  We consider the dynamics of the photon states in distant resonators coupled
to a common bus resonator at different positions. The frequencies of distant
resonators from a common bus resonator are equally detuned. These frequency
detunings are kept larger than the coupling strengths of each resonator to the
common bus resonator to satisfy the dispersive interaction regime. In the
dispersive regime, we show that the time dynamics of the system evolve to an
arbitrary W-type state in a single step at various interaction times. Our
results show that a one-step generation of arbitrary W-type states can be
achieved with high fidelity in a system of superconducting resonators.


  When Beppo-SAX measured the 0.1--12 keV spectrum of RE J1034+396,
observations in the optical, UV and EUV were also taken within a few weeks.
This multiwavelength spectrum placed very strong constraints on its unusually
hot big blue bump component, which has been attributed to a high (almost
Eddington) rate of accretion onto a disk surrounding a low mass black hole.
However, while a simple, geometrically-thin accretion disk provides a good fit
to the UV to X-ray continuum, it leaves a residual flat and featureless
component in the optical. We propose that the disk is actually flared or warped
and that the central ionizing EUV/X-ray continuum is irradiating the outer
parts of the disk and boosting the optical/UV continuum flux. The relatively
narrow permitted lines may be due to a resulting disk wind. This physical
interpretation may explain the link between ultrasoft X-ray excesses and broad
line velocity in the AGN class as a whole. It may also have implications for
the possible relationship between ultrasoft AGN and galactic black holes.


  A computationally-simplified and descriptor-richer Point Cloud Quality
Assessment (PCQA) metric, namely PointPCA+, is proposed in this paper, which is
an extension of PointPCA. PointPCA proposed a set of perceptually-relevant
descriptors based on PCA decomposition that were applied to both the geometry
and texture data of point clouds for full reference PCQA. PointPCA+ employs PCA
only on the geometry data while enriching existing geometry and texture
descriptors, that are computed more efficiently. Similarly to PointPCA, a total
quality score is obtained through a learning-based fusion of individual
predictions from geometry and texture descriptors that capture local shape and
appearance properties, respectively. Before feature fusion, a feature selection
module is introduced to choose the most effective features from a proposed
super-set. Experimental results show that PointPCA+ achieves high predictive
performance against subjective ground truth scores obtained from publicly
available datasets. The code is available at
\url{https://github.com/cwi-dis/pointpca_suite/}.


  A rigidity theorem that applies to smooth electrovac spacetimes which
represent either (A) an asymptotically flat stationary black hole or (B) a
cosmological spacetime with a compact Cauchy horizon ruled by closed null
geodesics was given in a recent work \cite{frw}. Here we enlarge the framework
of the corresponding investigations by allowing the presence of other type of
matter fields. In the first part the matter fields are involved merely
implicitly via the assumption that the dominant energy condition is satisfied.
In the second part Einstein-Klein-Gordon (EKG), Einstein-[non-Abelian] Higgs
(E[nA]H), Einstein-[Maxwell]-Yang-Mills-dilaton (E[M]YMd) and
Einstein-Yang-Mills-Higgs (EYMH) systems are studied. The black hole event
horizon or, respectively, the compact Cauchy horizon of the considered
spacetimes is assumed to be a smooth non-degenerate null hypersurface. It is
proven that there exists a Killing vector field in a one-sided neighborhood of
the horizon in EKG, E[nA]H, E[M]YMd and EYMH spacetimes. This Killing vector
field is normal to the horizon, moreover, the associated matter fields are also
shown to be invariant with respect to it. The presented results provide
generalizations of the rigidity theorems of Hawking (for case A) and of
Moncrief and Isenberg (for case B) and, in turn, they strengthen the validity
of both the black hole rigidity scenario and the strong cosmic censor
conjecture of classical general relativity.


  I present a new algorithm, CALCLENS, for efficiently computing weak
gravitational lensing shear signals from large N-body light cone simulations
over a curved sky. This new algorithm properly accounts for the sky curvature
and boundary conditions, is able to produce redshift-dependent shear signals
including corrections to the Born approximation by using multiple-plane ray
tracing, and properly computes the lensed images of source galaxies in the
light cone. The key feature of this algorithm is a new, computationally
efficient Poisson solver for the sphere that combines spherical harmonic
transform and multgrid methods. As a result, large areas of sky (~10, 000
square degrees) can be ray traced efficiently at high-resolution using only a
few hundred cores on widely available machines. Using this new algorithm and
curved-sky calculations that only use a slower but more accurate spherical
harmonic transform Poisson solver, I study the shear B-mode and rotation mode
power spectra. Employing full-sky E/B-mode decompositions, I confirm that the
shear B-mode and rotation mode power spectra are equal at high accuracy (~1%),
as expected from perturbation theory up to second order. Coupled with realistic
galaxy populations placed in large N-body light cone simulations, this new
algorithm is ideally suited for the construction of synthetic weak lensing
shear catalogs to be used to test for systematic effects in data analysis
procedures for upcoming large-area sky surveys. The implementation presented in
this work, written in C and employing widely available software libraries to
maintain portability, is publicly available at
http://code.google.com/p/calclens.


  We aim at assessing the states of the nodes in a network by means of
end-to-end monitoring paths. The contribution of this paper is twofold. First,
we consider a static failure scenario. In this context, we aim at minimizing
the number of probes to obtain failure identification. To face this problem, we
propose a progressive approach to failure localization based on stochastic
optimization, whose solution is the optimal sequence of monitoring paths to
probe.
  We address the complexity of the problem by proposing a greedy strategy in
two variants: one considers exact calculation of posterior probabilities of
node failures, given the observation, whereas the other approximates these
values by means of a novel failure centrality metric. Secondly, we adapt these
two strategies to a dynamic failure scenario where nodes states can change
throughout a monitoring period. By means of numerical experiments conducted on
real network topologies, we demonstrate the practical applicability of our
approach. Our performance evaluation evidences the superiority of our
algorithms with respect to state of the art solutions based on classic Boolean
Network Tomography as well as approaches based on sequential group testing.


  Fish kill events (FKE) in the caldera lake of Taal occur rarely (only 0.5\%
in the last 10 years) but each event has a long-term effect on the
environmental health of the lake ecosystem, as well as a devastating effect on
the financial and emotional aspects of the residents whose livelihood rely on
aquaculture farming. Predicting with high accuracy when within seven days and
where on the vast expanse of the lake will FKEs strike will be a very important
early warning tool for the lake's aquaculture industry. Mathematical models to
predict the occurrences of FKEs developed by several studies done in the past
use as predictors the physico-chemical characteristics of the lake water, as
well as the meteorological parameters above it. Some of the models, however,
did not provide acceptable predictive accuracy and enough early warning because
they were developed with unbalanced binary data set, i.e., characterized by
dense negative examples (no FKE) and highly sparse positive examples (with
FKE). Other models require setting up an expensive sensor network to measure
the water parameters not only at the surface but also at several depths.
Presented in this paper is a system for capturing, measuring, and visualizing
the contextual sentiment polarity (CSP) of dated and geolocated social media
microposts of residents within 10km radius of the Taal Volcano crater
($14^\circ$N, $121^\circ$E). High frequency negative CSP co-occur with FKE for
two occasions making human expressions a viable non-physical sensors for
impending FKE to augment existing mathematical models.


  Leveraging over 30,000 images each with up to 89 labels collected by
Recology---an integrated resource recovery company with both residential and
commercial trash, recycling and composting services---the authors develop
ContamiNet, a convolutional neural network, to identify contaminating material
in residential recycling and compost bins. When training the model on a subset
of labels that meet a minimum frequency threshold, ContamiNet preforms almost
as well human experts in detecting contamination (0.86 versus 0.88 AUC).
Recology is actively piloting ContamiNet in their daily municipal solid waste
(MSW) collection to identify contaminants in recycling and compost bins to
subsequently inform and educate customers about best sorting practices.


  We give a shorter proof of the following theorem of Kathryn Mann \cite{M}:
the identity component of the group of the compactly supported $C^r$
diffeomorphisms of $\R^n$ cannot admit a nontrivial $C^p$-action on $S^1$,
provided $n\geq2$, $r\neq n+1$ and $p\geq2$. We also give a new proof of
another theorem of Mann: any nontrivial endomorphism of the group of the
orientation preserving $C^r$ diffeomorphisms of the circle is the conjugation
by a $C^r$ diffeomorphism, if $r\geq3$.


  In our globalized world, a growing number of situations arise where people
are required to communicate in one or several foreign languages. In the case of
written communication, users with a good command of a foreign language may find
assistance from computer-aided translation (CAT) technologies. These
technologies often allow users to access external resources, such as
dictionaries, terminologies or bilingual concordancers, thereby interrupting
and considerably hindering the writing process. In addition, CAT systems assume
that the source sentence is fixed and also restrict the possible changes on the
target side. In order to make the writing process smoother, we present BiSync,
a bilingual writing assistant that allows users to freely compose text in two
languages, while maintaining the two monolingual texts synchronized. We also
include additional functionalities, such as the display of alternative prefix
translations and paraphrases, which are intended to facilitate the authoring of
texts. We detail the model architecture used for synchronization and evaluate
the resulting tool, showing that high accuracy can be attained with limited
computational resources. The interface and models are publicly available at
https://github.com/jmcrego/BiSync and a demonstration video can be watched on
YouTube at https://youtu.be/_l-ugDHfNgU .


  In crowdsourced preference aggregation, it is often assumed that all the
annotators are subject to a common preference or utility function which
generates their comparison behaviors in experiments. However, in reality
annotators are subject to variations due to multi-criteria, abnormal, or a
mixture of such behaviors. In this paper, we propose a parsimonious
mixed-effects model based on HodgeRank, which takes into account both the fixed
effect that the majority of annotators follows a common linear utility model,
and the random effect that a small subset of annotators might deviate from the
common significantly and exhibits strongly personalized preferences. HodgeRank
has been successfully applied to subjective quality evaluation of multimedia
and resolves pairwise crowdsourced ranking data into a global consensus ranking
and cyclic conflicts of interests. As an extension, our proposed methodology
further explores the conflicts of interests through the random effect in
annotator specific variations. The key algorithm in this paper establishes a
dynamic path from the common utility to individual variations, with different
levels of parsimony or sparsity on personalization, based on newly developed
Linearized Bregman Algorithms with Inverse Scale Space method. Finally the
validity of the methodology are supported by experiments with both simulated
examples and three real-world crowdsourcing datasets, which shows that our
proposed method exhibits better performance (i.e. smaller test error) compared
with HodgeRank due to its parsimonious property.


