  A real square matrix $A$ is called a $Q$-matrix if the linear complementarity
problem $LCP(A,q)$ has a solution for all $q \in \mathbb{R}^n$. This means that
for every vector $q$ there exists a vector $x$ such that $x \geq 0, y=Ax+q\geq
0$ and $x^Ty=0$. A well known result of Karamardian states that if the problems
$LCP(A,0)$ and $LCP(A,d)$ for some $d\in \mathbb{R}^n, d >0$ have only the zero
solution, then $A$ is a $Q$-matrix. By relaxing the condition on $d$ and
imposing a condition on the solution vector $x$ in the two problems as above,
the authors introduce a new class of matrices called Karamardian matrices,
requiring that these two modified problems have only zero as a solution. In
this article, a systematic treatment of Karamardian matrices is undertaken.
Among other things, it is shown how Karamardian matrices have properties that
are analogous to those of $Q$-matrices. A subclass of a recently introduced
notion of $P_{\#}$-matrices is shown to possess the Karamardian property, and
for this reason we undertake a thorough study of $P_{\#}$-matrices and make
some fundamental contributions.


  We analyze the prospects of the Tevatron for finding a Higgs boson in the two
photon decay mode. We conclude that the Standard Model (SM) Higgs boson will
likely not be discovered in this mode. However, we motivate several theories
beyond the SM, including the MSSM, that predict a Higgs boson with enhanced
branching fractions into photons, and calculate the luminosity needed to
discover a general Higgs boson at the Tevatron by a two-photon invariant mass
peak at large transverse momentum. We find that a high luminosity Tevatron will
play a significant role in discovering or constraining these theories.


  Low-mass X-ray binaries (LMXBs) have been studied in the Galaxy since the
beginning of X-ray astronomy. A lot has been learned about these bright X-ray
sources, but significant questions are still open. These questions are related
to the origin and evolution of LMXBs, dynamical evolution in globular clusters
(GC) or evolution of native field binaries, and on how their properties may
depend on those of the parent stellar population. The discovery of several
populations LMXB populations in elliptical galaxies with Chandra gives us tools
to look at these sources in a new way.


  We propose a hybrid quantum approach to threshold and binarize a grayscale
image through unsharp measurements (UM) relying on image histogram. Generally,
the histograms are characterized by multiple overlapping normal distributions
corresponding to objects, or image features with small but significant
overlaps, making it challenging to establish suitable thresholds. The proposed
methodology uses peaks of the overlapping Gaussians and the distance between
neighboring local minima as the variance, based on which the UM parameters are
chosen, that maps the normal distribution into a localized delta function. To
demonstrate its efficacy, subsequent implementation is done on noisy quantum
environments in Qiskit. This process is iteratively repeated for a multimodal
histogram to obtain more thresholds, which are then applied to various
life-like pictures to get high-contrast images, resulting in comparable peak
signal-to-noise ratio and structural similarity index measure values. The
obtained thresholds are used to binarize a grayscale image by using novel
enhanced quantum image representation integrated with a threshold encoder and
an efficient quantum comparator (QC) that depicts the whole binarized picture.
This approach significantly reduces the complexity of the proposed QC and of
the whole algorithm when compared to earlier models.


  We extend the discontinuous Galerkin (DG) framework to the analysis of
first-order hyperbolic and advection-dominated problems posed on implicitly
defined surfaces. The focus will be on the hyperbolic part, which is
discretised using a "discrete surface" generalisation of the jump-stabilised
upwind flux. A key issue arising in the analysis (which does not appear in the
planar setting) is the treatment of the discrete velocity field, choices of
which play an important role in the stability of the scheme. We then prove
optimal error estimates in an appropriate norm given a number of assumptions on
the discrete velocity field, which are then investigated and discussed in more
detail. The theoretical results are verified numerically for a number of test
problems exhibiting advection-dominated behaviour.


  Individual members of an ensemble of identical systems coupled to a common
probe can become entangled with one another, even when they do not interact
directly. We investigate how this type of multipartite entanglement is
generated in the context of a system consisting of two two-level atoms
resonantly coupled to a single mode of the electromagnetic field. The dynamical
evolution is studied in terms of the entanglements in the different bipartite
partitions of the system, as quantified by the I-tangle. We also propose a
generalization of the so-called residual tangle that quantifies the inherent
three-body correlations in our tripartite system. This enables us to completely
characterize the phenomenon of entanglement sharing in the case of the two-atom
Tavis-Cummings model, a system of both theoretical and experimental interest.


  A joint fit to neutrino-nucleon scattering and pion electroproduction data is
performed to evaluate the nucleon axial form factor in the two-component model
consisting of a three-quark intrinsic structure surrounded by a meson cloud.
Further constrains on the model are obtained by re-evaluating the
electromagnetic form factor using electron scattering data. The results of the
axial form factor show sizable differences with respect to the widely used
dipole model. The impact of such changes on the Charged-Current Quasi-Elastic
neutrino-nucleus cross-section is evaluated in the SuSAv2 nuclear model, based
on the Relativistic Mean Field and including the contribution of two-body
currents. How the different parametrizations of the axial form factor affect
the cross-section prediction is assessed in full details and comparisons to
recent T2K and MINERvA data are presented.


  The Heun-Racah operator is diagonalized with the help of the modified
algebraic Bethe ansatz. This operator is the most general bilinear expression
in two generators of the Racah algebra. A presentation of this algebra is given
in terms of dynamical operators, and allows the construction of Bethe vectors
for the Heun-Racah operator. The associated Bethe equations are derived for
both the homogeneous and inhomogeneous cases.


  This work investigates the importance of verification and validation (V&V) to
achieve predictive scale-resolving simulations (SRS) of turbulence, i.e.,
computations capable of resolving a fraction of the turbulent flow scales.
Toward this end, we propose a novel but simple V&V strategy based on grid and
physical resolution refinement studies that can be used even when the exact
initial flow conditions are unknown, or reference data are unavailable. This is
particularly relevant for transient and transitional flow problems, as well as
for the improvement of turbulence models. We start by presenting a literature
survey of results obtained with distinct SRS models for flows past circular
cylinders. It confirms the importance of V&V by illustrating a large
variability of results, which is independent of the selected mathematical model
and Reynolds number. The proposed V&V strategy is then used on three
representative problems of practical interest. The results illustrate that it
is possible to conduct reliable verification and validation exercises with SRS
models, and evidence the importance of V&V to predictive SRS of turbulence.
Most notably, the data also confirm the advantages and potential of the
proposed V&V strategy: separate assessment of numerical and modeling errors,
enhanced flow physics analysis, identification of key flow phenomena, and
ability to operate when the exact flow conditions are unknown or reference data
are unavailable.


  The most effective data-driven methods for human activities recognition (HAR)
are based on supervised learning applied to the continuous stream of sensors
data. However, these methods perform well on restricted sets of activities in
domains for which there is a fully labeled dataset. It is still a challenge to
cope with the intra- and inter-variability of activity execution among
different subjects in large scale real world deployment. Semi-supervised
learning approaches for HAR have been proposed to address the challenge of
acquiring the large amount of labeled data that is necessary in realistic
settings. However, their centralised architecture incurs in the scalability and
privacy problems when the process involves a large number of users. Federated
Learning (FL) is a promising paradigm to address these problems. However, the
FL methods that have been proposed for HAR assume that the participating users
can always obtain labels to train their local models. In this work, we propose
FedHAR: a novel hybrid method for HAR that combines semi-supervised and
federated learning. Indeed, FedHAR combines active learning and label
propagation to semi-automatically annotate the local streams of unlabeled
sensor data, and it relies on FL to build a global activity model in a scalable
and privacy-aware fashion. FedHAR also includes a transfer learning strategy to
personalize the global model on each user. We evaluated our method on two
public datasets, showing that FedHAR reaches recognition rates and
personalization capabilities similar to state-of-the-art FL supervised
approaches. As a major advantage, FedHAR only requires a very limited number of
annotated data to populate a pre-trained model and a small number of active
learning questions that quickly decrease while using the system, leading to an
effective and scalable solution for the data scarcity problem of HAR.


  We introduce the new combinatorial approach of plethystic type of tableaux,
as a method to understand coefficients of Schur functions appearing in
plethysms $s_\nu[h_\lambda]$ and $s_{\nu}[e_{\lambda}]$, for any partitions
$\lambda$ and $\nu$. We first give general results about this approach, then
use results on tableaux, ribbon tableaux and integer points in polytopes to
understand the case where $\nu$ is a partition of $3$ and $\lambda$ has one
part. We then use a \textit{Kronecker map} to extend these results to any
partition $\lambda$.


  The emergence of Big Data in recent years has resulted in a growing need for
efficient data processing solutions. While infrastructures with sufficient
compute power are available, the I/O bottleneck remains. The Linux page cache
is an efficient approach to reduce I/O overheads, but few experimental studies
of its interactions with Big Data applications exist, partly due to limitations
of real-world experiments. Simulation is a popular approach to address these
issues, however, existing simulation frameworks do not simulate page caching
fully, or even at all. As a result, simulation-based performance studies of
data-intensive applications lead to inaccurate results.
  In this paper, we propose an I/O simulation model that includes the key
features of the Linux page cache. We have implemented this model as part of the
WRENCH workflow simulation framework, which itself builds on the popular
SimGrid distributed systems simulation framework. Our model and its
implementation enable the simulation of both single-threaded and multithreaded
applications, and of both writeback and writethrough caches for local or
network-based filesystems. We evaluate the accuracy of our model in different
conditions, including sequential and concurrent applications, as well as local
and remote I/Os. We find that our page cache model reduces the simulation error
by up to an order of magnitude when compared to state-of-the-art, cacheless
simulations.


  The universality of the strange metal phase in many quantum materials is
often attributed to the presence of a quantum critical point (QCP), a
zero-temperature phase transition ruled by quantum fluctuations. In cuprates,
where superconductivity hinders direct QCP observation, indirect evidence comes
from the identification of fluctuations compatible with the strange metal
phase. Here we show that the recently discovered charge density fluctuations
(CDF) possess the right properties to be associated to a quantum phase
transition. Using resonant x-ray scattering, we studied the CDF in two families
of cuprate superconductors across a wide doping range (up to $p$=0.22). At
$p^*\approx$0.19, the putative QCP, the CDF intensity peaks, and the
characteristic energy $\Delta$ is minimum, marking a wedge-shaped region in the
phase diagram indicative of a quantum critical behavior, albeit with anomalies.
These findings strengthen the role of charge order in explaining strange metal
phenomenology and provide insights into high-temperature superconductivity.


