  We review the current status of flavor-changing neutral currents in the charm
sector. We focus on the standard-model predictions and identify the main
sources of theoretical uncertainties in both charm mixing and rare charm
decays. The potential of these observables for constraining short-distance
physics in the standard model and its extensions is compromised by the presence
of large nonperturbative effects. We examine the possible discovery windows in
which short-distance physics can be tested and study the effects of various
extensions of the standard model. The current experimental situation and future
prospects are reviewed.


  Kink dynamics in spatially discrete nonlinear Klein-Gordon systems is
considered. For special choices of the substrate potential, such systems
support continuous translation orbits of static kinks with no (classical)
Peierls-Nabarro barrier. It is shown that these kinks experience, nevertheless,
a lattice-periodic confining potential, due to purely quantum effects anaolgous
to the Casimir effect of quantum field theory. The resulting ``quantum
Peierls-Nabarro potential'' may be calculated in the weak coupling
approximation by a simple and computationally cheap numerical algorithm, which
is applied, for purposes of illustration, to a certain two-parameter family of
substrates.


  Recently, a spate of papers have provided positive theoretical results for
training over-parameterized neural networks (where the network size is larger
than what is needed to achieve low error). The key insight is that with
sufficient over-parameterization, gradient-based methods will implicitly leave
some components of the network relatively unchanged, so the optimization
dynamics will behave as if those components are essentially fixed at their
initial random values. In fact, fixing these explicitly leads to the well-known
approach of learning with random features. In other words, these techniques
imply that we can successfully learn with neural networks, whenever we can
successfully learn with random features. In this paper, we first review these
techniques, providing a simple and self-contained analysis for one-hidden-layer
networks. We then argue that despite the impressive positive results, random
feature approaches are also inherently limited in what they can explain. In
particular, we rigorously show that random features cannot be used to learn
even a single ReLU neuron with standard Gaussian inputs, unless the network
size (or magnitude of the weights) is exponentially large. Since a single
neuron is learnable with gradient-based methods, we conclude that we are still
far from a satisfying general explanation for the empirical success of neural
networks.


  The observed size distribution of Kuiper belt objects (KBOs)--small icy and
rocky solar system bodies orbiting beyond Neptune--is well described by a power
law at large KBO sizes. However, recent work by Bernstein et al. (2003)
indicates that the size spectrum breaks and becomes shallower for KBOs smaller
than about 70 km in size. Here we show that we expect such a break at KBO
radius ~40 km since destructive collisions are frequent for smaller KBOs.
Specifically, we assume that KBOs are rubble piles with low material strength
rather than solid monoliths. This gives a power-law slope q~3 where the number
N(r) of KBOs larger than a size r is given by $N(r) \propto r^{1-q}$; the break
location follows from this slope through a self-consistent calculation. The
existence of this break, the break's location, and the power-law slope we
expect below the break are consistent with the findings of Bernstein et al.
(2003). The agreement with observations indicates that KBOs are effectively
strengthless rubble piles.


  We present SCUBA imaging and photometry of the elliptical galaxy NGC 4374.
The imaging observations are used to examine the spatial distribution of
thermal emission from dust and the radio to infrared continuum spectrum. In the
SCUBA 850 um image, the galaxy is found to be a point source, constraining the
emission to less than 15'' (1.5 kpc for a distance of 20.74 Mpc). The simplest
interpretation is that the 2000 um to 850 um SCUBA emission is synchroton from
a compact core or inner-jet, and most unlikely thermal emission from cold
diffuse dust. We cannot exclude free-free emission, but this would be very
unexpected. The thermal emission from dust is shown in IRAS data and these
along with the 450 um SCUBA datum give a dust temperature of 35 K,
corresponding to a dust mass of 0.12 million solar masses. These are pilot
observations in a program to look for cold, diffusely distributed dust in
elliptical galaxies, however much deeper 450 um imaging is required to
investigate this in NGC 4374.


  We give a new non-trivial upper bound for the Selberg integral of the
three-divisor function $d_3(n)$. Our method applies our recent conjecture
together with Laporta, for the modified Selberg integral of $d_3(n)$, and a
kind of modified Gallagher Lemma for the exponential sums.


  In this review I focus on a few selected topics, where recent theoretical
and/or observational progress has been made and important developments are
expected in the future. They include: 1) Evolution of isotopic ratios, 2)
Mixing processes and dispersion in abundance ratios, 3) Abundance gradients in
the Galactic disk (and abundance patterns in the inner Galaxy), 4) The question
of primary Nitrogen and 5) Abundance patterns in extragalactic damped
Lyman-alpha systems (DLAs).


  I added an Imaginary term by hand to the proper time in special theory of
relativity, and I wanted to see what will happen to it if I tried to get the
time dialation relationship. I found that this added imaginary term of time
does not have to be zero.


  Parameter identification problems in partial differential equations (PDEs)
consist in determining one or more unknown functional parameters in a PDE.
Here, the Bayesian nonparametric approach to such problems is considered.
Focusing on the representative example of inferring the diffusivity function in
an elliptic PDE from noisy observations of the PDE solution, the performance of
Bayesian procedures based on Gaussian process priors is investigated. Recent
asymptotic theoretical guarantees establishing posterior consistency and
convergence rates are reviewed and expanded upon. An implementation of the
associated posterior-based inference is provided, and illustrated via a
numerical simulation study where two different discretisation strategies are
devised. The reproducible code is available at: https://github.com/MattGiord.


  We present results from the first two years of our fast-cadence 15 GHz
gamma-ray blazar monitoring program, part of the F-GAMMA radio monitoring
project. Our sample includes the 1158 blazars north of -20 degrees declination
from the Candidate Gamma-Ray Blazar Survey (CGRaBS), which encompasses a
significant fraction of the extragalactic sources detected by the Fermi
Gamma-ray Space Telescope. We introduce a novel likelihood analysis for
computing a time series variability amplitude statistic that separates
intrinsic variability from measurement noise and produces a quantitative error
estimate. We use this method to characterize our radio light curves. We also
present results indicating a statistically significant correlation between
simultaneous average 15 GHz radio flux density and gamma-ray photon flux.


  Many elements of culture made their first appearance in the Upper
Paleolithic. Previous hypotheses put forth to explain this unprecedented burst
of creativity are found wanting. Examination of the psychological basis of
creativity leads to the suggestion that it resulted from the onset of
contextual focus: the capacity to focus or defocus attention in response to the
situation, thereby shifting between analytic and associative modes of thought.
New ideas germinate in a defocused state in which one is receptive to the
possible relevance of many dimensions of a situation. They are refined in a
focused state, conducive to filtering out irrelevant dimensions and condensing
relevant ones.


  Integration of optically-active nanodiamonds with glass fibers is a powerful
method of scaling of diamond magnetic sensing functionality. We propose a novel
approach for integration of nanodiamonds containing nitrogen-vacancy centers
directly into the fiber core. The core is fabricated using nanostructurization,
that is by stacking the preform from 790 soft glass canes, drawn from a single
rod dip-coated with nanodiamonds suspended in isopropyl alcohol. This enables
manual control over distribution of nanoscale features, here - the nanodiamonds
across and along the fiber core. We verify this by mapping the nanodiamond
distribution in the core using confocal microscopy. The nanodiamonds are
separated longitudinally either by 15 microns or 24 microns, while in the
transverse plane separation of approximately 1 micron is observed,
corresponding to the individual cane diameter in the final fiber, without
significant agglomeration. Filtered, red fluorescence is observed with naked
eye uniformly along the fiber. Its magnetic sensitivity is confirmed by in
optically detected magnetic resonance recorded with a coiled, 60-cm-long fiber
sample with readout contrast limited mainly by microwave antenna coverage. NV
fluorescence intensity in 0 to 35 mT magnetic field is also demonstrated,
allowing magnetometry applications with a large B-field dynamic range in
absence of microwaves.


  This article is a brief survey of some approaches to implementing the
suggestion that collapse of the wave function is mediated by gravity. These
approaches include: a possible connection between the problem of time and
problem of quantum measurement, decoherence models based on space-time
uncertainty, the Schr\"{o}dinger-Newton equation, attempts to introduce gravity
into collapse models such as CSL, ideas based on the black hole - elementary
particle complementarity, and the possible role of a complex space-time metric.


  The constrained synchronization problem (CSP) asks for a synchronizing word
of a given input automaton contained in a regular set of constraints. It could
be viewed as a special case of synchronization of a discrete event system under
supervisory control. Here, we study the computational complexity of this
problem for the class of sparse regular constraint languages. We give a new
characterization of sparse regular sets, which equal the bounded regular sets,
and derive a full classification of the computational complexity of CSP for
letter-bounded regular constraint languages, which properly contain the
strictly bounded regular languages. Then, we introduce strongly
self-synchronizing codes and investigate CSP for bounded languages induced by
these codes. With our previous result, we deduce a full classification for
these languages as well. In both cases, depending on the constraint language,
our problem becomes NP-complete or polynomial time solvable.


  The question of the averaging of inhomogeneous spacetimes in cosmology is
important for the correct interpretation of cosmological data. In this paper we
suggest a conceptually simpler approach to averaging in cosmology based on the
averaging of scalars within unimodular gravity. As an illustration, we consider
the example of an exact spherically symmetric dust model, and show that within
this approach averaging introduces correlations (corrections) to the effective
dynamical evolution equation in the form of a spatial curvature term.


  Invasive plant species are detrimental to the ecology of both agricultural
and wildland areas. Euphorbia esula, or leafy spurge, is one such plant that
has spread through much of North America from Eastern Europe. When paired with
contemporary computer vision systems, unmanned aerial vehicles, or drones,
offer the means to track expansion of problem plants, such as leafy spurge, and
improve chances of controlling these weeds. We gathered a dataset of leafy
spurge presence and absence in grasslands of western Montana, USA, then
surveyed these areas with a commercial drone. We trained image classifiers on
these data, and our best performing model, a pre-trained DINOv2 vision
transformer, identified leafy spurge with 0.84 accuracy (test set). This result
indicates that classification of leafy spurge is tractable, but not solved. We
release this unique dataset of labelled and unlabelled, aerial drone imagery
for the machine learning community to explore. Improving classification
performance of leafy spurge would benefit the fields of ecology, conservation,
and remote sensing alike. Code and data are available at our website:
leafy-spurge-dataset.github.io.