  In real-world scenarios classification models are often required to perform
robustly when predicting samples belonging to classes that have not appeared
during its training stage. Open Set Recognition addresses this issue by
devising models capable of detecting unknown classes from samples arriving
during the testing phase, while maintaining a good level of performance in the
classification of samples belonging to known classes. This review
comprehensively overviews the recent literature related to Open Set
Recognition, identifying common practices, limitations, and connections of this
field with other machine learning research areas, such as continual learning,
out-of-distribution detection, novelty detection, and uncertainty estimation.
Our work also uncovers open problems and suggests several research directions
that may motivate and articulate future efforts towards more safe Artificial
Intelligence methods.


  It is now understood that the accretion of terrestrial planets naturally
involves giant collisions, the moon-forming impact being a well known example.
In the aftermath of such collisions the surface of the surviving planet is very
hot and potentially detectable. Here we explore the atmospheric chemistry,
photochemistry, and spectral signatures of post-giant-impact terrestrial
planets enveloped by thick atmospheres consisting predominantly of CO2, and
H2O. The atmospheric chemistry and structure are computed self-consistently for
atmospheres in equilibrium with hot surfaces with composition reflecting either
the bulk silicate Earth (which includes the crust, mantle, atmosphere and
oceans) or Earth's continental crust. We account for all major molecular and
atomic opacity sources including collision-induced absorption. We find that
these atmospheres are dominated by H2O and CO2, while the formation of CH4, and
NH3 is quenched due to short dynamical timescales. Other important constituents
are HF, HCl, NaCl, and SO2. These are apparent in the emerging spectra, and can
be indicative that an impact has occurred. The use of comprehensive opacities
results in spectra that are a factor of 2 lower in surface brightness in the
spectral windows than predicted by previous models. The estimated luminosities
show that the hottest post-giant-impact planets will be detectable with
near-infrared coronagraphs on the planned 30m-class telescopes. The 1-4um
region will be most favorable for such detections, offering bright features and
better contrast between the planet and a potential debris disk. We derive
cooling timescales on the order of 10^5-10^6 Myrs, based on the modeled
effective temperatures. This leads to the possibility of discovering tens of
such planets in future surveys.


  In this article, we show that a fixed point free locally nilpotent derivation
of an $\mathbb{A}^2$-fibration over a Noetherian ring containing $\mathbb{Q}$
has slice.


  We study the quark-gluon vertex in the limit of vanishing gluon momentum
using lattice QCD with 2 flavors of O(a) improved Wilson fermions, for several
lattice spacings and quark masses. We find that all three form factors in this
kinematics have a significant infrared strength, and that both the leading form
factor $\lambda_1$, multiplying the tree-level vertex structure, and the
scalar, chiral symmetry breaking form factor $\lambda_3$ are significantly
enhanced in the infrared compared to the quenched (Nf=0) case. These
enhancements are orders of magnitude larger than predicted by one-loop
perturbation theory. We find only a weak dependence on the lattice spacing and
quark mass.


  The processing of energy by transfer and redistribution plays a key role in
the evolution of dynamical systems. At the ultrasmall and ultrafast scale of
nanosystems, quantum coherence could in principle also play a role and has been
reported in many pulse-driven nanosystems (e.g. quantum dots and even the
microscopic Light-Harvesting Complex II (LHC-II) aggregate). Typical
theoretical analyses cannot easily be scaled to describe these general
$N$-component nanosystems; they do not treat the pulse dynamically; and they
approximate memory effects. Here our aim is to shed light on what new physics
might arise beyond these approximations. We adopt a purposely minimal model
such that the time-dependence of the pulse is included explicitly in the
Hamiltonian. This simple model generates complex dynamics: specifically, pulses
of intermediate duration generate highly entangled vibronic (i.e.
electronic-vibrational) states that spread multiple excitons -- and hence
energy -- maximally within the system. Subsequent pulses can then act on such
entangled states to efficiently channel subsequent energy capture. The
underlying pulse-generated vibronic entanglement increases in strength and
robustness as $N$ increases.


  The last decade has seen a revolution in the theory and application of
machine learning and pattern recognition. Through these advancements, variable
ranking has emerged as an active and growing research area and it is now
beginning to be applied to many new problems. The rationale behind this fact is
that many pattern recognition problems are by nature ranking problems. The main
objective of a ranking algorithm is to sort objects according to some criteria,
so that, the most relevant items will appear early in the produced result list.
Ranking methods can be analyzed from two different methodological perspectives:
ranking to learn and learning to rank. The former aims at studying methods and
techniques to sort objects for improving the accuracy of a machine learning
model. Enhancing a model performance can be challenging at times. For example,
in pattern classification tasks, different data representations can complicate
and hide the different explanatory factors of variation behind the data. In
particular, hand-crafted features contain many cues that are either redundant
or irrelevant, which turn out to reduce the overall accuracy of the classifier.
In such a case feature selection is used, that, by producing ranked lists of
features, helps to filter out the unwanted information. Moreover, in real-time
systems (e.g., visual trackers) ranking approaches are used as optimization
procedures which improve the robustness of the system that deals with the high
variability of the image streams that change over time. The other way around,
learning to rank is necessary in the construction of ranking models for
information retrieval, biometric authentication, re-identification, and
recommender systems. In this context, the ranking model's purpose is to sort
objects according to their degrees of relevance, importance, or preference as
defined in the specific application.


  We analyse the deconfining phase transition in the SU(N) Georgi-Glashow model
in 2+1 dimensions. We show that the phase transition is second order for any N,
and the universality class is different from the Z(N) invariant Villain model.
At large N the conformal theory describing the fixed point is a deformed
SU(N)_1 WZNW model which has N-1 massless fields. It is therefore likely that
its self-dual infrared fixed point is described by the Fateev-Zamolodchikov
theory of Z(N) parafermions.


  Hackathons are time-bounded collaborative events which have become a global
phenomenon adopted by both researchers and practitioners in a plethora of
contexts. Hackathon events are generally used to accelerate the development of,
for example, scientific results and collaborations, communities, and innovative
prototypes addressing urgent challenges. As hackathons have been adopted into
many different contexts, the events have also been adapted in numerous ways
corresponding to the unique needs and situations of organizers, participants
and other stakeholders. While these interdisciplinary adaptions, in general
affords many advantages - such as tailoring the format to specific needs - they
also entail certain challenges, specifically: 1) limited exchange of best
practices, 2) limited exchange of research findings, and 3) larger overarching
questions that require interdisciplinary collaboration are not discovered and
remain unaddressed. We call for interdisciplinary collaborations to address
these challenges. As a first initiative towards this, we performed an
interdisciplinary collaborative analysis in the context of a workshop at the
Lorentz Center, Leiden in December 2021. In this paper, we present the results
of this analysis in terms of six important areas which we envision to
contribute to maturing hackathon research and practice: 1) hackathons for
different purposes, 2) socio-technical event design, 3) scaling up, 4) making
hackathons equitable, 5) studying hackathons, and 6) hackathon goals and how to
reach them. We present these areas in terms of the state of the art and
research proposals and conclude the paper by suggesting next steps needed for
advancing hackathon research and practice.


  A flop of electric polarization from $P$$\parallel$$c$ ($P_c$) to
$P$$\parallel$$a$ ($P_a$) is observed in MnTiO$_3$ as a spin flop transition is
triggered by a $c$-axis magnetic field, $H_{\|c}$=7 T. The critical magnetic
field $H_{\|c}$ for $P_a$ is significantly reduced in Mn$_{1-x}$Ni$_x$TiO$_3$
(x=0.33). $P_a$ and $P_c$ have been observed with both $H_{\|c}$ and $H_{\|a}$.
Neutron diffraction measurements revealed similar magnetic arrangements for the
two compositions where the ordered spins couple antiferromagnetically with
their nearest intra- and inter-planar neighbors. In the x=0.33 system, the
uniaxial and planar anisotropies of Mn$^{2+}$ and Ni$^{2+}$ compete and give
rise to a spin reorientation transition at $T_R$. A magnetic field, $H_{\|c}$,
aligns the spins along $c$ for $T_R$$<$$T$$<$$T_N$. The rotation of the
collinear spins away from the $c$-axis for $T$$<$$T_R$ alters the magnetic
point symmetry and gives rise to a new ME susceptibility tensor form. Such
linear ME response provides satisfactory explanation for the behavior of the
field-induced electric polarization in both compositions. As the Ni content
increases to x=0.5 and 0.68, the ME effect disappears as a new magnetic phase
emerges.


  Both pulsation and mass loss are commonly observed in stars and are important
ingredients for understanding stellar evolution and structure, especially for
massive stars. There is a growing body of evidence that pulsation can also
drive and enhance mass loss in massive stars and that pulsation-driven mass
loss is important for stellar evolution. In this review, I will discuss recent
advances in understanding pulsation driven mass loss in massive main sequence
stars, classical Cepheids and red supergiants and present some challenges
remaining.


  Currently, newly developed artificial intelligence techniques, in particular
convolutional neural networks, are being investigated for use in
data-processing and classification of particle physics collider data. One such
challenging task is to distinguish quark-initiated jets from gluon-initiated
jets. Following previous work, we treat the jet as an image by pixelizing track
information and calorimeter deposits as reconstructed by the detector. We test
the deep learning paradigm by training several recently developed,
state-of-the-art convolutional neural networks on the quark-gluon
discrimination task. We compare the results obtained using various network
architectures trained for quark-gluon discrimination and also a boosted
decision tree (BDT) trained on summary variables.