  We classify the irreducible integrable modules for the twisted toroidal
extended affine Lie algebras with fnite diemnsional weight spaces where the
fnite dimensional center acts trivially. We have proved that the entire central
extension part acts trivially on the modules and our modules turn out to be
highest weight modules.


  We give upper and lower bounds for the spectral radius of a nonnegative
matrix by using its average 2-row sums, and characterize the equality cases if
the matrix is irreducible. We also apply these bounds to various nonnegative
matrices associated with a graph, including the adjacency matrix, the signless
Laplacian matrix, the distance matrix, the distance signless Laplacian matrix,
and the reciprocal distance matrix.


  Forecasting time series data is an important subject in economics, business,
and finance. Traditionally, there are several techniques to effectively
forecast the next lag of time series data such as univariate Autoregressive
(AR), univariate Moving Average (MA), Simple Exponential Smoothing (SES), and
more notably Autoregressive Integrated Moving Average (ARIMA) with its many
variations. In particular, ARIMA model has demonstrated its outperformance in
precision and accuracy of predicting the next lags of time series. With the
recent advancement in computational power of computers and more importantly
developing more advanced machine learning algorithms and approaches such as
deep learning, new algorithms are developed to forecast time series data. The
research question investigated in this article is that whether and how the
newly developed deep learning-based algorithms for forecasting time series
data, such as "Long Short-Term Memory (LSTM)", are superior to the traditional
algorithms. The empirical studies conducted and reported in this article show
that deep learning-based algorithms such as LSTM outperform traditional-based
algorithms such as ARIMA model. More specifically, the average reduction in
error rates obtained by LSTM is between 84 - 87 percent when compared to ARIMA
indicating the superiority of LSTM to ARIMA. Furthermore, it was noticed that
the number of training times, known as "epoch" in deep learning, has no effect
on the performance of the trained forecast model and it exhibits a truly random
behavior.


  We present Hubble Space Telescope optical and near-ultraviolet transmission
spectra of the transiting hot-Jupiter HD189733b, taken with the repaired Space
Telescope Imaging Spectrograph (STIS) instrument. The resulting spectra cover
the range 2900-5700 Ang and reach per-exposure signal-to-noise levels greater
than 11,000 within a 500 Ang bandwidth. We used time series spectra obtained
during two transit events to determine the wavelength dependance of the
planetary radius and measure the exoplanet's atmospheric transmission spectrum
for the first time over this wavelength range. Our measurements, in conjunction
with existing HST spectra, now provide a broadband transmission spectrum
covering the full optical regime. The STIS data also shows unambiguous evidence
of a large occulted stellar spot during one of our transit events, which we use
to place constraints on the characteristics of the K dwarf's stellar spots,
estimating spot temperatures around Teff~4250 K. With contemporaneous
ground-based photometric monitoring of the stellar variability, we also measure
the correlation between the stellar activity level and transit-measured
planet-to-star radius contrast, which is in good agreement with predictions. We
find a planetary transmission spectrum in good agreement with that of Rayleigh
scattering from a high-altitude atmospheric haze as previously found from HST
ACS camera. The high-altitude haze is now found to cover the entire optical
regime and is well characterised by Rayleigh scattering. These findings suggest
that haze may be a globally dominant atmospheric feature of the planet which
would result in a high optical albedo at shorter optical wavelengths.


  Given $A_n:=\frac{1}{\sqrt{n}}(a_{ij})$ an $n\times n$ symmetric random
matrix, with elements above the diagonal given by i.i.d. random variables
having mean zero and unit variance. It is known that when
$\lim_{x\to\infty}x^4\mathbb{P}(|a_{ij}|>x)=0$, then fluctuation of the largest
eigenvalue of $A_n$ follows a Tracy-Widom distribution. When the law of
$a_{ij}$ is regularly varying with index $\alpha\in(0,4)$, then the largest
eigenvalue has a Fr\'echet distribution. An intermediate regime is recently
uncovered in \cite{diaconu2023more}: when
$\lim_{x\to\infty}x^4\mathbb{P}(|a_{ij}|>x)=c\in(0,\infty)$, then the law of
the largest eigenvalue follows a deformed Fr\'echet distribution. In this work
we vastly extend the scope where the latter distribution may arise. We show
that the same deformed Fr\'echet distribution arises (1) for sparse Wigner
matrices with an average of $n^{O(1)}$ nonzero entries on each row; (2) for
periodically banded Wigner matrices with bandwidth $d_n=n^{O(1)}$; and more
generally for weighted adjacency matrices of any $k_n$-regular graphs with
$k_n=n^{O(1)}$. In all these cases, we further prove that the joint
distribution of the finitely many largest eigenvalues of $A_n$ form a deformed
Poisson process, and that eigenvectors of the outlying eigenvalues of $A_n$ are
localized, implying a mobility edge phenomenon at the spectral edge $2$. The
sparser case with average degree $n^{o(1)}$ is also explored. Our technique
extends to sample covariance matrices, proving for the first time that its
largest eigenvalue still follows a deformed Fr\'echet distribution, assuming
the matrix entries satisfy
$\lim_{x\to\infty}x^4\mathbb{P}(|a_{ij}|>x)=c\in(0,\infty)$.


  Multi-camera multiple people tracking has become an increasingly important
area of research due to the growing demand for accurate and efficient indoor
people tracking systems, particularly in settings such as retail, healthcare
centers, and transit hubs. We proposed a novel multi-camera multiple people
tracking method that uses anchor-guided clustering for cross-camera
re-identification and spatio-temporal consistency for geometry-based
cross-camera ID reassigning. Our approach aims to improve the accuracy of
tracking by identifying key features that are unique to every individual and
utilizing the overlap of views between cameras to predict accurate trajectories
without needing the actual camera parameters. The method has demonstrated
robustness and effectiveness in handling both synthetic and real-world data.
The proposed method is evaluated on CVPR AI City Challenge 2023 dataset,
achieving IDF1 of 95.36% with the first-place ranking in the challenge. The
code is available at: https://github.com/ipl-uw/AIC23_Track1_UWIPL_ETRI.


  In this work we prove that the unique 1-convex solution of the Monge problem
contructed from the solution of the Monge-Kantorovitch problem between the
Wiener measure and a target measure which has a log-concave density w.r.to the
Wiener measure is also the strong solution of the Monge-Ampere equation in the
frame of infinite dimensional Frechet spaces. We enhance also the polar
factorization results of the mappings which transform a spread measure to
another one of finite Wasserstein distance. Finally we calculate the
semimartingale decomposition of the transport process with respect to its
natural filtration and make the connection between the curved Brownian motion
and the polar decomposition of the corresponding shifts.


  In this paper, we test the hypothesis that interesting events in unstructured
videos are inherently audiovisual. We combine deep image representations for
object recognition and scene understanding with representations from an
audiovisual affect recognition model. To this set, we include content agnostic
audio-visual synchrony representations and mel-frequency cepstral coefficients
to capture other intrinsic properties of audio. These features are used in a
modular supervised model. We present results from two experiments: efficacy
study of single features on the task, and an ablation study where we leave one
feature out at a time. For the video summarization task, our results indicate
that the visual features carry most information, and including audiovisual
features improves over visual-only information. To better study the task of
highlight detection, we run a pilot experiment with highlights annotations for
a small subset of video clips and fine-tune our best model on it. Results
indicate that we can transfer knowledge from the video summarization task to a
model trained specifically for the task of highlight detection.


  We study linear-perturbation equations for the two-body system of a charged
dilaton black hole, of which dilaton coupling constant is $\alpha$, and a
static particle with mass $m$, electric charge $q$, and dilatonic charge $\beta
m$. We find that a consistent condition for the coupled equations corresponds
to the equilibrium condition of the test particle. The expressions of classical
fields are given in closed analytical formulas in the most interesting case
with $\beta=\alpha$. We examine the electrical field around a charged dilaton
black hole especially in the limit of the maximum electric charge and we find
the electric Meissner effect which has been found for the Reissner-Nordstr\"om
black hole in the Einstein-Maxwell system.


  We present the results of the study of an optical resonant cell filled by a
vapor of the Rb atoms and coated with a non-stick polydimethylsiloxane (PDMS)
polymer. We show that it is possible to define correctly the diffusion
coefficient of the atoms in the coating, using geometric parameters of the cell
and the vapor density in the cell volume only. The dependence of the diffusion
coefficient on the cell curing time is presented. It is shown that the
mysterious cell curing process can be explained in terms of the polymerization
of the polymer coating by alkali atoms. Anomalous long dwell time of the Rb
atoms on the PDMS coating is discussed as well.


  We review recent progress in understanding the different spatial broken
symmetries that occur in the normal states of the family of charge-transfer
solids (CTS) that exhibit superconductivity (SC), and discuss how this
knowledge gives insight to the mechanism of the unconventional SC in these
systems. We show that a unified theory of the diverse broken symmetry states
necessarily requires explicit incorporation of strong electron-electron
interactions and lattice discreteness, and most importantly, the correct
bandfilling of one-quarter. Uniquely in the quarter-filled band, there is a
very strong tendency to form nearest neighbor spin-singlets, in both one and
two dimensions. The tendency to spin-singlets, a quantum effect, drives a
commensurate charge-order in the correlated quarter-filled band. This
charge-ordered spin-singlet, which we label as a paired-electron crystal (PEC),
is different from and competes with both the antiferromagnetic state and the
Wigner crystal of single electrons. Further, unlike these classical broken
symmetries, the PEC is characterized by a spin gap. The tendency to the PEC in
two dimensions is enhanced by lattice frustration. Following this
characterization of the spatial broken symmetries, we critically reexamine
spin-fluctuation and resonating valence bond theories of frustration-driven SC
within half-filled band Hubbard and Hubbard-Heisenberg Hamiltonians for the
superconducting CTS. We develop a valence-bond theory of SC within which the
superconducting state is reached by the destabilization of the PEC by
additional pressure-induced lattice frustration that makes the spin-singlets
mobile. Our proposed mechanism for SC is the same for CTS in which the
proximate semiconducting state is antiferromagnetic instead of charge-ordered,
with the only difference that SC in the former is generated via a fluctuating
spin-singlet state as opposed to static PEC.


