  We demonstrate that Robb-Geroch's definition of a relativistic interval
admits a simple and fairly natural generalization leading to a Finsler
extension of special relativity. Another justification for such an extension
goes back to the works of Lalan and Alway and, finally, was put on a solid
basis and systematically investigated by Bogoslovsky under the name
"Special-relativistic theory of locally anisotropic space-time". The isometry
group of this space-time, $\mathrm{DISIM}_b(2)$, is a deformation of the Cohen
and Glashow's very special relativity symmetry group $\mathrm{ISIM(2)}$. Thus,
the deformation parameter b can be regarded as an analog of the cosmological
constant characterizing the deformation of the Poincare group into the de
Sitter (anti-de Sitter) group. The simplicity and naturalness of Finslerian
extension in the context of this article adds weight to the argument that the
possibility of a nonzero value of $b$ should be carefully considered.


  We construct a weakly coupled, renormalizable ultraviolet completion of the
Littlest Higgs model with T-parity (LHT), based on an SU(5)xSU(2)xU(1) gauge
theory with a discrete Z_2 symmetry. Our model reproduces the complete
structure of the LHT below the 10 TeV scale, including the collective symmetry
breaking mechanism which solves the little hierarchy problem. The model is
manifestly free of anomalies, including both gauge/gravitational anomalies and
anomalies involving T-parity. At the TeV scale, the model contains additional
states not present in the LHT. We estimate the impact of these states on
precision electroweak observables, and show that the model is realistic. We
also discuss how our model can be embedded into a supersymmetric theory or a
five-dimensional setup with a warped extra dimension, stabilyzing the hierarchy
between the 10 TeV and the Planck scale.


  In the present paper we investigate Banach--Kantorovich algebras over
faithful solid subalgebras of algebras measurable functions. We prove that any
Banach--Kantorovich algebra over faithful solid subalgebras of algebra
measurable functions represented as a measurable bundle of Banach algebras with
vector-valued lifting. We apply such representation to the spectrum of elements
Banach--Kantorovich algebras.


  This paper deals with the dynamics of a shearfree charged radiating collapse
in modified Gauss-Bonnet gravity. The field equations for shearfree spherical
interior geometry of a charged dissipative star are formulated. To study the
dynamical behavior of collapsing matter, we derive the dynamical as well as
transport equations. We conclude that the gravitational force in modified
Gauss-Bonnet gravity is much stronger as compared to general relativity which
implies the increase in the rate of collapse. Finally, we study the effect of
charge on the dynamics of collapse.


  The residential buildings sector is one of the largest electricity consumers
worldwide and contributes disproportionally to peak electricity demand in many
regions. Strongly driven by occupant activities at home, household energy
consumption is stochastic and heterogeneous in nature. However, most
residential building energy models applied by industry use homogeneous,
deterministic occupant activity schedules, which work well for predictions of
annual energy consumption, but can result in unrealistic hourly or sub-hourly
electric load profiles, with exaggerated or muted peaks. This mattered less in
the past, but the increasing proportion of variable renewable energy generators
in power systems means that representing the heterogeneity and stochasticity of
occupant behavior is crucial for reliable energy planning. This is particularly
true for systems that include distributed energy resources, such as
grid-interactive efficient buildings, solar photovoltaics, and battery storage.
This work presents a stochastic occupant behavior simulator that models the
energy use behavior of individual household members. It also presents an
integration with a building stock model to simulate residential building loads
more accurately at community, city, state, and national scales. More
specifically, we first employ clustering techniques to identify distinct
patterns of occupant behavior. Then, we combine time-inhomogeneous Markov chain
simulations with probabilistic sampling of event durations to realistically
simulate occupant behaviors. This stochastic simulator is integrated with
ResStock, a large-scale residential building stock simulation tool, to
demonstrate the capability of stochastic residential building load modeling at
scale. The simulation results were validated against both American Time Use
Survey data and measured end-use electricity data for accuracy and reliability.


  Gram-negative bacteria are a serious health concern due to the strong
multidrug resistance that they display, partly due to the presence of a
permeability barrier comprising two membranes with active efflux. New
approaches are urgently needed to design antibiotics effective against these
pathogens. In this work, we present a novel topological fragment-based approach
("Hunting Fragments Of X" or "Hunting FOX") to rationally "hunt for" chemical
fragments that promote compound ability to permeate the outer membrane. Our
approach generalizes to other drug design applications. We measure minimum
inhibitory concentrations of compounds in two strains of Pseudomonas aeruginosa
with variable permeability barriers and use them as an input to the Hunting FOX
algorithm to identify molecular fragments responsible for enhanced outer
membrane permeation properties and candidate molecules from an external library
that demonstrate good permeation ability. Overall, we present proof of concept
for a novel method that is expected to be valuable for rational design of
hybrid drugs.


  The detector built at KEK to search for T-violating transverse muon
polarization in K+ --> pi0 mu+ nu (Kmu3) decay of stopped kaons is described.
Sensitivity to the transverse polarization component is obtained from
reconstruction of the decay plane by tracking the mu+ through a toroidal
spectrometer and detecting the pi0 in a segmented CsI(Tl) photon calorimeter.
The muon polarization was obtained from the decay positron asymmetry of muons
stopped in a polarimeter. The detector included features which minimized
systematic errors while maintaining high acceptance.


  In this article we consider T-dualization of a $3D$ closed bosonic string
that is propagating in space-time metric that has infinitesimal linear
dependence on the coordinates $x^\mu$. Other fields, Kalb-Ramond and dilaton
fields are set to zero. Action with this configuration of fields is not
invariant to translations. In order to find T-dual theory we will employ
generalization of the Buscher procedure that can be applied to such cases where
we have coordinate dependent fields that do not possess translational isometry.
Finally, using transformation laws that connect coordinates of starting and
T-dual theories, we will be able to examine the geometric structure of T-dual
theory.


  These are lecture notes for five lectures given at MPI Leipzig in May 2024.
We study the moduli space M_{0,n} of n distinct points on P^1 as a positive
geometry and a binary geometry. We develop mathematical formalism to study
Cachazo-He-Yuan's scattering equations and the associated scalar and Yang-Mills
amplitudes. We discuss open superstring amplitudes and relations to tropical
geometry.


  An array of resistively and capacitively shunted Josephson junctions with
nonsinusoidal current-phase relation is considered for modelling the transition
in high-T$_c$ superconductors. The emergence of higher harmonics, besides the
simple sinusoid $I_{c}\sin\phi$, is expected for dominant \emph{d}-wave
symmetry of the Cooper pairs, random distribution of potential drops, dirty
grains, or nonstationary conditions. We show that additional cosine and sine
terms act respectively by modulating the global resistance and by changing the
Josephson coupling of the mixed superconductive-normal states. First, the
approach is applied to simulate the transition in disordered granular
superconductors with the weak-links characterized by nonsinusoidal
current-phase relation. In granular superconductors, the emergence of
higher-order harmonics affects the slope of the transition. Then, arrays of
intrinsic Josephson junctions, naturally formed by the CuO$_2$ planes in
cuprates, are considered. The critical temperature suppression, observed at
values of hole doping close to $p=1/8$, is investigated. Such suppression,
related to the sign change and modulation of the Josephson coupling across the
array, is quantified in terms of the intensities of the first and second
sinusoids of the current-phase relation. Applications are envisaged for the
design and control of quantum devices based on stacks of intrinsic Josephson
junctions.


  This paper aims to detect the potential injury risk of the anterior cruciate
ligament (ACL) by proposing an ACL potential injury risk assessment algorithm
based on key points of the human body detected using computer vision
technology. To obtain the key points data of the human body in each frame,
OpenPose, an open source computer vision algorithm, was employed. The obtained
data underwent preprocessing and were then fed into an ACL potential injury
feature extraction model based on the Landing Error Evaluation System (LESS).
This model extracted several important parameters, including the knee flexion
angle, the trunk flexion on the sagittal plane, trunk flexion angle on the
frontal plane, the ankle knee horizontal distance, and the ankle shoulder
horizontal distance. Each of these features was assigned a threshold interval,
and a segmented evaluation function was utilized to score them accordingly. To
calculate the final score of the participant, the score values were input into
a weighted scoring model designed based on the Analytic Hierarchy Process
(AHP). The AHP based model takes into account the relative importance of each
feature in the overall assessment. The results demonstrate that the proposed
algorithm effectively detects the potential risk of ACL injury. The proposed
algorithm demonstrates its effectiveness in detecting ACL injury risk, offering
valuable insights for injury prevention and intervention strategies in sports
and related fields. Code is available at:
https://github.com/ZiyuGong-proj/Assessment-of-ACL-Injury-Risk-Based-on-Openpose


  Let $\E$ be a commutative ring with identity and $P\in\E[x]$ be a polynomial.
In the present paper we consider digit representations in the residue class
ring $\E[x]/(P)$. In particular, we are interested in the question whether each
$A\in\E[x]/(P)$ can be represented modulo $P$ in the form $e_0+e_1 X + \cdots +
e_h X^h$, where the $e_i\in\E[x]/(P)$ are taken from a fixed finite set of
digits. This general concept generalises both canonical number systems and
digit systems over finite fields. Due to the fact that we do not assume that
$0$ is an element of the digit set and that $P$ need not be monic, several new
phenomena occur in this context.


  The cost of communication is a substantial factor affecting the scalability
of many distributed applications. Every message sent can incur a cost in
storage, computation, energy and bandwidth. Consequently, reducing the
communication costs of distributed applications is highly desirable. The best
way to reduce message costs is by communicating without sending any messages
whatsoever. This paper initiates a rigorous investigation into the use of
silence in synchronous settings, in which processes can fail. We formalize
sufficient conditions for information transfer using silence, as well as
necessary conditions for particular cases of interest. This allows us to
identify message patterns that enable communication through silence. In
particular, a pattern called a {\em silent choir} is identified, and shown to
be central to information transfer via silence in failure-prone systems. The
power of the new framework is demonstrated on the {\em atomic commitment}
problem (AC). A complete characterization of the tradeoff between message
complexity and round complexity in the synchronous model with crash failures is
provided, in terms of lower bounds and matching protocols. In particular, a new
message-optimal AC protocol is designed using silence, in which processes
decide in~3 rounds in the common case. This significantly improves on the best
previously known message-optimal AC protocol, in which decisions were performed
in $\Theta(n)$ rounds.


