  The Schr\"odinger equation in the presence of an external electromagnetic
field is an important problem in computational quantum mechanics. It also
provides a nice example of a differential equation whose flow can be split with
benefit into three parts. After presenting a splitting approach for three
operators with two of them being unbounded, we exemplarily prove first-order
convergence of Lie splitting in this framework. The result is then applied to
the magnetic Schr\"odinger equation, which is split into its potential, kinetic
and advective parts. The latter requires special treatment in order not to lose
the conservation properties of the scheme. We discuss several options.
Numerical examples in one, two and three space dimensions show that the method
of characteristics coupled with a nonequispaced fast Fourier transform (NFFT)
provides a fast and reliable technique for achieving mass conservation at the
discrete level.


  Diverse parallel stitched two-dimensional heterostructures are synthesized,
including metal-semiconductor (graphene-MoS2), semiconductor-semiconductor
(WS2-MoS2), and insulator-semiconductor (hBN-MoS2), directly through selective
sowing of aromatic molecules as the seeds in chemical vapor deposition (CVD)
method. Our methodology enables the large-scale fabrication of lateral
heterostructures with arbitrary patterns, and clean and precisely aligned
interfaces, which offers tremendous potential for its application in integrated
circuits.


  "Bottom-up" approaches to the many-body physics of fermions have demonstrated
recently precise number and site-resolved preparations with tunability of
interparticle interactions in single-well, SW, and double-well, DW, nano-scale
confinements created by manipulating ultracold fermionic atoms with optical
tweezers. These experiments emulate an analogue-simulator mapping onto the
requisite microscopic hamiltonian, approaching realization of Feynman's vision
of quantum simulators that "will do exactly the same as nature". Here we report
on exact benchmark configuration-interaction computational microscopy solutions
of the hamiltonian, uncovering the spectral evolution, wave-function anatomy,
and entanglement properties of the interacting fermions in the entire parameter
range, including crossover from a SW to a DW confinement and a controllable
energy imbalance between the wells. We demonstrate attractive pairing and
formation of repulsive, highly-correlated, ultracold Wigner molecules,
well-described in the natural orbital representation. The agreement with the
measurements affirms the henceforth gained deep insights into ultracold
molecules and opens access to the size-dependent evolution of nano-clustered
and condensed-matter phases and ultracold-atoms quantum information.


  Let $P$ be the isotropic nearest neighbor transition operator on a
homogeneous tree. We consider the $\lambda$-eigenfunctions of $P$ for $\lambda$
outside its $\ell^2$ spectrum, i.e., the eigenfunctions with eigenvalue
$\gamma=\lambda - 1$ of the Laplace operator $Delta=P- \mathbb I$, and also the
$\lambda-$polyharmonic functions, that is, the union of the kernels of
$(Delta-\gamma \mathbb I)^n$ for $n\geqslant 0$. We prove that, on a suitable
Banach space generated by the $\lambda-$polyharmonic functions, the operator
$e^{Delta-\gamma \mathbb I}$ is hypercyclic, although $Delta-\gamma \mathbb I$
is not.


  The norm kernel of the generator-coordinate method is shown to be a symmetric
kernel of an integral equation with eigenfunctions defined in the
Fock--Bargmann space and forming a complete set of orthonormalized states
(classified with the use of SU(3) symmetry indices) satisfying the Pauli
exclusion principle. This interpretation allows to develop a method which, even
in the presence of the SU(3) degeneracy, provides for a consistent way to
introduce additional quantum numbers for the classification of the basis
states. In order to set the asymptotic boundary conditions for the expansion
coefficients of a wave function in the SU(3) basis, a complementary basis of
functions with partial angular momenta as good quantum numbers is needed. Norm
kernels of the binary systems 6He+p, 6He+n, 6He+4He, and 8He+4He are considered
in detail.


  Surface treatment tasks such as grinding, sanding or polishing are a vital
step of the value chain in many industries, but are notoriously challenging to
automate. We present RoboGrind, an integrated system for the intuitive,
interactive automation of surface treatment tasks with industrial robots. It
combines a sophisticated 3D perception pipeline for surface scanning and
automatic defect identification, an interactive voice-controlled wizard system
for the AI-assisted bootstrapping and parameterization of robot programs, and
an automatic planning and execution pipeline for force-controlled robotic
surface treatment. RoboGrind is evaluated both under laboratory and real-world
conditions in the context of refabricating fiberglass wind turbine blades.


  Spatial Gaussian process regression models typically contain finite
dimensional covariance parameters that need to be estimated from the data. We
study the Bayesian estimation of covariance parameters including the nugget
parameter in a general class of stationary covariance functions under
fixed-domain asymptotics, which is theoretically challenging due to the
increasingly strong dependence among spatial observations. We propose a novel
adaptation of the Schwartz's consistency theorem for showing posterior
contraction rates of the covariance parameters including the nugget. We derive
a new polynomial evidence lower bound, and propose consistent higher-order
quadratic variation estimators that satisfy concentration inequalities with
exponentially small tails. Our Bayesian fixed-domain asymptotics theory leads
to explicit posterior contraction rates for the microergodic and nugget
parameters in the isotropic Matern covariance function under a general
stratified sampling design. We verify our theory and the Bayesian predictive
performance in simulation studies and an application to sea surface temperature
data.


  The light-front formalism for a covariant description of the European Muon
Collaboration (EMC) effect, already applied to $^3$He, is formally extended to
any nucleus, and used for actually calculating the $^3$H and $^4$He cases. The
realistic and accurate nuclear description of few-nucleon bound systems,
obtained with both phenomenological and chiral potentials, has been properly
combined with the Poincare' covariance and macroscopic locality, automatically
satisfying both number of particles and momentum sum rule. While retaining the
on-mass-shell nucleon structure functions, one is then able to predict a
sizable EMC effect for $^4$He, as already observed for $^3$He. Moreover, the
impact on the EMC effect of both i) the short-range correlations, such as those
generated by modern nuclear interactions, and ii) the ratio between the neutron
and proton structure functions has been studied. The short-range correlations
generated by retaining only the standard nuclear degrees of freedom act on the
depth of the minimum in the EMC ratio, while the uncertainties linked to the
ratio of neutron to proton structure functions are found to be very small.
These light-front results facilitates ascribing deviations from experimental
data due to genuine QCD effects, not included in a standard nuclear
description, and initiating unbiased investigations.


  State transition algorithm (STA) has been emerging as a novel stochastic
method for global optimization in recent few years. To make better
understanding of continuous STA, a matlab toolbox for continuous STA has been
developed. Firstly, the basic principles of continuous STA are briefly
described. Then, a matlab implementation of the standard continuous STA is
explained, with several instances given to show how to use to the matlab
toolbox to minimize an optimization problem with bound constraints. In the same
while, a link is provided to download the matlab toolbox via available
resources.


  The present article is part of a research program the aim of which is to find
all indecomposable solvable extensions of a given class of nilpotent Lie
algebras. Specifically in this article we consider a nilpotent Lie algebra n
that is isomorphic to the nilradical of the Borel subalgebra of a complex
simple Lie algebra, or of its split real form. We treat all classical and
exceptional simple Lie algebras in a uniform manner. We identify the nilpotent
Lie algebra n as the one consisting of all positive root spaces. We present
general structural properties of all solvable extensions of n. In particular,
we study the extension by one nonnilpotent element and by the maximal number of
such elements. We show that the extension of maximal dimension is always unique
and isomorphic to the Borel subalgebra of the corresponding simple Lie algebra.


  The spin structure of the system of quasifree fermions having total angular
momentum $J=1/2$ is studied in a consistently covariant approach. Within this
model the relations between the spin functions are obtained. Their particular
cases are the sum rules Wanzura - Wilczek, Efremov - Leader - Teryaev,
Burkhardt - Cottingham and also the expression for the Wanzura - Wilczek twist
2 term $g_{2}^{WW}$. With the use of the proton valence quark distributions as
an input, the corresponding spin functions are obtained. The resulting
structure functions $g_{1}$ and $g_{2}$ are well compatible with the
experimental data.


  Modern deep learning (DL) architectures are trained using variants of the SGD
algorithm that is run with a $\textit{manually}$ defined learning rate
schedule, i.e., the learning rate is dropped at the pre-defined epochs,
typically when the training loss is expected to saturate. In this paper we
develop an algorithm that realizes the learning rate drop
$\textit{automatically}$. The proposed method, that we refer to as AutoDrop, is
motivated by the observation that the angular velocity of the model parameters,
i.e., the velocity of the changes of the convergence direction, for a fixed
learning rate initially increases rapidly and then progresses towards soft
saturation. At saturation the optimizer slows down thus the angular velocity
saturation is a good indicator for dropping the learning rate. After the drop,
the angular velocity "resets" and follows the previously described pattern - it
increases again until saturation. We show that our method improves over SOTA
training approaches: it accelerates the training of DL models and leads to a
better generalization. We also show that our method does not require any extra
hyperparameter tuning. AutoDrop is furthermore extremely simple to implement
and computationally cheap. Finally, we develop a theoretical framework for
analyzing our algorithm and provide convergence guarantees.


  We calculate the contribution to the electron scattering rate from the
surface level atoms (SLA), proposed in [A.M. Dyugaev, P.D. Grigoriev, JETP
Lett. 78, 466 (2003)]. The inclusion of these states into account was
sufficient to explain the long-standing puzzles in the temperature dependence
of the surface tension of both He isotopes and to reach a very good agreement
between theory and experiment. We calculate the contribution from these SLA to
the surface electron scattering rate and explain some features in the
temperature dependence of the surface electron mobility. This contribution is
essential at low temperature $T<0.5$ when the He vapor concentration is
exponentially small. For an accurate calculation of the electron mobility one
also needs to consider the influence of the clamping electric field on the
surface electron wave function and the temperature dependence of the He3
chemical potential.


  In this work, we revisit the problem of fairly allocating a number of
indivisible items that are located on a line to multiple agents. A feasible
allocation requires that the allocated items to each agent are connected on the
line. The items can be goods on which agents have non-negative utilities, or
chores on which the utilities are non-positive. Our objective is to understand
the extent to which welfare is inevitably sacrificed by enforcing the
allocations to be fair, i.e., price of fairness (PoF). We study both
egalitarian and utilitarian welfare. Previous works by Suksompong [Discret.
Appl. Math., 2019] and H\"ohne and van Stee [Inf. Comput., 2021] have studied
PoF regarding the notions of envy-freeness and proportionality. However, these
fair allocations barely exist for indivisible items, and thus in this work, we
focus on the relaxations of maximin share fairness and proportionality up to
one item, which are guaranteed to be satisfiable. For most settings, we give
(almost) tight ratios of PoF and all the upper bounds are proved by designing
polynomial time algorithms.