  We study stochastic heat equations driven by a class of L\'evy processes: du
= \De u dt + g dX_t \quad in \quad \bR^d_T, \qquad u(0,x)= 0 \quad in \quad x
\in \bR^d. We prove the corresponding estimate \[\norm{u}_{\bH_p^k(\RT)} \le
c(p,T) \norm{g}_{\bB_p^{k-\frac2p}(\RT)}\] for $2\le p<\infty$ and $k \in \bR$.


  We propose that the dissipative dynamics of topological defects in a spiral
state is responsible for the transport properties in the spin-glass phase of
cuprates. Using the collective-coordinate method, we show that topological
defects are coupled to a bath of magnetic excitations. By integrating out the
bath degrees of freedom, we find that the dynamical properties of the
topological defects are dissipative. The calculated damping matrix is related
to the in-plane resistivity, which exhibits an anisotropy and linear
temperature dependence in agreement with experimental data.


  We show that the number of tropical curves of given genus and degree through
some given general points in the plane does not depend on the position of the
points. In the case when the degree of the curves contains only primitive
integral vectors this statement has been known for a while now, but the only
known proof was indirect with the help of Mikhalkin's Correspondence Theorem
that translates this question into the well-known fact that the numbers of
complex curves in a toric surface through some given points do not depend on
the position of the points. This paper presents a direct proof entirely within
tropical geometry that is in addition applicable to arbitrary degree of the
curves.


  This paper will analyze and implement a time series dynamic neural network to
predict daily closing stock prices. Neural networks possess unsurpassed
abilities in identifying underlying patterns in chaotic, non-linear, and
seemingly random data, thus providing a mechanism to predict stock price
movements much more precisely than many current techniques. Contemporary
methods for stock analysis, including fundamental, technical, and regression
techniques, are conversed and paralleled with the performance of neural
networks. Also, the Efficient Market Hypothesis (EMH) is presented and
contrasted with Chaos theory using neural networks. This paper will refute the
EMH and support Chaos theory. Finally, recommendations for using neural
networks in stock price prediction will be presented.


  By using an exact analytical non-Hermitian formalism involving the full set
of resonance (quasinormal) states and complex energy eigenvalues for quantum
tunneling decay, we show that unitarity holds at any instant of time for the
nonstationary decaying probability density in the whole space, thus providing a
fundamental description of the quantum mechanical decay process.


  Following our earlier work on the 3-dimensional effective velocity
distribution of Galactic WIMPs (not only impinging on our detectors but also)
scattering off target nuclei, in this paper, we demonstrate the normal and a
"reverse" annual modulations of elastic WIMP-nucleus scattering signals, which
could be observed in direct Dark Matter detection experiments. Our simulations
show that, once the WIMP mass is as light as only a few tens GeV, the event
number and the accumulated recoil energy of WIMP-induced scattering events off
both of light and heavy target nuclei would indeed be maximal (minimal) in
summer (winter). However, once the WIMP mass is as heavy as a few hundreds GeV,
the event number and the accumulated recoil energy of WIMP scattering events
off heavy nuclei would inversely be minimal in summer. Understandably, for an
intermediate WIMP mass, the event number and the accumulated recoil energy of
scattering events off some middle-mass nuclei would show an approximately
uniform time dependence.


  We constrain generic nonstandard neutrino interactions with existing
experimental data on neutrino transition magnetic moments and derive strong
bounds on tensorial couplings of neutrinos to charged fermions. We also discuss
how some of these tensorial couplings can be constrained by other experiments,
e.g., on neutrino-electron and neutrino-nucleus scattering.


  Data scientists are constantly creating methods to efficiently and accurately
populate big data sets for use in large-scale applications. Many recent efforts
utilize crowd-sourcing and textual interfaces. In this paper, we propose a new
method of curating data; namely, creating a multi-device Amazon Alexa Skill in
the form of a research trivia game. Users experience a synchronized gaming
experience with other Amazon Echo users, competing against one another while
filling in gaps of a connected knowledge base. This allows for full
exploitation of the speed improvement offered by voice interface technology in
a game-based format.


  The red-shift $z_{eq}$, marking the end of radiation era and the beginning of
matter-dominated era, can play an important role to reconstruct dark-energy
models. A variable equation of state for matter that can bring a smooth
transition from radiation to matter-dominated era in a single model is proposed
to estimate $z_{eq}$ in dark energy models and hence its viability. Two
one-parameter models with minimally coupled scalar fields playing the role of
dark energy are chosen to demonstrate this point. It is found that for desired
late time behavior of the models, the estimated value of $z_{eq}$ is highly
sensitive on the value of the parameter in each of these models.


  Classical motion-compensated video coding methods have been standardized by
MPEG over the years and video codecs have become integral parts of media
entertainment applications. Despite the ubiquitous use of video coding
techniques, it is interesting to note that a closed form rate-distortion
characterization for video coding is not available in the literature. In this
paper, we develop a simple, yet, fundamental characterization of
rate-distortion region in video coding based on information-theoretic first
principles. The concept of conditional motion estimation is used to derive the
closedform expression for rate-distortion region without losing its generality.
Conditional motion estimation offers an elegant means to analyze the
rate-distortion trade-offs and demonstrates the viability of achieving the
bounds derived. The concept involves classifying image regions into active and
inactive based on the amount of motion activity. By appropriately modeling the
residuals corresponding to active and inactive regions, a closed form
expression for rate-distortion function is derived in terms of motion activity
and spatio-temporal correlation that commonly exist in video content.
Experiments on real video clips using H.264 codec are presented to demonstrate
the practicality and validity of the proposed rate-distortion analysis.


  We present a theory for the spin excitations of the Kondo lattice. We derive
an effective Hamiltonian, which describes Fermionic spin 1/2 charge
fluctuations interacting with Bosonic triplet spin fluctuations. We show that
already the simplest approximation possible, i.e. replacing the magnon
self-energy by the free polarization bubble for the charge excitation Greens
function, gives a quantitative description of the `spin gap' and `charge gap'
as obtained in numerical calculations for the Kondo insulator.


  Attaining animal-like legged locomotion on rough outdoor terrain with sparse
foothold affordances -a primary use-case for legs vs other forms of locomotion-
is a largely open problem. New advancements in control and perception have
enabled bipeds to walk on flat and uneven indoor environments. But tasks that
require reliable contact with unstructured world surfaces, for example walking
on natural rocky terrain, need new perception and control algorithms.
  This thesis introduces 3D perception algorithms for contact tasks such as
foot placement in rough terrain environments. We introduce a new method to
identify and model potential contact areas between the robot's foot and a
surface using a set of bounded curved patches. We present a patch
parameterization model and an algorithm to fit and perceptually validate
patches to 3D point samples. Having defined the environment representation
using the patch model, we introduce a way to assemble patches into a spatial
map. This map represents a sparse set of local areas potentially appropriate
for contact between the robot and the surface. The process of creating such a
map includes sparse seed point sampling, neighborhood searching, as well as
patch fitting and validation. Various ways of sampling are introduced including
a real time bio-inspired system for finding patches statistically similar to
those that humans select while traversing rocky trails. These sparse patch
algorithms are integrated with a dense volumetric fusion of range data from a
moving depth camera, maintaining a dynamic patch map of relevant contact
surfaces around a robot in real time. We integrate and test the algorithms as
part of a real-time foothold perception system on a mini-biped robot,
performing foot placements on rocks.


  We obtain necessary optimality conditions for a semi-discretized optimal
control problem for the classical system of nonlinear partial differential
equations modelling the water-oil (isothermal dead-oil model).


  The Design Reference Asteroid (DRA) is a compilation of all that is known
about the OSIRIS-REx mission target, asteroid (101955) Bennu. It contains our
best knowledge of the properties of Bennu based on an extensive observational
campaign that began shortly after its discovery, and has been used to inform
mission plan development and flight system design. The DRA will also be
compared with post-encounter science results to determine the accuracy of our
Earth-based characterization efforts. The extensive observations of Bennu in
1999 has made it one of the best-characterized near-Earth asteroids. Many
physical parameters are well determined, and span a number of categories:
Orbital, Bulk, Rotational, Radar, Photometric, Spectroscopic, Thermal, Surface
Analog, and Environment Properties. Some results described in the DRA have been
published in peer-reviewed journals while others have been reviewed by
OSIRIS-REx Science Team members and/or external reviewers. Some data, such as
Surface Analog Properties, are based on our best knowledge of asteroid
surfaces, in particular those of asteroids Eros and Itokawa. This public
release of the OSIRIS-REx Design Reference Asteroid is a annotated version of
the internal OSIRIS-REx document OREX-DOCS-04.00-00002, Rev 9 (accepted by the
OSIRIS-REx project on 2014-April-14). The supplemental data products that
accompany the official OSIRIS-REx version of the DRA are not included in this
release. We are making this document available as a service to future mission
planners in the hope that it will inform their efforts.


  Results of a long-term spectral monitoring of the active galactic nucleus of
NGC 4151 are presented (11 years, from 1996 to 2006). High quality spectra
(S/N>50 in the continuum near Halpha and Hbeta) were obtained in the spectral
range ~4000 to 7500 \AA, with a resolution between 5 and 15 A, using the 6-m
and the 1-m SAO's telescopes (Russia), the GHAO's 2.1-m telescope (Cananea,
Mexico), and the OAN-SPM's 2.1-m telescope (San-Pedro, Mexico). The observed
fluxes of the Halpha, Hbeta, Hgamma and HeII emission lines and of the
continuum at the observed wavelength 5117 A, were corrected for the position
angle, the seeing and the aperture effects.
  We found that the continuum and line fluxes varied strongly (up to a factor
6) during the monitoring period. The emission was maximum in 1996-1998, and
there were two minima, in 2001 and in 2005. The Halpha, Hgamma and He II fluxes
were well correlated with the Hbeta flux. We considered three characteristic
periods during which the Hbeta and Halpha profiles were similar: 1996-1999,
2000-2001 and 2002-2006. The line to continuum flux ratios were different; in
particular during the first period, the lines were not correlated with the
continuum and saturated at high fluxes. In the second and third period, where
the continuum flux was small, the Halpha and Hbeta fluxes were well correlated
to the continuum flux, meaning that the ionizing continuum was a good
extrapolation of the optical continuum. The CCFs are often asymmetrical and the
time lags between the lines and the continuum are badly defined indicating the
presence of a complex BLR, with dimensions from 1 to 50 light-days.