  An efficient quantum secret sharing scheme is proposed. In this scheme, the
particles in an entangled pair group form two particle sequences. One sequence
is sent to Bob and the other is sent to Charlie after rearranging the particle
orders. Bob and Charlie make coding unitary operations and send the particles
back. Alice makes Bell-basis measurement to read their coding operations.


  We propose and experimentally demonstrate a chaotic Brillouin optical
correlation-domain analysis (BOCDA) system for distributed fiber sensing. The
utilization of the chaotic laser with low coherent state ensures high spatial
resolution. The experimental results demonstrate a 3.92-cm spatial resolution
over a 906-m measurement range. The uncertainty in the measurement of the local
Brillouin frequency shift is 1.2MHz. The measurement signal-to-noise ratio is
given, which is agreement with the theoretical value.


  Automatic document summarization aims to produce a concise summary covering
the input document's salient information. Within a report document, the salient
information can be scattered in the textual and non-textual content. However,
existing document summarization datasets and methods usually focus on the text
and filter out the non-textual content. Missing tabular data can limit produced
summaries' informativeness, especially when summaries require covering
quantitative descriptions of critical metrics in tables. Existing datasets and
methods cannot meet the requirements of summarizing long text and multiple
tables in each report. To deal with the scarcity of available data, we propose
FINDSum, the first large-scale dataset for long text and multi-table
summarization. Built on 21,125 annual reports from 3,794 companies, it has two
subsets for summarizing each company's results of operations and liquidity. To
summarize the long text and dozens of tables in each report, we present three
types of summarization methods. Besides, we propose a set of evaluation metrics
to assess the usage of numerical information in produced summaries. Dataset
analyses and experimental results indicate the importance of jointly
considering input textual and tabular data when summarizing report documents.


  Using the HiVIS spectropolarimeter built for the Haleakala 3.7m AEOS
telescope, we have obtained a large number of high precision spectropolarimetrc
observations (284) of Herbig AeBe stars collected over 53 nights totaling more
than 300 hours of observing. Our sample of five HAeBe stars: AB Aurigae,
MWC480, MWC120, MWC158 and HD58647, all show systematic variations in the
linear polarization amplitude and direction as a function of time and
wavelength near the H-alpha line. In all our stars, the H-alpha line profiles
show evidence of an intervening disk or outflowing wind, evidenced by strong
emission with an absorptive component. The linear polarization varies by 0.2%
to 1.5% with the change typically centered in the absorptive part of the line
profile. These observations are inconsistent with a simple disk-scattering
model or a depolarization model which produce polarization changes centered on
the emmissive core. We speculate that polarized absorption via optical pumping
of the intervening gas may be the cause.


  The use of topological descriptors in modern machine learning applications,
such as Persistence Diagrams (PDs) arising from Topological Data Analysis
(TDA), has shown great potential in various domains. However, their practical
use in applications is often hindered by two major limitations: the
computational complexity required to compute such descriptors exactly, and
their sensitivity to even low-level proportions of outliers. In this work, we
propose to bypass these two burdens in a data-driven setting by entrusting the
estimation of (vectorization of) PDs built on top of point clouds to a neural
network architecture that we call RipsNet. Once trained on a given data set,
RipsNet can estimate topological descriptors on test data very efficiently with
generalization capacity. Furthermore, we prove that RipsNet is robust to input
perturbations in terms of the 1-Wasserstein distance, a major improvement over
the standard computation of PDs that only enjoys Hausdorff stability, yielding
RipsNet to substantially outperform exactly-computed PDs in noisy settings. We
showcase the use of RipsNet on both synthetic and real-world data. Our
open-source implementation is publicly available at
https://github.com/hensel-f/ripsnet and will be included in the Gudhi library.


  The entangled state that results when a detector measures a superposed
quantum system has spawned decades of concern about the problem of definite
outcomes or "Schrodinger's cat." This state seems to describe a detector in an
indefinite or "smeared" situation of indicating two macroscopic configurations
simultaneously. This would be paradoxical. Since all entangled states are known
to have nonlocal properties, and since measurements have obvious nonlocal
characteristics, it's natural to turn to nonlocality experiments for insight
into this question. Unlike the measurement situation where the phase is fixed
at zero for perfect correlations, nonlocality experiments cover the full range
of superposition phases and can thus show precisely what entangled states
superpose. For two-state systems, these experiments reveal that the measurement
state is not a superposition of two macroscopically different detector states
but instead a superposition of two coherent correlations between distinct
detector states and corresponding system states. In the measurement situation
(i.e. at zero phase), and assuming the Schrodinger's cat scenario, the
entangled state can be read as follows: An undecayed nucleus is perfectly
correlated with an alive cat, AND a decayed nucleus is perfectly correlated
with a dead cat, where "AND" indicates the superposition. This is not
paradoxical.


  The XLF of AGN offers a robust tool to study the evolution and the growth of
SMBHs over cosmic time. Owing to the limited area probed by X-ray surveys,
optical surveys are routinely used to probe the accretion in the high redshift
Universe $z\geq 3$. However, optical surveys may be incomplete because they are
strongly affected by dust redenning. In this work, we derive the XLF and its
evolution at high redshifts using a large sample of AGNs selected in different
fields with various areas and depths covering a wide range of luminosities.
Additionally, we put the tightest yet constraints on the absorption function in
this redshift regime. In particular, we use more than 600 soft X-ray selected
high-z sources in the Chandra Deep fields, the Chandra COSMOS Legacy survey and
the XMM-XXL northern field. We derive the X-ray spectral properties for all
sources via spectral fitting, using a consistent technique and model. For
modeling the parametric form of the XLF and the absorption function, we use a
Bayesian methodology allowing us to correctly propagate the uncertainties for
the observed X-ray properties of our sources and also the absorption effects.
The evolution of XLF is in agreement with a pure density evolution model
similar to what is witnessed at optical wavelengths, although a luminosity
dependent density evolution model cannot be securely ruled out. A large
fraction ($60\%)$ of our sources are absorbed by column densities of $\rm N_H
\geq 10^{23} cm^{-2} $, while $17$\% of the sources are CTK. Our results favor
a scenario where both the ISM of the host and the AGN torus contribute to the
obscuration. The derived BHAD is in agreement with the simulations, if one
takes into account that the X-ray AGN are hosted by massive galaxies, while it
differs from the one derived using JWST data. The latter could be due to the
differences in the AGN and host-galaxy properties.


  An off-line ion source station has been commissioned at the IGISOL (Ion Guide
Isotope Separator On-Line) facility. It offers the infrastructure needed to
produce stable ion beams from three off-line ion sources in parallel with the
radioactive ion beams produced from the IGISOL target chamber. This has
resulted in improved feasibility for new experiments by offering reference ions
for Penning-trap mass measurements, laser spectroscopy and atom trap
experiments.


  We study a new class of infinite dimensional Lie algebras, which has
important applications to the theory of integrable equations. The construction
of these algebras is very similar to the one for automorphic functions and this
motivates the name automorphic Lie algebras. For automorphic Lie algebras we
present bases in which they are quasigraded and all structure constants can be
written out explicitly. These algebras have a useful factorisations on two
subalgebras similar to the factorisation of the current algebra on the positive
and negative parts.


  3D models of humans are commonly used within computer graphics and vision,
and so the ability to distinguish between body shapes is an important shape
retrieval problem. We extend our recent paper which provided a benchmark for
testing non-rigid 3D shape retrieval algorithms on 3D human models. This
benchmark provided a far stricter challenge than previous shape benchmarks. We
have added 145 new models for use as a separate training set, in order to
standardise the training data used and provide a fairer comparison. We have
also included experiments with the FAUST dataset of human scans. All
participants of the previous benchmark study have taken part in the new tests
reported here, many providing updated results using the new data. In addition,
further participants have also taken part, and we provide extra analysis of the
retrieval results. A total of 25 different shape retrieval methods.


  Wideband spectrum sensing detects the unused spectrum holes for dynamic
spectrum access (DSA). Too high sampling rate is the main problem. Compressive
sensing (CS) can reconstruct sparse signal with much fewer randomized samples
than Nyquist sampling with high probability. Since survey shows that the
monitored signal is sparse in frequency domain, CS can deal with the sampling
burden. Random samples can be obtained by the analog-to-information converter.
Signal recovery can be formulated as an L0 norm minimization and a linear
measurement fitting constraint. In DSA, the static spectrum allocation of
primary radios means the bounds between different types of primary radios are
known in advance. To incorporate this a priori information, we divide the whole
spectrum into subsections according to the spectrum allocation policy. In the
new optimization model, the minimization of the L2 norm of each subsection is
used to encourage the cluster distribution locally, while the L0 norm of the L2
norms is minimized to give sparse distribution globally. Because the L0/L2
optimization is not convex, an iteratively re-weighted L1/L2 optimization is
proposed to approximate it. Simulations demonstrate the proposed method
outperforms others in accuracy, denoising ability, etc.


  The purpose of a clickbait is to make a link so appealing that people click
on it. However, the content of such articles is often not related to the title,
shows poor quality, and at the end leaves the reader unsatisfied.
  To help the readers, the organizers of the clickbait challenge
(http://www.clickbait-challenge.org/) asked the participants to build a machine
learning model for scoring articles with respect to their "clickbaitness".
  In this paper we propose to solve the clickbait problem with an ensemble of
Linear SVM models, and our approach was tested successfully in the challenge:
it showed great performance of 0.036 MSE and ranked 3rd among all the solutions
to the contest.


