  We study distributed average consensus problems in multi-agent systems with
directed communication links that are subject to quantized information flow.
The goal of distributed average consensus is for the nodes, each associated
with some initial value, to obtain the average (or some value close to the
average) of these initial values. In this paper, we present and analyze a
distributed averaging algorithm which operates exclusively with quantized
values (specifically, the information stored, processed and exchanged between
neighboring agents is subject to deterministic uniform quantization) and relies
on event-driven updates (e.g., to reduce energy consumption, communication
bandwidth, network congestion, and/or processor usage). We characterize the
properties of the proposed distributed averaging protocol on quantized values
and show that its execution, on any time-invariant and strongly connected
digraph, will allow all agents to reach, in finite time, a common consensus
value represented as the ratio of two integer that is equal to the exact
average. We conclude with examples that illustrate the operation, performance,
and potential advantages of the proposed algorithm.


  Control of single photon wave-packets is an important resource for developing
hybrid quantum systems which are composed of different physical systems
interacting via photons. Here we extend this control to triggered photons
emitted by a quantum dot, temporally shaping single photon wave-packets on
timescales fast compared to their radiative decay by electro-optic modulation.
In particular, telecommunications-band single photons resulting from the
recombination of an exciton in a quantum dot with exponentially decaying
wave-packets are synchronously modulated to create Gaussian-shaped single
photon wave-packets. We explore other pulse-shapes and investigate the
feasibility of this technique for increasing the indistinguishability of
quantum dot generated single photons.


  Nonlinear optimal control problems are often solved with numerical methods
that require knowledge of system's dynamics which may be difficult to infer,
and that carry a large computational cost associated with iterative
calculations. We present a novel neurobiologically inspired hierarchical
learning framework, Reinforcement Learning Optimal Control, which operates on
two levels of abstraction and utilises a reduced number of controllers to solve
nonlinear systems with unknown dynamics in continuous state and action spaces.
Our approach is inspired by research at two levels of abstraction: first, at
the level of limb coordination human behaviour is explained by linear optimal
feedback control theory. Second, in cognitive tasks involving learning symbolic
level action selection, humans learn such problems using model-free and
model-based reinforcement learning algorithms. We propose that combining these
two levels of abstraction leads to a fast global solution of nonlinear control
problems using reduced number of controllers. Our framework learns the local
task dynamics from naive experience and forms locally optimal infinite horizon
Linear Quadratic Regulators which produce continuous low-level control. A
top-level reinforcement learner uses the controllers as actions and learns how
to best combine them in state space while maximising a long-term reward. A
single optimal control objective function drives high-level symbolic learning
by providing training signals on desirability of each selected controller. We
show that a small number of locally optimal linear controllers are able to
solve global nonlinear control problems with unknown dynamics when combined
with a reinforcement learner in this hierarchical framework. Our algorithm
competes in terms of computational cost and solution quality with sophisticated
control algorithms and we illustrate this with solutions to benchmark problems.


  We have identified 139 cool carbon stars in the near-infrared
spectro-photometric survey of the InfraRed Telescope in Space (IRTS) from the
conspicuous presence of molecular absorption bands at 1.8, 3.1 and 3.8 microns.
Among them 14 are new, bright (K ~ 4.0-7.0), carbon stars. We find a trend
relating the 3.1 microns band strength to the K-L' color index, which is known
to correlate with mass-loss rate. This could be an effect of a relation between
the depth of the 3.1 microns feature and the degree of development of the
extended stellar atmosphere where dust starts to form.


  Detecting carried objects is one of the requirements for developing systems
to reason about activities involving people and objects. We present an approach
to detect carried objects from a single video frame with a novel method that
incorporates features from multiple scales. Initially, a foreground mask in a
video frame is segmented into multi-scale superpixels. Then the human-like
regions in the segmented area are identified by matching a set of extracted
features from superpixels against learned features in a codebook. A carried
object probability map is generated using the complement of the matching
probabilities of superpixels to human-like regions and background information.
A group of superpixels with high carried object probability and strong edge
support is then merged to obtain the shape of the carried object. We applied
our method to two challenging datasets, and results show that our method is
competitive with or better than the state-of-the-art.


  Recent releases of open-source research codes and solvers for numerically
solving partial differential equations in Python present a great opportunity
for educators to integrate these codes into the classroom in a variety of ways.
The ease with which a problem can be implemented and solved using these codes
reduce the barrier to entry for users. We demonstrate how one of these
codes,FiPy, can be introduced to students through a short course using
progression as the guiding philosophy. Four exercises of increasing complexity
were developed. Basic concepts from more advanced numerical methods courses are
also introduced at appropriate points. To further engage students, we
demonstrate how an open research problem can be readily implemented and also
incorporate the use of ParaView to post-process their results. Student
engagement and learning outcomes were evaluated through a pre and post-course
survey and a focus group discussion. Students broadly found the course to be
engaging and useful with the ability to easily visualise the solution to PDEs
being greatly valued. Due to the introductory nature of the course, due care in
terms of set-up and the design of learning activities during the course is
essential. This course, if integrated with appropriate level of support, can
encourage students to use the provided codes and improve their understanding of
concepts used in numerical analysis and PDEs.


  We show how to perform error correction of single qubit dephasing by encoding
a single qubit into a minimum of three. This may be performed in a manner
closely analogous to classical error correction schemes. Further, the resulting
quantum error correction schemes are trivially generalized to the minimal
encoding of arbitrarily many qubits so as to allow for multiqubit dephasing
correction under the sole condition that the environment acts independently on
each qubit.


  A new computational method for finite-temperature properties of strongly
correlated electrons is proposed by extending the variational Monte Carlo
method originally developed for the ground state. The method is based on the
path integral in the imaginary-time formulation, starting from the
infinite-temperature state that is well approximated by a small number of
certain random initial states. Lower temperatures are progressively reached by
the imaginary-time evolution. The algorithm follows the framework of the
quantum transfer matrix and finite-temperature Lanczos methods, but we extends
them to treat much larger system sizes without the negative sign problem by
optimizing the truncated Hilbert space on the basis of the time-dependent
variational principle (TDVP). This optimization algorithm is equivalent to the
stochastic reconfiguration (SR) method that has been frequently used for the
ground state to optimally truncate the Hilbert space. The obtained
finite-temperature states allow an interpretation based on the thermal pure
quantum (TPQ) state instead of the conventional canonical-ensemble average. Our
method is tested for the one- and two-dimensional Hubbard models and its
accuracy and efficiency are demonstrated.


  Entanglement of dipole-dipole interacting spins 1/2 is usually investigated
when the energy of interaction with an external magnetic field (the Zeeman
energy) is greater than the energy of dipole interactions by three orders.
Under this condition only a non-equilibrium state of the spin system, realized
by pulse radiofrequence irradiations, results in entanglement. The present
paper deals with the opposite case: the dipolar interaction energy is the order
of magnitude or even larger than the Zeeman one. It was shown that entanglement
appears under the thermodynamic equilibrium conditions and the concurrence
reaches the maximum when the external field is directed perpendicular to the
vector connecting the nuclei. For this direction of the field and a system of
two spins with the Hamiltonian accounting the realistic dipole-dipole
interactions in low external magnetic field, the exact analytical expression
for concurrence was also obtained. The condition of the entanglement appearance
and the dependence of concurrence on the external magnetic field, temperature,
and dipolar coupling constant were studied.


  This work is dedicated to obtaining of analog of Bogoliubov's chain for the
case of complex scalar field in QFT and renormalization problem of obtained
equations is discussed.


  Botnets continue to be an active threat against firms or companies and
individuals worldwide. Previous research regarding botnets has unveiled
information on how the system and their stakeholders operate, but an insight on
the economic structure that supports these stakeholders is lacking. The
objective of this research is to analyse the business model and determine the
revenue stream of a botnet owner. We also study the botnet life-cycle and
determine the costs associated with it on the basis of four case studies. We
conclude that building a full scale cyber army from scratch is very expensive
where as acquiring a previously developed botnet requires a little cost. We
find that initial setup and monthly costs were minimal compared to total
revenue.


  We study the elliptic curves given by $y^2 = x^3 + b x + t^{3^n+1}$ over
global function fields of characteristic $3$; in particular we perform an
explicit computation of the $L$-function by relating it to the zeta function of
a certain superelliptic curve $u^3 + b u = v^{3^n + 1}$.
  In this way, using the N\'eron-Tate height on the Mordell--Weil group, we
obtain lattices in dimension $2 \cdot 3^n$ for every $n \geq 1$, which improve
on the currently best known sphere packing densities in dimensions 162 (case
$n=4$) and 486 (case $n=5$). For $n=3$, the construction has the same packing
density as the best currently known sphere packing in dimension $54$, and for
$n=1$ it has the same density as the lattice $E_6$ in dimension $6$.


  Axial algebras are commutative nonassociative algebras generated by a finite
set of primitive idempotents which action on an algebra is semisimple, and the
fusion laws on the products between eigenvectors for these idempotents are
fulfilled. We find the sufficient conditions in terms of the Frobenius form and
of the properties of idempotents under which an axial algebra of Jordan type
half is unital.


  There are strong evidences that the melting in two dimensions depends
crucially on the form and range of the interaction potentials between
particles. We study with Monte Carlo simulations the phase diagram and the
melting of a monolayer of point-particles interacting with repulsive Inverse
Power Law Interactions, $V(r)=Q^2(\sigma/r)^n$ where $n$ can take any real
positive value ($n$-OCP monolayer). As $n$ is varied from 0 to $\infty$ (Hard
Disks), including Coulomb ($n=1$) and Dipolar ($n=3$), melting occurs with
different mechanisms and the overall picture permits to understand the
diversity of mechanisms found experimentally or in computer simulations for 2D
melting. The empirical transition curves for $n\leq 3$ and the excellent
qualitative and semi-quantitative agreements with the KTHNY theory found for
the melting of $n$-OCP monolayers with $n\leq 3$ are the main results of the
present work.


