth solution $u$ will blow up on the
time $T^*=-\frac{1}{\min{H(\xi,\eta)}}$ when $\min{H(\xi,\eta})<0$ holds for
$H(\xi,\eta)=\partial_{\xi}(F'(u_0(\xi,\eta)))+\partial_{\eta}(G'(u_0(\xi,\eta)))$,
more precisely, only the first order derivatives $\nabla_{t,x,y}u$ blow up on
$t=T^*$ meanwhile $u$ itself is still continuous until $t=T^*$. Under the
generic nondegenerate condition of $H(\xi,\eta)$, we construct a local weak
entropy solution $u$ for $t\ge T^*$ which is not uniformly Lipschitz continuous
on two sides of a shock surface $\Sigma$. The strength of the constructed shock
is zero on the initial blowup curve $\Gamma$ and then gradually increases for
$t>T^*$. Additionally, in the neighbourhood of $\Gamma$, some detailed and
precise descriptions on the singularities of solution $u$ are given.


Abstract:
  We study the task of clustering in directed networks. We show that using the
eigenvalue/eigenvector decomposition of the adjacency matrix is simpler than
all common methods which are based on a combination of data regularization and
SVD truncation, and works well down to the very sparse regime where the edge
density has constant order. Our analysis is based on a Master Theorem
describing sharp asymptotics for isolated eigenvalues/eigenvectors of sparse,
non-symmetric matrices with independent entries. We also describe the limiting
distribution of the entries of these eigenvectors; in the task of digraph
clustering with spectral embeddings, we provide numerical evidence for the
superiority of Gaussian Mixture clustering over the widely used k-means
algorithm.


Abstract:
  We present ground-based optical transmission spectroscopy of the low-density
hot Jupiter WASP-88b covering the wavelength range 4413-8333 {\AA} with the
FORS2 spectrograph on the Very Large Telescope. The FORS2 white light curves
exhibit a significant time-correlated noise which we model using a Gaussian
Process and remove as a wavelength-independent component from the spectroscopic
light curves. We analyse complementary photometric observations from the
Transiting Exoplanet Survey Satellite and refine the system properties and
ephemeris. We find a featureless transmission spectrum with increased
absorption towards shorter wavelengths. We perform an atmospheric retrieval
analysis with the AURA code, finding tentative evidence for haze in the upper
atmospheric layers and a lower likelihood for a dense cloud deck. Whilst our
retrieval analysis results point toward clouds and hazes, further evidence is
needed to definitively reject a clear-sky scenario.


Abstract:
  Behavior of quantum liquids is a fascinating topic in physics. Even in a
strongly correlated case, the linear response of a given system to an external
field is described by the fluctuation-dissipation relations based on the
two-body correlations in the equilibrium. However, to explore nonlinear
non-equilibrium behaviors of the system beyond this well-established regime,
the role of higher order correlations starting from the three-body correlations
must be revealed. In this work, we experimentally investigate a controllable
quantum liquid realized in a Kondo-correlated quantum dot and prove the
relevance of the three-body correlations in the nonlinear conductance at finite
magnetic field, which validates the recent Fermi liquid theory extended to the
non-equilibrium regime.


Abstract:
  Healthy cartilage is a remarkable tissue, able to withstand tens of millions
of loading cycles with minimal damage. While much is known about the structural
origins of its compressive mechanics, how composition determines its mechanical
behavior in shear, a major mode of failure, is poorly understood. Through a
combination of microscale structure-function experiments and modeling, we
develop a rigidity percolation framework to explain the structural origins of
cartilage shear mechanics. This framework provides a new quantitative
understanding for how the known degradative events in osteoarthritis determine
the mechanical changes that are a hallmark of this disease. As such, this work
provides a road map for understanding disease progression and in combination
with non-invasive techniques such as MRI will enable more effective diagnosis
and treatment.


Abstract:
  We consider an age-size structured cell population model based on the cell
cycle length. The model is described by a first order partial differential
equation with initial-boundary conditions. Using the theory of semigroups of
positive operators we establish new criteria for an asynchronous exponential
growth of solutions to such equations. We discuss the question of exponential
size growth of cells. We study in detail a constant size growth model and a
model with target size division. We also present versions of the model when the
population is heterogeneous.


Abstract:
  Violation of the Wiedemann Franz law through decoupling the charge and heat
transports in a material not only leads to new fundamental physics, but also is
a boon for many of the advanced materials including thermoelectric materials
for achieving their novel or superior properties. Here, we demonstrate this in
nickel nanoparticles with incredible enhancement in Lorentz number to several
orders of magnitude as size drops. This is in stark contrast to Fermi liquid
behavior of conventional metals, revealing the compelling confirmation for
unconventional quasiparticle dynamics where charge and heat transport
independent of each other.


Abstract:
  In this preliminary (and unpolished) version of the paper, we study an
asynchronous online learning setting with a network of agents. At each time
step, some of the agents are activated, requested to make a prediction, and pay
the corresponding loss. Some feedback is then revealed to these agents and is
later propagated through the network. We consider the case of full, bandit, and
semi-bandit feedback. In particular, we construct a reduction to delayed
single-agent learning that applies to both the full and the bandit feedback
case and allows to obtain regret guarantees for both settings. We complement
these results with a near-matching lower bound.


Abstract:
  We have recently proposed two pile loading controllers that learn from human
demonstrations: a neural network (NNet) [1] and a random forest (RF) controller
[2]. In the field experiments the RF controller obtained clearly better success
rates. In this work, the previous findings are drastically revised by
experimenting summer time trained controllers in winter conditions. The winter
experiments revealed a need for additional sensors, more training data, and a
controller that can take advantage of these. Therefore, we propose a revised
neural controller (NNetV2) which has a more expressive structure and uses a
neural attention mechanism to focus on important parts of the sensor and
control signals. Using the same data and sensors to train and test the three
controllers, NNetV2 achieves better robustness against drastically changing
conditions and superior success rate. To the best of our knowledge, this is the
first work testing a learning-based controller for a heavy-duty machine in
drastically varying outdoor conditions and delivering high success rate in
winter, being trained in summer.