  To enable intelligent automated driving systems, a promising strategy is to
understand how human drives and interacts with road users in complicated
driving situations. In this paper, we propose a 3D-aware egocentric
spatial-temporal interaction framework for automated driving applications.
Graph convolution networks (GCN) is devised for interaction modeling. We
introduce three novel concepts into GCN. First, we decompose egocentric
interactions into ego-thing and ego-stuff interaction, modeled by two GCNs. In
both GCNs, ego nodes are introduced to encode the interaction between thing
objects (e.g., car and pedestrian), and interaction between stuff objects
(e.g., lane marking and traffic light). Second, objects' 3D locations are
explicitly incorporated into GCN to better model egocentric interactions.
Third, to implement ego-stuff interaction in GCN, we propose a MaskAlign
operation to extract features for irregular objects.
  We validate the proposed framework on tactical driver behavior recognition.
Extensive experiments are conducted using Honda Research Institute Driving
Dataset, the largest dataset with diverse tactical driver behavior annotations.
Our framework demonstrates substantial performance boost over baselines on the
two experimental settings by 3.9% and 6.0%, respectively. Furthermore, we
visualize the learned affinity matrices, which encode ego-thing and ego-stuff
interactions, to showcase the proposed framework can capture interactions
effectively.


  Engineering non trivial topological phases in materials, specially
skyrmion-like arrangements, has been of great interest in the last decade due
to its potential technological applications. In this work, we study a model of
electrons coupled to a magnetic texture in the kagome lattice interacting with
magnetic moments via Rashba spin orbit coupling in the large Hund interaction
limit. We obtain the effective spin Hamiltonian and study the emergent low
temperature phases under an external magnetic field using large scale Monte
Carlo simulations. We show that strong geometric frustration, characteristic of
the kagome lattice, and the competition between the effective exchange,
antisymmetric and anisotropic couplings, gives rise to a large variety of
non-trivial topological phases. On the one hand, for antiferromagnetic exchange
coupling a pseudo-antiferromagnetic skyrmion crystal is stabilized for a broad
range of parameters. As the exchange coupling gets smaller, chiral single-q and
double-q phases emerge. On the other hand, in the ferromagnetic case, even
though the competition of the different interactions produce a series of exotic
textures, a remarkable parallel may be drawn with the pure ferromagnetic model
with antisymmetric interactions. Finally, for the special case where the
exchange coupling is completely suppressed, we show that, coming from a higher
temperature cooperative paramagnet, an "umbrella-like" plaquette order with
semiextensive degeneracy is induced by the external magnetic field.


  We report the first localization of diffuse, non-thermal, X-ray emission from
a nearby galaxy cluster. Using Chandra data, we have isolated a diffuse
non-thermal X-ray component with a photon index, Gamma_ X = 2.21 +0.14 -0.15
and a flux of 9.5 +1.1 -2.5 x 10^-5 photons cm^-2 s^-1 keV^-1 at 1 keV, that
extends from ~1'.5 to ~2'.5 to the south of the X-ray flux peak. Comparison to
simulations implies that the diffuse non-thermal emission is produced by
primary electrons, accelerated at shocks to relativistic velocities. Using
these results and the flux and hardness maps produced with data from the
Chandra Advanced CCD Imaging Spectrometer, we conclude that a smaller subclump
coming from the north merged with IC1262. The offset of the cD galaxy from the
X-ray peak and large peculiar velocity indicate that the subclump's impact
parameter was to the west and on the near side of IC1262.


  We give an alternative approach to the computation of the dimension of the
tangent space of the deformation space of curves with automorphisms. A
homological version of the local-global principle similar to the one of
J.Bertin, A. M\'ezard is proved, and a computation in the case of ordinary
curves is obtained, by application of the results of S. Nakajima for the Galois
module structure of the space of 2-holomorphic differentials on them.


  The Casselman-Shalika method is a way to compute explicit formulas for
periods of irreducible unramified representations of p-adic groups that are
associated to unique models (i.e. multiplicity-free induced representations).
We apply this method to the case of the Shalika model of GL_n, which is known
to distinguish lifts from odd orthogonal groups. In the course of our proof, we
further develop a variant of the method, that was introduced by Y.Hironaka, and
in effect reduce many such problems to straightforward calculations on the
group.


  Scattering of the Gaussian video pulse by a perfectly conducting circular
cone coated with dielectric is considered. The problem is solved using the
method of integral equations in the low and resonance frequency bands followed
by applying the Fourier transform to obtain time-domain responses.
Backscattered fields are investigated for different permittivities of the
dielectric in the case of the axial incidence of a plane wave.


  Fractionally integrated autoregressive moving average (FIARMA) processes have
been widely and successfully used to model and predict univariate time series
exhibiting long range dependence. Vector and functional extensions of these
processes have also been considered more recently. Here we study these
processes by relying on a spectral domain approach in the case where the
processes are valued in a separable Hilbert space H0. In this framework, the
usual univariate long memory parameter d is replaced by a long memory operator
D acting on H0, leading to a class of H0-valued FIARMA(D, p, q) processes,
where p and q are the degrees of the AR and MA polynomials. When D is a normal
operator, we provide a necessary and sufficient condition for the D-fractional
integration of an H0-valued ARMA(p, q) process to be well defined. Then, we
derive the best predictor for a class of causal FIARMA processes and study how
this best predictor can be consistently estimated from a finite sample of the
process. To this end, we provide a general result on quadratic functionals of
the periodogram, which incidentally yields a result of independent interest.
Namely, for any ergodic stationary process valued in H0 with finite second
moment, the empirical autocovariance operator converges, in trace-norm, to the
true autocovariance operator almost surely at each lag.


  We build a minimal, mean-field, model of plasticity of amorphous solids,
based upon a phenomenology of dissipative events derived, in a preceding paper
[A. Lemaitre, C. Caroli, arXiv:0705.0823] from extensive molecular simulations.
It reduces to the dynamics of an ensemble of identical shear transformation
zones interacting via the dynamic noise due to the long ranged elastic fields
induced by zone flips themselves. We find that these ingredients are sufficient
to generate flip avalanches with a power-law scaling with system size,
analogous to that observed in molecular simulations. We further show that the
scaling properties of avalanches sensitively depend on the detailed shape of
the noise spectrum. This points out the importance of developing a realistic
coarse-grained description of elasticity in these systems.


  We consider the inhomogeneous generalization of the density matrix of a
finite segment of length $m$ of the antiferromagnetic Heisenberg chain. It is a
function of the temperature $T$ and the external magnetic field $h$, and
further depends on $m$ `spectral parameters' $\xi_j$. For short segments of
length 2 and 3 we decompose the known multiple integrals for the elements of
the density matrix into finite sums over products of single integrals. This
provides new numerically efficient expressions for the two-point functions of
the infinite Heisenberg chain at short distances. It further leads us to
conjecture an exponential formula for the density matrix involving only a
double Cauchy-type integral in the exponent. We expect this formula to hold for
arbitrary $m$ and $T$ but zero magnetic field.


  We consider a particle system with uniform coupling between a macroscopic
component and individual particles. The constraint for each particle is of full
rank, which implies that each movement of the macroscopic component leads to a
movement of all particles and vice versa. Skeletal muscle tissues share a
similar property which motivates this work.
  We prove convergence of the mean-field limit, well-posedness and a stability
estimate for the mean-field PDE.


  We revisit the model of an AdS$_2$ black hole in JT gravity evaporating into
an external bath. We study when, and how much, information about the black hole
interior can be accessed through different portions of the Hawking radiation
collected in the bath, and we obtain the corresponding full quantitative Page
curves. As a refinement of previous results, we describe the island phase
transition for a semi-infinite segment of radiation in the bath, establishing
access to the interior for times within the regime of applicability of the
model. For finite-size segments in the bath, one needs to include the purifier
of the black hole microscopic dual together with the radiation segment in order
to access the interior information. We identify four scenarios of the entropy
evolution in this case, including a possibility where the interior
reconstruction window is temporarily interrupted. Analyzing the phase structure
of the Page curve of a finite segment with length comparable to the Page time,
we demonstrate that it is very sensitive to changes of the parameters of the
model. We also discuss the evolution of the subregion complexity of the
radiation during the black hole evaporation.


  Bott and Samuelson constructed explicit cycles representing a basis of the
Z_2-homology of the orbits of variationally complete representations of compact
Lie groups. As a consequence, all those orbits are taut. We were able to show
that an irreducible representation of a compact Lie group, all of whose orbits
are taut, is either variationally complete or it is one of the following
orthogonal representations (n bigger than or equal to 2): the (standard) x_R
(spin) representation of SO(2)xSpin(9); or the (standard) x_C (standard)
representation of U(2)xSp(n); or the (standard)^3 x_ H (standard)
representation of SU(2)xSp(n). In this paper we will show how to adapt the
construction of the cycles of Bott and Samelson to the orbits of these three
representations. As a result, they also admit explicit cycles representing a
basis of their Z_2-homology and, in particular, this provides another proof of
their tautness.


  Using a spontaneous-downconversion photon source, we produce true
non-maximally entangled states, i.e., without the need for post-selection. The
degree and phase of entanglement are readily tunable, and are characterized
both by a standard analysis using coincidence minima, and by quantum state
tomography of the two-photon state. Using the latter, we experimentally
reconstruct the reduced density matrix for the polarization. Finally, we use
these states to measure the Hardy fraction, obtaining a result that is $122
\sigma$ from any local-realistic result.


  We have studied quantum data compression for finite quantum systems where the
site density matrices are not independent, i.e., the density matrix cannot be
given as direct product of site density matrices and the von Neumann entropy is
not equal to the sum of site entropies. Using the density-matrix
renormalization group (DMRG) method for the 1-d Hubbard model, we have shown
that a simple relationship exists between the entropy of the left or right
block and dimension of the Hilbert space of that block as well as of the
superblock for any fixed accuracy. The information loss during the RG procedure
has been investigated and a more rigorous control of the relative error has
been proposed based on Kholevo's theory. Our results are also supported by the
quantum chemistry version of DMRG applied to various molecules with system
lengths up to 60 lattice sites. A sum rule which relates site entropies and the
total information generated by the renormalization procedure has also been
given which serves as an alternative test of convergence of the DMRG method.


  We introduce the notion of entropic Niebrzydowski tribrackets or just
entropic tribrackets, analogous to entropic (also known as abelian or medial )
quandles and biquandles. We show that if X is a finite entropic tribracket then
for any tribracket T , the homset Hom(T, X) (and in particular, for any
oriented link L, the homset Hom(T (L), X)) also has the structure of an
entropic tribracket. This operation yields a product on the category of
entropic tribrackets; we compute the operation table for entropic tribrackets
of small cardinality and prove a few results. We conjecture that this structure
can be used to distinguish links which have the same counting invariant with
respect to a chosen entropic coloring tribracket X.