  Presented is a quantum computing representation of Dirac particle dynamics.
The approach employs an operator splitting method that is an analytically
closed-form product decomposition of the unitary evolution operator. This
allows the Dirac equation to be cast as a unitary finite-difference equation in
a high-energy limit. The split evolution operator (with separate kinetic and
interaction terms) is useful for efficient quantum simulation. For pedagogical
purposes, here we restrict the treatment to Dirac particle dynamics in 1+1
spacetime dimensions. Independent derivations of the quantum algorithm are
presented and the model's validity is tested in several quantum simulations by
comparing the numerical results against analytical predictions. Using the
relativistic quantum algorithm in the case when mc^2 >> pc, quantum simulations
of a nonrelativistic particle in an external scalar square well and parabolic
potential is presented.


  Software-Defined Networking (SDN) significantly simplifies programming,
reconfiguring, and optimizing network devices, such as switches and routers.
The de facto standard for programmming SDN devices is the P4 language. However,
the flexibility and power of P4, and SDN more generally, gives rise to
important risks. As a number of incidents at major cloud providers have shown,
errors in SDN programs can compromise the availability of networks, leaving
them in a non-functional state. The focus of this paper are errors in
control-plane programs that interact with P4-enabled network devices via the
standardized P4Runtime API. For clients of the P4Runtime API it is easy to make
mistakes that lead to catastrophic failures, despite the use of Google's
Protocol Buffers as an interface definition language.
  This paper proposes P4R-Type, a novel verified P4Runtime API for Scala that
performs static checks for P4 control plane operations, ruling out mismatches
between P4 tables, allowed actions, and action parameters. As a formal
foundation of P4R-Type, we present the $F_{\text{P4R}}$ calculus and its typing
system, which ensure that well-typed programs never get stuck by issuing
invalid P4Runtime operations. We evaluate the safety and flexibility of
P4R-Type with 3 case studies. To the best of our knowledge, this is the first
work that formalises P4Runtime control plane applications, and a typing
discipline ensuring the correctness of P4Runtime operations.


  The behavior of hyperelastic energies depending on an internal parameter,
which is a function of the deformation gradient, is discussed. As an example,
the analysis of two models where the parameter describes the activation of a
tetanized skeletal muscle tissue is presented. In those models, the activation
parameter depends on the strain and it is shown the importance of considering
the derivative of the parameter with respect to the strain in order to capture
the proper stress-strain relations.


  In the main result of the paper we extend Rosenthal's characterization of
Banach spaces with the Schur property by showing that for a quasi-complete
locally convex space $E$ whose separable bounded sets are metrizable the
following conditions are equivalent: (1) $E$ has the Schur property, (2) $E$
and $E_w$ have the same sequentially compact sets, where $E_w$ is the space $E$
with the weak topology, (3) $E$ and $E_w$ have the same compact sets, (4) $E$
and $E_w$ have the same countably compact sets, (5) $E$ and $E_w$ have the same
pseudocompact sets, (6) $E$ and $E_w$ have the same functionally bounded sets,
(7) every bounded non-precompact sequence in $E$ has a subsequence which is
equivalent to the unit basis of $\ell_1$ and (8) every bounded non-precompact
sequence in $E$ has a subsequence which is discrete and $C$-embedded in $E_w$.


  This is a short survey on existing upper and lower bounds on the probability
of the union of a finite number of events using partial information given in
terms of the individual or pairwise event probabilities (or their sums). New
proofs for some of the existing bounds are provided and new observations
regarding the existing Gallot--Kounias bound are given.


  An important concept in Physics is the notion of an isolated system. It is
used in many different areas to describe the properties of a physical system
which has been isolated from its environment. The interaction with the
`outside' is then usually reduced to a scattering process, in which incoming
radiation interacts with the system, which in turn emits outgoing radiation. In
Einstein's theory of gravitation isolated systems are modeled as asymptotically
flat space-times. They provide the appropriate paradigm for the study of
gravitational waves and their interaction with a material system or even only
with themselves. In view of the emerging era of gravitational wave astronomy,
in which gravitational wave signals from many different astrophysical sources
are detected and interpreted, it is necessary to have a foundation for the
theoretical and numerical treatments of these signals. Furthermore, from a
purely mathematical point of view, it is important to have a full understanding
of the implications of imposing the condition of asymptotic flatness onto
solutions of the Einstein equations. While it is known that there exists a
large class of asymptotically flat solutions of Einstein's equations, it is not
known what the necessary and sufficient conditions at infinity are that have to
be imposed on initial data so that they evolve into regular asymptotically flat
space-times. The crux lies in the region near space-like infinity $i^0$ where
incoming and outgoing radiation `meet'. In this paper we review the current
knowledge and some of the analytical and numerical work that has gone into the
attempt to understand the structure of asymptotically flat space-times near
space-like and null-infinity.


  Cold atom optical lattices typically simulate zero-range Hubbard models. We
discuss the theoretical possibility of using excited states of optical lattices
to generate extended range Hubbard models. We find that bosons confined to
higher bands of optical lattices allow for a rich phase diagram, including the
supersolid phase. Using Gutzwiller, mean field theory we establish the
parameter regime necessary to maintain metastable states generated by an
extended Bose-Hubbard model.


  We identify conditions for the entanglement entropy as a function of spatial
region to be compatible with causality in an arbitrary relativistic quantum
field theory. We then prove that the covariant holographic entanglement entropy
prescription (which relates entanglement entropy of a given spatial region on
the boundary to the area of a certain extremal surface in the bulk) obeys these
conditions, as long as the bulk obeys the null energy condition. While
necessary for the validity of the prescription, this consistency requirement is
quite nontrivial from the bulk standpoint, and therefore provides important
additional evidence for the prescription. In the process, we introduce a
codimension-zero bulk region, named the entanglement wedge, naturally
associated with the given boundary spatial region. We propose that the
entanglement wedge is the most natural bulk region corresponding to the
boundary reduced density matrix.


  In this thesis, we construct an approximate series solution of the Wigner
equation in terms of Airy functions, which are semiclassically concentrated on
certain Lagrangian curves in two-dimensional phase space. These curves are
defined by the eigenvalues and the Hamiltonian function of the associated
one-dimensional Schr\"odinger operator, and they play a crucial role in the
quantum interference mechanism in phase space. We assume that the potential of
the Schr\"odinger operator is a single potential well, such that the spectrum
is discrete.
  The construction starts from an eigenfunction series expansion of the
solution, which is derived here for first time in a systematic way, by
combining the elementary technique of separation of variables with involved
spectral results for the Moyal star exponential operator. The eigenfunctions of
the Wigner equation are the Wigner transforms of the Schr\"odinger
eigenfunctions, and they are approximated in terms of Airy functions by a
uniform stationary phase approximation of the Wigner transforms of the WKB
expansions of the Schr\"odinger eigenfunctions.
  The approximation of the eigenfunction series is an approximated solution of
the Wigner equation, which by projection onto the configuration space provides
an approximate wave amplitude, free of turning point singularities. It is
generally expected that, the derived wave amplitude is bounded, and correctly
scaled, even on caustics, since only finite terms of the approximate terms are
significant for WKB initial wave functions with finite energy.
  The details of the calculations are presented for the simple potential of the
harmonic oscillator, in order to be able to check our approximations
analytically. But, the same construction can be applied to any potential well,
which behaves like the harmonic oscillator near the bottom of the well.


  In the pursuit of reducing the number of trainable parameters in deep
transformer networks, we employ Reinforcement Learning to dynamically select
layers during training and tie them together. Every few iterations, the RL
agent is asked whether to train each layer $i$ independently or to copy the
weights of a previous layer $j<i$. This facilitates weight sharing, reduces the
number of trainable parameters, and also serves as an effective regularization
technique. Experimental evaluations validate that our model modestly
outperforms the baseline transformer model with regard to perplexity and
drastically reduces the number of trainable parameters. In particular, the
memory consumption during training is up to one order of magnitude less than
the conventional training method.


  Let $U$ be either classical or quantized universal enveloping algebra of
$\s\l(n+1)$ extended over the field of fractions of the Cartan subalgebra. We
suggest a PBW basis in $U$ over the extended Cartan subalgebra diagonalizing
the contravariant Shapovalov form on generic Verma module. The matrix
coefficients of the form are calculated and the inverse of the form is
explicitly constructed.


  We report on the results from observations of the most recent outbursts of
XTE J1739-302 and IGR J17544-2619, which are considered to be the prototypes of
the supergiant fast X-ray transient (SFXT) class. They triggered the Swift/BAT
on 2011 February 22 and March 24, respectively, and each time a prompt Swift
slew allowed us to obtain the rich broad-band data we present. The XRT light
curves show the descending portion of very bright flares that reached
luminosities of ~2x10^{36} and ~5x10^{36} erg/s, respectively. The broad-band
spectra, when fit with the usual phenomenological models adopted for accreting
neutron stars, yield values of both high energy cut-off and e-folding energy
consistent with those obtained from previously reported outbursts from these
sources. In the context of more physical models, the spectra of both sources
can be well fitted either with a two-blackbody model, or with a single
unsaturated Comptonization model. In the latter case, the model can be either a
classical static Comptonization model, such as COMPTT, or the recently
developed COMPMAG model, which includes thermal and bulk Comptonization for
cylindrical accretion onto a magnetized neutron star. We discuss the possible
accretion scenarios derived by the different models, and we also emphasize the
fact that the electron density derived from the Comptonization models, in the
regions where the X-ray spectrum presumably forms, is lower than that estimated
using the continuity equation at the magnetospheric radius and the source X-ray
luminosity, and we give some possible explanations.


  A Markov network characterizes the conditional independence structure, or
Markov property, among a set of random variables. Existing work focuses on
specific families of distributions (e.g., exponential families) and/or certain
structures of graphs, and most of them can only handle variables of a single
data type (continuous or discrete). In this work, we characterize the
conditional independence structure in general distributions for all data types
(i.e., continuous, discrete, and mixed-type) with a Generalized Precision
Matrix (GPM). Besides, we also allow general functional relations among
variables, thus giving rise to a Markov network structure learning algorithm in
one of the most general settings. To deal with the computational challenge of
the problem, especially for large graphs, we unify all cases under the same
umbrella of a regularized score matching framework. We validate the theoretical
results and demonstrate the scalability empirically in various settings.