  This paper studies the risk-adjusted optimal timing to liquidate an option at
the prevailing market price. In addition to maximizing the expected discounted
return from option sale, we incorporate a path-dependent risk penalty based on
shortfall or quadratic variation of the option price up to the liquidation
time. We establish the conditions under which it is optimal to immediately
liquidate or hold the option position through expiration. Furthermore, we study
the variational inequality associated with the optimal stopping problem, and
prove the existence and uniqueness of a strong solution. A series of analytical
and numerical results are provided to illustrate the non-trivial optimal
liquidation strategies under geometric Brownian motion (GBM) and exponential
Ornstein-Uhlenbeck models. We examine the combined effects of price dynamics
and risk penalty on the sell and delay regions for various options. In
addition, we obtain an explicit closed-form solution for the liquidation of a
stock with quadratic penalty under the GBM model.


  We address the question as to whether data for J/\psi mesons produced
exclusively in the forward direction at the LHC can be used in global parton
analyses (based on collinear factorization) to pin down the low x gluon PDF. We
show that it may be possible to overcome the problems that (i) the process is
described by a skewed or Generalized Parton Distribution (GPD), (ii) it is very
sensitive to the choice of factorization scale and (iii) there is bad LO,
NLO,... perturbative stability to the predictions. However, we start by briefly
explaining how the alternative k_T factorization approach has been used to
describe the process.


  In the staggered fermion formulation of lattice QCD, we construct diquark
operators which are to be embedded in singly heavy baryons. The group
theoretical connections between continuum and lattice staggered diquark
representations are established.


  We continue the study of 3d ${\mathcal N}=2$ Chern-Simons (CS) quiver gauge
theories on $\Sigma_{\mathfrak{g}}\times S^1$. Using localization results, we
compute the twisted index of recently constructed SCFTs in the large rank
limit. According to AdS/CFT correspondence, this field theory computation gives
a prediction for two quantities corresponding to their holographic duals: the
volumes of certain 7-dimensional Sasaki-Einstein manifolds and the entropy of
black holes in $\text{AdS}_4\times Y_7$.


  We investigate the modification of meson spectral densities in dense nuclear
matter at zero temperature. These effects are studied in a fully relativistic
mean field model which goes beyond the linear density approximation and also
includes baryon resonances. In particular, the role of N*(1520) and N*(1720) on
the rho meson spectral density is highlighted. Even though the nucleon-nucleon
loop and the nucleon-resonance loop contribute with the opposite sign, an
overall reduction of rho meson mass is still observed at high density.
Importantly, it is shown that the resonances cause substantial broadening of
the rho meson spectral density in matter and also induces non-trivial momentum
dependence. The spectral density of the a0 meson is also shown. We study the
dispersion relations and collective oscillations induced by the rho meson
propagation in nuclear matter together with the influence of the mixing of rho
with the a0 meson. The relevant expression for the plasma frequency is also
recovered analytically in the appropriate limit.


  Spline wavelet tight frames of Ron-Shen have been used widely in frame based
image analysis and restorations. However, except for the tight frame property
and the approximation order of the truncated series, there are few other
properties of this family of spline wavelet tight frames to be known. This
paper is to present a few new properties of this family that will provide
further understanding of it and, hopefully, give some indications why it is
efficient in image analysis and restorations. In particular, we present a
recurrence formula of computing generators of higher order spline wavelet tight
frames from the lower order ones. We also represent each generator of spline
wavelet tight frames as certain order of derivative of some univariate box
spline. With this, we further show that each generator of sufficiently high
order spline wavelet tight frames is close to a right order of derivative of a
properly scaled Gaussian function. This leads to the result that the wavelet
system generated by a finitely many consecutive derivatives of a properly
scaled Gaussian function forms a frame whose frame bounds can be almost tight.


  We investigate collider signatures of a top-philic W' model, in which the W'
boson couples only to the third-generation quarks of the standard model. The
main discovery channel for this W' is through associated production of the W'
and top quark, yielding a top-quark pair plus an extra bottom quark jet as a
signal. We do a full simulation of the signal and relevant backgrounds. We
develop a method of analysis that allows us to conclude that discovery of the
W' is promising at the LHC despite large standard model backgrounds. Bottom
quark tagging of the extra jet is key to suppressing the backgrounds.


  Neural Radiance Fields (NeRF) offer the potential to benefit 3D
reconstruction tasks, including aerial photogrammetry. However, the scalability
and accuracy of the inferred geometry are not well-documented for large-scale
aerial assets,since such datasets usually result in very high memory
consumption and slow convergence.. In this paper, we aim to scale the NeRF on
large-scael aerial datasets and provide a thorough geometry assessment of NeRF.
Specifically, we introduce a location-specific sampling technique as well as a
multi-camera tiling (MCT) strategy to reduce memory consumption during image
loading for RAM, representation training for GPU memory, and increase the
convergence rate within tiles. MCT decomposes a large-frame image into multiple
tiled images with different camera models, allowing these small-frame images to
be fed into the training process as needed for specific locations without a
loss of accuracy. We implement our method on a representative approach,
Mip-NeRF, and compare its geometry performance with threephotgrammetric MVS
pipelines on two typical aerial datasets against LiDAR reference data. Both
qualitative and quantitative results suggest that the proposed NeRF approach
produces better completeness and object details than traditional approaches,
although as of now, it still falls short in terms of accuracy.


  We present an extended study of single impurity atoms and atomic swaps in
half-metallic CrAs, CrSb and CrSe zinc-blende compounds. Although the perfect
alloys present a rather large gap in the minority-spin band, all defects under
study, with the exception of void impurities at Cr and sp sites and Cr
impurities at sp sites (as long as no swap occurs), induce new states within
the gap. The Fermi level can be pinned within these new minority states
depending on the lattice constant used for the calculations and the
electronegativity of the sp atoms. Although these impurity states are localized
in space around the impurity atoms and very fast we regain the bulk behavior,
their interaction can lead to wide bands within the gap and thus loss of the
half-metallic character.


  The Levinson theorem for nonrelativistic quantum mechanics in two spatial
dimensions is generalized to Dirac particles moving in a central field. The
theorem relates the total number of bound states with angular momentum $j$
($j=\pm 1/2, \pm 3/2, ... $), $n_j$, to the phase shifts $\eta_j(\pm E_k)$ of
scattering states at zero momentum as follows: $\eta_j(\mu)+\eta_j(-\mu)=
n_j\pi$.


  In this article, we introduce a notion of size for sets called thickness that
can be used to guarantee that two Cantor sets intersect (the Gap Lemma), and
show a connection among Thickness, Schmidt Games and Patterns. We work mostly
in the real line, but we also introduce the topic in higher dimensions.


  The current paper is a corrected version of our previous paper
arXiv:adap-org/9608001. Similarly to previous version we investigate the
problem of flame propagation. This problem is studied as an example of unstable
fronts that wrinkle on many scales. The analytic tool of pole expansion in the
complex plane is employed to address the interaction of the unstable growth
process with random initial conditions and perturbations. We argue that the
effect of random noise is immense and that it can never be neglected in
sufficiently large systems. We present simulations that lead to scaling laws
for the velocity and acceleration of the front as a function of the system size
and the level of noise, and analytic arguments that explain these results in
terms of the noisy pole dynamics.This version corrects some very critical
errors made in arXiv:adap-org/9608001 and makes more detailed description of
excess number of poles in system, number of poles that appear in the system in
unit of time, life time of pole. It allows us to understand more correctly
dependence of the system parameters on noise than in arXiv:adap-org/9608001


  We investigate the upper tail distribution of the partition function of the
directed polymer in a random environment on $\mathbb Z^d$ in the weak disorder
phase. We show that the distribution of the infinite volume partition function
$W^{\beta}_{\infty}$ displays a power-law decay, with an exponent
$p^*(\beta)\in [1+\frac{2}{d},\infty)$. We also prove that the distribution of
the suprema of the point-to-point and point-to-line partition functions display
the same behavior. On the way to these results, we prove a technical estimate
of independent interest: the $L^p$-norm of the partition function at the time
when it overshoots a high value $A$ is comparable to $A$. We use this estimate
to extend the validity of many recent results that were proved under the
assumption that the environment is upper bounded.


  In this paper we research the differential geometric and algebro-geometric
proper- ties of the noncollasping limit in the conical continuity equation.


  We develop estimators of agreement and disagreement between correlated
cosmological data sets. These account for data correlations when computing the
significance of both tensions and excess confirmation while remaining
statistically optimal. We discuss and thoroughly characterize different
approaches commenting on the ones that have the best behavior in practical
applications. We complement the calculation of their statistical distribution
within the Gaussian model with one estimator that takes non-Gaussianities fully
into account. To illustrate the use of our techniques, we apply these
estimators to supernovae measurements of the distance-redshift relation,
absolutely calibrated by the local distance ladder. The suite of best
estimators that we discuss finds results that are in excellent agreement
between estimators and find no indications of significant internal
inconsistencies in this data set above the $1\%$ probability threshold. This
shows the robustness of local determinations of the Hubble constant to features
in the distance-redshift relation.


  With the formal construction of a thermodynamic spring, I describe the
mechanics, energetics, entropy, and kinetics of a binary mechanical model
system. A protein that transitions between two metastable structural states
behaves as a molecular switch, and an ensemble of molecular switches that
displace compliant elements equilibrated with a system force constitutes a
binary mechanical model system. In biological systems, many protein switches
equilibrate with cellular forces, yet the statistical mechanical problem
relevant to this system has remained unsolved. A binary mechanical model system
establishes a limited number of macroscopic parameters into which structural
and mechanistic details must be fit. Novel advances include a non-equilibrium
kinetic and energetic equivalence; scalable limits on kinetics and energetics;
and entropic effects on kinetics and mechanics. The model unifies disparate
models of molecular motor mechanochemistry, accounts for the mechanical
performance of muscle in both transient and steady states, and provides a new
perspective on biomechanics with a focus here on how muscle and molecular motor
ensembles work.


  We study the A+B -> l+ l- + jet +X process in nucleus-nucleus collisions at
relativistic energies. The dilepton as well as the jet will pass through the
matter produced in such collisions. The recoiling dilepton will carry
information about the kinematical features of the jet, and will thus prove to
be a very effective tool in isolating in-medium effects such as energy-loss and
fragmentation function modifications. We estimate the contributions due to
correlated charm and bottom decay and we identify a window where they are small
as compared to pairs from the NLO Drell-Yan process.