Abstract:
  The high cost of density functional theory has hitherto limited the ab initio
prediction of equation of state (EOS). In this article, we employ a combination
of large scale computing, advanced simulation techniques, and smart data
science strategies to provide an unprecedented, ab initio performance analysis
of the high explosive pentaerythritol tetranitrate (PETN). Comparison to both
experiment and thermochemical predictions reveals important quantitative
limitations of DFT for EOS prediction, and thus the assessment of high
explosives. In particular, we find DFT predicts the energy of PETN detonation
products to be systematically too high relative to the unreacted neat
crystalline material, resulting in an underprediction of the detonation
velocity, pressure, and temperature at the Chapman-Jouguet (CJ) state. The
energetic bias can be partially accounted for by high-level electronic
structure calculations of the product molecules. We also demonstrate a modeling
strategy for mapping chemical composition across a wide parameter space with
limited numerical data, the results of which suggest additional molecular
species to consider in thermochemical modeling.


Abstract:
  In many industrial applications, rubber-based materials are routinely used in
conjunction with various penetrants or diluents in gaseous or liquid form. It
is of interest to estimate theoretically the penetration depth as well as the
amount of diffusants stored inside the material. In this framework, we prove
the global solvability and explore the large time-behavior of solutions to a
one-phase free boundary problem with nonlinear kinetic condition that is able
to describe the migration of diffusants into rubber. The key idea in the proof
of the large time behavior is to benefit of a contradiction argument, since it
is difficult to obtain uniform estimates for the growth rate of the free
boundary due to the use of a Robin boundary condition posed at the fixed
boundary.


Abstract:
  Student evaluations of teaching (SET) are commonly used in universities for
assessing teaching quality. However, previous literature shows that in software
engineering students tend to rate certain topics higher than others: In
particular students tend to value programming and software construction over
software design, software engineering models and methods, or soft skills. We
hypothesize that these biases also play a role in SET responses collected from
students. The objective of this study is to investigate how the topic of a
software engineering course affects the SET metrics. We accomplish this by
performing multilevel regression analysis on SET data collected in a software
engineering programme. We analyzed a total of 1295 student evaluations from 46
university courses in a Finnish university. The results of the analysis
verifies that the student course evaluations exhibit similar biases as
distinguished by previous software engineering education research. The type of
the course can predict a higher SET rating. In our dataset, software
construction and programming courses received higher SET ratings compared to
courses on software engineering processes, models, and methods.


Abstract:
  We consider the problem of learning structures and parameters of
Continuous-time Bayesian Networks (CTBNs) from time-course data under minimal
experimental resources. In practice, the cost of generating experimental data
poses a bottleneck, especially in the natural and social sciences. A popular
approach to overcome this is Bayesian optimal experimental design (BOED).
However, BOED becomes infeasible in high-dimensional settings, as it involves
integration over all possible experimental outcomes. We propose a novel
criterion for experimental design based on a variational approximation of the
expected information gain. We show that for CTBNs, a semi-analytical expression
for this criterion can be calculated for structure and parameter learning. By
doing so, we can replace sampling over experimental outcomes by solving the
CTBNs master-equation, for which scalable approximations exist. This alleviates
the computational burden of sampling possible experimental outcomes in
high-dimensions. We employ this framework in order to recommend interventional
sequences. In this context, we extend the CTBN model to conditional CTBNs in
order to incorporate interventions. We demonstrate the performance of our
criterion on synthetic and real-world data.


Abstract:
  Over the complex numbers, there are 92 plane conics meeting 8 general lines
in projective 3-space. Using the Euler class and local degree from motivic
homotopy theory, we give an enriched version of this result over any perfect
field. This provides a weighted count of the number of plane conics meeting 8
general lines, where the weight of each conic is determined the geometry of its
intersections with the 8 given lines. As a corollary, real conics meeting 8
general lines come in two families of equal size.


Abstract:
  This paper studies the optimal state estimation problem for interconnected
systems. Each subsystem can obtain its own measurement in real time, while, the
measurements transmitted between the subsystems suffer from random delay. The
optimal estimator is analytically designed for minimizing the conditional error
covariance. Due to the random delay, the error covariance of the estimation is
random. The boundedness of the expected error covariance (EEC) is analyzed. In
particular, a new condition that is easy to verify is established for the
boundedness of EEC. Further, the properties about EEC with respect to the delay
probability is studied. We found that there exists a critical probability such
that the EEC is bounded if the delay probability is below the critical
probability. Also, a lower and upper bound of the critical probability is
effectively computed. Finally, the proposed results are applied to a power
system, and the effectiveness of the designed methods is illustrated by
simulations.


Abstract:
  Chromates are widely used for their anticorrosive properties. Unfortunately,
they are highly hazardous with environmental agencies regulating their levels
to below 10 ppb in drinking water. As anion exchange resins are typically used
for removal, predictive dynamic models are necessary to make quick decisions
rather than relying on experimental data that could take several days to
implement. With various dynamic models currently applied to simulate the ion
exchange process, the Thomas model was picked for its simplicity and better
accuracy when compared to other models. The Thomas model contains two
parameters, the constant (KT) and the maximum resin capacity (qm), which are
empirically calculated. Unfortunately, the model demonstrated large parameter
fluctuations with no correlation to varying contact times or inlet chromate
concentrations. Therefore, fixing both parameters will lead to failed model
predictive behavior. By fixing the value of qm and proposing a linear
relationship of KT with resin contact time and inlet chromate concentration,
the accuracy of the model was improved five-fold, demonstrating its potential
for better process controls.