  Random Forest (RF) is an ensemble supervised machine learning technique that
was developed by Breiman over a decade ago. Compared with other ensemble
techniques, it has proved its accuracy and superiority. Many researchers,
however, believe that there is still room for enhancing and improving its
performance accuracy. This explains why, over the past decade, there have been
many extensions of RF where each extension employed a variety of techniques and
strategies to improve certain aspect(s) of RF. Since it has been proven
empiricallthat ensembles tend to yield better results when there is a
significant diversity among the constituent models, the objective of this paper
is twofold. First, it investigates how data clustering (a well known diversity
technique) can be applied to identify groups of similar decision trees in an RF
in order to eliminate redundant trees by selecting a representative from each
group (cluster). Second, these likely diverse representatives are then used to
produce an extension of RF termed CLUB-DRF that is much smaller in size than
RF, and yet performs at least as good as RF, and mostly exhibits higher
performance in terms of accuracy. The latter refers to a known technique called
ensemble pruning. Experimental results on 15 real datasets from the UCI
repository prove the superiority of our proposed extension over the traditional
RF. Most of our experiments achieved at least 95% or above pruning level while
retaining or outperforming the RF accuracy.


  The delineation of tumor target and organs-at-risk is critical in the
radiotherapy treatment planning. Automatic segmentation can be used to reduce
the physician workload and improve the consistency. However, the quality
assurance of the automatic segmentation is still an unmet need in clinical
practice. The patient data used in our study was a standardized dataset from
AAPM Thoracic Auto-Segmentation Challenge. The OARs included were left and
right lungs, heart, esophagus, and spinal cord. Two groups of OARs were
generated, the benchmark dataset manually contoured by experienced physicians
and the test dataset automatically created using a software AccuContour. A
resnet-152 network was performed as feature extractor, and one-class support
vector classifier was used to determine the high or low quality. We evaluate
the model performance with balanced accuracy, F-score, sensitivity, specificity
and the area under the receiving operator characteristic curve. We randomly
generated contour errors to assess the generalization of our method, explored
the detection limit, and evaluated the correlations between detection limit and
various metrics such as volume, Dice similarity coefficient, Hausdorff
distance, and mean surface distance. The proposed one-class classifier
outperformed in metrics such as balanced accuracy, AUC, and others. The
proposed method showed significant improvement over binary classifiers in
handling various types of errors. Our proposed model, which introduces residual
network and attention mechanism in the one-class classification framework, was
able to detect the various types of OAR contour errors with high accuracy. The
proposed method can significantly reduce the burden of physician review for
contour delineation.


  The fact that repeated projective measurements can slow down (the Zeno
effect) or speed up (the anti-Zeno effect) quantum evolution is well-known.
However, to date, studies of these effects focus on quantum systems that are
weakly interacting with their environment. In this paper, we investigate what
happens to a quantum system under the action of repeated measurements if the
quantum system is strongly interacting with its environment. We consider as the
quantum system a single two-level system coupled strongly to a collection of
harmonic oscillators. A so-called polaron transformation is then used to make
the problem in the strong system-environment coupling regime tractable. We find
that the strong coupling case exhibits quantitative and qualitative differences
as compared with the weak coupling case. In particular, the effective decay
rate does not depend linearly on the spectral density of the environment. This
then means that, in the strong coupling regime that we investigate, increasing
the system-environment coupling strength can actually decrease the effective
decay rate. We also consider a collection of two-level atoms coupled strongly
with a common environment. In this case, we find that there are further
differences between the weak and strong coupling cases since the two-level
atoms can now indirectly interact with one another due to the common
environment.


  We have shown previously that our parameter-reduced variants of Long
Short-Term Memory (LSTM) Recurrent Neural Networks (RNN) are comparable in
performance to the standard LSTM RNN on the MNIST dataset. In this study, we
show that this is also the case for two diverse benchmark datasets, namely, the
review sentiment IMDB and the 20 Newsgroup datasets. Specifically, we focus on
two of the simplest variants, namely LSTM_6 (i.e., standard LSTM with three
constant fixed gates) and LSTM_C6 (i.e., LSTM_6 with further reduced cell body
input block). We demonstrate that these two aggressively reduced-parameter
variants are competitive with the standard LSTM when hyper-parameters, e.g.,
learning parameter, number of hidden units and gate constants are set properly.
These architectures enable speeding up training computations and hence, these
networks would be more suitable for online training and inference onto portable
devices with relatively limited computational resources.


  We present a same-level comparison of the most prominent inversion methods
for the reconstruction of the matter density field in the quasi-linear regime
from the Ly$\alpha$ forest flux. Moreover, we present a pathway for refining
the reconstruction in the framework of numerical optimization. We apply this
approach to construct a novel hybrid method. The methods which are used so far
for matter reconstructions are the Richardson-Lucy algorithm, an iterative
Gauss-Newton method and a statistical approach assuming a one-to-one
correspondence between matter and flux. We study these methods for high
spectral resolutions such that thermal broadening becomes relevant. The
inversion methods are compared on synthetic data (generated with the lognormal
approach) with respect to their performance, accuracy, their stability against
noise, and their robustness against systematic uncertainties. We conclude that
the iterative Gauss-Newton method offers the most accurate reconstruction, in
particular at small S/N, but has also the largest numerical complexity and
requires the strongest assumptions. The other two algorithms are faster,
comparably precise at small noise-levels, and, in the case of the statistical
approach, more robust against inaccurate assumptions on the thermal history of
the intergalactic medium (IGM). We use these results to refine the statistical
approach using regularization. Our new approach has low numerical complexity
and makes few assumptions about the history of the IGM, and is shown to be the
most accurate reconstruction at small S/N, even if the thermal history of the
IGM is not known. Our code will be made publicly available under
https://github.com/hmuellergoe/reglyman.


  Let $K$ be an algebraically closed field of characteristic different from
$2$, $g$ a positive integer, $f(x)\in K[x]$ a degree $2g+1$ monic polynomial
without repeated roots, $C_f: y^2=f(x)$ the corresponding genus g hyperelliptic
curve over $K$, and $J$ the jacobian of $C_f$. We identify $C_f$ with the image
of its canonical embedding into $J$ (the infinite point of $C_f$ goes to the
zero of group law on $J$). It is known (arXiv:1809.03061 [math.AG]) that if
$g>1$ then $C_f(K)$ does not contain torsion points, whose order lies between
$3$ and $2g$.
  In this paper we study torsion points of order $2g+1$ on $C_f(K)$. Despite
the striking difference between the cases of $g=1$ and $g> 1$, some of our
results may be viewed as a generalization of well-known results about points of
order $3$ on elliptic curves. E.g., if $p=2g+1$ is a prime that coincides with
$char(K)$, then every odd degree genus $g$ hyperelliptic curve contains, at
most, two points of order $p$. If $g$ is odd and $f(x)$ has real coefficients,
then there are, at most, two real points of order $2g+1$ on $C_f$. If $f(x)$
has rational coefficients and $g<52$, then there are, at most, two rational
points of order $2g+1$ on $C_f$. (However, there are exist genus $52$
hyperelliptic curves over the field of rational numbers that have, at least,
four rational points of order 105.)


  Under appropriate assumptions, we show that all bounded entire solutions to a
class of semilinear elliptic systems are confined in a convex domain. Moreover,
we prove a Liouville type theorem in the case where the domain is strictly
convex. Our result represents an extension, under less regularity assumptions,
of a recent result of Smyrnelis. We also provide several applications.


  We develop a general framework, which combines exact diagonalization in small
clusters with a density matrix variational principle, to study frustrated
magnets at finite temperature. This thermodynamic hierarchical mean-field
technique is used to determine the phase diagram and magnetization process of
the three-dimensional spin-1/2 $J_1$-$J_2$ antiferromagnet on a stacked square
lattice. Its non-magnetic phase exhibits a thermal crossover from a quantum to
a classical paramagnet at a temperature $T=T_0$ which can be extracted from
thermodynamic measurements. At low temperature an applied magnetic field
stabilizes, through order-by-disorder, a variety of phases with non-trivial
spin textures and a magnetization plateau at half-saturation which continuously
disappears at $T\sim T_0$. Our results are relevant for frustrated vanadium
oxides.


  Quantitative analysis of brain MRI at the age of 6 months is difficult
because of the limited contrast between white matter and gray matter. In this
study, we use a dilated triplanar convolutional neural network in combination
with a non-dilated 3D convolutional neural network for the segmentation of
white matter, gray matter and cerebrospinal fluid in infant brain MR images, as
provided by the MICCAI grand challenge on 6-month infant brain MRI
segmentation.


  An observational study of Koronis family members' spin properties was
undertaken with two primary objectives: to reduce selection biases for object
rotation period and lightcurve amplitude in the sample of members' known spin
vectors, and to better constrain future modeling of spin properties evolution.
Here we report rotation lightcurves of nineteen Koronis family members, and
derived results that increase the sample of determined spin vectors in the
Koronis family to include 34 of the largest 36 family members, completing it to
$H \approx 11.3$ ($D \sim 16$ km) for the largest 32 members. The program
observations were made during a total of 72 apparitions between 2005-2021, and
are reported here along with several earlier unpublished lightcurves. All of
the reported data were analyzed together with previously published lightcurves
to determine the objects' sidereal rotation periods, spin vector orientations,
and convex model shape solutions. The derived distributions of retrograde
rotation rates and pole obliquities appear to be qualitatively consistent with
outcomes of modification by thermal YORP torques. The distribution of spin
rates for the prograde rotators remains narrower than that for the retrograde
rotators; in particular, the absence of prograde rotators having periods longer
than about 20 h is real, while among the retrograde rotators are several
objects having longer periods up to about 65 h. None of the prograde objects
newly added to the sample appear to be trapped in an $s_6$ spin-orbit resonance
that is characteristic of most of the largest prograde objects; these smaller
objects either could have been trapped previously and have already evolved out,
or have experienced spin evolution tracks that did not include the resonance.