  Unsupervised domain adaptation (DA) with the aid of pseudo labeling
techniques has emerged as a crucial approach for domain-adaptive 3D object
detection. While effective, existing DA methods suffer from a substantial drop
in performance when applied to a multi-class training setting, due to the
co-existence of low-quality pseudo labels and class imbalance issues. In this
paper, we address this challenge by proposing a novel ReDB framework tailored
for learning to detect all classes at once. Our approach produces Reliable,
Diverse, and class-Balanced pseudo 3D boxes to iteratively guide the
self-training on a distributionally different target domain. To alleviate
disruptions caused by the environmental discrepancy (e.g., beam numbers), the
proposed cross-domain examination (CDE) assesses the correctness of pseudo
labels by copy-pasting target instances into a source environment and measuring
the prediction consistency. To reduce computational overhead and mitigate the
object shift (e.g., scales and point densities), we design an overlapped boxes
counting (OBC) metric that allows to uniformly downsample pseudo-labeled
objects across different geometric characteristics. To confront the issue of
inter-class imbalance, we progressively augment the target point clouds with a
class-balanced set of pseudo-labeled target instances and source objects, which
boosts recognition accuracies on both frequently appearing and rare classes.
Experimental results on three benchmark datasets using both voxel-based (i.e.,
SECOND) and point-based 3D detectors (i.e., PointRCNN) demonstrate that our
proposed ReDB approach outperforms existing 3D domain adaptation methods by a
large margin, improving 23.15% mAP on the nuScenes $\rightarrow$ KITTI task.
The code is available at https://github.com/zhuoxiao-chen/ReDB-DA-3Ddet.


  The star HD 28363 in the Hyades cluster has been known for over a century as
a visual binary with a period of 40 yr. The secondary is, in turn, a
single-lined spectroscopic binary with a 21-day period. Here we report
extensive spectroscopic monitoring of this hierarchical triple system that
reveals the spectral lines of the third star for the first time. Combined with
astrometric information, this makes it possible to determine the dynamical
masses of all three stars. Only six other binaries in the Hyades have had their
individual component masses determined dynamically. We infer the properties of
the system by combining our radial velocity measurements with visual
observations, lunar occultation measurements, and with proper motions from the
Hipparcos and Gaia missions that provide a constraint on the astrometric
acceleration. We derive a mass of 1.341 +/- 0.026/0.024 M(Sun) for the visual
primary, and 1.210 +/- 0.021 M(Sun) and 0.781 +/- 0.014 M(Sun) for the other
two stars. These measurements along with those for the other six systems
establish an empirical mass-luminosity relation in the Hyades that is in broad
agreement with current models of stellar evolution for the known age and
chemical composition of the cluster.


  A sorting network (also known as a reduced decomposition of the reverse
permutation), is a shortest path from $12 \cdots n$ to $n \cdots 21$ in the
Cayley graph of the symmetric group $S_n$ generated by adjacent transpositions.
We prove that in a uniform random $n$-element sorting network $\sigma^n$, all
particle trajectories are close to sine curves with high probability. We also
find the weak limit of the time-$t$ permutation matrix measures of $\sigma^n$.
As a corollary of these results, we show that if $S_n$ is embedded into
$\mathbb{R}^n$ via the map $\tau \mapsto (\tau(1), \tau(2), \dots \tau(n))$,
then with high probability, the path $\sigma^n$ is close to a great circle on a
particular $(n-2)$-dimensional sphere in $\mathbb{R}^n$. These results prove
conjectures of Angel, Holroyd, Romik, and Virag.


  We obtain conditions for existence of unique global or maximally extended
solutions to generalized neural field equations. We also study continuous
dependence of these solutions on the spatiotemporal integration kernel, delay
effects, firing rate and prehistory functions.


  We consider the problem of learning to map from natural language instructions
to state transitions (actions) in a data-efficient manner. Our method takes
inspiration from the idea that it should be easier to ground language to
concepts that have already been formed through pre-linguistic observation. We
augment a baseline instruction-following learner with an initial
environment-learning phase that uses observations of language-free state
transitions to induce a suitable latent representation of actions before
processing the instruction-following training data. We show that mapping to
pre-learned representations substantially improves performance over systems
whose representations are learned from limited instructional data alone.


  The effective spin-1/2 antiferromagnetic Heisenberg-Ising chain materials,
ACo$_2$V$_2$O$_8$, A = Sr, Ba, are a rich source of exotic fundamental
phenomena and have been investigated for their model magnetic properties both
in zero and non-zero magnetic fields. Here we investigate a new member of the
family, namely PbCo$_2$V$_2$O$_8$. We synthesize powder and single crystal
samples of PbCo$_2$V$_2$O$_8$ and determine its magnetic structure using
neutron diffraction. Furthermore, the magnetic field/temperature phase diagrams
for magnetic field applied along the c, a, and [110] crystallographic
directions in the tetragonal unit cell are determined via magnetization and
heat capacity measurements. A complex series of phases and quantum phase
transitions are discovered that depend strongly on both the magnitude and
direction of the field. Our results show that \pcvo is an effective spin-1/2
antiferromagnetic Heisenberg-Ising chain with properties that are in general
comparable to those of SrCo$_2$V$_2$O$_8$ and BaCo$_2$V$_2$O$_8$. One
interesting departure from the results of these related compounds, is however,
the discovery of a new field-induced phase for the field direction $H\|$[110]
which has not been previously observed.


  In this paper we explore the geometric space parametrized by (tree level)
Wilson loops in SYM $N=4$. We show that, this space can be seen as a vector
bundle over a totally non-negative subspace of the Grassmannian,
$\mathcal{W}_{k,cn}$. Furthermore, we explicitly show that this bundle is
non-orientable in the majority of the cases, and conjecture that it is
non-orientable in the remaining situation. Using the combinatorics of the
Deodhar decomposition of the Grassmannian, we identify subspaces $\Sigma(W)
\subset \mathcal{W}_{k,n}$ for which the restricted bundle lies outside the
positive Grassmannian. Finally, while probing the combinatorics of the Deodhar
decomposition, we give a diagrammatic algorithm for reading equations
determining each Deodhar component as a semialgebraic set.


  We report an analysis of the nuclear dependence of the yield of Drell-Yan
dimuons from the 800 GeV/c proton bombardment of $^2H$, C, Ca, Fe, and W
targets. Employing a new formulation of the Drell-Yan process in the rest frame
of the nucleus, this analysis examines the effect of initial-state energy loss
and shadowing on the nuclear-dependence ratios versus the incident proton's
momentum fraction and dimuon effective mass. The resulting energy loss per unit
path length is $-dE/dz = 2.32 \pm 0.52\pm 0.5$ GeV/fm. This is the first
observation of a nonzero energy loss of partons traveling in nuclear
environment.


  We report on a ~5th magnitude flash detected for approximately 10 minutes by
two CONCAM all-sky cameras located in Cerro Pachon - Chile and La Palma -
Spain. A third all-sky camera, located in Cerro Paranal - Chile did not detect
the flash, and therefore the authors of this paper suggest that the flash was a
series of cosmic-ray hits, meteors, or satellite glints. Another proposed
hypothesis is that the flash was an astronomical transient with variable
luminosity. In this paper we discuss bright optical transient detection using
fish-eye all-sky monitors, analyze the apparently false-positive optical
transient, and propose possible causes to false optical transient detection in
all-sky cameras.


  A homomorphism height function on the $d$-dimensional torus $\mathbb{Z}_n^d$
is a function taking integer values on the vertices of the torus with
consecutive integers assigned to adjacent vertices. A Lipschitz height function
is defined similarly but may also take equal values on adjacent vertices. In
each model, we consider the uniform distribution over such functions, subject
to boundary conditions. We prove that in high dimensions, with zero boundary
values, a typical function is very flat, having bounded variance at any fixed
vertex and taking at most $C(\log n)^{1/d}$ values with high probability. Our
results extend to any dimension $d\ge 2$, if $\mathbb{Z}_n^d$ is replaced by an
enhanced version of it, the torus $\mathbb{Z}_n^d\times\mathbb{Z}_2^{d_0}$ for
some fixed $d_0$. This establishes one side of a conjectured roughening
transition in $2$ dimensions. The full transition is established for a class of
tori with non-equal side lengths. We also find that when $d$ is taken to
infinity while $n$ remains fixed, a typical function takes at most $r$ values
with high probability, where $r=5$ for the homomorphism model and $r=4$ for the
Lipschitz model. Suitable generalizations are obtained when $n$ grows with $d$.
Our results apply also to the related model of uniform 3-coloring and
establish, for certain boundary conditions, that a uniformly sampled proper
3-coloring of $\mathbb{Z}_n^d$ will be nearly constant on either the even or
odd sub-lattice.
  Our proofs are based on a combinatorial transformation and on a careful
analysis of the properties of a class of cutsets which we term odd cutsets. For
the Lipschitz model, our results rely also on a bijection of Yadin. This work
generalizes results of Galvin and Kahn, refutes a conjecture of Benjamini,
Yadin and Yehudayoff and answers a question of Benjamini, H\"aggstr\"om and
Mossel.


  In 1851 Prouhet showed that when $N=j^{k+1}$ where $j$ and $k$ are positive
integers, $j \geq 2$, the first $N$ consecutive positive integers can be
separated into $j$ sets, each set containing $j^k$ integers, such that the sum
of the $r$-th powers of the members of each set is the same for
$r=1,\,2,\,\ldots,\,k$. In this paper we show that even when $N$ has the much
smaller value $2j^k$, the first $N$ consecutive positive integers can be
separated into $j$ sets, each set containing $2j^{k-1}$ integers, such that the
integers of each set have equal sums of $r$-th powers for
$r=1,\,2,\,\ldots,\,k$. Moreover, we show that this can be done in at least
$\{(j-1)!\}^{k-1}$ ways. We also show that there are infinitely many other
positive integers $N=js$ such that the first $N$ consecutive positive integers
can similarly be separated into $j$ sets of integers, each set containing $s$
integers, with equal sums of $r$-th powers for $r=1,\,2,\,\ldots,\,k$, with the
value of $k$ depending on the integer $N$.