  First-order nonadiabatic coupling matrix elements (fo-NACMEs) are the basic
quantities in theoretical descriptions of electronically nonadiabatic processes
that are ubiquitous in molecular physics and chemistry. Given the large size of
systems of chemical interests, time-dependent density functional theory (TDDFT)
is usually the first choice. However, the lack of wave functions in TDDFT
renders the formulation of NAC-TDDFT for fo-NACMEs conceptually difficult. The
present account aims to analyze the available variants of NAC-TDDFT in a
critical but concise manner and meanwhile point out the proper ways for
implementation. It can be concluded, from both theoretical and numerical points
of view, that the equation of motion-based variant of NAC-TDDFT is the right
choice. Possible future developments of this variant are also highlighted.


  We study spectral properties of a class of global infinite order
pseudo-differential operators and obtain the asymptotic behaviour of the
spectral counting functions of such operators. Unlike their finite order
counterparts, their spectral asymptotics are not of power-log-type but of
log-type. The ultradistributional setting of such operators of infinite order
makes the theory more complex so that the standard finite order global Weyl
calculus cannot be used in this context.


  The production of science-ready data from major solar telescopes requires
expertise beyond that of the typical observer. This is a consequence of the
increasing complexity of instruments and observing sequences, which require
calibrations and corrections for instrumental and seeing effects that are not
only difficult to measure, but are also coupled in ways that require careful
analysis in the design of the correction procedures. Modern space-based
telescopes have data-processing pipelines capable of routinely producing
well-characterized data products. High-resolution imaging spectropolarimeters
at ground-based telescopes need similar data pipelines.
  We present new methods for flat-fielding spectropolarimetric data acquired
with telecentric Fabry-Perot instruments and a new approach for accurate camera
co-alignment for image restoration. We document a procedure that forms the
basis of current state of the art processing of data from the CRISP imaging
spectropolarimeter at the Swedish 1-m Solar Telescope (SST). By collecting,
implementing, and testing a suite of computer programs, we have defined a data
reduction pipeline for this instrument. This pipeline, CRISPRED, streamlines
the process of making science-ready data. It is implemented and operated in
IDL, with time-consuming steps delegated to C. CRISPRED will be the basis also
for the data pipeline of the forthcoming CHROMIS instrument.


  A formal hierarchy of exact evolution equations are derived for physically
relevant space-time averages of state functions of microscopic dislocation
dynamics. While such hierarchies are undoubtedly of some value, a primary goal
here is to expose the intractable complexity of such systems of nonlinear
partial differential equations that, furthermore, remain `non-closed' and
therefore subject to phenomenological assumptions to be useful. It is instead
suggested that such hierarchies be terminated at the earliest stage possible
and effort be expended to derive closure relations for the `non-closed' terms
that arise from the formal averaging by taking into account the
full-stress-coupled microscopic dislocation dynamics, a matter on which these
formal hierarchies, whether of kinetic theory type or as pursued here, are
silent.


  The dynamical evolution of an open quantum system can be governed by the
Lindblad equation of the density matrix. In this paper, we propose to
characterize the density matrix topology by the topological invariant of its
modular Hamiltonian. Since the topological classification of such Hamiltonians
depends on their symmetry classes, a primary issue we address is determining
the requirement for the Lindbladian operators, under which the modular
Hamiltonian can preserve its symmetry class during the dynamical evolution. We
solve this problem for the fermionic Gaussian state and for the modular
Hamiltonian being a quadratic operator of a set of fermionic operators. When
these conditions are satisfied, along with a nontrivial topological
classification of the symmetry class of the modular Hamiltonian, a topological
transition can occur as time evolves. We present two examples of
dissipation-driven topological transitions where the modular Hamiltonian lies
in the AIII class with U(1) symmetry and the DIII class without U(1) symmetry.
By a finite size scaling, we show that this density matrix topology transition
occurs at a finite time. We also present the physical signature of this
transition.


  We report the discovery of KELT-10b, the first transiting exoplanet
discovered using the KELT-South telescope. KELT-10b is a highly inflated
sub-Jupiter mass planet transiting a relatively bright $V = 10.7$ star (TYC
8378-64-1), with T$_{eff}$ = $5948\pm74$ K, $\log{g}$ =
$4.319_{-0.030}^{+0.020}$ and [Fe/H] = $0.09_{-0.10}^{+0.11}$, an inferred mass
M$_{*}$ = $1.112_{-0.061}^{+0.055}$ M$_{\odot}$ and radius R$_{*}$ =
$1.209_{-0.035}^{+0.047}$ R$_{\odot}$. The planet has a radius R$_{P}$ =
$1.399_{-0.049}^{+0.069}$ R$_{J}$ and mass M$_{P}$ = $0.679_{-0.038}^{+0.039}$
M$_{J}$. The planet has an eccentricity consistent with zero and a semi-major
axis $a$ = $0.05250_{-0.00097}^{+0.00086}$ AU. The best fitting linear
ephemeris is $T_{0}$ = 2457066.72045$\pm$0.00027 BJD$_{TDB}$ and P =
4.1662739$\pm$0.0000063 days. This planet joins a group of highly inflated
transiting exoplanets with a radius much larger and a mass much less than those
of Jupiter. The planet, which boasts deep transits of 1.4%, has a relatively
high equilibrium temperature of T$_{eq}$ = $1377_{-23}^{+28}$ K, assuming zero
albedo and perfect heat redistribution. KELT-10b receives an estimated
insolation of $0.817_{-0.054}^{+0.068}$ $\times$ 10$^9$ erg s$^{-1}$ cm$^{-2}$,
which places it far above the insolation threshold above which hot Jupiters
exhibit increasing amounts of radius inflation. Evolutionary analysis of the
host star suggests that KELT-10b is unlikely to survive beyond the current
subgiant phase, due to a concomitant in-spiral of the planet over the next
$\sim$1 Gyr. The planet transits a relatively bright star and exhibits the
third largest transit depth of all transiting exoplanets with V $<$ 11 in the
southern hemisphere, making it a promising candidate for future atmospheric
characterization studies.


  In quantum gravity, fields may lose quantum coherence by scattering off
vacuum fluctuations in which virtual black hole pairs appear and disappear.
Although it is not possible to properly compute the scattering off such
fluctuations, we argue that one can get useful qualitative results, which
provide a guide to the possible effects of such scattering, by considering a
quantum field on the $C$ metric, which has the same topology as a virtual black
hole pair. We study a scalar field on the Lorentzian $C$ metric background,
with the scalar field in the analytically-continued Euclidean vacuum state. We
find that there are a finite number of particles at infinity in this state,
contrary to recent claims made by Yi. Thus, this state is not determined by
data at infinity, and there is loss of quantum coherence in this semi-classical
calculation.


  It is becoming increasingly important to explain complex, black-box machine
learning models. Although there is an expanding literature on this topic,
Shapley values stand out as a sound method to explain predictions from any type
of machine learning model. The original development of Shapley values for
prediction explanation relied on the assumption that the features being
described were independent. This methodology was then extended to explain
dependent features with an underlying continuous distribution. In this paper,
we propose a method to explain mixed (i.e. continuous, discrete, ordinal, and
categorical) dependent features by modeling the dependence structure of the
features using conditional inference trees. We demonstrate our proposed method
against the current industry standards in various simulation studies and find
that our method often outperforms the other approaches. Finally, we apply our
method to a real financial data set used in the 2018 FICO Explainable Machine
Learning Challenge and show how our explanations compare to the FICO challenge
Recognition Award winning team.


  We propose an effective technique to solving review-level sentiment
classification problem by using sentence-level polarity correction. Our
polarity correction technique takes into account the consistency of the
polarities (positive and negative) of sentences within each product review
before performing the actual machine learning task. While sentences with
inconsistent polarities are removed, sentences with consistent polarities are
used to learn state-of-the-art classifiers. The technique achieved better
results on different types of products reviews and outperforms baseline models
without the correction technique. Experimental results show an average of 82%
F-measure on four different product review domains.


  Squeezed back-to-back correlation (SBBC) of a boson-antiboson pair is
sensitive to the time distribution of the particle-emitting source, and the
SBBC function for an evolving source is expected to be affected by the
relaxation time of the system. In this paper, we investigate the effect of
relaxation time on the SBBC function. We put forth a method to calculate the
SBBC function with relaxation-time modification for evolving sources. The SBBC
functions of $D^0\!{\bar D}^0$ in relativistic heavy-ion collisions are
investigated by using a hydrodynamic model. It is found that the relaxation
time reduces the amplitudes of the SBBC functions. This change becomes serious
for a long relaxation time and large initial relative deviations of the chaotic
and squeezed amplitudes from their equilibrium values, respectively, in the
temporal steps.


  (ABRIDGED) We present a power spectrum analysis of the 10K catalogue from the
2dF QSO Redshift Survey. We compare the redshift-space power spectra of QSOs to
those measured for galaxies and Abell clusters at low redshift and find that
they show similar shapes in their overlap range, 50-150h^{-1}Mpc, with
P_QSO(k)\propto k^{-1.4}. The amplitude of the QSO power spectrum at z~1.4 is
almost comparable to that of galaxies at the present day if Omega_m=0.3 and
Omega_Lambda=0.7 (the Lambda cosmology), and a factor of ~3 lower if Omega_m=1
(the EdS cosmology) is assumed. The amplitude of the QSO power spectrum is a
factor of ~10 lower than that measured for Abell clusters at the present day.
At larger scales, the QSO power spectra continue to rise robustly to ~400
h^{-1}Mpc, implying more power at large scales than in the APM galaxy power
spectrum measured by Baugh & Efstathiou.
  We split the QSO sample into two redshift bins and find little evolution in
the amplitude of the power spectrum. The QSO power spectrum may show a spike
feature at ~90h^{-1}Mpc assuming the Lambda cosmology or ~65 h^{-1}Mpc assuming
an EdS cosmology. Although the spike appears to reproduce in both the North and
South strips and in two independent redshift ranges, its statistical
significance is still marginal and more data is needed to test further its
reality.
  We compare the QSO power spectra to CDM models to obtain a constraint on the
shape parameter, Gamma. For two choices of cosmology (Omega_m=1, Omega_Lambda=0
and Omega_m=0.3, Omega_Lambda=0.7), we find the best fit model has Gamma~0.1
+-0.1.


