  In this paper, we confront the problem of applying reinforcement learning to
agents that perceive the environment through many sensors and that can perform
parallel actions using many actuators as is the case in complex autonomous
robots. We argue that reinforcement learning can only be successfully applied
to this case if strong assumptions are made on the characteristics of the
environment in which the learning is performed, so that the relevant sensor
readings and motor commands can be readily identified. The introduction of such
assumptions leads to strongly-biased learning systems that can eventually lose
the generality of traditional reinforcement-learning algorithms. In this line,
we observe that, in realistic situations, the reward received by the robot
depends only on a reduced subset of all the executed actions and that only a
reduced subset of the sensor inputs (possibly different in each situation and
for each action) are relevant to predict the reward. We formalize this property
in the so called 'categorizability assumption' and we present an algorithm that
takes advantage of the categorizability of the environment, allowing a decrease
in the learning time with respect to existing reinforcement-learning
algorithms. Results of the application of the algorithm to a couple of
simulated realistic-robotic problems (landmark-based navigation and the
six-legged robot gait generation) are reported to validate our approach and to
compare it to existing flat and generalization-based reinforcement-learning
approaches.


  Low concentration hydrogen gas detection is of paramount importance both in
space applications as well as medical applications. It is also critically
important for safe handling of hydrogen below the explosive limit. Here, we
report a novel hybrid Pd metal-polymer chemiresistive sensor that can sense
0.5% hydrogen ($H_2$) gas in ambient conditions of temperature and pressure
with the highest reported sensitivity($\sim$30%) obtained earlier by a physical
deposition technique, making it an extremely good sensor for real life low
concentration hydrogen gas detection. The sensor is easy to fabricate and is
also extremely cost-effective for commercial applications. The obtained hybrid
chemiresistive sensor comprises palladium (Pd) nanocrystals bound by oxygen and
nitrogen atoms of a stabilizer Polyvinylepyrollidone (PVP), grown on top of a
selfassembled monolayer. The exceptional rise time-constant is proposed to
arise from hydrogen loading at the (111) surface of the palladium nanocrystal
which is a very fast process and subsequent fast diffusion of the H atoms from
the surface into the bulk. An effort to increase the number of available sites
by UV-ozone cleaning, resulted in a degradation of the sensing device due to
the poisoning of the available sites by oxygen.


  We report a novel phenomenon in carbon nanotube (CNT) based devices, the
transphonon effects, which resemble the transonic effects in aerodynamics. It
is caused by dissipative resonance of nanotube phonons similar to the radial
breathing mode, and subsequent drastic surge of the dragging force on the
sliding tube, and multiple phonon barriers are encountered as the intertube
sliding velocity reaches critical values. It is found that the transphonon
effects can be tuned by applying geometric constraints or varying chirality
combinations of the nanotubes.


  In this work, we combine two different ranking methods together with several
other predictors in a joint random forest approach for the scores of soccer
matches. The first ranking method is based on the bookmaker consensus, the
second ranking method estimates adequate ability parameters that reflect the
current strength of the teams best. The proposed combined approach is then
applied to the data from the two previous FIFA Women's World Cups 2011 and
2015. Finally, based on the resulting estimates, the FIFA Women's World Cup
2019 is simulated repeatedly and winning probabilities are obtained for all
teams. The model clearly favors the defending champion USA before the host
France.


  NISP, a multifaceted near-infrared instrument for the upcoming 2.5m IR
telescope at MIRO Gurushikhar, Mount Abu, Rajasthan, India is being developed
at PRL, Ahmedabad. NISP will have wide (FOV = 10' x 10') field imaging,
moderate (R=3000) spectroscopy and imaging polarimetry operating modes. It is
designed based on 0.8 to 2.5 micron sensitive, 2048 X 2048 HgCdTe (MCT) array
detector from Teledyne. Optical, Mechanical and Electronics subsystems are
being designed and developed in-house at PRL. HAWAII-2RG (H2RG) detector will
be mounted along with controlling SIDECAR ASIC inside LN2 filled cryogenic
cooled Dewar. FPGA based controller for H2RG and ASIC will be mounted outside
the Dewar at room temperature. Smart stepper motors will facilitate motion of
filter wheels and optical components to realize different operating modes.
Detector and ASIC temperatures are servo controlled using Lakeshore's
Temperature Controller (TC) 336. Also, several cryogenic temperatures will be
monitored by TC for health checking of the instrument. Detector, Motion and
Temperature controllers onboard telescope will be interfaced to USB Hub and
fiber-optic trans-receiver. Remote Host computer interface to remote end
trans-receiver will be equipped with in-house developed GUI software to control
all functionalities of NISP. Design and development aspects of NISP Electronics
will be presented in this conference.


  Weak gravitational lensing by the intervening large-scale structure of the
Universe induces high-order correlations in the cosmic microwave background
(CMB) temperature and polarization fields. We construct minimum variance
estimators of the intervening mass distribution out of the six quadratic
combinations of the temperature and polarization fields. Polarization begins to
assist in the reconstruction when E-mode mapping becomes possible on
degree-scale fields, i.e. for an experiment with a noise level of ~40 uK-arcmin
and beam of ~7', similar to the Planck experiment; surpasses the temperature
reconstruction at ~26 uK-arcmin and 4'; yet continues to improve the
reconstruction until the lensing B-modes are mapped to l ~ 2000 at ~0.3
uK-arcmin and 3'. Ultimately, the correlation between the E and B modes can
provide a high signal-to-noise mass map out to multipoles of L ~ 1000,
extending the range of temperature-based estimators by nearly an order of
magnitude. We outline four applications of mass reconstruction: measurement of
the linear power spectrum in projection to the cosmic variance limit out to L ~
1000 (or wavenumbers 0.002 < k < 0.2 in h/Mpc), cross-correlation with cosmic
shear surveys to probe the evolution of structure tomographically,
cross-correlation of the mass and temperature maps to probe the dark energy,
and the separation of lensing and gravitational wave B-modes.


  We study the impact of the inverse seesaw mechanism on several leptonic and
hadronic low-energy flavour-violating observables in the context of the Minimal
Supersymmetric Standard Model. Indeed, the contributions of the light
right-handed sneutrinos from the inverse seesaw significantly enhance the
Higgs-mediated penguin diagrams. We find that this can increase the different
branching ratios by as much as two orders of magnitude.


  We show that there exists a hyperbolic entire function of finite order of
growth such that the hyperbolic dimension---that is, the Hausdorff dimension of
the set of points in the Julia set of whose orbit is bounded---is equal to two.
This is in contrast to the rational case, where the Julia set of a hyperbolic
map must have Hausdorff dimension less than two, and to the case of all known
explicit hyperbolic entire functions.
  In order to obtain this example, we prove a general result on constructing
entire functions in the Eremenko-Lyubich class with prescribed behavior near
infinity, using Cauchy integrals. This result significantly increases the class
of functions that were previously known to be approximable in this manner.
  Furthermore, we show that the approximating functions are quasiconformally
conjugate to their original models, which simplifies the construction of
dynamical counterexamples. We also give some further applications of our
results to transcendental dynamics.


  The massive amounts of web-mined parallel data contain large amounts of
noise. Semantic misalignment, as the primary source of the noise, poses a
challenge for training machine translation systems. In this paper, we first
study the impact of real-world hard-to-detect misalignment noise by proposing a
process to simulate the realistic misalignment controlled by semantic
similarity. After quantitatively analyzing the impact of simulated misalignment
on machine translation, we show the limited effectiveness of widely used
pre-filters to improve the translation performance, underscoring the necessity
of more fine-grained ways to handle data noise. By observing the increasing
reliability of the model's self-knowledge for distinguishing misaligned and
clean data at the token-level, we propose a self-correction approach which
leverages the model's prediction distribution to revise the training
supervision from the ground-truth data over training time. Through
comprehensive experiments, we show that our self-correction method not only
improves translation performance in the presence of simulated misalignment
noise but also proves effective for real-world noisy web-mined datasets across
eight translation tasks.


  Current knowledge of the finite-density QCD equation of state from first
principles is limited to a Taylor expansion in the baryonic chemical potential
around $\mu_B=0$. By means of a scaling form for the equation of state of the
3D Ising model and a non-universal, parametrized map to QCD coordinates, we
construct a family of equations of state matching state of the art first
principle Lattice QCD calculations and including the correct critical behavior,
which can be readily employed in hydrodynamical simulations of heavy ion
collisions at finite density, covering most of the BES range at RHIC. This
contribution reports on work done within the Fluctuations/Equation of State
working group of the BEST Collaboration.