  Superoscillations are a phenomenon in physics, where linear combinations of
low-frequency plane waves interfere almost destructively in such a way that the
resulting wave has a higher frequency than any of the individual waves. The
evolution of superoscillatory initial datum under the time dependent
Schr\"odinger equation is stable in free space, but in general it is unclear
whether it can be preserved in the presence of an external potential. In this
paper, we consider the two-dimensional problem of superoscillations interacting
with a half-plane barrier, where homogenous Dirichlet or Neumann boundary
conditions are imposed on the negative $x_2$-semiaxis. We use the Fresnel
integral technique to write the wave function as an absolute convergent Green's
function integral. Moreover, we introduce the propagator of the Schr\"odinger
equation in form of an infinite order differential operator, acting
continuously on the function space of exponentially bounded entire functions.
In particular, this operator allows to prove that the property of
superoscillations is preserved in the form of a similar phenomenon called
supershift, which is stable over time.


  Planning under process and measurement uncertainties is a challenging
problem. In its most general form it can be modeled as a Partially Observed
Markov Decision Process (POMDP) problem. However POMDPs are generally difficult
to solve when the underlying spaces are continuous, particularly when beliefs
are non-Gaussian, and the difficulty is further exacerbated when there are also
non-convex constraints on states. Existing algorithms to address such
challenging POMDPs are expensive in terms of computation and memory. In this
paper, we provide a feedback policy in non-Gaussian belief space via solving a
convex program for common non-linear observation models. The solution involves
a Receding Horizon Control strategy using particle filters for the non-Gaussian
belief representation. We develop a way of capturing non-convex constraints in
the state space and adapt the optimization to incorporate such constraints, as
well. A key advantage of this method is that it does not introduce additional
variables in the optimization problem and is therefore more scalable than
existing constrained problems in belief space. We demonstrate the performance
of the method on different scenarios.


  Graph autoencoders (AE) and variational autoencoders (VAE) recently emerged
as powerful node embedding methods. In particular, graph AE and VAE were
successfully leveraged to tackle the challenging link prediction problem,
aiming at figuring out whether some pairs of nodes from a graph are connected
by unobserved edges. However, these models focus on undirected graphs and
therefore ignore the potential direction of the link, which is limiting for
numerous real-life applications. In this paper, we extend the graph AE and VAE
frameworks to address link prediction in directed graphs. We present a new
gravity-inspired decoder scheme that can effectively reconstruct directed
graphs from a node embedding. We empirically evaluate our method on three
different directed link prediction tasks, for which standard graph AE and VAE
perform poorly. We achieve competitive results on three real-world graphs,
outperforming several popular baselines.


  We propose a new algorithm, call Sam to determinate the existence of the
solutions for the equation $x^3+y^3+z^3=n$ for a fixed value $n > 0$ unknown.


  In nonrelativistic models of nuclei, the underlying mass scales of low-energy
quantum chromodynamics (QCD) are largely hidden. In contrast, the covariant
formulations used in relativistic phenomenology manifest the QCD scales in
nuclei through large Lorentz scalar and four-vector nucleon self-energies. The
abundant and varied evidence in support of this connection and the consequences
are reviewed.


  An experiment to demonstrate the Fourier transform of an electric signal
using the Kundt's tube is described. The results of finding the component
frequencies and an approximation to the amplitudes of two sinusoidal signals
which compose an input electric signal is presented. Undergraduate students are
expected to more easily relate to the meaning of a Fourier transform through
such mechanical demonstrations.


  Cyclic codes are an interesting class of linear codes due to their efficient
encoding and decoding algorithms as well as their theoretical importance. BCH
codes form a subclass of cyclic codes and are very important in both theory and
practice as they have good error-correcting capability and are widely used in
communication systems, storage devices and consumer electronics. However, the
dimension and minimum distance of BCH codes are not known in general. The
objective of this paper is to study the dimension and minimum distance of a
family of BCH codes over finite fields, i.e., a class of reversible BCH codes.


  This work is concerned with branes and differential equations for
one-parameter Calabi-Yau hypersurfaces in weighted projective spaces. For a
certain class of B-branes we derive the inhomogeneous Picard--Fuchs equations
satisfied by the brane superpotential. In this way we arrive at a prediction
for the real BPS invariants for holomorphic maps of worldsheets with low Euler
characteristics, ending on the mirror A-branes.


  We prove a very general lower bound technique for quantum and randomized
query complexity, that is easy to prove as well as to apply. To achieve this,
we introduce the use of Kolmogorov complexity to query complexity. Our
technique generalizes the weighted, unweighted methods of Ambainis, and the
spectral method of Barnum, Saks and Szegedy. As an immediate consequence of our
main theorem, adversary methods can only prove lower bounds for boolean
functions $f$ in $O(\min(\sqrt{n C_0(f)},\sqrt{n C_1(f)}))$, where $C_0, C_1$
is the certificate complexity, and $n$ is the size of the input. We also derive
a general form of the ad hoc weighted method used by Hoyer, Neerbek and Shi to
give a quantum lower bound on ordered search and sorting.


  The industry of wearable remote health monitoring system keeps growing. In
the diagnosis of cardiovascular disease, Electrocardiography~(ECG) waveform is
one of the major tools which is thus widely taken as the monitoring objective.
For the purpose of reducing bit expenditure in the monitoring systems, we study
the compression of ECG signal and propose a new compressor in low complexity.
Different from the traditional ECG compressors, most of which are built on a
single sensor, our compression scheme is based on multiple ECG sensors. The
multi-sensor based compression scheme is able to provide more accurate sensing
results. Besides the investigation into the structure of the compressor, we
also jointly optimize the period and the bit number per sample in the
transmission of ECG signal. Experiments are performed on records in MIT-BIH
Arrhythmis database and European ST-T database. Experimental results show that
our method outperforms conventional ones with respect to ECG reconstruction
accuracy at the same bit rate consumption


  In this paper, we introduce the concept of $\Sigma$-semicommutative ring, for
$\Sigma$ a finite family of endomorphisms of a ring $R$. We relate this class
of rings with other classes of rings such that Abelian, reduced,
$\Sigma$-rigid, nil-reversible and rings satisfying the $\Sigma$-skew reflexive
nilpotent property. Also, we study some ring-theoretical properties of skew PBW
extensions over $\Sigma$-semicommutative rings. We prove that if a ring $R$ is
$\Sigma$-semicommutative with certain conditions of compatibility on
derivations, then for every skew PBW extension $A$ over $R$, $R$ is Baer if and
only if $R$ is quasi-Baer, and equivalently, $A$ is quasi-Baer if and only if
$A$ is Baer. Finally, we consider some topological conditions for skew PBW
extensions over $\Sigma$-semicommutative rings.


  We study a two-dimensional rotating Bose-Einstein condensate confined by an
anharmonic trap in the framework of the Gross-Pitaevksii theory. We consider a
rapid rotation regime close to the transition to a giant vortex state. It was
proven in [M. Correggi {\it et al}, {\it J. Math. Phys. \textbf{53}(2012)] that
such a transition occurs when the angular velocity is of order $ \varepsilon
^{-4}$, with $ \varepsilon ^{-2} $ denoting the coefficient of the nonlinear
term in the Gross-Pitaevskii functional and $ \varepsilon \ll 1 $ (Thomas-Fermi
regime). In this paper we identify a finite value $ \Omega_{\mathrm{c}} $ such
that, if $ \Omega = \Omega_0/\varepsilon ^4 $ with $ \Omega_0 >
\Omega_{\mathrm{c}} $, the condensate is in the giant vortex phase. Under the
same condition we prove a refined energy asymptotics and an estimate of the
winding number of any Gross-Pitaevskii minimizer.


  Processing and analyzing of massive clinical data are resource intensive and
time consuming with traditional analytic tools. Electroencephalogram (EEG) is
one of the major technologies in detecting and diagnosing various brain
disorders, and produces huge volume big data to process. In this study, we
propose a big data framework to diagnose sleep disorders by classifying the
sleep stages from EEG signals. The framework is developed with open source
SparkMlib Libraries. We also tested and evaluated the proposed framework by
measuring the scalabilities of well-known classification algorithms on
physionet sleep records.


  This article addresses some issues related to statistical description of
gravitating systems in an expanding backgrounds. In particular, I describe (a)
how the non linear mode-mode coupling transfers power from one scale to another
in the Fourier space if the initial power spectrum is sharply peaked at a given
scale and (b) what are the asymptotic characteristics of gravitational
clustering that are independent of the initial conditions. The analysis uses a
new approach based on an integro-differential equation for the evolution of the
gravitational potential in the Fourier space. I show how this equation allows
one to understand several aspects of nonlinear gravitational clustering and
provides insight in to the transfer of power from one scale to another through
nonlinear mode coupling. Numerical simulations as well as analytic work shows
that power transfer leads to a universal power spectrum at late times, somewhat
reminiscent of the existence of Kolmogorov spectrum in fluid turbulence.


  Answering a question of P. Bankston, we show that the pseudoarc is a
co-existentially closed continuum. We also show that $C(X)$, for $X$ a
nondegenerate continuum, can never have quantifier elimination, answering a
question of the the first and third named authors and Farah and Kirchberg.


  Employing the Maximum Entropy Method algorithm, we fit interstellar
extinction measurements which span the wavelength range 0.125-3 micron. We
present a uniform set of MEM model fits, all using the same grain materials,
optical constants and abundance constraints. In addition, we are taking
advantage of improved UV and IR data and better estimates of the gas-to-dust
ratio. The model fits cover the entire range of extinction properties that have
been seen in the Galaxy and the Magellanic Clouds. The grain models employed
for this presentation are the simplistic homogeneous spheres models (i.e.,
Mathis, Rumpl, & Nordsieck 1977) with two (graphite, silicate) or three
(graphite, silicate, amorphous carbon) components. Though such usage is only a
first step, the results do provide interesting insight into the use of grain
size as a diagnostic of dust environment. We find that the SMC Bar extinction
curve cannot be fit using carbon grains alone. This is a challenge to the
recent observational result indicating little silicon depletion in the SMC.


  We prove that the geodesic equation for any semi-Riemannian metric of
regularity $C^{0,1}$ possesses $C^1$-solutions in the sense of Filippov.