Abstract:
  A new method of reaction analysis for proton elastic scattering is proposed,
combining systematic analyses of nuclear structure and reactions in a series of
isotopes. This method is applied to $^{204}$Pb$(p,p)$, $^{206}$Pb$(p,p)$, and
$^{208}$Pb$(p,p)$ at $E_p=295$ MeV to obtain improved neutron densities and
radii from experimental cross section data. The reaction calculation is
performed according to the relativistic impulse approximation using the
modified Murdock and Horowitz model with density-dependent effective $NN$
interaction. Analysis of Pb isotopes is performed using theoretical densities
given by the relativistic Hartree-Bogoliubov and nonrelativistic Skyrme
Hartree-Fock-Bogoliubov calculations and the experimental density extracted
from the $(p,p)$ data at 295 MeV. The isotopic ratios ($R(\sigma)$) of the
$^{A}$Pb$(p,p)$-to-$^{206}$Pb$(p,p)$ cross sections are analyzed in connection
with the isotopic differences ($D(\rho_n)$ and $D(r_n)$) in neutron densities
$(\rho_n(r))$ and radii $(r_n)$ between $^A$Pb and $^{208}$Pb. A hole-model
analysis is performed, assuming $^{204}$Pb and $^{206}$Pb as a $^{208}$Pb core
and neutron holes to clarify the one-to-one correspondence between isotopic
structure properties such as $D(\rho_n)$ and $D(r_n)$ and the isotopic
cross-section ratio. By fitting $R(\sigma)$, the values of $D(\rho_n)$ and
$D(r_n)$ are extracted from the experimental $(p,p)$ cross section data with
less uncertainty of the structure and reaction models. The isotopic neutron
radius difference between $^{206}$Pb and $^{208}$Pb was obtained as
$D(r_n)=-0.012$ fm with an acceptable range of $D(r_n)=-0.03 \sim -0.006$ fm.


Abstract:
  We present a comprehensive analysis of the loop induced top quark FCNC
signals at the LHC within one class of the simplified model. The loop level
FCNC interactions are well motivated to avoid the hierarchy of the top quark
couplings from the new physics and standard model. Such a theory will posit a
Majorana dark matter candidate and could be tested through dark matter relic
density, direct detection experiments (the scattering between dark matter and
heavy nuclei), and the collider signals at the LHC. We find that the
spin-independent (SI) scattering between Majorana dark matter and nuclei will
vanish at the leading order, while the next-to-leading order correction to the
SI scattering becomes significance to constrain the parameter space of the
model. A detailed comparison from direct detection experiments and LHC searches
is also discussed and both of them are very important to full constrain the
model.


Abstract:
  We show that for any $d=d(n)$ with $d_0(\epsilon) \le d =o(n)$, with high
probability, the size of a largest induced cycle in the random graph $G(n,d/n)$
is $(2\pm \epsilon)\frac{n}{d}\log d$. This settles a long-standing open
problem in random graph theory.


Abstract:
  Conformation-dependent design of polymer sequences can be considered as a
tool to control macromolecular self-assembly. We consider the monomer unit
sequences created via the modification of polymers in a homogeneous melt in
accordance with the spatial positions of the monomer units. The geometrical
patterns of lamellae, hexagonally packed cylinders, and balls arranged in a
body-centered cubic lattice are considered as typical microphase-separated
morphologies of block copolymers. Random trajectories of polymer chains are
described by the diffusion-type equations and, in parallel, simulated in the
computer modeling. The probability distributions of block length $k$, which are
analogous to the first-passage probabilities, are calculated analytically and
determined from the computer simulations. In any domain, the probability
distribution can be described by the asymptote $~k^{-3/2}$ at moderate values
of $k$ if the spatial size of the block is less than the smallest
characteristic size of the domain. For large blocks, the exponential asymptote
$exp(-const \, k a^2/d_{as}^2)$ is valid, $d_{as}$ being the asymptotic domain
length (a is the monomer unit size). The number average block lengths and their
dispersities change linearly with the block length for lamellae, cylinders, and
balls, when the domain is characterized by a single characteristic size. If the
domain is described by more than one size, the number average block length can
grow nonlinearly with the domain sizes and the length das can depend on all of
them.


Abstract:
  Convolutional neural networks (CNNs) have shown outstanding performance on
image denoising with the help of large-scale datasets. Earlier methods naively
trained a single CNN with many pairs of clean-noisy images. However, the
conditional distribution of the clean image given a noisy one is too
complicated and diverse, so that a single CNN cannot well learn such
distributions. Therefore, there have also been some methods that exploit
additional noise level parameters or train a separate CNN for a specific noise
level parameter. These methods separate the original problem into easier
sub-problems and thus have shown improved performance than the naively trained
CNN. In this step, we raise two questions. The first one is whether it is an
optimal approach to relate the conditional distribution only to noise level
parameters. The second is what if we do not have noise level information, such
as in a real-world scenario. To answer the questions and provide a better
solution, we propose a novel Bayesian framework based on the variational
approximation of objective functions. This enables us to separate the
complicated target distribution into simpler sub-distributions. Eventually, the
denoising CNN can conquer noise from each sub-distribution, which is generally
an easier problem than the original. Experiments show that the proposed method
provides remarkable performance on additive white Gaussian noise (AWGN) and
real-noise denoising while requiring fewer parameters than recent
state-of-the-art denoisers.


Abstract:
  Human brain performs remarkably well in segregating a particular speaker from
interfering ones in a multi-speaker scenario. It has been recently shown that
we can quantitatively evaluate the segregation capability by modelling the
relationship between the speech signals present in an auditory scene and the
cortical signals of the listener measured using electroencephalography (EEG).
This has opened up avenues to integrate neuro-feedback into hearing aids
whereby the device can infer user's attention and enhance the attended speaker.
Commonly used algorithms to infer the auditory attention are based on linear
systems theory where the speech cues such as envelopes are mapped on to the EEG
signals. Here, we present a joint convolutional neural network (CNN) - long
short-term memory (LSTM) model to infer the auditory attention. Our joint
CNN-LSTM model takes the EEG signals and the spectrogram of the multiple
speakers as inputs and classifies the attention to one of the speakers. We
evaluated the reliability of our neural network using three different datasets
comprising of 61 subjects where, each subject undertook a dual-speaker
experiment. The three datasets analysed corresponded to speech stimuli
presented in three different languages namely German, Danish and Dutch. Using
the proposed joint CNN-LSTM model, we obtained a median decoding accuracy of
77.2% at a trial duration of three seconds. Furthermore, we evaluated the
amount of sparsity that our model can tolerate by means of magnitude pruning
and found that the model can tolerate up to 50% sparsity without substantial
loss of decoding accuracy.