  A Drude-Sommerfeld topological model (DSTM) is proposed to describe Weyl
fermions under residual collisions. They are nearly free and dressed by their
own weak magnetic field that breaks the reflection and time symmetries around a
layer. This weak magnetic field brings topological stability to the states
through a non-trivial Chern-Simons number which is here calculated in the limit
of a Dirac linear spectrum. The Weyl fermions display an energy gap and much
above this gap the spectrum becomes Dirac linear. They are obtained from a
Schroedinger like hamiltonian for particles with spin and magnetic energy which
are momentum confined to a layer. The electrical and the thermal conductivities
of the Weyl fermions as well as the corresponding Wiedemman-Franz law are
derived in the framework of a constant relaxation time. The Lorenz number
coefficient acquires asymptotic value $6.5552$ times the bulk value of
$\pi^2/3$. The relaxation time is shown to be renormalized by the inverse of
the square of the gap, and so, leads to a ballistic regime in the linear Dirac
spectrum limit.


  People use web search engines to find information before forming opinions,
which can lead to practical decisions with different levels of impact. The
cognitive effort of search can leave opinionated users vulnerable to cognitive
biases, e.g., the confirmation bias. In this paper, we investigate whether
stance labels and their explanations can help users consume more diverse search
results. We automatically classify and label search results on three topics
(i.e., intellectual property rights, school uniforms, and atheism) as against,
neutral, and in favor, and generate explanations for these labels. In a user
study (N =203), we then investigate whether search result stance bias (balanced
vs biased) and the level of explanation (plain text, label only, label and
explanation) influence the diversity of search results clicked. We find that
stance labels and explanations lead to a more diverse search result
consumption. However, we do not find evidence for systematic opinion change
among users in this context. We believe these results can help designers of
search engines to make more informed design decisions.


  We introduce a nonperturbative, first-principles approach to time-dependent
problems in quantum field theory. In this approach, the time-evolution of
quantum field configurations is calculated in real time and at the amplitude
level. This method is particularly suitable for treating systems interacting
with a time-dependent background field. As a test problem, we apply this
approach to QED and study electron acceleration and the associated photon
emission in a time- and space-dependent electromagnetic background field.


  Swarm behavior using Boids-like models has been studied primarily using
close-proximity spatial sensory information (e.g. vision range). In this study,
we propose a novel approach in which the classic definition of
boids\textquoteright \ neighborhood that relies on sensory perception and
Euclidian space locality is replaced with graph-theoretic network-based
proximity mimicking communication and social networks. We demonstrate that
networking the boids leads to faster swarming and higher quality of the
formation. We further investigate the effect of adversarial learning, whereby
an observer attempts to reverse engineer the dynamics of the swarm through
observing its behavior. The results show that networking the swarm demonstrated
a more robust approach against adversarial learning than a local-proximity
neighborhood structure.


  This paper studies linear time-invariant descriptor systems which are not
necessarily regular. We introduce the notion of partial detectability and
characterize this concept by means of a simple rank criterion involving the
system coefficient matrices. Three particular cases of this characterization
are discussed in detail. Furthermore, we show that partial detectability is
necessary for the existence of a generalized functional observer, but not
sufficient. We identify a condition which together with partial detectability
gives sufficiency.


  Robust image watermarking that can resist camera shooting has become an
active research topic in recent years due to the increasing demand for
preventing sensitive information displayed on computer screens from being
captured. However, many mainstream schemes require human assistance during the
watermark detection process and cannot adapt to scenarios that require
processing a large number of images. Although deep learning-based schemes
enable end-to-end watermark embedding and detection, their limited
generalization ability makes them vulnerable to failure in complex scenarios.
In this paper, we propose a carefully crafted watermarking system that can
resist camera shooting. The proposed scheme deals with two important problems:
automatic watermark localization (AWL) and automatic watermark detection (AWD).
AWL automatically identifies the region of interest (RoI), which contains
watermark information, in the camera-shooting image by analyzing the local
statistical characteristics. Meanwhile, AWD extracts the hidden watermark from
the identified RoI after applying perspective correction. Compared with
previous works, the proposed scheme is fully automatic, making it ideal for
application scenarios. Furthermore, the proposed scheme is not limited to any
specific watermark embedding strategy, allowing for improvements in the
watermark embedding and extraction procedure. Extensive experimental results
and analysis show that the embedded watermark can be automatically and reliably
extracted from the camera-shooting image in different scenarios, demonstrating
the superiority and applicability of the proposed approach.


  A data-driven framework is proposed towards the end of predictive modeling of
complex spatio-temporal dynamics, leveraging nested non-linear manifolds. Three
levels of neural networks are used, with the goal of predicting the future
state of a system of interest in a parametric setting. A convolutional
autoencoder is used as the top level to encode the high dimensional input data
along spatial dimensions into a sequence of latent variables. A temporal
convolutional autoencoder (TCAE) serves as the second level, which further
encodes the output sequence from the first level along the temporal dimension,
and outputs a set of latent variables that encapsulate the spatio-temporal
evolution of the dynamics. The use of dilated temporal convolutions grows the
receptive field exponentially with network depth, allowing for efficient
processing of long temporal sequences typical of scientific computations. A
fully-connected network is used as the third level to learn the mapping between
these latent variables and the global parameters from training data, and
predict them for new parameters. For future state predictions, the second level
uses a temporal convolutional network to predict subsequent steps of the output
sequence from the top level. Latent variables at the bottom-most level are
decoded to obtain the dynamics in physical space at new global parameters
and/or at a future time. Predictive capabilities are evaluated on a range of
problems involving discontinuities, wave propagation, strong transients, and
coherent structures. The sensitivity of the results to different modeling
choices is assessed. The results suggest that given adequate data and careful
training, effective data-driven predictive models can be constructed.
Perspectives are provided on the present approach and its place in the
landscape of model reduction.


  In this paper Bianchi type I spacetimes are completely classified by their
homothetic vectors in the context of Lyra geometry. The non-linear coupled Lyra
homothetic equations are obtained and solved completely for different cases. In
some cases, Bianchi type I spacetimes admit proper Lyra homothetic vectors
(LHVs) for special choices of the metric functions, while there exist other
cases where the spacetime under consideration admits only Lyra Killing vectors
(LKVs). In all the possible cases where Bianchi type I spacetimes admit proper
LHVs or LKVs, we obtained homothetic and Killing vectors for Bianchi type I
spacetimes in general relativity by taking the displacement vector of Lyra
geometry as zero. Matter collineation symmetry is explained by taking the
matter field as a perfect fluid. The obtained proper LHVs and LKVs are used in
matter collineation equations and a barotropic equation of state having
$\rho(t)\,=\,\gamma\,p(t)$, $0\,\leq\,\gamma\,\leq\,1$ form is always obtained
when the displacement vector is considered as a function of $t$ or treated as a
constant.


  The flavor singlet axial charge has been a source of study in the last years
due to its relation to the so called {\it Proton Spin Problem}. The relevant
flavor singlet axial current is anomalous, i.e., its divergence contains a
piece which is the celebrated $U_A(1)$ anomaly. This anomaly is intimately
associated with the $\eta^\prime$ meson, which gets its mass from it. When the
gauge degrees of freedom of QCD are confined within a volume as is presently
understood, the $U_A(1)$ anomaly is known to induce color anomaly leading to
"leakage" of the color out of the confined volume (or bag). For consistency of
the theory, this anomaly should be cancelled by a boundary term. This ``color
boundary term" inherits part or most of the dynamics of the volume (i.e., QCD).
In this thesis, we exploit this mapping of the volume to the surface via the
color boundary condition to perform a complete analysis of the flavor singlet
axial charge in the chiral bag model using the Cheshire Cat Principle. This
enables us to obtain the hitherto missing piece in the axial charge associated
with the gluon Casimir effect. The result is that the flavor singlet axial
charge is small independent of the confinement (bag) size ranging from the
skyrmion picture to the MIT bag picture, thereby confirming the (albeit
approximate) Cheshire Cat phenomenon.


  Anisotropic charge transport is observed in a two-dimensional (2D) hole
system in a perpendicular magnetic field at filling factors nu=7/2 and nu=11/2
for temperatures below 150mK. In stark contrast, the transport at nu=9/2 is
isotropic for all temperatures. Our results for a two-dimensional hole system
differ substantially from 2D electron transport where no anisotropy has been
observed at nu=7/2, the strongest anisotropy occurs at nu=9/2, and reentrant
behavior is not evident. We attribute this difference to strong spin-orbit
coupling in the hole system.


  Golodness of 2-dimensional simplicial complexes is studied through polyhedral
products, and combinatorial and topoogical characterization of Golodness of
surface triangulations is given. An answer to the question of Berglund is also
given so that there is a 2-dimensional simplicial complex which is rationally
Golod but is not Golod over $\mathbb{Z}/p$.


  New linear polarization measurements (mainly in the V band) are presented for
203 quasi-stellar objects (QSOs). The sample is made up of 94 QSOs located in
the North Galactic Pole (NGP) region and of 109 QSOs in the South Galactic Pole
(SGP) region. First time measurements have been obtained for 184 QSOs. Among
them, 109 known radio-emitters, 42 known Broad Absorption Line (BAL) QSOs, and
1 gravitationally lensed quasi-stellar object. We found high polarization
levels (p > 3%) for 12 QSOs, including the BAL QSO SDSS J1409+0048. For 10
objects, measurements obtained at different epochs do exist. Two of them show
evidence for variability: the highly polarized BL Lac candidate PKS 1216-010
and the radio source PKS 1222+037


  We develop solution-generating techniques for stationary metrics with one
angular momentum and axial symmetry, in the presence of a cosmological constant
and in arbitrary spacetime dimension. In parallel we study the related lower
dimensional Einstein-Maxwell-dilaton static spacetimes with a Liouville
potential. For vanishing cosmological constant, we show that the field
equations in more than four dimensions decouple into a four dimensional
Papapetrou system and a Weyl system. We also show that given any four
dimensional 'seed' solution, one can construct an infinity of higher
dimensional solutions parametrised by the Weyl potentials, associated to the
extra dimensions. When the cosmological constant is non-zero, we discuss the
symmetries of the field equations, and then extend the well known works of
Papapetrou and Ernst (concerning the complex Ernst equation) in
four-dimensional general relativity, to arbitrary dimensions. In particular, we
demonstrate that the Papapetrou hypothesis generically reduces a stationary
system to a static one even in the presence of a cosmological constant. We also
give a particular class of solutions which are deformations of the (planar) adS
soliton and the (planar) adS black hole. We give example solutions of these
techniques and determine the four-dimensional seed solutions of the 5
dimensional black ring and the Myers-Perry black hole.