  Topological phases for free fermions in systems with crystal symmetry are
classified by the topology of the valence band viewed as a vector bundle over
the Brillouin zone. Additional symmetries, such as crystal symmetries which act
non-trivially on the Brillouin zone, or time-reversal symmetry, endow the
vector bundle with extra structure. These vector bundles are classified by a
suitable version of K-theory. While relatively easy to define, these K-theory
groups are notoriously hard to compute in explicit examples. In this paper we
describe in detail how one can compute these K-theory groups starting with a
decomposition of the Brillouin zone in terms of simple submanifolds on which
the symmetries act nicely. The main mathematical tool is the Atiyah-Hirzebruch
spectral sequence associated to such a decomposition, which will not only yield
the explicit result for several crystal symmetries, but also sheds light on the
origin of the topological invariants. This extends results that have appeared
in the literature so far. We also describe examples in which this approach
fails to directly yield a conclusive answer, and discuss various open problems
and directions for future research.


  Recently, because of the high-quality representations of contrastive learning
methods, rehearsal-based contrastive continual learning has been proposed to
explore how to continually learn transferable representation embeddings to
avoid the catastrophic forgetting issue in traditional continual settings.
Based on this framework, we propose Contrastive Continual Learning via
Importance Sampling (CCLIS) to preserve knowledge by recovering previous data
distributions with a new strategy for Replay Buffer Selection (RBS), which
minimize estimated variance to save hard negative samples for representation
learning with high quality. Furthermore, we present the Prototype-instance
Relation Distillation (PRD) loss, a technique designed to maintain the
relationship between prototypes and sample representations using a
self-distillation process. Experiments on standard continual learning
benchmarks reveal that our method notably outperforms existing baselines in
terms of knowledge preservation and thereby effectively counteracts
catastrophic forgetting in online contexts. The code is available at
https://github.com/lijy373/CCLIS.


  We investigate the relative importance of initial and final state effects on
azimuthal correlations of gluons in low and high multiplicity p+Pb collisions.
To achieve this, we couple Yang-Mills dynamics of pre-equilibrium gluon fields
(IP-GLASMA) to a perturbative QCD based parton cascade for the final state
evolution (BAMPS) on an event-by-event basis. We find that signatures of both
the initial state correlations and final state interactions are seen in
azimuthal correlation observables, such as
$v_2\left\lbrace2PC\right\rbrace(p_T)$, their strength depending on the event
multiplicity and transverse momentum. Initial state correlations dominate
$v_2\left\lbrace2PC\right\rbrace(p_T)$ in low multiplicity events for
transverse momenta $p_T>2~{\rm GeV}$. While final state interactions are
dominant in high multiplicity events, initial state correlations affect
$v_2\left\lbrace2PC\right\rbrace(p_T)$ for $p_T>2~{\rm GeV}$ as well as the pT
integrated $v_2\left\lbrace2PC\right\rbrace$.


  The influence of dilute impurities on the structure of a fluid solvent is
investigated theoretically. General arguments, which do not rely on particular
models, are used to derive an extension of the Ornstein-Zernike form for the
solvent structure factor at small scattering vectors. It is shown that dilute
impurities can influence the solvent structure only if they are composed of
ions with significantly different sizes. Non-ionic impurities or ions of
similar size are shown to not alter the solvent structure qualitatively. This
picture is compatible with available experimental data. The derived form of the
solvent structure factor is expected to be useful to infer information on the
impurity-solvent interactions form measured scattering intensities.


  With climate change predicted to increase the likelihood of landslide events,
there is a growing need for rapid landslide detection technologies that help
inform emergency responses. Synthetic Aperture Radar (SAR) is a remote sensing
technique that can provide measurements of affected areas independent of
weather or lighting conditions. Usage of SAR, however, is hindered by domain
knowledge that is necessary for the pre-processing steps and its interpretation
requires expert knowledge. We provide simplified, pre-processed,
machine-learning ready SAR datacubes for four globally located landslide events
obtained from several Sentinel-1 satellite passes before and after a landslide
triggering event together with segmentation maps of the landslides. From this
dataset, using the Hokkaido, Japan datacube, we study the feasibility of
SAR-based landslide detection with supervised deep learning (DL). Our results
demonstrate that DL models can be used to detect landslides from SAR data,
achieving an Area under the Precision-Recall curve exceeding 0.7. We find that
additional satellite visits enhance detection performance, but that early
detection is possible when SAR data is combined with terrain information from a
digital elevation model. This can be especially useful for time-critical
emergency interventions. Code is made publicly available at
https://github.com/iprapas/landslide-sar-unet.


  Defect modes are investigated in a band gap of an electrically tunable
one-dimensional photonic crystal infiltrated with a twisted-nematic liquid
crystal (1D PC/TN). Their frequency shift and interference under applied
voltage are studied both experimentally and theoretically. We deal with the
case where the defect layer thickness is much larger than the wavelength
(Mauguin condition). It is shown theoretically that the defect modes could have
a complex structure with the elliptic polarization. Two series of polarized
modes interact with each other and exhibit an avoided crossing phenomenon in
the case of opposite parity.


  We apply the pseudoparticle approach to SU(2) Yang-Mills theory and perform a
detailed study of the potential between two static charges for various
representations. Whereas for charges in the fundamental representation we find
a linearly rising confining potential, we clearly observe string breaking, when
considering charges in the adjoint representation. We also demonstrate Casimir
scaling and compute gluelump masses for different spin and parity. Numerical
results are in qualitative agreement with lattice results.


  The measurement of forward jet cross sections has been suggested as a
promising probe of new small x parton dynamics and the question is whether the
new HERA data provide an indication of this. In this paper the influence of
resolved photon processes has been investigated and it has been studied to what
extent the inclusion of such processes in addition to normal deep inelastic
scattering leads to agreement with data. It is shown that two DGLAP evolution
chains from the hard scattering process towards the proton and the photon
respectively, are sufficient to describe effects observed in the HERA data,
which have been attributed to BFKL dynamics.


  We revisit the $m \alpha^6 (m/M)$ order corrections to the hyperfine
splitting in the H$_2^+$ ion, and find a hitherto unrecognized second-order
relativistic contribution associated with the vibrational motion of the nuclei.
Inclusion of this correction term produces theoretical predictions which are in
excellent agreement with experimental data [K. B. Jefferts, Phys.\ Rev.\ Lett.\
\textbf{23}, 1476 (1969)], thereby concluding a nearly fifty years long
theoretical quest to explain the experimental results within their 1-ppm error.
The agreement between theory and experiment corroborates the proton structural
properties as derived from the hyperfine structure of atomic hydrogen. Our work
furthermore indicates that for future improvements, a full three-body
evaluation of the $m \alpha^6 (m/M)$ correction term will be mandatory.


  Recently, a novel $4D$ Einstein-Gauss-Bonnet (EGB) gravity was formulated and
a spherically symmetric black hole solution in this theory was derived by D.
Glavan and C. Lin \cite{Glavan:2019inb}. In this paper, we study the geodesic
motions in the background of the spherically symmetric black hole, by focusing
on the innermost stable circular orbits (ISCO) for massive particle and photon
sphere and shadow. Also, we find that a negative GB coupling constant is
allowable in this theory, as in which case the singular behavior of the black
hole can be hidden inside the event horizon. Moreover, we find that due to this
extension a recently proposed universal bound on black hole size in
\cite{Lu:2019zxb} can be broken.


  We investigate dynamics of semi-quantal spin systems in which quantum bits
are attached to classically and possibly stochastically moving classical
particles. The interaction between the quantum bits takes place when the
respective classical particles get close to each other in space. We find that
with Heisenberg XX couplings quantum homogenization takes place after a time
long enough, regardless of the details of the underlying classical dynamics.
This is accompanied by the development of a stationary bipartite entanglement.
If the information on the details of the motion of a stochastic classical
system is disregarded, the stationary state of the whole quantum subsystem is
found to be a complete mixture in the studied cases, though the transients
depend on the properties of the classical motion.


  The study of Entanglement of Formation of a mixed state of a bipartite system
in high-dimensional Hilbert space is not easy in general. So, we focus on
determining the amount of entanglement for a bipartite mixed state based on the
concept of decomposable optimal entanglement witness (DOEW), that can be
calculated as a minimum distance of an entangled state from the edge of
positive partial transpose (PPT) states which has the most negative (positive)
expectation value for non-PPT (bound) entangled states. We have constructed
DOEWs based on the convex optimization method, then by using of it we quantify
the degree of entanglement for two spin half particles under the Lorentz
transformations. For convenience, we restrict ourselves to 2D momentum subspace
and under this constraint when the momentum and the Lorentz boost are parallel,
we have shown that the entanglement is not relativistic invariant. Keywords :
Relativistic entanglement, Measure of entanglement, Optimal entanglement
witnesses, Convex optimization PACS numbers: 03.67.Hk, 03.65.Ta


  Here we report on the unique observation of flaring coronal loops at the
solar limb using high resolution imaging spectropolarimetry from the Swedish
1-meter Solar Telescope. The vantage position, orientation and nature of the
chromospheric material that filled the flare loops allowed us to determine
their magnetic field with unprecedented accuracy using the weak-field
approximation method. Our analysis reveals coronal magnetic field strengths as
high as 350 Gauss at heights up to 25 Mm above the solar limb. These
measurements are substantially higher than a number of previous estimates and
may have considerable implications for our current understanding of the
extended solar atmosphere.


