  We study the gauge dependence of one-loop divergences in a general
matter-coupled $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory in the
harmonic superspace formulation. Our analysis is based on the effective action
constructed by the background superfield method, with the gauge-fixing term
involving one real parameter $\xi_0$. A manifestly gauge invariant and ${\cal
N}=(1,0)$ supersymmetric procedure for calculating the one-loop effective
action is developed. It yields the one-loop divergences in an explicit form and
allows one to investigate their gauge dependence. As compared to the minimal
gauge, $\xi_0=1$, the divergent part of the general-gauge effective action
contains a new term depending on $\xi_0\,$. This term vanishes for the
background superfields satisfying the classical equations of motion, so that
the $S$-matrix divergences are gauge-independent. In the case of $6D$, ${\cal
N} = (1,1)$ SYM theory we demonstrate that some divergent contributions in the
non-minimal gauges do not vanish off shell, as opposed to the minimal gauge.


  Proton-proton collisions at new high energies ($\sqrt {s}=$2.36 and 7 TeV) at
LHC resulted into a greater mean multiplicities ($<e n >$) of charged particles
in the mid-rapidity region than estimated $< n >$s by different models and
event generators. Another significant observation in multiplicity data is a
change in slope in the distribution of primary charged hadrons in
pseudorapidity intervals $|\eta|<2.4$ at $\sqrt{s} = 7$ TeV. These new
observations merit further studies. We consider a two-component model of
particle production to analyze the multiplicity distributions of charged
hadrons from the proton-proton collisions at centre-of-mass energies $\sqrt{s}
= 0.9$ TeV, $\sqrt{s} = 2.36$ TeV and $\sqrt{s} = 7$ TeV in pseudorapidity
intervals $|\eta|$ of increasing width around the centre-of-mass pseudorapidity
$\eta_{cm} =0$. The model, based on quantum statistical formalism, considers
one chaotic and another coherent source of particle productions. The LHC data
has been found to be consistent with characteristic features of the model. The
analysis provides a reasonable explanation to the observed change in slope in
the distribution and suggests a possible reason for underestimations of mean
multiplicities by the event generators. In addition, an interesting revelation
is the deviation from a scaling law, involving information entropy in quantum
statistical viewpoint, derived as a function of chaotic multiplicity obtained
from the two-component model.


  We present the first X-ray reflection model for testing the assumption that
the metric of astrophysical black holes is described by the Kerr solution. We
employ the formalism of the transfer function proposed by Cunningham. The
calculations of the reflection spectrum of a thin accretion disk are split into
two parts: the calculation of the transfer function and the calculation of the
local spectrum at any emission point in the disk. The transfer function only
depends on the background metric and takes into account all the relativistic
effects (gravitational redshift, Doppler boosting, and light bending). Our code
computes the transfer function for a spacetime described by the Johannsen
metric and can easily be extended to any stationary, axisymmetric, and
asymptotically flat spacetime. Transfer functions and single line shapes in the
Kerr metric are compared with those calculated from existing codes to check
that we reach the necessary accuracy. We also simulate some observations with
NuSTAR and LAD/eXTP and fit the data with our new model to show the potential
capabilities of current and future observations to constrain possible
deviations from the Kerr metric.


  Phase segregation, the process by which the components of a binary mixture
spontaneously separate, is a key process in the evolution and design of many
chemical, mechanical, and biological systems. In this work, we present a
data-driven approach for the learning, modeling, and prediction of phase
segregation. A direct mapping between an initially dispersed, immiscible binary
fluid and the equilibrium concentration field is learned by conditional
generative convolutional neural networks. Concentration field predictions by
the deep learning model conserve phase fraction, correctly predict phase
transition, and reproduce area, perimeter, and total free energy distributions
up to 98% accuracy.


  Causal ordering in an asynchronous system has many applications in
distributed computing, including in replicated databases and real-time
collaborative software. Previous work in the area focused on ordering
point-to-point messages in a fault-free setting, and on ordering broadcasts
under various fault models. To the best of our knowledge, Byzantine
fault-tolerant causal ordering has not been attempted for point-to-point
communication in an asynchronous setting. In this paper, we first show that
existing algorithms for causal ordering of point-to-point communication fail
under Byzantine faults. We then prove that it is impossible to causally order
messages under point-to-point communication in an asynchronous system with one
or more Byzantine failures. We then present two algorithms that can causally
order messages under Byzantine failures, where the network provides an upper
bound on the message transmission time. The proofs of correctness for these
algorithms show that it is possible to achieve causal ordering for
point-to-point communication under a stronger asynchrony model where the
network provides an upper bound on message transmission time. We also give
extensions of our two algorithms for Byzantine fault-tolerant causal ordering
of multicasts.


  We show that some Lorentz components of the Feynman integrals calculated in
terms of the light-cone variables may contain end-point singularities which
originate from the contribution of the big-circle integral in the complex k_
plane. These singularities appear in various types of diagrams (two-point
functions, three-point functions, etc) and provide the covariance of the
Feynman integrals on the light-cone. We propose a procedure for calculating
Feynman integrals which guarantees that the end-point singularities do not
appear in the light-cone representations of the invariant amplitudes.


  Today, Machine Learning (ML) applications can have access to tens of
thousands of features. With such feature sets, efficiently browsing and
curating subsets of most relevant features is a challenge. In this paper, we
present a novel approach to visualize up to several thousands of features in a
single image. The image not only shows information on individual features, but
also expresses feature interactions via the relative positioning of features.


  We analyze the z=2 Ly-alpha and CIV forest along two adjacent lines-of-sight
at high S/N and spectral resolution to assess the question of the origin of
metals in the intergalactic medium. We find that the gas containing detectable
amounts of metals (as seen in absorption by CIV) is less quiescent on scales of
a few kpc than the gas without metals. Although it is difficult to discriminate
unequivocally between possible sources of enrichment and the extent to which
each contributes to line-of-sight differences, those suggest that the
metal-enriched systems are bound to galaxies (i.e., they do not arise in the
IGM nor in galactic winds).


  Most Active Galactic Nuclei (AGN) in the local Universe are obscured. In
these obscured AGN an excess is usually observed in the soft X-rays below ~2
keV above the absorbed X-ray continuum. This spectral component is associated
with the scattering of X-ray photons off free electrons in the Narrow Line
Region (NLR), and/or to photoionised lines. Recent studies have found that in
highly obscured AGN this component has lower flux relative to the primary X-ray
continuum than in less obscured AGN. This is measured by the scattering
fraction, or fscatt, which is the ratio of the scattered flux to the continuum.
Here, we use the ray-tracing platform RefleX to perform simulations of
scattered X-ray radiation to test two possible explanations for this
phenomenon: (1) sources with lower fscatt are viewed at higher inclinations or
(2) low fscatt sources are characterized by larger covering factors. We
consider a conical NLR of free electrons, while allowing the column density and
opening angle (and hence covering factor) to vary. We also consider electron
densities inferred from observations, and from simulations carried out with the
spectral synthesis code Cloudy. Our simulations show fscatt is expected to be
related to both the inclination angle and covering factor of the torus;
however, the observed negative correlation between fscatt and NH can only be
explained by a positive relation between the column density and the covering
factor of the obscuring material. Additional contributions to fscatt can come
from unresolved photoionised lines and ionised outflowing gas.


  In this paper we provide a step towards the understanding of the O($n$) bulk
operator algebra. By using a mixture of analytical and numerical methods, we
compute (ratios of) structure constants, and analyse the logarithmic structure
of the transfer matrix. We believe that the O($n$) model for a generic value of
$n = q + q^{-1}$ (i.e. for $q$ not a root of unity) provides a toy model of a
bulk logarithmic CFT that is considerably simpler than its counterparts at $q$
a root of unity.


  Maximum eigenvalue detection (MED) is an important application of random
matrix theory in spectrum sensing and signal detection. However, in small
signal-to-noise ratio environment, the maximum eigenvalue of the representative
signal is at the edge of Marchenko-Pastur (M-P) law bulk and meets the
Tracy-Widom distribution. Since the distribution of Tracy-Widom has no
closed-form expression, it brings great difficulty in processing. In this
paper, we propose a shifting maximum eigenvalue (SMED) algorithm, which shifts
the maximum eigenvalue out of the M-P law bulk by combining an auxiliary signal
associated with the signal to be detected. According to the random matrix
theory, the shifted maximum eigenvalue is consistent with Gaussian
distribution. The proposed SMED not only simplifies the detection algorithm,
but also greatly improve the detection performance. In this paper, the
performance of SMED, MED and trace (FMD) algorithm is analyzed and the
theoretical performance comparisons are obtained. The algorithm and theoretical
results are verified by the simulations in different signal environments.


  Generative adversarial networks (GANs) are one of the greatest advances in AI
in recent years. With their ability to directly learn the probability
distribution of data, and then sample synthetic realistic data. Many
applications have emerged, using GANs to solve classical problems in machine
learning, such as data augmentation, class unbalance problems, and fair
representation learning. In this paper, we analyze and highlight fairness
concerns of GANs model. In this regard, we show empirically that GANs models
may inherently prefer certain groups during the training process and therefore
they're not able to homogeneously generate data from different groups during
the testing phase. Furthermore, we propose solutions to solve this issue by
conditioning the GAN model towards samples' group or using ensemble method
(boosting) to allow the GAN model to leverage distributed structure of data
during the training phase and generate groups at equal rate during the testing
phase.


  We find the generating function of self-avoiding walks and trails on a
semi-regular lattice called the $3.12^2$ lattice in terms of the generating
functions of simple graphs, such as self-avoiding walks, polygons and tadpole
graphs on the hexagonal lattice. Since the growth constant for these graphs is
known on the hexagonal lattice we can find the growth constant for both walks
and trails on the $3.12^2$ lattice. A result of Watson then allows us to find
the generating function and growth constant of neighbour-avoiding walks on the
covering lattice of the $3.12^2$ lattice which is tetra-valent. A mapping into
walks on the covering lattice allows us to obtain improved bounds on the growth
constant for a range of lattices.