  These are notes for a very rapid introduction to the basics of exterior
differential systems and their connection with what is now known as Lie theory,
together with some typical and not-so-typical applications to illustrate their
use.


  Roles of paramagnetic and diamagnetic pair-breaking effects in
superconductivity in electric-field-induced surface metallic state are studied
by Bogoliubov-de Gennes equation, when magnetic fields are applied parallel to
the surface. The multi-gap states of sub-bands are related to the depth
dependence and the magnetic field dependence of superconductivity. In the
Fermi-energy density of states and the spin density, sub-band contributions
successively appear from higher-level sub-bands with increasing magnetic
fields. The characteristic magnetic field dependence may be a key feature to
identify the multi-gap structure of the surface superconductivity.


  We study the continuous one-dimensional hard-sphere model and present
irreversible local Markov chains that mix on faster time scales than the
reversible heatbath or Metropolis algorithms. The mixing time scales appear to
fall into two distinct universality classes, both faster than for reversible
local Markov chains. The event-chain algorithm, the infinitesimal limit of one
of these Markov chains, belongs to the class presenting the fastest decay. For
the lattice-gas limit of the hard-sphere model, reversible local Markov chains
correspond to the symmetric simple exclusion process (SEP) with periodic
boundary conditions. The two universality classes for irreversible Markov
chains are realized by the totally asymmetric simple exclusion process (TASEP),
and by a faster variant (lifted TASEP) that we propose here. Lifted Markov
chains and the recently introduced factorized Metropolis acceptance rule extend
the irreversible Markov chains discussed here to general pair interactions and
to higher dimensions.


  We investigate when effective theories of a scalar field on (quasi-)de Sitter
background break down through the stochastic formalism. We derive the
Fokker-Planck equation leaving the second order time derivative of the scalar
field. Assuming there exists an equilibrium distribution for the field
velocity, we obtain a mean value and a variance of the field velocity caused by
the quantum fluctuation. Introducing coarse-grained Einstein equations, we
obtain bounds for the non-eternal inflation phase and for maintaining the exact
de Sitter background. We point out that those bounds derived in our formalism
correspond to the de Sitter entropy bound proposed by Arkani-Hamed,
\textit{et.al.}, up to $O(1)$ factor, even for a massless free scalar field on
exact de Sitter background. We discuss connections of our results to the
quantum field theory also.


  The Internet has recently witnessed unprecedented growth of a class of
connected assets called the Internet of Things (IoT). Due to relatively
immature manufacturing processes and limited computing resources, IoTs have
inadequate device-level security measures, exposing the Internet to various
cyber risks. Prior research leveraged predictable patterns in IoT network
traffic to develop inference models. However, they fall short of expectations
in addressing practical challenges, preventing them from being deployed in
production settings. This thesis identifies four practical challenges and
develops techniques to address them which can help secure businesses and
protect user privacy against growing cyber threats.
  My first contribution balances prediction gains against computing costs of
traffic features for IoT traffic classification and monitoring. My second
contribution addresses the challenges of measurement costs and data quality. I
develop an inference method that uses stochastic and deterministic modeling to
predict IoT devices in home networks from opaque and coarse-grained IPFIX flow
data. Evaluations show that false positive rates can be reduced by 75% compared
to related work without significantly affecting true positives. My third
contribution focuses on the challenge of concept drifts by analyzing over six
million flow records collected from 12 real home networks. Finally, my fourth
contribution studies the resilience of machine learning models against
adversarial attacks with a specific focus on decision tree-based models.


  We present a theory of the acoustic phonon assisted spin-flip Raman
scattering (SFRS), or resonant photoluminescence with the spin flip of a
photoexcited exciton localized in a bulk cubic-phase perovskite semiconductor.
We consider the spin-flip transitions between the ground-state exciton spin
sublevels in external magnetic field B and discuss the variation of their
probability rate and polarization selection rules with the increase of B. The
transitions are treated as two-quantum processes with the virtual to and fro
transfer of the electron in the electron-hole pair between the bottom and first
excited conduction bands. The transfer occurs due to both the electron-hole
exchange interaction and the electron-phonon interaction. The theoretical
results allow one to distinguish the phonon assisted Raman scattering from (a)
the resonant Raman scattering with the combined spin flip of the localized
resident electron and hole and (b) the biexciton-mediated SFRS analyzed
previously.


  A nonstationary spherically symmetric problem for conformal geometrodynamics
equations is considered and general exact solutions in quadratures are
obtained. Involvement of Weyl degrees of freedom allows us to consider the
problem with arbitrary initial data, as for the conformal geometrodynamics
equations the Cauchy problem is set up without connections to initial data. The
results of this paper are not confined with the framework of the perturbation
theory and open up new avenues for study of the process of space-time
singularity evolution in time.


  Evolutions of X-ray clusters of galaxies are studied by N-body (shell model)
+ mesh code (TVD) simulations on the assumption of spherical symmetry. We
consider a density perturbation of $10^{15} M_{\odot}$ composed of dark matter
and gas in cold dark matter dominated universe with the cosmological density
parameter, $\Omega_0 = 1$ or $0.2$. A shock front appears during its initial
collapse, moving outward as ambient gas accretes towards cluster center. The
shock front separates the inner X-ray emitting, hot region, where gas is almost
in hydrostatic equilibrium but with small radial infall ($\sim 100$km s$^{-1}$)
being left, from the outer cool region. Gas inside the shock is strongly
compressed and heated by shock so that X-ray luminosity rapidly rises in the
early stage. In the late stage, however, the X-ray luminosity rises only
gradually due partly to the expansion of the inner high temperature region and
partly to the increase of X-ray emissivity of gas as the results of continuous
adiabatic compression inside the shock. The shock front structure, which was
not clearly resolved in the previous SPH simulations, is clearly captured by
the present simulations. In addition, we find a sound wave propagating outward,
thereby producing spatial modulations with amplitudes of $\sim$ 10 % in the
radial temperature and density profiles and time variations in the strength of
the shock. Such modulations, if observed, could be used as a probe to
investigate the structure of clusters.


  We show that any Brauer tree algebra has precisely $\binom{2n}{n}$
$2$-tilting complexes, where $n$ is the number of edges of the associated
Brauer tree. More explicitly, for an external edge $e$ and an integer $j\neq0$,
we show that the number of $2$-tilting complexes $T$ with $g_e(T)=j$ is
$\binom{2n-|j|-1}{n-1}$, where $g_e(T)$ denotes the $e$-th of the $g$-vector of
$T$. To prove this, we use a geometric model of Brauer graph algebras on the
closed oriented marked surfaces and a classification of $2$-tilting complexes
due to Adachi-Aihara-Chan.


  We suppose that lepton number is explicitly broken at low energy scale(M) in
the framework of the Higgs triplet($\Delta$) model. The scalar sector of the
model is developed considering the particular assumption $M=v_\Delta \approx$
eV. We show that such assumption infers a particular mass spectrum for the
scalars that compose the triplet and cause a decoupling of these scalars from
those that compose the standard scalar doublet.


  The k-projection method provides an approach to separate the contributions
from different constituents in heterostructure systems and can act as an aid to
connect the results of experiments and calculations. We show that the technique
can be used to "unfold" the calculated electronic bands of interfaces and
supercells, and provide local band structure by integrating the projected
states over specified regions of space, a step that can be implemented
efficiently using fast Fourier transforms. We apply the method to investigate
the effects of interfaces in heterostructures consisting of a graphene bilayer
on H-saturated SiC(0001), BAs monolayer on the ferromagnetic semiconductor
CrI3, silicene on Ag(111), and to the Bi2Se3 surface. Our results reveal that
the band structure of the graphene bilayer around the Dirac point is strongly
dependent on the termination of SiC(0001): on the C face, the graphene is n
doped and a gap of ~0.13 eV is opened, whereas, on the Si face, the graphene is
essentially unchanged and neutral. We show that for BAs/CrI3, the magnetic
proximity effect can effectively induce a spin splitting up to about 50 meV in
BAs. For silicene/Ag(111), our calculations reproduce the angle-resolved
photoemission spectroscopy results, including linearly dispersing bands at the
edge of the first Brillouin zone of Ag(111); although these states result from
the interaction between the silicene overlayer and the substrate, we
demonstrate that they are not Dirac states.


  Multi-unit organizations such as retail chains are interested in the
diffusion of best practices throughout all divisions. However, the strict
guidelines or incentive schemes may not always be effective in promoting the
replication of a practice. In this paper we analyze how the individual belief
systems, namely the desire of individuals to conform, may be used to spread
knowledge between departments. We develop an agent-based simulation of an
organization with different network structures between divisions through which
the knowledge is shared, and observe the resulting synchrony. We find that the
effect of network structures on the diffusion of knowledge depends on the
interdependencies between divisions, and that peer-to-peer exchange of
information is more effective in reaching synchrony than unilateral sharing of
knowledge from one division. Moreover, we find that centralized network
structures lead to lower performance in organizations.


  The mass of compact objects in General Relativity (GR), which as is well
known, is obtained via the Tolman - Oppenheimer - Volkov (TOV) equations, is a
well defined quantity. However, in alternative gravity, this is not in general
the case. In the particular case of $f(T)$ gravity, where $T$ is the scalar
torsion, some authors consider that this is still an open question, since it is
not guaranteed that the same equation used in TOV GR holds. In this paper we
consider such an important issue and compare different ways to calculate the
mass of compact objects in $f(T)$ gravity. In particular, we argue that one of
them, the asymptotic mass, may be the most appropriate way to calculate mass in
this theory. We adopt realistic equations of state in all the models presented
in this article.


  We discuss various numerical approaches for studying the chaotic dynamics of
multidimensional Hamiltonian systems, focusing our analysis on the chaotic
evolution of initially localized energy excitations in the disordered
Klein-Gordon oscillator chain in one spatial dimension.


