  The abundance of metals in galaxies is a key parameter which permits to
distinguish between different galaxy formation and evolution models. Most of
the metallicity determinations are based on optical line ratios. However, the
optical spectral range is subject to dust extinction and, for high-z objects (z
> 3), some of the lines used in optical metallicity diagnostics are shifted to
wavelengths not accessible to ground based observatories. For this reason, we
explore metallicity diagnostics using far-infrared (IR) line ratios which can
provide a suitable alternative in such situations. To investigate these far-IR
line ratios, we modeled the emission of a starburst with the photoionization
code CLOUDY. The most sensitive far-IR ratios to measure metallicities are the
[OIII]52$\mu$m and 88$\mu$m to [NIII]57$\mu$m ratios. We show that this ratio
produces robust metallicities in the presence of an AGN and is insensitive to
changes in the age of the ionizing stellar. Another metallicity sensitive ratio
is the [OIII]88$\mu$m/[NII]122$\mu$m ratio, although it depends on the
ionization parameter. We propose various mid- and far-IR line ratios to break
this dependency. Finally, we apply these far-IR diagnostics to a sample of 19
local ultraluminous IR galaxies (ULIRGs) observed with Herschel and Spitzer. We
find that the gas-phase metallicity in these local ULIRGs is in the range 0.7 <
Z_gas/Z_sun < 1.5, which corresponds to 8.5 < 12 + log (O/H) < 8.9. The
inferred metallicities agree well with previous estimates for local ULIRGs and
this confirms that they lie below the local mass-metallicity relation.


  A simple expression for the composition dependence of the Flory-Huggins
interaction parameter of polymer/solvent systems reported earlier is used to
model the demixing of polymer solutions into two liquid phases. To this end the
system specific parameters zeta and ny of that approach are calculated as a
function of temperature using the thermodynamic expressions resulting for the
critical conditions on one side and from experimentally determined critical
data for polymers of different molar mass on the other side. By means of data
reported for the system cyclohexane/polystyrene it is demonstrated that binodal
and spinodal lines are very accurately modeled at low temperatures (UCSTs) and
at high temperatures (LCSTs). The parameters obtained from the demixing
behavior match well with that calculated from the composition dependence of the
vapor pressure at temperatures where the components are completely miscible.
Information on the phase separation of the system trans-decalin/poly-styrene
for different molecular weights and at different elevated pressures is used to
show that the approach is also apt to model pressure influences. The thus
obtained zeta (T;p) and ny (T;p) enable the prediction of the (endothermal)
theta temperature of the system as a function of pressure in quantitative
agreement with the data directly obtained from light scattering measurements
with dilute solutions.


  The alternate row and column scaling algorithm applied to a positive $n\times
n$ matrix $A$ converges to a doubly stochastic matrix $S(A)$, sometimes called
the \emph{Sinkhorn limit} of $A$. For every positive integer $n$, a two
parameter family of row but not column stochastic $n\times n$ positive matrices
is constructed that become doubly stochastic after exactly one column scaling.


  We consider the time-dependent non linear Schrodinger equations with a double
well potential in dimensions d =1 and d=2. We prove, in the semiclassical
limit, that the finite dimensional eigenspace associated to the lowest two
eigenvalues of the linear operator is almost invariant for any time.


  The collapse of an inclined cohesive granular layer triggered by a certain
perturbation can be a model for not only landslides on Earth but also
relaxations of asteroidal surface terrains. To understand such terrain
dynamics, we conduct a series of experiments of a solid-projectile impact onto
an inclined wet granular layer with various water contents and inclination
angles. As a result, we find two types of outcomes: "crater formation" and
"collapse". The "collapse" phase is observed when the inclination angle is
close to the maximum stable angle and the impact-induced vibration at the
bottom of wet granular layer is sufficiently strong. To explain the collapse
condition, we propose a simple block model considering the maximum stable
angle, inclination angle, and impact-induced vibrational acceleration.
Additionally, the attenuating propagation of the impact-induced vibrational
acceleration is estimated on the basis of three-dimensional numerical
simulations with discrete element method using dry particles. By combining
wet-granular experiments and dry-granular simulations, we find that the
impact-induced acceleration attenuates anisotropically in space. With a help of
this attenuation form, the physical conditions to induce the collapse can be
estimated using the block model.


  Annotating 3D LiDAR point clouds for perception tasks is fundamental for many
applications e.g., autonomous driving, yet it still remains notoriously
labor-intensive. Pretraining-finetuning approach can alleviate the labeling
burden by fine-tuning a pre-trained backbone across various downstream datasets
as well as tasks. In this paper, we propose SPOT, namely Scalable Pre-training
via Occupancy prediction for learning Transferable 3D representations under
such a label-efficient fine-tuning paradigm. SPOT achieves effectiveness on
various public datasets with different downstream tasks, showcasing its general
representation power, cross-domain robustness and data scalability which are
three key factors for real-world application. Specifically, we both
theoretically and empirically show, for the first time, that general
representations learning can be achieved through the task of occupancy
prediction. Then, to address the domain gap caused by different LiDAR sensors
and annotation methods, we develop a beam re-sampling technique for point cloud
augmentation combined with class-balancing strategy. Furthermore, scalable
pre-training is observed, that is, the downstream performance across all the
experiments gets better with more pre-training data. Additionally, such
pre-training strategy also remains compatible with unlabeled data. The hope is
that our findings will facilitate the understanding of LiDAR points and pave
the way for future advancements in LiDAR pre-training.


  In this paper I present a classifier for automatic identification of
linguistic politeness in Hindi texts. I have used the manually annotated corpus
of over 25,000 blog comments to train an SVM. Making use of the discursive and
interactional approaches to politeness the paper gives an exposition of the
normative, conventionalised politeness structures of Hindi. It is seen that
using these manually recognised structures as features in training the SVM
significantly improves the performance of the classifier on the test set. The
trained system gives a significantly high accuracy of over 77% which is within
2% of human accuracy.


  The search for chemically peculiar (CP) stars in open clusters using
photoelectric photometry sampling the presence of the characteristic flux
depression feature at 5200A via the Delta a-system (Maitzen 1976) has so far
delivered data for objects usually no more distant than 1000 pc from the Sun.
If one intends to study the presence of CP stars at larger distances from the
Sun, classical photometry has to be replaced by CCD photometry.
  For the first time, our investigation presents the results of CCD-photometry
in the Delta a-system for a rich open cluster which is at a distance clearly
beyond hitherto studied objects, Melotte 105 (2 kpc, log age = 8.5).
  Comparison with published uvby-photometry yields the calibration of the
colour index g_1-y of our system, which is necessary for deriving the
peculiarity index Delta a. For this we achieve an average accuracy of 0.007
mag.
  Six objects with only marginally peculiar Delta a-values were found, but
spectroscopic and additional photometric evidence is needed to substantiate
their peculiarity.


  Several aspects of the manifestation of the causality principle in LQP (local
quantum physics) are reviewed or presented. Particular emphasis is given to
those properties which are typical for LQP in the sense that they do go beyond
the structure of general quantum theory and even escape the Lagrangian
quantization methods of standard QFT. The most remarkable are those relating
causality to the modular Tomita-Takesaki theory, since they bring in the basic
concepts of antiparticles, charge superselections as well as internal and
external (geometric and hidden) symmetries.


  In loop quantum cosmology there may be a super-inflation phase in the very
early universe, in which a single scalar field with a negative power-law
potential $V= -M^4(\phi/M)^\beta$ plays important roles. Since the effective
horizon $\sqrt{SD}/H$ controls the behavior of quantum fluctuation instead of
the usual Hubble horizon, we assume the following inflation scenario; the
super-inflation starts when the quantum state of the scalar field emerges into
the classical regime,and ends when the effective horizon becomes the Hubble
horizon, and the effective horizon scale never gets shorter than the Planck
length. From consistency with the WMAP 5-year data, we place a constraint on
the parameters of the potential ($\beta$ and $M$) and the energy density at the
end of the super-inflation, depending on the volume correction parameter $n$.


  COVID-19 resulted in some of the largest supply chain disruptions in recent
history. To mitigate the impact of future disruptions, we propose an integrated
hybrid simulation framework to couple nonstationary demand signals from an
event like COVID-19 with a model of an end-to-end supply chain. We first create
a system dynamics susceptible-infected-recovered (SIR) model, augmenting a
classic epidemiological model to create a realistic portrayal of demand
patterns for oxygen concentrators (OC). Informed by this granular demand
signal, we then create a supply chain discrete event simulation model of OC
sourcing, manufacturing, and distribution to test production augmentation
policies to satisfy this increased demand. This model utilizes publicly
available data, engineering teardowns of OCs, and a supply chain illumination
to identify suppliers. Our findings indicate that this coupled approach can use
realistic demand during a disruptive event to enable rapid recommendations of
policies for increased supply chain resilience with controlled cost.


  In this letter, we present a simple and new idea to generate two types of
novel integrable multi-L\'evy-index and mix-L\'evy-index (mixed) fractional
nonlinear soliton hierarchies, containing multi-index and mixed fractional
higher-order nonlinear Schr\"odinger (NLS) hierarchy, fractional complex
modified Korteweg-de Vries (cmKdV) hierarchy, and fractional mKdV hierarchy.
Their explicit forms can be given using the completeness of squared
eigenfunctions. Moreover, we present their anomalous dispersion relations via
their linearizations, and fractional multi-soliton solutions via the inverse
scattering transform with matrix Riemann-Hilbert problems. These obtained
fractional multi-soliton solutions may be useful to understand the related
super-dispersion transports of nonlinear waves in multi-index fractional
nonlinear media.


  We discuss Bose-Einstein condensation in a trapped gas of bosonic particles
interacting dominantly via dipole-dipole forces. We find that in this case the
mean-field interparticle interaction and, hence, the stability diagram are
governed by the trapping geometry. Possible physical realisations include
ultracold heteronuclear molecules, or atoms with laser induced electric dipole
moments.


  We prove essential self-adjointness of Dirac operators with Lorentz scalar
potentials which grow sufficiently fast near the boundary $\partial\Omega$ of
the spatial domain $\Omega\subset\mathbb R^d$. On the way, we first consider
general symmetric first order differential systems, for which we identify a
new, large class of potentials, called scalar potentials, ensuring essential
self-adjointness. Furthermore, using the supersymmetric structure of the Dirac
operator in the two dimensional case, we prove confinement of Dirac particles,
i.e. essential self-adjointness of the operator, solely by magnetic fields
$\mathcal{B}$ assumed to grow, near $\partial\Omega$, faster than
$1/\big(2\text{dist} (x, \partial\Omega)^2\big)$.