Abstract:
  Combining the ideas of Riesz $s$-energy and $\log$-energy, we introduce the
so-called $s,\log^t$-energy. In this paper, we investigate the asymptotic
behaviors for $N,t$ fixed and $s$ varying of minimal $N$-point
$s,\log^t$-energy constants and configurations of an infinite compact metric
space of diameter less than $1$. In particular, we study certain continuity and
differentiability properties of minimal $N$-point $s,\log^t$-energy constants
in the variable $s$ and we show that in the limits as $s\rightarrow \infty$ and
as $s\rightarrow s_0>0,$ minimal $N$-point $s,\log^t$-energy configurations
tend to an $N$-point best-packing configuration and a minimal $N$-point
$s_0,\log^t$-energy configuration, respectively. Furthermore, the optimality of
$N$ distinct equally spaced points on circles in $\mathbb{R}^2$ for some
certain $s,\log^t$ energy problems was proved.


Abstract:
  Let $R$ be a commutative ring with identity and $S$ a multiplicatively closed
subset of $R$. This paper aims to introduce the concept of $S$-$n$-ideals as a
generalization of $n$-ideals. An ideal $I$ of $R$ disjoint with $S$ is called
an $S$-$n$-ideal if there exists $s\in S$ such that whenever $ab\in I$ for
$a,b\in R$, then $sa\in\sqrt{0}$ or $sb\in I$. The relationship among $S$%
-$n$-ideals, $n$-ideals, $S$-prime and $S$-primary ideals are clarified.
Several properties, characterizations and examples are presented such as
investigating $S$-$n$-ideals under various contexts of constructions including
direct products, localizations and homomorphic images. Furthermore, for $m\in%
%TCIMACRO{\U{2115} }% %BeginExpansion \mathbb{N} %EndExpansion $ and some
particular $S$, all $S$-$n$-ideals of the ring $% %TCIMACRO{\U{2124} }%
%BeginExpansion \mathbb{Z} %EndExpansion _{m}$ are completely determined. The
last section is devoted for studying the $S$-$n$-ideals of the idealization
ring and amalgamated algebra.


Abstract:
  In the recent decade, high-throughput plant phenotyping techniques, which
combine non-invasive image analysis and machine learning, have been
successfully applied to identify and quantify plant health and diseases.
However, these techniques usually do not consider the progressive nature of
plant stress and often require images showing severe signs of stress to ensure
high confidence detection, thereby reducing the feasibility for early detection
and recovery of plants under stress. To overcome the problem mentioned above,
we propose a deep learning pipeline for the temporal analysis of the visual
changes induced in the plant due to stress and apply it to the specific water
stress identification case in Chickpea plant shoot images. For this, we have
considered an image dataset of two chickpea varieties JG-62 and Pusa-372, under
three water stress conditions; control, young seedling, and before flowering,
captured over five months. We have employed a variant of Convolutional Neural
Network - Long Short Term Memory (CNN-LSTM) network to learn spatio-temporal
patterns from the chickpea plant dataset and use them for water stress
classification. Our model has achieved ceiling level classification performance
of 98.52% on JG-62 and 97.78% on Pusa-372 chickpea plant data and has
outperformed the best reported time-invariant technique by at least 14% for
both JG-62 and Pusa-372 species, to the best of our knowledge. Furthermore, our
CNN-LSTM model has demonstrated robustness to noisy input, with a less than
2.5% dip in average model accuracy and a small standard deviation about the
mean for both species. Lastly, we have performed an ablation study to analyze
the performance of the CNN-LSTM model by decreasing the number of temporal
session data used for training.


Abstract:
  The starting point of securing a network is having a concise overview of it.
As networks are becoming more and more complex both in general and with the
introduction of IoT technology and their topological peculiarities in
particular, this is increasingly difficult to achieve. Especially in
cyber-physical environments, such as smart factories, gaining a reliable
picture of the network can be, due to intertwining of a vast amount of devices
and different protocols, a tedious task. Nevertheless, this work is necessary
to conduct security audits, compare documentation with actual conditions or
found vulnerabilities using an attacker's view, for all of which a reliable
topology overview is pivotal. For security auditors, however, there might not
much information, such as asset management access, be available beforehand,
which is why this paper assumes network to audit as a complete black box. The
goal is therefore to set security auditors in a condition of, without having
any a priori knowledge at all, automatically gaining a topology oversight. This
paper describes, in the context of a bigger system that uses active scanning to
determine the network topology, an approach to automate the first steps of this
procedure: passively scanning the network and determining the network's scope,
as well as gaining a valid address to perform the active scanning. This allows
for bootstrapping an automatic network discovery process without prior
knowledge.


Abstract:
  The aim of this paper is to study the logarithmic submajorisations
inequalities for operators in a finite von Neumann algebra. Firstly, some
logarithmic submajorisations inequalities due to Garg and Aulja are extended to
the case of operators in a finite von Neumann algebra. As an application, we
get some new Fuglede-Kadison determinant inequalities of operators in that
circumstance. Secondly, we improve and generalize to the setting of finite von
Neumann algebras, a generalized H\"{o}lder type generalized singular numbers
inequality.