  In strongly nonequilibrium Bose-Einstein condensates described by the
generalized Gross-Pitaevskii equation, vortex motion becomes self-accelerated
while the long-range vortex-antivortex interaction appears to be repulsive. We
numerically study the impact of these rather unusual vortex properties on the
dynamics of multivortex systems. We show that at strong nonequilibrium the
repulsion between vortices and antivortices leads to a dramatic slowdown of
their annihilation. Moreover, in finite-size samples, relaxation of multivortex
systems can lead to the formation of metastable vortex-antivortex clusters,
whose shape and size depend, in particular, on the sample geometry, boundary
conditions and deviations from equilibrium. We further demonstrate that at
strong nonequilibrium the interaction of self-accelerated vortices with
inhomogeneous condensate flows can lead to generation of new vortex-antivortex
pairs.


  A new type of transverse instability in dispersively nonlinear optical
cavities, called the optical whistle, is discussed. This instability occurs in
the mean-field, soliton forming limit when the cavity is driven with a
finite-width Gaussian beam, and gives rise to oscillation, period doubling, and
chaos. It is also seen that bistability is strongly affected due to the
oscillation within the upper transmission branch. The phenomenon is interpreted
as a mode-mismatch in the soliton formation process and is believed to have
broad applicability.


  We show that a measure on the real line that is the image of a log-concave
measure under a polynomial of degree $d$ possesses a density from the
Nikol'skii--Besov class of fractional order $1/d$. This result is used to prove
an estimate of the total variation distance between such measures in terms of
the Fortet--Mourier distance.


  This work is concerned with the theory of initial and progressive
enlargements of a reference filtration F with a random time {\tau}. We provide,
under an equivalence assumption, slightly stronger than the absolute continuity
assumption of Jacod, alternative proofs to results concerning canonical
decomposition of an F-martingale in the enlarged filtrations. Also, we address
martingales' characterization in the enlarged filtrations in terms of
martingales in the reference filtration, as well as predictable representation
theorems in the enlarged filtrations.


  We present an energy-conserving multiple-relaxation-time finite difference
lattice Boltzmann model for compressible flows. This model is based on a
16-discrete-velocity model. The collision step is first calculated in the
moment space and then mapped back to the velocity space. The moment space and
corresponding transformation matrix are constructed according to the group
representation theory. Equilibria of the nonconserved moments are chosen
according to the need of recovering compressible Navier-Stokes equations
through the Chapman-Enskog expansion. Numerical experiments showed that
compressible flows with strong shocks can be well simulated by the present
model. The used benchmark tests include (i) shock tubes, such as the Sod, Lax,
Sjogreen, Colella explosion wave and collision of two strong shocks, (ii)
regular and Mach shock reflections, and (iii) shock wave reaction on
cylindrical bubble problems. The new model works for both low and high speeds
compressible flows. It contains more physical information and has better
numerical stability and accuracy than its single-relaxation-time version.


  Exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic
equations in the stationary planar Couette flow is found at non-vanishing
Knudsen numbers. A new method of solving LB kinetic equations which combines
the method of moments with boundary conditions for populations enables to
derive closed-form solutions for all higher-order moments. Convergence of
results suggests that the LB hierarchy with larger velocity sets is the novel
way to approximate kinetic theory.


  Using the recently developed transfer-matrix renormalization group method, we
have studied the thermodynamic properties of two-leg antiferromagnetic ladders
in the magnetic field. Based on different behavior of magnetization, we found
disordered spin liquid, Luttinger liquid, spin-polarized phases and a classical
regime depending on magnetic field and temperature. Our calculations in
Luttinger liquid regime suggest that both the divergence of the NMR relaxation
rate and the anomalous specific heat behavior observed on
Cu$_2$(C$_5$H$_{12}$N$_2$)$_2$Cl$_4$}are due to quasi-one-dimensional effect
rather than three-dimensional ordering.


  QED-effects are known to occur in a strong laser pulse interaction with a
counter-propagating electron beam, among these effects being electron-positron
pair creation. We discuss the range of laser pulse intensities of J > 5*10^22
W/cm2 combined with electron beam energies of tens of GeV. In this regime
multiple pairs may be generated from a single beam electron, some of the
newborn particles being capable of further pair production. Radiation
back-reaction prevents avalanche development and limits pair creation. The
system of integro-differential kinetic equations for electrons, positrons and
\gamma-photons is derived and solved numerically.


  The geometric measure of entanglement, which expresses the minimum distance
to product states, has been generalized to distances to sets that remain
invariant under the stochastic reducibility relation. For each such set, an
associated entanglement monotone can be defined. The explicit analytical forms
of these measures are obtained for bipartite entangled states. Moreover, the
three qubit case is discussed and argued that the distance to the W states is a
new monotone.


  We apply the Regge-Wheeler formalism to study axial and polar gravitational
waves in Kantowski-Sachs universe. The background field equations and the
linearised perturbation equations for the modes are derived in presence of
matter. To find analytical solutions, we analyze the propagation of waves in
vacuum spacetime. The background field equations in absence of matter are
solved by assuming the expansion scalar to be proportional to the shear scalar.
Using the method of separation of variables, the axial perturbation parameter $
h_0(t, r) $ is obtained from its wave equation. The other perturbation $ h_1(t,
r) $ is then determined from $ h_0(t, r) $. The anisotropy of the background
spacetime is responsible for the damping of the axial waves. The polar
perturbation equations are much more involved compared to their FLRW
counterparts, as well as to the axial perturbations in Kantowski-Sachs
background. In both the axial and polar cases, the radial and temporal
solutions separate out as products. The temporal part of the polar perturbation
solutions are plotted against time to obtain an order of magnitude estimate of
the frequency of the propagating GWs and lies in the range 1000-2000 Hz. Using
standard observational data for the GW strain we have placed constraints on the
parameters in the polar perturbation solutions. The perturbation equations in
presence of matter show that the axial waves can cause perturbations only in
the azimuthal velocity of the fluid without deforming the matter field. But the
polar waves must perturb the energy density, the pressure and also the
non-azimuthal components of the fluid velocity.


  We present a new analysis of the main empirical calibrators of oxygen
abundance for ionised gas nebulae. With that aim we have compiled an extensive
sample of objects with emission line data including the near IR [SIII] lines
and the weak auroral lines which allow for the determination of the gas
electron temperature. For all the objects the oxygen abundances have been
derived in a homogeneus way, using the most recent sets of atomic coefficients
and taking into the account the effect of particle density on the temperature
of O$^+$. The residuals between directly and empirically-derived abundances as
a function of abundance have been studied. A grid of photo-ionisation models,
covering the range of physical properties of the gas, has been used to explain
the origin of the uncertainties affecting each abundance calibrator. The range
of validity for each abundance parameter has been identified and its average
uncertainty has been quantified.


  Since a significant time ago, although time runs very fast,nanotechnology
transformed from one of the most promising scientific hopes in uncountable
human domains into a marvelous certainty. Innumerable scientific studies in
several areas of knowledge were made since nanoscale emergence, carrying their
contribution to the nanoscience development, leading to a great development of
technical and scientific knowledge but also raising numerous problems in the
ethical field. In this work, nanotechnology is discussed both in terms of
ethics and in terms of borders that nanotechnology applications must satisfy
and concluding notes are presented, highlighting the results of the analysis.
Significant considerations are made on the close connection between ethics and
the nanotechnology and the effects over the society and values.


  We explores the Pantheon+SH0ES dataset to identify patterns that can
discriminate between different cosmological models. We focus on determining
whether the behaviour of dark energy is consistent with the standard
$\Lambda$CDM model or suggests novel cosmological features. The central goal is
to evaluate the robustness of the $\Lambda$CDM model compared with other dark
energy models, and to investigate whether there are deviations that might
indicate new cosmological insights. The study takes into account a data-driven
approach, using both traditional statistical methods and machine learning
techniques. Initially, we evaluate six different dark energy models using
traditional statistical methods like Markov Chain Monte Carlo (MCMC), Static
and Dynamic Nested Sampling to infer the cosmological parameters. Subsequently,
we adopt a machine learning approach, developing a regression model to compute
the distance modulus of each supernova, expanding the feature set to 74
statistical features. Traditional statistical analysis confirms that the
$\Lambda$CDM model is robust, yielding expected parameter values. Other models
show deviations, with the Generalised and Modified Chaplygin Gas models
performing poorly. In the machine learning analysis, feature selection
techniques, particularly Boruta, significantly improve model performance. In
particular, models initially considered weak (Generalised/Modified Chaplygin
Gas) show significant improvement after feature selection. The study
demonstrates the effectiveness of a data-driven approach to cosmological model
evaluation. The $\Lambda$CDM model remains robust, while machine learning
techniques, in particular feature selection, reveal potential improvements in
alternative models which could be relevant for new observational campaigns like
the recent DESI survey.


  We give a canonical form for a complex matrix, whose square is normal, under
transformations of unitary similarity as well as a canonical form for a real
matrix, whose square is normal, under transformations of orthogonal similarity.


  Simulated configurations of flexible knotted rings confined inside a
spherical cavity are fed into long-short term memory neural networks (LSTM NNs)
designed to distinguish knot types. The results show that they perform well in
knot recognition even if tested against flexible, strongly confined and
therefore highly geometrically entangled rings. In agreement with the
expectation that knots are delocalized in dense polymers, a suitable
coarse-graining procedure on configurations boosts the performance of the LSTMs
when knot identification is applied to rings much longer than those used for
training. Notably, when the NNs fail, usually the wrong prediction still
belongs to the same topological family of the correct one. The fact that the
LSTMs are able to grasp some basic properties of the ring's topology is
corroborated by a test on knot types not used for training. We also show that
the choice of the NN architecture is important: simpler convolutional NNs do
not perform so well. Finally, all results depend on the features used for
input: surprisingly, coordinates or bond directions of the configurations
provide the best accuracy to the NNs, even if they are not invariant under
rotations (while the knot type is invariant). Other rotational invariant
features we tested are based on distances, angles, and dihedral angles.