  We use a one-dimensional model system to compare the predictions of two
different 'yardsticks' to compute the position of a particle from its quantum
field theoretical state. Based on the first yardstick (defined by the
Newton-Wigner position operator), the spatial density can be arbitrarily narrow
and its time-evolution is superluminal for short time intervals. Furthermore,
two spatially distant particles might be able to interact with each other
outside the light cone, which is manifested by an asymmetric spreading of the
spatial density. The second yardstick (defined by the quantum field operator)
does not permit localized states and the time evolution is subluminal.


  We examine the relationship between source radio luminosity and kinetic power
in Active Galactic Nucleus (AGN) jets. We show that neglecting various loss
processes can introduce a systematic bias in the jet powers inferred from radio
luminosities for a sample of radio galaxies. This bias can be corrected for by
considering source size as well as radio luminosity; effectively the source
size acts as a proxy for source age. Based on a sample of FR-II radio sources
with jet powers derived from the measured hotspot parameters, we empirically
determine a new expression for jet power that accounts for the source size,
Q_jet / 10^{36} W = 1.5 (L_151 / 10^{27} W/Hz)^{0.8} (1+z)^{1.0} (D /
kpc)^{0.58 \pm 0.17}, where D is source size and L_151 the 151 MHz radio
luminosity. By comparing a flux-limited and volume-limited sample, we show that
any derived radio luminosity - jet power relation depends sensitively on sample
properties, in particular the source size distribution and the size-luminosity
correlation inherent in the sample. Such bias will affect the accuracy of the
kinetic luminosity function derived from lobe radio luminosities and should be
treated with caution.


  Lagrange's four-square theorem states that every natural number $n$ can be
represented as the sum of four integer squares: $n=x_1^2+x_2^2+x_3^2+x_4^2$.
Ramanujan generalized Lagrange's result by providing, up to equivalence, all
$54$ quadratic forms $ax_1^2+bx_2^2+cx_3^2+dx_4^2$ that represent all positive
integers. In this article, we prove the following extension of Lagrange's
theorem: given a prime number $p$ and $v_1\in Z^4$, $\dots$, $v_k\in Z^4$,
$1\leq k\leq 3$, such that $\|v_i\|^2=p$ for all $1\leq i\leq k$ and $\langle
v_i|v_j\rangle=0$ for all $1\leq i<j\leq k$, then there exists
$v=(x_1,x_2,x_3,x_4)\in Z^4$ such that $\langle v_i|v\rangle=0$ for all $1\leq
i\leq k$ and $$ \|v\|^2=x_1^2+x_2^2+x_3^2+x_4^2=p $$ This means that, in $Z^4$,
any system of orthogonal vectors of norm $p$ can be completed to a base. We
conjecture that the result holds for every norm $p\geq 1$. The problem comes up
from the study of a discrete quantum computing model in which the qubits have
Gaussian integers as coordinates, except for a normalization factor
$\sqrt{2^{-k}}$.


  We consider the online and nonparametric detection of abrupt and persistent
anomalies, such as a change in the regular system dynamics at a time instance
due to an anomalous event (e.g., a failure, a malicious activity). Combining
the simplicity of the nonparametric Geometric Entropy Minimization (GEM) method
with the timely detection capability of the Cumulative Sum (CUSUM) algorithm we
propose a computationally efficient online anomaly detection method that is
applicable to high-dimensional datasets, and at the same time achieve a
near-optimum average detection delay performance for a given false alarm
constraint. We provide new insights to both GEM and CUSUM, including new
asymptotic analysis for GEM, which enables soft decisions for outlier
detection, and a novel interpretation of CUSUM in terms of the discrepancy
theory, which helps us generalize it to the nonparametric GEM statistic. We
numerically show, using both simulated and real datasets, that the proposed
nonparametric algorithm attains a close performance to the clairvoyant
parametric CUSUM test.


  Piezoelectric energy harvesters (PEHs) can be used as an additional power
supply for a Structural Health Monitoring (SHM) system. Its design can be
optimised for the best performance; however, the optimal design depends on the
input vibration, e.g. acceleration of a bridge due to wind loads and passing
traffic. In previous studies, we have shown that optimal design tunes to some
predominant frequency of the signal spectrum. However, our previous study was
limited to a single location of a PEH on a bridge. In this work, we extend the
rigorous optimisation framework to include the effect of the PEH's location.
The optimisation framework uses the PEH plate model discretised by IsoGeometric
Analysis (IGA) and coupled with the Particle Swarm Optimisation algorithm to
find the designs with maximum energy outputs for many acceleration histories,
extracted from the recorded dynamic response data of a real cable-stayed bridge
in Australia. Then, clustering is performed to find several best candidates for
the entire bridge. An additional study is performed to quantify the effect of
traffic intensity on the produced energy. It is shown that variation in traffic
volume throughout the 24hr time window leads to variation in optimal PEH
designs. The study concludes the impact of location and traffic on energy
harvesting by identifying the optimal PEH design and placement throughout the
bridge structure. The results indicate that the key factors of maximising
energy harvesting efficiency are related to the input excitation and the mode
of vibration being excited. The position of maximum displacement in the
vibration mode corresponds to the best location for energy harvesting. Also,
the change in traffic intensity affects the amount of convertible mechanical
energy and also directs the fundamental frequency of a PEH to shift within a
specific range of frequencies to achieve the highest energy conversion.


  The concept of dataspaces aims to facilitate secure and sovereign data
exchange among multiple stakeholders. Technical implementations known as
"connectors" support the definition of usage control policies and the
verifiable enforcement of such policies. This paper provides an overview of
existing literature and reviews current open-source dataspace connector
implementations that are compliant with the International Data Spaces (IDS)
standard. To assess maturity and readiness, we review four implementations with
regard to their architecture, underlying data model and usage control language.


  It has been a long history in testing whether a mean vector with a fixed
dimension has a specified value. Some well-known tests include the Hotelling
$T^2$-test and the empirical likelihood ratio test proposed by Owen [Biometrika
75 (1988) 237-249; Ann. Statist. 18 (1990) 90-120]. Recently, Hotelling
$T^2$-test has been modified to work for a high-dimensional mean, and the
empirical likelihood method for a mean has been shown to be valid when the
dimension of the mean vector goes to infinity. However, the asymptotic
distributions of these tests depend on whether the dimension of the mean vector
is fixed or goes to infinity. In this paper, we propose to split the sample
into two parts and then to apply the empirical likelihood method to two
equations instead of d equations, where d is the dimension of the underlying
random vector. The asymptotic distribution of the new test is independent of
the dimension of the mean vector. A simulation study shows that the new test
has a very stable size with respect to the dimension of the mean vector, and is
much more powerful than the modified Hotelling $T^2$-test.


  To understand the whole set of positive and null data on the
Theta+(1530)-production, we suggest the hypothesis that multiquark hadrons are
mainly generated from many-quark states, which emerge either as short-term
hadron fluctuations, or as hadron remnants in hard processes. This approach
allows us to describe both non-observation of the Theta+ in current null
experiments and peculiar features of its production in positive experiments.
Further, we are able to propose new experiments that might be decisive for the
problem of the Theta+ existence. Distributions of the Theta+ in such
experiments can give important information both on higher Fock components of
conventional hadrons and about structure and hadronization properties of hadron
remnants produced in hard processes. We also explain that description of
multiquark hadrons may require a modified form of the constituent quark model,
with quark masses and couplings being intermediate between their values for the
familiar constituent quarks and the current ones.


  We study spectral properties of a non-Hermitian Hamiltonian describing a
quantum particle propagating in a random imaginary scalar potential. Cast in
the form of an effective field theory, we obtain an analytical expression for
the ensemble averaged one-particle Green function from which we obtain the
density of complex eigenvalues. Based on the connection between non-Hermitian
quantum mechanics and the statistical mechanics of polymer chains, we determine
the distribution function of a self-interacting polymer in dimensions $d>4$.


  We design and analyze an approximation method for
advection-diffusion-reaction equations where the (generalized) degrees of
freedom are polynomials of order $k\ge0$ at mesh faces. The method hinges on
local discrete reconstruction operators for the diffusive and advective
derivatives and a weak enforcement of boundary conditions. Fairly general
meshes with polytopal and nonmatching cells are supported. Arbitrary polynomial
orders can be considered, including the case $k=0$ which is closely related to
Mimetic Finite Difference/Mixed-Hybrid Finite Volume methods. The error
analysis covers the full range of P\'eclet numbers, including the delicate case
of local degeneracy where diffusion vanishes on a strict subset of the domain.
Computational costs remain moderate since the use of face unknowns leads to a
compact stencil with reduced communications. Numerical results are presented.


  Regarding a particular class of pure $F(R)$ gravity in three dimensions, we
obtain an analytical rotating Lifshitz-like black hole solution. We first
investigate some geometrical properties of the obtained solution that reduces
to a charged rotating BTZ black hole in a special limit. Then, we study the
optical features of such a black hole like the photon orbit and the energy
emission rate and discuss how electric charge, angular momentum, and exponents
affect them. In order to have an acceptable optical behavior, we should apply
some constraints on the exponents. We continue our investigation with the study
of the thermodynamic behavior of the solutions in the extended phase space and
examine the validity of the first law of thermodynamics besides local thermal
stability through using of heat capacity. Evaluating the existence of van der
Waals-like phase transition, we obtain critical quantities and show how they
change under the variation of black hole parameters. Finally, we construct a
holographic heat engine of such a black hole and obtain its efficiency in a
cycle. By comparing the obtained efficiency with the Carnot one, we examine the
second law of thermodynamics.


  In this report, we present the ReLER@ZJU1 submission to the Ego4D Moment
Queries Challenge in ECCV 2022. In this task, the goal is to retrieve and
localize all instances of possible activities in egocentric videos. Ego4D
dataset is challenging for the temporal action localization task as the
temporal duration of the videos is quite long and each video contains multiple
action instances with fine-grained action classes. To address these problems,
we utilize a multi-scale transformer to classify different action categories
and predict the boundary of each instance. Moreover, in order to better capture
the long-term temporal dependencies in the long videos, we propose a
segment-level recurrence mechanism. Compared with directly feeding all video
features to the transformer encoder, the proposed segment-level recurrence
mechanism alleviates the optimization difficulties and achieves better
performance. The final submission achieved Recall@1,tIoU=0.5 score of 37.24,
average mAP score of 17.67 and took 3-rd place on the leaderboard.