  Can health entities collaboratively train deep learning models without
sharing sensitive raw data? This paper proposes several configurations of a
distributed deep learning method called SplitNN to facilitate such
collaborations. SplitNN does not share raw data or model details with
collaborating institutions. The proposed configurations of splitNN cater to
practical settings of i) entities holding different modalities of patient data,
ii) centralized and local health entities collaborating on multiple tasks and
iii) learning without sharing labels. We compare performance and resource
efficiency trade-offs of splitNN and other distributed deep learning methods
like federated learning, large batch synchronous stochastic gradient descent
and show highly encouraging results for splitNN.


  Object permanence, which refers to the concept that objects continue to exist
even when they are no longer perceivable through the senses, is a crucial
aspect of human cognitive development. In this work, we seek to incorporate
this understanding into interactive robots by proposing a set of assumptions
and rules to represent object permanence in multi-object, multi-agent
interactive scenarios. We integrate these rules into the particle filter,
resulting in the Object Permanence Filter (OPF). For multi-object scenarios, we
propose an ensemble of K interconnected OPFs, where each filter predicts
plausible object tracks that are resilient to missing, noisy, and kinematically
or dynamically infeasible measurements, thus bringing perceptional robustness.
Through several interactive scenarios, we demonstrate that the proposed OPF
approach provides robust tracking in human-robot interactive tasks agnostic to
measurement type, even in the presence of prolonged and complete occlusion.
Webpage: https://opfilter.github.io/.


  We present a comprehensive benchmark of JSON-compatible binary serialization
specifications using the SchemaStore open-source test suite collection of over
400 JSON documents matching their respective schemas and representative of
their use across industries. We benchmark a set of schema-driven (ASN.1, Apache
Avro, Microsoft Bond, Cap'n Proto, FlatBuffers, Protocol Buffers, and Apache
Thrift) and schema-less (BSON, CBOR, FlexBuffers, MessagePack, Smile, and
UBJSON) JSON-compatible binary serialization specifications. Existing
literature on benchmarking JSON-compatible binary serialization specifications
demonstrates extensive gaps when it comes to binary serialization
specifications coverage, reproducibility and representativity, the role of data
compression in binary serialization and the choice and use of obsolete versions
of binary serialization specifications. We introduce a tiered taxonomy for JSON
documents consisting of 36 categories classified as Tier 1, Tier 2 and Tier 3
as a common basis to class JSON documents based on their size, type of content,
characteristics of their structure and redundancy criteria. We built and
published a free-to-use online tool to automatically categorize JSON documents
according to our taxonomy that generates related summary statistics. In the
interest of fairness and transparency, we adhere to reproducible software
development standards and publicly host the benchmark software and results on
GitHub.


  Performing active quantum error correction to protect fragile quantum states
highly depends on the correctness of error information--error syndromes. To
obtain reliable error syndromes using imperfect physical circuits, we propose
the idea of quantum data-syndrome (DS) codes that are capable of correcting
both data qubits and syndrome bits errors. We study fundamental properties of
quantum DS codes, including split weight enumerators, generalized MacWilliams
identities, and linear programming bounds. In particular, we derive Singleton
and Hamming-type upper bounds on degenerate quantum DS codes. Then we study
random DS codes and show that random DS codes with a relatively small
additional syndrome measurements achieve the Gilbert-Varshamov bound of
stabilizer codes. Constructions of quantum DS codes are also discussed. A
family of quantum DS codes is based on classical linear block codes, called
syndrome measurement codes, so that syndrome bits are encoded in additional
redundant stabilizer measurements. Another family of quantum DS codes is
CSS-type quantum DS codes based on classical cyclic codes, and this includes
the Steane code and the quantum Golay code.


  The strong suppression of high-$p_T$ jets in heavy ion collisions is a result
of elastic and inelastic energy loss suffered by the jet multi-prong collection
of color charges that are resolved by medium interactions. Hence, quenching
effects depend on the fluctuations of the jet substructure that are probed by
the cone size dependence of the spectrum. In this letter, we present the first
complete, analytic calculation of the inclusive $R$-dependent jet spectrum in
PbPb collisions at LHC energies, including resummation of energy loss effects
from hard, vacuum-like emissions occurring in the medium and modeling of soft
energy flow and recovery at the jet cone. Both the geometry of the collision
and the local medium properties, such as the temperature and fluid velocity,
are given by a hydrodynamic evolution of the medium, leaving only the coupling
constant in the medium as a free parameter. The calculation yields a good
description of the centrality and $p_T$ dependence of jet suppression for
$R=0.4$ together with a mild cone size dependence, which is in agreement with
recent experimental results. Gauging the theoretical uncertainties, we find
that the largest sensitivity resides in the leading logarithmic approximation
of the phase space of resolved splittings, which can be improved
systematically, while non-perturbative modeling of the soft-gluon sector is of
relatively minor importance up to large cone sizes.


  Shape analysis is ubiquitous in problems of pattern and object recognition
and has developed considerably in the last decade. The use of shapes is natural
in applications where one wants to compare curves independently of their
parametrisation. One computationally efficient approach to shape analysis is
based on the Square Root Velocity Transform (SRVT). In this paper we propose a
generalised SRVT framework for shapes on homogeneous manifolds. The method
opens up for a variety of possibilities based on different choices of Lie group
action and giving rise to different Riemannian metrics.


  Physics at a multi-TeV muon collider needs a change of perspective for the
detector design due to the large amount of background induced by muon beam
decays. Preliminary studies, based on simulated data, on the composition and
the characteristics of the particles originated from the muon decays and
reaching the detectors are presented here. The reconstruction performance of
the physics processes $H\to b\bar b$ and $Z\to b\bar b$ has been investigated
for the time being without the effect of the machine induced background. A
preliminary study of the environment hazard due to the radiation induced by
neutrino interactions with the matter is presented using the FLUKA simulation
program.


  The gluon propagator is calculated in quenched QCD for two different lattice
sizes (16^3x48 and 32^3x64) at beta=6.0. The volume dependence of the
propagator in Landau gauge is studied. The smaller lattice is instrumental in
revealing finite volume and anisotropic lattice artefacts. Methods for
minimising these artefacts are developed and applied to the larger lattice
data. New structure seen in the infrared region survives these conservative
cuts to the lattice data. This structure serves to rule out a number of models
that have appeared in the literature. A fit to a simple analytical form
capturing the momentum dependence of the nonperturbative gluon propagator is
also reported.


  A detailed study of the waiting times for the first (multi)-collision in a
drawing process.


  We say that a germ G of a geometric structure can be transplanted into a
manifold M if there is a suitable geometric structure on M which agrees with G
on a neighborhood of some point P of M. We show for a wide variety of geometric
structures that this transplantation is always possible provided that M does in
fact admit some such structure of this type. We use this result to show that a
curvature identity which holds in the category of compact manifolds admitting
such a structure holds for germs as well and we present examples illustrating
this result. We also use this result to show geometrical realization problems
which can be solved for germs of structures can in fact be solved in the
compact setting as well.


  We extend a theorem of Ottaviani on cohomological splitting criterion for
vector bundles over the Grassmannian to the case of the symplectic isotropic
Grassmanian. We find necessary and sufficient conditions for the case of the
Grassmanian of symplectic isotropic lines. For the general case the
generalization of Ottaviani's conditions are sufficient for vector bundles over
the symplectic isotropic Grassmannian. By a calculation in the program LiE, we
find that Ottaviani's conditions are necessary for Lagrangian Grassmannian of
isotropic $k$-planes for $k\leq 6$, but they fail to be necessary for the case
of the Lagrangian Grassmannian of isotropic 7-planes. Finally, we find a
related set of necessary and sufficient splitting criteria for the Lagrangian
Grassmannian.


  New families of nonnegative biquadratic forms that have 8, 9 or 10 real zeros
in $\mathbb{P}^2\times \mathbb{P}^2$ are constructed. These are the first
examples with 8, 9 or 10 real zeros. It is known that nonnegative biquadratic
forms with finitely many real zeros can have at most 10 zeros; our examples
show that the upper bound is obtained. Such biquadratic forms define positive
linear maps on real symmetric $3\times 3$ matrices that are not completely
positive. Our constructions are explicit, and moreover we are able to determine
which of the examples are extremal. We extend the examples to positive maps on
complex matrices and find families of extreme rays in the cone of positive
maps.


  Optical and transport properties of materials depend heavily upon features of
electronic band structures in proximity to energy extrema in the Brillouin zone
(BZ). Such features are generally described in terms of multi-dimensional
quadratic expansions and corresponding definitions of effective masses.
Multi-dimensional expansions, however, are permissible only under strict
conditions that are typically violated by degenerate bands and even some
non-degenerate bands. Suggestive terms such as "band warping" or "corrugated
energy surfaces" have been used to refer to such situations and ad hoc methods
have been developed to treat them. While numerical calculations may reflect
such features, a complete theory of band warping has not been developed. We
develop a generally applicable theory, based on radial expansions, and a
corresponding definition of angular effective mass. Our theory also accounts
for effects of band non-parabolicity and anisotropy, which hitherto have not
been precisely distinguished from, if not utterly confused with, band warping.
Based on our theory, we develop precise procedures to evaluate band warping
quantitatively. As a benchmark demonstration, we analyze the warping features
of valence bands in silicon using first-principles calculations and we compare
those with previous semi-empirical models. We use our theory and angular
effective masses to generalize derivations of tensorial transport coefficients
for cases of either single or multiple electronic bands, with either
quadratically expansible or warped energy surfaces. From that theory we
discover the formal existence at critical points of transport-equivalent
ellipsoidal bands that yield identical results from the standpoint of any
transport property. Additionally, we illustrate the drastic effects that band
warping can induce on thermoelectric properties using multi-band models.


  We examine the effect of one loop quantum corrections on the formation of
nontopological solitons in a strongly coupled scalar-fermionic Yukawa theory.
The exact one fermion loop contribution is incorporated by using a nonlocal
method to correct the local derivative expansion approximation (DE) of the
effective action. As the Yukawa coupling is increased we find that the nonlocal
corrections play an increasingly important role. The corrections cause the
scalar field to increase in depth while maintaining its size. This increases
the energy of the bag configuration, but this is compensated for by more
tightly bound fermionic states with lower energy. In contrast to the
semi-classical picture without quantum corrections, the binding energy is
small, and the total energy scales directly with the Yukawa coupling. This
confirms the qualitative behavior found in earlier work using the second order
DE, although the quantitative solutions differ.