  The Euler-Mascheroni constant $\gamma=0.5772\dots\!$ is the $K=\mathbb{Q}$
example of an Euler-Kronecker constant $\gamma_K$ of a number field $K.$ In
this note we consider the size of the $\gamma_q=\gamma_{K_q}$ for cyclotomic
fields $K_q:=\mathbb{Q}(\zeta_q).$ Assuming the Elliott-Halberstam Conjecture
(EH), we prove uniformly in $Q$ that $$\frac{1}{Q}\sum_{Q<q\le 2Q} \left
|\gamma_q - \log q\right |= o(\log Q).$$ In other words, under EH the $\gamma_q
/ \log q$ in these ranges converge to the one point distribution at $1$. This
theorem refines and extends a previous result of Ford, Luca, and Moree for
prime $q.$


  We present a set of log-price integrated variance estimators, equal to the
sum of open-high-low-close bridge estimators of spot variances within $n$
subsequent time-step intervals. The main characteristics of some of the
introduced estimators is to take into account the information on the occurrence
times of the high and low values. The use of the high's and low's of the bridge
associated with the original process makes the estimators significantly more
efficient that the standard realized variance estimators and its
generalizations. Adding the information on the occurrence times of the high and
low values improves further the efficiency of the estimators, much above those
of the well-known realized variance estimator and those derived from the sum of
Garman and Klass spot variance estimators. The exact analytical results are
derived for the case where the underlying log-price process is an It\^o
stochastic process. Our results suggests more efficient ways to record
financial prices at intermediate frequencies.


  Observational determinism is a security property that characterizes secure
information flow for multithreaded programs. Most of the methods that have been
used to verify observational determinism are based on either type systems or
conventional model checking techniques. A conventional model checker is
stateful and often verifies a system model usually constructed manually. As
these methods are based on stateful model checking, they are confronted with
the state space explosion problem. In order to verify and test computer
programs, stateless code model checking is more appropriate than conventional
techniques. It is an effective method for systematic testing of large and
complicated concurrent programs, and for exploring the state space of such
programs. In this paper, we propose a new method for verifying information flow
security in concurrent programs. For the first time, we use stateless code
model checking to verify observational determinism.


  Understanding how the release of stored magnetic energy contributes to the
generation of non-thermal high energy particles during solar flares is an
important open problem in solar physics. Magnetic reconnection plays a
fundamental role in the energy release and conversion processes taking place
during flares. A common approach for investigating particle acceleration is to
use test particles in fields derived from magnetohydrodynamic (MHD) simulations
of reconnection. These MHD simulations use anomalous resistivities that are
much larger than the Spitzer resistivity based on Coulomb collisions. The
processes leading to enhanced resistivity should also affect the test
particles. We explore the link between resistivity and particle orbits building
on a previous study using a 2D MHD simulation of magnetic reconnection. This
paper extends the previous investigation to a 3D magnetic reconnection
configuration and to study the effect on test particle orbits. We carried out
orbit calculations using a 3D MHD simulation of separator reconnection. We use
the relativistic guiding centre approximation including stochastic pitch angle
scattering. The effects of varying the resistivity and the models for pitch
angle scattering on particle orbit trajectories, final positions, energy
spectra, final pitch angle distribution, and orbit duration are all studied in
detail. Pitch angle scattering widens collimated beams of orbit trajectories,
allowing orbits to access previously unaccessible field lines; this causes
final positions to spread to topological structures that were previously
inaccessible. Scattered orbit energy spectra are found to be predominantly
affected by the level of anomalous resistivity, with the pitch angle scattering
model only playing a role in isolated cases. Scattering is found to play a
crucial role in determining the pitch angle and orbit duration distributions.


  We consider a class of wild initial data to the compressible Euler system
that give rise to infinitely many admissible weak solutions via the method of
convex integration. We identify the closure of this class in the natural
$L^1$-topology and show that its complement is rather large, specifically it is
an open dense set.


  Ryu and Takayanagi conjectured a formula for the entanglement (von Neumann)
entropy of an arbitrary spatial region in an arbitrary holographic field
theory. The von Neumann entropy is a special case of a more general class of
entropies called Renyi entropies. Using Euclidean gravity, Fursaev computed the
entanglement Renyi entropies (EREs) of an arbitrary spatial region in an
arbitrary holographic field theory, and thereby derived the RT formula. We
point out, however, that his EREs are incorrect, since his putative saddle
points do not in fact solve the Einstein equation. We remedy this situation in
the case of two-dimensional CFTs, considering regions consisting of one or two
intervals. For a single interval, the EREs are known for a general CFT; we
reproduce them using gravity. For two intervals, the RT formula predicts a
phase transition in the entanglement entropy as a function of their separation,
and that the mutual information between the intervals vanishes for separations
larger than the phase transition point. By computing EREs using gravity and CFT
techniques, we find evidence supporting both predictions. We also find evidence
that large-$N$ symmetric-product theories have the same EREs as holographic
ones.


  An $(n_k)$-configuration is a set of $n$ points and $n$ lines in the
projective plane such that their point-line incidence graph is $k$-regular. The
configuration is geometric, topological, or combinatorial depending on whether
lines are considered to be straight lines, pseudolines, or just combinatorial
lines. We provide an algorithm for generating, for given $n$ and $k$, all
topological $(n_k)$-configurations up to combinatorial isomorphism, without
enumerating first all combinatorial $(n_k)$-configurations. We apply this
algorithm to confirm efficiently a former result on topological
$(18_4)$-configurations, from which we obtain a new geometric
$(18_4)$-configuration. Preliminary results on $(19_4)$-configurations are also
briefly reported.


  Multi-view clustering attracts much attention recently, which aims to take
advantage of multi-view information to improve the performance of clustering.
However, most recent work mainly focus on self-representation based subspace
clustering, which is of high computation complexity. In this paper, we focus on
the Markov chain based spectral clustering method and propose a novel essential
tensor learning method to explore the high order correlations for multi-view
representation. We first construct a tensor based on multi-view transition
probability matrices of the Markov chain. By incorporating the idea from robust
principle component analysis, tensor singular value decomposition (t-SVD) based
tensor nuclear norm is imposed to preserve the low-rank property of the
essential tensor, which can well capture the principle information from
multiple views. We also employ the tensor rotation operator for this task to
better investigate the relationship among views as well as reduce the
computation complexity. The proposed method can be efficiently optimized by the
alternating direction method of multipliers~(ADMM). Extensive experiments on
six real world datasets corresponding to five different applications show that
our method achieves superior performance over other state-of-the-art methods.


  In gravitation theory, a fermion field must be regarded only in a pair with a
certain tetrad gravitational field. These pairs can be represented by sections
of the composite spinor bundle $S\to\Si\to X^4$ where values of gravitational
fields play the role of parameter coordinates, besides the familiar world
coordinates.


  With the wide adoption of mobile devices, today's location tracking systems
such as satellites, cellular base stations and wireless access points are
continuously producing tremendous amounts of location data of moving objects.
The ability to discover moving objects that travel together, i.e., traveling
companions, from their trajectories is desired by many applications such as
intelligent transportation systems and location-based services. Existing
algorithms are either based on pattern mining methods that define a particular
pattern of traveling companions or based on representation learning methods
that learn similar representations for similar trajectories. The former methods
suffer from the pairwise point-matching problem and the latter often ignore the
temporal proximity between trajectories. In this work, we propose a generic
deep representation learning model using autoencoders, namely, ATTN-MEAN, for
the discovery of traveling companions. ATTN-MEAN collectively injects spatial
and temporal information into its input embeddings using skip-gram, positional
encoding techniques, respectively. Besides, our model further encourages
trajectories to learn from their neighbours by leveraging the
Sort-Tile-Recursive algorithm, mean operation and global attention mechanism.
After obtaining the representations from the encoders, we run DBSCAN to cluster
the representations to find travelling companion. The corresponding
trajectories in the same cluster are considered as traveling companions.
Experimental results suggest that ATTN-MEAN performs better than the
state-of-the-art algorithms on finding traveling companions.


  In this paper, we propose a clean and general proof framework to establish
the convergence analysis of the Difference-of-Convex (DC) programming algorithm
(DCA) for both standard DC program and convex constrained DC program. We first
discuss suitable assumptions for the well-definiteness of DCA. Then, we focus
on the convergence analysis of DCA, in particular, the global convergence of
the sequence $\{x^k\}$ generated by DCA under the Lojasiewicz subgradient
inequality and the Kurdyka-Lojasiewicz property respectively. Moreover, the
convergence rate for the sequences $\{f(x^k)\}$ and $\{\|x^k-x^*\|\}$ are also
investigated. We hope that the proof framework presented in this article will
be a useful tool to conveniently establish the convergence analysis for many
variants of DCA and new DCA-type algorithms.


  Modeling of frictional contacts is crucial for investigating mechanical
performances of composite materials under varying service environments. The
paper considers a linear elasticity system with strongly heterogeneous
coefficients and quasistatic Tresca friction law, and studies the
homogenization theories under the frameworks of H-convergence and small
$\epsilon$-periodicity. The qualitative result is based on H-convergence, which
shows the original oscillating solutions will converge weakly to the
homogenized solution, while our quantitative result provides an estimate of
asymptotic errors in $H^1$-norm for the periodic homogenization. This paper
also designs several numerical experiments to validate the convergence rates in
the quantitative analysis.


  We generalize a previously obtained result, for the case of a few other
static hyperbolic universes with manifolds of nontrivial topology as spatial
sections.


  In this paper we test the hypothesis that the Pioneer anomaly can be of
gravitational origin by comparing the predicted model-independent shifts Delta
a/a for the semimajor axis of Uranus and Neptune with the Voyager 2
radio-technical distance measurements performed at JPL-NASA. As in the case of
other tests based on different methods and data sets (secular perihelion
advance, right ascension/declination residuals over about one century), the
orbits of the investigated planets are not affected by any anomalous
acceleration like that experienced by the Pioneer 10/11 spacecraft.