  We analyze the dynamics of intersecting D3/D3' brane system overlapping in
1+1 dimensions, in a holographic treatment where $N$ D3-branes are manifested
as anti-de-Sitter Schwartzschild geometry, and the D3'-brane is treated as a
probe. We extract the thermodynamic equation of state from the set of embedding
solutions, and analyze the stability at the perturbative and the
non-perturbative level. We review a systematic procedure to resolve local
instabilities and multi-valuedness in the equations of state based on classic
ideas of convexity in microcanonical ensumble. We then identify a run-away
behavior which was not noticed previously for this system.


  Modern autonomous systems rely on perception modules to process complex
sensor measurements into state estimates. These estimates are then passed to a
controller, which uses them to make safety-critical decisions. It is therefore
important that we design perception systems to minimize errors that reduce the
overall safety of the system. We develop a risk-driven approach to designing
perception systems that accounts for the effect of perceptual errors on the
performance of the fully-integrated, closed-loop system. We formulate a risk
function to quantify the effect of a given perceptual error on overall safety,
and show how we can use it to design safer perception systems by including a
risk-dependent term in the loss function and generating training data in
risk-sensitive regions. We evaluate our techniques on a realistic vision-based
aircraft detect and avoid application and show that risk-driven design reduces
collision risk by 37% over a baseline system.


  Near the center of the Puppis A SNR a series of nested optically emitting
rings of high velocity ejecta (known as `the Swirl') were identified several
decades ago by Winkler et al. (1989). To date no follow-up observations of
these rings have been published, and their physical origin has remained a
mystery. We present results of integral field spectroscopy of the Swirl using
the Wide Field Integral Spectrograph (\wifes) on the 2.3\,m telescope at Siding
Spring Observatory in Australia. The outermost ring exhibits a nitrogen-rich
spectrum blueshifted to 1350 km/s, with smaller blueshifted rings within the
first exhibiting mostly oxygen-rich spectra moving at 1000 km/s and 750 km/s.
The structures are connected by material of intermediate velocity and variable
composition, including sulfur-rich material. The Swirl is turbulent and shock
excited, and contains as much as 0.5 M$_{\odot}$ of metal-rich material. The
chemical composition and exclusively blueshifted radial velocities of the Swirl
are consistent with progressively deeper nucleosynthetic layers in a massive
progenitor star. We suggest the possibility that the Swirl marks a `funnel'
carved into the supernova ejecta by a close, massive binary companion at the
moment of explosion.


  Due to that the polarization states in optical fibers change randomly during
transmission, polarization-independent (PID) devices are demanded to receive
lights with arbitrary polarization states. Compared with their orthogonal
polarization states, the optical profiles of various modes of the same
polarization are similar, and their directions of the main electric field are
same. Therefore, it's much easier to design PID devices using multi-modes of
one polarization state instead of orthogonal polarizations. This paper firstly
presents a scalable method to achieve PID devices and systems by transforming
the light orthogonal polarization states into one polarization with different
modes. Taking thermo-optical switches as an example, the PDL of the fabricated
2 x 2 switch cell was about 0.8 dB at 1300-1360 nm, and its extinction ratio
(ER) was larger than 19 dB for both polarizations. A 4 x 4 switch was also
demonstrated and its function of dual polarization switching was implemented,
whose ER was larger than 11 dB for both polarizations. This method has
potential in constructing PID on-chip systems for optical communications,
optical interconnections, etc.


  Air pollution is one of the most concerns for urban areas. Many countries
have constructed monitoring stations to hourly collect pollution values.
Recently, there is a research in Daegu city, Korea for real-time air quality
monitoring via sensors installed on taxis running across the whole city. The
collected data is huge (1-second interval) and in both Spatial and Temporal
format. In this paper, based on this spatiotemporal Big data, we propose a
real-time air pollution prediction model based on Convolutional Neural Network
(CNN) algorithm for image-like Spatial distribution of air pollution. Regarding
to Temporal information in the data, we introduce a combination of a Long
Short-Term Memory (LSTM) unit for time series data and a Neural Network model
for other air pollution impact factors such as weather conditions to build a
hybrid prediction model. This model is simple in architecture but still brings
good prediction ability.


  In many image-related tasks, learning expressive and discriminative
representations of images is essential, and deep learning has been studied for
automating the learning of such representations. Some user-centric tasks, such
as image recommendations, call for effective representations of not only images
but also preferences and intents of users over images. Such representations are
termed \emph{hybrid} and addressed via a deep learning approach in this paper.
We design a dual-net deep network, in which the two sub-networks map input
images and preferences of users into a same latent semantic space, and then the
distances between images and users in the latent space are calculated to make
decisions. We further propose a comparative deep learning (CDL) method to train
the deep network, using a pair of images compared against one user to learn the
pattern of their relative distances. The CDL embraces much more training data
than naive deep learning, and thus achieves superior performance than the
latter, with no cost of increasing network complexity. Experimental results
with real-world data sets for image recommendations have shown the proposed
dual-net network and CDL greatly outperform other state-of-the-art image
recommendation solutions.


  Andrews and Newman introduced the mex-function $\text{mex}_{A,a}(\lambda)$
for an integer partition $\lambda$ of a positive integer $n$ as the smallest
positive integer congruent to $a$ modulo $A$ that is not a part of $\lambda$.
They then defined $p_{A,a}(n)$ to be the number of partitions $\lambda$ of $n$
satisfying $\text{mex}_{A,a}(\lambda)\equiv a\pmod{2A}$. They found the
generating function for $p_{t,t}(n)$ and $p_{2t,t}(n)$ for any positive integer
$t$, and studied their arithmetic properties for some small values of $t$. In
this article, we study the partition function $p_{mt,t}(n)$ for all positive
integers $m$ and $t$. We show that for sufficiently large $X$, the number of
all positive integer $n\leq X$ such that $p_{mt,t}(n)$ is an even number is at
least $\mathcal{O}(\sqrt{X/3})$ for all positive integers $m$ and $t$. We also
prove that for sufficiently large $X$, the number of all positive integer
$n\leq X$ such that $p_{mp,p}(n)$ is an odd number is at least
$\mathcal{O}(\log \log X)$ for all $m\not \equiv 0\pmod{3}$ and all primes
$p\equiv 1\pmod{3}$. Finally, we establish identities connecting the ordinary
partition function to $p_{mt,t}(n)$.


  Let \cal A be a family of subsets of an n-set such that \cal A does not
contain distinct sets A and B with |A\B| = 2|B\A|. How large can \cal A be? Our
aim in this note is to determine the maximum size of such an \cal A. This
answers a question of Kalai. We also give some related results and conjectures.


  An elementary analytic proof of the famous Riemann hypothesis is given. The
main "accent" of the proof is a both using of the 2-dimensional double real and
complex Laplace integral representations of the Green function $\mid z
\mid^{-2}$.


  Proper Orthogonal Decomposition (POD) is a widely used technique for the
construction of low-dimensional approximation spaces from high-dimensional
input data. For large-scale applications and an increasing amount of input data
vectors, however, computing the POD often becomes prohibitively expensive. This
work presents a generic, easy-to-implement approach to compute an approximate
POD based on arbitrary tree hierarchies of worker nodes, where each worker
computes a POD of only a small amount of input vectors. The tree hierarchy can
be freely adapted to optimally suit the available computational resources. In
particular, this hierarchical approximate POD (HAPOD) allows for both simple
parallelization with low communication overhead, as well as live sequential POD
computation under restricted memory capacities. Rigorous error estimates ensure
the reliability of our approach, and extensive numerical examples underline its
performance.


  We describe the main features of our most recent Hartree-Fock-Bogoliubov
nuclear mass models, based on 16-parameter generalized Skyrme forces. They have
been fitted to the data of the 2012 Atomic Mass Evaluation, and favour a value
of 30 MeV for the symmetry coefficient J, the corresponding root-mean square
deviation being 0.549 MeV. We find that this conclusion is compatible with
measurements of neutron-skin thickness. By constraining the underlying
interactions to fit various equations of state of neutron matter calculated
{\it ab initio} our models are well adapted to a realistic and unified
treatment of all regions of neutron stars. We use our models to calculate the
composition, the equation of state, the mass-radius relation and the maximum
mass. Comparison with observations of neutron stars again favours a value of J
= 30 MeV.


  We present results from a survey of dwarf galaxy candidates in the vicinity
of strongly interacting galaxies. The goal of the survey was a test of the
hypothesis that massive condensations of stars and HI in tidal tails of large
interacting galaxies may be a significant source of independent,
self-gravitating dwarf galaxies. These so called tidal dwarf galaxies (TDG) can
be expected to resemble the blue luminous knots found in tidal tails, but also
might appear as redder, evolved systems if formed much before they are being
observed. For the present study, a homogeneous subsample of 6 fields was
selected from the catalog of extended objects in fields around 15 strongly
interacting galaxies by Deeg et al. (1998). Criteria for the subsample were:
similar redshifts of the central interacting galaxies, and photometric
completeness of the extended objects in V and R. The number density of these
TDG candidates was compared with expected background galaxy densities. Within
the statistical errors, background galaxies account for most, if not all of the
extended objects. There is no evidence for a substantial locally formed dwarf
galaxy population. Thus, we conclude that field galaxy-galaxy interactions are
likely to result in the formation of only a few long-lived TDG.


  Feedback-controlled electric breakdown of graphene in air or vacuum is a
well-established way of fabricating tunnel junctions, nanogaps, and quantum
dots. We show that the method is equally applicable to encapsulated graphene
constrictions fabricated using hydrogen silsesquioxane. The silica-like layer
left by hydrogen silsesquioxane resist after electron-beam exposure remains
intact after electric breakdown of the graphene. We explore the conductance
switching behavior that is common in graphene nanostructures fabricated via
feedback-controlled breakdown, and show that it can be attributed to
atomic-scale fluctuations of graphene below the encapsulating layer. Our
findings open up new ways of fabricating encapsulated room-temperature
single-electron nanodevices and shed light on the underlying physical mechanism
of conductance switching in these graphene nanodevices.