  We use Hopf algebras to prove a version of the Littlewood-Richardson rule for
skew Schur functions, which implies a conjecture of Assaf and McNamara. We also
establish skew Littlewood-Richardson rules for Schur P- and Q-functions and
noncommutative ribbon Schur functions, as well as skew Pieri rules for k-Schur
functions, dual k-Schur functions, and for the homology of the affine
Grassmannian of the symplectic group.


  Chaotic transients occur in many experiments including those in fluids, in
simulations of the plane Couette flow, and in coupled map lattices and they are
a common phenomena in dynamical systems. Superlong chaotic transients are
caused by the presence of chaotic saddles whose stable sets have fractal
dimensions that are close to phase-space dimension. For many physical systems
chaotic saddles have a big impact on laboratory measurements, and it is
important to compute the dimension of such stable sets including fractal basin
boundaries through a direct method. In this work, we present a new method to
compute the dimension of stable sets of chaotic saddles directly, fast, and
reliable.


  The gradient of the gravitational redshift in the potential of the Milky-Way
induces an apparent spurious radial migration. I show that this effect is
simply related to the local acceleration, which was measured recently by Gaia
eDR3, implying a spectroscopic shift of $[-2.4x10^{-2}/(r/8kpc)] km/s/kpc. The
transverse Doppler effect yields a comparable contribution. The spurious radial
velocity from both relativistic effects amounts to crossing a major portion of
the Milky-Way disk during the age of the universe, and must be corrected for in
any future measurement of the actual radial migration of stars.


  Workshops are used for academic social networking, but connections can be
superficial and result in few enduring collaborations. This unworkshop offers a
novel interactive format to create deep connections, peer- learning, and
produces a technology-enhanced experience. Participants will generate
interactive technological artifacts before the unworkshop, which will be used
together and orchestrated at the unworkshop to engage all participants in an
alternate reality game set in local places at the conference.


  In these four lectures, aiming at senior undergraduate and junior graduate
Physics and Mathematics students, basic elements of the theory of elliptic
functions are presented. Simple applications in classical mechanics are
discussed, including a point particle in a cubic, sinusoidal or hyperbolic
potential, as well as simple applications in quantum mechanics, namely the n=1
Lame potential. These lectures were given at the School of Applied Mathematics
and Physical Sciences of the National Technical University of Athens in May
2017.


  We investigate the production of a pseudoscalar Higgs-boson $A^0$ using the
reaction $e\,\gamma\rightarrow e\,A^0$ at an $e\bar{e}$ collider with center of
mass energy of 500 GeV. Supersymmetric contributions are included and provide a
substantial enhancement to the cross section for most values of the symmetry
breaking parameters. We find that, despite the penalty incurred in converting
one of the beams into a source of backscattered photons, the $e\, \gamma$
process is a promising channel for the detection of the $A^0$.


  We present an analysis of the wind circulation in the vecinity of the ground
surface, for a region centered around Guatemala. We used the regional climate
model RegCM to simulate the atmospheric dynamics above that region during the
full year 2016. The purpose of the study is to obtain the mesoscale variation
(tens of kilometers) of the wind velocity field. It can be seen that as
resolution is increased, the details in topography are better represented, they
in turn influence the wind circulation patterns on scales of a few kilometers.
With a fine resolution of 2 km it is possible to confirm the existence of
intense wind flux zones over the surface; such as Pal\'in, Escuintla. We are
also able to observe diurnally varying circulations, which are the product of
the daily cycle of terrain heating due to the sun and the subsecuent cooling
during the night. This is the first report in a line of studies where we plan
to analyze the climatic features of the Guatemalan region.


  While many different models for $(\infty,1)$-categories are currently being
used, it is known that they are Quillen equivalent to one another. Several
higher-order analogues of them are being developed as models for $(\infty,
n)$-categories. In this paper, we establish model structures for some naturally
arising categories of objects which should be thought of as
$(\infty,n)$-categories. Furthermore, we establish Quillen equivalences between
them.


  Planar acoustically dominated magneto\-hydro\-dynamic waves are initiated at
the high-$\beta$ base of a simulated 2D isothermal stratified atmosphere with
potential magnetic field exhibiting both open and closed field regions as well
as neutral points. They shock on their way upward toward the Alfv\'en-acoustic
equipartition surface $a=c$, where $a$ and $c$ are the Alfv\'en and sound
speeds respectively. Expanding on recent 1.5D findings that such shocks
mode-convert to fast shocks and slow smoothed waves on passing through $a=c$,
we explore the implications for these more complex magnetic geometries. It is
found that the 1.5D behaviour carries over to the more complex case, with the
fast shocks strongly attracted to neutral points, which are disrupted producing
extensive fine structure. It is also observed that shocks moving in the
opposite direction, from $a>c$ to $a<c$, split into fast and slow components
too, and that again it is the slow component that is smoothed.


  We classify transverse Hopf links in the standard contact 3-space up to
transverse isotopy in terms of their components' self-linking number.


  Solar flare prediction is a central problem in space weather forecasting and
has captivated the attention of a wide spectrum of researchers due to recent
advances in both remote sensing as well as machine learning and deep learning
approaches. The experimental findings based on both machine and deep learning
models reveal significant performance improvements for task specific datasets.
Along with building models, the practice of deploying such models to production
environments under operational settings is a more complex and often
time-consuming process which is often not addressed directly in research
settings. We present a set of new heuristic approaches to train and deploy an
operational solar flare prediction system for $\geq$M1.0-class flares with two
prediction modes: full-disk and active region-based. In full-disk mode,
predictions are performed on full-disk line-of-sight magnetograms using deep
learning models whereas in active region-based models, predictions are issued
for each active region individually using multivariate time series data
instances. The outputs from individual active region forecasts and full-disk
predictors are combined to a final full-disk prediction result with a
meta-model. We utilized an equal weighted average ensemble of two base
learners' flare probabilities as our baseline meta learner and improved the
capabilities of our two base learners by training a logistic regression model.
The major findings of this study are: (i) We successfully coupled two
heterogeneous flare prediction models trained with different datasets and model
architecture to predict a full-disk flare probability for next 24 hours, (ii)
Our proposed ensembling model, i.e., logistic regression, improves on the
predictive performance of two base learners and the baseline meta learner
measured in terms of two widely used metrics True Skill Statistic (TSS) and
Heidke Skill core (HSS), and (iii) Our result analysis suggests that the
logistic regression-based ensemble (Meta-FP) improves on the full-disk model
(base learner) by $\sim9\%$ in terms TSS and $\sim10\%$ in terms of HSS.
Similarly, it improves on the AR-based model (base learner) by $\sim17\%$ and
$\sim20\%$ in terms of TSS and HSS respectively. Finally, when compared to the
baseline meta model, it improves on TSS by $\sim10\%$ and HSS by $\sim15\%$.


  We discuss properties of Quantum Chromodynamics at finite temperature
obtained by means of lattice simulations with overlap fermions. This fermion
discretization preserves chiral symmetry even at finite lattice spacing. We
present details of the lattice formulation, first results for the chiral
observables and discuss the behaviour of the system near the chiral thermal
phase transition.


  Gaussian Markov random fields (GMRFs) are frequently used as computationally
efficient models in spatial statistics. Unfortunately, it has traditionally
been difficult to link GMRFs with the more traditional Gaussian random field
models as the Markov property is difficult to deploy in continuous space.
Following the pioneering work of Lindgren et al. (2011), we expound on the link
between Markovian Gaussian random fields and GMRFs. In particular, we discuss
the theoretical and practical aspects of fast computation with continuously
specified Markovian Gaussian random fields, as well as the clear advantages
they offer in terms of clear, parsimonious and interpretable models of
anisotropy and non-stationarity.


  In this paper, we study the intrinsic mean curvature flow on certain closed
spacelike manifolds, and prove the existence of hyperbolic structures on them.


  The Steiner ratio characterizes the greatest possible deviation of the length
of a minimal spanning tree from the length of the minimal Steiner tree. In this
paper, estimates of the Steiner ratio on Riemannian manifolds are obtained. As
a corollary, the Steiner ratio for flat tori, flat Klein bottles, and
projective plane of constant positive curvature are computed. Steiner ratio -
Steiner problem - Gilbert--Pollack conjecture - surfaces of constant curvature


  Highly filled conductive polymer composites (CPCs) are widely used in
applications such as bipolar plate materials for polymer electrolyte membrane
fuel cells and redox flow batteries, electromagnetic interference shielding and
sensors due to their useful electrical properties. A common method for
determining through-plane electrical conductivities $\left(\sigma_{\rm tp}
\right)$ of such highly filled CPCs applies a conductive carbon paper between
electrodes and sample with application of external pressure to improve
electrical contact. We show the pressure-dependence of the measured
$\sigma_{\rm tp}$ can be eliminated by using a liquid metal such as the
gallium-indium eutectic alloy (EGaIn) as contact material. Results indicate
that EGaIn reduces contact resistances and cause three to five times larger
$\sigma_{\rm tp}$ compared to measurements with carbon paper contacts and
pressures up to 20 bar.


  Often, recommendation systems employ continuous training, leading to a
self-feedback loop bias in which the system becomes biased toward its previous
recommendations. Recent studies have attempted to mitigate this bias by
collecting small amounts of unbiased data. While these studies have
successfully developed less biased models, they ignore the crucial fact that
the recommendations generated by the model serve as the training data for
subsequent training sessions. To address this issue, we propose a framework
that learns an unbiased estimator using a small amount of uniformly collected
data and focuses on generating improved training data for subsequent training
iterations. To accomplish this, we view recommendation as a contextual
multi-arm bandit problem and emphasize on exploring items that the model has a
limited understanding of. We introduce a new offline sequential training schema
that simulates real-world continuous training scenarios in recommendation
systems, offering a more appropriate framework for studying self-feedback bias.
We demonstrate the superiority of our model over state-of-the-art debiasing
methods by conducting extensive experiments using the proposed training schema.