  We report the first experimental observation of reversals of a dynamo field
generated in a laboratory experiment based on a turbulent flow of liquid
sodium. The magnetic field randomly switches between two symmetric solutions B
and -B. We observe a hierarchy of time scales similar to the Earth's magnetic
field: the duration of the steady phases is widely distributed, but is always
much longer than the time needed to switch polarity. In addition to reversals
we report excursions. Both coincide with minima of the mechanical power driving
the flow. Small changes in the flow driving parameters also reveal a large
variety of dynamo regimes.


  In terms of the replica method we consider the low temperature limit of (2+1)
directed polymers in a random potential. The proposed approach allows to
compute the scaling exponent $\theta$ of the free energy fluctuations as well
as the left tail of its probability distribution function. It is argued that
$\theta = 1/4$ which is slightly different from the zero-temperature numerical
value which is close to $0.241$.


  In a previous paper [Phys. Rev. E 90, 022506 (2014)], we had studied
thermodynamic and structural properties of a three-dimensional simple-cubic
lattice model with dipolar-like interaction, truncated at nearest-neighbor
separation, for which the existence of an ordering transition at finite
temperature had been proven mathematically; here we extend our investigation
addressing the full-ranged counterpart of the model, for which the critical
behavior had been investigated theoretically and experimentally. In addition
the existence of an ordering transition at finite temperature had been proven
mathematically as well. Both models exhibited the same continuously degenerate
ground-state configuration, possessing full orientational order with respect to
a suitably defined staggered magnetization (polarization), but no nematic
second-rank order; in both cases, thermal fluctuations remove the degeneracy,
so that nematic order does set in at low but finite temperature via a mechanism
of order by disorder. On the other hand, there were recognizable quantitative
differences between the two models as for ground-state energy and critical
exponent estimates; the latter were found to agree with early Renormalization
Group calculations and with experimental results.


  This article is devoted to the variational study of two functions defined
over some Teichmueller spaces of hyperbolic surfaces. One is the systole of
geodesic loops based at some fixed point, and the other one is the systole of
arcs.\par For each of them we determine all the critical points. It appears
that the systole of arcs is a topological Morse function, whereas the systole
of geodesic loops have some degenerate critical points. However, these
degenerate critical points are in some sense the obvious one, and they do not
interfere in the variational study of the function.\par At a nondegenerate
critical point, the systolic curves (arcs or loops depending on the function
involved) decompose the surface into regular polygons. This enables a complete
classification of these points, and some explicit computations. In particular
we determine the global maxima of these functions. This generalizes optimal
inequalities due to Bavard and Deblois. We also observe that there is only one
local maximum, this was already proved in some cases by Deblois.\par Our
approach is based on the geometric Vorono\''i theory developed by Bavard. To
use this variational framework, one has to show that the length functions (of
arcs or loops) have positive definite Hessians with respect to some system of
coordinates for the Teichm\''uller space. Following a previous work, we choose
Bonahon's shearing coordinates, and we compute explicitly the Hessian of the
length functions of geodesic loops. Then we use a characterization of the
nondegenerate critical points due to Akrout.


  The A-hypergeometric system was introduced by Gel'fand, Kapranov and
Zelevinsky in the 1980's. Among several classes of A-hypergeometric functions,
those for 1-simplex $\times$ (n-1)-simplex are known to be a very nice class.
We will study an incomplete analog of this class.


  In this work we study the phase transitions between the planar charged AdS
black hole and the planar charged soliton. The planar soliton is obtained as a
double analytic continuation of the charged black hole metric, which also
involves analytically continuing the electric charge. We show that there are
phase transitions between both solutions depending on the electric potential,
magnetic flux and temperature. The analysis is carried out in the
Grand-Canonical ensemble.


  Let $k$ be a field and let $\Lambda$ be an indecomposable finite dimensional
$k$-algebra such that there is a stable equivalence of Morita type between
$\Lambda$ and a self-injective split basic Nakayama algebra over $k$. We show
that every indecomposable finitely generated $\Lambda$-module $V$ has a
universal deformation ring $R(\Lambda,V)$ and we describe $R(\Lambda,V)$
explicitly as a quotient ring of a power series ring over $k$ in finitely many
variables. This result applies in particular to Brauer tree algebras, and hence
to $p$-modular blocks of finite groups with cyclic defect groups.


  In this paper I study a variant of the general vertex coloring problem called
precoloring. Specifically, I study graph precolorings, by developing new
theory, for characterizing the minimal non-extensible precolorings. It is
interesting per se that, for graphs of arbitrarily large chromatic number, the
minimal number of colored vertices, in a non-extensible precoloring, remains
constant; only two vertices $u,v$ suffice. Here, the relation between such
$u,v$ is called an implicit-relation, distinguishing two cases: (i)
implicit-edges where $u,v$ are precolored with the same color and (ii)
implicit-identities where $u,v$ are precolored distinct.


  In this paper, we consider half-flat $SU(3)$-structures and the subclasses of
coupled and double structures. In the general case we show that the intrinsic
torsion form $w_1^-$ is constant in each of the two subclasses. We then
consider the problem of finding half-flat structures inducing Einstein metrics
on homogeneous spaces. We give an example of a left invariant half-flat (non
coupled and non double) structure inducing an Einstein metric on $S^3\times
S^3$ and we show there does not exist any left invariant coupled structure
inducing an ${\rm Ad}(S^1)$-invariant Einstein metric on it. Finally, we show
that there are no coupled structures inducing the Einstein metric on Einstein
solvmanifolds and on homogeneous Einstein manifolds of nonpositive sectional
curvature.


  There are different models based on the gauge symmetry $SU(3)_C \otimes
SU(3)_L \otimes U(1)_X$ (331) some of them includes exotic particles and others
are constructed without any exotic charges assigned to the fermionic spectrum.
Each model build up on 331 symmetry has its own interesting properties
according to the representations of the gauge group used for the fermionic
spectrum; that is the main reason to explore and identify the possible sources
of flavor changing neutral currents and lepton flavor violation at tree level.


  We show the explicit expression of the geometric phase for $n$-partite
Gaussian states. In our analysis, the covariance matrix can be obtained as a
boundary term of the geometric phase.


  The important result achieved in our recent study of a large sample of HgMn
stars using UVES at the VLT and FEROS at the ESO 2.2m telescope is the finding
that most HgMn stars exhibit spectral variability of various chemical elements,
proving that the presence of an inhomogeneous distribution on the surface of
these stars is a rather common characteristics and not a rare phenomenon.


  We derive the two loop expressions for polygonal Wilson loops by starting
from the one loop expressions and applying an operator product expansion. We do
this for polygonal Wilson loops in R^{1,1} and find a result in agreement with
previous computations. We also discuss the spectrum of excitations around flux
tube that connects two null Wilson lines.


  In this paper we studied the behavior of radial photons from the point of
view of the coordinate time in (asymptotically) Lifshitz space-times, and we
found a generalization to the result reported in previous works by Cruz et. al.
[Eur. Phys. J. C {\bf 73}, 7 (2013)], Olivares et. al. [Astrophys. Space Sci.
{\bf 347}, 83-89 (2013)], and Olivares et. al. [arXiv: 1306.5285]. We
demonstrate that all asymptotically Lifshitz space-times characterized by a
lapse funcion $f(r)$ which tends to one when $r\rightarrow \infty$, present the
same behavior, in the sense that an external observer will see that photons
arrive at spatial infinity in a finite coordinate time. Also, we show that
radial photons in the proper system cannot determine the presence of the black
hole in the region $r_+<r<\infty$, because the proper time results to be
independent of the lapse function $f(r)$.


  The Rashomon Effect describes the following phenomenon: for a given dataset
there may exist many models with equally good performance but with different
solution strategies. The Rashomon Effect has implications for Explainable
Machine Learning, especially for the comparability of explanations. We provide
a unified view on three different comparison scenarios and conduct a
quantitative evaluation across different datasets, models, attribution methods,
and metrics. We find that hyperparameter-tuning plays a role and that metric
selection matters. Our results provide empirical support for previously
anecdotal evidence and exhibit challenges for both scientists and
practitioners.


  We present time-resolved photoluminescence measurements on two series of
oligo-p-phenylenevinylene materials that self-assemble into supramolecular
nanostructures with thermotropic reversibility in dodecane. One set of
derivatives form chiral, helical stacks while the second set form less
organised, frustrated stacks. Here we study the effects of supramolecular
organisation on the resonance energy transfer rates. We measure these rates in
nanoassemblies formed with mixed blends of oligomers and compare them with the
rates predicted by Foerster theory. Our results and analysis show that control
of supramolecular order in the nanometre lengthscale has a dominant effect on
the efficiency and dimentionality of resonance energy transfer.


  The active-sterile neutrino conversion probability is calculated for neutrino
propagating in a medium in the presence of random magnetic field fluctuations.
Necessary condition for the probability to be positive definite is obtained.
Using this necessary condition we put constraint on the neutrino magnetic
moment from active-sterile electron neutrino conversion in the early universe
hot plasma and in supernova.


  We identify natural conditions for a countable group acting on a countable
tree which imply that the orbit equivalence relation of the induced action on
the Gromov boundary is Borel hyperfinite. Examples of this condition include
acylindrical actions. We also identify a natural weakening of the
aforementioned conditions that implies measure hyperfinitenss of the boundary
action. We then document examples of group actions on trees whose boundary
action is not hyperfinite.


  The nature of carbon burning flames in Type Ia supernovae is explored as they
interact with Kolmogorov turbulence. One-dimensional calculations using the
Linear Eddy Model of Kerstein (1991) elucidate three regimes of turbulent
burning. In the simplest case, large scale turbulence folds and deforms thin
laminar flamelets to produce a flame brush with a total burning rate given
approximately by the speed of turbulent fluctuations on the integral scale,
U_L. This is the regime where the supernova explosion begins and where most of
its pre-detonation burning occurs. As the density declines, turbulence starts
to tear the individual flamelets, making broader structures that move faster.
For a brief time, these turbulent flamelets are still narrow compared to their
spacing and the concept of a flame brush moving with an overall speed of U_L
remains valid. However, the typical width of the individual flamelets, which is
given by the condition that their turnover time equals their burning time,
continues to increase as the density declines. Eventually, mixed regions almost
as large as the integral scale itself are transiently formed. At that point, a
transition to detonation can occur. The conditions for such a transition are
explored numerically and it is estimated that the transition will occur for
densities near 1 x 10**7 g/cm**3, provided the turbulent speed on the integral
scale exceeds about 15% sonic. An example calculation shows the details of a
detonation actually developing.