  The conventional LoRa system is not able to sustain long-range communication
over fading channels. To resolve the challenging issue, this paper investigates
a two-hop opportunistic amplify-and-forward relaying LoRa system. Based on the
best relay-selection protocol, the analytical and asymptotic bit error rate
(BER), achievable diversity order, coverage probability, and throughput of the
proposed system are derived over the Nakagamim fading channel. Simulative and
numerical results show that although the proposed system reduces the throughput
compared to the conventional LoRa system, it can significantly improve BER and
coverage probability. Hence, the proposed system can be considered as a
promising platform for low-power, long-range and highly reliable
wireless-communication applications.


  Algorithms for the numerical evaluation of the incomplete gamma function
ratios $P(a,x)=\gamma(a,x)/\Gamma(a)$ and $Q(a,x)=\Gamma(a,x)/\Gamma(a)$ are
described for positive values of $a$ and $x$. Also, inversion methods are given
for solving the equations $P(a,x)=p$, $Q(a,x)=q$, with $0<p,q<1$. Both the
direct computation and the inversion of the incomplete gamma function ratios
are used in many problems in statistics and applied probability. The analytical
approach from earlier literature is summarized and new initial estimates are
derived for starting the inversion algorithms. The performance of the
associated software to our algorithms (the Fortran 90 module {\bf IncgamFI}) is
analyzed and compared with earlier published algorithms.


  The time irreversible evolution of quantum systems with infinite number of
particles (QSINP) was studied within a newly constructed algebraic framework.
The QSINP could be described by the quantum infinite lattice field. The
*-Algebra R is the set of all dynamic variables of the QSINP, in which a
special addition and multiplication operations were defined. The full pure
state vector (FPSV) \rho, the pure state vector {\rho_f} and the equivalent
relations within them are also well defined. The set of all pure state vectors,
which are equivalent to the FPSV \rho, is a Hilbert Space {H_\rho}, if the
addition, the inner product and the norm were defined in it. The set of all
linear transformation {N_\rho} on {H_\rho} is isomorphic to R, and
{{N_\rho},{H_\rho}} is the representation of R, associated with \rho. The
*-Algebra R has infinitely many non-equivalent irreducible GNS constructions
(representations), associated with different nonequivalent FPSVs respectively.
  It is proved that, the dynamical motions of the QSINP is totally within the
GNS construction associated with the initial pure state vector; However, the
time reversal transformation makes the initial FPSV and its corresponding
dynamical evolution into another non-equivalent GNS construction. Therefore,
within the GNS construction associated with the FPSV, the dynamics of the QSINP
is time irreversible.
  Finally, due to the Liouville operator has real continuous spectrum within
the GNS construction, the longtime asymptotic solution of Liouville equation in
the GNS construction could be treated by the formal scattering theory. The
Master equation with dissipative term was obtained, which is formally
irrelevant of the initial state and the corresponding GNS construction. This
master equation could be regarded as the evolution equation of the QSINP on R.


  We construct merger trees of dark matter haloes and quantify their merger
rates and mass growth rates using the joint dataset from the Millennium and
Millennium-II simulations. The finer resolution of the Millennium-II Simulation
has allowed us to extend our earlier analysis of halo merger statistics to an
unprecedentedly wide range of descendant halo mass (10^10 < M0 < 10^15 Msun),
progenitor mass ratio (10^-5 < xi < 1), and redshift (0 < z < 15). We update
our earlier fitting form for the mean merger rate per halo as a function of
M_0, xi, and z. The overall behavior of this quantity is unchanged: the rate
per unit redshift is nearly independent of z out to z~15; the dependence on
halo mass is weak (M0^0.13); and it is nearly a power law in the progenitor
mass ratio (xi^-2). We also present a simple and accurate fitting formula for
the mean mass growth rate of haloes as a function of mass and redshift. This
mean rate is 46 Msun/yr for 10^12 Msun haloes at z=0, and it increases with
mass as M^{1.1} and with redshift as (1+z)^2.5 (for z > 1). When the fit for
the mean mass growth rate is integrated over a halo's history, we find
excellent match to the mean mass assembly histories of the simulated haloes. By
combining merger rates and mass assembly histories, we present results for the
number of mergers over a halo's history and the statistics of the redshift of
the last major merger.


  The outbreak of the COVID-19 pandemic has deeply influenced the lifestyle of
the general public and the healthcare system of the society. As a promising
approach to address the emerging challenges caused by the epidemic of
infectious diseases like COVID-19, Internet of Medical Things (IoMT) deployed
in hospitals, clinics, and healthcare centers can save the diagnosis time and
improve the efficiency of medical resources though privacy and security
concerns of IoMT stall the wide adoption. In order to tackle the privacy,
security, and interoperability issues of IoMT, we propose a framework of
blockchain-enabled IoMT by introducing blockchain to incumbent IoMT systems. In
this paper, we review the benefits of this architecture and illustrate the
opportunities brought by blockchain-enabled IoMT. We also provide use cases of
blockchain-enabled IoMT on fighting against the COVID-19 pandemic, including
the prevention of infectious diseases, location sharing and contact tracing,
and the supply chain of injectable medicines. We also outline future work in
this area.


  Automated essay scoring (AES) to evaluate second language (L2) proficiency
has been a firmly established technology used in educational contexts for
decades. Although holistic scoring has seen advancements in AES that match or
even exceed human performance, analytic scoring still encounters issues as it
inherits flaws and shortcomings from the human scoring process. The recent
introduction of large language models presents new opportunities for automating
the evaluation of specific aspects of L2 writing proficiency. In this paper, we
perform a series of experiments using GPT-4 in a zero-shot fashion on a
publicly available dataset annotated with holistic scores based on the Common
European Framework of Reference and aim to extract detailed information about
their underlying analytic components. We observe significant correlations
between the automatically predicted analytic scores and multiple features
associated with the individual proficiency components.


  Continuing previous work, we show the existence of stable, anisotropic future
attractors in Bianchi invariant sets with a $p$-form field ($p\,\in\,\{1,3\}$)
and a perfect fluid. In particular, we consider the not previously investigated
Bianchi invariant sets $\mathcal{B}$(II), $\mathcal{B}$(IV),
$\mathcal{B}$(VII$_0$) and $\mathcal{B}$(VII$_{h})$ and examine their
asymptotic behaviour. We find that the isolated equilibrium set Wonderland is a
future attractor on all of its existence ($2/3<\,\gamma\,<2$) in all these sets
except in $\mathcal{B}$(II), where the peculiar equilibrium sets Edge and Rope
show up, taking over the stability for certain values of $\gamma$. In addition,
in $\mathcal{B}$(IV) and $\mathcal{B}$(VII$_h$) plane gravitational wave
solutions (with a non-zero $p$-form) serve as attractors whenever
$2/3<\,\gamma\,<2$.


  Let $S \subset \mathbb{R}^{n}$ be an arbitrary nonempty compact set such that
the $d$-Hausdorff content $\mathcal{H}^{d}_{\infty}(S) > 0$ for some $d \in
(0,n]$. For each $p \in (\max\{1,n-d\},n]$, an almost sharp intrinsic
description of the trace space $W_{p}^{1}(\mathbb{R}^{n})|_{S}$ of the Sobolev
space $W_{p}^{1}(\mathbb{R}^{n})$ to the set $S$ is obtained. Furthermore, for
each $p \in (\max\{1,n-d\},n]$ and $\varepsilon \in (0, \min\{p-(n-d),p-1\})$,
new bounded linear extension operators from the trace space
$W_{p}^{1}(\mathbb{R}^{n})|_{S}$ into the space
$W_{p-\varepsilon}^{1}(\mathbb{R}^{n})$ are constructed.


  We consider an anisotropic curvature flow $V= A(\mathbf{n})H + B(\mathbf{n})$
in a band domain $\Omega :=[-1,1]\times R$, where $\mathbf{n}$, $V$ and $H$
denote the unit normal vector, normal velocity and curvature, respectively, of
a graphic curve $\Gamma_t$. We consider the case when $A>0>B$ and the curve
$\Gamma_t$ contacts $\partial_\pm \Omega$ with slopes equaling to $\pm 1$ times
of its height (which are unbounded when the solution moves to infinity). First,
we present the global well-posedness and then, under some symmetric assumptions
on $A$ and $B$, we show the uniform interior gradient estimates for the
solution. Based on these estimates, we prove that $\Gamma_t$ converges as $t\to
\infty$ in $C^{2,1}_{\text{loc}} ((-1,1)\times R)$ topology to a cup-like
traveling wave with {\it infinite} derivatives on the boundaries.