  Nonlinear, i.e., multi-photon microscopy is a powerful technique for imaging
deep into biological tissues. Its penetration depth can be increased further
using adaptive optics. In this work, we present a fast, feedback-based
adaptive-optics algorithm, termed C-DASH, for multi-photon imaging through
multiply-scattering media. C-DASH utilises complex-valued light shaping (i.e.,
joint shaping of amplitude and phase), which offers several advantages over
phase-only techniques: it converges faster, it delivers higher image quality
enhancement, it shows a robust performance largely insensitive to the axial
position of the correction plane, and it has a higher ability to cope with, on
the one hand, scattering media that vary over time and, on the other hand,
scattering media that are partially absorbing. Furthermore, our method is
practically self-aligning. We also present a simple way to implement C-DASH
using a single reflection off a phase-only spatial light modulator. We provide
a thorough characterisation of our method, presenting results of numerical
simulations as well as two-photon excited fluorescence imaging experiments.


  We present new features of the FeynRules and MadGraph5/aMC@NLO programs for
the automatic computation of decay widths that consistently include channels of
arbitrary final-state multiplicity. The implementations are generic enough so
that they can be used in the framework of any quantum field theory, possibly
including higher-dimensional operators. We extend at the same time the
conventions of the Universal FeynRules Output (or UFO) format to include decay
tables and information on the total widths. We finally provide a set of
representative examples of the usage of the new functions of the different
codes in the framework of the Standard Model, the Higgs Effective Field Theory,
the Strongly Interacting Light Higgs model and the Minimal Supersymmetric
Standard Model and compare the results to available literature and programs for
validation purposes.


  We deduce a procedure to apply balanced truncation to parameter-dependent
differential-algebraic systems. For that we solve multiple projected Lyapunov
equations for different parameter values to compute the Gramians that are
required for the truncation procedure. As this process would lead to high
computational costs if we perform it for a large number of parameters, we
combine this approach with the reduced basis method that determines a reduced
representation of the Lyapunov equation solutions for the parameters of
interest. Residual-based error estimators are then used to evaluate the quality
of the approximations. After introducing the procedure for a general class of
differential-algebraic systems we turn our focus to systems with a specific
structure, for which the method can be applied particularly efficiently. We
illustrate the efficiency of our approach on several models from fluid dynamics
and mechanics.


  Provisioning of Quality of Service (QoS) is a key issue in any multi-media
system. However, in wireless systems, supporting QoS requirements of different
traffic types is more challenging due to the need to minimize two performance
metrics - the probability of dropping a handover call and the probability of
blocking a new call. Since QoS requirements are not as stringent for
non-real-time traffic types, as opposed to real-time traffic, more calls can be
accommodated by releasing some bandwidth from the already admitted
non-real-time traffic calls. If we require that such a released bandwidth to
accept a handover call ought to be larger than the bandwidth to accept a new
call, then the resulting probability of dropping a handover call will be
smaller than the probability of blocking a new call. In this paper we propose
an efficient Call Admission Control (CAC) that relies on adaptive multi-level
bandwidth-allocation scheme for non-real-time calls. The scheme allows
reduction of the call dropping probability along with increase of the bandwidth
utilization. The numerical results show that the proposed scheme is capable of
attaining negligible handover call dropping probability without sacrificing
bandwidth utilization.


  The capacitance of a parallel plate capacitor can depend on applied magnetic
field. Previous studies have identified capacitance changes induced via
classical Lorentz force or spin-dependent Zeeman effects. Here we measure a
magnetization direction dependent capacitance in parallel-plate capacitors
where one plate is a ferromagnetic semiconductor, gallium manganese arsenide.
This anisotropic magneto-capacitance is due to the anisotropy in the density of
states dependent on the magnetization through the strong spin-orbit
interaction.


  We analyse and compare various empirical models of wall pressure spectra
beneath turbulent boundary layers and propose an alternative machine learning
approach using Artificial Neural Networks (ANN). The analysis and the training
of the ANN are performed on data from experiments and high-fidelity simulations
by various authors, covering a wide range of flow conditions. We present a
methodology to extract all the turbulent boundary layer parameters required by
these models, also considering flows experiencing strong adverse pressure
gradients. Moreover, the database is explored to unveil important dependencies
within the boundary layer parameters and to propose a possible set of features
from which the ANN should predict the wall pressure spectra. The results show
that the ANN outperforms traditional models in adverse pressure gradients, and
its predictive capabilities generalise better over the range of investigated
conditions. The analysis is completed with a deep ensemble approach for
quantifying the uncertainties in the model prediction and integrated gradient
analysis of the model sensitivity to its inputs. Uncertainties and
sensitivities allow for identifying the regions where new training data would
be most beneficial to the model's accuracy, thus opening the path towards a
self-calibrating modelling approach.


  Dyna-style reinforcement learning is a powerful approach for problems where
not much real data is available. The main idea is to supplement real
trajectories, or sequences of sampled states over time, with simulated ones
sampled from a learned model of the environment. However, in large state
spaces, the problem of learning a good generative model of the environment has
been open so far. We propose to use deep belief networks to learn an
environment model for use in Dyna. We present our approach and validate it
empirically on problems where the state observations consist of images. Our
results demonstrate that using deep belief networks, which are full generative
models, significantly outperforms the use of linear expectation models,
proposed in Sutton et al. (2008)


  We developed a time-dependent radiative model for the atmosphere of HD209458b
to investigate its thermal structure and chemical composition. Time-dependent
temperature profiles were calculated, using a uniform zonal wind modelled as a
solid body rotation. We predict day/night temperature variations of 600K around
0.1 bar, for a 1 km/s wind velocity, in good agreement with the predictions by
Showman & Guillot (2002). On the night side, the low temperature allows the
sodium to condense. Depletion of sodium in the morning limb may explain the
lower than expected abundance found by Charbonneau et al (2002).


  Devised towards geophysical applications for various processes in the
lithosphere or the crust, a model of poro-elastodynamics with inelastic strains
and other internal variables like damage (aging) and porosity as well as with
diffusion of water is formulated fully in the Eulerian setting. Concepts of
gradient of the total strain rate as well as the additive splitting of the
total strain rate are used while eliminating the displacement from the
formulation. It relies on that the elastic strain is small while only the
inelastic and the total strains can be large. The energetics behind this model
is derived and used for analysis as far as the existence of global weak
energy-conserving solutions concerns. By this way, the model in [V. Lyakhovsky
et al., Pure Appl. Geophys., 171:3099-3123, 2014] and [V. Lyakhovsky et al.,
Izvestiya, Physics of the Solid Earth, 43:13-23, 2007] is completed to make it
mechanically consistent and amenable for analysis.


  This paper determines tangential structure set of $\#_k\mathbb{C}P^{n}$, for
$3\leq n \leq 7$, by analyzing their stable cohomotopy groups and $KO$-groups.
As a consequence, it establishes the existence of manifolds with tangential
homotopy type but not homeomorphic to $\#_k\mathbb{C}P^{n}$ for $n=4,5$.


  We present a neural radiance field method for urban-scale semantic and
building-level instance segmentation from aerial images by lifting noisy 2D
labels to 3D. This is a challenging problem due to two primary reasons.
Firstly, objects in urban aerial images exhibit substantial variations in size,
including buildings, cars, and roads, which pose a significant challenge for
accurate 2D segmentation. Secondly, the 2D labels generated by existing
segmentation methods suffer from the multi-view inconsistency problem,
especially in the case of aerial images, where each image captures only a small
portion of the entire scene. To overcome these limitations, we first introduce
a scale-adaptive semantic label fusion strategy that enhances the segmentation
of objects of varying sizes by combining labels predicted from different
altitudes, harnessing the novel-view synthesis capabilities of NeRF. We then
introduce a novel cross-view instance label grouping strategy based on the 3D
scene representation to mitigate the multi-view inconsistency problem in the 2D
instance labels. Furthermore, we exploit multi-view reconstructed depth priors
to improve the geometric quality of the reconstructed radiance field, resulting
in enhanced segmentation results. Experiments on multiple real-world
urban-scale datasets demonstrate that our approach outperforms existing
methods, highlighting its effectiveness.


  Given a graph H, a graph G is called a Ramsey graph of H if there is a
monochromatic copy of H in every coloring of the edges of G with two colors.
Two graphs G, H are called Ramsey equivalent if they have the same set of
Ramsey graphs. Fox et al. [J. Combin. Theory Ser. B 109 (2014), 120--133] asked
whether there are two non-isomorphic connected graphs that are Ramsey
equivalent. They proved that a clique is not Ramsey equivalent to any other
connected graph. Results of Nesetril et al. showed that any two graphs with
different clique number [Combinatorica 1(2) (1981), 199--202] or different odd
girth [Comment. Math. Univ. Carolin. 20(3) (1979), 565--582] are not Ramsey
equivalent. These are the only structural graph parameters we know that
"distinguish" two graphs in the above sense. This paper provides further
supportive evidence for a negative answer to the question of Fox et al. by
claiming that for wide classes of graphs, chromatic number is a distinguishing
parameter. In addition, it is shown here that all stars and paths and all
connected graphs on at most 5 vertices are not Ramsey equivalent to any other
connected graph. Moreover two connected graphs are not Ramsey equivalent if
they belong to a special class of trees or to classes of graphs with
clique-reduction properties.


  In this paper, we propose an adaptive panoramic video semantic transmission
(APVST) framework enabled by rate splitting multiple access (RSMA). The APVST
framework consists of a semantic transmitter and receiver, utilizing a deep
joint source-channel coding structure to adaptively extract and encode semantic
features from panoramic frames. To achieve higher spectral efficiency and
conserve bandwidth, APVST employs an entropy model and a dimension-adaptive
module to control the transmission rate. Additionally, we take
weighted-to-spherically-uniform peak signal-to-noise ratio (WS-PSNR) and
weighted-to-spherically-uniform structural similarity (WS-SSIM) as distortion
evaluation metrics for panoramic videos and design a weighted self-attention
module for APVST. This module integrates weights and feature maps to enhance
the quality of the immersive experience. Considering the overlap in the field
of view when users watch panoramic videos, we further utilize RSMA to split the
required panoramic video semantic streams into common and private messages for
transmission. We propose an RSMA-enabled semantic stream transmission scheme
and formulate a joint problem of latency and immersive experience quality by
optimizing the allocation ratios of power, common rate, and channel bandwidth,
aiming to maximize the quality of service (QoS) scores for users. To address
the above problem, we propose a deep reinforcement learning algorithm based on
proximal policy optimization (PPO) with high efficiency to handle dynamically
changing environments. Simulation results demonstrate that our proposed APVST
framework saves up to 20% and 50% of channel bandwidth compared to other
semantic and traditional video transmission schemes, respectively. Moreover,
our study confirms the efficiency of RSMA in panoramic video transmission,
achieving performance gains of 13% and 20% compared to NOMA and OFDMA.