  Ultracold molecules offer entirely new possibilities for the control of
quantum processes due to their rich internal structure. Recently, near quantum
degenerate gases of molecules have been prepared in their rovibronic ground
state. For future experiments, it is crucial to also control their hyperfine
state. Here, we report the preparation of a rovibronic ground state molecular
quantum gas in a single hyperfine state and in particular in the absolute
lowest quantum state. The demonstrated and presented scheme is general for
bialkali polar molecules and allows the preparation of molecules in a single
hyperfine state or in an arbitrary coherent superposition of hyperfine states.
The scheme relies on electric-dipole, two-photon microwave transitions through
rotationally excited states and makes use of electric nuclear quadrupole
interactions to transfer molecular population between different hyperfine
states.


  In this paper we show a method for creating multiple independent
quasi-perfect vector vortex beams with real-time programmable radii,
topological charges, polarization orders and position in 3 dimensions, using a
device based on a phase-only liquid crystal on silicon display. We achieved the
simultaneous generation of up to 7 independent beams, with topological charges
from -3 to 3, and found great agreement between the simulated and the measured
phases and polarization structures. Additionally, we used the same scheme for
enhancing the depth of focus of a single beam, resulting in a "tube" beam that
preserves its properties during propagation.


  We study the $1$- or $2$-level density of families of $L$-functions for
Hecke--Maass forms over an imaginary quadratic field $F$. For test functions
whose Fourier transform is supported in $\left(-\frac 32, \frac 32\right)$, we
prove that the $1$-level density for Hecke--Maass forms over $F$ of square-free
level $\mathfrak{q}$, as $\mathrm{N}(\mathfrak{q})$ tends to infinity, agrees
with that of the orthogonal random matrix ensembles. For Hecke--Maass forms
over $F$ of full level, we prove similar statements for the $1$- and $2$-level
densities, as the Laplace eigenvalues tends to infinity.


  In a series of papers (see \cite{CDT02} and the pertinent references therein)
the 3D Navier-Stokes-$\alpha$ model were shown to be a useful complement to the
3D Navier-Stokes equations; and in particular, to be a good Reynolds version of
the latter equations. In this work, we introduce a simple Reynolds averaging
which, due to the wall roughness, transforms the Navier-Stokes equations into
the Navier-Stokes-$\alpha$ model.


  In this paper we simultaneously fit the orbits and line-of-sight velocities
of the ionized gas around the supermassive black hole, Sagittarius A$^{\ast}$
(Sgr A$^{\ast}$), at the center of the Milky Way. The data we use are taken
with the K-band Multi Object Spectrograph (KMOS), presented in Feldmeier-Krause
et al. (2015) and cover the central $\sim$ 2 pc of the Milky Way. From the
brightest gas emission line in the K-band, the Br$\gamma$ line, we derive the
spatial distribution and line-of-sight velocities of the gas in the minispiral.
Using the flux distribution and the line-of-sight velocity information, we
perform a fit to the three main gas streamers in the minispiral, the Northern
Arm, Eastern Arm, and Western Arc, using a Bayesian modelling method, and are
able to reconstruct the three-dimensional orbits of these gas streamers. With
the best fit orbital parameters and the measured line-of-sight velocities, we
constrain the mass of Sgr A$^{\ast}$. The orbit of the Eastern Arm is the one
that is best constrained using our data. It gives a best-fit orbital period of
$17.4_{-11.6}^{+31.0}\cdot 10^3$ years and results in an enclosed mass of
$14.9_{-10.4}^{+69.4}\cdot 10^6 M_{\odot}.$


  Parallel tempering Monte Carlo has proven to be an efficient method in
optimization and sampling applications. Having an optimized temperature set
enhances the efficiency of the algorithm through more-frequent replica visits
to the temperature limits. The approaches for finding an optimal temperature
set can be divided into two main categories. The methods of the first category
distribute the replicas such that the swapping ratio between neighbouring
replicas is constant and independent of the temperature values. The
second-category techniques including the feedback-optimized method, on the
other hand, aim for a temperature distribution that has higher density at
simulation bottlenecks, resulting in temperature-dependent replica-exchange
probabilities. In this paper, we compare the performance of various temperature
setting methods on both sparse and fully-connected spin-glass problems as well
as fully-connected Wishart problems that have planted solutions. These include
two classes of problems that have either continuous or discontinuous phase
transitions in the order parameter. Our results demonstrate that there is no
performance advantage for the methods that promote nonuniform swapping
probabilities on spin-glass problems where the order parameter has a smooth
transition between phases at the critical temperature. However, on Wishart
problems that have a first-order phase transition at low temperatures, the
feedback-optimized method exhibits a time-to-solution speedup of at least a
factor of two over the other approaches.


  In this article we present a novel method of hit time and hit position
reconstruction in long scintillator detectors. We take advantage of the fact
that for this kind of detectors amplitude and shape of registered signals
depends strongly on the position where particle hit the detector. The
reconstruction is based on determination of the degree of similarity between
measured and averaged signals stored in a library for a set of well-defined
positions along the scintillator. Preliminary results of validation of the
introduced method with experimental data obtained by means of the double strip
prototype of the J-PET detector are presented.


  We slightly generalize a notion of rank introduced by Glasner and
Megrelishvili, which captures the oscillations of elements of Ellis semigroups,
so that it can be applied to any compact Hausdorff space instead of being
limited to the metric case. Then, we relate this rank to classical dividing
lines in the model-theoretic stability hierarchy. For example, that the rank is
ordinal-valued if and only if the background theory is NIP.


  Adhesive interactions strongly characterize the contact mechanics of soft
bodies as they lead to large elastic deformations and contact instabilities. In
this paper, we extend the Interacting and Coalescing Hertzian Asperities (ICHA)
model to the case of adhesive contact. Adhesion is modeled according to an
improved version of the Johnson, Kendall & Roberts (JKR) theory, in which
jump-in contact instabilities are conveniently considered as well as the
lateral interaction of the asperities and the coalescence of merging contact
spots. Results obtained on complex fractal geometries with several length
scales are accurate as demonstrated by the comparison with fully numerical
simulations and experimental investigations taken from the literature. Also,
the model quite well captures the distributions of the contact stresses, gaps,
and contact spots.


  It is shown that the complex phase of the Feynman propagator is a solution of
the quantum Hamilton Jacobi equation


  A systematic study of the influence of the viscous effect on both the spectra
and the nonlinear fluxes of conserved as well as non conserved quantities in
Navier-Stokes turbulence is proposed. This analysis is used to estimate the
helicity dissipation scale which is shown to coincide with the energy
dissipation scale. However, it is shown using the decomposition of helicity
into eigen modes of the curl operator, that viscous effects have to be taken
into account for wave vector smaller than the Kolomogorov wave number in the
evolution of these eigen components of the helicity.


  The associated production of Higgs and $W$ bosons via vector-boson fusion
(VBF) is highly sensitive to the relative sign of the Higgs boson couplings to
$W$ and $Z$ bosons. In this Letter, two searches for this process are
presented, using 140 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ =
13 TeV recorded by the ATLAS detector at the LHC. The first search targets
scenarios with opposite-sign couplings of the $W$ and $Z$ bosons to the Higgs
boson, while the second targets Standard Model-like scenarios with same-sign
couplings. Both analyses consider Higgs decays into a pair of $b$-quarks and
$W$ decays with an electron or muon. The opposite-sign coupling hypothesis is
excluded with significance much greater than $5\sigma$, and the observed
(expected) upper limit set on the cross-section for VBF $WH$ production is 9.0
(8.7) times the Standard Model value.


  We report experimental evidences of anomalous kinetic roughening in the
stable displacement of an oil-air interface in a Hele-Shaw cell with strong
quenched disorder. The disorder consists on a random modulation of the gap
spacing transverse to the growth direction (tracks). We have performed
experiments varying average interface velocity and gap spacing, and measured
the scaling exponents. We have obtained beta=0.50, beta*=0.25, alpha=1.0,
alpha_l=0.5, and z=2. When there is no fluid injection, the interface is driven
solely by capillary forces, and a higher value of beta around beta=0.65 is
measured. The presence of multiscaling and the particular morphology of the
interfaces, characterized by high slopes that follow a L\'evy distribution,
confirms the existence of anomalous scaling. From a detailed study of the
motion of the oil--air interface we show that the anomaly is a consequence of
different local velocities over tracks plus the coupling in the motion between
neighboring tracks. The anomaly disappears at high interface velocities, weak
capillary forces, or when the disorder is not sufficiently persistent in the
growth direction. We have also observed the absence of scaling when the
disorder is very strong or when a regular modulation of the gap spacing is
introduced.


  Few-Shot Learning (FSL) is a challenging task, \emph{i.e.}, how to recognize
novel classes with few examples? Pre-training based methods effectively tackle
the problem by pre-training a feature extractor and then predicting novel
classes via a cosine nearest neighbor classifier with mean-based prototypes.
Nevertheless, due to the data scarcity, the mean-based prototypes are usually
biased. In this paper, we attempt to diminish the prototype bias by regarding
it as a prototype optimization problem. To this end, we propose a novel
meta-learning based prototype optimization framework to rectify prototypes,
\emph{i.e.}, introducing a meta-optimizer to optimize prototypes. Although the
existing meta-optimizers can also be adapted to our framework, they all
overlook a crucial gradient bias issue, \emph{i.e.}, the mean-based gradient
estimation is also biased on sparse data. To address the issue, we regard the
gradient and its flow as meta-knowledge and then propose a novel Neural
Ordinary Differential Equation (ODE)-based meta-optimizer to polish prototypes,
called MetaNODE. In this meta-optimizer, we first view the mean-based
prototypes as initial prototypes, and then model the process of prototype
optimization as continuous-time dynamics specified by a Neural ODE. A gradient
flow inference network is carefully designed to learn to estimate the
continuous gradient flow for prototype dynamics. Finally, the optimal
prototypes can be obtained by solving the Neural ODE. Extensive experiments on
miniImagenet, tieredImagenet, and CUB-200-2011 show the effectiveness of our
method.