  Considering large scale implementation of electric vehicles (EVs), public EV
charging stations are served as fuel tanks for EVs to meet the need of longer
travelling distance and overcome the shortage of private charging piles. The
allocation of local battery energy storage (BES) can enhance the flexibility of
the EV charging station. This paper proposes an optimal decision making model
of the BES-assisted EV charging station considering the incentive demand
response. Firstly, the detailed models of the BES-assisted EV charging station
are presented. Secondly, as a representative incentive demand response, the
emergency demand response (EDR) model is introduced. Thirdly, based on the
charging load forecast data, an optimal decision making model of the
BES-assisted EV charging station considering the EDR to maximize the charging
station's operating profit is established. Finally, the feasibility of the
proposed method is verified through case studies. The conclusions of this paper
are as follows: 1) Through the optimal decision making model, correct and
profitable EDR participation decision can be determined for the BES-assisted EV
charging station effectively. 2) Local BES in the EV charging station can
improve the charging station's ability to participate in the EDR.


  The work herein investigates the impact of resin molecular weight and solvent
choice on drying kinetics and sag velocity in polymer films. These films,
ranging in thickness from ~60 micrometer to ~120 micrometer were formulated
with 45% by weight polymer resin in one of two solvent packages with different
relative evaporation rates (RER). Gravimetry was initially used to track drying
kinetics and a one-dimensional diffusion model was utilized to compute the
apparent solvent diffusivity. In addition, the film thickness was tracked with
optical profilometry. Results from these measurements showed that for fixed
molecular weight the drying kinetics increased by approximately two-fold for
the high RER solvent, whereas the apparent diffusivity tended to increase with
increasing polymer molecular weight. Films formulated from higher molecular
weight resins had greater initial viscosities and thicknesses for identical
draw down blade clearance. By extension, the higher apparent diffusivities at
greater molecular weights were attributed to effects of prolonged evaporation
times for the thicker films. The sag velocity was measured through the
thickness of the film for these systems at a 5 degree incline using the
Variable Angle Inspection Microscope (VAIM). Measurements showed an increase in
sag velocity for thinner and less viscous films, which was somewhat surprising
both because a thinner film will experience lower gravitational stress and
quicker drying times as compared to a thicker film. From these data we conclude
that formulating a coating with higher molecular weight resin, although likely
to increase drying time, will tend to deter sag because of the large impact of
viscosity on these phenomena.


  The group Gamma of automorphisms of the polynomial kappa(x,y,z) = x^2 + y^2 +
z^2 - xyz -2 is isomorphic to PGL(2,Z) semi-direct product with (Z/2+Z/2). For
t in R, Gamma-action on ktR = kappa^{-1}(t) intersect R displays rich and
varied dynamics. The action of Gamma preserves a Poisson structure defining a
Gamma-invariant area form on each ktR. For t < 2, the action of Gamma is
properly discontinuous on the four contractible components of ktR and ergodic
on the compact component (which is empty if t < -2). The contractible
components correspond to Teichmueller spaces of (possibly singular) hyperbolic
structures on a torus M-bar. For t = 2, the level set ktR consists of
characters of reducible representations and comprises two ergodic components
corresponding to actions of GL(2,Z) on (R/Z)^2 and R^2 respectively. For 2 < t
<= 18, the action of Gamma on ktR is ergodic. Corresponding to the Fricke space
of a three-holed sphere is a Gamma-invariant open subset Omega subset R^3 whose
components are permuted freely by a subgroup of index 6 in Gamma. The level set
ktR intersects Omega if and only if t > 18, in which case the Gamma-action on
the complement ktR - Omega is ergodic.


  A throughout investigation is made of the exact black hole solution in
five-dimensional warped conformal dilaton gravity, found in an earlier
investigation. The singularities of the dynamical black hole spacetime are
determined by the zeros of a meromorphic quintic polynomial, which has no
essential singularities. The solutions of the polynomial are analyzed in the
complex plane in relation to the icosahedron group and by the Hopf-fibrations
of the Klein surface. The model fits the antipodal boundary condition, i.e.,
antipodal points in the projected space are identified using the embedding of a
Klein surface in $\mathds{C}^2$, using the $\mathds{Z}_2$ symmetry on the two
sides of the brane. If one writes $^{(5)}g_{\mu\nu}=\omega^{4/3}{^{(5)}}{\tilde
g_{\mu\nu}}, {^{(5)}}{\tilde g_{\mu\nu}}={^{(4)}}{\tilde g_{\mu\nu}}+n_\mu
n_\nu$, $ ^{(4)}\tilde g_{\mu\nu}=\bar\omega^2 {^{(4)}}\bar g_{\mu\nu}$, with
$n_\mu$ the normal to the brane and $\omega$ the dilaton field, then
${^{(4)}}\bar g_{\mu\nu}$ is conformally flat. It is the contribution from the
bulk which determines the real pole on the effective four-dimensional
spacetime. There is no objection applying 't Hooft's back reaction method in
constructing the unitary S-matrix for the Hawking radiation. Again, there is no
"inside" of the black hole.


  On-chip cavity optomechanics, in which strong co-localization of light and
mechanical motion is engineered, relies on efficient coupling of light both
into and out of the on-chip optical resonator. Here we detail our particular
style of tapered and dimpled optical fibers, pioneered by the Painter group at
Caltech, which are a versatile and reliable solution to efficient on-chip
coupling. First, a brief overview of tapered, single mode fibers is presented,
in which the single mode cutoff diameter is highlighted. The apparatus used to
create a dimpled tapered fiber is then described, followed by a comprehensive
account of the procedure by which a dimpled tapered fiber is produced and
mounted in our system. The custom-built optical access vacuum chambers in which
our on-chip optomechanical measurements are performed are then discussed.
Finally, the process by which our optomechanical devices are fabricated and the
method by which we explore their optical and mechanical properties is
explained. It is our expectation that this manuscript will enable the novice to
develop advanced optomechanical experiments.


  In previous papers we showed that a division of the f-shell into two
subsystems gives a better understanding of cohesive properties as well the
general behavior of lanthanide systems. In this paper we present numerical
computations using the suggested method. We show that the picture is consistent
with most experimental data, e.g. the equilibrium volume and electronic
structure in general. Compared to standard energy band calculations, or to
calculations based on the self interaction correction and LDA+U, in the present
approach f-(non-f)-mixing interaction is decreased by spectral weights of the
many-body states of the f-ion are involved.


  We show that the dynamics, in particular the Kelvin-Helmholtz (KH)
instability, of an inviscid fluid with velocity shear admits Parity-Time (PT)
symmetry, which provides a physical explanation to the well-known observation
that the spectrum of the perturbation eigenmodes of the system is symmetric
with respect to the real axis. It is found that the KH instability is triggered
when and only when the PT symmetry is spontaneously broken. The analysis of PT
symmetry also reveals that the relative phase between parallel velocity and
pressure perturbations needs to be locked at $\pi/2$ when the instability is
suppressed.


  We generalize the notion of "localization landscape," introduced by M.
Filoche and S. Mayboroda [Proc. Natl. Acad. Sci. USA 109, 14761 (2012)] for the
single-particle Schrodinger operator, to a wide class of interacting many-body
Hamiltonians. The many-body localization landscape (MBLL) is defined on a graph
in the Fock space, whose nodes represent the basis vectors in the Fock space
and edges correspond to transitions between the nodes connected by the hopping
term in the Hamiltonian. It is shown that in analogy to the single-particle
case, the inverse MBLL plays the role of an effective potential in the Fock
space. We construct a generalized discrete Agmon metric and prove Agmon
inequalities and locality theorems on the Fock-state graph to obtain bounds on
the exponential decay of the many-body wave-functions in the Fock space. Using
the MBLL and the locator expansion, we provide considerable analytical evidence
for the existence of many-body localization for a wide-class of lattice models
in any physical dimension for at least a part of their Hilbert space. The key
to this argument is the observation that in sharp contrast to the conventional
locator expansion for the Green's function, the locator expansion for the
landscape function contains no resonances. For short-range hopping, which
limits the connectivity of the Fock-state graph, the locator series is proven
to be convergent and bounded by a simple geometric series. This, in combination
with the Agmon inequalities and locality theorems, indicates that localization
should survive weak interactions and weak hopping for a subset of states in the
Hilbert space, but cannot prove or rule out localization of the other states.
We also qualitatively discuss potential breakdown of the locator expansion in
the MBLL for long-range hopping and the appearance of a mobility edge in
higher-dimensional theories.


  Let $X$ be a compact K\"ahler manifold of dimension $n$, and let $T$ be a
closed positive $(1,1)$-current in a nef cohomology class on $X$. We establish
an optimal upper bound for the volume of components of Lelong upper level sets
of $T$ in terms of cohomology classes of non-pluripolar self-products of $T$.


  Raynaud--Gruson characterized flat and pure morphisms between affine schemes
in terms of projective modules. We give a similar characterization for
non-affine morphisms. As an application, we show that every quasi-coherent
sheaf is the union of its finitely generated quasi-coherent subsheaves on any
quasi-compact and quasi-separated algebraic stack.


  Computation of the probability that a random graph is connected is a
challenging problem, so it is natural to turn to approximations such as Monte
Carlo methods. We describe sequential importance resampling and splitting
algorithms for the estimation of these probabilities. The importance sampling
steps of these algorithms involve identifying vertices that must be present in
order for the random graph to be connected, and conditioning on the
corresponding events. We provide numerical results demonstrating the
effectiveness of the proposed algorithm.


  Dimension is a fundamental property of objects and the space in which they
are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not
always translate to physical spaces, which can be constrained by boundaries and
distorted by inhomogeneities, or to intrinsically discrete systems such as
networks. To take into account locality, finiteness and discreteness, dynamical
processes can be used to probe the space geometry and define its dimension.
Here we show that each point in space can be assigned a relative dimension with
respect to the source of a diffusive process, a concept that provides a
scale-dependent definition for local and global dimension also applicable to
networks. To showcase its application to physical systems, we demonstrate that
the local dimension of structural protein graphs correlates with structural
flexibility, and the relative dimension with respect to the active site
uncovers regions involved in allosteric communication. In simple models of
epidemics on networks, the relative dimension is predictive of the spreading
capability of nodes, and identifies scales at which the graph structure is
predictive of infectivity. We further apply our dimension measures to neuronal
networks, economic trade, social networks, ocean flows, and to the comparison
of random graphs.