  Homogeneous active Brownian particle (ABP) systems with purely repulsive
interactions are considered to have simple phase behavior, but various physical
attributes of active entities can lead to variation in the collective dynamics.
Recent studies have shown that even homogeneous ABPs exhibit complex behavior
due to an interplay between particle softness and motility. However, the
heterogeneity in composition of ABPs has not been explored yet. In this paper,
we study the structural properties of a binary mixture of ABPs with different
particle softness, by varying the relative softness and composition. We found
that upon varying the motility parameter, the system underwent a
motility-induced phase separation (MIPS) followed by a percolation transition
similar to the homogeneous systems; however, there is complex structure
formation within the dense phase of the MIPS which depends on the relative
softness of the binary system. Furthermore, the presence of a non-linear
scaling for different compositions of heterogeneous ABPs suggests that there is
a complex relationship between the composition and the structural properties.
Our study demonstrates that the composition heterogeneity of ABPs can also lead
to complex phase behavior.


  Video prediction is commonly referred to as forecasting future frames of a
video sequence provided several past frames thereof. It remains a challenging
domain as visual scenes evolve according to complex underlying dynamics, such
as the camera's egocentric motion or the distinct motility per individual
object viewed. These are mostly hidden from the observer and manifest as often
highly non-linear transformations between consecutive video frames. Therefore,
video prediction is of interest not only in anticipating visual changes in the
real world but has, above all, emerged as an unsupervised learning rule
targeting the formation and dynamics of the observed environment. Many of the
deep learning-based state-of-the-art models for video prediction utilize some
form of recurrent layers like Long Short-Term Memory (LSTMs) or Gated Recurrent
Units (GRUs) at the core of their models. Although these models can predict the
future frames, they rely entirely on these recurrent structures to
simultaneously perform three distinct tasks: extracting transformations,
projecting them into the future, and transforming the current frame. In order
to completely interpret the formed internal representations, it is crucial to
disentangle these tasks. This paper proposes a fully differentiable building
block that can perform all of those tasks separately while maintaining
interpretability. We derive the relevant theoretical foundations and showcase
results on synthetic as well as real data. We demonstrate that our method is
readily extended to perform motion segmentation and account for the scene's
composition, and learns to produce reliable predictions in an entirely
interpretable manner by only observing unlabeled video data.


  We study the exact physical quantities of a competing spin chain which
contains many interesting and meaningful couplings including the nearest
neighbor, next nearest neighbor, chiral three spins, Dzyloshinsky-Moriya
interactions and unparallel boundary magnetic fields in the thermodynamic
limit. We obtain the density of zero roots, surface energies and elementary
excitations in different regimes of model parameters. Due to the competition of
various interactions, the surface energy and excited spectrum show many
different pictures from those of the Heisenberg spin chain.


  We study the expectation value of the energy momentum tensor during thin
shell collapse for a massive, real, scalar field theory. At tree-level, we find
thermal, Hawking-type, behaviour for the energy flux. Using the
Schwinger-Keldysh technique, we calculate two-loop corrections to the
tree-level correlation functions and show that they exhibit secular growth,
suggesting the breakdown of the perturbation theory.


  Two-dimensional turbulent flows, and to some extent, geophysical flows, are
systems with a large number of degrees of freedom, which, albeit fluctuating,
exhibit some degree of organization: coherent structures emerge spontaneously
at large scales. In this short course, we show how the principles of
equilibrium statistical mechanics apply to this problem and predict the
condensation of energy at large scales and allow for computing the resulting
coherent structures. We focus on the structure of the theory using the language
of large deviation theory.


  The class imbalance problem can cause machine learning models to produce an
undesirable performance on the minority class as well as the whole dataset.
Using data augmentation techniques to increase the number of samples is one way
to tackle this problem. We introduce a novel counterfactual data augmentation
by verb replacement for the identification of medical claims. In addition, we
investigate the impact of this method and compare it with 3 other data
augmentation techniques, showing that the proposed method can result in a
significant (relative) improvement in the minority class.


  We construct a series of stochastic differential equations of the form $dX_t
= b(t, X_t) dt + dB_t$ which exhibit nonuniqueness in the path-by-path sense
while having a unique adapted solution in the sense of stochastic processes,
i.e. pathwise uniqueness holds.


  We discuss the dispersion relations of Nambu-Goldstone (NG) modes associated
with spontaneous breaking of internal symmetries at finite temperature and/or
density. We show that the dispersion relations of type-A (I) and type-B (II) NG
modes are linear and quadratic in momentum, whose imaginary parts are quadratic
and quartic, respectively. In both cases, the real parts of the dispersion
relations are larger than the imaginary parts when the momentum is small, so
that the NG modes can propagate far away. We derive the gap formula for NG
modes in the presence of a small explicit breaking term. We also discuss the
gapped partners of type-B NG modes, when type-A and type-B NG modes coexist.


  Reduced-order models are essential tools to deal with parametric problems in
the context of optimization, uncertainty quantification, or control and inverse
problems. The set of parametric solutions lies in a low-dimensional manifold
(with dimension equal to the number of independent parameters) embedded in a
large-dimensional space (dimension equal to the number of degrees of freedom of
the full-order discrete model). A posteriori model reduction is based on
constructing a basis from a family of snapshots (solutions of the full-order
model computed offline), and then use this new basis to solve the subsequent
instances online. Proper Orthogonal Decomposition (POD) reduces the problem
into a linear subspace of lower dimension, eliminating redundancies in the
family of snapshots. The strategy proposed here is to use a nonlinear
dimensionality reduction technique, namely the kernel Principal Component
Analysis (kPCA), in order to find a nonlinear manifold, with an expected much
lower dimension, and to solve the problem in this low-dimensional manifold.
Guided by this paradigm, the methodology devised here introduces different
novel ideas, namely: 1) characterizing the nonlinear manifold using local
tangent spaces, where the reduced-order problem is linear and based on the
neighbouring snapshots, 2) the approximation space is enriched with the
cross-products of the snapshots, introducing a quadratic description, 3) the
kernel for kPCA is defined ad-hoc, based on physical considerations, and 4) the
iterations in the reduced-dimensional space are performed using an algorithm
based on a Delaunay tessellation of the cloud of snapshots in the reduced
space. The resulting computational strategy is performing outstandingly in the
numerical tests, alleviating many of the problems associated with POD and
improving the numerical accuracy.


  Efficient and long-lived field-free molecular orientation is achieved using
only two kicks appropriately delayed in time. The understanding of the
mechanism rests upon a molecular target state providing the best efficiency
versus persistence compromise. An optimal control scheme is referred to for
fixing the free parameters (amplitudes and the time delay between them). The
limited number of kicks, the robustness and the transposability to different
molecular systems advocate in favor of the process, when considering its
experimental feasibility.


  Prompt Transfer (PoT) is a recently-proposed approach to improve
prompt-tuning, by initializing the target prompt with the existing prompt
trained on similar source tasks. However, such a vanilla PoT approach usually
achieves sub-optimal performance, as (i) the PoT is sensitive to the similarity
of source-target pair and (ii) directly fine-tuning the prompt initialized with
source prompt on target task might lead to forgetting of the useful general
knowledge learned from source task. To tackle these issues, we propose a new
metric to accurately predict the prompt transferability (regarding (i)), and a
novel PoT approach (namely PANDA) that leverages the knowledge distillation
technique to alleviate the knowledge forgetting effectively (regarding (ii)).
Extensive and systematic experiments on 189 combinations of 21 source and 9
target datasets across 5 scales of PLMs demonstrate that: 1) our proposed
metric works well to predict the prompt transferability; 2) our PANDA
consistently outperforms the vanilla PoT approach by 2.3% average score (up to
24.1%) among all tasks and model sizes; 3) with our PANDA approach,
prompt-tuning can achieve competitive and even better performance than
model-tuning in various PLM scales scenarios. We have publicly released our
code in https://github.com/WHU-ZQH/PANDA.


  We exhibit a tachyonic mode in a linearized analysis of perturbations of
large anti-de Sitter Reissner-Nordstrom black holes in four dimensions. In the
large black hole limit, and up to a 0.7% discrepancy which is probably
round-off error in the numerical analysis, the tachyon appears precisely when
the black hole becomes thermodynamically unstable.


  Modern smart distribution system requires storage, transmission and
processing of big data generated by sensors installed in electric meters. On
one hand, this data is essentially required for intelligent decision making by
smart grid but on the other hand storage, transmission and processing of that
huge amount of data is also a challenge. Present approaches to compress this
information have only relied on the traditional matrix decomposition techniques
benefitting from low number of principal components to represent the entire
data. This paper proposes a cascaded data compression technique that blends
three different methods in order to achieve high compression rate for efficient
storage and transmission. In the first and second stages, two lossy data
compression techniques are used, namely Singular Value Decomposition (SVD) and
Normalization; Third stage achieves further compression by using the technique
of Sparsity Encoding (SE) which is a lossless compression technique but only
having appreciable benefits for sparse data sets. Our simulation results show
that the combined use of the 3 techniques achieves data compression ratio to be
15% higher than state of the art SVD for small, sparse datasets and up to 28%
higher in large, non-sparse datasets with acceptable Mean Absolute Error (MAE).


  We present a new computational model for gaze prediction in egocentric videos
by exploring patterns in temporal shift of gaze fixations (attention
transition) that are dependent on egocentric manipulation tasks. Our assumption
is that the high-level context of how a task is completed in a certain way has
a strong influence on attention transition and should be modeled for gaze
prediction in natural dynamic scenes. Specifically, we propose a hybrid model
based on deep neural networks which integrates task-dependent attention
transition with bottom-up saliency prediction. In particular, the
task-dependent attention transition is learned with a recurrent neural network
to exploit the temporal context of gaze fixations, e.g. looking at a cup after
moving gaze away from a grasped bottle. Experiments on public egocentric
activity datasets show that our model significantly outperforms
state-of-the-art gaze prediction methods and is able to learn meaningful
transition of human attention.