  Game-theoretic models of learning are a powerful set of models that optimize
multi-objective architectures. Among these models are zero-sum architectures
that have inspired adversarial learning frameworks. An important shortcoming of
these zeros-sum architectures is that gradient-based training leads to weak
convergence and cyclic dynamics.
  We propose a novel follow the leader training algorithm for zeros-sum
architectures that guarantees convergence to mixed Nash equilibrium without
cyclic behaviors. It is a special type of follow the perturbed leader algorithm
where perturbations are the result of a neural mediating agent.
  We validate our theoretical results by applying this training algorithm to
games with convex and non-convex loss as well as generative adversarial
architectures. Moreover, we customize the implementation of this algorithm for
adversarial imitation learning applications. At every step of the training, the
mediator agent perturbs the observations with generated codes. As a result of
these mediating codes, the proposed algorithm is also efficient for learning in
environments with various factors of variations. We validate our assertion by
using a procedurally generated game environment as well as synthetic data.
Github implementation is available.


  We consider a network of nodes distributed in physical space without physical
links communicating through message broadcasting over specified distances.
Typically, communication using smaller distances is desirable due to savings in
energy or other resources. We introduce a network formation mechanism to enable
reducing the distances while retaining connectivity. Nodes, which initially
transmit signals at a prespecified maximum distance, subject links to
preferential detachment by autonomously decreasing their transmission radii
while satisfying conditions of zero communication loss and fixed maximum
node-hopping distance for signaling. Applied to networks with various spatial
topologies, we find cost reductions as high as 90% over networks that are
restricted to have all nodes with equal transmission distance.


  Ordinal regression refers to classifying object instances into ordinal
categories. It has been widely studied in many scenarios, such as medical
disease grading, movie rating, etc. Known methods focused only on learning
inter-class ordinal relationships, but still incur limitations in
distinguishing adjacent categories thus far. In this paper, we propose a simple
sequence prediction framework for ordinal regression called Ord2Seq, which, for
the first time, transforms each ordinal category label into a special label
sequence and thus regards an ordinal regression task as a sequence prediction
process. In this way, we decompose an ordinal regression task into a series of
recursive binary classification steps, so as to subtly distinguish adjacent
categories. Comprehensive experiments show the effectiveness of distinguishing
adjacent categories for performance improvement and our new approach exceeds
state-of-the-art performances in four different scenarios. Codes are available
at https://github.com/wjh892521292/Ord2Seq.


  Digital devices are widely used by children, and children nowadays are
spending more time online than with other media sources, such as watching
television or playing offline video games. In the UK, 44% of children aged five
to ten have been provided with their own tablets, with this percentage
increasing annually, while in the US, ownership of tablets by children in this
age group grew fivefold between 2011 and 2013. Our previous research found that
UK children and parents need better support in dealing with online privacy
risks. Interestingly, very few research was done on Chinese children and
parents. In this report, we present findings from our online survey of 593
Chinese parents with children aged 6-10 in February and March 2019. Our study
particularly focused on understanding Chinese parents' awareness and management
of their children's online privacy risks. The goal of the survey was to examine
the current adoption pattern of digital devices by Chinese families with young
children, the concerns Chinese parents have about their children's online
activities and the current practices they use for safeguarding their children
online. Our findings imply that we need to continue presenting specific
guidance to parents in order to support their choice of digital content for
their young children. Further, we need to look more deeply into the roles
schools are taking in children's online activities, how can we support schools
and teachers when they are making recommendations to parents and children.


  Fluid Antenna System (FAS) is recognized as a promising technology for
enhancing communication performance. In this context, we explored the potential
of FAS-assisted wireless powered communication systems. Specifically, the
transmitter, equipped with FAS, harvests the radio frequency (RF) signal from a
power beacon and utilizes the harvested energy for data transmission to the
receiver. To evaluate the performance of the considered systems, we derive both
the analytical and asymptotic expressions of the outage probability. Simulation
results indicate that the diversity of the considered network closely aligns
with the number of ports. Besides, it is also revealed that the port selection
criteria based solely on single-hop configurations yield a diversity order of
only one.


  We examine the single-photon processes in the frame work of supersymmetric
models at future e+e- linear colliders. According to the recent experimental
achievement, the optimistic polarization degrees for both electron and positron
beams are taken into account to enhance the signal-to-noise ratio revealing the
observable difference between supersymmetry breaking models. The minimal
supergravity model and the minimal SU(5) grand unified model in gaugino
mediation have been examined as examples. We see that after several years of
accummulating data, the difference of the number of single-photon events
between the two models received from the collider would be in excess of three
times the statistical error, providing us the possibility to probe which model
would be realized in nature. The result is well suitable for the future running
of the International Linear Collider.


  We develop a theory of singular support for various infinite dimensional
stacks and establish several functoriality properties. Then we apply this
theory to compute the singular support of the Grothendieck-Springer affine
Springer sheaf and rely it to the local constancy conjecture of
Goresky-Kottwitz-McPherson on the homology of affine Springer fibers along the
root valuation stratification.


  Optical bound states in the continuum (BICs), which are exotic localized
eigenstates embedded in the continuum spectrum and topological polarization
singularity in momentum space, have attracted great attentions in both
fundamental and applied physics. Here, based on magneto-optical photonic
crystal slab placed in external magnetic fields to break the time-reversal
symmetry, we theoretically demonstrate magnetically tunable BICs with arbitrary
polarization covering the entire Poincar\'e sphere and efficient off-{\Gamma}
chiral emission of circularly polarized states. More interestingly, by further
breaking the in-plane inversion symmetry of the magneto-optical photonic
crystal slab to generate a pair of circularly polarized states (C point)
spawning from the eliminated BICs and tuning the external magnetic field
strength to move one C point to the {\Gamma} point, one at-{\Gamma} intrinsic
chiral BICs with near-unity circular dichroism exceeding 0.99 and a high
quality factor of 46000 owning to the preserved out-of-plane mirror symmetry
can be observed. These findings may lead to a plethora of potential
applications in chiral-optical effects, structured light, and tunable optical
devices.


  Online content platforms are concerned about the freshness of their content
updates to their end customers, and increasingly more platforms now invite and
pay the crowd to sample real-time information (e.g., traffic observations and
sensor data) to help reduce their ages of information (AoI). How much
crowdsourced data to sample and buy over time is a critical question for a
platform's AoI management, requiring a good balance between its AoI and the
incurred sampling cost. This question becomes more interesting by considering
the stage after sampling, where multiple platforms coexist in sharing the
content delivery network of limited bandwidth, and one platform's update may
jam or preempt the others' under negative network externalities. When these
selfish platforms know each other's sampling cost, we formulate their
competition as a non-cooperative game and show they want to over-sample to
reduce their own AoIs, causing the price of anarchy (PoA) to be infinity. To
remedy this huge efficiency loss, we propose a trigger mechanism of
non-monetary punishment in a repeated game to enforce the platforms'
cooperation to approach the social optimum. We also study the more challenging
scenario of incomplete information that some new platform hides its private
sampling cost information from the other incumbent platforms in the Bayesian
game. Perhaps surprisingly, we show that even the platform with more
information may get hurt. We successfully redesign the trigger-and-punishment
mechanism to negate the platform's information advantage and ensure no
cheating. Our extensive simulations show that the mechanisms can remedy the
huge efficiency loss due to platform competition, and the performance improves
as we have more incumbent platforms with known cost information.


  We analyse the effects of the ban of ChatGPT, a generative pre-trained
transformer chatbot, on individual productivity. We first compile data on the
hourly coding output of over 8,000 professional GitHub users in Italy and other
European countries to analyse the impact of the ban on individual productivity.
Combining the high-frequency data with the sudden announcement of the ban in a
difference-in-differences framework, we find that the output of Italian
developers decreased by around 50% in the first two business days after the ban
and recovered after that. Applying a synthetic control approach to daily Google
search and Tor usage data shows that the ban led to a significant increase in
the use of censorship bypassing tools. Our findings show that users swiftly
implement strategies to bypass Internet restrictions but this adaptation
activity creates short-term disruptions and hampers productivity.


  A $\Sigma$-construction of Solovay is partially extended to the case of
intermediate sets which are not necessarily subsets of the ground model. As an
application, we prove that, for a given name $t$, the set of all sets $t[G]$,
$G$ being generic over the ground model, is Borel. This result was first
established by Zapletal by a totally different descriptive set theoretic
argument.


  Two XUV-photon double ionization of Ne, induced by an intense few-pulse
attosecond train with a ~ 4 fs envelope duration is investigated experimentally
and theoretically. The experiment is performed at ELI-ALPS utilizing the
recently constructed 10 Hz gas phase high-order harmonic generation SYLOS
GHHG-COMPACT beamline. A total pulse energy up to ~1 {\mu}J generated in Argon
in conjunction with high reflectivity optics in the XUV region, allowed the
observation of the doubly charged state of Ne induced by 40 eV central XUV
photon energies. The interaction of the intense attosecond pulse train with Ne
is also theoretically studied via a second-order time dependent perturbation
theory equations-of-motion. The results of this work, combined with the
feasibility of conducting XUV-pump-XUV-probe experiments, constitute a powerful
tool for many potential applications. Those include attosecond pulse metrology
as well as time resolved investigations of the dynamics underlying direct and
sequential double ionization and their electron correlation effects.


  Uncompensated non-equilibrium orbital magnetization may arise at sample edges
in the presence of charge current. The value of the effect scales as the
product of the current density and the electron mean free path without any
additional smallness. This non-relativistic phenomenon originates in a lack of
inversion symmetry of the electron wave functions in a vicinity of sample
interfaces. In a conducting layer, where $z$ direction is chosen perpendicular
to the surface, and the current flows in $x$ direction, the non-equilibrium
orbital magnetization points in $y$ direction. In a top-bottom symmetric layer,
the orbital magnetization has an opposite sign near the top and bottom
interfaces thus mimicking the symmetry of the spin-Hall effect but can exceed
the latter by orders of magnitude.


  A bilinear estimate in Fourier restriction norm spaces with applications to
the Cauchy problem associated to u_t - |D|^{\alpha}u_x + uu_x =0 is proved, for
1< \alpha <2. As a consequence, local well-posedness in H^s(\R) \cap
\dot{H}^{-\omega}(\R) follows for s >-{3/4}(\alpha-1) and \omega=1/\alpha-1/2.
This extends to global well-posedness for all s \geq 0.