  We present high angular resolution (0.7'') observations made with the Very
Large Array (VLA) of the radio recombination line (RRL) H53alpha and radio
continuum emission at 43 GHz from the ultraluminous infrared galaxy (ULIRG) Arp
220. The 43 GHz continuum emission shows a compact structure (~2'') with two
peaks separated by ~1'', the East (E) and West (W) components, that correspond
to each galactic nucleus of the merger. The spectral indices for both the E and
W components, using radio continuum images at 8.3 and 43 GHz are typical of
synchrotron emission (alpha ~ -1.0). Our 43 GHz continuum and H53alpha line
observations confirm the flux densities predicted by the models proposed by
Anantharamaiah et al. This agreement with the models implies the presence of
high-density (~ 100,000 cm^-3) compact HII regions (~ 0.1 pc) in Arp 220. The
integrated H53alpha line emission is stronger toward the non-thermal radio
continuum peaks, which are also coincident with the peaks of molecular emission
of the H2CO. The coincidence between the integrated H53alpha and the H2CO maser
line emission suggests that the recent star forming regions, traced by the high
density gas, are located mainly in regions that are close to the two radio
continuum peaks. A velocity gradient of ~ 0.30 km/s/pc in the H53alpha RRL is
observed toward the E component and a second velocity gradient of ~ 0.15
km/s/pc is detected toward the W component. The orientations of these velocity
gradients are in agreement with previous CO, HI and OH observations. The
kinematics of the high-density ionized gas traced by the H53alpha line are
consistent with two counter rotating disks as suggested by the CO and HI
observations.


  Steganography conceals the secret message into the cover media, generating a
stego media which can be transmitted on public channels without drawing
suspicion. As its countermeasure, steganalysis mainly aims to detect whether
the secret message is hidden in a given media. Although the steganography
techniques are improving constantly, the sophisticated steganalysis can always
break a known steganographic method to some extent. With a stego media
discovered, the adversary could find out the sender or receiver and coerce them
to disclose the secret message, which we name as coercive attack in this paper.
Inspired by the idea of deniable encryption, we build up the concepts of
deniable steganography for the first time and discuss the feasible
constructions for it. As an example, we propose a receiver-deniable
steganographic scheme to deal with the receiver-side coercive attack using deep
neural networks (DNN). Specifically, besides the real secret message, a piece
of fake message is also embedded into the cover. On the receiver side, the real
message can be extracted with an extraction module; while once the receiver has
to surrender a piece of secret message under coercive attack, he can extract
the fake message to deceive the adversary with another extraction module.
Experiments demonstrate the scalability and sensitivity of the DNN-based
receiver-deniable steganographic scheme.


  A logarithmic type Harnack inequality is established for the semigroup of
solutions to a stochastic differential equation in Hilbert spaces with
non-additive noise. As applications, the strong Feller property as well as the
entropy-cost inequality for the semigroup are derived with respect to the
corresponding distance (cost function).


  We give a review of recent ANOVA-like procedures for testing group
differences based on data in a metric space and present a new such procedure.
Our statistic is based on the classic Levene's test for detecting differences
in dispersion. It uses only pairwise distances of data points and and can be
computed quickly and precisely in situations where the computation of
barycenters ("generalized means") in the data space is slow, only by
approximation or even infeasible. We show the asymptotic normality of our test
statistic and present simulation studies for spatial point pattern data, in
which we compare the various procedures in a 1-way ANOVA setting. As an
application, we perform a 2-way ANOVA on a data set of bubbles in a mineral
flotation process.


  In the absence of any proper clinical solution, human civilization is only
left with sophisticated intervention measures to contain the spread of
COVID-19. However, the existing models to estimate the intervention does not
take into account the realistic connectivity of the epicentres of the pandemic.
We generalise our earlier model of interacting hotspots to test various
possibilities of intervention in a model state consisting of multiple
epicentres. We also analyse situations when the hotspots are spatially
correlated and the interaction is limited to population exchanges with the
nearest neighbours. We show that the heterogeneity in the infection propagation
is solely dependent on the protocol of the containment and its strength. We
explore many such situations and discuss possibilities.


  Polarimetry is widely considered a powerful observational technique in X-ray
astronomy, useful to enhance our understanding of the emission mechanisms,
geometry and magnetic field arrangement of many compact objects. However, the
lack of suitable sensitive instrumentation in the X-ray energy band has been
the limiting factor for its development in the last three decades. Up to now,
polarization measurements have been made exclusively with Bragg diffraction at
45 degrees or Compton scattering at 90 degrees and the only unambiguous
detection of X-ray polarization has been obtained for one of the brightest
object in the X-ray sky, the Crab Nebula. Only recently, with the development
of a new class of high sensitivity imaging detectors, the possibility to
exploit the photoemission process to measure the photon polarization has become
a reality. We will report on the performance of an imaging X-ray polarimeter
based on photoelectric effect. The device derives the polarization information
from the track of the photoelectrons imaged by a finely subdivided Gas Pixel
Detector. It has a great sensitivity even with telescopes of modest area and
can perform simultaneously good imaging, moderate spectroscopy and high rate
timing. Being truly 2D it is non-dispersive and does not require any rotation.
This device is included in the scientific payload of many proposals of
satellite mission which have the potential to unveil polarimetry also in X-rays
in a few years.


  We have investigated the electronic structure of the equiatomic EuAuMg,
GdAuMg, YbAuMg and GdAgMg intermetallics using x-ray photoelectron
spectroscopy. The spectra revealed that the Yb and Eu are divalent while the Gd
is trivalent. The spectral weight in the vicinity of the Fermi level is
dominated by the mix of Mg $s$, Au/Ag $sp$ and $RE$ $spd$ bands, and not by the
$RE$ $4f$. We also found that the Au and Ag $d$ bands are extraordinarily
narrow, as if the noble metal atoms were impurities submerged in a low density
$sp$ metal host. The experimental results were compared with band structure
calculations, and we found good agreement provided that the spin-orbit
interaction in the Au an Ag $d$ bands is included and correlation effects in an
open $4f$ shell are accounted for using the local density approximation +
Hubbard $U$ scheme. Nevertheless, limitations of such a mean-field scheme to
explain excitation spectra are also evident.


  Path and path deviation equations for neutral, charged, spinning and spinning
charged test particles, using a modified Bazanski Lagrangian, are derived. We
extend this approach to strings and branes. We show how the Bazanski Lagrangian
for charged point particles and charged branes arises `a la Kaluza-Klein from
the Bazanski Lagrangian in 5-dimensions.


  The Continuous Electron Beam Accelerator Facility (CEBAF) was built with a
thermionic electron source and the three original experimental hall lines
reflected this. A few years after beam delivery began a parity violation
experiment was approved and two polarimeters were installed in the Hall A beam
line without consultation with the accelerator physics group. The beam raster
system was placed after the new Compton polarimeter, before one accelerator
quadrupole and four quadrupoles in the new Moller polarimeter. It was very
difficult to meet experimental requirements on envelope functions and raster
shape with this arrangement so a member of the accelerator physics group had a
sixth quadrupole installed downstream of the Moller polarimeter. All of the
parity experiments in Hall A have been run with this still-unsatisfactory
configuration. The MOLLER experiment is predicated on achieving a 2% error on a
32 ppb asymmetry. Beam line changes are required to meet the systematic error
budget. This paper documents the existing beam line, an interim change which
can be accomplished during a annual maintenance down, and the final
configuration for MOLLER and subsequent experiments.


  We study possible contributions of heavy sterile neutrinos $\nu_h$ to the
decays $\tau^-\to e^{\pm}(\mu^{\pm})\pi^{\mp}\pi^-$. From the experimental
upper bounds on their rates we derive new constraints on the $\nu_h-\nu_{\tau}$
mixing in the mass region $140.5{MeV}\leq m_{\nu_h}\leq 1637$ MeV. We discuss
cosmological and astrophysical status of $\nu_h$ in this mass region and
compare our constraints with those recently derived by the NOMAD collaboration.


  We study soft hadron production in relativistic heavy ion collisions in a
wide range of reaction energy, 4.8 GeV <sqrt{s_ NN}<200 GeV, and make
predictions about yields of particles using the statistical hadronization
model. In fits to experimental data, we obtain both statistical parameters as
well as physical properties of the hadron source. We identify the properties of
the fireball at the critical energy threshold, 6.26 GeV < sqrt{s_NN}^cr} <7.61
GeV, delineating for higher energies hadronization of an entropy rich phase. In
terms of the chemical composition, one sees a phase which at low energy is
chemically under-saturated, and which turns into a chemically over-saturated
state persisting up to the maximum accessible energy. Assuming that there is no
change in physical mechanisms in the energy range 15>sqrt{s_NN} \ge 200 GeV, we
use continuity of particle yields and statistical parameters to predict the
hadron production at sqrt{s_NN}=62.4 GeV, and obtain total yields of hadrons at
sqrt{s_NN}=130 GeV. We consider, in depth, the pattern we uncover within the
hadronization condition, and discuss possible mechanisms associated with the
identified rapid change in system properties at sqrt{s_NN ^cr}. We propose that
the chemically over-saturated 2+1 flavor hadron matter system undergoes a 1st
order phase transition.


  It is shown that the Clebsch parameterization, upon canonizing the
Hamiltonian system of ideal fluid or plasma dynamics, converts the Casimir
invariants (mass and helicities) in the original noncanonical formulation into
the Noether charges pertinent to the gauge symmetries of the parameterization.
The problem is addressed in the context of magnetohydrodynamics. The concrete
forms of the gauge symmetries of Clebsch parameterization are worked out.


  With an effective Lagrangian approach, we analyze the $K^-p\to \pi^0\Sigma^0$
reaction to study the $\Lambda$ hyperon resonances by fitting the Crystal Ball
data on differential cross sections and $\Sigma^0$ polarization with the
center-of-mass energies of $1536\sim 1676$ MeV. Besides well established PDG
4-star $\Lambda$ resonances around this energy range, the $\Lambda(1600){1\over
2}^+$ resonance, listed as a 3-star resonance in PDG, is found to be definitely
needed. In addition, there is strong evidence for the existence of a new
$\Lambda({3\over 2}^+)$ resonance around 1680 MeV.