  Over the past decades, temperature and density of the upper atmosphere show
negative trends and decrease of the upper atmospheric temperature is attributed
to the declining neutral density. Specifically, nitric oxide (NO) and carbon
dioxide (CO2) govern thermospheric cooling at 5.3 and 15 micron, respectively.
While a lot of efforts have focused on the CO2 effects on the long-term trends,
relatively less attention has been paid to the impacts by NO, which responds to
solar and geomagnetic activities dynamically. In this study, we investigate the
role of NO in climatological global energy budget for the recent three solar
cycles using the Global Ionosphere Thermosphere Model. From 1982 to 2013, the
F10.7 and Ap indices showed a decadal decrease of ~8% and ~20%, respectively.
By imposing temporal-varying F10.7 and Ap values in the simulations, we find a
decadal change of -0.28x1011 W or -17.3% in total NO cooling power, which
agrees well with that (-0.34x1011 W or -17.2%) from the empirical Thermosphere
Climate Index derived from the TIMED/SABER data. Neutral density decreases by
10-20% at 200-450km and Tex decreases by 25.3 K per decade. The deduced-decadal
change of NO cooling reaches ~25% of the sum of total heating at ~130 km and
its significance decreases with altitude.


  Let A be a unital algebra over a commutative unital ring R. We say that A is
a SLIP algebra if every R-linear map on A that leaves invariant every left
ideal of A is a left multiplier. In this paper we study whether a triangular
algebra Tri(A,M,B) is a SLIP algebra and give some necessary or sufficient
conditions for a triangular algebra be a SLIP algebra, and various examples are
given which illustrate limitations on extending some of the theory developed.
Then our results are applied to generalized triangular matrix algebras and
block upper triangular algebras. Also, some SLIP algebras other that triangular
algebras are provided.


  The inclusive electron neutrino charged-current cross section is measured in
the NOvA near detector using $8.02\times10^{20}$ protons-on-target (POT) in the
NuMI beam. The sample of GeV electron neutrino interactions is the largest
analyzed to date and is limited by $\simeq$ 17\% systematic rather than the
$\simeq$ 7.4\% statistical uncertainties. The double-differential cross section
in final-state electron energy and angle is presented for the first time,
together with the single-differential dependence on $Q^{2}$ (squared
four-momentum transfer) and energy, in the range 1 GeV $ \leq E_{\nu} < $6 GeV.
Detailed comparisons are made to the predictions of the GENIE, GiBUU, NEUT, and
NuWro neutrino event generators. The data do not strongly favor a model over
the others consistently across all three cross sections measured, though some
models have especially good or poor agreement in the single differential cross
section vs. $Q^{2}$.


  We built a catalog of 122 FR~II radio galaxies, called FRII{\sl{CAT}},
selected from a published sample obtained by combining observations from the
NVSS, FIRST, and SDSS surveys. The catalog includes sources with redshift $\leq
0.15$, an edge-brightened radio morphology, and those with at least one of the
emission peaks located at radius $r$ larger than 30 kpc from the center of the
host. The radio luminosity at 1.4 GHz of the \FRII\ sources covers the range
$L_{1.4} \sim 10^{39.5} - 10^{42.5}$ $\ergs$. The \FRII\ catalog has 90\% of
low and 10\% of high excitation galaxies (LEGs and HEGs), respectively. The
properties of these two classes are significantly different. The FRII{\sl{CAT}}
LEGs are mostly luminous ($-20 \gtrsim M_r \gtrsim -24$), red early-type
galaxies with black hole masses in the range $10^8 \lesssim M_{\rm BH} \lesssim
10^9 M_\odot$; they are essentially indistinguishable from the FR~Is belonging
to the FRI{\sl{CAT}}. The HEG FR~IIs are associated with optically bluer and
mid-IR redder hosts than the LEG FR~IIs and to galaxies and black holes that
are smaller, on average, by a factor $\sim$2.
  FR~IIs have a factor $\sim$ 3 higher average radio luminosity than FR~Is.
Nonetheless, most ($\sim 90$ \%) of the selected FR~IIs have a radio power that
is lower, by as much as a factor of $\sim$100, than the transition value
between FR~Is and FR~IIs found in the 3C sample. The correspondence between the
morphological classification of FR~I and FR~II and the separation in radio
power disappears when including sources selected at low radio flux thresholds,
which is in line with previous results. In conclusion, a radio source produced
by a low power jet can be edge brightened or edge darkened, and the outcome is
not related to differences in the optical properties of the host galaxy.


  This paper formulates a new approach to the study of chaos in discrete
dynamical systems based on the notions of inverse ill-posed problems,
set-valued mappings, generalized and multivalued inverses, graphical
convergence of a net of functions in an extended multifunction space, and the
topological theory of convergence. Order, chaos, and complexity are described
as distinct components of this unified mathematical structure that can be
viewed as an application of the theory of convergence in topological spaces to
increasingly nonlinear mappings, with the boundary between order and complexity
in the topology of graphical convergence being the region in Multi(X) that is
susceptible to chaos. The paper uses results from the discretized spectral
approximation in neutron transport theory and concludes that the numerically
exact results obtained by this approximation of the Case singular eigenfunction
solution is due to the graphical convergence of the Poisson and conjugate
Poisson kernels to the Dirac delta and the principal value multifunctions
respectively. In Multi(X), the continuous spectrum is shown to reduce to a
point spectrum, and we introduce a notion of latent chaotic states to interpret
superposition over generalized eigenfunctions. Along with these latent states,
spectral theory of nonlinear operators is used to conclude that nature supports
complexity to attain efficiently a multiplicity of states that otherwise would
remain unavailable to it.


  It is shown that pairs of maximal linear recursive sequences (m-sequences)
typically have mean square aperiodic crosscorrelation on par with that of
random sequences, but that if one takes a pair of m-sequences where one is the
reverse of the other, and shifts them appropriately, one can get significantly
lower mean square aperiodic crosscorrelation. Sequence pairs with even lower
mean square aperiodic crosscorrelation are constructed by taking a Legendre
sequence, cyclically shifting it, and then cutting it (approximately) in half
and using the halves as the sequences of the pair. In some of these
constructions, the mean square aperiodic crosscorrelation can be lowered
further if one truncates or periodically extends (appends) the sequences. Exact
asymptotic formulae for mean squared aperiodic crosscorrelation are proved for
sequences derived from additive characters (including m-sequences and modified
versions thereof) and multiplicative characters (including Legendre sequences
and their relatives). Data is presented that shows that sequences of modest
length have performance that closely approximates the asymptotic formulae.


  We report on the BeppoSAX observation of the X-ray source X1724-308 in the
globular cluster Terzan 2. The broadband spectrum can be described as the
superposition of a power-law with photon spectral index 1.6-1.9 and a thermal
component with typical temperature ~1 keV. X1724-308is detected in the PDS up
to 150 keV with a S/N ratio >3, notwithstanding a sharp exponential cutoff at
\~90 keV. The broadband spectrum can be best interpreted as due to the
Comptonization of a Wien photon distribution with kT ~1 keV by a
spherically-symmetric hot plasma with electron temperature ~30 keV and optical
depth ~3. A comparison with the fainter and steeper state, which was observed
by EXOSAT, suggests a correlation between the temperature of the Comptonizing
electron distribution (or the plasma optical depth) and the X-ray intensity.
The X-ray thermal component could originate from a boundary layer between the
accretion disk and the compact object, or from the accretion disk itself.


  In this paper, we prove that the Reidemeister torsion twisted by the adjoint
representation, which is considered as a 1-form, on the SU(2)-character variety
of a knot exterior is invariant under mutation along a Conway sphere.


  Brane worlds are theories with extra spatial dimensions in which ordinary
matter is localized on a (3+1) dimensional submanifold. Such theories could
have interesting consequences for particle physics and gravitational physics.
In this essay we concentrate on the cosmological constant (CC) problem in the
context of brane worlds. We show how extra-dimensional scenarios may violate
Lorentz invariance in the gravity sector of the effective 4D theory, while
particle physics remains unaffected. In such theories the usual no-go theorems
for adjustment of the CC do not apply, and we indicate a possible explanation
of the smallness of the CC. Lorentz violating effects would manifest themselves
in gravitational waves travelling with a speed different from light, which can
be searched for in gravitational wave experiments.


  The paper deals with the question of homometry in the dihedral groups $D_{n}$
of order $2n$. These groups have the specificity to be non-commutative. It
leads to a new approach as compared as the one used in the traditional
framework of the commutative group $ \mathbb{Z}_{n}$. We give here a musical
interpretation of homometry in $D_{12}$ using the well-known neo-Riemannian
groups, some computational results concerning enumeration of homometric sets
for small values of $n$, and some properties disclosing important links between
homometry in $\mathbb{Z}_{n}$ and homometry in $D_{n}$. Finally we propose an
extension of musical applications for this non-commutative homometry.


  We discuss a two-dimensional lagrangian model with $N=2$ supersymmetry
described by a K\"{a}hler potential $K(X,\bar{X})$ and superpotential $gX^k$
which explicitly exhibits renormalization group flows to infrared fixed points
where the central charge has a value equal that of the $N=2$, $A_{k-1}$ minimal
model. We consider the dressing of such models by N=2 supergravity: in
contradistinction to bosonic or $N=1$ models, no modification of the
$\b$-function takes place.