  We have implemented the newly-introduced, coherence-based technique of x-ray
near-field speckle (XNFS) at 8-ID-I at the Advanced Photon Source. In the near
field regime of high-brilliance synchrotron x-rays scattered from a sample of
interest, it turns out, that, when the scattered radiation and the main beam
both impinge upon an x-ray area detector, the measured intensity shows
low-contrast speckles, resulting from interference between the incident and
scattered beams. We built a micrometer-resolution XNFS detector with a high
numerical aperture microscope objective and demonstrate its capability for
studying static structures and dynamics at longer length scales than
traditional far field x-ray scattering techniques. Specifically, we
characterized the structure and dynamics of dilute silica and polystyrene
colloidal samples. Our study reveals certain limitations of the XNFS technique,
which we discuss.


  In this paper, a novel design methodology-Agile Behaviour Design-is presented
that accommodates the requirements for developing complex game agents suitable
for industrial environments. An essential part of the design approach is to
support independent work of both designers and programmers by reducing
bottleneck situations. The approach fosters the creation of more loose and
fluid interactions between design and implementation, leaving more freedom for
creative expression.


  The stability of copolymer tethers is investigated theoretically.
Self-assembly of diblockor triblock copolymers can lead to tubular polymersomes
which are known experimentallyto undergo shape instability under thermal,
chemical and tension stresses. It leads to aperiodic modulation of the radius
which evolves to assembly-line pearls connected by tinytethers. We study the
contributions of shear surface viscosity and spontaneous curvatureand their
interplay to understand the pearling instability. The performed linear
analysisof stability of this cylinder-to-pearls transition shows that such
systems are unstable if themembrane tension is larger than a finite critical
value contrary to the Rayleigh-Plateau in-stability, an already known or if the
spontaneous curvature is in a specific range whichdepends on membrane tension.
For the case of spontaneous curvature-induced shape insta-bility, two dynamical
modes are identified. The first one is analog to the tension-inducedinstability
with a marginal mode. Its wavenumber associated to the most unstable
modedecreases continuously to zero as membrane viscosity increases. The
unexpected secondone has a finite range of unstable wavenumbers. The wavenumber
of the most unstablemode tends to a constant as membrane viscosity increases.
In this mode, its growth ratebecomes independent of the bulk viscosity in the
limit of high membrane viscosity andbehaves as a pure viscous surface.


  This paper proposes a novel approach to controller design for MR-damped
vehicle suspension system. This approach is predicated on the premise that the
optimal control strategy can be learned through real-world or simulated
experiments utilizing a reinforcement learning algorithm with continuous
states/actions. The sensor data is fed into a Twin Delayed Deep Deterministic
Policy Gradient (TD3) algorithm, which generates the actuation voltage required
for the MR damper. The resulting suspension space (displacement), sprung mass
acceleration, and dynamic tire load are calculated using a quarter vehicle
model incorporating the modified Bouc-Wen MR damper model. Deep RL's reward
function is based on sprung mass acceleration. The proposed approach
outperforms traditional suspension control strategies regarding ride comfort
and stability, as demonstrated by multiple simulated experiments


  Accurately forecasting extreme rainfall is notoriously difficult, but is also
ever more crucial for society as climate change increases the frequency of such
extremes. Global numerical weather prediction models often fail to capture
extremes, and are produced at too low a resolution to be actionable, while
regional, high-resolution models are hugely expensive both in computation and
labour. In this paper we explore the use of deep generative models to
simultaneously correct and downscale (super-resolve) global ensemble forecasts
over the Continental US. Specifically, using fine-grained radar observations as
our ground truth, we train a conditional Generative Adversarial Network --
coined CorrectorGAN -- via a custom training procedure and augmented loss
function, to produce ensembles of high-resolution, bias-corrected forecasts
based on coarse, global precipitation forecasts in addition to other relevant
meteorological fields. Our model outperforms an interpolation baseline, as well
as super-resolution-only and CNN-based univariate methods, and approaches the
performance of an operational regional high-resolution model across an array of
established probabilistic metrics. Crucially, CorrectorGAN, once trained,
produces predictions in seconds on a single machine. These results raise
exciting questions about the necessity of regional models, and whether
data-driven downscaling and correction methods can be transferred to data-poor
regions that so far have had no access to high-resolution forecasts.


  APEmille is a SIMD parallel processor under development at the Italian
National Institute for Nuclear Physics (INFN). APEmille is very well suited for
Lattice QCD applications, both for its hardware characteristics and for its
software and language features. APEmille is an array of custom arithmetic
processors arranged on a tridimensional torus. The replicated processor is a
pipelined VLIW device performing integer and single/double precision IEEE
floating point operations. The processor is optimized for complex computations
and has a peak performance of 528Mflop at 66MHz and of 800Mflop at 100MHz. In
principle an array of 2048 nodes is able to break the Tflops barrier. A
powerful programming language named TAO is provided and is highly optimized for
QCD. A C++ compiler is foreseen. Specific data structures, operators and even
statements can be defined by the user for each different application. Effort
has been made to define the language constructs for QCD.


  A detailed understanding of the material response to rapid compression is
challenging and demanding. For instance, the element gold under dynamic
compression exhibits complex phase transformations where there exist some large
discrepancies between experimental and theoretical studies. Here, we combined
large-scale molecular dynamics simulations with a deep potential to elucidate
the dynamic compression processes of gold from an atomic level. The potential
is constructed by accurately reproducing the free energy surfaces of
density-functional-theory calculations for gold, from ambient conditions to 15
500 K and 500 GPa. Within this framework, we extend the simulations up to 200
000 atoms size, and found a much lower pressure threshold for phase
transitioning from face-centered cubic (FCC) to body-centered (BCC), as
compared to previous calculations. Furthermore, the transition pressure is
strongly dependent on the shock direction, namely 159 GPa for (100) orientation
and 219 GPa for (110) orientation, respectively. Most importantly, the accurate
atomistic perspective presents that the shocked BCC structure contains unique
features of medium-range and short-range orders, which is named disorders here.
We propose a model and demonstrate that the existence of disorders
significantly reduces the Gibbs free energies of shocked structures, therefore
leading to the lowering of the phase transition pressure. The present study
provides a new path to understand the structure dynamics under extreme
conditions.


  We study the reflection of Bloch wavepackets at the interface of optical
lattice possessing a shallow longitudinal out-of-phase refractive index
modulation in adjacent waveguides. We show that the relation between the
transmitted and reflected energy flows can be efficiently controlled by tuning
the frequency and the depth of the modulation. Thus, complete beam reflection
may be achieved for a set of resonant modulation frequencies at which light
tunneling between adjacent guides of modulated lattice is inhibited.


  Baryon and lepton numbers of the Universe in leptogenesis with Dirac neutrino
and leptogenesis with Majorana neutrino scenarios are considered. It is shown
that despite quite different features of Dirac and Majorana fermions both
scenarios yield the same relation among the initial lepton and the final baryon
asymmetries. Moreover right-handed neutrinos in the leptogenesis with Dirac
neutrino scenario have very little impact on the effective number of
relativistic degrees of freedom, constrained by BBN. Thus the two scenarios are
similar from the cosmological point of view. It is also pointed out that in
thermal equilibrium the 3B+L sum is zero for left-handed fermions.


  We show how semiclassical black holes can be reinterpreted as an effective
geometry, composed of a large ensamble of horizonless naked singularities
(eventually smoothed at the Planck scale). We call this new items {\it
frizzyballs}, which can be rigorously defined by euclidean path integral
approach. This has interesting implications regarding information paradoxes. We
demonstrate that infalling information will chaotically propagate inside this
system before going to the full quantum gravity regime (Planck scale).


  Quantization prescriptions that realize generalized uncertainty relations
(GUP) are motivated by quantum gravity arguments that incorporate a fundamental
length scale. We apply two such methods, polymer and deformed Heisenberg
quantization, to scalar field theory in Fourier space. These alternative
quantizations modify the oscillator spectrum for each mode, which in turn
affects the blackbody distribution. We find that for a large class of
modifications, the equation of state relating pressure $P$ and energy density
$\rho$ interpolates between $P=\rho/3$ at low $T$ and $P=2\rho/3$ at high $T$,
where $T$ is the temperature. Furthermore, the Stefan-Boltzman law gets
modified from $\rho \propto T^{4}$ to $\rho \propto T^{5/2}$ at high
temperature. This suggests an effective reduction to 2.5 spacetime dimensions
at high energy.


  Nonresponse is a common problem in survey sampling. Appropriate treatment can
be challenging, especially when dealing with detailed breakdowns of totals.
Often, the nearest neighbor imputation method is used to handle such incomplete
multinomial data. In this article, we investigate the nearest neighbor ratio
imputation estimator, in which auxiliary variables are used to identify the
closest donor and the vector of proportions from the donor is applied to the
total of the recipient to implement ratio imputation. To estimate the
asymptotic variance, we first treat the nearest neighbor ratio imputation as a
special case of predictive matching imputation and apply the linearization
method of \cite{yang2020asymptotic}. To account for the non-negligible sampling
fractions, parametric and generalized additive models are employed to
incorporate the smoothness of the imputation estimator, which results in a
valid variance estimator. We apply the proposed method to estimate expenditures
detail items based on empirical data from the 2018 collection of the Service
Annual Survey, conducted by the United States Census Bureau. Our simulation
results demonstrate the validity of our proposed estimators and also confirm
that the derived variance estimators have good performance even when the
sampling fraction is non-negligible.


  The class of substitutions of some primitive components is introduced. A
bilateral subshift arising from a substitution of some primitive components is
decomposed into pairwise disjoint, locally compact, shift-invariant sets, on
each of which an invariant Radon measure is unique up to scaling. It is
completely characterized in terms of eigenvalues of an incidence matrix when
the unique invariant measure is finite.