  We investigate the spectrum of glueballs in 3D and 4D SU(N) gauge theories.
Our motivation is to determine whether the states lie on straight Regge
trajectories. To this end we develop new lattice techniques to reliably
determine the states carrying higher spin. It has been conjectured for a long
time that glueballs are the physical states lying on the pomeron, the
trajectory responsible for the slowly rising hadronic cross-sections at large
centre-of-mass energy.


  We report on the peculiar activity of the radio source located at the center
of the cooling flow cluster RBS797 (z=0.35), the first distant cluster in which
two pronounced X-ray cavities have been discovered. New multifrequency (1.4,
4.8, and 8.4 GHz) observations obtained with the Very Large Array clearly
reveal the presence of radio emission on three different scales showing
orientation in different directions, all of which indicates that RBS797
represents a very peculiar case. The lowest resolution images show large-scale
radio emission characterized by amorphous morphology and a steep spectrum,
extended on a scale of hundreds of kpc. On a scale of tens of kpc, there is
evidence of 1.4 GHz radio emission elongated in the northeast-southwest
direction exactly towards the holes detected in X-rays. The highest resolution
image shows the details of the innermost 4.8 GHz radio jets on a kpc scale;
they are remarkably oriented in a direction that is perpendicular to that of
the extended structure detected at a lower resolution. We therefore find
evidence of a strong interaction between the central radio source and the
intra-cluster medium in RBS797. We suggest a scenario in which the 1.4 GHz
emission filling the X-ray cavities consists of buoyant bubbles of radio
emitting plasma that are created by twin jets in the past and whose expansion
has displaced the thermal gas that was formerly in the X-ray holes, whereas the
two jets visible at 4.8 GHz are related to the present nuclear activity that
has restarted at a different position angle from the original outburst that
created the outer radio lobes. The total radio luminosity is ~ 10^42 erg/s,
corresponding to a factor of a few thousand times less than the estimated
cooling luminosity.


  Reinforcement learning (RL) has emerged as a promising solution for
addressing traffic signal control (TSC) challenges. While most RL-based TSC
systems typically employ an online approach, facilitating frequent active
interaction with the environment, learning such strategies in the real world is
impractical due to safety and risk concerns. To tackle these challenges, this
study introduces an innovative offline data-driven approach, called DataLight.
DataLight employs effective state representations and reward function by
capturing vehicular speed information within the environment. It then segments
roads to capture spatial information and further enhances the spatially
segmented state representations with sequential modeling. The experimental
results demonstrate the effectiveness of DataLight, showcasing superior
performance compared to both state-of-the-art online and offline TSC methods.
Additionally, DataLight exhibits robust learning capabilities concerning
real-world deployment issues. The code is available at
https://github.com/LiangZhang1996/DataLight.


  In recent years, self-supervised learning (SSL) has achieved tremendous
success in various speech tasks due to its power to extract representations
from massive unlabeled data. However, compared with tasks such as speech
recognition (ASR), the improvements from SSL representation in speech
separation (SS) and enhancement (SE) are considerably smaller. Based on HuBERT,
this work investigates improving the SSL model for SS and SE. We first update
HuBERT's masked speech prediction (MSP) objective by integrating the separation
and denoising terms, resulting in a multiple pseudo label pre-training scheme,
which significantly improves HuBERT's performance on SS and SE but degrades the
performance on ASR. To maintain its performance gain on ASR, we further propose
an adapter-based architecture for HuBERT's Transformer encoder, where only a
few parameters of each layer are adjusted to the multiple pseudo label MSP
while other parameters remain frozen as default HuBERT. Experimental results
show that our proposed adapter-based multiple pseudo label HuBERT yield
consistent and significant performance improvements on SE, SS, and ASR tasks,
with a faster pre-training speed, at only marginal parameters increase.


  Most existing person re-identification algorithms either extract robust
visual features or learn discriminative metrics for person images. However, the
underlying manifold which those images reside on is rarely investigated. That
raises a problem that the learned metric is not smooth with respect to the
local geometry structure of the data manifold.
  In this paper, we study person re-identification with manifold-based affinity
learning, which did not receive enough attention from this area. An
unconventional manifold-preserving algorithm is proposed, which can 1) make the
best use of supervision from training data, whose label information is given as
pairwise constraints; 2) scale up to large repositories with low on-line time
complexity; and 3) be plunged into most existing algorithms, serving as a
generic postprocessing procedure to further boost the identification
accuracies. Extensive experimental results on five popular person
re-identification benchmarks consistently demonstrate the effectiveness of our
method. Especially, on the largest CUHK03 and Market-1501, our method
outperforms the state-of-the-art alternatives by a large margin with high
efficiency, which is more appropriate for practical applications.


  Gentrification--the transformation of a low-income urban area caused by the
influx of affluent residents--has many revitalizing benefits. However, it also
poses extremely concerning challenges to low-income residents. To help
policymakers take targeted and early action in protecting low-income residents,
researchers have recently proposed several machine learning models to predict
gentrification using socioeconomic and image features. Building upon previous
studies, we propose a novel graph-based multimodal deep learning framework to
predict gentrification based on urban networks of tracts and essential
facilities (e.g., schools, hospitals, and subway stations). We train and test
the proposed framework using data from Chicago, New York City, and Los Angeles.
The model successfully predicts census-tract level gentrification with 0.9
precision on average. Moreover, the framework discovers a previously unexamined
strong relationship between schools and gentrification, which provides a basis
for further exploration of social factors affecting gentrification.


  We present spectra for 14 high-redshift (0.17 < z < 0.83) supernovae, which
were discovered by the Supernova Cosmology Project as part of a campaign to
measure cosmological parameters. The spectra are used to determine the redshift
and classify the supernova type, essential information if the supernovae are to
be used for cosmological studies. Redshifts were derived either from the
spectrum of the host galaxy or from the spectrum of the supernova itself. We
present evidence that these supernovae are of Type Ia by matching to spectra of
nearby supernovae. We find that the dates of the spectra relative to maximum
light determined from this fitting process are consistent with the dates
determined from the photometric light curves, and moreover the spectral
time-sequence for SNe Type Ia at low and high redshift is indistinguishable. We
also show that the expansion velocities measured from blueshifted CaHK are
consistent with those measured for low-redshift Type Ia supernovae. From these
first-level quantitative comparisons we find no evidence for evolution in SNIa
properties between these low- and high-redshift samples. Thus even though our
samples may not be complete, we conclude that there is a population of SNe Ia
at high redshift whose spectral properties match those at low redshift.


  This paper proposes a privacy-preserving algorithm to solve the average
consensus problem based on Shamir's secret sharing scheme, in which a network
of agents reach an agreement on their states without exposing their individual
state until an agreement is reached. Unlike other methods, the proposed
algorithm renders the network resistant to the collusion of any given number of
neighbors (even with all neighbors' colluding). Another virtue of this work is
that such a method can protect the network consensus procedure from
eavesdropping.


  We study the spreading of quantum information in a recently introduced family
of brickwork quantum circuits that generalises the dual-unitary class. These
circuits are unitary in time, while their spatial dynamics is unitary only in a
restricted subspace. First, we show that local operators spread at the speed of
light as in dual-unitary circuits, i.e., the butterfly velocity takes the
maximal value allowed by the geometry of the circuit. Then, we prove that the
entanglement spreading can still be characterised exactly for a family of
compatible initial states (in fact, for an extension of the compatible family
of dual-unitary circuits) and that the asymptotic entanglement slope is again
independent on the R\'enyi index. Remarkably, however, we find that the
entanglement velocity is generically smaller than one. We use these properties
to find a closed-form expression for the entanglement membrane in these
circuits.


  We study the low temperature $(2+1)$D Solid-On-Solid model on $[[1, L ]]^2$
with zero boundary conditions and non-negative heights (a floor at height $0$).
Caputo et al. (2016) established that this random surface typically admits
either $\mathfrak h $ or $\mathfrak h+1$ many nested macroscopic level line
loops $\{\mathcal L_i\}_{i\geq 0}$ for an explicit $\mathfrak h\asymp \log L$,
and its top loop $\mathcal L_0$ has cube-root fluctuations: e.g., if $\rho(x)$
is the vertical displacement of $\mathcal L_0$ from the bottom boundary point
$(x,0)$, then $\max \rho(x) = L^{1/3+o(1)}$ over $x\in
I_0:=L/2+[[-L^{2/3},L^{2/3}]]$. It is believed that rescaling $\rho$ by
$L^{1/3}$ and $I_0$ by $L^{2/3}$ would yield a limit law of a diffusion on
$[-1,1]$. However, no nontrivial lower bound was known on $\rho(x)$ for a fixed
$x\in I_0$ (e.g., $x=\frac L2$), let alone on $\min\rho(x)$ in $I_0$, to
complement the bound on $\max\rho(x)$. Here we show a lower bound of the
predicted order $L^{1/3}$: for every $\epsilon>0$ there exists $\delta>0$ such
that $\min_{x\in I_0} \rho(x) \geq \delta L^{1/3}$ with probability at least
$1-\epsilon$. The proof relies on the Ornstein--Zernike machinery due to
Campanino-Ioffe-Velenik, and a result of Ioffe, Shlosman and Toninelli (2015)
that rules out pinning in Ising polymers with modified interactions along the
boundary. En route, we refine the latter result into a Brownian excursion limit
law, which may be of independent interest. We further show that in a $ K
L^{2/3}\times K L^{2/3}$ box with boundary conditions $\mathfrak h-1,\mathfrak
h,\mathfrak h,\mathfrak h$ (i.e., $\mathfrak h-1$ on the bottom side and
$\mathfrak h$ elsewhere), the limit of $\rho(x)$ as $K,L\to\infty$ is a
Ferrari--Spohn diffusion.


  Deep networks are prone to performance degradation when there is a domain
shift between the source (training) data and target (test) data. Recent
test-time adaptation methods update batch normalization layers of pre-trained
source models deployed in new target environments with streaming data to
mitigate such performance degradation. Although such methods can adapt
on-the-fly without first collecting a large target domain dataset, their
performance is dependent on streaming conditions such as mini-batch size and
class-distribution, which can be unpredictable in practice. In this work, we
propose a framework for few-shot domain adaptation to address the practical
challenges of data-efficient adaptation. Specifically, we propose a constrained
optimization of feature normalization statistics in pre-trained source models
supervised by a small support set from the target domain. Our method is easy to
implement and improves source model performance with as few as one sample per
class for classification tasks. Extensive experiments on 5 cross-domain
classification and 4 semantic segmentation datasets show that our method
achieves more accurate and reliable performance than test-time adaptation,
while not being constrained by streaming conditions.