  We prove perturbative renormalizability of projectable Horava gravity. The
key element of the argument is the choice of a gauge which ensures the correct
anisotropic scaling of the propagators and their uniform falloff at large
frequencies and momenta. This guarantees that the counterterms required to
absorb the loop divergences are local and marginal or relevant with respect to
the anisotropic scaling. Gauge invariance of the counterterms is achieved by
making use of the background-covariant formalism. We also comment on the
difficulties of this approach when addressing the renormalizability of the
non-projectable model.


  The Eureka-147 Digital Audio Broadcasting (DAB) standard defines the 'dynamic
labels' data field for holding information about the transmission content.
However, this information does not follow a well-defined structure since it is
designed to carry text for direct output to displays, for human interpretation.
This poses a problem when machine interpretation of DAB content information is
desired. Extensible Markup Language (XML) was developed to allow for the
well-defined, structured machine-to-machine exchange of data over computer
networks. This article proposes a novel technique of machine-interpretable DAB
content annotation and receiver hardware control, involving the utilisation of
XML as metadata in the transmitted DAB frames.


  Phonon polaritons (PhPs) -- lattice vibrations coupled to electromagnetic
fields -- in highly anisotropic media display a plethora of intriguing optical
phenomena (including ray-like propagation, anomalous refraction, and
topological transitions, among others), which have potential for unprecedented
manipulation of the flow of light at the nanoscale. However, the propagation
properties of these PhPs are intrinsically linked to the anisotropic crystal
structure of the host material. Although in-plane anisotropic PhPs can be
steered (and even canalized) by twisting individual crystal slabs in a van der
Waals (vdW) stack, active control of their propagation via external stimuli
presents a significant challenge. Here, we report on a technology in which
anisotropic PhPs supported by biaxial vdW slabs are actively tunable by simply
gating an integrated graphene layer. Excitingly, we predict active tuning of
optical topological transitions, which enable controlling the canalization of
PhPs along different in-plane directions in twisted heterostructures. Apart
from their fundamental interest, our findings hold promises for the development
of optoelectronic devices (sensors, photodetectors, etc.) based on PhPs with
dynamically controllable properties.


  A detailed investigation of the electronic - and magneto - transport
properties of Nd0.8Sr0.2MnO3 with the variation of grain size (down to 42 nm)
is presented here. Interestingly, we observe that the ferromagnetic insulating
state is suppressed and a metallic state is stabilized as the grain size of the
sample is reduced. As a result, metal insulator transition is observed in this
low doped manganite which is insulating in nature in its bulk form.
Destabilization of polaronic order in the ferromagnetic insulating state due to
enhanced surface disorder on grain size reduction has been attributed to this
effect. A phenomenological model has been proposed to represent the concept of
destabilization of polaron formation in the surface region of the nano grains.
Resistivity and magnetoresistance data have been carefully analyzed employing
different suitable models. Electrical third harmonic resistance has been
measured to directly probe the electrical nonlinearity in the samples.


  We report detailed magnetic measurements on history and metastability effects
in the intermediate state of mesoscopic cylinders of type I superconducting
Indium. This includes the observation of topological hysteresis with the
signature occurrence of different critical fields during flux entry and flux
exit. We show the existence of a plethora of metastable configuration and
recipes to access them. We also demonstrate the manifestation of superheating
and supercooling of superconducting and normal states, respectively across the
superconductivity transition.


  We propose novel connections between several neural network architectures and
viscosity solutions of some Hamilton--Jacobi (HJ) partial differential
equations (PDEs) whose Hamiltonian is convex and only depends on the spatial
gradient of the solution. To be specific, we prove that under certain
assumptions, the two neural network architectures we proposed represent
viscosity solutions to two sets of HJ PDEs with zero error. We also implement
our proposed neural network architectures using Tensorflow and provide several
examples and illustrations. Note that these neural network representations can
avoid curve of dimensionality for certain HJ PDEs, since they do not involve
neither grids nor discretization. Our results suggest that efficient dedicated
hardware implementation for neural networks can be leveraged to evaluate
viscosity solutions of certain HJ PDEs.


  We present a novel numerical routine (oscode) with a C++ and Python interface
for the efficient solution of one-dimensional, second-order, ordinary
differential equations with rapidly oscillating solutions. The method is based
on a Runge-Kutta-like stepping procedure that makes use of the
Wentzel-Kramers-Brillouin (WKB) approximation to skip regions of integration
where the characteristic frequency varies slowly. In regions where this is not
the case, the method is able to switch to a made-to-measure Runge-Kutta
integrator that minimises the total number of function evaluations. We
demonstrate the effectiveness of the method with example solutions of the Airy
equation and an equation exhibiting a burst of oscillations, discussing the
error properties of the method in detail. We then show the method applied to
physical systems. First, the one-dimensional, time-independent Schr\"odinger
equation is solved as part of a shooting method to search for the energy
eigenvalues for a potential with quartic anharmonicity. Then, the method is
used to solve the Mukhanov-Sasaki equation describing the evolution of
cosmological perturbations, and the primordial power spectrum of the
perturbations is computed in different cosmological scenarios. We compare the
performance of our solver in calculating a primordial power spectrum of scalar
perturbations to that of BINGO, an efficient code specifically designed for
such applications.


  Detecting a diverse range of objects under various driving scenarios is
essential for the effectiveness of autonomous driving systems. However, the
real-world data collected often lacks the necessary diversity presenting a
long-tail distribution. Although synthetic data has been utilized to overcome
this issue by generating virtual scenes, it faces hurdles such as a significant
domain gap and the substantial efforts required from 3D artists to create
realistic environments. To overcome these challenges, we present ARSim, a fully
automated, comprehensive, modular framework designed to enhance real multi-view
image data with 3D synthetic objects of interest. The proposed method
integrates domain adaptation and randomization strategies to address covariate
shift between real and simulated data by inferring essential domain attributes
from real data and employing simulation-based randomization for other
attributes. We construct a simplified virtual scene using real data and
strategically place 3D synthetic assets within it. Illumination is achieved by
estimating light distribution from multiple images capturing the surroundings
of the vehicle. Camera parameters from real data are employed to render
synthetic assets in each frame. The resulting augmented multi-view consistent
dataset is used to train a multi-camera perception network for autonomous
vehicles. Experimental results on various AV perception tasks demonstrate the
superior performance of networks trained on the augmented dataset.


  The main purpose here is the study of dispersive blow-up for solutions of the
Zakharov-Kuznetsov equation. Dispersive blow-up refers to point singularities
due to the focusing of short or long waves. We will construct initial data such
that solutions of the linear problem present this kind of singularities. Then
we show that the corresponding solutions of the nonlinear problem present
dispersive blow-up inherited from the linear component part of the equation.
Similar results are obtained for the generalized Zakharov-Kuznetsov equation.


  It is shown how a proof of the Bell-Kochen-Specker (BKS) theorem given by
Kernaghan and Peres can be experimentally realized using a scheme of
measurements derived from a related proof of the same theorem by Mermin. It is
also pointed out that if this BKS experiment is carried out independently by
two distant observers who repeatedly make measurements on a specially
correlated state of six qubits, it provides an inequality-free demonstration of
Bell's theorem as well.


  In the present paper we demonstrate the possibility of the [SUSY(5)]^3 SUSY
unification at the energy scale $\mu_{GUT}\approx 10^{18.3} GeV$ with the value
of GUT inverse finestructure constant $\alpha_{GUT}^{-1}\approx 34.4$, which is
very close to its critical value $\alpha_{5, crit}^{-1}\approx 34.0$, existing
at the Planck scale.


  We describe a simple framework to assess the LISA scientific performance
(more specifically, its sensitivity and expected parameter-estimation precision
for prescribed gravitational-wave signals) under the assumption of failure of
one or two inter-spacecraft laser measurements (links) and of one to four
intra-spacecraft laser measurements. We apply the framework to the simple case
of measuring the LISA sensitivity to monochromatic circular binaries, and the
LISA parameter-estimation precision for the gravitational-wave polarization
angle of these systems. Compared to the six-link baseline configuration, the
five-link case is characterized by a small loss in signal-to-noise ratio (SNR)
in the high-frequency section of the LISA band; the four-link case shows a
reduction by a factor of sqrt(2) at low frequencies, and by up to ~2 at high
frequencies. The uncertainty in the estimate of polarization, as computed in
the Fisher-matrix formalism, also worsens when moving from six to five, and
then to four links: this can be explained by the reduced SNR available in those
configurations (except for observations shorter than three months, where five
and six links do better than four even with the same SNR). In addition, we
prove (for generic signals) that the SNR and Fisher matrix are invariant with
respect to the choice of a basis of TDI observables; rather, they depend only
on which inter-spacecraft and intra-spacecraft measurements are available.


  Volatile organic molecules formed by photochemistry in the upper atmosphere
of Titan can undergo condensation as pure ices in the stratosphere and the
troposphere as well as condense as ice layers onto the organic aerosols that
are visible as the haze layers of Titan. As solar photons penetrate through
Titan s atmosphere, shorter-wavelength photons are attenuated and
longerwavelength photons make it into the lower altitudes, where aerosols
become abundant. We conducted an experimental study to evaluate the long
wavelength ( > 300 nm) photo-reactivity of these ices accreted on the Titan
aerosol-analogs (also known as tholins) made in the laboratory. We have focused
on acetylene, the third most abundant hydrocarbon in Titan s atmosphere after
CH4 and C2H6. Further, acetylene is the most abundant unsaturated hydrocarbon
in Titan s atmosphere. Our results indicate that the aerosols can act as
activation centers to drive the photoreactivity of acetylene with the aerosols
at the accretion interface at wavelengths where acetylene-ice alone does not
show photoreactivity. We found that along with photochemistry, photodesorption
plays an important role. We observed that about 15% of the initial acetylene is
photodesorbed, with a photodesorption rate of (2.1 +/- 0.2) x 10-6
molecules.photon-1 at 355 nm. This photodesorption is wavelength-dependent,
confirming that it is mediated by the UV absorption of the aerosol analogues,
similar to photochemistry. We conclude that the UV-Vis properties of aerosols
would determine how they evolve further in Titan s atmosphere and on the
surface through photochemical alterations involving longer wavelength photons.