  This paper presents a comparison of two reduced-order, sequential and
variational data assimilation methods: the SEEK filter and the R-4D-Var. A
hybridization of the two, combining the variational framework and the
sequential evolution of covariance matrices, is also preliminarily investigated
and assessed in the same experimental conditions. The comparison is performed
using the twin-experiment approach on a model of the Tropical Pacific domain.
The assimilated data are simulated temperature profiles at the locations of the
TAO/TRITON array moorings. It is shown that, in a quasi-linear regime, both
methods produce similarly good results. However the hybrid approach provides
slightly better results and thus appears as potentially fruitful. In a more
non-linear regime, when Tropical Instability Waves develop, the global nature
of the variational approach helps control model dynamics better than the
sequential approach of the SEEK filter. This aspect is probably enhanced by the
context of the experiments in that there is a limited amount of assimilated
data and no model error.


  For a pair $(G,N)$ of a group $G$ and its normal subgroup $N$, we consider
the space of quasimorphisms and quasi-cocycles on $N$ non-extendable to $G$. To
treat this space, we establish the five-term exact sequence of cohomology
relative to the bounded subcomplex. As its application, we study the spaces
associated with the kernel of the (volume) flux homomorphism, the
IA-automorphism group of a free group, and certain normal subgroups of
Gromov-hyperbolic groups.
  Furthermore, we employ this space to prove that the stable commutator length
is equivalent to the stable mixed commutator length for certain pairs of a
group and its normal subgroup.


  We present detailed broadband UV/optical to X-ray spectral variability of the
Seyfert 1 galaxy 1H 0419-577 using six XMM-Newton observations performed during
2002-2003. These observations covered a large amplitude variability event in
which the soft X-ray (0.3-2 keV) count rate increased by a factor of ~4 in six
months. The X-ray spectra during the variability are well described by a model
consisting of a primary power law, blurred and distant reflection. The 2-10 keV
power-law flux varied by a factor ~7 while the 0.3-2 keV soft X-ray excess flux
derived from the blurred reflection component varied only by a factor of ~2.
The variability event was also observed in the optical and UV bands but the
variability amplitudes were only at the 6-10% level. The variations in the
optical and UV bands appear to follow the variations in the X-ray band. During
the rising phase, the optical bands appear to lag behind the UV band but during
the declining phase, the optical bands appear to lead the UV band. Such
behavior is not expected in the reprocessing models where the optical/UV
emission is the result of reprocessing of X-ray emission in the accretion disc.
The delayed contribution of the broad emission lines in the UV band or the
changes in the accretion disc/corona geometry combined with X-ray reprocessing
may give rise to the observed behavior of the variations.


  A number of authors have proposed stochastic versions of the Schr\"odinger
equation, either as effective evolution equations for open quantum systems or
as alternative theories with an intrinsic collapse mechanism. We discuss here
two directions for generalization of these equations. First, we study a general
class of norm preserving stochastic evolution equations, and show that even
after making several specializations, there is an infinity of possible
stochastic Schr\"odinger equations for which state vector collapse is provable.
Second, we explore the problem of formulating a relativistic stochastic
Schr\"odinger equation, using a manifestly covariant equation for a quantum
field system based on the interaction picture of Tomonaga and Schwinger. The
stochastic noise term in this equation can couple to any local scalar density
that commutes with the interaction energy density, and leads to collapse onto
spatially localized eigenstates. However, as found in a similar model by
Pearle, the equation predicts an infinite rate of energy nonconservation
proportional to $\delta^3(\vec 0)$, arising from the local double commutator in
the drift term.


  Planet formation is generally described in terms of a system containing the
host star and a protoplanetary disc, of which the internal properties (e.g.
mass and metallicity) determine the properties of the resulting planetary
system. However, (proto)planetary systems are predicted and observed to be
affected by the spatially-clustered stellar formation environment, either
through dynamical star-star interactions or external photoevaporation by nearby
massive stars. It is challenging to quantify how the architecture of planetary
systems is affected by these environmental processes, because stellar groups
spatially disperse within <1 billion years, well below the ages of most known
exoplanets. Here we identify old, co-moving stellar groups around exoplanet
host stars in the astrometric data from the Gaia satellite and demonstrate that
the architecture of planetary systems exhibits a strong dependence on local
stellar clustering in position-velocity phase space, implying a dependence on
their formation or evolution environment. After controlling for host stellar
age, mass, metallicity, and distance from the Sun, we obtain highly significant
differences (with $p$-values of $10^{-5}{-}10^{-2}$) in planetary (system)
properties between phase space overdensities and the field. The median
semi-major axis and orbital period of planets in overdensities are 0.087 au and
9.6 days, respectively, compared to 0.81 au and 154 days for planets around
field stars. 'Hot Jupiters' (massive, close-in planets) predominantly exist in
stellar phase space overdensities, strongly suggesting that their extreme
orbits originate from environmental perturbations rather than internal
migration or planet-planet scattering. Our findings reveal that stellar
clustering is a key factor setting the architectures of planetary systems.


  MaxCut is a key NP-Hard combinatorial optimization graph problem with
extensive theoretical and industrial applications, including the Ising model
and chip design. While quantum computing offers new solutions for such
combinatorial challenges which are potentially better than classical schemes,
with the Quantum Approximate Optimization Algorithm (QAOA) being a
state-of-the-art example, its performance is currently hindered by hardware
noise and limited qubit number. Here, we present a new variational
Qubit-Efficient MaxCut (QEMC) algorithm that requires a logarithmic number of
qubits with respect to the graph size, an exponential reduction compared to
QAOA. We demonstrate cutting-edge performance for graph instances consisting of
up to 32 nodes (5 qubits) on real superconducting hardware, and for graphs with
up to 2048 nodes (11 qubits) using noiseless simulations, outperforming the
established classical algorithm of Goemans and Williamson (GW). The QEMC
algorithm's innovative encoding scheme empowers it with great noise-resiliency
on the one hand, but also enables its efficient classical simulation on the
other, thus obscuring a distinct quantum advantage. Nevertheless, even in the
absence of quantum advantage, the QEMC algorithm serves as a potential
quantum-inspired algorithm, provides a challenging benchmark for QAOA, and
presents a novel encoding paradigm with potential applications extending to
other quantum and classical algorithms.


  Smart premise selection is essential when using automated reasoning as a tool
for large-theory formal proof development. A good method for premise selection
in complex mathematical libraries is the application of machine learning to
large corpora of proofs. This work develops learning-based premise selection in
two ways. First, a newly available minimal dependency analysis of existing
high-level formal mathematical proofs is used to build a large knowledge base
of proof dependencies, providing precise data for ATP-based re-verification and
for training premise selection algorithms. Second, a new machine learning
algorithm for premise selection based on kernel methods is proposed and
implemented. To evaluate the impact of both techniques, a benchmark consisting
of 2078 large-theory mathematical problems is constructed,extending the older
MPTP Challenge benchmark. The combined effect of the techniques results in a
50% improvement on the benchmark over the Vampire/SInE state-of-the-art system
for automated reasoning in large theories.


  Anomaly detection (AD) is the machine learning task of identifying highly
discrepant abnormal samples by solely relying on the consistency of the normal
training samples. Under the constraints of a distribution shift, the assumption
that training samples and test samples are drawn from the same distribution
breaks down. In this work, by leveraging tools from causal inference we attempt
to increase the resilience of anomaly detection models to different kinds of
distribution shifts. We begin by elucidating a simple yet necessary statistical
property that ensures invariant representations, which is critical for robust
AD under both domain and covariate shifts. From this property, we derive a
regularization term which, when minimized, leads to partial distribution
invariance across environments. Through extensive experimental evaluation on
both synthetic and real-world tasks, covering a range of six different AD
methods, we demonstrated significant improvements in out-of-distribution
performance. Under both covariate and domain shift, models regularized with our
proposed term showed marked increased robustness. Code is available at:
https://github.com/JoaoCarv/invariant-anomaly-detection.


  Similarity index is an important scientific tool frequently used to determine
whether different pairs of entities are similar with respect to some prefixed
characteristics. Some standard measures of similarity index include Jaccard
index, S{\o}rensen-Dice index, and Simpson's index. Recently, a better index
($\hat{\alpha}$) for the co-occurrence and/or similarity has been developed,
and this measure really outperforms and gives theoretically supported
reasonable predictions. However, the measure $\hat{\alpha}$ is not data
dependent. In this article we propose a new measure of similarity which depends
strongly on the data before introducing randomness in prevalence. Then, we
propose a new method of randomization which changes the whole pattern of
results. Before randomization our measure is similar to the Jaccard index,
while after randomization it is close to $\hat{\alpha}$. We consider the
popular ecological dataset from the Tuscan Archipelago, Italy; and compare the
performance of the proposed index to other measures. Since our proposed index
is data dependent, it has some interesting properties which we illustrate in
this article through numerical studies.