  We establish an algorithm which computes formulae for the CR GJMS operators,
the $P^\prime$-operator, and the $Q^\prime$-curvature in terms of CR tractors.
When applied to torsion-free pseudo-Einstein contact forms, this algorithm both
gives an explicit factorisation of the CR GJMS operators and the
$P^\prime$-operator, and shows that the $Q^\prime$-curvature is constant, with
the constant explicitly given in terms of the Webster scalar curvature. We also
use our algorithm to derive local formulae for the $P^\prime$-operator and
$Q^\prime$-curvature of a five-dimensional pseudo-Einstein manifold. Comparison
with Marugame's formulation of the Burns--Epstein invariant as the integral of
a pseudohermitian invariant yields new insights into the class of local
pseudohermitian invariants for which the total integral is independent of the
choice of pseudo-Einstein contact form.


  We examine dijet production at large rapidity intervals at Tevatron energies
by comparing an exact ${\cal O}(\alpha_s^3)$ calculation with the BFKL
approximation, which resums the leading powers of the rapidity interval $y$ to
all orders in $\alpha_s$. We analyze the dependence of the exact ${\cal
O}(\alpha_s^3)$ calculation on the jet cone-size as a function of $y$, and use
this cross section to define an ``effective rapidity'' $\hat y$ which reduces
the error that the large-$y$ approximation induces on the kinematics. Using
$\hat y$ in the BFKL resummation, we reexamine jet production at large
transverse momenta and the transverse momentum decorrelation of the tagging
jets. We find less dramatic, but still significant, effects than found
previously using the large-$y$ approximation.


  Social media platforms often assume that users can self-correct against
misinformation. However, social media users are not equally susceptible to all
misinformation as their biases influence what types of misinformation might
thrive and who might be at risk. We call "diverse misinformation" the complex
relationships between human biases and demographics represented in
misinformation. To investigate how users' biases impact their susceptibility
and their ability to correct each other, we analyze classification of deepfakes
as a type of diverse misinformation. We chose deepfakes as a case study for
three reasons: 1) their classification as misinformation is more objective; 2)
we can control the demographics of the personas presented; 3) deepfakes are a
real-world concern with associated harms that must be better understood. Our
paper presents an observational survey (N=2,016) where participants are exposed
to videos and asked questions about their attributes, not knowing some might be
deepfakes. Our analysis investigates the extent to which different users are
duped and which perceived demographics of deepfake personas tend to mislead. We
find that accuracy varies by demographics, and participants are generally
better at classifying videos that match them. We extrapolate from these results
to understand the potential population-level impacts of these biases using a
mathematical model of the interplay between diverse misinformation and crowd
correction. Our model suggests that diverse contacts might provide "herd
correction" where friends can protect each other. Altogether, human biases and
the attributes of misinformation matter greatly, but having a diverse social
group may help reduce susceptibility to misinformation.


  In the first part of this thesis Bell's theorem is revisited. It points at a
difference between the quantum and the classical world. This difference is
often behind the advantages of solutions using quantum mechanics. New and more
general versions of Bell inequalities are presented. These inequalities involve
multiple settings per observer. Compared with the two-setting inequalities, the
new ones reveal the non-classical character of a broader class of states. Some
of them are also proven to be optimal (tight). Next, we go beyond Bell's
theorem. It is shown, both in theory and in experiment, that incompatibility
between quantum mechanics and realistic theories can be extended into an
important class of nonlocal models. We also show that the violation of Bell
inequalities disqualifies local realistic models with a limited lack of the
experimenter's freedom. This, at first glance quite philosophical result, has
its down-to-earth implications for quantum communication. In the second part of
the thesis well-known examples of quantum communication are reviewed. Next, new
results concerning quantum cryptography and quantum communication complexity
are given.


  Medical image analysis typically includes several tasks such as enhancement,
segmentation, and classification. Traditionally, these tasks are implemented
using separate deep learning models for separate tasks, which is not efficient
because it involves unnecessary training repetitions, demands greater
computational resources, and requires a relatively large amount of labeled
data. In this paper, we propose a multi-task training approach for medical
image analysis, where individual tasks are fine-tuned simultaneously through
relevant knowledge transfer using a unified modality-specific feature
representation (UMS-Rep). We explore different fine-tuning strategies to
demonstrate the impact of the strategy on the performance of target medical
image tasks. We experiment with different visual tasks (e.g., image denoising,
segmentation, and classification) to highlight the advantages offered with our
approach for two imaging modalities, chest X-ray and Doppler echocardiography.
Our results demonstrate that the proposed approach reduces the overall demand
for computational resources and improves target task generalization and
performance. Further, our results prove that the performance of target tasks in
medical images is highly influenced by the utilized fine-tuning strategy.


  Action recognition is an important problem in multimedia understanding. This
paper addresses this problem by building an expressive compositional action
model. We model one action instance in the video with an ensemble of
spatio-temporal compositions: a number of discrete temporal anchor frames, each
of which is further decomposed to a layout of deformable parts. In this way,
our model can identify a Spatio-Temporal And-Or Graph (STAOG) to represent the
latent structure of actions e.g. triple jumping, swinging and high jumping. The
STAOG model comprises four layers: (i) a batch of leaf-nodes in bottom for
detecting various action parts within video patches; (ii) the or-nodes over
bottom, i.e. switch variables to activate their children leaf-nodes for
structural variability; (iii) the and-nodes within an anchor frame for
verifying spatial composition; and (iv) the root-node at top for aggregating
scores over temporal anchor frames. Moreover, the contextual interactions are
defined between leaf-nodes in both spatial and temporal domains. For model
training, we develop a novel weakly supervised learning algorithm which
iteratively determines the structural configuration (e.g. the production of
leaf-nodes associated with the or-nodes) along with the optimization of
multi-layer parameters. By fully exploiting spatio-temporal compositions and
interactions, our approach handles well large intra-class action variance (e.g.
different views, individual appearances, spatio-temporal structures). The
experimental results on the challenging databases demonstrate superior
performance of our approach over other competing methods.


  Conventional active array radars often jointly design the transmit and
receive beamforming for effectively suppressing interferences. To further
promote the interference suppression performance, this paper introduces a
reconfigurable intelligent surface (RIS) to assist the radar receiver because
the RIS has the ability to bring plentiful additional degrees-of-freedom. To
maximize the output signal-to-interference-plus-noise ratio (SINR) of receive
array, we formulate the codesign of transmit beamforming and RIS-assisted
receive beamforming into a nonconvex constrained fractional programming
problem, and then propose an alternating minimization-based algorithm to
jointly optimize the transmitor beamfmer, receive beamformer and RIS reflection
coefficients. Concretely, we translate the RIS reflection coefficients design
into a series of unimodular quadratic programming (UQP) subproblems by
employing the Dinkelbach transform, and offer the closed-form optimal solutions
of transmit and receive beamformers according to the minimum variance
distortionless response principle. To tackle the UQP subproblems efficiently,
we propose a second-order Riemannian Newton method (RNM) with improved
Riemannian Newton direction, which avoids the line search and has better
convergence speed than typical first-order Riemannian manifold optimization
methods. Moreover, we derive the convergence of the proposed codesign algorithm
by deducing the explicit convergence condition of RNM. We also analyze the
computational complexity. Numerical results demonstrate that the proposed
RIS-assisted array radar has superior performance of interference suppression
to the RIS-free one, and the SINR improvement is proportional to the number of
RIS elements.


  This article introduces a model-agnostic approach to study statistical
synergy, a form of emergence in which patterns at large scales are not
traceable from lower scales. Our framework leverages various multivariate
extensions of Shannon's mutual information, and introduces the O-information as
a metric capable of characterising synergy- and redundancy-dominated systems.
We develop key analytical properties of the O-information, and study how it
relates to other metrics of high-order interactions from the statistical
mechanics and neuroscience literature. Finally, as a proof of concept, we use
the proposed framework to explore the relevance of statistical synergy in
Baroque music scores.


  In this paper, we study the distribution of the so-called "Yule's nonsense
correlation statistic" on a time interval $[0,T]$ for a time horizon $T>0$ ,
when $T$ is large, for a pair $(X_{1},X_{2})$ of independent Ornstein-Uhlenbeck
processes. This statistic is by definition equal to : \begin{equation*} \rho
(T):=\frac{Y_{12}(T)}{\sqrt{Y_{11}(T)}\sqrt{Y_{22}(T)}}, \end{equation*} where
the random variables $Y_{ij}(T)$, $i,j=1,2$ are defined as \begin{equation*}
Y_{ij}(T):=\int_{0}^{T}X_{i}(u)X_{j}(u)du-T\bar{X}_{i}\bar{X_{j}},
\bar{X}_{i}:=\frac{1}{T}\int_{0}^{T}X_{i}(u)du. \end{equation*} We assume
$X_{1}$ and $X_{2}$ have the same drift parameter $\theta >0$. We also study
the asymptotic law of a discrete-type version of $\rho (T)$, where $Y_{ij}(T)$
above are replaced by their Riemann-sum discretizations. In this case,
conditions are provided for how the discretization (in-fill) step relates to
the long horizon $T$. We establish identical normal asymptotics for
standardized $\rho (T)$ and its discrete-data version. The asymptotic variance
of $\rho (T)T^{1/2}$ is $\theta ^{-1}$. We also establish speeds of convergence
in the Kolmogorov distance, which are of Berry-Ess\'een-type
(constant*$T^{-1/2}$) except for a $\ln T$ factor. Our method is to use the
properties of Wiener-chaos variables, since $\rho (T)$ and its discrete version
are comprised of ratios involving three such variables in the 2nd Wiener chaos.
This methodology accesses the Kolmogorov distance thanks to a relation which
stems from the connection between the Malliavin calculus and Stein's method on
Wiener space.