  The present work is motivated by the recent experimental realization of the
Townes soliton in an effective two-component Bose-Einstein condensate by B.
Bakkali-Hassan et al. [Phys. Rev. Lett. 127, 023603 (2021)]. Here, we use a
similar multicomponent platform to exemplify theoretically and numerically,
within the mean-field Gross-Pitaevskii framework, the potential toward the
experimental realization of a different fundamental wave structure, namely the
Peregrine soliton. Leveraging the effective attractive interaction produced
within the mixture's minority species in the immiscible regime, we illustrate
how initialization of the condensate with a suitable power-law decaying spatial
density pattern yields the robust emergence of the Peregrine wave in the
absence and in the presence of a parabolic trap. We then showcase the
spontaneous emergence of the Peregrine soliton via a suitably crafted wide
Gaussian initialization, again both in the homogeneous case and in the trap
scenario. It is also found that narrower wave packets may result in periodic
revivals of the Peregrine soliton, while broader ones give rise to a cascade of
Peregrine solitons arranged in a so-called Christmas-tree structure.
Strikingly, the persistence of these rogue-wave structures is demonstrated in
certain temperature regimes as well as in the presence of transversal
excitations through three-dimensional computations in a quasi-one-dimensional
regime. This proof-of-principle illustration is expected to represent a
practically feasible way to generate and observe this rogue wave in realistic
current ultracold atom experimental settings.


  A large population of Intermediate Mass Black Holes (IMBHs) might be produced
at early cosmic times as a left over of the evolution of the very massive first
stars. Accretion onto IMBHs provides a source of (re)ionizing radiation. We
show that the baryon mass fraction locked into IMBHs and their growth is
strongly constrained by the observed residual Soft X-ray Background (SXRB)
intensity. Thus, unless they are extremely X-ray quiet, miniquasars must be
quite rare and/or have a short shining phase. As a byproduct, we find that
miniquasars can not be the only source of reionization and that their alleged
contribution to the near infrared bands is completely negligible.


  Inverse problems, such as accelerated MRI reconstruction, are ill-posed and
an infinite amount of possible and plausible solutions exist. This may not only
lead to uncertainty in the reconstructed image but also in downstream tasks
such as semantic segmentation. This uncertainty, however, is mostly not
analyzed in the literature, even though probabilistic reconstruction models are
commonly used. These models can be prone to ignore plausible but unlikely
solutions like rare pathologies. Building on MRI reconstruction approaches
based on diffusion models, we add guidance to the diffusion process during
inference, generating two meaningfully diverse reconstructions corresponding to
an upper and lower bound segmentation. The reconstruction uncertainty can then
be quantified by the difference between these bounds, which we coin the
'uncertainty boundary'. We analyzed the behavior of the upper and lower bound
segmentations for a wide range of acceleration factors and found the
uncertainty boundary to be both more reliable and more accurate compared to
repeated sampling. Code is available at https://github.com/NikolasMorshuis/SGR


  A proper definition of the path integral of quantum gravity has been a
long-standing puzzle because the Weyl factor of the Euclidean metric has a
wrong-sign kinetic term. We propose a definition of two-dimensional Liouville
quantum gravity with cosmological constant using conformal bootstrap for the
timelike Liouville theory coupled to supercritical matter. We prove a no-ghost
theorem for the states in the BRST cohomology. We show that the four-point
function constructed by gluing the timelike Liouville three-point functions is
well defined and crossing symmetric (numerically) for external Liouville
energies corresponding to \textit{all} physical states in the BRST cohomology
with the choice of the Ribault-Santachiara contour for the internal energy.


  Hybrid systems of ultracold atoms and trapped ions or Rydberg atoms can be
useful for quantum simulation purposes. By tuning the geometric arrangement of
the impurities it is possible to mimic solid state and molecular systems. Here
we study a single trapped atom interacting with a set of arbitrarily arranged
static impurities and show that the problem admits an analytical solution. We
analyze in detail the case of two impurities, finding multiple trap-induced
resonances which can be used for entanglement generation. Our results serve as
a building block for the studies of quantum dynamics of complex systems.


  We perform a model independent analysis on $q \bar{q} \rightarrow t \bar{t}$
using an effective lagrangian with dim-6 four-quark operators, and derive
necessary conditions on new physics that are consistent with the $t\bar{t}$
production cross section %($\sigma_{t\bar{t}}$) and and the forward-backward
(FB) asymmetry ($A_{\rm FB}$) measured at the Tevatron. We also propose a new
FB spin-spin correlation that is strongly correlated with the $A_{\rm FB}$, and
discuss possible new physics scenarios that could generate such dim-6
operators.


  In this paper, I comment on a recent paper by Michel Janssen and J\"urgen
Renn. In his published paper of November 18, 1915, Einstein presented a
solution to the problem of the perihelion motion of Mercury and obtained the
correct result of 43 seconds of arc per century. Before 1915, Einstein had
established non-covariant field equations (the Entwurf field equations). But in
1915, he changed his mind and dropped these equations and was led to general
covariance. In a manuscript written in 1913, Einstein and his best friend
Michele Besso tried to solve the Entwurf field equations to attain the
perihelion advance of Mercury. The end result arrived at by Einstein was 1821
seconds of arc per century. To make a long story short, the field of a static
Sun produced an advance of the perihelion of Mercury of 18 seconds of arc per
century. Einstein kept quiet about this result and continued to work on the
Entwurf theory. Janssen and Renn ask: If we follow the prescriptions of Karl
Popper, why did Einstein not accept that his Entwurf theory had been falsified?
They further ask: Given the undeniable importance of Besso's earlier
calculations, why did Einstein not invite Besso as a co-author of his November
1915 paper on the perihelion motion of Mercury? Besso did not even get an
acknowledgment in Einstein's paper. After a brief review of Einstein's and
Besso's early attempts at calculating the advance of the perihelion of Mercury,
I discuss falsification and confirmation by previously known evidence and then
propose an answer to the above two questions.


  Measuring close proximity interactions between individuals can provide key
information on social contacts in human communities. With the present study, we
report the quantitative assessment of contact patterns in a village in rural
Malawi, based on proximity sensors technology that allows for high-resolution
measurements of social contacts. The system provided information on community
structure of the village, on social relationships and social assortment between
individuals, and on daily contacts activity within the village. Our findings
revealed that the social network presented communities that were highly
correlated with household membership, thus confirming the importance of family
ties within the village. Contacts within households occur mainly between adults
and children, and adults and adolescents. This result suggests that the
principal role of adults within the family is the care for the youngest. Most
of the inter-household interactions occurred among caregivers and among
adolescents. We studied the tendency of participants to interact with
individuals with whom they shared similar attributes (i.e., assortativity). Age
and gender assortativity were observed in inter-household network, showing that
individuals not belonging to the same family group prefer to interact with
people with whom they share similar age and gender. Age disassortativity is
observed in intra-household networks. Family members congregate in the early
morning, during lunch time and dinner time. In contrast, individuals not
belonging to the same household displayed a growing contact activity from the
morning, reaching a maximum in the afternoon. The data collection
infrastructure used in this study seems to be very effective to capture the
dynamics of contacts by collecting high resolution temporal data and to give
access to the level of information needed to understand the social context of
the village.


  In this paper we show that the universal C*-algebra satisfying the Cuntz-Li
relations is generated by an inverse semigroup of partial isometries. We apply
Exel's theory of tight representations to this inverse semigroup. We identify
the universal C*-algebra as the C*-algebra of the tight groupoid associated to
the inverse semigroup.


  Artificial Neural Networks (ANN) are already heavily involved in methods and
applications for frequent tasks in the field of computational chemistry such as
representation of potential energy surfaces (PES) and spectroscopic
predictions. This perspective provides an overview of the foundations of neural
network-based full-dimensional potential energy surfaces, their architectures,
underlying concepts, their representation and applications to chemical systems.
Methods for data generation and training procedures for PES construction are
discussed and means for error assessment and refinement through transfer
learning are presented. A selection of recent results illustrates the latest
improvements regarding accuracy of PES representations and system size
limitations in dynamics simulations, but also NN application enabling direct
prediction of physical results without dynamics simulations. The aim is to
provide an overview for the current state-of-the-art NN approaches in
computational chemistry and also to point out the current challenges in
enhancing reliability and applicability of NN methods on larger scale.


  We carry out a detailed analysis of fluxes of cosmic ray antiprotons,
positrons, electrons and photons to be expected from the annihilation of relic
heavy neutrinos in the galactic halo. The spectra of particles are evaluated by
Monte Carlo simulation. The results of calculations show that the investigation
of cosmic ray positron spectra at high energies could provide a distinctive
signal for annihilation of very heavy neutrinos in the Galaxy and give an
important information on parameters of dark matter particles.


  We present a method to derive implicit solvent models of electrolyte
solutions from all-atom descriptions; providing analytical expressions of the
thermodynamic and structural properties of the ions consistent with the
underlying explicit solvent representation. Effective potentials between ions
in solution are calculated to perform perturbation theory calculations, in
order to derive the best possible description in terms of charged hard spheres.
Applying this method to NaCl solutions yields excellent agreement with the
all-atom model, provided ion association is taken into account.


  Precision measurements by the Alpha Magnetic Spectrometer (AMS-02) on the
International Space Station of the primary cosmic-ray electron flux and the
positron flux will be discussed. The electron flux and the positron flux each
require a description beyond a single power-law spectrum. Both the electron
flux and the positron flux change their behavior at ~30 GeV but the fluxes are
significantly different in their magnitude and energy dependence. Between 20
and 200 GeV the positron spectral index is significantly harder than the
electron spectral index. The determination of the different behavior of the
spectral indices versus energy is a new observation and provides important
information on the origins of cosmic-ray electrons and positrons.


  The evolution of the magnetic field and plasma quantities inside a coronal
mass ejection (CME) with distance are known from statistical studies using data
from 1 au monitors, planetary missions, Helios, and Ulysses. This does not
cover the innermost heliosphere, below 0.29 au, where no data are yet publicly
available. Here, we describe the evolution of the properties of simulated CMEs
in the inner heliosphere using two different initiation mechanisms. We compare
the radial evolution of these properties with that found from statistical
studies based on observations in the inner heliosphere by Helios and MESSENGER.
We find that the evolution of the radial size and magnetic field strength is
nearly indistinguishable for twisted flux rope from that of writhed CMEs. The
evolution of these properties is also consistent with past studies, primarily
with recent statistical studies using in situ measurements and with studies
using remote observations of CMEs.