Abstract:
  The performance of deep reinforcement learning methods prone to degenerate
when applied to environments with non-stationary dynamics. In this paper, we
utilize the latent context recurrent encoders motivated by recent Meta-RL
materials, and propose the Latent Context-based Soft Actor Critic (LC-SAC)
method to address aforementioned issues. By minimizing the contrastive
prediction loss function, the learned context variables capture the information
of the environment dynamics and the recent behavior of the agent. Then combined
with the soft policy iteration paradigm, the LC-SAC method alternates between
soft policy evaluation and soft policy improvement until it converges to the
optimal policy. Experimental results show that the performance of LC-SAC is
significantly better than the SAC algorithm on the MetaWorld ML1 tasks whose
dynamics changes drasticly among different episodes, and is comparable to SAC
on the continuous control benchmark task MuJoCo whose dynamics changes slowly
or doesn't change between different episodes. In addition, we also conduct
relevant experiments to determine the impact of different hyperparameter
settings on the performance of the LC-SAC algorithm and give the reasonable
suggestions of hyperparameter setting.


Abstract:
  We consider the problem of under and over-approximating the image of general
vector-valued functions over bounded sets, and apply the proposed solution to
the estimation of reachable sets of uncertain non-linear discrete-time
dynamical systems. Such a combination of under and over-approximations is very
valuable for the verification of properties of embedded and cyber-physical
controlled systems. Over-approximations prove properties correct, while
under-approximations can be used for falsification. Coupled, they provide a
measure of the conservatism of the analysis. This work introduces a general
framework relying on computations of robust ranges of vector-valued functions.
This framework allows us to extend for under-approximation many precision
refinements that are classically used for over-approximations, such as affine
approximations, Taylor models, quadrature formulae and preconditioning methods.
We end by evaluating the efficiency and precision of our approach, focusing on
the application to the analysis of discrete-time dynamical systems with inputs
and disturbances, on different examples from the literature.


Abstract:
  A comparison was made between $Gaia$ magnitudes and magnitudes obtained from
ground-based observations for astrometric radio sources . The comparison showed
that these magnitudes often not agree well. There may be several reasons for
this disagreement. Nevertheless, such an analysis can serve as an additional
filter for verification of the object cross-identification. On the other hand,
it can help to detect possible errors in optical magnitudes of astrometric
radio sources coming from unreliable or inconsistent data sources.


Abstract:
  We generate high-order harmonics in gaseous medium with tunable photon energy
using time domain interferometry of double pulses in a non-collinear generation
geometry. The method is based on the fact that the generated harmonics inherit
certain spectral properties of the driving laser. The two temporally delayed
ultrashort laser pulses, identical in all parameters, are produced by a
custom-made split-and-delay unit utilizing wave front splitting without a
significant energy loss. The arrangement is easy to implement in any attosecond
pulse generation beamline, and is suitable for the production of an extreme
ultraviolet source with simply and quickly variable central photon energy,
useful for a broad range of applications.


Abstract:
  Let $G$ be a connected $n$-vertex graph in a proper minor-closed class
$\mathcal G$. We prove that the extension complexity of the spanning tree
polytope of $G$ is $O(n^{3/2})$. This improves on the $O(n^2)$ bounds following
from the work of Wong (1980) and Martin (1991). It also extends a result of
Fiorini, Huynh, Joret, and Pashkovich (2017), who obtained a $O(n^{3/2})$ bound
for graphs embedded in a fixed surface. Our proof works more generally for all
graph classes admitting strongly sublinear balanced separators: We prove that
for every constant $\beta$ with $0<\beta<1$, if $\mathcal G$ is a graph class
closed under induced subgraphs such that all $n$-vertex graphs in $\mathcal G$
have balanced separators of size $O(n^\beta)$, then the extension complexity of
the spanning tree polytope of every connected $n$-vertex graph in $\mathcal{G}$
is $O(n^{1+\beta})$. We in fact give two proofs of this result, one is a direct
construction of the extended formulation, the other is via communication
protocols. Using the latter approach we also give a short proof of the $O(n)$
bound for planar graphs due to Williams (2002).


Abstract:
  In this article, we prove new geometric integral inequalities for free
boundary hypersurfaces in the unit ball of a space form. We also give some
applications of these formula in order to obtain some rigidity results. For
instance, we are able to show, in the three dimensional case, a relationship
between the geometry of a hypersurface and the topology of its boundary.
Moreover, we also reobtain the classical Nitsche Theorem as well as its
generalisation for constant mean curvature surfaces in space forms balls, and
we provide a new point of view to the Catenoid Conjecture.


Abstract:
  Metric learning algorithms aim to learn a distance function that brings the
semantically similar data items together and keeps dissimilar ones at a
distance. The traditional Mahalanobis distance learning is equivalent to find a
linear projection. In contrast, Deep Metric Learning (DML) methods are proposed
that automatically extract features from data and learn a non-linear
transformation from input space to a semantically embedding space. Recently,
many DML methods are proposed focused to enhance the discrimination power of
the learned metric by providing novel sampling strategies or loss functions.
This approach is very helpful when both the training and test examples are
coming from the same set of categories. However, it is less effective in many
applications of DML such as image retrieval and person-reidentification. Here,
the DML should learn general semantic concepts from observed classes and employ
them to rank or identify objects from unseen categories. Neglecting the
generalization ability of the learned representation and just emphasizing to
learn a more discriminative embedding on the observed classes may lead to the
overfitting problem. To address this limitation, we propose a framework to
enhance the generalization power of existing DML methods in a Zero-Shot
Learning (ZSL) setting by general yet discriminative representation learning
and employing a class adversarial neural network. To learn a more general
representation, we propose to employ feature maps of intermediate layers in a
deep neural network and enhance their discrimination power through an attention
mechanism. Besides, a class adversarial network is utilized to enforce the deep
model to seek class invariant features for the DML task. We evaluate our work
on widely used machine vision datasets in a ZSL setting.