  Einstein's gravity in AdS space coupled to nonlinear electrodynamics is
studied. We analyse the metric, mass functions and corrections to the
Reissner-Nordstrom solution. Magnetic black holes thermodynamics in extended
phase space is investigated. We formulate the first law of black hole
thermodynamics showing that the generalized Smarr relation holds. The black
hole stability is studied by evaluating the Gibbs free energy and heat
capacity. To study the cooling and heating phase transitions of black holes we
consider the Joule--Thomson isenthalpic expansion. The Joule--Thomson
coefficient and the inversion temperature are calculated.


  Let $\{D_i\}_{i=1}^{n+1}$ be $n+1$ hypersurfaces in
$\mathbb{P}^n(\mathbb{C})$ with total degrees $\sum_{i=1}^{n+1} \deg
D_i\geqslant n+2$, in general position and satisfying a generic geometric
condition: every $n$ hypersurfaces intersect only at smooth points and the
intersection is transversal. Then, for every algebraically nondegenerate entire
holomorphic curve $f\colon\mathbb{C}\rightarrow\mathbb{P}^n(\mathbb{C})$, we
show a Second Main Theorem: $$ \sum_{i=1}^{n+1} \delta_f(D_i) < n+1 $$ in terms
of defect inequality in Nevanlinna theory. This is the first result in the
literature on Second Main Theorem for $n+1$ general hypersurfaces in
$\mathbb{P}^n(\mathbb{C})$ with optimal total degrees.


  We investigate the effects of 1/f noise on the ability of a particular class
of Cosmic Microwave Background experiments to measure the angular power
spectrum of temperature anisotropy. We concentrate on experiments that operate
primarily in raster-scan mode and develop formalism that allows us to calculate
analytically the effect of 1/f noise on power spectrum sensitivity for this
class of experiments and determine the benefits of raster-scanning at different
angles relative to the sky field versus scanning at only a single angle
(cross-linking versus not cross-linking). We find that the sensitivity of such
experiments in the presence of 1/f noise is not significantly degraded at
moderate spatial scales (l ~ 100) for reasonable values of scan speed and 1/f
knee. We further find that the difference between cross-linked and
non-cross-linked experiments is small in all cases and that the
non-cross-linked experiments are preferred from a raw sensitivity standpoint in
the noise-dominated regime -- i.e., in experiments in which the instrument
noise is greater than the sample variance of the target power spectrum at the
scales of interest. This analysis does not take into account systematic
effects.


  In this article, we define a very important sequence of functions, all the
functions of this sequence present behaviors very close to that of the Collatz
function. The study of such functions allows us to obtain very interesting
results concerning the collatz conjecture and more precisely concerning the
generalization of this problem, the nature of the Collatz function, on the
statement of the Collatz conjecture we show that this conjecture can be stated
for each function on a well-determined subset of Z and other interesting
properties in relation to the behaviors of Collatz sequences are studied and
proved in this article.


  The CERN IT provides a set of Hadoop clusters featuring more than 5 PBytes of
raw storage with different open-source, user-level tools available for
analytical purposes. The CMS experiment started collecting a large set of
computing meta-data, e.g. dataset, file access logs, since 2015. These records
represent a valuable, yet scarcely investigated, set of information that needs
to be cleaned, categorized and analyzed. CMS can use this information to
discover useful patterns and enhance the overall efficiency of the distributed
data, improve CPU and site utilization as well as tasks completion time. Here
we present evaluation of Apache Spark platform for CMS needs. We discuss two
main use-cases CMS analytics and ML studies where efficient process billions of
records stored on HDFS plays an important role. We demonstrate that both Scala
and Python (PySpark) APIs can be successfully used to execute extremely I/O
intensive queries and provide valuable data insight from collected meta-data.


  Earth is unusual in bearing life, and in having a large moon. A number of
authors have suggested a possible connection between the two, e.g. through
lunar stabilisation of the earth's obliquity, or through the effects of the
oceanic tides. The various suggestions are reviewed.


  Structural or crystal asymmetry are necessary conditions for emergence of
zero-bias photocurrent in light detectors. Structural asymmetry has been
typically achieved via $p-n$ doping being a technologically complex process.
Here, we propose an alternative approach to achieve zero-bias photocurrent in
2d material flakes exploiting the geometrical non-equivalence of source and
drain contacts. As a prototypical example, we equip a square-shaped flake of
PdSe$_2$ with mutually orthogonal metal leads. Upon uniform illumination with
linearly-polarized light, the device demonstrates non-zero photocurrent which
flips its sign upon 90$^\circ$ polarization rotation. The origin of zero-bias
photocurrent lies in polarization-dependent lightning-rod effect. It enhances
the electromagnetic field at one contact from the orthogonal pair, and
selectively activates the internal photoeffect at the respective metal-PdSe$_2$
Schottky junction. The proposed technology of contact engineering can be
extended to arbitrary 2d materials and detection of both polarized and natural
light.


  If two species exhibit different nonlinear responses to a single shared
resource, and if each species modifies the resource dynamics such that this
favors its competitor, they may stably coexist. This coexistence mechanism,
known as relative nonlinearity of competition, is well understood
theoretically, but less is known about its evolutionary properties and its
prevalence in real communities. We address this challenge by using adaptive
dynamics theory and individual-based simulations to compare community
stabilization and evolutionary stability of species that coexist by relative
nonlinearity. In our analysis, evolution operates on the species'
density-compensation strategies, and we consider a trade-off between population
growth rates at high and low resource availability. We confirm previous
findings that, irrespective of the particular model of density dependence,
there are many combinations of overcompensating and undercompensating
density-compensation strategies that allow stable coexistence by relative
nonlinearity. However, our analysis also shows that most of these strategy
combinations are not evolutionarily stable and will be outcompeted by an
intermediate density-compensation strategy. Only very specific trade-offs lead
to evolutionarily stable coexistence by relative nonlinearity. As we find no
reason why these particular trade-offs should be common in nature, we conclude
that the sympatric evolution and evolutionary stability of relative
nonlinearity, while possible in principle, seems rather unlikely. We speculate
that this may, at least in part, explain why empirical demonstrations of this
coexistence mechanism are rare, noting, however, that the difficulty to detect
relative nonlinearity in the field [...]


  Blind image deblurring remains a topic of enduring interest. Learning based
approaches, especially those that employ neural networks have emerged to
complement traditional model based methods and in many cases achieve vastly
enhanced performance. That said, neural network approaches are generally
empirically designed and the underlying structures are difficult to interpret.
In recent years, a promising technique called algorithm unrolling has been
developed that has helped connect iterative algorithms such as those for sparse
coding to neural network architectures. However, such connections have not been
made yet for blind image deblurring. In this paper, we propose a neural network
architecture based on this idea. We first present an iterative algorithm that
may be considered as a generalization of the traditional total-variation
regularization method in the gradient domain. We then unroll the algorithm to
construct a neural network for image deblurring which we refer to as Deep
Unrolling for Blind Deblurring (DUBLID). Key algorithm parameters are learned
with the help of training images. Our proposed deep network DUBLID achieves
significant practical performance gains while enjoying interpretability at the
same time. Extensive experimental results show that DUBLID outperforms many
state-of-the-art methods and in addition is computationally faster.


  In this paper, we study the problem of learning to satisfy temporal logic
specifications with a group of agents in an unknown environment, which may
exhibit probabilistic behaviour. From a learning perspective these
specifications provide a rich formal language with which to capture tasks or
objectives, while from a logic and automated verification perspective the
introduction of learning capabilities allows for practical applications in
large, stochastic, unknown environments. The existing work in this area is,
however, limited. Of the frameworks that consider full linear temporal logic or
have correctness guarantees, all methods thus far consider only the case of a
single temporal logic specification and a single agent. In order to overcome
this limitation, we develop the first multi-agent reinforcement learning
technique for temporal logic specifications, which is also novel in its ability
to handle multiple specifications. We provide correctness and convergence
guarantees for our main algorithm - ALMANAC (Automaton/Logic Multi-Agent
Natural Actor-Critic) - even when using function approximation. Alongside our
theoretical results, we further demonstrate the applicability of our technique
via a set of preliminary experiments.


  A conceptual variable is any variable defined by a person or by a group of
persons. Such variables may be inaccessible, meaning that they cannot be
measured with arbitrary accuracy on the physical system under consideration at
any given time. An example may be the spin vector of a particle; another
example may be the vector (position, momentum). In this paper, a space of
inaccessible conceptual variables is defined, and group actions are defined on
this space. Accessible functions are then defined on the same space. Assuming
this structure, the basic Hilbert space structure of quantum theory is derived:
Operators on a Hilbert space corresponding to the accessible variables are
introduced; when these operators have a discrete spectrum, a natural model
reduction implies a new model in which the values of the accessible variables
are the eigenvalues of the operator. The principle behind this model reduction
demands that a group action may also be defined also on the accessible
variables; this is possible if the corresponding functions are permissible, a
term that is precisely defined. The following recent principle from statistics
is assumed: every model reduction should be to an orbit or to a set of orbits
of the group. From this derivation, a new interpretation of quantum theory is
briefly discussed: I argue that a state vector may be interpreted as connected
to a focused question posed to nature together with a definite answer to this
question. Further discussion of these topics is provided in a recent book
published by the author of this paper.


  The paper is devoted to the study and applications of criticality of Lagrange
multipliers in variational systems, which are associated with the class of
problems in composite optimization known as extended nonlinear programming
(ENLP). The importance of both ENLP and the concept of multiplier criticality
in variational systems has been recognized in theoretical and numerical aspects
of optimization and variational analysis, while the criticality notion has
never been investigated in the ENLP framework. We present here a systematic
study of critical and noncritical multipliers in a general variational setting
that covers, in particular, KKT systems in ENLP with establishing their
verifiable characterizations as well as relationships between noncriticality
and other stability notions in variational analysis. Our approach is mainly
based on advanced tools of second-order variational analysis and generalized
differentiation.