  5-brane configurations describing 5d field theories are promoted to an M
theory description a la Witten in terms of polynomials in two complex
variables. The coefficients of the polynomials are the Coulomb branch. This
picture resolves apparent singularities at vertices and reveals exponentially
small corrections. These corrections ask to be compared to world line instanton
corrections. From a different perspective this procedure may be used to define
a diagrammatic representation of polynomials in two variables.


  Topological phononic states, facilitating acoustic unique transports
immunizing to defects and disorders, have significantly revolutionized our
scientific cognition of acoustic wave systems. Up to now, the theoretical and
experimental demonstrations of topologically protected one-way transports with
pseudospin states in a phononic crystal beyond the graphene lattice with C6v
symmetry are still unexploited. Furthermore, the tunable topological states, in
form of robust reconfigurable acoustic pathways, have been evaded in the
topological phononic insulators. Here, we realize a topological phase
transition in the double Dirac degenerate cone of rotatable triangular phononic
crystals with C3v symmetry, by introducing the zone folding mechanism. Along a
topological domain wall between two portions of phononic crystals with distinct
topological phases, we experimentally observe the quantum spin Hall (QSH)
effect for sound, characterized by the robust pseudospin-dependent one-way edge
model. As the triangular phononic crystals can freely rotate, we
straightforward reconfigure an arbitrary contour defined by the topological
domain wall along which the acoustic waves can unimpededly transport. Our
research develops a new route for the exploration of the topological phenomena
in experiments and provides an excellent framework for freely steering the
acoustic immune-backscattering propagation within topological phononic
structures.


  Recommender systems suffer from confounding biases when there exist
confounders affecting both item features and user feedback (e.g., like or not).
Existing causal recommendation methods typically assume confounders are fully
observed and measured, forgoing the possible existence of hidden confounders in
real applications. For instance, product quality is a confounder since
affecting both item prices and user ratings, but is hidden for the third-party
e-commerce platform due to the difficulty of large-scale quality inspection;
ignoring it could result in the bias effect of over-recommending high-price
items. This work analyzes and addresses the problem from a causal perspective.
The key lies in modeling the causal effect of item features on a user's
feedback. To mitigate hidden confounding effects, it is compulsory but
challenging to estimate the causal effect without measuring the confounder.
Towards this goal, we propose a Hidden Confounder Removal (HCR) framework that
leverages front-door adjustment to decompose the causal effect into two partial
effects, according to the mediators between item features and user feedback.
The partial effects are independent from the hidden confounder and
identifiable. During training, HCR performs multi-task learning to infer the
partial effects from historical interactions. We instantiate HCR for two
scenarios and conduct experiments on three real-world datasets. Empirical
results show that the HCR framework provides more accurate recommendations,
especially for less-active users. We will release the code once accepted.


  A new step-by-step diagonalization procedure for evaluating exact solutions
of the nuclear deformed mean-field plus pairing interaction model is proposed
via a simple Bethe ansatz in each step from which the eigenvalues and
corresponding eigenstates can be obtained progressively. This new approach
draws upon an observation that the original one- plus two-body problem in a
$k$-particle Hilbert subspace can be mapped unto a one-body grand hard-core
boson picture that can be solved step by step with a simple Bethe ansatz known
from earlier work. Based on this new procedure, it is further shown that the
extended pairing model for deformed nuclei [Phys. Rev. Lett. 92, 112503 (2004)
] is similar to the standard pairing model with the first step approximation,
in which only the lowest energy eigenstate of the standard pure pairing
interaction part is taken into consideration. Our analysis show that the
standard pairing model with the first step approximation displays similar pair
structures of first few exact low-lying states of the model, which, therefore,
provides a link between the two models.


  The power spectrum of the nonlinearly evolved large-scale mass distribution
recovers only a minority of the information available on the mass fluctuation
amplitude. We investigate the recovery of this information in 2D "slabs" of the
mass distribution averaged over $\approx100$~$h^{-1}$Mpc along the line of
sight, as might be obtained from photometric redshift surveys. We demonstrate a
Hamiltonian Monte Carlo (HMC) method to reconstruct the non-Gaussian mass
distribution in slabs, under the assumption that the projected field is a
point-transformed Gaussian random field, Poisson-sampled by galaxies. When
applied to the \textit{Quijote} $N$-body suite at $z=0.5$ and at a transverse
resolution of 2~$h^{-1}$Mpc, the method recovers $\sim 30$ times more
information than the 2D power spectrum in the well-sampled limit, recovering
the Gaussian limit on information. At a more realistic galaxy sampling density
of $0.01$~$h^3$Mpc$^{-3}$, shot noise reduces the information gain to a factor
of 5 improvement over the power spectrum at resolutions of 4~$h^{-1}$Mpc or
smaller.


  The author has recently introduced an abstract algebraic framework of
analogical proportions within the general setting of universal algebra. The
purpose of this paper is to lift that framework from universal algebra to the
strictly more expressive setting of full first-order logic. We show that the
so-obtained logic-based framework preserves all desired properties and we prove
novel results in that extended setting.


  Let $A$ and $B$ be unital Banach algebras with $A$ a subalgebra of $B$.
Denote the algebra of all $n\times n$ matrices with entries from $A$ by
$M_{n}(A)$. In this paper we prove some results concerning the open question:
If $A$ is inverse closed in $B$, then is $M_{n}(A)$ inverse closed in
$M_{n}(B)$? We also study related questions in the setting where $A$ is a
symmetric Banach *-algebra.


  We consider an $n$ by $n$ matrix of the form $A=UTV$, with $U, V$ some
independent Haar-distributed unitary matrices and $T$ a deterministic matrix.
We prove that for $k\sim n^{1/6}$ and
$b^2:=\frac{1}{n}\operatorname{Tr}(|T|^2)$, as $n$ tends to infinity, we have
$$\mathbb{E} \operatorname{Tr} (A^{k}(A^{k})^*) \ \lesssim \ b^{2k}\qquad
\textrm{and} \qquad\mathbb{E}[|\operatorname{Tr} (A^{k})|^2] \ \lesssim \
b^{2k}.$$ This gives a simple proof (with slightly weakened hypothesis) of the
convergence of the support in the Single Ring Theorem, improves the available
error bound for this convergence from $n^{-\alpha}$ to $e^{-cn^{1/6}}$ and
proves that the rate of this convergence is at most $n^{-1/6}\log n$.


  We calculate radiatively driven wind models of main-sequence B stars and
provide the wind mass-loss rates and terminal velocities. The main-sequence
mass-loss rate strongly depends on the stellar effective temperature. For the
hottest B stars the mass-loss rate amounts to
$10^{-9}\,\text{M}_\odot\,\text{year}^{-1}$, while for the cooler ones
themass-loss rate is lower by more than three orders of magnitude.
Main-sequence B stars with solar abundance and effective temperatures lower
than about$15\,000\,\text{K}$ (later than spectral type B5) do not have any
homogeneous line-driven wind. We predict the wind mass-loss rates for the solar
chemical composition and for the modified abundance of heavier elements to
study the winds of chemically peculiar stars. The mass-loss rate may either
increase or decrease with increasing abundance, depending on the importance of
the induced emergent flux redistribution. Stars with overabundant silicon may
have homogeneous winds even below the solar abundance wind limit at
$15\,000\,\text{K}$. The winds of main-sequence B stars lie below the static
limit, that is, a static atmosphere solution is also possible. This points to
an important problem regarding the initiation of these winds. We discuss the
implications of our models for rotational braking, filling the magnetosphere of
Bp stars, and for chemically peculiar stars.


  We study, using Hepp's method, the propagation of coherent states for a
general class of self interacting bosonic quantum field theories with spatial
cutoffs. This includes models with non-polynomial interactions in the field
variables. We show indeed that the time evolution of coherent states, in the
classical limit, is well approximated by time-dependent affine Bogoliubov
unitary transformations. Our analysis relies on a non-polynomial Wick
quantization and a specific hypercontractive estimate.


  We describe a new mechanism that gives rise to dissipation during cosmic
inflation. In the simplest implementation, the mechanism requires the presence
of a massive scalar field with a softly-broken global $U(1)$ symmetry, along
with the inflaton field. Particle production in this scenario takes place on
parametrically sub-horizon scales, at variance with the case of dissipation
into gauge fields. Consequently, the backreaction of the produced particles on
the inflationary dynamics can be treated in a \textit{local} manner, allowing
us to compute their effects analytically. We determine the parametric
dependence of the power spectrum which deviates from the usual slow-roll
expression. Non-Gaussianities are always sizeable whenever perturbations are
generated by the noise induced by dissipation: $f_{\rm NL}^{\rm eq} \gtrsim
{O}(10)$.


  Measurement of $t\bar{t}$ pair production cross sections with an integrated
luminosity of around 1 fb$^{-1}$ at $\sqrt{s}$ = 7 TeV obtained with the ATLAS
and CMS detectors are reported. The inclusive cross sections in dilepton (ee,
$e\mu$, $\mu\mu$ and $\mu\tau$), lepton+jets (e, $\mu$) and all hadronic decay
modes are measured. In addition to inclusive cross section measurement, the
study of jet multiplicity with additional jets are also presented, which is
important to constrain the initial state radiation. Measurement of the charge
asymmetry at the LHC is also presented. All measurements are compatible with
Standard Model predictions.


  We present an a posteriori error estimate based on equilibrated stress
reconstructions for the finite element approximation of a unilateral contact
problem with weak enforcement of the contact conditions. We start by proving a
guaranteed upper bound for the dual norm of the residual. This norm is shown to
control the natural energy norm up to a boundary term, which can be removed
under a saturation assumption. The basic estimate is then refined to
distinguish the different components of the error, and is used as a starting
point to design an algorithm including adaptive stopping criteria for the
nonlinear solver and automatic tuning of a regularization parameter. We then
discuss an actual way of computing the stress reconstruction based on the
Arnold-Falk-Winther finite elements. Finally, after briefly discussing the
efficiency of our estimators, we showcase their performance on a panel of
numerical tests.