  We prove that every planar triangle-free graph on $n$ vertices has fractional
chromatic number at most $3-\frac{1}{n+1/3}$.


  It is known that Vilkovisky-DeWitt's effective action is gauge invariant
off-shell and independent of quantum field parametrization. In this work, we
perform the calculation of the divergences in two-loop Vilkovisky-DeWitt's
effective action for the theory of a massive scalar field minimally coupled to
gravity. We quantize both gravity and scalar field around a flat Minkowski
metric and a constant scalar field background. The quantum corrections are
computed up to second order in the background scalar field for the purpose of
mass renormalization.


  With thousands of academic articles shared on a daily basis, it has become
increasingly difficult to keep up with the latest scientific findings. To
overcome this problem, we introduce a new task of disentangled paper
summarization, which seeks to generate separate summaries for the paper
contributions and the context of the work, making it easier to identify the key
findings shared in articles. For this purpose, we extend the S2ORC corpus of
academic articles, which spans a diverse set of domains ranging from economics
to psychology, by adding disentangled "contribution" and "context" reference
labels. Together with the dataset, we introduce and analyze three baseline
approaches: 1) a unified model controlled by input code prefixes, 2) a model
with separate generation heads specialized in generating the disentangled
outputs, and 3) a training strategy that guides the model using additional
supervision coming from inbound and outbound citations. We also propose a
comprehensive automatic evaluation protocol which reports the relevance,
novelty, and disentanglement of generated outputs. Through a human study
involving expert annotators, we show that in 79%, of cases our new task is
considered more helpful than traditional scientific paper summarization.


  After briefly reviewing the methods that allow us to derive consistently new
Lie (super)algebras from given ones, we consider enlarged superspaces and
superalgebras, their relevance and some possible applications.


  We present sufficient conditions for the existence of a periodic solution for
a class of systems describing the periodically forced motion of a massive point
on a compact surface with a boundary.


  We have combined the benefits of two catalytic growth phenomena to form
nanostructures of transition metal trichalcogenides (TMTs), materials that are
challenging to grow in a nanostructured form by conventional techniques, as
required to exploit their exotic physics. Our growth strategy combines the
benefits of vapor-liquid-solid (VLS) growth in controlling dimension and growth
location, and salt-assisted growth for fast growth at moderate temperatures.
This salt-assisted VLS growth is enabled through use of a catalyst that
includes Au and an alkali metal halide. We demonstrate high yields of NbS3 1D
nanostructures with sub-ten nanometer diameter, tens of micrometers length, and
distinct 1D morphologies consisting of nanowires and nanoribbons with [010] and
[100] growth orientations, respectively. We present strategies to control the
growth location, size, and morphology. We extend the growth method to
synthesize other TMTs, NbSe3 and TiS3, as nanowires. Finally, we discuss the
growth mechanism based on the relationships we measure between the materials
characteristics (growth orientation, morphology and dimensions) and the growth
conditions (catalyst volume and growth time). Our study introduces
opportunities to expand the library of emerging 1D vdW materials and their
heterostructures with controllable nanoscale dimensions.


  Recently, operator quantum error-correcting codes have been proposed to unify
and generalize decoherence free subspaces, noiseless subsystems, and quantum
error-correcting codes. This note introduces a natural construction of such
codes in terms of Clifford codes, an elegant generalization of stabilizer codes
due to Knill. Character-theoretic methods are used to derive a simple method to
construct operator quantum error-correcting codes from any classical additive
code over a finite field.


  A generic characteristic of self-graviting systems is that they have a
negative heat capacity. An important example of this behaviour is given by the
Schwarzschild black hole. The case of charged and rotating black holes is even
more interesting, since a change of sign of the specific heat takes place
through an infinite discontinuity. This has been usually associated with a
black hole thermodynamic phase transition appearing at the points where the
heat capacity diverges, the so-called Davies points. This aspect of black hole
thermodynamics has been addressed from different perspectives, motivating
different interpretations since its discovery in the 1970s. In this paper, a
physical reinterpretation of the heat capacity is provided for spherically
symmetric and static black holes. Our analysis is partially based on a
reformulation of the black hole heat capacity using the Newman--Penrose
formalism. The application to the Reissner--Nordstr\"om--de Sitter black hole
case reveals a clear physical interpretation of the Newman--Penrose scalars
evaluated at the event horizon. This allows us to write the heat capacity as a
balance of pressures defined at the horizon. In particular, a matter pressure
(coming from the energy-momentum tensor) and a thermal pressure (coming from
the holographic energy equipartition of the horizon). The Davies point is
identified with the point where the Komar thermal energy density matches the
matter pressure at the horizon. We also compare the black hole case with the
case of self-graviting objects and their corresponding thermal evolutions. We
conclude that the heat capacity of black holes and self-graviting systems can
be understood qualitatively in similar terms.


  Recent studies of the phase diagram for spherical, purely repulsive, active
particles established the existence of a transition from a liquid-like to a
solid-like phase analogous to the one observed in colloidal systems at thermal
equilibrium, in particular in two dimensions an intermediate hexatic phase is
observed. Here, we present evidence that the active dense phases (solid,
hexatic and liquid) exhibit interesting dynamical anomalies. First, we unveil
the growth - with density and activity - of ordered domains where the
particles' velocities align in parallel or vortex-like patches. Second, when
activity is strong, the spatial distribution of kinetic energy becomes
heterogeneous with high energy regions correlated to defects of the crystalline
structure. This spatial heterogeneity is accompanied by temporal intermittency,
with sudden peaks in the time-series of kinetic energy. The observed dynamical
anomalies are not present in a dense equilibrium system and cannot be detected
by considering only the structural properties of the system.


  We show that a three dimensional topological insulator doped with magnetic
impurities in the bulk can have a regime where the surface is magnetically
ordered but the bulk is not. This is in contrast to conventional materials
where bulk ordered phases are typically more robust than surface ordered
phases. The difference originates from the topologically protected gapless
surface states characteristic of topological insulators. We study the problem
using a mean field approach in two concrete models that give the same
qualitative result, with some interesting differences. Our findings could help
explain recent experimental results showing the emergence of a spectral gap in
the surface state of Bi2Se3 doped with Mn or Fe atoms, but with no measurable
bulk magnetism.


  We consider a spinless fermionic $p\pm ip$ superfluid living on a
two-dimensional sphere. Using superfluid hydrodynamics we show that the ground
state necessarily exhibits topological defects: either a pair of elementary
vortices or a domain wall between $p\pm ip$ phases. In the topologically
nontrivial BCS phase we identify the chiral fermion modes localized on the
topological defects and compute their low-energy spectrum.


  We show generalisation error bounds for deep learning with two main
improvements over the state of the art. (1) Our bounds have no explicit
dependence on the number of classes except for logarithmic factors. This holds
even when formulating the bounds in terms of the $L^2$-norm of the weight
matrices, where previous bounds exhibit at least a square-root dependence on
the number of classes. (2) We adapt the classic Rademacher analysis of DNNs to
incorporate weight sharing -- a task of fundamental theoretical importance
which was previously attempted only under very restrictive assumptions. In our
results, each convolutional filter contributes only once to the bound,
regardless of how many times it is applied. Further improvements exploiting
pooling and sparse connections are provided. The presented bounds scale as the
norms of the parameter matrices, rather than the number of parameters. In
particular, contrary to bounds based on parameter counting, they are
asymptotically tight (up to log factors) when the weights approach
initialisation, making them suitable as a basic ingredient in bounds sensitive
to the optimisation procedure. We also show how to adapt the recent technique
of loss function augmentation to our situation to replace spectral norms by
empirical analogues whilst maintaining the advantages of our approach.


  Since the proposal of the graph neural network (GNN) by Gori et al. (2005)
and Scarselli et al. (2008), one of the major problems in training GNNs was
their struggle to propagate information between distant nodes in the graph. We
propose a new explanation for this problem: GNNs are susceptible to a
bottleneck when aggregating messages across a long path. This bottleneck causes
the over-squashing of exponentially growing information into fixed-size
vectors. As a result, GNNs fail to propagate messages originating from distant
nodes and perform poorly when the prediction task depends on long-range
interaction. In this paper, we highlight the inherent problem of over-squashing
in GNNs: we demonstrate that the bottleneck hinders popular GNNs from fitting
long-range signals in the training data; we further show that GNNs that absorb
incoming edges equally, such as GCN and GIN, are more susceptible to
over-squashing than GAT and GGNN; finally, we show that prior work, which
extensively tuned GNN models of long-range problems, suffers from
over-squashing, and that breaking the bottleneck improves their
state-of-the-art results without any tuning or additional weights. Our code is
available at https://github.com/tech-srl/bottleneck/ .


  In this paper, the sum-rate maximization problem is studied for wireless
networks that use downlink rate splitting multiple access (RSMA). In the
considered model, each base station (BS) divides the messages that must be
transmitted to its users into a `private' part and a `common' part. Here, the
common message is a message that all users want to receive and the private
message is a message that is dedicated to only a specific user. The RSMA
mechanism enables a BS to adjust the split of common and private messages so as
to control the interference by decoding and treating interference as noise and,
thus optimizing the data rate of users. To maximize the users' sum-rate, the
network can determine the rate allocation for the common message to meet the
rate demand, and adjust the transmit power for the private message to reduce
the interference. This problem is formulated as an optimization problem whose
goal is to maximize the sum-rate of all users. To solve this nonconvex
maximization problem, the optimal power used for transmitting the private
message to the users is first obtained in closed form for a given rate
allocation and common message power. Based on the optimal private message
transmission power, the optimal rate allocation is then derived under a fixed
common message transmission power. Subsequently, a one-dimensional search
algorithm is proposed to obtain the optimal solution of common message
transmission power. Simulation results show that the RSMA can achieve up to
15.6\% and 21.5\% gains in terms of data rate compared to non-orthogonal
multiple access (NOMA) and orthogonal frequency-division multiple access
(OFDMA), respectively.