Abstract:
  Sheet cavitation appears in many hydraulic applicationss and can lead to
technical issues. Some fundamental outcomes such as the complex topology of
3-Dimensional cavitation pockets and their associated dynamics need to be
carefully visited.In the present paper, the dynamics of partial cavitation
developing in a 3-D Venturi geometry and the interaction with sidewalls are
numerically investigated. The simulations are performed usinf a one-fluid
compressible Reynolds-Averaged Navier-Stokes (RANS solver associated to a
non-linear turbulence model and a void transport-equation model. A detailed
analysis of this cavitating flow is carried out using innovative tools such as
Spectral Proper Orthogonal Decompositions. Particular attenttion is paid in the
study of 3-D effects by comparing numerical results obtained with sidewalls and
periodic conditions. A three-dimensional dynamics of the sheet cavitation,
unrelated to the presence of sidewalls, is identified and discussed.


Abstract:
  This paper addresses the dynamics of locally-resonant sandwich beams, where
multi-degree-of-freedom viscously-damped resonators are periodically
distributed within the core matrix. Using an equivalent single-layer Timoshenko
beam model coupled with mass-spring-dashpot subsystems representing the
resonators, two solution methods are presented. The first is a direct
integration method providing the exact frequency response under arbitrary
loads. The second is a complex modal analysis approach obtaining exact modal
impulse and frequency response functions, upon deriving appropriate
orthogonality conditions for the complex modes. The challenging issue of
calculating all eigenvalues, without missing anyone, is solved applying a
recently-introduced contour-integral algorithm to a characteristic equation
built as determinant of an exact frequency-response matrix, whose size is $4
\times 4$ regardless of the number of resonators. Numerical applications prove
exactness and robustness of the proposed solutions.


Abstract:
  Communication is a critical part of enabling multi-agent systems to
cooperate. This means that applying formal methods to protocols governing
communication within multi-agent systems provides useful confidence in its
reliability. In this paper, we describe the formal verification of a complex
communication protocol that coordinates agents merging maps of their
environment. The protocol was used by the LFC team in the 2019 edition of the
Multi-Agent Programming Contest (MAPC). Our specification of the protocol is
written in Communicating Sequential Processes (CSP), which is a well-suited
approach to specifying agent communication protocols due to its focus on
concurrent communicating systems. We validate the specification's behaviour
using scenarios where the correct behaviour is known, and verify that
eventually all the maps have merged.


Abstract:
  We argue that novel (highly nonclassical) quantum extremal surfaces play a
crucial role in reconstructing the black hole interior even for isolated,
single-sided, non-evaporating black holes (i.e. with no auxiliary reservoir).
Specifically, any code subspace where interior outgoing modes can be excited
will have a quantum extremal surface in its maximally mixed state. We argue
that as a result, reconstruction of interior outgoing modes is always
exponentially complex. Our construction provides evidence in favor of a strong
Python's lunch proposal: that nonminimal quantum extremal surfaces are the
exclusive source of exponential complexity in the holographic dictionary. We
also comment on the relevance of these quantum extremal surfaces to the
geometrization of state dependence in the typicality arguments for firewalls.


Abstract:
  Self-driving cars must detect other vehicles and pedestrians in 3D to plan
safe routes and avoid collisions. State-of-the-art 3D object detectors, based
on deep learning, have shown promising accuracy but are prone to over-fit to
domain idiosyncrasies, making them fail in new environments -- a serious
problem if autonomous vehicles are meant to operate freely. In this paper, we
propose a novel learning approach that drastically reduces this gap by
fine-tuning the detector on pseudo-labels in the target domain, which our
method generates while the vehicle is parked, based on replays of previously
recorded driving sequences. In these replays, objects are tracked over time,
and detections are interpolated and extrapolated -- crucially, leveraging
future information to catch hard cases. We show, on five autonomous driving
datasets, that fine-tuning the object detector on these pseudo-labels
substantially reduces the domain gap to new driving environments, yielding
drastic improvements in accuracy and detection reliability.


Abstract:
  Covariate-specific treatment effects (CSTEs) represent heterogeneous
treatment effects across subpopulations defined by certain selected covariates.
In this article, we consider marginal structural models where CSTEs are
linearly represented using a set of basis functions of the selected covariates.
We develop a new approach in high-dimensional settings to obtain not only
doubly robust point estimators of CSTEs, but also model-assisted confidence
intervals, which are valid when a propensity score model is correctly specified
but an outcome regression model may be misspecified. With a linear outcome
model and subpopulations defined by discrete covariates, both point estimators
and confidence intervals are doubly robust for CSTEs. In contrast, confidence
intervals from existing high-dimensional methods are valid only when both the
propensity score and outcome models are correctly specified. We establish
asymptotic properties of the proposed point estimators and the associated
confidence intervals. We present simulation studies and empirical applications
which demonstrate the advantages of the proposed method compared with competing
ones.


Abstract:
  In a recent paper (Hajdukovic 2020a) quantum vacuum was considered as a
source of gravity and, the simplest phenomenon, the gravitational polarization
of the quantum vacuum by an immersed point-like body, was studied. In the
present paper, we have derived the effective gravitational charge density of
the quantum vacuum, caused by two point-like bodies. Among others, the obtained
result proves that quantum vacuum can have regions with a negative effective
gravitational charge density. Hence, quantum vacuum, the "ocean" in which all
matter of the Universe is immersed, acts as a complex fluid with a very
variable gravitational charge density that might include both positive and
negative densities; a crucial prediction that can be tested within the Solar
System. In general case of N>2 point-like bodies, immersed in the quantum
vacuum, the analytical solutions are not possible, and the use of numerical
methods is inevitable. The key point is that an appropriate numerical method,
for the calculation of the effective gravitational charge of the quantum vacuum
induced by N immersed bodies, might be crucial in description of galaxies,
without the involvement of dark matter or a modification of gravity. The
development of such a valuable numerical method, is not possible, without a
previous (and in this study achieved) understanding of the impact of a two-body
system.