  Heat flow is an important constraint on planetary formation and evolution. It
has been suggested that Martian obliquity cycles might cause periodic collapses
in atmospheric pressure, leading to corresponding decreases in regolith thermal
conductivity (which is controlled by gas in the pore spaces). Geothermal heat
would then build up in the subsurface, potentially affecting present-day heat
flow - and thus the measurements made by a heat-flow probe such as the InSight
HP$^{3}$ instrument. To gauge the order of magnitude of this effect, we model
the diffusion of a putative heat pulse caused by thermal conductivity changes
with a simple numerical scheme and compare it to the heat-flow perturbations
caused by other effects. We find that an atmospheric collapse to 300 Pa in the
last 40 kyr would lead to a present-day heat flow that is up to $2-8\%$ larger
than the average geothermal background. Considering the InSight mission with
expected $5-15\%$ error bars on the HP$^{3}$ measurement, this perturbation
would only be significant in the best-case scenario of full instrument
deployment, completed measurement campaign, and a well-modelled surface
configuration. The prospects for detecting long-term climate perturbations via
spacecraft heat-flow experiments remain challenging.


  We consider the quantum scattering off a time dependent barrier in one
dimension. Our initial state is a right going eigenstate of the Hamiltonian at
time t=0. It consists of a plane wave incoming from the left, a reflected plane
wave on the left of the barrier and a transmitted wave on its right. We find
that at later times, the evolving wave function has a finite overlap with left
going eigenstates of the Hamiltonian at time t=0. For simplicity we present an
exact result for a time dependent delta function potential. Then we show that
our result is not an artifact of that specific choice of the potential. This
surprising result does not agree with our interpretation of the eigenstates of
the Hamiltonian at time t=0. A numerical study of evolving wave packets, does
not find any corresponding real effect. Namely, we do not see on the right hand
side of the barrier any evidence for a left going packet. Our conclusion is
thus that the intriguing result mentioned above is intriguing only due to the
semantics of the interpretation.


  In this manuscript the three types of late-time behavior of spherically
symmetric Boson Stars are presented, these are: stable configurations, unstable
bounded that collapse to form black holes and unstable unbounded that explode.
The results are found by solving the spherically symmetric
Einstein-Klein-Gordon system of equations for a complex scalar field with
initial conditions corresponding to a Boson Star. The solution is based on a
constrained evolution that uses the method of lines for the scalar field and
solves the constraint equations for the geometry on the fly.


  Covariate balance is crucial in obtaining unbiased estimates of treatment
effects in observational studies. Methods based on inverse probability weights
have been widely used to estimate treatment effects with observational data.
Machine learning techniques have been proposed to estimate propensity scores.
These techniques however target accuracy instead of covariate balance. Methods
that target covariate balance have been successfully proposed and largely
applied to estimate treatment effects on continuous outcomes. However, in many
medical and epidemiological applications, the interest lies in estimating
treatment effects on time-to-event outcomes. With this type of data, one of the
most common estimands of interest is the marginal hazard ratio of the Cox
proportional hazard model. In this paper, we start by presenting robust
orthogonality weights (ROW), a set of weights obtained by solving a quadratic
constrained optimization problem that maximizes precision while constraining
covariate balance defined as the sample correlation between confounders and
treatment. By doing so, ROW optimally deal with both binary and continuous
treatments. We then evaluate the performance of the proposed weights in
estimating marginal hazard ratios of binary and continuous treatments with
time-to-event outcomes in a simulation study. We finally apply ROW on the
evaluation of the effect of hormone therapy on time to coronary heart disease
and on the effect of red meat consumption on time to colon cancer among 24,069
postmenopausal women enrolled in the Women's Health Initiative observational
study.


  Fermi has provided the largest sample of gamma-ray selected blazars to date.
In this work we use a uniformly selected set of 211 BL Lacertae (BL Lac)
objects detected by it Fermi during its first year of operation. We have
obtained redshift constraints for 206 out of the 211 BL Lacs in our sample
making it the largest and most complete sample of BL Lacs available in the
literature. We use this sample to determine the luminosity function of BL Lacs
and its evolution with cosmic time. We find that for most BL Lac classes, the
evolution is positive with a space density peaking at modest redshift (z~1.2).
The low-luminosity, high-synchrotron peaked (HSP) BL Lacs are an exception,
showing strong negative evolution, with number density increasing for
z$\lesssim$0.5. Since this rise corresponds to a drop-off in the density of
flat-spectrum radio quasars (FSRQs), a possible interpretation is that these
HSPs represent an accretion-starved end-state of an earlier merger-driven
gas-rich phase. We additionally find that the known BL Lac correlation between
luminosity and photon spectral index persists after correction for the
substantial observational selection effects with implications for the so called
`blazar sequence'. Finally, estimating the beaming corrections to the
luminosity function, we find that BL Lacs have an average Lorentz factor of
$\gamma=6.1^{+1.1}_{-0.8}$, and that most are seen within 10$^{\circ}$ of the
jet axis.


  Context. Bright heads of penumbral filaments, penumbral grains (PGs), show
apparent horizontal motions inwards, towards the umbra, or outwards, away from
the umbra.
  Aims. We aim to prove statistically whether the direction of PGs' apparent
motion is related to the inclination of the surrounding magnetic field.
  Methods. We use spectropolarimetric observations of five sunspot penumbrae to
compare magnetic inclinations inside PGs with those in their surroundings. The
data are taken by three observatories: Hinode satellite, Swedish Solar
Telescope, and GREGOR solar telescope. The direction of PGs' motion is
determined by feature tracking. The atmospheric conditions in PGs and their
surroundings, including the magnetic field information, are retrieved by means
of height-stratified spectropolarimetric inversions.
  Results. On a sample of 444 inward- and 269 outward-moving PGs we show that
43% of the inward-moving PGs have magnetic inclination larger by $8^\circ \pm
4^\circ$ than the inclination in their surroundings and 51% of the
outward-moving PGs have the inclination smaller by $13^\circ \pm 7^\circ$ than
the surrounding one. The opposite relation of inclinations is observed at only
one-fifth of the inward- and outward-moving PGs.
  Conclusions. Rising hot plasma in PGs surrounded by a less inclined magnetic
field may adapt its trajectory to be more vertical, causing an inward apparent
motion of PGs. Oppositely, it may be dragged by a more horizontal surrounding
magnetic field such that an outward apparent motion is observed.


  We prove energy stability of a standard operator-splitting method for the
Cahn-Hilliard equation. We establish uniform bound of Sobolev norms of the
numerical solution and convergence of the splitting approximation. This is the
first unconditional energy stability result for the operator-splitting method
for the Cahn-Hilliard equation. Our analysis can be extended to many other
models.


  The propagation of Gravitational Waves has been reliably recognised as a
test-bed for beyond standard models of gravity and cosmology. We utilise this
property to examine the effects of a class of parametrised beyond-$\Lambda$CDM
cosmology on inferece of GW parameters. We find that the combined
beyond-$\Lambda$CDM likelihood function exhibits correlations between the
parameters which are especially dependent upon binary eccentricity. Expanding
on previous results, we demonstrate through Fisher forecasts that we would need
nearly 1 year of 3G GW data to be able to infer the beyond-$\Lambda$CDM model
to $2\sigma$ significance. We also find counter-intuitively that errors of
source-modelling leave large biases upon the inference of the
beyond-$\Lambda$CDM parameters which come into play only during GW propagation.


  We have previously shown that most of the anomalies in the superconducting
characteristics of cuprates and ferropnictides observed at dopant
concentrations within the superconducting dome, as well as the position of the
domes in the phase diagrams, do not require knowledge of the details of their
electronic structure for explanation, but can be understood and calculated with
high accuracy within the framework of a simple model describing the cluster
structure of the superconducting phase. This fact suggests a change in the
paradigm that forms our understanding of HTSC. In this paper, we propose a
unified view on the transformation of the electronic structure of cuprates and
ferropnictides upon heterovalent and isovalent doping, based on the assumption
of self-localization of doped carriers. In this representation, in undoped
cuprates and ferropnictides, which initially have different electronic
structures (Mott insulator and semimetal), local doping forms percolation
clusters with the same electronic structure of a self-doped excitonic insulator
where a specific mechanism of superconducting pairing is implemented, which is
genetically inherent in such a system. The proposed model includes a mechanism
for generating additional free carriers under heterovalent and isovalent doping
and makes it possible to predict their sign, which, in the general case, does
not coincide with the sign of doped carriers.


  The LCDM standard model, although an excellent parametrization of the present
cosmological data, requires two as yet unobserved components, Dark Matter and
Dark Energy, for more than 95% of the Universe, and a high level of
fine-tuning. Faced to this unsatisfactory situation, we study an unconventional
cosmology, the Dirac-Milne universe, a matter-antimatter symmetric cosmology,
in which antimatter is supposed to present a negative active gravitational
mass. We show that this universe remarkably satisfies the cosmological tests
for the age of the Universe, Big-Bang Nucleosynthesis, and Type Ia Supernovae
data. Most surprisingly, it also provides the degree scale for the first
acoustic peak of the Cosmological Microwave Background. This simple model,
without any adjustable parameter or need for Dark Matter or Dark Energy, is a
reminder that we should look for simpler and more motivated cosmological models
than the present LCDM standard model.


  For nonuniform cofinite Fuchsian groups $\Gamma$ which satisfy a certain
additional geometric condition, we show that the Maass cusp forms for $\Gamma$
are isomorphic to 1-eigenfunctions of a finite-term transfer operator. The
isomorphism is constructive.


  Blind source separation is a common processing tool to analyse the
constitution of pixels of hyperspectral images. Such methods usually suppose
that pure pixel spectra (endmembers) are the same in all the image for each
class of materials. In the framework of remote sensing, such an assumption is
no more valid in the presence of intra-class variabilities due to illumination
conditions, weathering, slight variations of the pure materials, etc... In this
paper, we first describe the results of investigations highlighting intra-class
variability measured in real images. Considering these results, a new
formulation of the linear mixing model is presented leading to two new methods.
Unconstrained Pixel-by-pixel NMF (UP-NMF) is a new blind source separation
method based on the assumption of a linear mixing model, which can deal with
intra-class variability. To overcome UP-NMF limitations an extended method is
proposed, named Inertia-constrained Pixel-by-pixel NMF (IP-NMF). For each
sensed spectrum, these extended versions of NMF extract a corresponding set of
source spectra. A constraint is set to limit the spreading of each source's
estimates in IP-NMF. The methods are tested on a semi-synthetic data set built
with spectra extracted from a real hyperspectral image and then numerically
mixed. We thus demonstrate the interest of our methods for realistic source
variabilities. Finally, IP-NMF is tested on a real data set and it is shown to
yield better performance than state of the art methods.