  Vulnerable road users (VRUs, i.e. cyclists and pedestrians) will play an
important role in future traffic. To avoid accidents and achieve a highly
efficient traffic flow, it is important to detect VRUs and to predict their
intentions. In this article a holistic approach for detecting intentions of
VRUs by cooperative methods is presented. The intention detection consists of
basic movement primitive prediction, e.g. standing, moving, turning, and a
forecast of the future trajectory. Vehicles equipped with sensors, data
processing systems and communication abilities, referred to as intelligent
vehicles, acquire and maintain a local model of their surrounding traffic
environment, e.g. crossing cyclists. Heterogeneous, open sets of agents
(cooperating and interacting vehicles, infrastructure, e.g. cameras and laser
scanners, and VRUs equipped with smart devices and body-worn sensors) exchange
information forming a multi-modal sensor system with the goal to reliably and
robustly detect VRUs and their intentions under consideration of real time
requirements and uncertainties. The resulting model allows to extend the
perceptual horizon of the individual agent beyond their own sensory
capabilities, enabling a longer forecast horizon. Concealments,
implausibilities and inconsistencies are resolved by the collective
intelligence of cooperating agents. Novel techniques of signal processing and
modelling in combination with analytical and learning based approaches of
pattern and activity recognition are used for detection, as well as intention
prediction of VRUs. Cooperation, by means of probabilistic sensor and knowledge
fusion, takes place on the level of perception and intention recognition. Based
on the requirements of the cooperative approach for the communication a new
strategy for an ad hoc network is proposed.


  Monte Carlo Tree Search (MCTS) is a relatively new sampling method with
multiple variants in the literature. They can be applied to a wide variety of
challenging domains including board games, video games, and energy-based
problems to mention a few. In this work, we explore the use of the vanilla MCTS
and the MCTS with Rapid Action Value Estimation (MCTS-RAVE) in the game of
Carcassonne, a stochastic game with a deceptive scoring system where limited
research has been conducted. We compare the strengths of the MCTS-based methods
with the Star2.5 algorithm, previously reported to yield competitive results in
the game of Carcassonne when a domain-specific heuristic is used to evaluate
the game states. We analyse the particularities of the strategies adopted by
the algorithms when they share a common reward system. The MCTS-based methods
consistently outperformed the Star2.5 algorithm given their ability to find and
follow long-term strategies, with the vanilla MCTS exhibiting a more robust
game-play than the MCTS-RAVE.


  Machine reading comprehension (MRC) is a challenging natural language
processing (NLP) task. Recently, the emergence of pre-trained models (PTM) has
brought this research field into a new era, in which the training objective
plays a key role. The masked language model (MLM) is a self-supervised training
objective that widely used in various PTMs. With the development of training
objectives, many variants of MLM have been proposed, such as whole word
masking, entity masking, phrase masking, span masking, and so on. In different
MLM, the length of the masked tokens is different. Similarly, in different
machine reading comprehension tasks, the length of the answer is also
different, and the answer is often a word, phrase, or sentence. Thus, in MRC
tasks with different answer lengths, whether the length of MLM is related to
performance is a question worth studying. If this hypothesis is true, it can
guide us how to pre-train the MLM model with a relatively suitable mask length
distribution for MRC task. In this paper, we try to uncover how much of MLM's
success in the machine reading comprehension tasks comes from the correlation
between masking length distribution and answer length in MRC dataset. In order
to address this issue, herein, (1) we propose four MRC tasks with different
answer length distributions, namely short span extraction task, long span
extraction task, short multiple-choice cloze task, long multiple-choice cloze
task; (2) four Chinese MRC datasets are created for these tasks; (3) we also
have pre-trained four masked language models according to the answer length
distributions of these datasets; (4) ablation experiments are conducted on the
datasets to verify our hypothesis. The experimental results demonstrate that
our hypothesis is true.


  In this paper we start from the Schr\"odinger equation to revisit some
classical quantum mechanics from the perspective of phase transition process.
Here the relativistic effect of particles moving at high speed can be regarded
as the phase transition process when the velocity variable increases.
Considering that the catastrophe models could describe qualitatively any phase
transition process, we adopt the simplest folding catastrophe type as the
potential function in the Schr\"odinger equation to obtain a revised
Schr\"odinger relativistic equation through the dimensionless analysis first,
and then further to derive out the steady-state Klein-Gordon equation and Dirac
relativistic equation gradually. These results reveal that the quantum
relativistic effect could be considered as the phase transition process, which
could be described by adopting the catastrophe models as the potential function
in the classical Schr\"odinger equation.


  In this paper, we propose a new quality link metric, interference and
bandwidth adjusted ETX (IBETX) for wireless multi-hop networks. As MAC layer
affects the link performance and consequently the route quality, the metric
therefore, tackles the issue by achieving twofold MAC-awareness. Firstly,
interference is calculated using cross-layered approach by sending probes to
MAC layer. Secondly, the nominal bit rate information is provided to all nodes
in the same contention domain by considering the bandwidth sharing mechanism of
802.11. Like ETX, our metric also calculates link delivery ratios that directly
affect throughput and selects those routes that bypass dense regions in the
network. Simulation results by NS-2 show that IBETX gives 19% higher throughput
than ETX and 10% higher than Expected Throughput (ETP). Our metric also
succeeds to reduce average end-to-end delay up to 16% less than Expected Link
Performance (ELP) and 24% less than ETX.


  The successful prediction of earthquakes is one of the holy grails in Earth
Sciences. Traditional predictions use statistical information on recurrence
intervals, but those predictions are not accurate enough. In a recent paper, a
machine learning approach was proposed and applied to data of laboratory
earthquakes. The machine learning algorithm utilizes continuous measurements of
radiated energy through acoustic emissions and the authors were able to
successfully predict the timing of laboratory earthquakes. Here, we reproduced
their model which was applied to a gouge layer of glass beads and applied it to
a data set obtained using a gouge layer of salt. In this salt experiment
different load point velocities were set, leading to variable recurrence times.
The machine learning technique we use is called random forest and uses the
acoustic emissions during the interseismic period. The random forest model
succeeds in making a relatively reliable prediction for both materials, also
long before the earthquake. Apparently there is information in the data on the
timing of the next earthquake throughout the experiment. For glass beads energy
is gradually and increasingly released whereas for salt energy is only released
during precursor activity, therefore the important features used in the
prediction are different. We interpret the difference in results to be due to
the different micromechanics of slip. The research shows that a machine
learning approach can reveal the presence of information in the data on the
timing of unstable slip events (earthquakes). Further research is needed to
identify the responsible micromechanical processes which might be then be used
to extrapolate to natural conditions.


  This paper proposes a complete IFoF system architecture derived from
simplified IEEE802.15.3c PHY layer proposal to successfully ensure near 1 Gbps
on the air interface. The system architecture utilizes low complexity baseband
processing modules. The byte/frame synchronization technique is designed to
provide a high value of preamble detection probability and a very small value
of the false detection probability. Conventional Reed-Solomon RS (255, 239)
coding is used for Channel Forward Error Correction (FEC). Good communication
link quality and Bit Error Rate (BER) results at 875 Mbps are achieved with
directional antennas.


  We aim at analytically modelling the solar wind proton trajectories during
their interaction with a partially ionised cometary atmosphere, not in terms of
bulk properties of the flow but in terms of single particle dynamics. We first
derive a generalised gyromotion, in which the electric field is reduced to its
motional component. Steady-state is assumed, and simplified models of the
cometary density and of the electron fluid are used to express the force
experienced by individual solar wind protons during the interaction. A
three-dimensional (3D) analytical expression of the gyration of two interacting
plasma beams is obtained. Applying it to a comet case, the force on protons is
always perpendicular to their velocity and has an amplitude proportional to
1/r^2. The solar wind deflection is obtained at any point in space. The
resulting picture presents a caustic of intersecting trajectories, and a
circular region is found that is completely free of particles. The particles do
not lose any kinetic energy and this absence of deceleration, together with the
solar wind deflection pattern and the presence of a solar wind ion cavity, is
in good agreement with the general results of the Rosetta mission. The
qualitative match between the model and the in situ data highlights how
dominant the motional electric field is throughout most of the interaction
region for the solar wind proton dynamics. The model provides a simple general
kinetic description of how momentum is transferred between these two
collisionless plasmas. It also shows the potential of this semi-analytical
model for a systematic quantitative comparison to the data.


  In recent years, cloud computing has been developing rapidly and is widely
used in various fields such as commerce and scientific research. However,
security issues, including access control, are a very important problem in
popularizing cloud computing and this has influenced its wide application of
cloud computing. As one of the solutions to these problems, we have proposed a
blockchain-based role-based access control model with the separation of duties
constraints in a cloud environment. In the model, we used Hyperledger Fabric as
a blockchain platform for storing the access control policies and provided
several functions for effective role management. In addition, we presented an
access control scheme for cloud storage data by combining the proposed model
and the verification mechanism for the user's ownership of a role and analyzed
the security properties of the scheme. Finally, we deployed Hyperledger Fabric
test network, implemented an online test system that performs access control
using the proposed scheme in the Ali cloud environment, and evaluated the model
performance in this scenario.


  We provide a family of expressions of $\pi$ in terms of the golden ratio
$\phi$ in the same spirit of the formula obtained by Bailey, Borwein and
Plouffe for $\pi$. Connection with cyclotomic polynomials is outlined.


  The classification of glomerular lesions is a routine and essential task in
renal pathology. Recently, machine learning approaches, especially deep
learning algorithms, have been used to perform computer-aided lesion
characterization of glomeruli. However, one major challenge of developing such
methods is the naturally imbalanced distribution of different lesions. In this
paper, we propose CircleMix, a novel data augmentation technique, to improve
the accuracy of classifying globally sclerotic glomeruli with a hierarchical
learning strategy. Different from the recently proposed CutMix method, the
CircleMix augmentation is optimized for the ball-shaped biomedical objects,
such as glomeruli. 6,861 glomeruli with five classes (normal, periglomerular
fibrosis, obsolescent glomerulosclerosis, solidified glomerulosclerosis, and
disappearing glomerulosclerosis) were employed to develop and evaluate the
proposed methods. From five-fold cross-validation, the proposed CircleMix
augmentation achieved superior performance (Balanced Accuracy=73.0%) compared
with the EfficientNet-B0 baseline (Balanced Accuracy=69.4%)


  Legged robots are being used to explore rough terrains as they are capable of
traversing gaps and obstacles. In this paper, a new mechanism is designed to
replicate a robotic lizard using integrated five-bar mechanisms. There are two
five bar mechanisms from which two more are formed by connecting the links in a
particular order. The legs are attached to the links of the five bar mechanism
such that, when the mechanism is actuated, they move the robot forward.
Position analysis using vector loop approach has been done for the mechanism. A
prototype has been built and controlled using servo motors to verify the
robotic lizard mechanism.