  The 4-qubit unextendible product basis (UPB) has been recently studied by
[Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. From this result we show
that there is only one UPB of size $6$ and six UPBs of size $9$ in
$\cH=\bbC^2\ox\bbC^2\ox\bbC^4$, three UPBs of size $9$ in
$\cK=\bbC^4\ox\bbC^4$, and no UPB of size $7$ in $\cH$ and $\cK$. Furthermore
we construct a 4-qubit positive-partial-transpose (PPT) entangled state $\r$ of
rank seven, and show that it is also a PPT entangled state in $\cH$ and $\cK$,
respectively. We analytically derive the geometric measure of entanglement of a
special $\r$.


  The 3x+1 problem is one of the most classical problems in computer science,
related to many fields. As it is thought by scientists a highly hard problem,
resolving it successfully not only can improve the research in many relating
fields, but also be meaningful to the method study. By deep analyzing the 3x+1
calculation process with the input positive integer becoming greater, we find a
useful way for solving this problem with high probability. By making use of the
greater calculating ability of great computers and the internet, our way is a
valid and powerful way for utterly solving the 3x+1 problem. This way can be
expressed in three points: 1) If we can find a positive integer N, for any
positive integer less than 2N, the times of dividing 2 out of its stopping time
is less than or equal to N, then the 3x+1 conjecture is true; 2) This N may be
big, so the calculation may be too big. Our way for solving this is: to find a
positive integer K, for all positive integers less than 2K, not all the times
of dividing 2 out of their stopping time for these integers are less than or
equal to K, some part of these are greater than K, but the number of this part
becomes less and less with the K increasing; 3) This K and the calculation may
also be too big, our way for solving this is: to find a positive integer R, for
all positive integers less than 2R, as above, out of their stopping time, the
times of dividing 2 of some part of these integers are greater than R, also the
number of this part integers does not become less immediately with the R
increasing, but the increasing rate of this number is less and less until to
below zero.


  This paper examines the statistical properties of a distributional form that
arises from pooled testing for the prevalence of a binary outcome. Our base
distribution is a two-parameter distribution using a prevalence and excess
intensity parameter; the latter is included to allow for a dilution or
intensification effect with larger pools. We also examine a generalised form of
the distribution where pools have covariate information that affects the
prevalence through a linked linear form. We study the general pooled binomial
distribution in its own right and as a special case of broader forms of
binomial GLMs using the complementary log-log link function. We examine the
information function and show the information content of individual sample
items. We demonstrate that pooling reduces information content of sample units
and we give simple heuristics for choosing an "optimal" pool size for testing.
We derive the form of the log-likelihood function and its derivatives and give
results for maximum likelihood estimation. We also discuss diagnostic testing
of the positive pool probabilities, including testing for
intensification/dilution in the testing mechanism. We illustrate the use of
this distribution by applying it to pooled testing data on virus prevalence in
a mosquito population.


  The theory of the ion cyclotron (IC) electrostatic parametric instabilities
of the inhomogeneous plasma which are driven by the inhomogeneous electric
field of the fast wave (FW) in front of FW antenna is developed. It is found
that the spatial inhomogeneity of the parametric IC turbulence and of the drift
turbulence is at the origin of the flows which transport a large part of FW
power, deposited to the pedestal plasma, to the scrape-off layer and later to
the divertor mostly along field lines.


  In the context of QoE management, network and service providers commonly rely
on models that map system QoS conditions (e.g., system response time, paket
loss, etc.) to estimated end user QoE values. Observable QoS conditions in the
system may be assumed to follow a certain distribution, meaning that different
end users will experience different conditions. On the other hand, drawing from
the results of subjective user studies, we know that user diversity leads to
distributions of user scores for any given test conditions (in this case
referring to the QoS parameters of interest). Our previous studies have shown
that to correctly derive various QoE metrics (e.g., Mean Opinion Score (MOS),
quantiles, probability of users rating "good or better", etc.) in a system
under given conditions, there is a need to consider rating distributions
obtained from user studies, which are often times not available. In this paper
we extend these findings to show how to approximate user rating distributions
given a QoS-to-MOS mapping function and second order statistics. Such a user
rating distribution may then be combined with a QoS distribution observed in a
system to finally derive corresponding distributions of QoE scores. We provide
two examples to illustrate this process: 1) analytical results using a Web QoE
model relating waiting times to QoE, and 2) numerical results using
measurements relating packet losses to video stall pattern, which are in turn
mapped to QoE estimates. The results in this paper provide a solution to the
problem of understanding the QoE distribution in a system, in cases where the
necessary data is not directly available in the form of models going beyond the
MOS, or where the full details of subjective experiments are not available.


  We present a method for calculating the dynamics of a bosonic mixture, the
multi-component correlated basis function (CBF) method. For single components,
CBF results for the excitation energies agree quite well with experimental
results, even for highly correlated systems like $^4$He, and recent systematic
improvements of CBF achieve perfect agreement. We give a full derivation of
multi-component CBF, and apply the method to a dipolar Bose gas cut into
two-dimensional layers by a deep optical lattice, with coupling between layers
due to the long-ranged dipole-dipole interaction. We consider the case of
strong coupling, leading to large positive interlayer correlations. We
calculate the spectrum for a system of 8 layers and show that the strong
coupling can lead to a simpler spectrum than in the uncoupled case, with a
single peak carrying most of the spectral weight.


  We present the study of a sample of seven "bare" active galactic nuclei (AGN)
observed with Suzaku. We interpret the spectrum of these sources with a
relativistic reflection component and we employ our model RELXILL_NK to test
the Kerr nature of their supermassive black holes. We constrain the Johannsen
deformation parameters $\alpha_{13}$ and $\alpha_{22}$, in which the Kerr
metric is recovered when $\alpha_{13} = \alpha_{22} = 0$. All our measurements
are consistent with the hypothesis that the spacetime geometry around these
supermassive objects is described by the Kerr solution. For some sources, we
obtain quite strong constraints on $\alpha_{13}$ and $\alpha_{22}$ when
compared to those found in our previous studies. We discuss the systematic
uncertainties in our tests and the implications of our results.


  We introduce two new exactly solvable (stochastic) interacting particle
systems which are discrete time versions of q-TASEP. We call these geometric
and Bernoulli discrete time q-TASEP. We obtain concise formulas for
expectations of a large enough class of observables of the systems to
completely characterize their fixed time distributions when started from step
initial condition. We then extract Fredholm determinant formulas for the
marginal distribution of the location of any given particle.
  Underlying this work is the fact that these expectations solve closed systems
of difference equations which can be rewritten as free evolution equations with
k-1 two-body boundary conditions -- discrete q-deformed versions of the quantum
delta Bose gas. These can be solved via a nested contour integral ansatz. The
same solutions also arise in the study of Macdonald processes, and we show how
the systems of equations our expectations solve are equivalent to certain
commutation relations involving the Macdonald first difference operator.


  $\rm Yb_2Ti_2O_7$ is a celebrated example of a pyrochlore magnet with
highly-frustrated, anisotropic exchange interactions. To date, attention has
largely focused on its unusual, static properties, many of which can be
understood as coming from the competition between different types of magnetic
order. Here we use inelastic neutron scattering with exceptionally high energy
resolution to explore the dynamical properties of $\rm Yb_2Ti_2O_7$. We find
that spin correlations exhibit dynamical scaling, analogous to behavior found
near to a quantum critical point. We show that the observed scaling collapse
can be explained within a phenomenological theory of multiple--phase
competition, and confirm that a scaling collapse is also seen in
semi--classical simulations of a microscopic model of $\rm Yb_2Ti_2O_7$. These
results suggest a general picture for dynamics in systems with competing ground
states.


  Non-unitary quantum mechanics has been used in the past to study
irreversibility, dissipation and decay in a variety of physical systems. In
this letter, we propose a general scheme to deal with systems governed by
non-Hermitian Hamiltonians. We argue that the Schwinger-Keldysh formalism gives
a natural description for those problems. To elucidate the method, we study a
simple model inspired by mesoscopic physics --an asymmetric junction. The
system is governed by a non-Hermitian Hamiltonian which captures essential
aspects of irreversibility.


  The number of events suitable for a determination of the gluon distribution
function g(x,Q^2) in a proton at the LHC for various intervals of x and Q^2 are
estimated. The contributions of main background sources to ``direct
photon+jet'' production processes are studied. The values of discrimination
powers between quark and gluon jets as well as between a single photon and the
products of pi^0, eta, K^0_s mesons decaying through the neutral channels are
applied to estimate the final contributions of various event types to the
"photon+jet" production in different intervals of x and Q^2. Monte Carlo events
generated by help of the PYTHIA 6.1 generator are used for this analysis.


  Open data platforms such as data.gov or opendata.socrata. com provide a huge
amount of valuable information. Their free-for-all nature, the lack of
publishing standards and the multitude of domains and authors represented on
these platforms lead to new integration and standardization problems. At the
same time, crowd-based data integration techniques are emerging as new way of
dealing with these problems. However, these methods still require input in form
of specific questions or tasks that can be passed to the crowd. This paper
discusses integration problems on Open Data Platforms, and proposes a method
for identifying and ranking integration hypotheses in this context. We will
evaluate our findings by conducting a comprehensive evaluation using on one of
the largest Open Data platforms.


  We prove that for the Activated Random Walks model on transitive unimodular
graphs, if there is fixation, then every particle eventually fixates, almost
surely. We deduce that the critical density is at most 1.
  Our methods apply for much more general processes on unimodular graphs.
Roughly put, our result apply whenever the path of each particle has an
automorphism invariant distribution and is independent of other particles'
paths, and the interaction between particles is automorphism invariant and
local. This allows us to answer a question of Rolla and Sidoravicius, in a more
general setting then had been previously known (by Shellef).


  We propose an experiment using a conventional optical telescope to determine
whether aberration of starlight results from special relativistic effects
external to a measurement sensor or from optical effects within a sensor. The
proposed measurements would discriminate between the two starlight aberration
models in an Earth-based experiment. In addition, the measurements would yield
an independent experimental test of relativistic time dilation.