Abstract:
  We derive semiclassical equations of motion for an accelerated wavepacket in
a two-band system. We show that these equations can be formulated in terms of
the static band geometry described by the quantum metric. We consider the
specific cases of the Rashba Hamiltonian with and without a Zeeman term. The
semiclassical trajectories are in full agreement with the ones found by solving
the Schr\"odinger equation. This formalism successfully describes the adiabatic
limit and the anomalous Hall effect traditionally attributed to Berry
curvature. It also describes the opposite limit of coherent band superposition
giving rise to a spatially oscillating Zitterbewegung motion. At $k=0$, such
wavepacket exhibits a circular trajectory in real space, with its radius given
by the square root of the quantum metric. This quantity appears as a universal
length scale, providing a geometrical origin of the Compton wavelength.


Abstract:
  The bulk polarization is a $\mathbb{Z}_2$ topological invariant
characterizing non-interacting systems in one dimension with chiral or
particle-hole symmetries. We show that the bulk polarization can always be
determined from the single-particle entanglement spectrum, even in the absence
of symmetries that quantize it. In the symmetric case, the known relation
between the bulk polarization and the number of virtual topological edge modes
is recovered. We use the bulk polarization to compute Chern numbers in 1D and
2D, which illuminates their known relation to the entanglement spectrum.
Furthermore we discuss an alternative bulk polarization that can carry more
information about the surface spectrum than the conventional one and can
simplify the calculation of Chern numbers.


Abstract:
  Due to agile developments in the field of robotics and human-robot
interaction, prospective robotic agents are intended to play the role of
teammates and partner with humans to perform operations, rather than tools that
are replacing humans helping humans in a specific task. this notion of
partnering with robots raises new challenges for human-robot interaction (HRI),
which gives rise to a new field of research in HRI, namely human-robot trust.
Where humans and robots are working as partners, the performance of the work
can be diminished if humans do not trust robots appropriately. Considering the
impact of human-robot trust observed in different HRI fields, many researchers
have investigated the field of human-robot trust and examined various concerns
related to human-robot trust. In this work, we review the past works on
human-robot trust based on the research topics and discuss selected trends in
this field. Based on these reviews, we finally propose some ideas and areas of
potential future research at the end of this paper.


Abstract:
  Differential wavefront sensing is an essential technique for optimising the
performance of many precision interferometric experiments. Perhaps the most
extensive application of this is for alignment sensing using radio-frequency
beats measured with quadrant photodiodes. Here we present a new technique that
uses optical demodulation to measure such optical beats at significantly higher
resolutions using commercial laboratory equipment. We experimentally
demonstrate that the images captured can be digitally processed to generate
wavefront error signals and use these in a closed loop control system for
correct wavefront errors for alignment and mode-matching a beam into an optical
cavity to 99.9\%. This experiment paves the way for the correction of even
higher order errors when paired with higher order wavefront actuators. Such a
sensing scheme could find use in optimizing complex interferometers consisting
of coupled cavities, such as those found in gravitational wave detectors, or
simply just for sensing higher order wavefront errors in heterodyne
interferometric table-top experiments.


Abstract:
  We describe how simple machine learning methods successfully predict
geometric properties from Hilbert series (HS). Regressors predict embedding
weights in projective space to ${\sim}1$ mean absolute error, whilst
classifiers predict dimension and Gorenstein index to $>90\%$ accuracy with
${\sim}0.5\%$ standard error. Binary random forest classifiers managed to
distinguish whether the underlying HS describes a complete intersection with
high accuracies exceeding $95\%$. Neural networks (NNs) exhibited success
identifying HS from a Gorenstein ring to the same order of accuracy, whilst
generation of 'fake' HS proved trivial for NNs to distinguish from those
associated to the three-dimensional Fano varieties considered.


Abstract:
  In this work we introduce a novel stochastic algorithm dubbed SNIPS, which
draws samples from the posterior distribution of any linear inverse problem,
where the observation is assumed to be contaminated by additive white Gaussian
noise. Our solution incorporates ideas from Langevin dynamics and Newton's
method, and exploits a pre-trained minimum mean squared error (MMSE) Gaussian
denoiser. The proposed approach relies on an intricate derivation of the
posterior score function that includes a singular value decomposition (SVD) of
the degradation operator, in order to obtain a tractable iterative algorithm
for the desired sampling. Due to its stochasticity, the algorithm can produce
multiple high perceptual quality samples for the same noisy observation. We
demonstrate the abilities of the proposed paradigm for image deblurring,
super-resolution, and compressive sensing. We show that the samples produced
are sharp, detailed and consistent with the given measurements, and their
diversity exposes the inherent uncertainty in the inverse problem being solved.


Abstract:
  These lecture notes have been prepared for a series of lectures given at the
Summer School "From kinetic equations to statistical mechanics", (see
https://www.lebesgue.fr/content/sem2021-equat_cynet ) organised by the Henri
Lebesgue Center in Saint Jean de Monts, from June 28th to July 2nd 2021.


Abstract:
  In this paper, we study the problem of blood glucose forecasting and provide
a deep personalized solution. Predicting blood glucose level in people with
diabetes has significant value because health complications of abnormal glucose
level are serious, sometimes even leading to death. Therefore, having a model
that can accurately and quickly warn patients of potential problems is
essential. To develop a better deep model for blood glucose forecasting, we
analyze the data and detect important patterns. These observations helped us to
propose a method that has several key advantages over existing methods: 1- it
learns a personalized model for each patient as well as a global model; 2- it
uses an attention mechanism and extracted time features to better learn
long-term dependencies in the data; 3- it introduces a new, robust training
procedure for time series data. We empirically show the efficacy of our model
on a real dataset.


Abstract:
  The Burkhardt-Cottingham (BC) sum rule connects the twist-3 light-cone parton
distribution function (PDF) $g_{T}(x)$ to the twist-2 helicity PDF $g_{1}(x)$.
The chiral-odd counterpart of the BC sum rule relates the twist-3 light-cone
PDF $h_{L}(x)$ to the twist-2 transversity PDF $h_{1}(x)$. These BC-type sum
rules can also be derived for the corresponding quasi-PDFs. We perform a
perturbative check of the BC-type sum rules in the quark target model and the
Yukawa model, by going beyond the ultra-violet (UV) divergent terms. We employ
dimensional regularization (DR) and cut-off schemes to regulate UV divergences,
and show that the BC-type sum rules hold for DR, while they are generally
violated when using a cut-off. This violation can be traced back to the
breaking of rotational invariance. We find corresponding results for the sum
rule relating the mass of the target to the twist-3 PDF $e(x)$. Moreover, we
supplement our analytical results with numerical calculations.