  The topological order is equivalent to the pattern of long-range quantum
entanglements, which cannot be measured by any local observable. Here we
perform an exact diagonalization study to establish the non-Abelian topological
order through entanglement entropy measurement. We focus on the quasiparticle
statistics of the non-Abelian Moore-Read and Read-Rezayi states on the lattice
boson models. We identify multiple independent minimal entangled states (MESs)
in the groundstate manifold on a torus. The extracted modular $\mathcal{S}$
matrix from MESs faithfully demonstrates the Majorana quasiparticle or
Fibonacci quasiparticle statistics, including the quasiparticle quantum
dimensions and the fusion rules for such systems. These findings support that
MESs manifest the eigenstates of quasiparticles for the non-Abelian topological
states and encode the full information of the topological order.


  In this paper we derive optimal relaxation rates for the Cahn-Hilliard
equation on the one-dimensional torus and the line. We consider initial
conditions with a finite (but not small) $L^1$-distance to an appropriately
defined bump. The result extends the relaxation method developed previously for
a single transition layer (the ``kink'') to the case of two transition layers
(the ``bump''). As in the previous work, the tools include Nash-type
inequalities, duality arguments, and Schauder estimates. For both the kink and
the bump, the energy gap is translation invariant and its decay alone cannot
specify to which member of the family of minimizers the solution converges.
Whereas in the case of the kink, the conserved quantity singles out the
longtime limit, in the case of a bump, a new argument is needed. On the torus,
we quantify the (initially algebraic and ultimately exponential) convergence to
the bump that is the longtime limit; on the line, the bump-like states are
merely metastable and we quantify the initial algebraic relaxation behavior.


  We present a simple, real-time approach for pupil tracking from live video on
mobile devices. Our method extends a state-of-the-art face mesh detector with
two new components: a tiny neural network that predicts positions of the pupils
in 2D, and a displacement-based estimation of the pupil blend shape
coefficients. Our technique can be used to accurately control the pupil
movements of a virtual puppet, and lends liveliness and energy to it. The
proposed approach runs at over 50 FPS on modern phones, and enables its usage
in any real-time puppeteering pipeline.


  For a domain $D$ in $\mathbb{C}_z$ with smooth boundary and for $a,b\in D,
a\ne b$, we have the circular (radial) slit mapping $P(z)(Q(z))$ on $D$ such
that $P(z)- \frac{1}{z-a}\ (Q(z)- \frac{1}{z-a})$ is regular at $a$ and
$P(b)(Q(b))=0$, and we call $p(z)=\log |P(z)|\ (q(z)=\log|Q(z)|)$ the
$L_1$-($L_0$-)principal function; \ $\alpha =\log|P'(b)|$ $(\beta
=\log|Q'(b)|)$ the $L_1$-($L_0$-)constant, and \ $s=\alpha - \beta $ the
harmonic span, for $D$. S.\,Hamano in \cite{hamano-2} showed the variation
formula of the second order for the $L_1$-const. $\alpha (t)$ for the moving
domain $D(t)$ in $\mathbb{C}_z$ with $t \in B:=\{t\in \mathbb{C}: |t|<\rho\}$.
We show the corresponding formula for the $L_0$-const. $\beta (t)$ for $D(t)$,
and combine these formulas to obtain, if the total space ${\mathcal
D}=\cup_{t\in B}(t, D(t)) $ is pseudoconvex in $ B \times \mathbb{C}_z$, then
$s(t)$ is subharmonic on $B$. Since the geometric meaning of $s(t)$ is showed,
this fact gives one of the relations between the conformal mappings on each
fiber $D(t), t\in B$ and the pseudoconvexity of ${\mathcal D}$. As a simple
application we obtain the subharmonicity of $\log \cosh d(t)$ on $B$, where
$d(t)$ is the Poincar\'e distance between $a$ and $b$.


  The Dirac equation may be thought as originating from a theory of
five-dimensional (5D) space-time. We define a special 5D Clifford algebra and
introduce a spin-1/2 constraint equation to describe null propagation in a 5D
space-time manifold. We explain how the 5D null formalism breaks down to four
dimensions to recover two single-particle theories. Namely, we obtain Dirac's
relativistic quantum mechanics and a formulation of statistical mechanics.
Exploring the non-relativistic limit in five and four dimensions, we identify a
new spin-electric interaction with possible applications to magnetic resonance
spectroscopy (within quantum mechanics) and superconductivity (within
statistical mechanics).


  We construct the first examples of families of bad Riemannian orbifolds which
are isospectral with respect to the Laplacian but not isometric. In our case
these are particular fixed weighted projective spaces equipped with isospectral
metrics obtained by a generalization of Sch\"uth's version of the torus method.


  When tasks change over time, meta-transfer learning seeks to improve the
efficiency of learning a new task via both meta-learning and transfer-learning.
While the standard attention has been effective in a variety of settings, we
question its effectiveness in improving meta-transfer learning since the tasks
being learned are dynamic and the amount of context can be substantially
smaller. In this paper, using a recently proposed meta-transfer learning model,
Sequential Neural Processes (SNP), we first empirically show that it suffers
from a similar underfitting problem observed in the functions inferred by
Neural Processes. However, we further demonstrate that unlike the meta-learning
setting, the standard attention mechanisms are not effective in meta-transfer
setting. To resolve, we propose a new attention mechanism, Recurrent Memory
Reconstruction (RMR), and demonstrate that providing an imaginary context that
is recurrently updated and reconstructed with interaction is crucial in
achieving effective attention for meta-transfer learning. Furthermore,
incorporating RMR into SNP, we propose Attentive Sequential Neural
Processes-RMR (ASNP-RMR) and demonstrate in various tasks that ASNP-RMR
significantly outperforms the baselines.


  Photons, acting as ``flying qubits'' in propagation geometries such as
waveguides, appear unavoidably in the form of wavepackets (pulses). The actual
shape of the photonic wavepacket, as well as possible temporal/spectral
correlations between the photons, play a critical role in successful scalable
computation. Currently, unentangled indistinguishable photons are considered as
a suitable resource for scalable photonic circuits. Here we show that using so
called coherent photon conversion, it is possible to construct flying-qubit
gates, which are not only insensitive to waveshapes of the photons and
temporal/spectral correlations between them, but which also fully preserve
these waveshapes and correlations upon the processing. This allows using
photons with correlations and purity in a very broad range for a scalable
computation. Moreover, such gates can process entangled photonic wavepackets
even more effectively than unentangled ones.


  We work with $N-$dimensional compact real hyperbolic space $X_{\Gamma}$ with
universal covering $M$ and fundamental group $\Gamma$. Therefore, $M$ is the
symmetric space $G/K$, where $G=SO_1(N,1)$ and $K=SO(N)$ is a maximal compact
subgroup of $G$. We regard $\Gamma$ as a discrete subgroup of $G$ acting
isometrically on $M$, and we take $X_{\Gamma}$ to be the quotient space by that
action: $X_{\Gamma}=\Gamma\backslash M = \Gamma\backslash G/K$. The natural
Riemannian structure on $M$ (therefore on $X$) induced by the Killing form of
$G$ gives rise to a connection $p-$form Laplacian ${\frak L}_p$ on the quotient
vector bundle (associated with an irreducible representation of K). We study
gauge theories based on abelian $p-$forms on the real compact hyperbolic
manifold $X_{\Gamma}$. The spectral zeta function related to the operator
${\frak L}_p$, considering only the co-exact part of the $p-$forms and
corresponding to the physical degrees of freedom, can be represented by the
inverse Mellin transform of the heat kernel. The explicit thermodynamic
fuctions related to skew-symmetric tensor fields are obtained by using the
zeta-function regularization and the trace tensor kernel formula (which
includes the identity and hyperbolic orbital integrals). Thermodynamic
quantities in the high and low temperature expansions are calculated and new
entropy/energy ratios established.


  Modern weather forecast models perform uncertainty quantification using
ensemble prediction systems, which collect nonparametric statistics based on
multiple perturbed simulations. To provide accurate estimation, dozens of such
computationally intensive simulations must be run. We show that deep neural
networks can be used on a small set of numerical weather simulations to
estimate the spread of a weather forecast, significantly reducing computational
cost. To train the system, we both modify the 3D U-Net architecture and explore
models that incorporate temporal data. Our models serve as a starting point to
improve uncertainty quantification in current real-time weather forecasting
systems, which is vital for predicting extreme events.


  Biological and artificial learning agents face numerous choices about how to
learn, ranging from hyperparameter selection to aspects of task distributions
like curricula. Understanding how to make these meta-learning choices could
offer normative accounts of cognitive control functions in biological learners
and improve engineered systems. Yet optimal strategies remain challenging to
compute in modern deep networks due to the complexity of optimizing through the
entire learning process. Here we theoretically investigate optimal strategies
in a tractable setting. We present a learning effort framework capable of
efficiently optimizing control signals on a fully normative objective:
discounted cumulative performance throughout learning. We obtain computational
tractability by using average dynamical equations for gradient descent,
available for simple neural network architectures. Our framework accommodates a
range of meta-learning and automatic curriculum learning methods in a unified
normative setting. We apply this framework to investigate the effect of
approximations in common meta-learning algorithms; infer aspects of optimal
curricula; and compute optimal neuronal resource allocation in a continual
learning setting. Across settings, we find that control effort is most
beneficial when applied to easier aspects of a task early in learning; followed
by sustained effort on harder aspects. Overall, the learning effort framework
provides a tractable theoretical test bed to study normative benefits of
interventions in a variety of learning systems, as well as a formal account of
optimal cognitive control strategies over learning trajectories posited by
established theories in cognitive neuroscience.