  With Gaia in orbit since December 2013 it is time to look at the future of
fundamental astrometry and a time frame of 50 years is needed in this matter. A
space mission with Gaia-like astrometric performance is required, but not
necessarily a Gaia-like satellite. It should be studied whether this can be
obtained within the budget of a medium-size ESA mission. A dozen science issues
for a Gaia successor mission in twenty years, with launch about 2033, are
presented and in this context also other possibilities for absolute astrometry
with milliarcsecond (mas) or sub-mas accuracies are discussed. The three
powerful techniques: VLBI, the MICADO camera on the E-ELT, and the LSST are
described and documented by literature references and by an extensive
correspondence with leading astronomers who readily responded with all the
information I needed. In brief, the two Gaia-like missions would provide an
astrometric foundation for all branches of astronomy from the solar system and
stellar systems, including exo-planet systems, to compact galaxies, quasars and
dark matter (DM) substructures by data which cannot be surpassed in the next 50
years. - In April 2017 ESA selected our proposal Hobbs et al. (2016) for study
of a detector with NIR sensitivity for a Gaia successor mission, called
GaiaNIR.


  Littering quantification is an important step for improving cleanliness of
cities. When human interpretation is too cumbersome or in some cases
impossible, an objective index of cleanliness could reduce the littering by
awareness actions. In this paper, we present a fully automated computer vision
application for littering quantification based on images taken from the streets
and sidewalks. We have employed a deep learning based framework to localize and
classify different types of wastes. Since there was no waste dataset available,
we built our acquisition system mounted on a vehicle. Collected images
containing different types of wastes. These images are then annotated for
training and benchmarking the developed system. Our results on real case
scenarios show accurate detection of littering on variant backgrounds.


  Automated lobar segmentation allows regional evaluation of lung disease and
is important for diagnosis and therapy planning. Advanced statistical workflows
permitting such evaluation is a needed area within respiratory medicine; their
adoption remains slow, with poor workflow accuracy. Diseased lung regions often
produce high-density zones on CT images, limiting an algorithm's execution to
specify damaged lobes due to oblique or lacking fissures. This impact motivated
developing an improved machine learning method to segment lung lobes that
utilises tracheobronchial tree information to enhance segmentation accuracy
through the algorithm's spatial familiarity to define lobar extent more
accurately. The method undertakes parallel segmentation of lobes and auxiliary
tissues simultaneously by employing multi-task learning (MTL) in conjunction
with V-Net-attention, a popular convolutional neural network in the imaging
realm. In keeping with the model's adeptness for better generalisation, high
performance was retained in an external dataset of patients with four distinct
diseases: severe lung cancer, COVID-19 pneumonitis, collapsed lungs and Chronic
Obstructive Pulmonary Disease (COPD), even though the training data included
none of these cases. The benefit of our external validation test is
specifically relevant since our choice includes those patients who have
diagnosed lung disease with associated radiological abnormalities. To ensure
equal rank is given to all segmentations in the main task we report the
following performance (Dice score) on a per-segment basis: normal lungs 0.97,
COPD 0.94, lung cancer 0.94, COVID-19 pneumonitis 0.94 and collapsed lung 0.92,
all at p<0.05. Even segmenting lobes with large deformations on CT images, the
model maintained high accuracy. The approach can be readily adopted in the
clinical setting as a robust tool for radiologists.


  The factor complexity function $C_w(n)$ of a finite or infinite word $w$
counts the number of distinct factors of $w$ of length $n$ for each $n \ge 0$.
A finite word $w$ of length $|w|$ is said to be trapezoidal if the graph of its
factor complexity $C_w(n)$ as a function of $n$ (for $0 \leq n \leq |w|$) is
that of a regular trapezoid (or possibly an isosceles triangle); that is,
$C_w(n)$ increases by 1 with each $n$ on some interval of length $r$, then
$C_w(n)$ is constant on some interval of length $s$, and finally $C_w(n)$
decreases by 1 with each $n$ on an interval of the same length $r$. Necessarily
$C_w(1)=2$ (since there is one factor of length $0$, namely the empty word), so
any trapezoidal word is on a binary alphabet. Trapezoidal words were first
introduced by de Luca (1999) when studying the behaviour of the factor
complexity of finite Sturmian words, i.e., factors of infinite "cutting
sequences", obtained by coding the sequence of cuts in an integer lattice over
the positive quadrant of $\mathbb{R}^2$ made by a line of irrational slope.
Every finite Sturmian word is trapezoidal, but not conversely. However, both
families of words (trapezoidal and Sturmian) are special classes of so-called
"rich words" (also known as "full words") - a wider family of finite and
infinite words characterized by containing the maximal number of palindromes -
studied in depth by the first author and others in 2009.
  In this paper, we introduce a natural generalization of trapezoidal words
over an arbitrary finite alphabet $\mathcal{A}$, called generalized trapezoidal
words (or GT-words for short). In particular, we study combinatorial and
structural properties of this new class of words, and we show that, unlike the
binary case, not all GT-words are rich in palindromes when $|\mathcal{A}| \geq
3$, but we can describe all those that are rich.


  Turbulence models, such as the Smagorinsky model herein, are used to
represent the energy lost from resolved to under-resolved scales due to the
energy cascade (i.e. non-linearity). Analytic estimates of the energy
dissipation rates of a few turbulence models have recently appeared, but none
(yet) study energy dissipation restricted to resolved scales, i.e. after
spacial discretization with $h >$ micro scale. We do so herein for the
Smagorinsky model. Upper bounds are derived on the \textit{computed}
time-averaged energy dissipation rate, $\langle \varepsilon (u^h)\rangle$, for
an under-resolved mesh $h$ for turbulent shear flow. For coarse mesh size $
\mathcal{O}(\mathcal{Re}^{-1}) < h < L $, it is proven, $$ \langle \varepsilon
(u^h)\rangle\leq \big[ (\frac{C_s\, \delta}{h})^2+ \frac{L^5}{(C_s
\delta)^4\,h}+\frac{L^{\frac{5}{2}}}{(C_s\, \delta)^{4}}\,
{h^{\frac{3}{2}}}\big]\, \frac{U^3}{L}, $$ where $U$ and $L$ are global
velocity and length scale and $C_s$ and $\delta$ are model parameters. This
upper bound is independent of the viscosity at high Reynolds number, is in
accord with the scaling theory of turbulent. This estimate suggests
over-dissipation for any of $C_s>0$ and $\delta>0$, consistent with numerical
evidence on the effects of model viscosity (without wall damping function).
Moreover, the analysis indicates that the turbulent boundary layer is a more
important length scale for shear flow than the Kolmogorov microscale.


  In first-order phase transitions in the early universe, the bubble wall is
expected to be significantly slowed-down by its interaction with the
surrounding plasma. We examine the behaviour of the phase of the Higgs field
after two-bubble collisions, and find that phase differences equilibrate much
more quickly in slow-moving bubbles than in those which expand at the speed of
light. This could lead to a significant reduction in the initial density of
topological defects formed at a first-order phase transition.


  Koopman and von Neumann (KvN) extended the Liouville equation by introducing
a phase space function $S^{(K)}(q,p,t)$ whose physical meaning is unknown. We
show that a different $S(q,p,t)$, with well-defined physical meaning, may be
introduced without destroying the attractive "quantum-like" mathematical
features of the KvN theory. This new $S(q,p,t)$ is the classical action
expressed in phase space coordinates. It defines a mapping between observables
and operators which preserves the Lie bracket structure. The new evolution
equation reduces to Schr\"odinger's equation if functions on phase space are
reduced to functions on configuration space. This new kind of "quantization"
does not only establish a correspondence between observables and operators, but
provides in addition a derivation of quantum operators and evolution equations
from corresponding classical entities. It is performed by replacing
$\frac{\partial}{\partial p}$ by $0$ and $p$ by $\frac{\hbar}{\imath}
\frac{\partial}{\partial q}$, thus providing an explanation for the common
quantization rules.


  Single-top production processes have been studied using 0.7 fb-1 of data from
7 TeV center-of-mass energy proton-proton collisions collected with the ATLAS
detector at the LHC. Single-top is electroweak top production and the standard
model includes three production modes. Each contains a Wtb vertex, allowing the
possibility of a direct measurement of the CKM matrix element |Vtb|. Single-top
could also be sensitive to new physics, such as flavor changing neutral
currents or heavy W' bosons. Using cut-based selections, a limit of < 39.1 pb
is set for dilepton Wt production and < 26.5 pb for s-channel production. For
the t-channel measurement, both cut-based and neural network analyses are
performed and the cross-section is measured to be 90 +32 -22 pb, where 65 +28
-19 pb is expected according to standard model.


  Squeezed number states for a single mode Hamiltonian are investigated from
two complementary points of view. Firstly the more relevant features of their
photon distribution are discussed using the WKB wave functions. In particular
the oscillations of the distribution and the parity behavior are derived and
compared with the exact results. The accuracy is verified and it is shown that
for high photon number it fails to reproduce the true distribution. This is
contrasted with the fact that for moderate squeezing the WKB approximation
gives the analytical justification to the interpretation of the oscillations as
the result of the interference of areas with definite phases in phase space. It
is shown with a computation at high squeezing using a modified prescription for
the phase space representation which is based on Wigner-Cohen distributions
that the failure of the WKB approximation does not invalidate the area overlap
picture.


  We establish quantitative comparisons between classical distances for
probability distributions belonging to the class of convex probability
measures. Distances include total variation distance, Wasserstein distance,
Kullback-Leibler distance and more general R\'enyi divergences. This extends a
result of Meckes and Meckes (2014).


  Photons propagating in curved spacetime may, depending on their direction and
polarisation, have velocities exceeding the ``speed of light'' c. This
phenomenon arises through vacuum polarisation in QED and is a tidal
gravitational effect depending on the local curvature. It implies that the
Principle of Equivalence does not hold for interacting quantum field theories
in curved spacetime and reflects a quantum violation of local Lorentz
invariance. These results are illustrated for the propagation of photons in the
Reissner-Nordstr\"om spacetime characterising a charged black hole. A general
analysis of electromagnetic as well as gravitational birefringence is
presented.