  Supernova remnants (SNRs) are one of the most energetic astrophysical events
and are thought to be the dominant source of Galactic cosmic rays (CRs). A
recent report on observations from the Fermi satellite has shown a signature of
pion decay in the gamma-ray spectra of SNRs. This provides strong evidence that
high-energy protons are accelerated in SNRs. The actual gamma-ray emission from
pion decay should depend on the diffusion of CRs in the interstellar medium. In
order to quantitatively analyse the diffusion of high-energy CRs from
acceleration sites, we have performed test particle numerical simulations of CR
protons using a three-dimensional magnetohydrodynamics (MHD) simulation of an
interstellar medium swept-up by a blast wave. We analyse the diffusion of CRs
at a length scale of order a few pc in our simulated SNR, and find the
diffusion of CRs is precisely described by a Bohm diffusion, which is required
for efficient acceleration at least for particles with energies above 30 TeV
for a realistic interstellar medium. Although we find the possibility of a
superdiffusive process (travel distance proportional to t^0.75) in our
simulations, its effect on CR diffusion at the length scale of the turbulence
in the SNR is limited.


  We construct a generalized class of quantum gravity condensate states, that
allows the description of continuum homogeneous quantum geometries within the
full theory. They are based on similar ideas already applied to extract
effective cosmological dynamics from the group field theory formalism, and thus
also from loop quantum gravity. However, they represent an improvement over the
simplest condensates used in the literature, in that they are defined by an
infinite superposition of graph-based states encoding in a precise way the
topology of the spatial manifold. The construction is based on the definition
of refinement operators on spin network states, written in a second quantized
language. The construction lends itself easily to be applied also to the case
of spherically symmetric quantum geometries.


  For supersymmetric spacetimes in eleven dimensions admitting a null Killing
spinor, a set of explicit necessary and sufficient conditions for the existence
of any number of arbitrary additional Killing spinors is derived. The necessary
and sufficient conditions are comprised of algebraic relationships, linear in
the spinorial components, between the spinorial components and their first
derivatives, and the components of the spin connection and four-form. The
integrability conditions for the Killing spinor equation are also analysed in
detail, to determine which components of the field equations are implied by
arbitrary additional supersymmetries and the four-form Bianchi identity. This
provides a complete formalism for the systematic and exhaustive investigation
of all spacetimes with extended null supersymmetry in eleven dimensions. The
formalism is employed to show that the general bosonic solution of eleven
dimensional supergravity admitting a $G_2$ structure defined by four Killing
spinors is either locally the direct product of $\mathbb{R}^{1,3}$ with a
seven-manifold of $G_2$ holonomy, or locally the Freund-Rubin direct product of
$AdS_4$ with a seven-manifold of weak $G_2$ holonomy. In addition, all
supersymmetric spacetimes admitting a
$(G_2\ltimes\mathbb{R}^7)\times\mathbb{R}^2$ structure are classified.


  We study genus $4$ curves over finite fields and two invariants of the
$p$-torsion part of their Jacobians: the $a$-number ($a$) and $p$-rank ($f$).
We collect and analyze statistical data of curves over $\mathbb{F}_p$ for
$p=3,5,7,11$ and their invariants. Then, we study the existence of Cartier
points, which are also related to the structure of $J[p]$. For curves with
$0\leq a<g$, the number of Cartier points is bounded, and it depends on $a$ and
$f$.


  In this paper we prove a rate of escape theorem and a central limit theorem
for isotropic random walks on Fuchsian buildings, giving formulae for the speed
and asymptotic variance. In particular, these results apply to random walks
induced by bi-invariant measures on Fuchsian Kac-Moody groups, however they
also apply to the case where the building is not associated to any reasonable
group structure. Our primary strategy is to construct a renewal structure of
the random walk. For this purpose we define cones and cone types for buildings
and prove that the corresponding automata in the building and the underlying
Coxeter group are strongly connected. The limit theorems are then proven by
adapting the techniques in [21]. The moments of the renewal times are
controlled via the retraction of the walks onto an apartment of the building.


  We consider a particular (exactly soluble) model of the one discussed in a
previous work. We show numerical results for the time evolution of the main
dynamical quantities and compare them with analytical results.


  The computer code DECAY4 is developed to generate initial energy, time and
angular distributions of particles emitted in radioactive decays of nuclides
and nuclear (atomic) deexcitations. Data for description of nuclear and atomic
decay schemes are taken from the ENSDF and EADL database libraries. The
examples of use of the DECAY4 code in several underground experiments are
described.


  The SciBooNE Collaboration reports K+ production cross section and rate
measurements using high energy daughter muon neutrino scattering data off the
SciBar polystyrene (C8H8) target in the SciBooNE detector. The K+ mesons are
produced by 8 GeV protons striking a beryllium target in Fermilab Booster
Neutrino Beam line (BNB). Using observed neutrino and antineutrino events in
SciBooNE, we measure d2{\sigma}/dpd{\Omega} = (5.34 \times 0.76) mb/(GeV/c
\times sr) for p + Be -> K+ + X at mean K+ energy of 3.9 GeV and angle (with
respect to the proton beam direction) of 3.7 degrees, corresponding to the
selected K+ sample. Compared to Monte Carlo predictions using previous higher
energy K+ production measurements, this measurement, which uses the NUANCE
neutrino interaction generator, is consistent with a normalization factor of
0.85\times0.12. This agreement is evidence that the extrapolation of the higher
energy K+ measurements to an 8 GeV beam energy using Feynman scaling is valid.
This measurement reduces the error on the K+ production cross section from 40%
to 14%.


  The eigenvalue problem of stochastic Hamiltonian systems with boundary
conditions was studied by Peng \cite{peng} in 2000. For one-dimensional case,
denoting by $\{\lambda_n\}_{n=1}^{\infty}$ all the eigenvalues of such an
eigenvalue problem, Peng proved that $\lambda_n\to +\infty$. In this short
note, we prove that the growth order of $\lambda_n$ is the same as $n^2$ as
$n\to +\infty$. Apart from the interesting of its own, by this result, the
statistic period of solutions of FBSDEs can be estimated directly by
corresponding coefficients and time duration.


  In the conventional / most studied local distance ladder measurements, Type
Ia supernovae (SNe Ia) are used in two of the three rungs. In the second rung,
their luminosities are calibrated by standard candles like Cepheids or Tip of
the Red Giant Branch (TRGB). In the third rung, the high luminosities and
standardizability allow SNe to be used to calibrate the `Hubble' relation
between distances and redshifts. Locally, the majority of distance ladder
analyses find a high value of the Hubble Constant $H_0$ of $>70$ km/s/Mpc.
Given the discrepancy with the inferred value using CMB observations, great
scrutiny must be given to the role supernovae play in measuring $H_0$. Here, we
review the main methodology, the many crosschecks for the supernova component
of the distance ladder, and the various systematics studied. We review the
important role supernovae play to explain the small disagreements seen from
various local analyses. We also discuss analyses that employ an inverse
distance ladder, which use similar sets of supernovae, but in the reverse
direction, and yield a low value of $H_0$. We conclude given all available
evidence, it is difficult to find a way that a systematic in supernovae
measurements, or a non-$\Lambda$CDM component of the universe which could be
measured with supernovae, can help explain the Hubble tension.


  We compare the properties of optically dark GRBs, defined by the
optical-to-X-ray spectral index beta_OX<0.5, and normal ones discovered by the
Swift satellite before the year 2008 in a statistical way, using data collected
from the literature and online databases. Our sample include 200 long bursts,
19 short bursts, and 10 with measured high redshifts (z>=4). The ratio of dark
bursts is found to be about 10-20%, and is similar between long bursts, short
ones, and the high-z sub-sample. The result for long bursts is consistent with
both the pre-Swift sample and studies by other authors on smaller Swift
samples. The existence of dark short GRBs is pointed out for the first time.
The X-ray derived hydrogen column densities of dark GRBs clearly prefer large
values compared with those of normal bursts. This supports the dust extinction
scenario as the main cause of dark GRBs. Other possibilities like very high
redshifts and non-standard emission mechanisms are less likely although not
fully excluded.


  Research on fault diagnosis on highly nonlinear dynamic systems such as the
engine of a vehicle have garnered huge interest in recent years, especially
with the automotive industry heading towards self-driving technologies. This
article presents a novel opensource simulation testbed of a turbocharged spark
ignited (TCSI) petrol engine system for testing and evaluation of residuals
generation and fault diagnosis methods. Designed and developed using
Matlab/Simulink, the user interacts with the testbed using a GUI interface,
where the engine can be realistically simulated using industrial-standard
driving cycles such as the Worldwide harmonized Light vehicles Test Procedures
(WLTP), the New European Driving Cycle (NEDC), the Extra-Urban Driving Cycle
(EUDC), and EPA Federal Test Procedure (FTP-75). The engine is modeled using
the mean value engine model (MVEM) and is controlled using a
proportional-integral (PI)-based boost controller. The GUI interface also
allows the user to induce one of the 11 faults of interest, so that their
effects on the performance of the engine are better understood. This minimizes
the risk of causing permanent damages to the engine and shortening its
lifespan, should the tests be conducted onto the actual physical system. This
simulation testbed will serve 16 as an excellent platform where researchers can
generate critical data to develop and compare current and future research
methods for fault diagnosis of automotive engine systems.


  The flapping flag instability occurs when a flexible cantilevered plate is
immersed in a uniform airflow. To this day, the nonlinear aspects of this
aeroelastic instability are largely unknown. In particular, experiments in the
literature all report a large hysteresis loop, while the bifurcation in
numerical simulations is either supercritical or subcritical with a small
hysteresis loop. In this paper, this discrepancy is addressed. First weakly
nonlinear stability analyses are conducted in the slender-body and
two-dimensional limits, and second new experiments are performed with flat and
curved plates. The discrepancy is attributed to inevitable planeity defects of
the plates in the experiments.


  Bloch oscillations, the oscillatory motion of a quantum particle in a
periodic potential, are one of the most fascinating effects of coherent quantum
transport. Originally studied in the context of electrons in crystals, Bloch
oscillations manifest the wave nature of matter and are found in a wide variety
of different physical systems. Here we report on the first experimental
observation of fractional Bloch oscillations, using a photonic lattice as a
model system of a two-particle extended Bose-Hubbard Hamiltonian. In our
photonic simulator, the dynamics of two correlated particles hopping on a
one-dimensional lattice is mapped into the motion of a single particle in a
two-dimensional lattice with engineered defects and mimicked by light transport
in a square waveguide lattice with a bent axis.