  Since the invention of Zernike phase contrast method in 1930, it has been
widely used in optical microscopy and more recently in X-ray microscopy.
Considering the image contrast is a mixture of absorption and phase
information, we recently have proposed and demonstrated a method for
quantitative phase retrieval in Zernike phase contrast X-ray microscopy. In
this contribution, we analyzed the performance of this method at different
photon energies. Intensity images of PMMA samples are simulated at 2.5 keV and
6.2 keV, respectively, and phase retrieval is performed using the proposed
method. The results demonstrated that the proposed phase retrieval method is
applicable over a wide energy range. For weakly absorbing features, the optimal
photon energy is 2.5 keV, from the point of view of image contrast and accuracy
of phase retrieval. On the other hand, in the case of strong absorption
objects, a higher photon energy is preferred to reduce the error of phase
retrieval. Those results can be used as guidelines to perform quantitative
phase retrieval in Zernike phase contrast X-ray microscopy with the proposed
method.


  We present 7 sequential weekly observations of NGC 5548 conducted in 2007
with the \textit{Suzaku} X-ray Imaging Spectrometer (XIS) in the 0.2-12 keV
band and Hard X-ray Detector (HXD) in 10-600 keV band. The iron K$\alpha$ line
is well detected in all seven observations and K$\beta$ line is also detected
in four observations. In this paper, we investigate the origin of the Fe K
lines using both the width of the line and the reverberation mapping method.
  With the co-added XIS and HXD spectra, we identify Fe K$\alpha$ and K$\beta$
line at 6.396$_{-0.007}^{+0.009}$ keV and 7.08$_{-0.05}^{+0.05}$ keV,
respectively. The width of line obtained from the co-added spectra is
38$_{-18}^{+16}$ eV ($\textrm{FWHM}=4200_{-2000}^{+1800}$ km/s) which
corresponds to a radius of 20$_{-10}^{+50}$ light days, for the virial
production of $1.220\times10^7$ M$_{\odot}$ in NCG 5548.
  To quantitatively investigate the origin of the narrow Fe line by the
reverberation mapping method, we compare the observed light curves of Fe
K$\alpha$ line with the predicted ones, which are obtained by convolving the
continuum light curve with the transfer functions in a thin shell and an
inclined disk. The best-fit result is given by the disk case with $i=30^\circ$
which is better than a fit to a constant flux of the Fe K line at the 92.7%
level (F-test). We find that the emitting radius obtained from the light curve
is 25-37 light days, which is consistent with the radius derived from the Fe K
line width. Combining the results of the line width and variation, the most
likely site for the origin of the narrow iron lines is 20-40 light days away
from the central engine, though other possibilities are not completely ruled
out. (abridged)


  We present semi-analytical similarity solutions for the inside-out,
expansion-wave collapse of initially virialized gas clouds with non-isothermal
equations of state. Results are given for the family of negative-index
polytropes, but we focus especially on the so-called logotrope, P/P_c=1+A
ln(rho/rho_c). The formalism and interpretation of the present theory are
extensions of those in Shu's (1977) standard model for accretion in
self-gravitating isothermal spheres: a collapse front moves outwards into a
cloud at rest, and the gas behind it falls back to a collapsed core, or
protostar. The infalling material eventually enters free-fall, so that, at
small radii, the density profiles and velocity fields have the same power-law
forms in logotropic and isothermal spheres both. However, the accretion rate
onto a protostar is not constant in a logotrope, but grows in proportion to t^3
during the expansion wave. Thus, low-mass stars are accreted over longer times,
and high-mass stars over shorter times, than expected in isothermal clouds.
This result has implications for the form and origin of the stellar IMF. We
also find that infall velocities grow more slowly with time in a collapsing
logotrope. These results lead to older inferred collapse ages for Class 0
protostars in general, and for the Bok globule B335 in particular.


  For the purpose of the nonlocality test, we propose a general correlation
observable of two parties by utilizing local $d$-outcome measurements with
SU($d$) transformations and classical communications. Generic symmetries of the
SU($d$) transformations and correlation observables are found for the test of
nonlocality. It is shown that these symmetries dramatically reduce the number
of numerical variables, which is important for numerical analysis of
nonlocality. A linear combination of the correlation observables, which is
reduced to the Clauser-Horne-Shimony-Holt (CHSH) Bell's inequality for two
outcome measurements, is led to the Collins-Gisin-Linden-Massar-Popescu (CGLMP)
nonlocality test for $d$-outcome measurement. As a system to be tested for its
nonlocality, we investigate a continuous-variable (CV) entangled state with $d$
measurement outcomes. It allows the comparison of nonlocality based on
different numbers of measurement outcomes on one physical system. In our
example of the CV state, we find that a pure entangled state of any degree
violates Bell's inequality for $d(\ge 2)$ measurement outcomes when the
observables are of SU($d$) transformations.


  We consider theories describing the dynamics of a four-dimensional metric,
whose Lagrangian is diffeomorphism invariant and depends at most on second
derivatives of the metric. Imposing degeneracy conditions we find a set of
Lagrangians that, apart form the Einstein-Hilbert one, are either trivial or
contain more than two degrees of freedom. Among the partially degenerate
theories, we recover Chern-Simons gravity, endowed with constraints whose
structure suggests the presence of instabilities. Then, we enlarge the class of
parity violating theories of gravity by introducing new "chiral scalar-tensor
theories". Although they all raise the same concern as Chern-Simons gravity,
they can nevertheless make sense as low energy effective field theories or, by
restricting them to the unitary gauge (where the scalar field is uniform), as
Lorentz breaking theories with a parity violating sector.


  Caricature is an exaggerated form of artistic portraiture that accentuates
unique yet subtle characteristics of human faces. Recently, advancements in
deep end-to-end techniques have yielded encouraging outcomes in capturing both
style and elevated exaggerations in creating face caricatures. Most of these
approaches tend to produce cartoon-like results that could be more practical
for real-world applications. In this study, we proposed a high-quality,
unpaired face caricature method that is appropriate for use in the real world
and uses computer vision techniques and GAN models. We attain the exaggeration
of facial features and the stylization of appearance through a two-step
process: Face caricature generation and face caricature projection. The face
caricature generation step creates new caricature face datasets from real
images and trains a generative model using the real and newly created
caricature datasets. The Face caricature projection employs an encoder trained
with real and caricature faces with the pretrained generator to project real
and caricature faces. We perform an incremental facial exaggeration from the
real image to the caricature faces using the encoder and generator's latent
space. Our projection preserves the facial identity, attributes, and
expressions from the input image. Also, it accounts for facial occlusions, such
as reading glasses or sunglasses, to enhance the robustness of our model.
Furthermore, we conducted a comprehensive comparison of our approach with
various state-of-the-art face caricature methods, highlighting our process's
distinctiveness and exceptional realism.


  Up to now, researchers have applied segmentation techniques in their studies
on teeth images, with construction on tooth root length and depth. In this
paper, a new approach to the exact identification of the filled points of the
tooth is proposed. In this method, the filled teeth are detection by applying
the Bit-Plane algorithm on the OPG images. The novelty of the proposed method
is that we can use it in medicine for the detection of dental filling and we
calculate and present the area of the filled points which may help dentists to
assess the filled point of the tooth. The experimental results, confirmed by
the dentists, clearly indicate that this method is able to separate the filled
points from the rest of healthy teeth completely.


  Recently, it has been observed the extreme metal-poor stars in the Galactic
halo, which must be formed just after Pop III objects. On the other hand, the
first gas clouds of mass $\sim 10^6 M_{\odot}$ are supposed to be formed at $ z
\sim $ 10, 20, and 30 for the $1\sigma$, $2\sigma $ and $3\sigma$, where the
density perturbations are assumed of the standard $\Lambda$CDM cosmology. If we
could apply this gaussian distribution to the extreme small probability, the
gas clouds would be formed at $ z \sim $40, 60, and 80 for the $4\sigma$,
$6\sigma$, and $8\sigma$. The first gas clouds within our galaxy must be formed
around $z\sim 40$. Even if the gas cloud is metal poor, there is a lot of
possibility to form the planets around such stars. The first planetary systems
could be formed within $\sim 6\times 10^7$ years after the Big Bang in the
universe. Even in our galaxies, it could be formed within $\sim 1.7\times 10^8$
years. It is interesting to wait the observations of planets around metal-poor
stars. For the panspermia theory, the origin of life could be expected in such
systems.


  This note is an addendum to the results of P.O. Frederickson and A.C. Lazer
[1], and A.C. Lazer [4] on periodic oscillations, with linear part at
resonance. We show that a small modification of the argument in [4] provides a
more general result. It turns out that things are different for the
corresponding Dirichlet boundary value problem.


  In order to clarify the influence of ferromagnetism on superconductivity
through a normal metal layer, the superconducting properties of epitaxial
Nb(110)/Au(111)/Fe(110) trilayers were studied as a function of the thickness
tAu of the intervening Au layer. Structural characterization of the samples
revealed sharp interfaces, almost free from roughness. A strong suppression of
the superconducting transition temperature Tc was observed for tAu<10 A,
implying a strong spin-polarization of the Au layer in the vicinity of the
Au/Fe interface. A periodic change of Tc with a period of ~21 A (~9 atomic
monolayer of Au) was observed for 20 A<tAu<104 A. Neither the Fermi surface
nesting of the normal metal layer, nor Fulde-Ferrel-Larkin-Ovchinnikov
oscillations induced by a superconducting proximity effect in the ferromagnet
can by themselves account for the observed period. These results suggest that a
new and more subtle form of quantum interference occurs in very clean trilayer
systems.


  Koksma's equidistribution theorem from 1935 states that for Lebesgue almost
every $\alpha>1$, the fractional parts of the geometric progression
$(\alpha^{n})_{n\geq1}$ are equidistributed modulo one. In the present paper we
sharpen this result by showing that for almost every $\alpha>1$, the
correlations of all finite orders and hence the normalized gaps of
$(\alpha^{n})_{n\geq1}$ mod 1 have a Poissonian limit distribution, thereby
resolving a conjecture of the two first named authors. While an earlier
approach used probabilistic methods in the form of martingale approximation,
our reasoning in the present paper is of an analytic nature and based upon the
estimation of oscillatory integrals. This method is robust enough to allow us
to extend our results to a natural class of sub-lacunary sequences.