  Data-to-Text Generation (DTG) is a subfield of Natural Language Generation
aiming at transcribing structured data in natural language descriptions. The
field has been recently boosted by the use of neural-based generators which
exhibit on one side great syntactic skills without the need of hand-crafted
pipelines; on the other side, the quality of the generated text reflects the
quality of the training data, which in realistic settings only offer
imperfectly aligned structure-text pairs. Consequently, state-of-art neural
models include misleading statements - usually called hallucinations - in their
outputs. The control of this phenomenon is today a major challenge for DTG, and
is the problem addressed in the paper.
  Previous work deal with this issue at the instance level: using an alignment
score for each table-reference pair. In contrast, we propose a finer-grained
approach, arguing that hallucinations should rather be treated at the word
level. Specifically, we propose a Multi-Branch Decoder which is able to
leverage word-level labels to learn the relevant parts of each training
instance. These labels are obtained following a simple and efficient scoring
procedure based on co-occurrence analysis and dependency parsing. Extensive
evaluations, via automated metrics and human judgment on the standard WikiBio
benchmark, show the accuracy of our alignment labels and the effectiveness of
the proposed Multi-Branch Decoder. Our model is able to reduce and control
hallucinations, while keeping fluency and coherence in generated texts. Further
experiments on a degraded version of ToTTo show that our model could be
successfully used on very noisy settings.


  We determine the time dependence of pressure and shear stress distributions
on the surface of a pitching and deforming hydrofoil from measurements of the
three dimensional flow field. Period-averaged stress maps are obtained both in
the presence and absence of steady flow around the foil. The velocity vector
field is determined via volumetric three-component particle tracking
velocimetry and subsequently inserted into the Navier-Stokes equation to
calculate the total hydrodynamic stress tensor. In addition, we also present a
careful error analysis of such measurements, showing that local evaluations of
stress distributions are possible. The flapping foil used in the experiments is
designed to allow comparison with a small trapezoidal fish fin, in terms of the
scaling laws that govern the oscillatory flow regime. Unsteady Euler-Bernoulli
beam theory is employed to derive instantaneous transversal force distributions
on the deflecting hydrofoil from its deflection and thereby validate the
spatial distributions of hydrodynamic stresses obtained from the fluid velocity
field. The consistency of the force time-dependence is verified using a control
volume analysis.


  The charge asymmetry ($A_{\rm ch}$) dependence of the $\pi^{-}$ and $\pi^{+}$
elliptic flow difference, $\Delta v_{2}(A_{\rm ch})$, has been regarded as a
sensitive observable for the possible chiral magnetic wave (CMW) in
relativistic heavy ion collisions. In this work, we first demonstrate that, due
to non-flow backgrounds, the flow measurements by the Q-cumulant method using
all charged particles as reference introduce a trivial linear term to $\Delta
v_{2}(A_{\rm ch})$. The trivial slope can be negative in the triangle flow
difference $\Delta v_{3}(A_{\rm ch})$ if the non-flow is dominated by
back-to-back pairs. After eliminating the trivial term, we find that the
non-flow between like-sign pairs gives rise to an additional positive slope to
$\Delta v_{2}(A_{\rm ch})$ because of the larger dilution effect to $\pi^{+}$
($\pi^{-}$) at positive (negative) $A_{\rm ch}$. We further find that the
competition between different $\pi$ sources can introduce another non-trivial
linear-$A_{\rm ch}$ term due to their different multiplicity fluctuations and
anisotropic flows. We then study the effect of neutral cluster (resonance)
decays as a mechanism for local charge conservation on the slope parameter of
$\Delta v_{2}(A_{\rm ch})$. We find that the slope parameter is sensitive to
the kinematics of those neutral clusters. Light resonances give positive slopes
while heavy resonances give negative slopes. Local charge conservation from
continuum cluster mass distribution can give a positive slope parameter
comparable to experimental data. Our studies indicate that many non-CMW physics
mechanisms can give rise to a $A_{\rm ch}$-dependent $\Delta v_{2}(A_{\rm ch})$
and the interpretation of $\Delta v_{2}(A_{\rm ch})$ in terms of the CMW is
delicate.


  Seagrasses are vital organisms in coastal waters, and the drastic demise of
their population in the last decades has worrying implications for marine
ecosystems. Spatial models for seagrass meadows provide a mathematical
framework to study their dynamical processes and emergent collective behavior.
These models are crucial to predict the response of seagrasses to different
global warming scenarios, analyze the resilience of existing seagrass
distributions, and optimize restoration strategies. In this article, we propose
a model that includes interactions among different species based on the clonal
growth of seagrasses. We present a theoretical analysis of the model
considering the specific case of the seagrass-seaweed interaction between {\it
Cymodocea nodosa} and {\it Caulerpa prolifera}. Our simulations successfully
reproduce field observations of shoot densities in mixed meadows in the Ebro
River Delta in the Mediterranean Sea. Besides, the proposed model allows us to
investigate the possible underlying mechanisms that mediate the interaction
among the two macrophytes.


  A new nonlinear integral equation (NLIE) describing the thermodynamics of the
Heisenberg spin chain is derived based on the t-W relation of the quantum
transfer matrices. The free energy of the system in a magnetic field is thus
obtained by solving the NLIE. This method can be generalized to other lattice
quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an
example, we construct the corresponding NLIEs and compute the free energy. The
present results coincide exactly with those obtained via other methods
previously.


  A long-standing scientific puzzle has been to explain the origin of the
heaviest elements in the Universe and, more particularly, the production of the
elements heavier than iron up to uranium. The rapid neutron capture process (or
r-process) is known to synthesize about 50\% of these heavy elements and the
long-lived actinides observed in our solar system and so-called metal-poor
r-process-enhanced stars. This thesis aims to study the r-process
nucleosynthesis and some of the uncertainties that still govern our
predictions, namely, nuclear yields and heating rates. Our focus will be on the
r-process in neutron star (NS) mergers, which is in the spotlight after recent
``multi-messenger'' observations, including the combined detection of
gravitational waves from a NS-NS merger event and its subsequent
electromagnetic counterpart. In this work, we base our nucleosynthesis
calculations on hydrodynamical simulations of NS merger systems, which estimate
the amount of ejected mass and its properties during ejection. Through our
r-process calculations, we estimate the composition of this gravitationally
unbound material, which can contribute to the r-process enrichment of the
Galaxy. This work is divided into two studies, each addressing a remaining open
question regarding the r-process nucleosynthesis. First, a coherent study of
the impact of neutrino interactions on the r-process element nucleosynthesis
and the heating rate produced by the radioactive decay of nuclei synthesized in
the dynamical ejecta of NS-NS mergers is presented. We have studied the
material ejected from four NS-NS merger systems based on hydrodynamical
simulations...


  When working with a new dataset, it is important to first explore and
familiarize oneself with it, before applying any advanced machine learning
algorithms. However, to the best of our knowledge, no tools exist that quickly
and reliably give insight into the contents of a selection of documents with
respect to what distinguishes them from other documents belonging to different
categories. In this paper we propose to extract `relevant words' from a
collection of texts, which summarize the contents of documents belonging to a
certain class (or discovered cluster in the case of unlabeled datasets), and
visualize them in word clouds to allow for a survey of salient features at a
glance. We compare three methods for extracting relevant words and demonstrate
the usefulness of the resulting word clouds by providing an overview of the
classes contained in a dataset of scientific publications as well as by
discovering trending topics from recent New York Times article snippets.


  Target temperature in magnetron sputtering systems is a significant parameter
which not only affects the physical and chemical properties of the deposited
film but also stimulates the reactive sputtering process. Therefore, it is of
great interest to establish a relationship between the target temperature and
other parameters of magnetron sputtering process such as the gas pressure and
the discharge power. This paper is devoted to the experimental and numerical
studies on titanium target temperature in Argon medium. Numerical simulations
for the target temperature are performed by solving the Heat equation for the
magnetron sputtering system enclosed in Argon filled chamber. The simulations
are compared with the experimental temperature data. The difference between the
simulated results and experimental data on the power dependence of target
temperature is explained by an empirical model of heat transfer from the ions
to the gas.


  We find an exact analytic solution for the time evolution of a three Dirac
neutrino system adiabatically oscillating in matter, constructing explicitly
the relevant $3\times 3$ mixing matrix in matter. Using this result we
investigate the solar neutrino data in a scenario where the neutrino masses are
such that $m_1\alt m_2\ll m_3$, taking into account several phenomenological
constraints on neutrino mixing angles and masses. A solution of the solar
neutrino problem for large values of the parameter $\delta m^2=m_2^2-m_1^2$
which are not usually associated with a resonance is found. This is an
essentially three-generation effect.


  Interferometric observations of the W33A massive star-formation region,
performed with the Submillimeter Array (SMA) and the Very Large Array (VLA) at
resolutions from 5 arcsec (0.1 pc) to 0.5 arcsec (0.01 pc) are presented. Our
three main findings are: (1) parsec-scale, filamentary structures of cold
molecular gas are detected. Two filaments at different velocities intersect in
the zone where the star formation is occurring. This is consistent with
triggering of the star-formation activity by the convergence of such filaments,
as predicted by numerical simulations of star formation initiated by converging
flows. (2) The two dusty cores (MM1 and MM2) at the intersection of the
filaments are found to be at different evolutionary stages, and each of them is
resolved into multiple condensations. MM1 and MM2 have markedly different
temperatures, continuum spectral indices, molecular-line spectra, and masses of
both stars and gas. (3) The dynamics of the "hot-core" MM1 indicates the
presence of a rotating disk in its center (MM1-Main) around a faint free-free
source. The stellar mass is estimated to be approximately 10 Msun. A massive
molecular outflow is observed along the rotation axis of the disk.