Abstract:
  We examine the degree structure $\mathbf{ER}$ of equivalence relations on
$\omega$ under computable reducibility. We examine when pairs of degrees have a
join. In particular, we show that sufficiently incomparable pairs of degrees do
not have a join but that some incomparable degrees do, and we characterize the
degrees which have a join with every finite equivalence relation. We show that
the natural classes of finite, light, and dark degrees are definable in
$\mathbf{ER}$. We show that every equivalence relation has continuum many
self-full strong minimal covers, and that $\mathbf{d}\oplus \mathbf{Id_1}$
needn't be a strong minimal cover of a self-full degree $\mathbf{d}$. Finally,
we show that the theory of the degree structure $\mathbf{ER}$ as well as the
theories of the substructures of light degrees and of dark degrees are each
computably isomorphic with second order arithmetic.


Abstract:
  In this work, we consider a system of multidimensional wave equations coupled
by velocities with one localized fractional boundary damping. First, using a
general criteria of Arendt- Batty, by assuming that the boundary control region
satisfy some geometric conditions, under the equality speed propagation and the
coupling parameter of the two equations is small enough, we show the strong
stability of our system in the absence of the compactness of the resolvent. Our
system is not uniformly stable in general since it is the case of the interval.
Hence, we look for a polynomial decay rate for smooth initial data for our
system by applying a frequency domain approach combining with a multiplier
method. Indeed, by assuming that the boundary control region satisfy some
geometric conditions and the waves propagate with equal speed and the coupling
parameter term is small enough, we establish a polynomial energy decay rate for
smooth solutions, which depends on the order of the fractional derivative.


Abstract:
  Optimal transport is a framework that facilitates the most efficient
allocation of a limited amount of resources. However, the most efficient
allocation scheme does not necessarily preserve the most fairness. In this
paper, we establish a framework which explicitly considers the fairness of
dynamic resource allocation over a network with heterogeneous participants. As
computing the transport strategy in a centralized fashion requires significant
computational resources, it is imperative to develop computationally light
algorithm that can be applied to large scale problems. To this end, we develop
a fully distributed algorithm for fair and dynamic optimal transport with
provable convergence using alternating method of multipliers. In the designed
algorithm, each corresponding pair of resource supplier and receiver compute
their own solutions and update the transport schemes through negotiation
iteratively which do not require a central planner. The distributed algorithm
can yield a fair and efficient resource allocation mechanism over a network. We
corroborate the obtained results through case studies.


Abstract:
  An impressive effort is being placed in order to develop new strategies that
allow an efficient computation of multi-loop multi-leg Feynman integrals and
scattering amplitudes, with a particular emphasis on removing spurious
singularities and numerical instabilities. In this article, we describe an
innovative geometric approach based on graph theory to unveil the causal
structure of any multi-loop multi-leg amplitude in Quantum Field Theory. Our
purely geometric construction reproduces faithfully the manifestly causal
integrand-level behaviour of the Loop-Tree Duality representation. We found
that the causal structure is fully determined by the vertex matrix, through a
suitable definition of connected partitions of the underlying diagrams. Causal
representations for a given topological family are obtained by summing over
subsets of all the possible causal entangled thresholds that originate
connected and oriented partitions of the underlying topology. These results are
compatible with Cutkosky rules. Moreover, we found that diagrams with the same
number of vertices and multi-edges exhibit similar causal structures,
regardless of the number of loops.


Abstract:
  For given Boolean algebras $\mathbb{A}$ and $\mathbb{B}$ we endow the space
$\mathcal{H}(\mathbb{A},\mathbb{B})$ of all Boolean homomorphisms from
$\mathbb{A}$ to $\mathbb{B}$ with various topologies and study convergence
properties of sequences in $\mathcal{H}(\mathbb{A},\mathbb{B})$. We are in
particular interested in the situation when $\mathbb{B}$ is a measure algebra
as in this case we obtain a natural tool for studying topological convergence
properties of sequences of ultrafilters on $\mathbb{A}$ in random extensions of
the set-theoretical universe. This appears to have strong connections with Dow
and Fremlin's result stating that there are Efimov spaces in the random model.
We also investigate relations between topologies on
$\mathcal{H}(\mathbb{A},\mathbb{B})$ for a Boolean algebra $\mathbb{B}$
carrying a strictly positive measure and convergence properties of sequences of
measures on $\mathbb{A}$.


Abstract:
  Person re-identification (re-ID) in first-person (egocentric) vision is a
fairly new and unexplored problem. With the increase of wearable video
recording devices, egocentric data becomes readily available, and person
re-identification has the potential to benefit greatly from this. However,
there is a significant lack of large scale structured egocentric datasets for
person re-identification, due to the poor video quality and lack of individuals
in most of the recorded content. Although a lot of research has been done in
person re-identification based on fixed surveillance cameras, these do not
directly benefit egocentric re-ID. Machine learning models trained on the
publicly available large scale re-ID datasets cannot be applied to egocentric
re-ID due to the dataset bias problem. The proposed algorithm makes use of
neural style transfer (NST) that incorporates a variant of Convolutional Neural
Network (CNN) to utilize the benefits of both fixed camera vision and
first-person vision. NST generates images having features from both egocentric
datasets and fixed camera datasets, that are fed through a VGG-16 network
trained on a fixed-camera dataset for feature extraction. These extracted
features are then used to re-identify individuals. The fixed camera dataset
Market-1501 and the first-person dataset EGO Re-ID are applied for this work
and the results are on par with the present re-identification models in the
egocentric domain.