  Many parity violating gravity models suffer from the ghost instability
problem. In this paper, we consider a symmetric teleparallel gravity model that
extends the general relativity equivalent model by several parity violating
interactions between the gravitational field and a scalar field. These
interactions exclude higher derivatives and are quadratic in the nonmetricity
tensor. Through investigations on the linear cosmological perturbations, our
results show that, in general, this model suffers from the difficulty caused by
the existence of ghost mode in the vector perturbations. However, in cases
where a special condition is imposed on the coefficients of these parity
violating interactions, this model can be ghost free.


  A refined a priori error analysis of the lowest order (linear) nonconforming
Virtual Element Method (VEM) for approximating a model Poisson problem is
developed in both 2D and 3D. A set of new geometric assumptions is proposed on
shape regularity of polytopal meshes. A new error equation for the lowest order
(linear) nonconforming VEM is derived for any choice of stabilization, and a
new stabilization using a projection on an extended element patch is introduced
for the error analysis on anisotropic elements.


  We consider the model of a false vacuum bubble with a thin wall where the
surface energy density is composed of two different components, "domain-wall"
type and "dust" type, with opposite signs. We find stably oscillating
solutions, which we call "breathing bubbles". By decay to a lower mass state,
such a breathing bubble could become either i) a child universe or ii) a bubble
that "eats up" the original universe, depending on the sign of the surface
energy of the "domain-wall" component. We also discuss the effect of the
finite-thickness corrections to the thin-wall approximation and possible
origins of the energy contents of our model.


  Current psychiatric research is in crisis. In this review I will describe the
causes of this crisis and highlight recent efforts to overcome current
challenges. One particularly promising approach is the emerging field of
computational psychiatry. By using methods and insights from computational
cognitive neuroscience, computational psychiatry might enable us to move from a
symptom-based description of mental illness to descriptors based on objective
computational multidimensional functional variables. To exemplify this I will
survey recent efforts towards this goal. I will then describe a set of methods
that together form a toolbox of cognitive models to aid this research program.
At the core of this toolbox are sequential sampling models which have been used
to explain diverse cognitive neuroscience phenomena but have so far seen little
adoption in psychiatric research. I will then describe how these models can be
fitted to subject data and highlight how hierarchical Bayesian estimation
provides a rich framework with many desirable properties and benefits compared
to traditional optimization-based approaches. Finally, non-parametric Bayesian
methods provide general solutions to the problem of classifying mental illness
within this framework.


  A self-consistent model is presented for the simulation of a multi-component
plasma in the tokamak boundary. A deuterium plasma is considered, with the
plasma species that include electrons, deuterium atomic ions and deuterium
molecular ions, while the deuterium atoms and molecules constitute the neutral
species. The plasma and neutral models are coupled via a number of collisional
interactions, which include dissociation, ionization, charge-exchange and
recombination processes. The derivation of the three-fluid drift-reduced
Braginskii equations used to describe the turbulent plasma dynamics is
presented, including its boundary conditions. The kinetic advection equations
for the neutral species are also derived, and their numerical implementation
discussed. The first results of multi-component plasma simulations carried out
by using the GBS code are then presented and analyzed, being compared with
results obtained with the single-component plasma model.


  Deep Learning for Geometric Shape Understating has organized a challenge for
extracting different kinds of skeletons from the images of different objects.
This competition is organized in association with CVPR 2019. There are three
different tracks of this competition. The present manuscript describes the
method used to train the model for the dataset provided in the first track. The
first track aims to extract skeleton pixels from the shape pixels of 89
different objects. For the purpose of extracting the skeleton, a U-net model
which is comprised of an encoder-decoder structure has been used. In our
proposed architecture, unlike the plain decoder in the traditional Unet, we
have designed the decoder in the format of HED architecture, wherein we have
introduced 4 side layers and fused them to one dilation convolutional layer to
connect the broken links of the skeleton. Our proposed architecture achieved
the F1 score of 0.77 on test data.


  This work deals with accuracy analysis of dynamical systems interconnected in
a cascade structure. For a cascade network there are a number of experimental
settings for which the dynamic systems within the network can be identified. We
study the problem of choosing which excitation and measurement pattern delivers
the most accurate parameter estimates for the whole network. The optimal
experiment is based on the accuracy assessed through the asymptotic covariance
matrix of the prediction error method, while the cost criterion is the number
of excitations and measurements. We develop theoretical results under the
assumptions that all dynamic systems are equal and with equal signal-to-noise
ratio throughout the network. We show that there are experimental settings
which result in equal overall precision and that there is an excitation and
measurement pattern that yields more accurate results than others. From these
results a guideline based on the topology of the network emerges for the choice
of the experimental setting. We provide numerical results which attest that the
principles behind this guideline are also valid for more general situations.


  A full quantum mechanical calculation of partial cross-sections leading to
different final states of antiprotonic helium atom was performed. Calculations
were carried out for a wide range of antiprotonic helium states and incident
(lab) energies of the antiproton.


  We overview the recently proposed mode-sum regularization prescription (MSRP)
for the calculation of the local radiation-reaction forces, which are crucial
for the orbital evolution of binaries. We then describe some new results which
were obtained using MSRP, and discuss their importance for gravitational-wave
astronomy.


  Over these years, Correlation Filter-based Trackers (CFTs) have aroused
increasing interests in the field of visual object tracking, and have achieved
extremely compelling results in different competitions and benchmarks. In this
paper, our goal is to review the developments of CFTs with extensive
experimental results. 11 trackers are surveyed in our work, based on which a
general framework is summarized. Furthermore, we investigate different training
schemes for correlation filters, and also discuss various effective
improvements that have been made recently. Comprehensive experiments have been
conducted to evaluate the effectiveness and efficiency of the surveyed CFTs,
and comparisons have been made with other competing trackers. The experimental
results have shown that state-of-art performance, in terms of robustness, speed
and accuracy, can be achieved by several recent CFTs, such as MUSTer and SAMF.
We find that further improvements for correlation filter-based tracking can be
made on estimating scales, applying part-based tracking strategy and
cooperating with long-term tracking methods.


  A new definition of entropy is introduced using a model that simulates an
expanding space-time compatible with the fundamental principle of cosmology.
The entropy is obtained by mean of a state function that measures the variation
of the space-time normal curvature, from a highly compressed space to a lower
compressed space. The defined entropy leads to work out a new understanding of
the earliest conditions that last for a period estimated to 380 000 years after
the Big Bang. It leads to understand via a short period of inflation the
process that generates the uniform distribution of matter and energy at the
surface of the last scattering. It involves gravitational singularities in a
process of gradual decompression propitious to the incubation of matter
recombination, and it allows to trace back gravity origin.


  In this talk I discuss the relevance of atomic physics in understanding some
important questions about elementary particle physics. A particular attention
is devoted to atomic parity violation measurements which seem to suggest new
physics beyond the Standard Model. Atomic physics might also be relevant in
discovering possible violations of the CPT symmetry.


  We explain how angular correlations in leptonic decays of vector bosons and
top quarks can be included in Monte Carlo parton showers, in particular those
matched to NLO QCD computations. We consider the production of $n$ pairs of
leptons, originating from the decays of $n$ electroweak vector bosons or of $n$
top quarks, in the narrow-width approximation. In the latter case, the
information on the $n$ $b$ quarks emerging from the decays is also retained. We
give results of implementing this procedure in MC@NLO


  Eigenvector centrality is a standard network analysis tool for determining
the importance of (or ranking of) entities in a connected system that is
represented by a graph. However, many complex systems and datasets have natural
multi-way interactions that are more faithfully modeled by a hypergraph. Here
we extend the notion of graph eigenvector centrality to uniform hypergraphs.
Traditional graph eigenvector centralities are given by a positive eigenvector
of the adjacency matrix, which is guaranteed to exist by the Perron-Frobenius
theorem under some mild conditions. The natural representation of a hypergraph
is a hypermatrix (colloquially, a tensor). Using recently established
Perron-Frobenius theory for tensors, we develop three tensor eigenvectors
centralities for hypergraphs, each with different interpretations. We show that
these centralities can reveal different information on real-world data by
analyzing hypergraphs constructed from n-gram frequencies, co-tagging on stack
exchange, and drug combinations observed in patient emergency room visits.


  There are well-understood methods, going back to Givental and Hori--Vafa,
that to a Fano toric complete intersection X associate a Laurent polynomial f
that corresponds to X under mirror symmetry. We describe a technique for
inverting this process, constructing the toric complete intersection X directly
from its Laurent polynomial mirror f. We use this technique to construct a new
four-dimensional Fano manifold.


  In this paper we consider the Dirac spinor field in interaction with a
background of electrodynamics and torsion-gravity; by performing the polar
reduction we acquire the possibility to introduce a new set of objects that
have the geometrical status of non-vanishing tensors but which seem to contain
the same information of the connection: thus they appear to be describing
something that seems like an inertial force but which is also essentially
covariant. After a general introduction, we exemplify these tensors in the very
well known instance of the orbital of minimal energy for an electron in the
case of the Hydrogen atom: we will see that the invariants built with these
tensors remain different from zero even for free field configurations. An
outlook regarding possible interpretations of such a set of tensors will be
sketched. A few final comments will eventually be given.


  The Jaynes-Cummings model provides a simple and accurate description of the
interaction between a two-level quantum emitter and a single mode of quantum
radiation. Due to the multimode continuum of eigenmodes in free space and in
waveguides, the Jaynes-Cummings model should not be expected to properly
describe the interaction between an emitter and a traveling pulse of quantum
radiation. In this article, we review a cascaded quantum system approach that
accurately describes the interaction of a quantum system with an incident
quantum pulse of radiation. This approach leads to different formulations of
the theory, each of a similar structure as the Jaynes-Cummings model but with
important modifications.


  We propose a new backtesting framework for Expected Shortfall that could be
used by the regulator. Instead of looking at the estimated capital reserve and
the realised cash-flow separately, one could bind them into the secured
position, for which risk measurement is much easier. Using this simple concept
combined with monotonicity of Expected Shortfall with respect to its target
confidence level we introduce a natural and efficient backtesting framework.
Our test statistics is given by the biggest number of worst realisations for
the secured position that add up to a negative total. Surprisingly, this simple
quantity could be used to construct an efficient backtesting framework for
unconditional coverage of Expected Shortfall in a natural extension of the
regulatory traffic-light approach for Value-at-Risk. While being easy to
calculate, the test statistic is based on the underlying duality between
coherent risk measures and scale-invariant performance measures.