  PatentTransformer is our codename for patent text generation based on
Transformer-based models. Our goal is "Augmented Inventing." In this second
version, we leverage more of the structural metadata in patents. The structural
metadata includes patent title, abstract, and dependent claim, in addition to
independent claim previously. Metadata controls what kind of patent text for
the model to generate. Also, we leverage the relation between metadata to build
a text-to-text generation flow, for example, from a few words to a title, the
title to an abstract, the abstract to an independent claim, and the independent
claim to multiple dependent claims. The text flow can go backward because the
relation is trained bidirectionally. We release our GPT-2 models trained from
scratch and our code for inference so that readers can verify and generate
patent text on their own. As for generation quality, we measure it by both
ROUGE and Google Universal Sentence Encoder.


  Transmission spectroscopy presents one of the most successful approaches for
investigating the atmospheres of exoplanets. We analyzed the near-infrared
high-resolution transmission spectrum of a hot Saturn, HD 149026 b, taken using
CARMENES spectrograph ($\mathcal{R}\sim80,400$). We found evidence of H$_2$O at
an S/N of $\sim$4.8. We also performed grid search using a Bayesian framework
and constrained the orbital velocity $K_\mathrm{p}$ and rest velocity
$V_{\mathrm{rest}}$ to $158.17^{+8.31}_{-7.90}$ $\mathrm{km\ s}^{-1}$ and
$2.57^{+0.54}_{-0.57}$ $\mathrm{km\ s}^{-1}$, respectively. Whilst the
retrieved $K_\mathrm{p}$ value is consistent with theoretical prediction, the
retrieved $V_{\mathrm{rest}}$ value is highly red-shifted ($>$3-$\sigma$). This
might be an indication of either anomalous atmospheric dynamics at play or an
orbit with non-zero eccentricity. Additionally, we searched for HCN but no
successful detection has been made possibly due to the relatively low S/N
dataset. The detection of H$_2$O and subsequent abundance retrieval, coupled
with analysis of other species such as CO at the $K$-band, for example, might
help us to get some information about the atmospheric C/O ratio and
metallicity, which in turn could give us some insight into the planet formation
scenario.


  Hybrid quantum-classical algorithms such as the Quantum Approximate
Optimization Algorithm (QAOA) are considered as one of the most encouraging
approaches for taking advantage of near-term quantum computers in practical
applications. Such algorithms are usually implemented in a variational form,
combining a classical optimization method with a quantum machine to find good
solutions to an optimization problem. The solution quality of QAOA depends to a
high degree on the parameters chosen by the classical optimizer at each
iteration. However, the solution landscape of those parameters is highly
multi-dimensional and contains many low-quality local optima. In this study we
apply a Cross-Entropy method to shape this landscape, which allows the
classical optimizer to find better parameter more easily and hence results in
an improved performance. We empirically demonstrate that this approach can
reach a significant better solution quality for the Knapsack Problem.


  Mathieu Moonshine, the observation that the Fourier coefficients of the
elliptic genus on K3 can be interpreted as dimensions of representations of the
Mathieu group M24, has been proven abstractly, but a conceptual understanding
in terms of a representation of the Mathieu group on the BPS states, is
missing. Some time ago, Taormina and Wendland showed that such an action can be
naturally defined on the lowest non-trivial BPS states, using the idea of
`symmetry surfing', i.e., by combining the symmetries of different K3 sigma
models. In this paper we find non-trivial evidence that this construction can
be generalized to all BPS states.


  Graph invariants provide a powerful analytical tool for investigation of
abstract structures of graphs. They, combined in convenient relations, carry
global and general information about a graph and its various substructures such
as cycle structures, factors, matchings, colorings, coverings, and so on, whose
discovery is the primary problem of graph theory. The major goal of this paper
is to catalogue all pure relations between basic invariants of a graph and its
large cycle structures, namely Hamilton, longest and dominating cycles and some
their generalizations. Basic graph invariants and pure relations allow to focus
on results having no forerunners. These simplest kind of "ancestors" form a
source from which nearly all possible hamiltonian results can be developed
further by various additional new ideas, generalizations, extensions,
restrictions and structural limitations, as well as helping researchers to make
clear and simple imagination about "complicated" developmental mechanisms in
the area.


  Real-time intelligence applications in Internet of Things (IoT) environment
depend on timely data communication. However, it is challenging to transmit and
analyse massive data of various modalities. Recently proposed task-oriented
communication methods based on deep learning have showed its superiority in
communication efficiency. In this paper, we propose a cooperative task-oriented
communication method for the transmission of multi-modal data from multiple end
devices to a central server. In particular, we use the transmission result of
data of one modality, which is with lower rate, to control the transmission of
other modalities with higher rate in order to reduce the amount of transmitted
date. We take the human activity recognition (HAR) task in a smart home
environment and design the semantic-oriented transceivers for the transmission
of monitoring videos of different rooms and acceleration data of the monitored
human. The numerical results demonstrate that by using the transmission control
based on the obtained results of the received acceleration data, the
transmission is reduced to 2% of that without transmission control while
preserving the performance on the HAR task.


  A sequence of spin-1/2 particles polarised in one of two possible directions
is presented to an experimenter, who can wager in a double-or-nothing game on
the outcomes of measurements in freely chosen polarisation directions. Wealth
is accrued through astute betting. As information is gained from the stream of
particles, the measurement directions are progressively adjusted, and the
portfolio growth rate is raised. The optimal quantum strategy is determined
numerically and shown to differ from the classical strategy, which is
associated with the Kelly criterion. The paper contributes to the development
of quantum finance, as aspects of portfolio optimisation are extended to the
quantum realm.


  ReTest is a novel testing tool for Java applications with a graphical user
interface (GUI), combining monkey testing and difference testing. Since this
combination sidesteps the oracle problem, it enables the generation of
GUI-based regression tests. ReTest makes use of evolutionary computing (EC),
particularly a genetic algorithm (GA), to optimize these tests towards code
coverage. While this is indeed a desirable goal in terms of software testing
and potentially finds many bugs, it lacks one major ingredient: human behavior.
Consequently, human testers often find the results less reasonable and
difficult to interpret.
  This thesis proposes a new approach to improve the initial population of the
GA with the aid of machine learning (ML), forming an ML-technique enhanced-EC
(MLEC) algorithm. In order to do so, existing tests are exploited to extract
information on how human testers use the given GUI. The obtained data is then
utilized to train an artificial neural network (ANN), which ranks the available
GUI actions respectively their underlying GUI components at runtime---reducing
the gap between manually created and automatically generated regression tests.
Although the approach is implemented on top of ReTest, it can be easily used to
guide any form of monkey testing.
  The results show that with only little training data, the ANN is able to
reach an accuracy of 82% and the resulting tests represent an improvement
without reducing the overall code coverage and performance significantly.


  Jet flavour tagging is crucial in experimental high-energy physics. A tagging
algorithm, DeepJetTransformer, is presented, which exploits a transformer-based
neural network that is substantially faster to train.
  The DeepJetTransformer network uses information from particle flow-style
objects and secondary vertex reconstruction as is standard for $b$- and $c$-jet
identification supplemented by additional information, such as reconstructed
V$^0$s and $K^{\pm}/\pi^{\pm}$ discrimination, typically not included in
tagging algorithms at the LHC. The model is trained as a multiclassifier to
identify all quark flavours separately and performs excellently in identifying
$b$- and $c$-jets. An $s$-tagging efficiency of $40\%$ can be achieved with a
$10\%$ $ud$-jet background efficiency. The impact of including V$^0$s and
$K^{\pm}/\pi^{\pm}$ discrimination is presented.
  The network is applied on exclusive $Z \to q\bar{q}$ samples to examine the
physics potential and is shown to isolate $Z \to s\bar{s}$ events. Assuming all
other backgrounds can be efficiently rejected, a $5\sigma$ discovery
significance for $Z \to s\bar{s}$ can be achieved with an integrated luminosity
of $60~\text{nb}^{-1}$, corresponding to less than a second of the FCC-ee run
plan at the $Z$ resonance.


  Here we propose a new gravitational waves(GWs) detector in broad frequency
band, which is operated at exceptional points(EPs) in micro cavities. The
detected signal is an eigenfrequency split of the mechanical modes caused by
the spatial strain. Due to the complex square root topology near the EP, the
splitting is greatly enhanced for sufficiently small perturbations. Compared to
current strategies, it can be achieved at the room temperature and has
advantages in micro device scale, wide frequency band and higher sensitivity.


  An {\em $\ell$-offset Hamilton cycle} $C$ in a $k$-uniform hypergraph $H$
on~$n$ vertices is a collection of edges of $H$ such that for some cyclic order
of $[n]$ every pair of consecutive edges $E_{i-1},E_i$ in $C$ (in the natural
ordering of the edges) satisfies $|E_{i-1}\cap E_i|=\ell$ and every pair of
consecutive edges $E_{i},E_{i+1}$ in $C$ satisfies $|E_{i}\cap
E_{i+1}|=k-\ell$. We show that in general $\sqrt{e^{k}\ell!(k-\ell)!/n^k}$ is
the sharp threshold for the existence of the $\ell$-offset Hamilton cycle in
the random $k$-uniform hypergraph $H_{n,p}^{(k)}$. We also examine this
structure's natural connection to the 1-2-3 Conjecture.


  The algorithmic error of digital quantum simulations is usually explored in
terms of the spectral norm distance between the actual and ideal evolution
operators. In practice, this worst-case error analysis may be unnecessarily
pessimistic. To address this, we develop a theory of average-case performance
of Hamiltonian simulation with random initial states. We relate the
average-case error to the Frobenius norm of the multiplicative error and give
upper bounds for the product formula (PF) and truncated Taylor series methods.
As applications, we estimate average-case error for digital Hamiltonian
simulation of general lattice Hamiltonians and $k$-local Hamiltonians. In
particular, for the nearest-neighbor Heisenberg chain with $n$ spins, the error
is quadratically reduced from $\mathcal O(n)$ in the worst case to $\mathcal
O(\sqrt{n})$ on average for both the PF method and the Taylor series method.
Numerical evidence suggests that this theory accurately characterizes the
average error for concrete models. We also apply our results to error analysis
in the simulation of quantum scrambling.