  In this work we analyze the possibility of sudden cosmological singularities,
also known as type-II singularities, in the background of a
Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometry in an extension of
General Relativity (GR) known as Aether scalar-tensor theories (AeST).
Similarly to several scalar-tensor theories, we observe that sudden
singularities may occur in certain AeST models at the level of the second-order
time derivative of the scale factor. These singularities can either be induced
by AeST's scalar field itself in the absence of a fluid matter component, or by
a divergence of the pressure component of the fluid. In the latter case, one
observes that the second-order time derivative of the scalar field $Q$ is also
divergent at the instant the sudden singularity happens. We show that the
sudden singularities can be prevented by an appropriate choice of the action,
for which a divergence in the scalar field compensates the divergence in the
pressure component of the matter fluid, thus preserving the regularity of the
scale factor and all its time derivatives. For the models featuring a sudden
singularity in the second-order time derivative of the scale factor, an
analysis of the cosmographic parameters, namely the Hubble and the deceleration
parameters, indicates that cosmological models featuring sudden singularities
are allowed by the current cosmological measurements. Furthermore, an analysis
of the jerk parameter favours cosmological models that attain a sudden
singularity at a faster rate, up to a time of at most $t_s\sim 1.2 t_0$, where
$t_0$ is the current age of the universe, and with negative values for the
cosmological snap parameter.


  We report a zero-field Cu nuclear quadrupole resonance (NQR) study on the
effects of nonmagnetic Sr substitution for high-Tc superconductors,
Y(Ba1-xSrx)2Cu4O8 (Tc=82-80 K for x=0-0.4), using a spin-echo technique. The
site-disordering and chemical pressure effects associated with doping Sr were
observed in the broadened, shifted Cu NQR spectra. Nevertheless, the site
disorder did not significantly affect the homogeneity of Cu electron spin
dynamics, in contrast to the in-plane impurity. The peak shift of Cu NQR
spectrum due to Sr was different between the chain- and the plane-Cu sites,
more remarkably than those under a hydrostatic physical pressure, suggesting
anisotropic or nonuniform local structural strains. The small decrease of Tc
due to Sr can be traced back to either a cancellation effect on Tc between the
disorder and the pressure, or an anisotropic or nonuniform chemical pressure
effect on Tc.


  We study sigma-ideals and regularity properties related to the "filter-Laver"
and "dual-filter-Laver" forcing partial orders. An important innovation which
enables this study is a dichotomy theorem proved recently by Miller [1].
  [1] Arnold Miller, "Hechler and Laver Trees", Preprint 2012 (arXiv:1204.5198
[math.LO]).


  We have studied the concept of bipolarity of information in the soft sets. We
have defined bipolar soft sets and basic operations of union, intersection and
complementation for bipolar soft sets. Examples of bipolar soft sets and an
application of bipolar soft sets in a decision making problem with general
algorithms have also been presented at the end.


  The paper deals with a theoretical study of electrokinetic flow of a
rheological Herschel-Bulkley fluid through a cylindrical tube of variable
cross-section. The concern of this study is to analyze combined pressure-driven
and electroosmotic flow of Herschel-Bulkley fluid. The wall potential is
considered to vary slowly and periodically along the axis of the tube. With
reference to flow in the micro-vessels, the problem has been solved using the
lubrication theory. The Helmholtz-Smoluchowski (HS) slip boundary condition has
been employed in this study. Volumetric flow rate $Q$ is found to be
significantly affected by the yield stress parameter $\nu$ only if an applied
pressure force is active. The linear superposition of flow components
separately due to the hydrodynamic and electric force occurs only for a
strictly uniform tube. This linear relationship fails if non-uniformity appears
in either tube radius or in distribution of the electrokinetic slip boundary
condition. Moreover, converging/diverging nature of the mean tube radius plays
a crucial role on the fluid transport. For the benefit of readers, along with
the original contribution, some applications of external electrical stimulation
(ES) in the human body and HS slip velocity, studied in the past by previous
researchers have been discussed in the paper.


  This paper investigates the robust stability and stabilization analysis of
interval fractional-order systems with time-varying delay. The stability
problem of such systems is solved first, and then using the proposed results a
stabilization theorem is also included, where sufficient conditions are
obtained for designing a stabilizing controller with a predetermined order,
which can be chosen to be as low as possible. Utilizing efficient lemmas, the
stability and stabilization theorems are proposed in the form of LMIs, which is
more suitable to check due to various existing efficient convex optimization
parsers and solvers. Finally, two numerical examples have shown the
effectiveness of our results.


  We consider the single photon transistor in coupled cavity system of
resonators interacting with multilevel superconducting artificial atom
simultaneously. Effective single mode transformation is used for the
diagonalization of the the hamiltonian and impedance matching in terms of the
normal modes. Storage and transmission of the incident field are described by
the interactions between the cavities controlling the atomic transitions of
lowest lying states. Rabi splitting of vacuum induced multiphoton transitions
is considered in input/output relations by the quadrature operators in the
absence of the input field. Second order coherence functions are employed to
investigate the photon blockade and localization-delocalization transitions of
cavity fields in oscillating regime of photon states described by the the
population imbalance. Refection and transmission of cavity output fields are
investigated in the presence of the multilevel transitions. Accumulation and
firing of the reflected and transmitted fields are used to investigate the
synchronization of the bunching spike train of transmitted field and population
imbalance of cavity fields. In the presence of single photon gate field, gain
enhancement is explained for transmitted regime.


  This work presents the application of a recently developed parametric,
non-intrusive, and multi-fidelity reduced-order modeling method on
high-dimensional displacement and stress fields arising from the structural
analysis of geometries that differ in the size of discretization and structural
topology.The proposed approach leverages manifold alignment to fuse
inconsistent field outputs from high- and low-fidelity simulations by
individually projecting their solution onto a common subspace. The
effectiveness of the method is demonstrated on two multi-fidelity scenarios
involving the structural analysis of a benchmark wing geometry. Results show
that outputs from structural simulations using incompatible grids, or related
yet different topologies, are easily combined into a single predictive model,
thus eliminating the need for additional pre-processing of the data. The new
multi-fidelity reduced-order model achieves a relatively higher predictive
accuracy at a lower computational cost when compared to a single-fidelity
model.


  "We risk sliding down toward the standards where the validity of action is
decided by whether one can get away with it." (P. Doty)
  "We do not 'risk' sliding down toward such standards; we have reached them."
(S. Lang)
  This is an essay in which I try to express my fear about the establishment of
a culture of publishing, where no one is willing to take responsibility for the
correctness of mathematics, and readers finding mistakes in published proofs
are stamped as outcasts, because they are deemed to target the reputation of
authors and journals.


  It is expected that interferometric gravitational wave detectors such as LIGO
\cite{Barish99} will be eventually limited by fundamental noise sources like
shot noise and Brownian motion, as well as by seismic noise. In the
commissioning process, other technical noise sources (electronics noise,
alignment fluctuations) limit the sensitivity and are eliminated one by one. We
propose here a way to correlate the noise in the output of the gravitational
wave detector with other detector and environmental signals not through their
linear transfer functions (often unknown), but through their statistical
properties. This could prove useful for identifying the frequency bands
dominated by different noise sources in the final configuration, and also to
help the commissioning process.


  We present an almost complete classification of the parameterized complexity
of all operator fragments of the satisfiability problem in computation tree
logic CTL. The investigated parameterization is the sum of temporal depth and
structural pathwidth. The classification shows a dichotomy between W[1]-hard
and fixed-parameter tractable fragments. The only real operator fragment which
is confirmed to be in FPT is the fragment containing solely AX. Also we prove a
generalization of Courcelle's theorem to infinite signatures which will be used
to proof the FPT-membership case.


  R\'enyi divergence is related to R\'enyi entropy much like information
divergence (also called Kullback-Leibler divergence or relative entropy) is
related to Shannon's entropy, and comes up in many settings. It was introduced
by R\'enyi as a measure of information that satisfies almost the same axioms as
information divergence. We review the most important properties of R\'enyi
divergence, including its relation to some other distances. We show how R\'enyi
divergence appears when the theory of majorization is generalized from the
finite to the continuous setting. Finally, R\'enyi divergence plays a role in
analyzing the number of binary questions required to guess the values of a
sequence of random variables.


  In this paper, we design and implement an experiment aimed at testing the
level-k model of auctions. We begin by asking which (simple) environments can
best disentangle the level-k model from its leading rival, Bayes-Nash
equilibrium. We find two environments that are particularly suited to this
purpose: an all-pay auction with uniformly distributed values, and a
first-price auction with the possibility of cancelled bids. We then implement
both of these environments in a virtual laboratory in order to see which theory
can best explain observed bidding behaviour. We find that, when plausibly
calibrated, the level-k model substantially under-predicts the observed bids
and is clearly out-performed by equilibrium. Moreover, attempting to fit the
level-k model to the observed data results in implausibly high estimated
levels, which in turn bear no relation to the levels inferred from a game known
to trigger level-k reasoning. Finally, subjects almost never appeal to iterated
reasoning when asked to explain how they bid. Overall, these findings suggest
that, despite its notable success in predicting behaviour in other strategic
settings, the level-k model (and its close cousin cognitive hierarchy) cannot
explain behaviour in auctions.