  We have theoretically predicted the gigantic spikes of the orbital angular
momentum caused by the conversion processes of the centered optical vortex in
the circularly polarized components of the elliptic vortex beam propagating
perpendicular to the crystal optical axis. We have experimentally observed the
conversion process inside the subwave deviations of the crystal length. We have
found that the total orbital angular momentum of the wave beam is conserved.


  We present a tight analysis for the well-studied randomized 3-majority
dynamics of stabilizing consensus, hence answering the main open question of
Becchetti et al. [SODA'16].
  Consider a distributed system of n nodes, each initially holding an opinion
in {1, 2, ..., k}. The system should converge to a setting where all
(non-corrupted) nodes hold the same opinion. This consensus opinion should be
\emph{valid}, meaning that it should be among the initially supported opinions,
and the (fast) convergence should happen even in the presence of a malicious
adversary who can corrupt a bounded number of nodes per round and in particular
modify their opinions. A well-studied distributed algorithm for this problem is
the 3-majority dynamics, which works as follows: per round, each node gathers
three opinions --- say by taking its own and two of other nodes sampled at
random --- and then it sets its opinion equal to the majority of this set; ties
are broken arbitrarily, e.g., towards the node's own opinion.
  Becchetti et al. [SODA'16] showed that the 3-majority dynamics converges to
consensus in O((k^2\sqrt{\log n} + k\log n)(k+\log n)) rounds, even in the
presence of a limited adversary. We prove that, even with a stronger adversary,
the convergence happens within O(k\log n) rounds. This bound is known to be
optimal.


  Various applications of quantum algebraic techniques in nuclear structure
physics, such as the su$_q$(2) rotator model and its extensions, the use of
deformed bosons in the description of pairing correlations, and the
construction of deformed exactly soluble models (Interacting Boson Model,
Moszkowski model) are briefly reviewed. Emphasis is put in the study of the
symmetries of the anisotropic quantum harmonic oscillator with rational ratios
of frequencies, which underlie the structure of superdeformed and hyperdeformed
nuclei, the Bloch--Brink $\alpha$-cluster model and possibly the shell
structure in deformed atomic clusters.


  We study the mass spectra and spin alignment of vector meson $J/\psi$ in a
thermal magnetized background using a generalized theoretical framework based
on gauge/gravity duality. Utilizing a soft wall model for the QGP background
and a massive vector field for the $J/\psi$ meson, we delve into the meson's
spectral function and spin parameters $(\lambda_{\theta},\,
\lambda_\varphi,\,\lambda_{\theta\varphi})$ for different cases, assessing
their response to variations in magnetic field strength, momentum, and
temperature. We initially examine scenarios where a meson's momentum aligns
parallel to the magnetic field in helicity frame. Our results reveal a magnetic
field-induced positive $\lambda_\theta^\text{H}$ for low meson momentum,
transitioning to negative with increased momentum. As a comparison, we also
study the case of momentum perpendicular to the magnetic field and find the
direction of magnetic field does not affect the qualitative behavior for the
$eB$-dependence of $\lambda_\theta^\text{H}$. Moreover, we apply our model to
real heavy-ion collisions for three different spin quantization directions.
Further comparisons with experimental data show qualitative agreement for spin
parameters $\lambda_{\theta}$ and $\lambda_\varphi$ in the helicity and
Collins-Soper frames.


  Two dimensional particle in cell simulations of free charge creation by
collisional ionization of C12 and C60 molecules immersed in plasma for the
parameters of relevance to plasma gasification are presented. Our main findings
are that (i) in uniform plasmas with smooth walls two optimal values which
emerge for free electron production by collisional ionization (i.e. a most
efficient discharge condition creation) are $C60:C12$ fractions of $10:90$ and
$80:20$, (ii) in plasmas with rough walls, modelled by comb-like electric field
at the boundary, the case of tangential electric field creates significant
charge localization in C12+ and C60+ species, again creating most favorable
discharge condition for tribo-electrically generated plasma. The numerical
simulation results are discussed with reference to recent triboelectric plasma
experiments and are corroborated by suitable analytical models.


  We characterize the cone of GL-equivariant Betti tables of Cohen-Macaulay
modules of codimension 1, up to rational multiple, over the coordinate ring of
square matrices. This result serves as the base case for `Boij-S\"oderberg
theory for Grassmannians', with the goal of characterizing the cones of
GL_k-equivariant Betti tables of modules over the coordinate ring of k x n
matrices, and, dually, cohomology tables of vector bundles on the Grassmannian
Gr(k, C^n). The proof uses Hall's Theorem on perfect matchings in bipartite
graphs to compute the extremal rays of the cone, and constructs the
corresponding equivariant free resolutions by applying Weyman's geometric
technique to certain graded pure complexes of Eisenbud-Fl{\o}ystad-Weyman.


  We propose the gentle measurement principle (GMP) as one of the principles at
the foundation of quantum mechanics. It asserts that if a set of states can be
distinguished with high probability, they can be distinguished by a measurement
that leaves the states almost invariant, including correlation with a reference
system. While GMP is satisfied in both classical and quantum theories, we show,
within the framework of general probabilistic theories, that it imposes strong
restrictions on the law of physics. First, the measurement uncertainty of a
pair of observables cannot be significantly larger than the preparation
uncertainty. Consequently, the strength of the CHSH nonlocality cannot be
maximal. The parameter in the stretched quantum theory, a family of general
probabilistic theories that includes the quantum theory, is also limited.
Second, the conditional entropy defined in terms of a data compression theorem
satisfies the chain inequality. Not only does it imply information causality
and Tsirelson's bound, but it singles out the quantum theory from the stretched
one. All these results show that GMP would be one of the principles at the
heart of quantum mechanics.


  Conficker is a computer worm that erupted on the Internet in 2008. It is
unique in combining three different spreading strategies: local probing,
neighbourhood probing, and global probing. We propose a mathematical model that
combines three modes of spreading, local, neighbourhood and global to capture
the worm's spreading behaviour. The parameters of the model are inferred
directly from network data obtained during the first day of the Conifcker
epidemic. The model is then used to explore the trade-off between spreading
modes in determining the worm's effectiveness. Our results show that the
Conficker epidemic is an example of a critically hybrid epidemic, in which the
different modes of spreading in isolation do not lead to successful epidemics.
Such hybrid spreading strategies may be used beneficially to provide the most
effective strategies for promulgating information across a large population.
When used maliciously, however, they can present a dangerous challenge to
current internet security protocols.


  We count flags of primitive lattices, which are objects of the form
${0}=\Lambda^{(0)}<\Lambda^{(1)}< \cdots <\Lambda^{(\ell)}= \mathbb{Z}^n$,
where every $\Lambda^{(i)}$ is a primitive lattice in $\mathbb{Z}^n$. The
counting is with respect to two different natural height functions, allowing us
to give a new proof of the Manin conjecture for flag varieties over rational
numbers. We deduce the equidistribution of rational points in flag varieties,
as well as the equidistribution of the shapes of the successive quotient
lattices, $\Lambda^{(i)}/\Lambda^{(i-1)}$. In doing so, we generalize previous
work of Schmidt, as well as our own, on counting primitive lattices of rank
$d<n$.


  We study sampling problems associated with non-convex potentials that
meanwhile lack smoothness. In particular, we consider target distributions that
satisfy either logarithmic-Sobolev inequality or Poincar\'e inequality. Rather
than smooth, the potentials are assumed to be semi-smooth or the summation of
multiple semi-smooth functions. We develop a sampling algorithm that resembles
proximal algorithms in optimization for this challenging sampling task. Our
algorithm is based on a special case of Gibbs sampling known as the alternating
sampling framework (ASF). The key contribution of this work is a practical
realization of the ASF based on rejection sampling in the non-convex and
semi-smooth setting. This work extends the recent algorithm in
\cite{LiaChe21,LiaChe22} for non-smooth/semi-smooth log-concave distribution to
the setting with non-convex potentials. In almost all the cases of sampling
considered in this work, our proximal sampling algorithm achieves better
complexity than all existing methods.


  In this and a companion paper, we show that quantum field theories with gauge
symmetries permit a broader class of classical dynamics than typically assumed.
In this article, we show that the dynamics extracted from the path integral or
Hamiltonian formulation of general relativity allows for classical states that
do not satisfy the full set of Einstein's equations. This amounts to loosening
the Hamiltonian and momentum constraints that are imposed on the initial state.
Nevertheless, the quantum theory permits gauge invariant time evolution of
these states. The time evolution of these states is such that at the classical
level the full set of Einstein's equations would appear to hold, with the
physical effects of these states being attributable to an auxiliary,
covariantly conserved energy-momentum tensor with no internal degrees of
freedom. We derive the generalized Einstein equations for these states and show
that a homogeneous and isotropic initial background state contributes to
expansion identical to cold dark matter. The inhomogeneous components of this
state could source curvature perturbations that grow linearly at linear order.
This auxiliary contribution to Einstein's equations could have either sign and
thus provide a trivial way to violate the null energy condition, enabling novel
gravitational dynamics such as cosmic bounces and wormholes.


  We present first principles calculations of the electronic properties of
trigonal selenium with emphasis on photovoltaic applications. The band gap and
optical absorption spectrum of pristine selenium is calculated from many-body
perturbation theory yielding excellent agreement with experiments. We then
investigate the role of intrinsic as well as extrinsic defects and estimate the
equilibrium concentrations resulting from realistic synthesis conditions. The
intrinsic defects are dominated by vacancies and we show that these do not
result in significant non-radiative recombination. The charge balance remains
dominated by vacancies when extrinsic defects are included, but these may give
rise to sizable non-radiative recombination rates, which could severely limit
the performance of selenium based solar cells. Our results thus imply that the
pollution by external elements is a decisive factor for the photovoltaic
efficiency, which will be of crucial importance when considering synthesis
conditions for any type of device engineering.


  The main result of this paper is that for any $1/2 \leq s < 2 - \sqrt{2}
\approx 0.5858$, there is a number $\sigma = \sigma(s) < s$ with the following
property. Let $\delta > 0$ be small, assume that $A \subset [0,1]$ is a
$(\delta,1/2)$-set, and that $E \subset [0,1]$ contains $\gtrsim
\delta^{-\sigma}$ roughly $\delta^{s}$-separated points. Then there exists a
number $t \in E$ such that $A + tA$ contains $\gtrsim \delta^{-s}$
$\delta$-separated points.
  For $\sigma = s$, this is essentially a consequence of Kaufman's well-known
bound for exceptional sets of projections. Our proof consists of a structural
observation concerning sets, for which Kaufman's bound is near-optimal,
combined with (an adaptation of) Solymosi's argument for his "$4/3$"
sum-product theorem.