  We present the discovery of the radio-loud quasar PSO J352.4034-15.3373 at
z=5.84 pm 0.02. This quasar is the radio brightest source known, by an order of
magnitude, at z~6 with a flux density in the range of 8-100 mJy from 3GHz to
230MHz and a radio loudness parameter R>~1000. This source provides an
unprecedented opportunity to study powerful jets and radio-mode feedback at the
highest redshifts, and presents the first real chance to probe deep into the
neutral intergalactic medium by detecting 21 cm absorption at the end of cosmic
reionization.


  We use the resonant dipole-dipole interaction between Rydberg atoms and a
periodic external microwave field to engineer XXZ spin Hamiltonians with
tunable anisotropies. The atoms are placed in 1D and 2D arrays of optical
tweezers, allowing us to study iconic situations in spin physics, such as the
implementation of the Heisenberg model in square arrays, and the study of spin
transport in 1D. We first benchmark the Hamiltonian engineering for two atoms,
and then demonstrate the freezing of the magnetization on an initially
magnetized 2D array. Finally, we explore the dynamics of 1D domain wall systems
with both periodic and open boundary conditions. We systematically compare our
data with numerical simulations and assess the residual limitations of the
technique as well as routes for improvements. The geometrical versatility of
the platform, combined with the flexibility of the simulated Hamiltonians,
opens exciting prospects in the field of quantum simulation, quantum
information processing and quantum sensing.


  Non-Terrestrial Network (NTN) has been envisioned as a key component of the
sixth-generation (6G) mobile communication system. Meanwhile, unmanned aerial
vehicles (UAVs) play an important role in enabling and deploying NTNs. In this
paper, we focus on massive multi-input multi-output (MaMIMO) supported UAV
communications, where channel state information (CSI) was measured considering
different heights and trajectories of a rotary-wing drone. To characterize the
propagation channel for this air-to-ground link, some initial results were
analyzed, such as stationary distance. To investigate the impact of channels on
communication performance, we analyzed spectral efficiency (SE) by using
Maximum Ratio Combining (MRC). This study shows that the presented
space-time-frequency channel dataset facilitates channel correlation analysis
and supports performance evaluation for MaMIMO-UAV communications.


  We sketch a recent sum-rule extraction of the decay constants of the heavy
pseudoscalar mesons D, D_s, B, and B_s from the two-point correlator of
heavy-light pseudoscalar currents [1]. Our main emphasis lies on the control
over all the uncertainties in the decay constants, related both to the input
QCD parameters and to the limited accuracy of the method of sum rules. Gaining
this control has become possible by application of our new procedure of
extracting hadron observables based on a dual threshold depending on the Borel
parameter. For the charmed-meson decay constants, we find f_D=206.2\pm 7.3(OPE)
\pm 5.1(syst) MeV, f_Ds=245.3\pm 15.7(OPE) \pm 4.5(syst) MeV. For the beauty
mesons, the decay constants turn out to be extremely sensitive to the precise
value of the MSbar mass of the b-quark, mb(mb). By requiring our sum-rule
estimate to match the average of the lattice determinations of f_B, we extract
the rather accurate value mb(mb)=(4.245\pm 0.025) GeV. Feeding this parameter
value into our sum-rule formalism leads to the beauty-meson decay constants f_B
= 193.4 \pm 12.3(OPE) \pm 4.3(syst) MeV, f_Bs =232.5 \pm 18.6(OPE) \pm
2.4(syst) MeV.


  The effective spin pressure induced by an electric current on a domain wall
in a ferromagnet is determined using a simple classical model, which allows us
to extend previous theories to arbitrary domain wall widths. In particular, the
role of spatially non-uniform components of the torques are analyzed in detail.
We find that the effect of the current is mainly to distort the domain wall
which should enhance de-pinning. We also find that in the limit of thin domain
walls the current-induced pressure changes sign.


  This paper deals with homogenization problem for convolution type non-local
operators in random statistically homogeneous ergodic media. Assuming that the
convolution kernel has a finite second moment and satisfies the uniform
ellipticity and certain symmetry conditions, we prove the almost sure
homogenization result and show that the limit operator is a second order
elliptic differential operator with constant deterministic coefficients.


  We study the problem of reconstructing a hidden graph given access to a
distance oracle. We design randomized algorithms for the following problems:
reconstruction of a degree bounded graph with query complexity
$\tilde{O}(n^{3/2})$; reconstruction of a degree bounded outerplanar graph with
query complexity $\tilde{O}(n)$; and near-optimal approximate reconstruction of
a general graph.


  The extraction of rotational energy from a spinning black hole via the
Blandford-Znajek mechanism has long been understood as an important component
in models to explain energetic jets from compact astrophysical sources. Here we
show more generally that the kinetic energy of the black hole, both rotational
and translational, can be tapped, thereby producing even more luminous jets
powered by the interaction of the black hole with its surrounding plasma. We
study the resulting Poynting jet that arises from single boosted black holes
and binary black hole systems. In the latter case, we find that increasing the
orbital angular momenta of the system and/or the spins of the individual black
holes results in an enhanced Poynting flux.


  We propose to use deep convolutional neural networks to address the problem
of cross-view image geolocalization, in which the geolocation of a ground-level
query image is estimated by matching to georeferenced aerial images. We use
state-of-the-art feature representations for ground-level images and introduce
a cross-view training approach for learning a joint semantic feature
representation for aerial images. We also propose a network architecture that
fuses features extracted from aerial images at multiple spatial scales. To
support training these networks, we introduce a massive database that contains
pairs of aerial and ground-level images from across the United States. Our
methods significantly out-perform the state of the art on two benchmark
datasets. We also show, qualitatively, that the proposed feature
representations are discriminative at both local and continental spatial
scales.


  In this paper, we will study Heyting algebras endowed with tense negative
operators, which we call tense H-algebras and we proof that these algebras are
the algebraic semantics of the Intuitionistic Propositional Logic with Galois
Negations. Finally, we will develop a Priestley-style duality for H-algebras.


  Most accreting black holes emit a substantial fraction of their luminosity in
hard X-rays/soft $\gamma$-rays of up to $\sim{\rm few}\times100$ keV. The
observations suggest that the radiating gas is very hot, $T>10^9$ K, and
optically thin. Theoretical attempts to explain the observations are reviewed
and unresolved issues are highlighted.


  Cyber-physical systems (CPS) can be found everywhere: smart homes, autonomous
vehicles, aircrafts, healthcare, agriculture and industrial production lines.
CPSs are often critical, as system failure can cause serious damage to property
and human lives. Today's cyber-physical systems are extremely complex,
heterogeneous systems: to be able to manage their complexity in a unified way,
we need an infrastructure that ensures that our systems operate with the high
reliability as intended. In addition to the infrastructure, we need to provide
engineers a method to ensure system reliability at design time. The paradigm of
model-driven design provides a toolkit supporting the design and analysis and
by choosing the proper formalisms, the model-driven design approach allows us
to validate our system at design time.


  Electro-optical response of a current-carrying monolayer graphene is studied
theoretically. Our calculation takes into account full (diagonal and
non-diagonal) conductivity tensor obtained from a particle-conserving
out-of-equilibrium distribution function of doped graphene. Our analytical and
numerical results indicate that the presence of a moderate DC current
throughout a doped graphene channel induces large Kerr rotations within a
frequency range which can be tuned up to the mid-infrared frequency range.


  In this note, we study the boundedness and compactness of integral operators
$I_g$ and $T_g $ from analytic Morrey spaces to Bloch space. Furthermore, the
norm and essential norm of those operators are given.


  In this paper, we consider a statistical problem of learning a linear model
from noisy samples. Existing work has focused on approximating the least
squares solution by using leverage-based scores as an importance sampling
distribution. However, no finite sample statistical guarantees and no
computationally efficient optimal sampling strategies have been proposed. To
evaluate the statistical properties of different sampling strategies, we
propose a simple yet effective estimator, which is easy for theoretical
analysis and is useful in multitask linear regression. We derive the exact mean
square error of the proposed estimator for any given sampling scores. Based on
minimizing the mean square error, we propose the optimal sampling scores for
both estimator and predictor, and show that they are influenced by the
noise-to-signal ratio. Numerical simulations match the theoretical analysis
well.


  We investigate the validity of the Cosmological Principle by mapping the
cosmological parameters $H_0$ and $q_0$ through the celestial sphere. In our
analysis, performed in a low-redshift regime to follow a model-independent
approach, we use two compilations of type Ia Supernovae (SNe Ia), namely the
Union2.1 and the JLA datasets. Firstly, we show that the angular distributions
for both SNe Ia datasets are statistically anisotropic at high confidence level
($p$-value $<$ 0.0001), in particular the JLA sample. Then we find that the
cosmic expansion and acceleration are mainly of dipolar type, with maximal
anisotropic expansion [acceleration] pointing towards $(l,b) \simeq
(326^{\circ},12^{\circ})$ [$(l,b) \simeq (174^{\circ},27^{\circ})$], and $(l,b)
\simeq (58^{\circ},-60^{\circ})$ [$(l,b) \simeq (225^{\circ},51^{\circ})$] for
the Union2.1 and JLA data, respectively. Secondly, we use a geometrical method
to test the hypothesis that the non-uniformly distributed SNe Ia events could
introduce anisotropic imprints on the cosmological expansion and acceleration.
For the JLA compilation, we found significant correlations between the
celestial distribution of data points and the directional studies of $H_0$ and
$q_0$, suggesting that these results can be attributed to the intrinsic
anisotropy of the sample. In the case of the Union2.1 data, nonetheless, these
correlations are less pronounced, and we verify that the dipole asymmetry found
in the $H_0$ analyses coincides with the well-known bulk-flow motion of our
local group. From these analyses, we conclude that the directional asymmetry on
the cosmological parameters maps are mainly either of local origin or due to
celestial incompleteness of current SNe Ia samples.


  We examine an important combinatorial challenge in clearing clutter using a
mobile robot equipped with a manipulator, seeking to compute an optimal object
removal sequence for minimizing the task completion time, assuming that each
object is grasped once and then subsequently removed. On the structural side,
we establish that such an optimal sequence can be NP-hard to compute, even when
no two objects to be removed have any overlap. Then, we construct
asymptotically optimal and heuristic algorithms for clutter removal. Employing
dynamic programming, our optimal algorithm scales to 40 objects. On the other
hand, for random clutter, fast greedy algorithms tend to produce solutions
comparable to these generated by the optimal algorithm.