  Point cloud segmentation and classification are some of the primary tasks in
3D computer vision with applications ranging from augmented reality to
robotics. However, processing point clouds using deep learning-based algorithms
is quite challenging due to the irregular point formats. Voxelization or 3D
grid-based representation are different ways of applying deep neural networks
to this problem. In this paper, we propose PointResNet, a residual block-based
approach. Our model directly processes the 3D points, using a deep neural
network for the segmentation and classification tasks. The main components of
the architecture are: 1) residual blocks and 2) multi-layered perceptron (MLP).
We show that it preserves profound features and structural information, which
are useful for segmentation and classification tasks. The experimental
evaluations demonstrate that the proposed model produces the best results for
segmentation and comparable results for classification in comparison to the
conventional baselines.


  The generalized master equation or the equivalent continuous time random walk
equations can be used to compute the macroscopic first passage time
distribution (FPTD) of a complex stochastic system from short-term microscopic
simulation data. The computation of the mean first passage time and additional
low-order FPTD moments can be simplified by directly relating the FPTD moment
generating function to the moments of the local FPTD matrix. This relationship
can be physically interpreted in terms of steady-state relaxation, an extension
of steady-state flow. Moreover, it is amenable to a statistical error analysis
that can be used to significantly increase computational efficiency. The
efficiency improvement can be extended to the FPTD itself by modelling it using
a Gamma distribution or rational function approximation to its Laplace
transform.


  In this paper, we propose a continuous measurement and feedback scheme to
achieve strong Einstein-Podolsky-Rosen (EPR) steering and Bell nonlocality of
two macroscopic mechanical oscillators in cavity optomechanics. Our system
consists of two optomechanical cavities in which two cavity fields are coupled
to each other via a nondegenerate parametric downconversion. The two cavity
output fields are subject to continuous Bell-like homodyne detection and the
detection currents are fed back to drive the cavity fields. It is found that
when the feedback is absent, the two mechanical oscillators can only be
prepared in steady weakly entangled states which however do not display EPR
steering and Bell nonlocality, due to the so-called 3 dB limit. But when the
feedback is present, it is found that the mechanical entanglement is
considerably enhanced such that strong mechanical steering and Bell nonlocality
can be obtained in the steady-state regime. We analytically reveal that this is
because the feedback drives the mechanical oscillators into a steady
approximate two-mode squeezed vacuum state, with arbitrary squeezing in
principle. It is shown that the feedback can also obviously improve the purity
of the nonclassical mechanical states. The dependences of the mechanical
quantum nonlocality on the feedback strength and thermal fluctuations are
studied, and it is found that Bell nonlocality is much more vulnerable to
thermal noise than EPR steerable nonlocality.


  The Depth from Defocus (DFD) imaging technique for measuring the size and
number concentration of particles in a dispersed two-phase flow has up to now
been restricted to relatively sparse particle densities and to identifying only
spherical particles. The present study examines two advancements to the
technique, widening its range of application significantly. The first
advancement introduces an image processing procedure which can identify and
size particle images which are overlapping. This increases the tolerable number
concentration of particles which can be identified and processed within the
measurement volume. The second advancement explores the possibility of
determining the size and position of non-spherical particles within an
observation volume. Both advancements build on recent theoretical work,
utilizing not only the gray level of the blurred, out-of-focus images, but also
the gradient of the gray level normal to the nominal particle or particle
ensemble contour. This gray-level gradient is used to estimate the width of the
blur kernel, which is assumed to remain Gaussian.
  These enhancements are experimentally validated using a dedicated apparatus
in which particles of known size, shape and degree of overlapping images can be
systematically varied. This experimental setup provides benchmark data to
quantify the accuracy and limitations of the processing algorithms.


  Inspired by the foundational works by Spivak and Fong and Cruttwell et al.,
we introduce a categorical framework to formalize Bayesian inference and
learning. The two key ideas at play here are the notions of Bayesian inversions
and the functor GL as constructed by Cruttwell et al.. In this context, we find
that Bayesian learning is the simplest case of the learning paradigm. We then
obtain categorical formulations of batch and sequential Bayes updates while
also verifying that the two coincide in a specific example.


  In this paper, we define the Mycielskian of a signed graph and discuss the
properties of balance and switching in the Mycielskian of a given signed graph.
We provide a condition for ensuring the Mycielskian of a balanced signed graph
remains balanced, leading to the construction of a balanced Mycielskian. We
establish a relation between the chromatic numbers of a signed graph and its
Mycielskian. We also study the structure of different matrices related to the
Mycielskian of a signed graph.


  By globally embedding curved spaces into higher dimensional flat ones, we
show that Hawking thermal properties map into their Unruh equivalents: The
relevant curved space detectors become Rindler ones, whose temperature and
entropy reproduce the originals. Specific illustrations include Schwarzschild,
Schwarzschild-(anti)deSitter, Reissner-Nordstrom and BTZ spaces.


  In preprint alg-geom/9708009 we have constructed a (ten-dimensional)
symplectic desingularization of the moduli space of rank-two torsion-free
semistable sheaves on a $K3$, with trivial determinant and second Chern class
equal to 4. In the present paper we prove that (every deformation of) this
desingularization is a new irreducible symplectic variety. More precisely we
show that the desingularization is irreducible symplectic, and that its second
Betti number is at least 24.


  Future quantum internet aims to enable quantum communication between
arbitrary pairs of distant nodes through the sharing of end-to-end
entanglement, a universal resource for many quantum applications. As in
classical networks, quantum networks also have to resolve problems related to
routing and satisfaction of service at a sufficient rate. We deal here with the
problem of scheduling when multiple commodities must be served through a
quantum network based on first generation quantum repeaters, or quantum
switches. To this end, we introduce a novel discrete-time algebraic model for
arbitrary network topology, including transmission and memory losses, and
adapted to dynamic scheduling decisions. Our algebraic model allows the
scheduler to use the storage of temporary intermediate links to optimize the
performance, depending on the information availability, ranging from full
global information for a centralized scheduler to partial local information for
a distributed one. As an illustrative example, we compare a simple greedy
scheduling policy with several Max-Weight inspired scheduling policies and
illustrate the resulting achievable rate regions for two competing pairs of
clients through a network.


  High flow rate, water-driven hydraulic fractures are more common now than
ever in the oil and gas industry. Although the fractures are small, the high
injection rate and low viscosity of the water, lead to high Reynolds numbers
and potentially turbulence in the fracture. Here we present a semi-analytical
solution for a blade-shaped (PKN) geometry hydraulic fracture driven by a
turbulent fluid in the limit of zero fluid leak-off to the formation. We model
the turbulence in the PKN fracture using the Gaukler-Manning-Strickler
parametrization, which relates the the flow rate of the water to the pressure
gradient along the fracture. The key parameter in this relation is the
Darcy-Weisbach friction factor for the roughness of the crack wall. Coupling
this turbulence parametrization with conservation of mass allows us to write a
nonlinear pde for the crack width as a function of space and time. By way of a
similarity ansatz, we obtain a semi-analytical solution using an orthogonal
polynomial series. Embedding the asymptotic behavior near the fracture tip into
the polynomial series, we find very rapid convergence: a suitably accurate
solution is obtained with two terms of the series. This closed-form solution
facilitates clear comparisons between the results and parameters for laminar
and turbulent hydraulic fractures. In particular, it resolves one of the well
known problems whereby calibration of models to data has difficulty
simultaneously matching the hydraulic fracture length and wellbore pressure.


  Motivated by recent experiments, we develop a model for DNA toroids under
external tension. We find that tori are the equilibrium states for our model up
to a critical tension, above which they become only metstable. Above this
tension, we find a cascade of transitions between discrete toroid states that
successively lowers the winding number, until the ground state (rod) is
reached. In this process, this model predicts a nearly constant force plateau
as a function of extension, in agreement with experiment.


  For a finite group $G$ denote by $N(G)$ the set of conjugesy class sizes of
$G$. We show that every finite group $G$ with the property $N(G)=N(Alt_n), n>4$
or $N(G)=N(Sym_n), n>22$ is non-solvable.


  According to the Dold-Kan correspondence, the normalization functor
determines a categorical equivalence between simplicial abelian groups and
non-negatively graded chain complexes. Nevertheless, the same statement is no
longer true when extending to the context of algebras over an operad. In spite
of this, the existence of the Dold-Kan correspondence for operadic algebras can
still be realized from a homotopy-theoretic perspective. This was indeed
observed for $A_\infty$-algebras by Schwede-Shipley, and for
$E_\infty$-algebras by Mandell, and more generally, for algebras over any
$\Sigma$-cofibrant operad due to White-Yau. In the first part of the paper, we
shall prove further that the normalization functor induces an equivalence
between the $\infty$-categories of operads with non-fixed sets of colors, in
the Dwyer-Kan homotopy theory framework. Subsequently, we delve into
investigating the mapping spaces between enriched operads by relating them to
mapping spaces between operadic bimodules via nice fiber sequences. The
validity of the main statements is examined first for simplicial operads, and
then for connective dg operads due to the operadic Dold-Kan correspondence.


  In the field of swarm robotics, the design and implementation of spatial
density control laws has received much attention, with less emphasis being
placed on performance evaluation. This work fills that gap by introducing an
error metric that provides a quantitative measure of coverage for use with any
control scheme. The proposed error metric is continuously sensitive to changes
in the swarm distribution, unlike commonly used discretization methods. We
analyze the theoretical and computational properties of the error metric and
propose two benchmarks to which error metric values can be compared. The first
uses the realizable extrema of the error metric to compute the relative error
of an observed swarm distribution. We also show that the error metric extrema
can be used to help choose the swarm size and effective radius of each robot
required to achieve a desired level of coverage. The second benchmark compares
the observed distribution of error metric values to the probability density
function of the error metric when robot positions are randomly sampled from the
target distribution. We demonstrate the utility of this benchmark in assessing
the performance of stochastic control algorithms. We prove that the error
metric obeys a central limit theorem, develop a streamlined method for
performing computations, and place the standard statistical tests used here on
a firm theoretical footing. We provide rigorous theoretical development,
computational methodologies, numerical examples, and MATLAB code for both
benchmarks.