  We present a nonperturbative analysis of the top quark propagator using the
Schwinger Dyson equation in the ladder approximation including both the
electroweak as well as the infrared QCD effects.
  We find that the infrared effects are negligible only for top mass larger
than about 250 GeV.


  We study a Haldane model with nearest neighbor interactions. We find
one-dimensional like collective modes arising due to the interplay of
pseudo-spin and valley degrees of freedom. In the large band gap or moderate
interaction limit, these excitations are low energy modes lying in the band
gap. The dispersion relations are qualitatively different in trivial insulator
phase and Chern insulator phase, thus can be used to identify the topology of
the Haldane model with the bulk property. We also discuss how to detect these
modes in cold atom systems. An abelian gauge theory will emerge when a physical
current-current interaction is introduced to the Haldane model or the Kane-Mele
model.


  Consider the dynamics of a two-qubit entangled system in the decoherence
environment, we investigate the stability of pairwise entanglement under
decoherence. We find that for different decoherence models, there exist some
special class of entangled states of which the pairwise entanglement is the
most stable. The lifetime of the entanglement in these states is larger than
other states with the same initial entanglement. In addition, we also
investigate the dynamics of pairwise entanglement in the ground state of spin
models such as Heisenberg and XXY models.


  The system size dependence of dihadron azimuthal correlations in
ultra-relativistic heavy ion collision is simulated by a multi-phase transport
model. The structure of correlation functions and yields of associated
particles show clear participant path-length dependences in collision systems
with a partonic phase. The splitting parameter ($D$) and Root Mean Square Width
($\Delta \phi_{rms}$) of away side correlation functions increase with
collision system size from $^{14}$N+$^{14}$N to $^{197}$Au+$^{197}$Au
collisions. The double-peak structure of away side correlation functions can
only be formed in sufficient "large" collision systems. These properties
provide some hints to study onset of deconfinement, which is related to the QCD
phase boundary and QCD critical point, by an energy-size scan.


  Formal definitions of quantities, quantity spaces, dimensions and dimension
groups are introduced. Based on these concepts, a theoretical framework and a
practical algorithm for dimensional analysis are developed, and examples of
dimensional analysis are given.


  Directly imaged planets are self-luminous companions of pre-main sequence and
young main sequence stars. They reside in wider orbits
($\sim10\mathrm{s}-1000\mathrm{s}$~AU) and generally are more massive compared
to the close-in ($\lesssim 10$~AU) planets. Determining the host star
properties of these outstretched planetary systems is important to understand
and discern various planet formation and evolution scenarios. We present the
stellar parameters and metallicity ([Fe/H]) for a subsample of 18 stars known
to host planets discovered by the direct imaging technique. We retrieved the
high-resolution spectra for these stars from public archives and used the
synthetic spectral fitting technique and Bayesian analysis to determine the
stellar properties in a uniform and consistent way. For eight sources, the
metallicities are reported for the first time, while the results are consistent
with the previous estimates for the other sources. Our analysis shows that
metallicities of stars hosting directly imaged planets are close to solar with
a mean [Fe/H] = $-0.04\pm0.27$~dex. The large scatter in metallicity suggests
that a metal-rich environment may not be necessary to form massive planets at
large orbital distances. We also find that the planet mass-host star
metallicity relation for the directly imaged massive planets in wide-orbits is
very similar to that found for the well studied population of short period
($\lesssim 1$~yr) super-Jupiters and brown-dwarfs around main-sequence stars.


  We introduce and study a new 3d Topological Field Theory which can be
associated to any compact real manifold X. This TFT is analogous to the 2d
A-model and reduces to it upon compactification on an interval with suitable
boundary conditions. It plays a role in 3d mirror symmetry as well as in the
physical approach to the geometric Langlands duality. A similar TFT can be
defined in four dimensions.


  The inclusive Higgs boson production cross-section is measured in the
di-photon and the $ZZ^* \to 4 \ell$ decay channels using 31.4 and 29.0
fb$^{-1}$ of $pp$ collision data respectively, collected with the ATLAS
detector at a centre-of-mass energy of $\sqrt{s}=13.6$ TeV. To reduce the model
dependence, the measurement in each channel is restricted to a particle-level
phase space that closely matches the channel's detector-level kinematic
selection, and it is corrected for detector effects. These measured fiducial
cross-sections are $\sigma_{\mathrm{fid},\gamma \gamma} = 76^{+14}_{-13}$ fb,
and $\sigma_{\mathrm{fid},4 \ell} = 2.80 \pm 0.74$ fb, in agreement with the
corresponding Standard Model predictions of $67.6 \pm 3.7 $ fb and $3.67 \pm
0.19 $ fb. Assuming Standard Model acceptances and branching fractions for the
two channels, the fiducial measurements are extrapolated to the full phase
space yielding total cross-sections of $\sigma(pp \to H) = 67^{+12}_{-11}$ pb
and $46 \pm 12$ pb at $13.6$ TeV from the di-photon and $ZZ^* \to 4 \ell$
measurements respectively. The two measurements are combined into a total
cross-section measurement of $\sigma(pp \to H)= 58.2 \pm 8.7$ pb, to be
compared with the Standard Model prediction of $\sigma(pp \to H)_\mathrm{SM} =
59.9 \pm 2.6 $ pb.


  Kaon photoproduction on the nucleon has been investigated in the isobar
(Feynman) and Regge frameworks. Two possible combinations of the theories are
discussed. Results are compared with present experimental data.


  When $n$ is odd, a cohomology of type Hochschild for $n$-ary partially
associative algebras has been defined in Gnedbaye's thesis. Unfortunately, the
cohomology definition is not valid when $n$ is even. This fact is found again
in the computations of the $n$-ary partially associative free algebra.
  In this work, we define in a first time two approachs of an Hochschild
cohomology for $n$-ary partially associative algebras. First by reducing the
space of cochains, secondly by using a graded version. Next we compute the free
$n$-ary algebra, giving a basis of this algebra. At last we extend the notion
of coalgebras to $n$-ary algebras.


  Many interesting phenomena in nature are described by stochastic processes
with irreversible dynamics. To model these phenomena, we focus on a master
equation or a Fokker-Planck equation with rates which violate detailed balance.
When the system settles in a stationary state, it will be a nonequilibrium
steady state (NESS), with time independent probability distribution as well as
persistent probability current loops. The observable consequences of the latter
are explored. In particular, cyclic behavior of some form must be present: some
are prominent and manifest, while others are more obscure and subtle. We
present a theoretical framework to analyze such properties, introducing the
notion of "probability angular momentum" and its distribution. Using several
examples, we illustrate the manifest and subtle categories and how best to
distinguish between them. These techniques can be applied to reveal the NESS
nature of a wide range of systems in a large variety of areas. We illustrate
with one application: variability of ocean heat content in our climate system.


  This note applies Variable Zo technology to the design of an Ultra Wideband
(UWB) Yagi-Uda array optimized using Central Force Optimization. Variable Zo is
a novel and proprietary approach to antenna design and optimization that treats
the feed system characteristic impedance, Zo, as a design variable instead of a
fixed design parameter as is traditionally done. Variable Zo is applicable to
any antenna design or optimization methodology, and using it will generally
produce better antenna designs across any user-specified set of performance
objectives.


  In this paper, we are going to discuss several approaches to solve the
quadratic and linear simplicity constraints in the context of the canonical
formulations of higher dimensional General Relativity and Supergravity
developed in our companion papers. Since the canonical quadratic simplicity
constraint operators have been shown to be anomalous in any dimension D>2,
non-standard methods have to be employed to avoid inconsistencies in the
quantum theory. We show that one can choose a subset of quadratic simplicity
constraint operators which are non-anomalous among themselves and allow for a
natural unitary map of the spin networks in the kernel of these simplicity
constraint operators to the SU(2)-based Ashtekar-Lewandowski Hilbert space in
D=3. The linear constraint operators on the other hand are non-anomalous by
themselves, however their solution space will be shown to differ in D=3 from
the expected Ashtekar-Lewandowski Hilbert space. We comment on possible
strategies to make a connection to the quadratic theory. Also, we comment on
the relation of our proposals to existing work in the spin foam literature and
how these works could be used in the canonical theory. We emphasise that many
ideas developed in this paper are certainly incomplete and should be considered
as suggestions for possible starting points for more satisfactory treatments in
the future.


  We observe the occurrence of an Efros-Shklovskii gap in (Ga,Mn)As based
tunnel junctions. The occurrence of the gap is controlled by the extent of the
hole wave-function on the Mn acceptor atoms. Using k.p-type calculations we
show that this extent depends crucially on the direction of the magnetization
in the (Ga,Mn)As (which has two almost equivalent easy axes). This implies one
can reversibly tune the system into the insulating or metallic state by
changing the magnetization.