  This communication presents preliminary findings from comparing two recent
chatbots, OpenAI's ChatGPT and Google's Bard, in the context of fire
engineering by evaluating their responses in handling fire safety related
queries. A diverse range of fire engineering questions and scenarios were
created and examined, including structural fire design, fire prevention
strategies, evacuation, building code compliance, and fire suppression systems
(some of which resemble those commonly present in the Fire Protection exam
(FPE)). The results reveal some key differences in the performance of the
chatbots, with ChatGPT demonstrating a relatively superior performance. Then,
this communication highlights the potential for chatbot technology to
revolutionize fire engineering practices by providing instant access to
critical information while outlining areas for further improvement and
research. Evidently, and when it matures, this technology will likely be
elemental to our engineers' practice and education.


  Lifetimes of the first two metastable states in Sc^{2+} and Y^{2+} are
determined using the relativistic coupled-cluster theory. There is a
considerable interest in studying the electron correlation effects in these
ions as though their electronic configurations are similar to the neutral
alkali atoms, their structures are very different from the latter. We have made
a comparative study of the correlation trends between the above doubly ionized
systems with their corresponding neutral and singly ionized iso-electronic
systems. The lifetimes of the excited states of these ions are very important
in the field of astrophysics, especially for the study of post-main sequence
evolution of the cool giant stars.


  An analogous laser action of magnons would be a subject of interest and is
crucial for the study of nonlinear magnons spintronics. Here, we demonstrate
the magnon laser behavior based on Brillouin light scattering in a
ferrimagnetic insulator sphere which supports optical whispering gallery modes
and magnon resonances. We show that the excited magnon plays what has
traditionally been the role of the Stokes wave and is coherently amplified
during the Brillouin scattering process, making magnon laser possible.
Furthermore, the stimulating excited magnon number increasing exponentially
with the input light power can be manipulated by adjusting the external
magnetic field. In addition to providing insight into magneto-optical
interaction, the study of magnon laser action will help to develop novel
technologies for handling spin-wave excitations and could affect scientific
fields beyond magnonics. Potential applications range from preparing coherent
magnon sources to operating onchip functional magnetic devices.


  Two-timescale Stochastic Approximation (SA) algorithms are widely used in
Reinforcement Learning (RL). Their iterates have two parts that are updated
using distinct stepsizes. In this work, we develop a novel recipe for their
finite sample analysis. Using this, we provide a concentration bound, which is
the first such result for a two-timescale SA. The type of bound we obtain is
known as `lock-in probability'. We also introduce a new projection scheme, in
which the time between successive projections increases exponentially. This
scheme allows one to elegantly transform a lock-in probability into a
convergence rate result for projected two-timescale SA. From this latter
result, we then extract key insights on stepsize selection. As an application,
we finally obtain convergence rates for the projected two-timescale RL
algorithms GTD(0), GTD2, and TDC.


  The present work analyzes perturbed potentials due to test mass that is added
at the center of gravity of the non-singular equilibrium isothermal
self-gravitating gases. We examine gravitational polarization in the infinite
isothermal sheet, cylinder, and sphere, assuming that the systems are highly
collisional and reach a new state of thermal equilibrium after perturbation.
Under the assumptions, the isothermal sheet and cylinder amplify gravitational
fields due to test sheet and line masses by 68 % and 53 % maximally. On the one
hand, in the isothermal sphere, gravitational fields due to test point mass are
amplified oscillatorily with radius and show a repulsive effect at large radii.
Since the infinite isothermal sphere is gravitationally unstable, we confine it
in a spherical wall in contact with a thermal bath. We find that only
gravitational amplification occurs if the unperturbed finite sphere is
gravitationally stable. The oscillatory amplification appears if the sphere is
unstable, hence the repulsive effect is unrealistic in the canonical ensemble.


  We obtain the following analytical formula which describes the dependence of
the electric potential of a point-like charge on the distance away from it in
the direction of an external magnetic field B: \Phi(z) = e/|z| [ 1-
exp(-\sqrt{6m_e^2}|z|) + exp(-\sqrt{(2/\pi) e^3 B + 6m_e^2} |z|) ]. The
deviation from Coulomb's law becomes essential for B > 3\pi B_{cr}/\alpha = 3
\pi m_e^2/e^3 \approx 6 10^{16} G. In such superstrong fields, electrons are
ultra-relativistic except those which occupy the lowest Landau level (LLL) and
which have the energy epsilon_0^2 = m_e^2 + p_z^2. The energy spectrum on which
LLL splits in the presence of the atomic nucleus is found analytically. For B >
3 \pi B_{cr}/\alpha, it substantially differs from the one obtained without
accounting for the modification of the atomic potential.


  The logarithmic Schr\"odinger equation (LogSE) has a logarithmic nonlinearity
$f(u)=u\ln |u|^2$ that is not differentiable at $u=0.$ Compared with its
counterpart with a regular nonlinear term, it possesses richer and unusual
dynamics, though the low regularity of the nonlinearity brings about
significant challenges in both analysis and computation. Among very limited
numerical studies, the semi-implicit regularized method via regularising $f(u)$
as $ u^{\varepsilon}\ln ({\varepsilon}+ |u^{\varepsilon}|)^2$ to overcome the
blowup of $\ln |u|^2$ at $u=0$ has been investigated recently in literature.
With the understanding of $f(0)=0,$ we analyze the non-regularized first-order
Implicit-Explicit (IMEX) scheme for the LogSE. We introduce some new tools for
the error analysis that include the characterization of the H\"older continuity
of the logarithmic term, and a nonlinear Gr\"{o}nwall's inequality. We provide
ample numerical results to demonstrate the expected convergence. We position
this work as the first one to study the direct linearized scheme for the LogSE
as far as we can tell.


  Based on both the constituent quark picture and the instanton model for QCD
vacuum, we calculate the unpolarized and polarized gluon distributions in the
constituent quark and in the nucleon. Our approach consists of the two main
steps. At the first step, we calculate the gluon distributions inside the
constituent quark generated by the perturbative quark-gluon interaction, the
non-perturbative quark-gluon interaction, and the non-perturbative
quark-gluon-pion anomalous chromomagnetic interaction. The non-perturbative
interactions are related to the existence of the instantons, strong topological
fluctuations of gluon fields, in the QCD vacuum. At the second step, the
convolution model is applied to derive the gluon distributions in the nucleon.
A very important role of the pion field in producing the unpolarized and the
polarized gluon distributions in the hadrons is discovered. We discuss a
possible solution of the proton spin problem.


  We explore the formation of double-compact-object binaries in Milky Way (MW)
globular clusters (GCs) that may be detectable by the Laser Interferometer
Space Antenna (LISA). We use a set of 137 fully evolved GC models that,
overall, effectively match the properties of the observed GCs in the MW. We
estimate that, in total, the MW GCs contain $\sim21$ sources that will be
detectable by LISA. These detectable sources contain all combinations of black
hole (BH), neutron star, and white dwarf components. We predict $\sim7$ of
these sources will be BH-BH binaries. Furthermore, we show that some of these
BH-BH binaries can have signal-to-noise ratios large enough to be detectable at
the distance of the Andromeda galaxy or even the Virgo cluster.


  We propose an efficient approach for activity detection in video that unifies
activity categorization with space-time localization. The main idea is to pose
activity detection as a maximum-weight connected subgraph problem. Offline, we
learn a binary classifier for an activity category using positive video
exemplars that are "trimmed" in time to the activity of interest. Then, given a
novel \emph{untrimmed} video sequence, we decompose it into a 3D array of
space-time nodes, which are weighted based on the extent to which their
component features support the learned activity model. To perform detection, we
then directly localize instances of the activity by solving for the
maximum-weight connected subgraph in the test video's space-time graph. We show
that this detection strategy permits an efficient branch-and-cut solution for
the best-scoring---and possibly non-cubically shaped---portion of the video for
a given activity classifier. The upshot is a fast method that can search a
broader space of space-time region candidates than was previously practical,
which we find often leads to more accurate detection. We demonstrate the
proposed algorithm on four datasets, and we show its speed and accuracy
advantages over multiple existing search strategies.


  Twitter has arguably been the most popular among the data sources that form
the basis of so-called altmetrics. Tweets to scholarly documents have been
heralded as both early indicators of citations as well as measures of societal
impact. This chapter provides an overview of Twitter activity as the basis for
scholarly metrics from a critical point of view and equally describes the
potential and limitations of scholarly Twitter metrics. By reviewing the
literature on Twitter in scholarly communication and analyzing 24 million
tweets linking to scholarly documents, it aims to provide a basic understanding
of what tweets can and cannot measure in the context of research evaluation.
Going beyond the limited explanatory power of low correlations between tweets
and citations, this chapter considers what types of scholarly documents are
popular on Twitter, and how, when and by whom they are diffused in order to
understand what tweets to scholarly documents measure. Although this chapter is
not able to solve the problems associated with the creation of meaningful
metrics from social media, it highlights particular issues and aims to provide
the basis for advanced scholarly Twitter metrics.


  This article examines the existence and uniqueness of weak solutions to the
d-dimensional micropolar equations ($d=2$ or $d=3$) with general fractional
dissipation $(-\Delta)^{\alpha}u$ and $(-\Delta)^{\beta}w$. The micropolar
equations with standard Laplacian dissipation model fluids with microstructure.
The generalization to include fractional dissipation allows simultaneous study
of a family of equations and is relevant in some physical circumstances. We
establish that, when $\alpha\ge \frac12$ and $\beta\ge \frac12$, any initial
data $(u_0, w_0)$ in the critical Besov space $u_0\in
B^{1+\frac{d}{2}-2\alpha}_{2,1}(\mathbb R^d)$ and $w_0\in
B^{1+\frac{d}{2}-2\beta}_{2,1}(\mathbb R^d)$ yields a unique weak solution. For
$\alpha\ge 1$ and $\beta=0$, any initial data $u_0\in
B^{1+\frac{d}{2}-2\alpha}_{2,1}(\mathbb R^d)$ and $w_0\in
B^{\frac{d}{2}}_{2,1}(\mathbb R^d)$ also leads to a unique weak solution as
well. The regularity indices in these Besov spaces appear to be optimal and can
not be lowered in order to achieve the uniqueness. Especially, the 2D
micropolar equations with the standard Laplacian dissipation, namely
$\alpha=\beta=1$ have a unique weak solution for $(u_0, w_0)\in B^0_{2,1}$. The
proof involves the construction of successive approximation sequences and
extensive {\it a priori} estimates in Besov space settings.