  Facing the advent of the next generation cosmological surveys we present a
method to forecast knowledge gain on cosmological models. We propose this as a
well defined and general tool to quantify the performance of different
experiments in relation to different theoretical models. In particular, the
assessment of experimental performance will benefit enormously from the fact
that this method is invariant under re-parametrization of the model. We apply
this to future surveys and compare expected knowledge advancements to the most
relevant experiments performed over the history of modern cosmology. When
considering the standard cosmological model, we show that it will rapidly reach
knowledge saturation in the near future and forthcoming improvements will not
match the past ones. On the contrary, we find that new observations have the
potential for unprecedented knowledge jumps when extensions of the standard
scenario are considered.


  We establish the conjecture of Reiner and Yong for an explicit combinatorial
formula for the expansion of a Grothendieck polynomial into the basis of
Lascoux polynomials. This expansion is a subtle refinement of its symmetric
function version due to Buch, Kresch, Shimozono, Tamvakis, and Yong, which
gives the expansion of stable Grothendieck polynomials indexed by permutations
into Grassmannian stable Grothendieck polynomials. Our expansion is the
K-theoretic analogue of that of a Schubert polynomial into Demazure characters,
whose symmetric analogue is the expansion of a Stanley symmetric function into
Schur functions. Our expansions extend to flagged Grothendieck polynomials.


  Suppose $M$ is a closed Riemannian manifold. For a $C^2$ generic (in the
sense of Ma\~n\'e) Tonelli Hamiltonian $H: T^*M\rightarrow\mathbb{R}$, the
minimal viscosity solution $u_\lambda^-:M\rightarrow \mathbb{R}$ of the
negative discounted equation \[-\lambda u+H(x,d_xu)=c(H),\quad x\in M,\
\lambda>0 \] with the Ma\~n\'e's critical value $c(H)$ converges to a uniquely
established viscosity solution $u_0^-$ of the critical Hamilton-Jacobi equation
\[ H(x,d_x u)=c(H),\quad x\in M \] as $\lambda\rightarrow 0_+$. We also propose
a dynamical interpretation of $u_0^-$.


  Stationary droplets simulated by multi-phase lattice Boltzmann methods lead
to spurious velocities around them. In this article I report the origin of
these spurious velocities for one example and show how they can be avoided.


  Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic
modal logics with n-ary modalities whose arguments are all the same. WAML has
some interesting applications on epistemic logic and logic of games, so we
study some basic model theoretical aspects of WAML in this paper. Specifically,
we give a van Benthem-Rosen characterization theorem of WAML based on an
intuitive notion of bisimulation and show that each basic WAML system K_n lacks
Craig Interpolation.


  We prove that every continuous function $f:E\to Y$ depends on countably many
coordinates, if $E$ is an $(\aleph_1,\aleph_0)$-invariant
pseudo-$\aleph_1$-compact subspace of a product of topological spaces and $Y$
is a space with a regular $G_\delta$-diagonal. Using this fact for any
$\alpha<\omega_1$ we construct an $(\alpha+1)$-embedded subspace of a
completely regular space which is not $\alpha$-embedded.


  We prove that if $(X_n)_{n\geq 0}$ is a random walk on a transient graph such
that the Green's function decays at least polynomially along the random walk,
then $(X_n)_{n\geq 0}$ has infinitely many cut times almost surely. This
condition applies in particular to any graph of spectral dimension strictly
larger than $2$. In fact, our proof applies to general (possibly nonreversible)
Markov chains satisfying a similar decay condition for the Green's function
that is sharp for birth-death chains. We deduce that a conjecture of Diaconis
and Freedman (Ann. Probab. 1980) holds for the same class of Markov chains, and
resolve a conjecture of Benjamini, Gurel-Gurevich, and Schramm (Ann. Probab.
2011) on the existence of infinitely many cut times for random walks of
positive speed.


  We give a further study on chiral phase diagram in the improved soft-wall
AdS/QCD model with $2+1$ flavors. The equations of motion for the octet
pseudoscalar, vector and axial-vector mesons are derived to compute the octet
meson spectra and relevant decay constants, by which the model parameters are
determined. The chemical potential effects on thermal transition of chiral
condensate are investigated, which enables us to obtain the chiral phase
diagram in the $\mu-T$ plane. We find that the critical end point linking the
crossover transition with the first-order phase transition still exists and
locates at $(\mu_B, T_c) \simeq (390 \MeV, 145 \MeV)$, which along with the
crossover line are consistent with lattice result and experimental analysis
from relativistic heavy ion collisions.


  Let $p:X\rightarrow Y$ be a surjective holomorphic mapping between K\"ahler
manifolds. Let $D$ be a bounded smooth domain in $X$ such that every generic
fiber $D_y:=D\cap p^{-1}(y)$ for $y\in Y$ is a strongly pseudoconvex domain in
$X_y:=p^{-1}(y)$, which admits the complete K\"ahler-Einstein metric. This
family of K\"ahler-Einstein metrics induces a smooth $(1,1)$-form $\rho$ on
$D$. In this paper, we prove that $\rho$ is positive-definite on $D$ if $D$ is
strongly pseudoconvex. We also discuss the extensioin of $\rho$ as a positive
current across singular fibers.


  We investigated electron emissions in strong field enhanced ionization of
asymmetric diatomic molecules by quantum calculations. It is demonstrated that
the widely-used intuitive physical pic- ture, i.e., electron wave packet direct
ionization from the up-field site (DIU), is incomplete. Besides DIU, we find
another two new ionization channels, the field-induced excitation with
subsequent ionization from the down-field site (ESID), and the up-field site
(ESIU). The contributions from these channels depend on the molecular asymmetry
and internuclear distance. Our work provides a more comprehensive physical
picture for the long-standing issue about enhanced ionization of diatomic
molecules.


  The multipole response of neutron rich O and Sn isotopes is computed in
Tamm-Dancoff and random-phase approximations using the canonical
Hartree-Fock-Bogoliubov quasi-particle basis. The calculations are performed
using an intrinsic Hamiltonian composed of a $V_{lowk}$ potential, deduced from
the CD-Bonn nucleon-nucleon interaction, corrected with phenomenological
density dependent and spin-orbit terms. The effect of these two pieces on
energies and multipole responses is discussed. The problem of removing the
spurious admixtures induced by the center of mass motion and by the violation
of the number of particles is investigated. The differences between the two
theoretical approaches are discussed quantitatively. Attention is then focused
on the dipole strength distribution, including the low-lying transitions
associated to the pygmy resonance. Monopole and quadrupole responses are also
briefly investigated. A detailed comparison with the available experimental
spectra contributes to clarify the extent of validity of the two
self-consistent approaches.


  Matching pedestrians across multiple camera views known as human
re-identification (re-identification) is a challenging problem in visual
surveillance. In the existing works concentrating on feature extraction,
representations are formed locally and independent of other regions. We present
a novel siamese Long Short-Term Memory (LSTM) architecture that can process
image regions sequentially and enhance the discriminative capability of local
feature representation by leveraging contextual information. The feedback
connections and internal gating mechanism of the LSTM cells enable our model to
memorize the spatial dependencies and selectively propagate relevant contextual
information through the network. We demonstrate improved performance compared
to the baseline algorithm with no LSTM units and promising results compared to
state-of-the-art methods on Market-1501, CUHK03 and VIPeR datasets.
Visualization of the internal mechanism of LSTM cells shows meaningful patterns
can be learned by our method.


  This article treats global uniform exponential stability (GUES) of
discrete-time switched linear systems under restricted switching. Given
admissible minimum and maximum dwell times, we provide sufficient conditions on
the subsystems under which they admit a set of switching signals that obeys the
given restrictions on dwell times and preserves stability of the resulting
switched system. Our analysis relies on combinatorial arguments applied to
matrix commutators and avoids the employment of Lyapunov-like functions. The
proposed set of stabilizing switching signals is characterized in terms of
duration of activation of Schur stable subsystems and non-consecutive
activation of distinct unstable subsystems.


  The impact of including postcursors in the null hypothesis test is discussed.
Unequal prediction probabilities can be included in the null hypothesis test
using a generalization of the central limit theorem. A test for determining the
enhancement factor over random chance is given. The seismic earthquake signal
may preferentially precede earthquakes even if the VAN methodology fails to
forecast the earthquakes. We formulate a statistical test for this possibility.


  A simple model of species origin resulted from dynamic features of a
population, solely, is developed. The model is based on the evolution
optimality in space distribution, and the selection is gone over the mobility.
Some biological issues are discussed.


  The theory is presented for resonance interaction between two atoms in an
excited configuration: one atom, the "receptor" of information (i.e. energy),
adsorbed on a phospholipid surface and the other atom, the "emitter" of
information (i.e. energy), a long distance away. The dielectric function for a
specific phospholipid membrane is obtained from density functional theory
calculations. We present numerical results comparing the range and magnitude of
non-specific Casimir-Polder interactions with the much more long-ranged, and
highly specific, resonance interaction. A study of the resonance interaction
with one or both atoms adsorbed on a phospholipid membrane surface reveals a
possibility to have a cross over from attraction to repulsion or from repulsion
to attraction at separations between receptor and emitter atoms exceeding
several hundred {\AA}ngstr\"oms. The energy transfer and the observed
transitions in the sign of the interaction energies near surfaces provide
potential new ways to start recognition processes in biological systems.


  Let G be a connected reductive group. Recall that a G-variety X is called
spherical if X is normal and a Borel subgroup of G has an open orbit on X. To a
spherical homogeneous G-space one assigns certain combinatorial invariants: the
weight lattice, the valuation cone and the set of B-stable prime divisors. We
prove that two spherical homogeneous spaces with the same combinatorial
invariants are equivariantly isomorphic. Further, we show how to recover the
group of G-equivariant automorphisms from these invariants.


  In this paper, we study the random dynamical system $f_\omega^n$ generated by
a family of maps $\{f_{\omega_0}: \mathbb{S}^1 \to \mathbb{S}^1\}_{\omega_0 \in
[-\varepsilon,\varepsilon]},$ $f_{\omega_0}(x) = \alpha \xi (x+\omega_0) +a\
(\mathrm{mod }\ 1),$ where $\xi: \mathbb S^1 \to \mathbb R$ is a
non-degenerated map, $a\in [0,1)$, and $\alpha,\varepsilon>0$. Fixing a
constant $c\in (0,1)$, we show that for $\alpha$ sufficiently large and for
$\varepsilon > \alpha^{-1+c},$ the random dynamical system $f_\omega^n$
presents a random Young tower structure and quenched decay of correlations.