  The results of experimental studies of conductivity anomalies in film samples
of specially synthesized copolymer are analyzed, in which in PVC macromolecules
the polyacetylene molecular fragments are embedded with a variable
concentration. Previously, it has been experimentally found that in such
samples spontaneous and stimulated conductivity jumps by 12 orders of magnitude
occur, and the life of each of these states can be very large - minutes, hours
and more. In this paper we propose a qualitative model describing the anomalous
behavior of the conductivity of the PVC composite, comprising the mechanisms of
stabilization of high conductivity state, the conditions of development of
instability in the transitions between the states, as well as the reasons for
long living state of high conductivity even when the applied voltage is
switched off. Simple numerical estimates confirming the reality of the proposed
mechanisms are considered too.


  Most deep-learning-based continuous sign language recognition (CSLR) models
share a similar backbone consisting of a visual module, a sequential module,
and an alignment module. However, due to limited training samples, a
connectionist temporal classification loss may not train such CSLR backbones
sufficiently. In this work, we propose three auxiliary tasks to enhance the
CSLR backbones. The first task enhances the visual module, which is sensitive
to the insufficient training problem, from the perspective of consistency.
Specifically, since the information of sign languages is mainly included in
signers' facial expressions and hand movements, a keypoint-guided spatial
attention module is developed to enforce the visual module to focus on
informative regions, i.e., spatial attention consistency. Second, noticing that
both the output features of the visual and sequential modules represent the
same sentence, to better exploit the backbone's power, a sentence embedding
consistency constraint is imposed between the visual and sequential modules to
enhance the representation power of both features. We name the CSLR model
trained with the above auxiliary tasks as consistency-enhanced CSLR, which
performs well on signer-dependent datasets in which all signers appear during
both training and testing. To make it more robust for the signer-independent
setting, a signer removal module based on feature disentanglement is further
proposed to remove signer information from the backbone. Extensive ablation
studies are conducted to validate the effectiveness of these auxiliary tasks.
More remarkably, with a transformer-based backbone, our model achieves
state-of-the-art or competitive performance on five benchmarks, PHOENIX-2014,
PHOENIX-2014-T, PHOENIX-2014-SI, CSL, and CSL-Daily. Code and Models are
available at https://github.com/2000ZRL/LCSA_C2SLR_SRM.


  We report variational and diffusion Quantum Monte Carlo ground-state energies
of the three-dimensional electron gas using a model periodic Coulomb
interaction and backflow corrections for N=54, 102, 178, and 226 electrons. We
remove finite-size effects by extrapolation and we find lower energies than
previously reported. Using the Hellman-Feynman operator sampling method
introduced in Phys. Rev. Lett. 99, 126406 (2007), we compute accurately, within
the fixed-node pproximation, the separate kinetic and interaction contributions
to the total ground-state energy. The difference between the interaction
energies obtained from the original Slater-determinant nodes and the
backflow-displaced nodes is found to be considerably larger than the difference
between the corresponding kinetic energies.


  In 2007, the young star 1SWASP J140747.93-394542.6 (V1400 Cen) underwent a
complex series of deep eclipses over 56 days. This was attributed to the
transit of a ring system filling a large fraction of the Hill sphere of an
unseen substellar companion. Subsequent photometric monitoring has not found
any other deep transits from this candidate ring system, but if there are more
substellar companions and they are coplanar with the potential ring system,
there is a chance that they will transit the star as well. This young star is
active and the light curves show a 5% modulation in amplitude with a dominant
rotation period of 3.2 days due to star spots rotating in and out of view. We
model and remove the rotational modulation of the J1407 light curve and search
for additional transit signatures of substellar companions orbiting around
J1407. We combine the photometry of J1407 from several observatories, spanning
a 19 year baseline. We remove the rotational modulation by modeling the
variability as a periodic signal, whose periodicity changes slowly with time
over several years due to the activity cycle of the star. A Transit Least
Squares (TLS) analysis searches for any periodic transiting signals within the
cleaned light curve. We identify an activity cycle of J1407 with a period of
5.4 years. A Transit Least Squares search does not find any plausible periodic
eclipses in the light curve, from 1.2% amplitude at 5 days up to 1.9% at 20
days. This sensitivity is confirmed by injecting artificial transits into the
light curve and determining the recovery fraction as a function of transit
depth and orbital period. J1407 is confirmed as a young active star with an
activity cycle consistent with a rapidly rotating solar mass star. With the
rotational modulation removed, the TLS analysis rules out transiting companions
with radii larger than about 1 Jupiter.


  We consider the irreducibility of switch-based Markov chains for the
approximate uniform sampling of Hamiltonian cycles in a given undirected dense
graph on $n$ vertices. As our main result, we show that every pair of
Hamiltonian cycles in a graph with minimum degree at least $n/2+7$ can be
transformed into each other by switch operations of size at most $10$, implying
that the switch Markov chain using switches of size at most $10$ is
irreducible. As a proof of concept, we also show that this Markov chain is
rapidly mixing on dense monotone graphs.


  We report the results of a detailed calculation of nucleon weak interactions
relevant for the neutron to proton density ratio at the onset of primordial
nucleosynthesis. Radiative electromagnetic corrections, finite nucleon mass
terms, thermal radiative effects on weak processes and on neutrino temperature
are taken into account to reduce the theoretical uncertainty on $n
\leftrightarrow p $ rates to 1%. This translates into a sensitivity in $^4 He$
mass fraction $Y_p$ prediction up to $10^{-4}$. We find a positive total
correction to the Born prediction $\delta Y_p \simeq 0.004$.


  The status of lattice calculations in Quantum Field Theory is reviewed. A
major part is devoted to recent progress in formulating exact chiral symmetry
on the lattice. Another topic which has received a lot of attention is the
influence of dynamical quark effects. Attempts to quantify these effects for
the light hadron spectrum and flavour singlet amplitudes are discussed, as well
as other expected qualitative features of simulations with dynamical quarks.
The remaining parts of the review include recent results for the light quark
masses using non-perturbative renormalisation and the spectrum of glueballs and
heavy hybrids computed using anisotropic lattices.


  Let $K_\theta$ be a model space generated by an inner function $\theta$. We
study the Schatten class membership of embeddings $I : K_\theta \to L^2(\mu)$,
$\mu$ a positive measure, and of composition operators $C_\phi:K_\theta\to
H^2(\mathbb D)$ with a holomprphic function $\phi:\mathbb D\rightarrow \mathbb
D$. In the case of one-component inner functions $\theta$ we show that the
problem can be reduced to the study of natural extensions of $I$ and $C_\phi$
to the Hardy-Smirnov space $E^2(D)$ in some domain $D\supset \mathbb D$. In
particular, we obtain a characterization of Schatten membership of $C_\phi$ in
terms of Nevanlinna counting function. By example this characterization does
not hold true for general $\phi$.


  We investigate the properties of a dilute boson-fermion mixture at zero
temperature. The ground-state energy of the system is calculated to second
order in the Bose-Fermi coupling constant. The Green's function formalism is
applied to obtain results for the effect of Bose-Fermi interactions on the
spectrum of phonon excitations, the momentum distribution, the condensate
fraction and the superfluid density of the bosonic component. A quantitative
discussion of these effects is presented in the case of mixtures with
attractive interspecies interaction.


  In the 21st century ongoing rapid urbanization highlights the need to gain
deeper insights into the social structure of cities. While work on this
challenge can profit from abundant data sources, the complexity of this data
itself proves to be a challenge. In this paper we use diffusion maps, a
manifold learning method, to discover hidden manifolds in the UK 2011 census
data set. The census key statistics and quick statistics report 1450 different
statistical features for each census output area. Here we focus primarily on
the city of Bristol and the surrounding countryside, comprising 3490 of these
output areas. Our analysis finds the main variables that span the census
responses, highlighting that university student density and poverty are the
most important explanatory variables of variation in census responses.


  We present a catalogue of an HI-selected sample of 1129 low surface
brightness galaxies (LSBGs) searched from the alpha.40-SDSS DR7 survey. This
sample, consisting of various types of galaxies in terms of luminosity and
morphology, has extended the parameter space covered by the existing LSBG
samples. Based on a subsample of 173 LSBGs which are selected from our entire
LSBG sample to have the 2-horn shapes of the HI line profiles, minor-to-major
axial ratios (b/a) less than 0.6 and signal-to-noise ratio (S/N) of HI
detection greater than 6.5, we investigated the Tully-Fisher relation (TFr) of
LSBGs in the optical B, g and r bands and near-infrared J, H and K bands as
well. In optical bands, the LSBG subsample follows the fundamental TFr which
was previously defined for normal spiral galaxies. In NIR bands, the TFrs for
our LSBG subsample are slightly different from the TFrs for the normal bright
galaxies. This might be due to the internal extinction issue. Furthermore, the
mass-to-light ratio (M/L),disk scale length (h) and mass surface density
(sigma) for our LSBG subsample were deduced from the optical TFr results.
Compared with High Surface Brightness Galaxies(HSBGs), our LSBGs have higher
M/L, larger h and lower sigma than HSBGs.


  We study projective surfaces $X \subset \mathbb{P}^r$ (with $r \geq 5$) of
maximal sectional regularity and degree $d > r$, hence surfaces for which the
Castelnuovo-Mumford regularity $\reg(\mathcal{C})$ of a general hyperplane
section curve $\mathcal{C} = X \cap \mathbb{P}^{r-1}$ takes the maximally
possible value $d-r+3$. We use the classification of varieties of maximal
sectional regularity of \cite{BLPS1} to see that these surfaces are either
particular divisors on a smooth rational $3$-fold scroll $S(1,1,1)\subset
\mathbb{P}^5$, or else admit a plane $\mathbb{F} = \mathbb{P}^2 \subset
\mathbb{P}^r$ such that $X \cap \mathbb{F} \subset \mathbb{F}$ is a pure curve
of degree $d-r+3$. We show that our surfaces are either cones over curves of
maximal regularity, or almost non-singular projections of smooth rational
surface scrolls. We use this to show that the Castelnuovo-Mumford regularity of
such a surface $X$ satisfies the equality $\reg(X) = d-r+3$ and we compute or
estimate various of the cohomological invariants as well as the Betti numbers
of such surfaces. We also study the geometry of extremal secant lines of our
surfaces $X$, more precisely the closure $\Sigma(X)$ of the set of all proper
extremal secant lines to $X$ in the Grassmannian $\mathbb{G}(1, \mathbb{P}^r).$