  Let $C$ be a general plane quartic and let ${\rm Fl}(C)$ denote the
configuration of inflection lines of $C$. We show that if $D$ is any plane
quartic with the same configuration of inflection lines ${\rm Fl}(C)$, then the
quartics $C$ and $D$ coincide.


  The maximal center gauge, combined with center projection, is a means to
associate Yang-Mills lattice gauge configurations with closed center vortex
world-surfaces. This technique allows to study center vortex physics in lattice
gauge experiments. In the present work, the continuum analogue of the maximal
center gauge is constructed. This sheds new light on the meaning of the
procedure on the lattice and leads to a sketch of an effective vortex theory in
the continuum. Furthermore, the manner in which center vortex configurations
generate the Pontryagin index is investigated. The Pontryagin index is built up
from self-intersections of the vortex world-surfaces, where it is crucial that
the surfaces be globally non-oriented.


  We derive the slow-roll conditions for a non-minimally coupled scalar field
(extended quintessence) during the radiation/matter dominated era extending our
previous results for thawing quintessence. We find that the ratio
$\ddot\phi/3H\dot\phi$ becomes constant but negative, in sharp contrast to the
ratio for the minimally coupled scalar field. We also find that the functional
form of the equation of state of the scalar field asymptotically approaches
that of the minimally coupled thawing quintessence.


  In magic angle twisted bilayer graphene, electron-electron interactions play
a central role resulting in correlated insulating states at certain integer
fillings. Identifying the nature of these insulators is a central question and
potentially linked to the relatively high temperature superconductivity
observed in the same devices. Here we address this question using a combination
of analytical strong-coupling arguments and a comprehensive Hartree-Fock
numerical calculation which includes the effect of remote bands. The ground
state we obtain at charge neutrality is an unusual ordered state which we call
the Kramers intervalley-coherent (K-IVC) insulator. In its simplest form, the
K-IVC exhibits a pattern of alternating circulating currents which triples the
graphene unit cell leading to an "orbital magnetization density wave". Although
translation and time reversal symmetry are broken, a combined `Kramers' time
reversal symmetry is preserved. Our analytic arguments are built on first
identifying an approximate ${\rm U}(4) \times {\rm U}(4)$ symmetry, resulting
from the remarkable properties of the tBG band structure, which helps select a
low energy manifold of states, which are further split to favor the K-IVC. This
low energy manifold is also found in the Hartree-Fock numerical calculation. We
show that symmetry lowering perturbations can stabilize other insulators and
the semi-metallic state, and discuss the ground state at half filling and a
comparison with experiments.


  We report discovery of a shell like structure G354.4+0.0 of size 1.6' that
shows morphology of a shell supernova remnant. Part of the structure show
polarized emission in NRAO VLA sky survey (NVSS) map. Based on 330 MHz, 1.4 GHz
Giant Metrewave Radio Telescope (GMRT) observations and existing observations
at higher frequencies, we conclude the partial shell structure showing
synchrotron emission is embedded in an extended HII region of size ~4'. The
spectrum of the diffuse HII region turns over between 1.4 GHz and 330 MHz. HI
absorption spectrum shows it to be located more than 5 kpc away from Sun. Based
on morphology, non-thermal polarized emission and size, this object is one of
the youngest supernova remnants discovered in the Galaxy with an estimated age
of about 100-500 years.


  Supermassive Black Holes are the most entropic objects found in the universe.
The Holographic Bound (HB) to the entropy is used to constrain their formation
time with initial masses $\sim{10}^{6-8}M_{\odot}$, as inferred from
observations. We find that the entropy considerations are more limiting than
causality for this "direct" formation. Later we analyze the possibility of
SMBHs growing from seed black holes. The growth of the initial mass is studied
in the case of accretion of pure radiation and quintessence fields, and we find
that there is a class of models that may allow this metamorphosis. Our analysis
generalizes recent work for some models of quintessence capable of producing a
substantial growth in a short time, while simultaneously obeying the causal and
Holographic Bound limits.


  Following the findings in \cite{wangsawijaya2020}, we re-examine the
turbulent boundary layers developing over surfaces with spanwise heterogeneous
roughness of various roughness wavelengths $0.32 \leq S/\overline{\delta} \leq
3.63$, where $S$ is the width of the roughness strips and $\overline{\delta}$
is the spanwise-averaged boundary-layer thickness. The heterogeneous cases
induce counter-rotating secondary flows, and these are compared to the
large-scale turbulent structures that occur naturally over the smooth wall.
Both appear as meandering elongated high- and low-momentum streaks in the
instantaneous flow field. Results suggest that the secondary flows might be
spanwise-locked turbulent structures, with $S/\overline{\delta}$ governing the
strength of the turbulent structures and possibly the efficacy of the surface
in locking the structures in place (most effective when $S/\overline{\delta}
\approx 1$). Conditional averages of the fluctuating velocity fields of both
spanwise heterogeneous and smooth wall cases result in structures that are
strongly reminiscent of the streak-vortex instability model. Secondary flows
and large-scale structures coexist in the limits where either
$S/\overline{\delta} \gg 1$ or $S/\overline{\delta} \ll 1$, where the secondary
flows scale on $\delta$ or $S$, respectively. When $S/\overline{\delta} \gg 1$,
the secondary flows are locked about the roughness transition, while relatively
unaltered large-scale structures occur further from the transition. In the case
where $S/\overline{\delta} \ll 1$, $S$-scaled secondary flows are confined
close to the surface, coexisting with unaltered larger scale turbulent
structures that penetrate much deeper into the layer.


  For biologically relevant macromolecules such as intrinsically disordered
proteins, internal degrees of freedom that allow for shape changes have a large
influence on both the motion and function of the compound. A detailed
understanding of the effect of flexibility is needed in order to explain their
behavior. Here, we study a model system of freely-jointed chains of three to
six colloidal spheres, using both simulations and experiments. We find that in
spite of their short lengths, their conformational statistics are well
described by two-dimensional Flory theory, while their average translational
and rotational diffusivity follow the Kirkwood-Riseman scaling. Their maximum
flexibility does not depend on the length of the chain, but is determined by
the near-wall in-plane translational diffusion coefficient of an individual
sphere. Furthermore, we uncover shape-dependent effects in the short-time
diffusivity of colloidal tetramer chains, as well as non-zero couplings between
the different diffusive modes. Our findings may have implications for
understanding both the diffusive behavior and the most likely conformations of
macromolecular systems in biology and industry, such as proteins, polymers,
single-stranded DNA and other chain-like molecules.


  In this paper we consider a bootstrap class $\mathfrak C$ of countable
discrete groups, which is closed under countable unions and extensions by the
integers, and we study actions of such groups on C*-algebras. This class
includes all torsion-free abelian groups, poly-$\mathbb Z$-groups, as well as
other examples. Using the interplay between relative Rokhlin dimension and
semi-strongly self-absorbing actions established in prior work, we obtain the
following two main results for any group $\Gamma\in\mathfrak C$ and any
strongly self-absorbing C*-algebra $\mathcal D$: (1) There is a unique strongly
outer $\Gamma$-action on $\mathcal D$ up to (very strong) cocycle conjugacy.
(2) If $\alpha: \Gamma\curvearrowright A$ is a strongly outer action on a
separable, unital, nuclear, simple, $\mathcal D$-stable C*-algebra with at most
one trace, then it absorbs every $\Gamma$-action on $\mathcal D$ up to (very
strong) cocycle conjugacy. In fact we establish more general relative versions
of these two results for actions of amenable groups that have a predetermined
quotient in the class $\mathfrak C$. For the monotracial case, the proof
comprises an application of Matui--Sato's equivariant property (SI) as a key
method.


  We develop a general framework for the description of anomalies using
extended functorial field theories extending previous work by Freed and
Monnier. In this framework, anomalies are described by invertible field
theories in one dimension higher and anomalous field theories live on their
boundaries. We provide precise mathematical definitions for all concepts
involved using the language of symmetric monoidal bicategories. In particular,
field theories with anomalies will be described by symmetric monoidal
transformations. The use of higher categorical concepts is necessary to capture
the Hamiltonian picture of anomalies. The relation to the path integral and the
Hamiltonian description of anomalies will be explained in detail. Furthermore,
we discuss anomaly inflow in detail. We apply the general framework to the
parity anomaly in fermionic systems coupled to background gauge and
gravitational fields on odd-dimensional spacetimes. We use the extension of the
Atiyah-Patodi-Singer index theorem to manifolds with corners due to Loya and
Melrose to explicitly construct an extended invertible field theory encoding
the anomaly. This allows us to compute explicitly the 2-cocycle of the
projective representation of the gauge symmetry on the quantum state space. As
a second application, we study discrete symmetries of Dijkgraaf-Witten theories
and their gauging. Non-abelian group cohomology is used to describe discrete
symmetries and we derive concrete conditions for such a symmetry to admit 't
Hooft anomalies in terms of the Lyndon-Hochschild-Serre spectral sequence. We
give an explicit realization of a discrete gauge theory with 't Hooft anomaly
as a state on the boundary of a higher-dimensional Dijkgraaf-Witten theory.


  The reaction pi N -> pi pi N is studied at tree level up to next-to-leading
order in the framework of manifestly covariant baryon chiral perturbation
theory with explicit Delta(1232) degrees of freedom. Using total cross section
data to determine the relevant low-energy constants, predictions are made for
various differential as well as total cross sections at higher energies. A
detailed comparison of results based on the heavy-baryon and relativistic
formulations of chiral perturbation theory with and without explicit Delta
degrees of freedom is given.


  In this note, we study the celebrated virial theorem for dissipative systems,
both classical and quantum. The classical formulation is discussed and an
intriguing effect of the random force (noise) is made explicit in the context
of the virial theorem. Subsequently, we derive a generalized virial theorem for
a dissipative quantum oscillator, i.e. a quantum oscillator coupled with a
quantum heat bath. Such a heat bath is modeled as an infinite collection of
independent quantum oscillators with a certain distribution of initial
conditions. In this situation, the non-Markovian nature of the quantum noise
leads to novel bath-induced terms in the virial theorem. We also consider the
case of an electrical circuit with thermal noise and analyze the role of
non-Markovian noise in the context of the virial theorem.