  Over two decades ago, a prominent, mysterious emission band peaking at ~20.1
micrometer was serendipitously detected in four preplanetary nebulae (PPNe;
also known as "protoplanetary nebulae"). So far, this spectral feature,
designated as the "21 micrometer" feature, has been seen in 18 carbon-rich
PPNe. The nature of the carriers of this feature remains unknown although many
candidate materials have been proposed. The 21 micrometer sources also exhibit
an equally mysterious, unidentified emission feature peaking at 30 micrometer.
While the 21 micrometer feature is exclusively seen in PPNe, a short-lived
evolutionary stage between the end of the asymptotic giant branch (AGB) and
planetary nebula (PN) phases, the 30 micrometer feature is commonly observed in
all stages of stellar evolution from the AGB through PPN to PNe phases. We
derive the stellar mass loss rates (M_{loss}) of these 21 micrometer sources
from their dust infrared (IR) emission, using the "2-DUST" radiative transfer
code for axisymmetric dusty systems which allows one to distinguish the mass
loss rates of the AGB phase (\dot{M_{AGB}}) from that of the superwind
(\dot_{M_{SW}}) phase. We examine the correlation between \dot{M_{AGB}} or
\dot_{M_{SW}} and the fluxes emitted from the 21 and 30 micrometer features. We
find that both features tend to correlate with \dot{M_{AGB}}, suggesting that
their carriers are probably formed in the AGB phase. The nondetection of the 21
micrometer feature in AGB stars suggests that, unlike the 30 micrometer
feature, the excitation of the carriers of the 21 micrometer feature may
require ultraviolet photons which are available in PPNe but not in AGB stars.


  The second order perturbative field equations for slowly and rigidly rotating
perfect fluid balls of Petrov type D are solved numerically. It is found that
all the slowly and rigidly rotating perfect fluid balls up to second order,
irrespective of Petrov type, may be matched to a possibly non-asymptotically
flat stationary axisymmetric vacuum exterior. The Petrov type D interior
solutions are characterized by five integration constants, corresponding to
density and pressure of the zeroth order configuration, the magnitude of the
vorticity, one more second order constant and an independent spherically
symmetric second order small perturbation of the central pressure. A
four-dimensional subspace of this five-dimensional parameter space is
identified for which the solutions can be matched to an asymptotically flat
exterior vacuum region. Hence these solutions are completely determined by the
spherical configuration and the magnitude of the vorticity. The physical
properties like equations of state, shapes and speeds of sound are determined
for a number of solutions.


  This work focuses on cost reduction methods for forest species recognition
systems. Current state-of-the-art shows that the accuracy of these systems have
increased considerably in the past years, but the cost in time to perform the
recognition of input samples has also increased proportionally. For this
reason, in this work we focus on investigating methods for cost reduction
locally (at either feature extraction or classification level individually) and
globally (at both levels combined), and evaluate two main aspects: 1) the
impact in cost reduction, given the proposed measures for it; and 2) the impact
in recognition accuracy. The experimental evaluation conducted on two forest
species datasets demonstrated that, with global cost reduction, the cost of the
system can be reduced to less than 1/20 and recognition rates that are better
than those of the original system can be achieved.


  For a class of quantized open chaotic systems satisfying a natural dynamical
assumption, we show that the study of the resolvent, and hence of scattering
and resonances, can be reduced to the study of a family of open quantum maps,
that is of finite dimensional operators obtained by quantizing the Poincar\'e
map associated with the flow near the set of trapped trajectories.


  The properties of a front between two different phases in the presence of a
smoothly inhomogeneous external field that takes its critical value at the
crossing point is analyzed. Two generic scenarios are studied. In the first,
the system admits a bistable solution and the external field governs the rate
in which one phase invades the other. The second mechanism corresponds to a
second order transition that, in the case of reactive systems, takes the form
of a transcritical bifurcation at the crossing point. We solve for the front
shape and its response to external white noise, showing that static properties
and also some of the dynamics features cannot distinguish between the two
scenarios. The only reliable indicator turns out to be the fluctuation
statistics. These take a Gaussian form in the bifurcation case and a
double-peak shape in a bistable system. The results of a recent analysis of the
morphogenesis process in Drosophila embryos are reanalyzed and we show, in
contrast with the interpretation suggested by Krotov et. al., that the
plausible underlying dynamics is bistable and not bifurcational.


  Model-based approaches to imaging, like specialized image enhancements in
astronomy, facilitate explanations of relationships between observed inputs and
computed outputs. These models may be expressed with extended matrix-vector
(EMV) algebra, especially when they involve only scalars, vectors, and
matrices, and with n-mode or index notations, when they involve
multidimensional arrays, also called numeric tensors or, simply, tensors. While
this paper features an example, inspired by exoplanet imaging, that employs
tensors to reveal (inverse) 2D fast Fourier transforms in an image enhancement
model, the work is actually about the tensor algebra and software, or tensor
frameworks, available for model-based imaging. The paper proposes a
Ricci-notation tensor (RT) framework, comprising a dual-variant index notation,
with Einstein summation convention, and codesigned object-oriented software,
called the RTToolbox for MATLAB. Extensions to Ricci notation offer novel
representations for entrywise, pagewise, and broadcasting operations popular in
EMV frameworks for imaging. Complementing the EMV algebra computable with
MATLAB, the RTToolbox demonstrates programmatic and computational efficiency
via careful design of numeric tensor and dual-variant index classes. Compared
to its closest competitor, also a numeric tensor framework that uses index
notation, the RT framework enables superior ways to model imaging problems and,
thereby, to develop solutions.


  We present a simple method to automatically evaluate arbitrary tree-level
amplitudes involving the production or decay of a heavy quark pair QQbar in a
generic {2S+1}L_J^[1,8] state, i.e., the short distance coefficients appearing
in the NRQCD factorization formalism. Our approach is based on extracting the
relevant contributions from the open heavy quark-antiquark amplitudes through
an expansion with respect to the quark-antiquark relative momentum and the
application of suitable color and spin projectors. To illustrate the
capabilities of the method and its implementation in MadGraph a few
applications to quarkonium collider phenomenology are presented.


  In this paper, we discuss the application of extreme value theory in the
context of stationary $\beta$-mixing sequences that belong to the Fr\'echet
domain of attraction. In particular, we propose a methodology to construct
bias-corrected tail estimators. Our approach is based on the combination of two
estimators for the extreme value index to cancel the bias. The resulting
estimator is used to estimate an extreme quantile. In a simulation study, we
outline the performance of our proposals that we compare to alternative
estimators recently introduced in the literature. Also, we compute the
asymptotic variance in specific examples when possible. Our methodology is
applied to two datasets on finance and environment.


  To recognize sub-micron range low energy tracks recorded in a super fine
grained nuclear emulsion (Nano Imaging Tracker), an elliptical fitting method
was devised to analyze anisotropic images taken by an optical microscope. In
this paper, we will report on this newly developed method using discrete
Fourier transform and second-order moment analysis of the brightness
distribution. We succeeded in lowering the ellipticity threshold, thereby
improving the detection efficiency and angular resolution. Notably, the success
of detecting carbon 30 keV tracks is the first such achievement in the world,
where the incident direction of carbon 30 keV ions was determined with an
accuracy of 41 degree and an efficiency of 1.7%.


  Mixtures of Gaussians, factor analyzers (probabilistic PCA) and hidden Markov
models are staples of static and dynamic data modeling and image and video
modeling in particular. We show how topographic transformations in the input,
such as translation and shearing in images, can be accounted for in these
models by including a discrete transformation variable. The resulting models
perform clustering, dimensionality reduction and time-series analysis in a way
that is invariant to transformations in the input. Using the EM algorithm,
these transformation-invariant models can be fit to static data and time
series. We give results on filtering microscopy images, face and facial pose
clustering, handwritten digit modeling and recognition, video clustering,
object tracking, and removal of distractions from video sequences.


  What happens when a continuously evolving stochastic process is interrupted
with large changes at random intervals $\tau$ distributed as a power-law $\sim
\tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and
the large changes as abrupt resets to the initial condition, we obtain {\em
exact} closed-form expressions for both static and dynamic quantities, while
accounting for strong correlations implied by a power-law. Our results show
that the resulting dynamics exhibits a spectrum of rich long-time behavior,
from an ever-spreading spatial distribution for $\alpha < 1$, to one that is
time independent for $\alpha > 1$. The dynamics has strong consequences on the
time to reach a distant target for the first time; we specifically show that
there exists an optimal $\alpha$ that minimizes the mean time to reach the
target, thereby offering a step towards a viable strategy to locate targets in
a crowded environment.


  We study overconvergence phenomena for $\mathbb F_q$-linear functions on a
function field over a finite field $\mathbb F_q$. In particular, an analog of
the Dwork exponential is introduced.


  We extend our theory of amorphous packings of hard spheres to binary mixtures
and more generally to multicomponent systems. The theory is based on the
assumption that amorphous packings produced by typical experimental or
numerical protocols can be identified with the infinite pressure limit of long
lived metastable glassy states. We test this assumption against numerical and
experimental data and show that the theory correctly reproduces the variation
with mixture composition of structural observables, such as the total packing
fraction and the partial coordination numbers.


  One of the most promising methods to measure the spin of an accreting black
hole is fitting the broad iron K$\alpha$ line in the X-ray spectrum. The line
profile also depends on the geometry of the hard X-ray emitting corona. To put
constraints on the black hole spin and corona geometry, it is essential to
understand how do they affect the iron K$\alpha$ line emissivity profile. In
this work, we present calculations of the illumination and the iron K$\alpha$
emissivity profiles performed with the Monte-Carlo GR radiative transfer code
Monk. We focus on distinction between the illumination and emissivity profiles,
which is in most previous studies neglected. We show that especially for the
case of black hole X-ray binaries (BHXRBs), the difference is very large. For
active galactic nuclei (AGNs), the emissivity profile has a more similar shape
as the illumination profile, but it is notably steeper in the innermost region
within a few gravitational radii. We find out that the different behavior
between AGN and black hole X-ray binary discs is due to the different energy
spectra of the illuminating radiation. This suggests that the emissivity
profile of the iron K$\alpha$ line cannot be determined by black hole spin and
corona geometry alone and the energy spectrum of the illuminating radiation has
to be taken into account. We also examined the effect of including the
self-irradiation, and find it to be more important than the corona emission in
BHXRBs.