  We investigate the Leggett-Garg inequalities (LGIs) for a boson system whose
observables are given by deforming the Pegg-Barnett phase operators. We
consider two observables and show that the quantum Fourier transform is useful
in the realization of the required measurements. Deriving explicit forms for
the LGIs using the coherent state $|\alpha\rangle$ as the initial state, we
explore the regimes where they are violated when the time difference between
observations of the phase operators is varied. We show that the system remains
nonclassical in the large amplitude limit without dissipation, however with
dissipation, our violation diminishes rapidly.


  We consider a two-factor model for the valuation of a non callable
defaultable bond which pays coupons at certain given dates. The model under
consideration is the Jump to Default Constant Elasticity of Variance (JDCEV)
model. The JDCEV model is an improvement of the reduced form approach, which
unifies credit and equity models into a single framework allowing for
stochastic and possible negative interest rates. From the mathematical point of
view, the valuation involves two partial differential equation (PDE) problems
for each coupon. First, we obtain the existence of solution for these PDE
problems. In order to solve them, we propose appropriate numerical schemes
based on a Crank-Nicolson semi-Lagrangian method for time discretization
combined with bi-quadratic Lagrange finite elements for space discretization.
Once the numerical solutions of the PDEs are obtained, a post-processing
procedure is carried out in order to achieve the value of the bond. This
post-processing includes the computation of an integral term which is
approximated by using the composite trapezoidal rule. Finally, we present some
numerical results for real market bonds issued by different firms in order to
illustrate the proper behaviour of the numerical schemes. Moreover, we obtain
an agreement between the numerical results from the PDE approach and those ones
obtained by applying a Monte Carlo technique and an asymptotic approximation
method.


  We analyze the generation of entanglement in a multipartite optical network.
We generalize the twin-field strategy to the multipartie case and show that our
protocol has advantageous rate-loss scalings of distributing W states and Dicke
states over the star networks. We give precise theoretical formulas and
quantitative performance analyses. Also analysis of the same protocol using
Gaussian states as resources, which is a typical setup of many experimental
tests, is provided.


  Dynamically Interactive Visualization (DIVI) is a novel approach for
orchestrating interactions within and across static visualizations. DIVI
deconstructs Scalable Vector Graphics charts at runtime to infer content and
coordinate user input, decoupling interaction from specification logic. This
decoupling allows interactions to extend and compose freely across different
tools, chart types, and analysis goals. DIVI exploits positional relations of
marks to detect chart components such as axes and legends, reconstruct scales
and view encodings, and infer data fields. DIVI then enumerates candidate
transformations across inferred data to perform linking between views. To
support dynamic interaction without prior specification, we introduce a
taxonomy that formalizes the space of standard interactions by chart element,
interaction type, and input event. We demonstrate DIVI's usefulness for rapid
data exploration and analysis through a usability study with 13 participants
and a diverse gallery of dynamically interactive visualizations, including
single chart, multi-view, and cross-tool configurations.


  Solitary waves in one-dimensional periodic media are discussed employing the
nonlinear Schr\"odinger equation with a spatially periodic potential as a
model. This equation admits two families of gap solitons that bifurcate from
the edges of Bloch bands in the linear wave spectrum. These fundamental
solitons may be positioned only at specific locations relative to the
potential; otherwise, they become nonlocal owing to the presence of growing
tails of exponentially-small amplitude with respect to the wave peak amplitude.
Here, by matching the tails of such nonlocal solitary waves, higher-order
locally confined gap solitons, or bound states, are constructed. Details are
worked out for bound states comprising two nonlocal solitary waves in the
presence of a sinusoidal potential. A countable set of bound-state families,
characterized by the separation distance of the two solitary waves, is found,
and each family features three distinct solution branches that bifurcate near
Bloch-band edges at small, but finite, amplitude. Power curves associated with
these solution branches are computed asymptotically for large solitary-wave
separation, and the theoretical predictions are consistent with numerical
results.


  By measuring transverse single spin asymmetries one has access to the
transversity distribution function $\Delta_T q(x)$ and the transverse momentum
dependent Sivers function $q_0^T(x,\vec{k}_T)$. New measurements from
identified hadrons and hadron pairs, produced in deep inelastic scattering of a
transversely polarized $^6LiD$ target are presented. The data were taken in
2003 and 2004 by the COMPASS collaboration using the muon beam of the CERN SPS
at 160 GeV/c, resulting in small asymmetries.


  In a galaxy redshift survey the objects to be targeted for spectra are
selected from a photometrically observed sample. The observed magnitudes and
colours of galaxies in this parent sample will be affected by their peculiar
velocities, through relativistic Doppler and relativistic beaming effects. In
this paper we compute the resulting expected changes in galaxy photometry. The
magnitudes of the relativistic effects are a function of redshift, stellar
mass, galaxy velocity and velocity direction. We focus on the CMASS sample from
the Sloan Digital Sky Survey (SDSS), Baryon Oscillation Spectroscopic Survey
(BOSS), which is selected on the basis of colour and magnitude. We find that
0.10\% of the sample ($\sim 585$ galaxies) has been scattered into the targeted
region of colour-magnitude space by relativistic effects, and conversely 0.09\%
of the sample ($\sim 532$ galaxies) has been scattered out. Observational
consequences of these effects include an asymmetry in clustering statistics,
which we explore in a companion paper. Here we compute a set of weights which
can be used to remove the effect of modulations introduced into the density
field inferred from a galaxy sample. We conclude by investigating the possible
effects of these relativistic modulation on large scale clustering of the
galaxy sample.


  Bayesian optimization has been shown to be a powerful tool for solving black
box problems during online accelerator optimization. The major advantage of
Bayesian based optimization techniques is the ability to include prior
information about the problem to speed up optimization, even if that
information is not perfectly correlated with experimental measurements. In
parallel, neural network surrogate system models of accelerator facilities are
increasingly being made available, but at present they are not widely used in
online optimization. In this work, we demonstrate the use of an approximate
neural network surrogate model as a prior mean for Gaussian processes used in
Bayesian optimization in a realistic setting. We show that the initial
performance of Bayesian optimization is improved by using neural network
surrogate models, even when surrogate models make erroneous predictions.
Finally, we quantify requirements on surrogate prediction accuracy to achieve
optimization performance when solving problems in high dimensional input
spaces.


  Problem statement: Standardisation of AI fairness rules and benchmarks is
challenging because AI fairness and other ethical requirements depend on
multiple factors such as context, use case, type of the AI system, and so on.
In this paper, we elaborate that the AI system is prone to biases at every
stage of its lifecycle, from inception to its usage, and that all stages
require due attention for mitigating AI bias. We need a standardised approach
to handle AI fairness at every stage. Gap analysis: While AI fairness is a hot
research topic, a holistic strategy for AI fairness is generally missing. Most
researchers focus only on a few facets of AI model-building. Peer review shows
excessive focus on biases in the datasets, fairness metrics, and algorithmic
bias. In the process, other aspects affecting AI fairness get ignored. The
solution proposed: We propose a comprehensive approach in the form of a novel
seven-layer model, inspired by the Open System Interconnection (OSI) model, to
standardise AI fairness handling. Despite the differences in the various
aspects, most AI systems have similar model-building stages. The proposed model
splits the AI system lifecycle into seven abstraction layers, each
corresponding to a well-defined AI model-building or usage stage. We also
provide checklists for each layer and deliberate on potential sources of bias
in each layer and their mitigation methodologies. This work will facilitate
layer-wise standardisation of AI fairness rules and benchmarking parameters.


  This paper studies closed 3-manifolds which are the attractors of a system of
finitely many affine contractions that tile $\mathbb{R}^3$. Such attractors are
called self-affine tiles. Effective characterization and recognition theorems
for these 3-manifolds as well as theoretical generalizations of these results
to higher dimensions are established. The methods developed build a bridge
linking geometric topology with iterated function systems and their attractors.
  A method to model self-affine tiles by simple iterative systems is developed
in order to study their topology. The model is functorial in the sense that
there is an easily computable map that induces isomorphisms between the natural
subdivisions of the attractor of the model and the self-affine tile. It has
many beneficial qualities including ease of computation allowing one to
determine topological properties of the attractor of the model such as
connectedness and whether it is a manifold. The induced map between the
attractor of the model and the self-affine tile is a quotient map and can be
checked in certain cases to be monotone or cell-like. Deep theorems from
geometric topology are applied to characterize and develop algorithms to
recognize when a self-affine tile is a topological or generalized manifold in
all dimensions. These new tools are used to check that several self-affine
tiles in the literature are 3-balls. An example of a wild 3-dimensional
self-affine tile is given whose boundary is a topological 2-sphere but which is
not itself a 3-ball. The paper describes how any 3-dimensional handlebody can
be given the structure of a self-affine 3-manifold. It is conjectured that
every self-affine tile which is a manifold is a handlebody.


  Two common approaches to sequential decision-making are AI planning (AIP) and
reinforcement learning (RL). Each has strengths and weaknesses. AIP is
interpretable, easy to integrate with symbolic knowledge, and often efficient,
but requires an up-front logical domain specification and is sensitive to
noise; RL only requires specification of rewards and is robust to noise but is
sample inefficient and not easily supplied with external knowledge. We propose
an integrative approach that combines high-level planning with RL, retaining
interpretability, transfer, and efficiency, while allowing for robust learning
of the lower-level plan actions. Our approach defines options in hierarchical
reinforcement learning (HRL) from AIP operators by establishing a
correspondence between the state transition model of AI planning problem and
the abstract state transition system of a Markov Decision Process (MDP).
Options are learned by adding intrinsic rewards to encourage consistency
between the MDP and AIP transition models. We demonstrate the benefit of our
integrated approach by comparing the performance of RL and HRL algorithms in
both MiniGrid and N-rooms environments, showing the advantage of our method
over the existing ones.


  Dynamics of nanoscopic arrays of monodomain magnetic elements is simulated by
means of the Pardavi-Horvath algorithm. Experimental hysteresis loop is
reproduced for the arrays of Ni, with the period 100 nm and the mean coercive
field 710 Oe.We investigate the box-counting fractal dimension of a cluster of
elements with given orientation of magnetic moments. No fractal behavior is
found. Also, the damage spreading technique is applied to check the
criticality. We find that the consequences of a local flip of one magnetic
element remainlimited to a finite area. We conclude that the system does not
show a critical behavior.