  Real-world training data usually exhibits long-tailed distribution, where
several majority classes have a significantly larger number of samples than the
remaining minority classes. This imbalance degrades the performance of typical
supervised learning algorithms designed for balanced training sets. In this
paper, we address this issue by augmenting minority classes with a recently
proposed implicit semantic data augmentation (ISDA) algorithm, which produces
diversified augmented samples by translating deep features along many
semantically meaningful directions. Importantly, given that ISDA estimates the
class-conditional statistics to obtain semantic directions, we find it
ineffective to do this on minority classes due to the insufficient training
data. To this end, we propose a novel approach to learn transformed semantic
directions with meta-learning automatically. In specific, the augmentation
strategy during training is dynamically optimized, aiming to minimize the loss
on a small balanced validation set, which is approximated via a meta update
step. Extensive empirical results on CIFAR-LT-10/100, ImageNet-LT, and
iNaturalist 2017/2018 validate the effectiveness of our method.


  This dissertation uses supervised and unsupervised data mining techniques to
analyse office floor plans in an attempt to gain a better understanding of
their geometry-to-function relationship. This question was deemed relevant
after a background review of the state-of-the-art in automated floor-plan
generation tools showed that such tools have been prototyped since the 1960s,
but their search space is ill-informed because there are few formalisms to
describe spatial affordance. To show and evaluate the relationship of geometry
and use, data from visual graph analysis were used to train three supervised
learners and compare these to a baseline accuracy established with a ZeroR
classifier. This showed that for the office dataset examined, visual mean depth
and integration are most tightly linked to usage and that the supervised
learning algorithm J48 can correctly predict class performance on unseen
examples to up to 79.5%. The thesis also includes an evaluation of the layout
case studies with unsupervised learners, which showed that use could not be
immediately reverse-engineered based solemnly on the VGA information to achieve
a strong cluster-to-class evaluation.


  The search for different life forms elsewhere in the universe is a
fascinating area of research in astrophysics and astrobiology. Currently,
according to the NASA Exoplanet Archive database, 3876 exoplanets have been
discovered. The Earth Similarity Index (ESI) is defined as the geometric mean
of radius, density, escape velocity, and surface temperature and ranges from 0
(dissimilar to Earth) to 1 (similar to Earth). The ESI was created to index
exoplanets on the basis of their similarity to Earth. In this paper, we
examined rocky exoplanets whose physical conditions are potentially suitable
for the survival of rock-dependent extremophiles, such as the cyanobacteria
Chroococcidiopsis and the lichen Acarospora. The Rock Similarity Index (RSI) is
first introduced and then applied to 1659 rocky exoplanets. The RSI represents
a measure for Earth-like planets on which physical conditions are potentially
suitable for rocky extremophiles that can survive in Earth-like extreme
habitats (i.e., hot deserts and cold, frozen lands).


  Infinite-horizon optimal control of constrained piecewise affine (PWA)
systems has been approximately addressed by hybrid model predictive control
(MPC), which, however, has computational limitations, both in offline design
and online implementation. In this paper, we consider an alternative approach
based on approximate dynamic programming (ADP), an important class of methods
in reinforcement learning. We accommodate non-convex union-of-polyhedra state
constraints and linear input constraints into ADP by designing PWA penalty
functions. PWA function approximation is used, which allows for a mixed-integer
encoding to implement ADP. The main advantage of the proposed ADP method is its
online computational efficiency. Particularly, we propose two control policies,
which lead to solving a smaller-scale mixed-integer linear program than
conventional hybrid MPC, or a single convex quadratic program, depending on
whether the policy is implicitly determined online or explicitly computed
offline. We characterize the stability and safety properties of the closed-loop
systems, as well as the sub-optimality of the proposed policies, by quantifying
the approximation errors of value functions and policies. We also develop an
offline mixed-integer linear programming-based method to certify the
reliability of the proposed method. Simulation results on an inverted pendulum
with elastic walls and on an adaptive cruise control problem validate the
control performance in terms of constraint satisfaction and CPU time.


  The electrocardiogram (ECG) is a widely-used medical test, typically
consisting of 12 voltage versus time traces collected from surface recordings
over the heart. Here we hypothesize that a deep neural network can predict an
important future clinical event (one-year all-cause mortality) from ECG
voltage-time traces. We show good performance for predicting one-year mortality
with an average AUC of 0.85 from a model cross-validated on 1,775,926 12-lead
resting ECGs, that were collected over a 34-year period in a large regional
health system. Even within the large subset of ECGs interpreted as 'normal' by
a physician (n=297,548), the model performance to predict one-year mortality
remained high (AUC=0.84), and Cox Proportional Hazard model revealed a hazard
ratio of 6.6 (p<0.005) for the two predicted groups (dead vs alive one year
after ECG) over a 30-year follow-up period. A blinded survey of three
cardiologists suggested that the patterns captured by the model were generally
not visually apparent to cardiologists even after being shown 240 paired
examples of labeled true positives (dead) and true negatives (alive). In
summary, deep learning can add significant prognostic information to the
interpretation of 12-lead resting ECGs, even in cases that are interpreted as
'normal' by physicians.


  Since 2002 the VHE (>100 GeV) gamma-ray flux of the high-frequency peaked BL
Lac PKS 2155-304 has been monitored with the High Energy Stereoscopic System
(HESS). An extreme gamma-ray outburst was detected in the early hours of July
28, 2006 (MJD 53944). The average flux above 200 GeV observed during this
outburst is ~7 times the flux observed from the Crab Nebula above the same
threshold. Peak fluxes are measured with one-minute time scale resolution at
more than twice this average value. Variability is seen up to ~600 s in the
Fourier power spectrum, and well-resolved bursts varying on time scales of ~200
seconds are observed. There are no strong indications for spectral variability
within the data. Assuming the emission region has a size comparable to the
Schwarzschild radius of a ~10^9 solar mass black hole, Doppler factors greater
than 100 are required to accommodate the observed variability time scales.


  First, we describe the construction of a new type of gravity-matter models
based on the formalism of non-Riemannian space-time volume forms - alternative
generally covariant integration measure densities (volume elements) defined in
terms of auxiliary antisymmetric tensor gauge fields. Here gravity couples in a
non-conventional way to two distinct scalar fields providing a unified
Lagrangian action principle description of: (i) the evolution of both "early"
and "late" Universe - by the "inflaton" scalar field; (ii) dark energy and dark
matter as a unified manifestation of a single material entity - the "darkon"
scalar field. A physically very interesting phenomenon occurs when including in
addition interactions with the electro-weak model bosonic sector - we obtain a
gravity-assisted dynamical generation of electro-weak spontaneous gauge
symmetry breaking in the post-inflationary "late" Universe, while the
Higgs-like scalar remains massless in the "early" Universe. Next, we proceed to
the Wheeler-DeWitt minisuperspace quantization of the above models. The
"darkon" field plays here the role of cosmological "time". In particular, we
show the absence of cosmological space-time singularities.


  We present a method to control the two-dimensional shape of traveling wave
solutions to reaction-diffusion systems, as e.g. interfaces and excitation
pulses. Control signals that realize a pre-given wave shape are determined
analytically from nonlinear evolution equation for isoconcentration lines as
the perturbed nonlinear phase diffusion equation or the perturbed linear
eikonal equation. While the control enforces a desired wave shape perpendicular
to the local propagation direction, the wave profile along the propagation
direction itself remains almost unaffected. Provided that the one-dimensional
wave profile and its propagation velocity can be measured experimentally, and
the diffusion coefficients of the reacting species are given, the new approach
can be applied even if the underlying nonlinear reaction kinetics are unknown.


  Gaseous detectors have long been used by particle physics experiments at
beamlines or standalone experiments. Recently, their low momentum threshold has
made them interesting as active targets for long baseline neutrino experiments.
To increase statistics, but retain a low momentum threshold, pressurized Time
Projection Chambers have been proposed. The Deep Underground Neutrino
Experiment considers building one as part of their near detector complex. Gas
Monitoring Chambers are mini TPCs that are designed to measure gas properties.
Such a system with the capability of testing common and new drift gas mixtures
can provide input to the design process of new high pressure TPCs. This work
presents the construction of such a High Pressure Gas Monitoring Chamber
capable of operation up to \unit[10]{bar} pressure and a maximum drift field
close to \unit[1000]{V/cm}.


  We study the exterior product on 0-cycles modulo rational equivalence, and
prove some nonvanishing results. The main tools used are higher cycle- and
Abel-Jacobi- classes developed in articles of J. Lewis and the author. A
theorem of Rosenschon-Saito (in the case of 0-cycles) is a special case of our
results.


  In wireless networks with random node distribution, the underlying point
process model and the channel fading process are usually considered separately.
A unified framework is introduced that permits the geometric characterization
of fading by incorporating the fading process into the point process model.
Concretely, assuming nodes are distributed in a stationary Poisson point
process in $\R^d$, the properties of the point processes that describe the path
loss with fading are analyzed. The main applications are connectivity and
broadcasting.


  Recent advances in knowledge graph embedding (KGE) rely on
Euclidean/hyperbolic orthogonal relation transformations to model intrinsic
logical patterns and topological structures. However, existing approaches are
confined to rigid relational orthogonalization with restricted dimension and
homogeneous geometry, leading to deficient modeling capability. In this work,
we move beyond these approaches in terms of both dimension and geometry by
introducing a powerful framework named GoldE, which features a universal
orthogonal parameterization based on a generalized form of Householder
reflection. Such parameterization can naturally achieve dimensional extension
and geometric unification with theoretical guarantees, enabling our framework
to simultaneously capture crucial logical patterns and inherent topological
heterogeneity of knowledge graphs. Empirically, GoldE achieves state-of-the-art
performance on three standard benchmarks. Codes are available at
https://github.com/xxrep/GoldE.