  Nematic states are characterized by rotational symmetry breaking without
translational ordering. Recently, nematic superconductivity, in which the
superconducting gap spontaneously lifts the rotational symmetry of the lattice,
has been discovered. However the pairing mechanism and the mechanism
determining the nematic orientation remain unresolved. A first step is to
demonstrate control of the nematicity, through application of an external
symmetry-breaking field, to determine the sign and strength of coupling to the
lattice. Here, we report for the first time control of the nematic orientation
of the superconductivity of Sr$_x$Bi$_2$Se$_3$, through externally-applied
uniaxial stress. The suppression of subdomains indicates that it is the
$\Delta_{4y}$ state that is most favoured under compression along the basal
Bi-Bi bonds. These results provide an inevitable step towards understanding the
microscopic origin of the unique topological nematic superconductivity.


  We show that a nontrivial graph isomorphism problem of two undirected graphs,
and more generally, the permutation similarity of two given $n\times n$
matrices, is equivalent to equalities of volumes of the induced three convex
bounded polytopes intersected with a given sequence of balls, centered at the
origin with radii $t_i\in (0,\sqrt{n-1})$, where $\{t_i\}$ is an increasing
sequence converging to $\sqrt{n-1}$. These polytopes are characterized by $n^2$
inequalities in at most $n^2$ variables. The existence of fpras for computing
volumes of convex bodies gives rise to a semi-frpas of order $O^*(n^{14})$ at
most to find if given two undirected graphs are isomorphic.


  Rapid development of Internet technologies promotes traditional newspapers to
report news on social networks. However, people on social networks may have
different needs which naturally arises the question: whether can we analyze the
influence of writing style on news quality automatically and assist writers in
improving news quality? It's challenging due to writing style and 'quality' are
hard to measure. First, we use 'popularity' as the measure of 'quality'. It is
natural on social networks but brings new problems: popularity are also
influenced by event and publisher. So we design two methods to alleviate their
influence. Then, we proposed eight types of linguistic features (53 features in
all) according eight writing guidelines and analyze their relationship with
news quality. The experimental results show these linguistic features influence
greatly on news quality. Based on it, we design a news quality assessment model
on social network (SNQAM). SNQAM performs excellently on predicting quality,
presenting interpretable quality score and giving accessible suggestions on how
to improve it according to writing guidelines we referred to.


  The ultra-relativistic heavy-ion program at RHIC has shown that at
intermediate transverse momenta ($p_T \simeq 2$-6 GeV) standard (independent)
parton fragmentation can neither describe the observed baryon-to-meson ratios
nor the empirical scaling of the hadronic elliptic flow ($v_2$) according to
the number of valence quarks. Both aspects find instead a natural explanation
in a coalescence plus fragmentation approach to hadronization. After a brief
review of the main results for light quarks, we focus on heavy quarks showing
that a combined fragmentation and quark-coalescence framework is relevant also
here. Moreover, within relativistic Langevin simulations we find evidence for
the importance of heavy-light resonances in the Quark-Gluon Plasma (QGP) to
explain the strong energy loss and collective flow of heavy-quark spectra as
inferred from non-photonic electron observables. Such heavy-light resonances
can pave the way to a unified understanding of the microscopic structure of the
QGP and its subsequent hadronization by coalescence.


  Groups and clusters of galaxies occupy a special position in the hierarchy of
large-scale cosmic structures because they are the largest and the most massive
(from ~10^13 Msun to over 10^15 Msun) objects in the universe that have had
time to undergo gravitational collapse. The large masses of clusters imply that
their contents have been accreted from regions of ~8-40 comoving Mpc in size
and should thus be representative of the mean matter content of the universe.
During the next decade sensitive multi-wavelength observations should be able
to map the radial distributions of all main mass components (stars, cold, warm,
and hot gas and total mass) at z<~ 1 out to the virial radius. At the same
time, comparative studies of real and simulated cluster samples sould allow us
to use clusters as veritable astrophysical laboratories for studying galaxy
formation, as well as testing our theoretical models of structure formation and
underlying assumptions about fundamental physics governing the universe.


  Many magnetic point-group symmetries induce a topological classification on
crystalline insulators, dividing them into those that have a nonzero quantized
Chern-Simons magnetoelectric coupling ("axion-odd" or "topological"), and those
that do not ("axion-even" or "trivial"). For time-reversal or inversion
symmetries, the resulting topological state is usually denoted as a "strong
topological insulator" or an "axion insulator" respectively, but many other
symmetries can also protect this "axion $Z_2$" index. Topological states are
often insightfully characterized by choosing one crystallographic direction of
interest, and inspecting the hybrid Wannier (or equivalently, the non-Abelian
Wilson-loop) band structure, considered as a function of the two-dimensional
Brillouin zone in the orthogonal directions. Here, we systematically classify
the axion-quantizing symmetries, and explore the implications of such
symmetries on the Wannier band structure. Conversely, we clarify the conditions
under which the axion$Z_2$ index can be deduced from the Wannier band
structure. In particular, we identify cases in which a counting of Dirac
touchings between Wannier bands, or a calculation of the Chern number of
certain Wannier bands, or both, allows for a direct determination of the axion
$Z_2$ index. We also discuss when such symmetries impose a "flow" on the
Wannier bands, such that they are always glued to higher and lower bands by
degeneracies somewhere in the projected Brillouin zone, and the related
question of when the corresponding surfaces can remain gapped, thus exhibiting
a half-quantized surface anomalous Hall conductivity. Our formal arguments are
confirmed and illustrated in the context of tight-binding models for several
paradigmatic axion-odd symmetries including time reversal, inversion, simple
mirror, and glide mirror symmetries.


  We first investigate concentration and vanishing phenomena concerning Moser
type inequalities in the whole plane which involve complete and reduced Sobolev
norms. In particular we show that the critical Ruf inequality is equivalent to
an improved version of the subcritical Adachi-Tanaka inequality which we prove
to be attained. Then, we consider the limiting space
$\mathcal{D}^{1,2}(\mathbb{R}^2)$, completion of smooth compactly supported
functions with respect to the Dirichlet norm $\|\nabla\cdot\|_2$, and we prove
an optimal Lorentz-Zygmund type inequality with explicit extremals and from
which can be derived classical inequalities in $H^1(\mathbb{R}^2)$ such as the
Adachi-Tanaka inequality and a version of Ruf's inequality.


  Self-oscillating systems, described in classical dynamics as limit cycles,
are emerging as canonical models for driven dissipative nonequilibrium open
quantum systems, and as key elements in quantum technology. We consider a
family of models that interpolates between the classical textbook examples of
the Rayleigh and the van der Pol oscillators, and follow their transition from
the classical to the quantum domain, while properly formulating their
corresponding quantum descriptions. We derive an exact analytical solution for
the steady-state quantum dynamics of the simplest of these models, applicable
to any bosonic system---whether mechanical, optical, or otherwise---that is
coupled to its environment via single-boson and double-boson emission and
absorption. Our solution is a generalization to arbitrary temperature of
existing solutions for very-low, or zero, temperature, often misattributed to
the quantum van der Pol oscillator. We closely explore the classical to quantum
transition of the bifurcation to self-oscillations of this oscillator, while
noting changes in the dynamics and identifying features that are uniquely
quantum.


  Experimental results of the absolute air-fluorescence yield are given very
often in different units (photons/MeV or photons/m) and for different
wavelength intervals. In this work we present a comparison of available results
normalized to its value in photons/MeV for the 337 nm band at 1013 hPa and 293
K. The conversion of photons/m to photons/MeV requires an accurate
determination of the energy deposited by the electrons in the field of view of
the experimental set-up. We have calculated the energy deposition for each
experiment by means of a detailed Monte Carlo simulation and the results have
been compared with those assumed or calculated by the authors. As a result,
corrections to the reported fluorescence yields are proposed. These corrections
improve the compatibility between measurements in such a way that a reliable
average value with uncertainty at the level of 5% is obtained.


  Spherically symmetric solutions in Brans-Dicke theory of relativity with zero
coupling constant, $\omega=0$, are derived in the Schwarzschild line-element.
The solutions are obtained from a cubic transition equation with one small
parameter. The exterior space-time of one family of solutions is arbitrarily
close to the exterior Schwarzschild space-time. These nontopological solitons
have some similarity with soliton stars, and are proposed as candidates for
{\em approximate black holes} for the use in numerical relativity, in
particular for treatment of horizon boundary conditions.


  The multifractal formalism for measures in its original formulation is
checked for special classes of measures such as doubling, self-similar, and
Gibbs-like ones. Out of these classes, suitable conditions should be taken into
account to prove the validity of the multifractal formalism. In the present
work, a large class of measures satisfying a weak condition known as quasi
Ahlfors is considered in the framework of mixed multifractal analysis. A joint
multifractal analysis of finitely many quasi Ahlfors probability measures is
developed. Mixed variants of multifractal generalizations of Hausdorff and
packing measures, and corresponding dimensions are introduced. By applying
convexity arguments, some properties of these measures and dimensions are
established. Finally, an associated multifractal formalism is introduced and
proved to hold for the class of quasi Ahlfors measures.


  Finding optimal parameter configurations for tunable GPU kernels is a
non-trivial exercise for large search spaces, even when automated. This poses
an optimization task on a non-convex search space, using an expensive to
evaluate function with unknown derivative. These characteristics make a good
candidate for Bayesian Optimization, which has not been applied to this problem
before. However, the application of Bayesian Optimization to this problem is
challenging. We demonstrate how to deal with the rough, discrete, constrained
search spaces, containing invalid configurations. We introduce a novel
contextual variance exploration factor, as well as new acquisition functions
with improved scalability, combined with an informed acquisition function
selection mechanism. By comparing the performance of our Bayesian Optimization
implementation on various test cases to the existing search strategies in
Kernel Tuner, as well as other Bayesian Optimization implementations, we
demonstrate that our search strategies generalize well and consistently
outperform other search strategies by a wide margin.