  The discovery of true solar analogues is fundamental for a better
understanding of the Sun and of the solar system. The open cluster M67 offers a
unique opportunity to search for solar analogues because its chemical
composition and age are very similar to those of the Sun. We analyze FLAMES
spectra of a large number of M67 main sequence stars to identify solar
analogues in this cluster.We first determine cluster members which are likely
not binaries, by combining proper motions and radial velocity measurements. We
concentrate our analysis on the determination of stellar effective temperature,
using analyses of line-depth ratios and H$\alpha$ wings, making a direct
comparison with the solar spectrum obtained with the same instrument. We also
compute the lithium abundance for all the stars.Ten stars have both the
temperature derived by line-depth ratios and H$\alpha$ wings within 100 K from
the Sun. From these stars we derive, assuming a cluster reddening
$E(B-V)=0.041$, the solar colour $(B-V)_\odot=0.649\pm0.016$ and a cluster
distance modulus of 9.63. Five stars are most similar (within 60 K) to the Sun
and candidates to be true solar twins. These stars have also a low Li content,
comparable to the photospheric abundance of the Sun, likely indicating a
similar mixing evolution. We find several candidates for the best solar
analogues ever. These stars are amenable to further spectroscopic
investigations and planet search. The solar colours are determined with rather
high accuracy with an independent method, as well as the cluster distance
modulus.


  We want to establish the basic properties of a scale invariant cosmology,
that also accounts for the hypothesis of scale invariance of the empty space at
large scales. We write the basic analytical properties of the scale invariant
cosmological models. The hypothesis of scale invariance of the empty space at
large scale brings interesting simplifications in the scale invariant equations
for cosmology. There is one new term, depending on the scale factor of the
scale invariant cosmology, that opposes to gravity and favours an accelerated
expansion. We first consider a zero-density model and find an accelerated
expansion, going like t square. In models with matter present, the
displacements due to the new term make a significant contribution Omega_l to
the energy-density of the Universe, satisfying an equation of the form Omega_m
+ Omega_k + Omega_l = 1. Unlike the Friedman's models, there is a whole family
of flat models (k=0) with different density parameters Omega_m smaller than 1.
We examine the basic relations between the density and geometrical properties,
as well as the conservation laws. The models containing matter have an
inflexion point, with first a braking phase followed by an accelerated
expansion phase. The scale invariant models have interesting properties and
deserve further investigations.


  We study automorphism groups of sparse graphs from the viewpoint of
topological dynamics and the Kechris, Pestov, Todor\v{c}evi\'c correspondence.
We investigate amenable and extremely amenable subgroups of these groups using
the space of orientations of the graph and results from structural Ramsey
theory. Resolving one of the open questions in the area, we show that
Hrushovski's example of an $\omega$-categorical sparse graph has no
$\omega$-categorical expansion with extremely amenable automorphism group.


  Each memoryless binary-input channel (BIC) can be uniquely described by its
Blackwell measure, which is a probability distribution on the unit interval
$[0,1]$ with mean $1/2$. Conversely, any such probability distribution defines
a BIC. The evolution of the Blackwell measure under Arikan's polar transform is
derived for general BICs, and is analogous to density evolution as cited in the
literature. The present analysis emphasizes functional equations. Consequently,
the evolution of a variety of channel functionals is characterized, including
the symmetric capacity, Bhattacharyya parameter, moments of information
density, Hellinger affinity, Gallager's reliability function, the
Hirschfeld-Gebelein-Renyi maximal correlation, and the Bayesian information
gain. The evolution of measure is specialized for symmetric BICs according to
their decomposition into binary symmetric (sub)-channels (BSCs), which
simplifies iterative computations and the construction of polar codes. It is
verified that, as a consequence of the Blackwell--Sherman--Stein theorem, all
channel functionals $\mathrm{I}_f$ that can be expressed as an expectation of a
convex function $f$ with respect to the Blackwell measure of a channel polarize
in each iteration due to the polar transformation on the class of symmetric
BICs. Moreover, for $f$ either convex or non-convex, a necessary and sufficient
condition is established to determine whether the random process associated
with each $\mathrm{I}_f$ is a martingale, submartingale, or supermartingale.
Represented via functional inequalities in terms of $f$, this condition is
numerically verifiable for all $\mathrm{I}_f$, and can generate analytical
proofs. To exhibit one such proof, it is shown that the random process
associated with the squared maximal correlation parameter is a supermartingale,
and converges almost surely on the unit interval $[0,1]$.


  We use the local value of the Hubble constant recently measured with 2.4%
precision, as well as the latest compilation of cosmic chronometers data,
together with standard probes such as Supernovae Type Ia and Baryon Acoustic
Oscillation distance measurements, in order to impose constraints on the viable
and most used f(T) gravity models, where T is the torsion scalar in
teleparallel gravity. In particular, we consider three f(T) models with two
parameters, out of which one is independent, and we quantify their deviation
from $\Lambda$CDM cosmology through a sole parameter. Our analysis reveals that
for one of the models a small but non-zero deviation from $\Lambda$CDM
cosmology is slightly favored, while for the other models the best fit is very
close to $\Lambda$CDM scenario. Clearly, f(T) gravity is consistent with
observations, and it can serve as a candidate for modified gravity.


  Africa has been identified as a major driver of the current rise in
atmospheric methane, and this has been attributed to emissions from wetlands
and livestock. Here we show that rapidly increasing rice cultivation is another
important source, and estimate that it accounts for 7% of the current global
rise in methane emissions. Continued rice expansion to feed a rapidly growing
population should be considered in climate change mitigation goals.


  In contrast with extended Bloch waves, a single particle can become spatially
localized due to the so-called skin effect originating from non-Hermitian
pumping. Here we show that in a wide class of kinetically constrained many-body
systems, the skin effect can instead manifest as dynamical amplification within
the Fock space, beyond the intuitively expected and previously studied particle
localization and clustering. We exemplify this non-Hermitian Fock skin effect
in an asymmetric version of the PXP model and show that it gives rise to
ergodicity-breaking eigenstates, the non-Hermitian analogs of quantum many-body
scars. A distinguishing feature of these non-Hermitian scars is their enhanced
robustness against external disorders. We propose an experimental realization
of the non-Hermitian scar enhancement in a tilted Bose-Hubbard optical lattice
with laser-induced loss. Our results show that the Fock skin effect provides a
powerful tool for creating robust non-ergodic states in generic open quantum
systems.


  For a Pfaffian point process we show that its Palm measures, its normalised
compositions with multiplicative functionals, and its conditional measures with
respect to fixing the configuration in a bounded subset are Pfaffian point
processes whose kernels we find explicitly.


  We report on our recent evaluation of the s-channel cut contribution to J/psi
hadroproduction. We show that it is likely significantly larger than the usual
cut contribution of the colour-singlet model (CSM), which is known to
underestimate the experimental measurements. Here the s-channel cut develops
for configurations with off-shell quarks in the bound state. A correct
treatment of its contribution requires the introduction of a four point
function, partially constrained by gauge invariance and limiting behaviours at
small and large momenta. When the unconstrained degrees of freedom are fixed to
reproduce the Tevatron data, we show that RHIC data are remarkably well
reproduced down to very low transverse momenta P_T without need of resummation
of initial-state gluon effects. This unique feature might be typical of
s-channel cut contribution.


  Observations and theoretical principles indicate that electromagnetic waves,
including light, propagate in dielectric media at speeds lower than those in
free space, as eloquently expressed in Maxwell's equations featuring
material-dependent permittivity and permeability. This study reveals that the
observed slower propagation of waves in dielectric media arises from an
interference between two types of waves: a forward-moving primary wave and a
set of secondary waves induced by the primary wave's interaction with the
medium. The forward-moving primary wave and secondary waves travel at the speed
of light in vacuum. Notably, the reflected wave caused by the impedance
discontinuity on the boundary of a dielectric medium is manifested by the
induced secondary waves moving in the opposite direction to the primary wave.
From a photonic point of view, photons will be moving back and forth below the
slowly moving apparent front of the observed wave with the speed of light in
vacuum. Ahead of this front the probability of finding photons is zero due to
complete destructive interference of the waves in that region. From a photonic
perspective, beneath the gradually advancing facade of the observed wave,
photons move at the unyielding speed of light in vacuum. The likelihood of
detecting photons ahead of the front diminishes to zero, a consequence of the
thorough destructive interference manifesting within that specific region.


  The upcoming Hyper-Kamiokande (HyperK) experiment is expected to detect the
Diffuse Supernova Neutrino Background (DSNB). This requires to ponder all
possible sources of background. Sub-GeV dark matter (DM) which annihilates into
neutrinos is a potential background that has not been considered so far. We
simulate DSNB and DM signals, as well as backgrounds in the HyperK detector. We
find that DM-induced neutrinos could indeed alter the extraction of the correct
values of the parameters of interest for DSNB physics. Since the DSNB is an
isotropic signal, and DM originates primarily from the Galactic centre, we show
that this effect could be alleviated with an on-off analysis.


  A derivation of the Lax pair for the (1+1)-dimensional non-linear sigma-model
is described. Its main benefit is to have a clearer physical origin and to
allow the study of a generalization to higher dimensions.


  Computing the state-space topology of a dynamical system from scalar data
requires accurate reconstruction of those dynamics and construction of an
appropriate simplicial complex from the results. The reconstruction process
involves a number of free parameters and the computation of homology for a
large number of simplices can be expensive. This paper is a study of how to
avoid a full (diffeomorphic) reconstruction and how to decrease the
computational burden. Using trajectories from the classic Lorenz system, we
reconstruct the dynamics using the method of delays, then build a parsimonious
simplicial complex---the "witness complex"---to compute its homology.
Surprisingly, we find that the witness complex correctly resolves the homology
of the underlying invariant set from noisy samples of that set even if the
reconstruction dimension is well below the thresholds specified in the
embedding theorems for assuring topological conjugacy between the true and
reconstructed dynamics. We conjecture that this is because the requirements for
reconstructing homology, are less stringent than those in the embedding
theorems. In particular, to faithfully reconstruct the homology, a
homeomorphism is sufficient---as opposed to a diffeomorphism, as is necessary
for the full dynamics. We provide preliminary evidence that a homeomorphism, in
the form of a delay-coordinate reconstruction map, may manifest at a lower
dimension than that required to achieve an embedding.


  The results for dilatometric, ultrasonic velocity and the domain struct-ure
studies of Cs3Bi2I9 crystals in the course of ferroelastic phase trans-ition
are presented. It is shown that the phase transition in Cs3Bi2I9 is of the
first order. Basing on the thermal expansion results and the data obtained for
the elastic stiffness of Cs3Bi2I9 crystals, the latent heat Q=79J/kg at Tc is
calculated. The region between 183K and 221K (at cooling) is identified as a
heterostructure region, where ferroelastic and paraelastic phases coexist.