  Stereo depth estimation is used for many computer vision applications. Though
many popular methods strive solely for depth quality, for real-time mobile
applications (e.g. prosthetic glasses or micro-UAVs), speed and power
efficiency are equally, if not more, important. Many real-world systems rely on
Semi-Global Matching (SGM) to achieve a good accuracy vs. speed balance, but
power efficiency is hard to achieve with conventional hardware, making the use
of embedded devices such as FPGAs attractive for low-power applications.
However, the full SGM algorithm is ill-suited to deployment on FPGAs, and so
most FPGA variants of it are partial, at the expense of accuracy. In a non-FPGA
context, the accuracy of SGM has been improved by More Global Matching (MGM),
which also helps tackle the streaking artifacts that afflict SGM. In this
paper, we propose a novel, resource-efficient method that is inspired by MGM's
techniques for improving depth quality, but which can be implemented to run in
real time on a low-power FPGA. Through evaluation on multiple datasets (KITTI
and Middlebury), we show that in comparison to other real-time capable stereo
approaches, we can achieve a state-of-the-art balance between accuracy, power
efficiency and speed, making our approach highly desirable for use in real-time
systems with limited power.


  We present CineMPC, an algorithm to autonomously control a UAV-borne video
camera in a nonlinear Model Predicted Control (MPC) loop. CineMPC controls both
the position and orientation of the camera -- the camera extrinsics -- as well
as the lens focal length, focal distance, and aperture -- the camera
intrinsics. While some existing solutions autonomously control the position and
orientation of the camera, no existing solutions also control the intrinsic
parameters, which are essential tools for rich cinematographic expression. The
intrinsic parameters control the parts of the scene that are focused or
blurred, the viewers' perception of depth in the scene and the position of the
targets in the image. CineMPC closes the loop from camera images to UAV
trajectory and lens parameters in order to follow the desired relative
trajectory and image composition as the targets move through the scene.
  Experiments using a photo-realistic environment demonstrate the capabilities
of the proposed control framework to successfully achieve a full array of
cinematographic effects not possible without full camera control.


  Coherent manipulation of quantum bits (qubits) on time scales much shorter
than the coherence time is a key prerequisite for quantum information
processing. Electron spins in quantum dots (QDs) are particularly attractive
for implementations of qubits. Efficient optical methods for initialization and
readout of spins have been developed in recent years. Spin coherence times in
the microsecond range have been demonstrated, so that spin control by
picosecond optical pulses would be highly desirable. Then a large number of
spin rotations could be performed while coherence is maintained. A major
remaining challenge is demonstration of such rotations with high fidelity. Here
we use an ensemble of QD electron spins focused into a small number of
precession modes about a magnetic field by periodic optical pumping. We
demonstrate ultrafast optical rotations of spins about arbitrary axes on a
picosecond time scale using laser pulses as control fields.


  The nature and effects of the Goldstone mode in the ordered phase of helical
or chiral itinerant magnets such as MnSi are investigated theoretically. It is
shown that the Goldstone mode, or helimagnon, is a propagating mode with a
highly anisotropic dispersion relation, in analogy to the Goldstone mode in
chiral liquid crystals. Starting from a microscopic theory, a comprehensive
effective theory is developed that allows for an explicit description of the
helically ordered phase, including the helimagnons, for both classical and
quantum helimagnets. The directly observable dynamical spin susceptibility,
which reflects the properties of the helimagnon, is calculated.


  Let G = (V,E) be a finite, simple and undirected graph. For $S \subseteq V$,
let $\delta(S,G) = \{(u,v) \in E : u \in S \mbox {and} v \in V-S \}$ be the
edge boundary of $S$. Given an integer $i$, $1 \leq i \leq | V |$, let the edge
isoperimetric value of $G$ at $i$ be defined as $b_e(i,G) = \min_{S \subseteq
V; |S| = i} |\delta(S,G)|$. The edge isoperimetric peak of $G$ is defined as
$b_e(G)=\max_{1 \leq j \leq | V |} b_e(j,G)$. Let $b_v(G)$ denote the vertex
isoperimetric peak defined in a corresponding way. The problem of determining a
lower bound for the vertex isoperimetric peak in complete $t$-ary trees was
recently considered in \cite{OatYam}. In this paper we provide bounds which
improve those in \cite{OatYam}. We show that for a complete binary tree of
depth $d$ (denoted as $T_d^2$), $c_1d \leq b_e(T_d^2) \leq d$ and $c_2d \leq
b_v(T_d^2) \leq d$ where $c_1$, $c_2$ are constants. For a complete $t$-ary
tree of depth $d$ (denoted as $T_d^t$) and $d \geq c\log{t}$ where $c$ is a
constant, we show that $c_1\sqrt{t}d \leq b_e(T_d^t) \leq td$ and
$c_2\frac{d}{\sqrt{t}} \leq b_v(T_d^t) \leq d$ where $c_1$, $c_2$ are
constants. Our results are generalized to arbitrary(rooted) trees.


  Alloying offers a way to tune many of the properties of the transition metal
dichalcogenide (TMD) monolayers. While these systems in many cases have been
thoroughly investigated previously, the fundamental understanding of critical
temperatures, phase diagrams and band edge alignment is still incomplete. Based
on first principles calculations and alloy cluster expansions we compute the
phase diagrams 72 TMD monolayer alloys and classify the mixing behavior. We
show that ordered phases in general are absent at room temperature but that
there exists some alloys, which have a stable Janus phase at room temperature.
Furthermore, for a subset of these alloys, we quantify the band edge bowing and
show that the band edge positions for the mixing alloys can be continuously
tuned in the range set by the boundary phases.


  The fluctuation of the angular positions of reference extragalactic radio and
optical sources under the influence of the irregular gravitational field of
visible Galactic stars is considered. It is shown that these angular
fluctuations range from a few up to hundreds of microarcseconds. This leads to
a small rotation of the celestial reference frame. The nondiagonal coefficients
of the rotation matrix are of the order of a microarcsecond. The temporal
variation of these coefficients due to the proper motion of the foreground
stars is of the order of one microsecond per 20 years. Therefore, the celestial
reference frame can be considered inertial and homogeneous only to
microarcsecond accuracy. Astrometric catalogues with microarcsecond accuracy
will be unstable, and must be reestablished every 20 years.


  We resume former discussions of the conformally invariant wave equation on a
Schwarzschild background, with a particular focus on the behaviour of solutions
near the 'cylinder', i.e. Friedrich's representation of spacelike infinity.
This analysis can be considered a toy model for the behaviour of the full
Einstein equations and the resulting logarithmic singularities that appear to
be characteristic for massive spacetimes. The investigation of the Cauchy
problem for the conformally invariant wave equation (Frauendiener and Hennig
2018, Class. Quantum Grav. 35, 065015) showed that solutions generically
develop logarithmic singularities at infinitely many expansion orders at the
cylinder, but an arbitrary finite number of these singularities can be removed
by appropriately restricting the initial data prescribed at $t=0$. From a
physical point of view, any data at $t=0$ are determined from the earlier
history of the system and hence not exactly 'free data'. Therefore, it is
appropriate to ask what happens if we 'go further back in time' and prescribe
initial data as early as possible, namely at a portion of past null infinity,
and on a second past null hypersurface to complete the initial value problem.
Will regular data at past null infinity automatically lead to a regular
evolution up to future null infinity? Or does past regularity restrict the
solutions too much, and regularity at both null infinities is mutually
exclusive? Or do we still have suitable degrees of freedom for the data that
can be chosen to influence regularity of the solutions to any desired degree?
In order to answer these questions, we study the corresponding characteristic
initial value problem. In particular, we investigate in detail the appearance
of singularities at expansion orders $n=0,\dots,4$ for angular modes
$\ell=0,\dots,4$.


  Despite the rising popularity of automated visualization tools, existing
systems tend to provide direct results which do not always fit the input data
or meet visualization requirements. Therefore, additional specification
adjustments are still required in real-world use cases. However, manual
adjustments are difficult since most users do not necessarily possess adequate
skills or visualization knowledge. Even experienced users might create
imperfect visualizations that involve chart construction errors. We present a
framework, VizLinter, to help users detect flaws and rectify already-built but
defective visualizations. The framework consists of two components, (1) a
visualization linter, which applies well-recognized principles to inspect the
legitimacy of rendered visualizations, and (2) a visualization fixer, which
automatically corrects the detected violations according to the linter. We
implement the framework into an online editor prototype based on Vega-Lite
specifications. To further evaluate the system, we conduct an in-lab user
study. The results prove its effectiveness and efficiency in identifying and
fixing errors for data visualizations.


  Fix an infinite field $k$ of characteristic $p$, and let $\g$ be the
Kac-Moody algebra $\mathfrak{sl}_{\infty}$ if $p=0$ and $\hat{\mathfrak{sl}}_p$
otherwise. Let $\PP$ denote the category of strict polynomial functors defined
over $k$. We describe a $\g$-action on $\PP$ (in the sense of Chuang and
Rouquier) categorifying the Fock space representation of $\g$.


  We study the blow-up question for the diffusion equation involving a nonlocal
derivative in time defined by convolution with a nonnegative and nonincreasing
kernel, and a nonlocal operator in space driven by a nonnegative radial L\'evy
kernel. We show that the existence of solutions that blow up in finite time or
exist globally depends only on the behaviour of the spatial kernel at infinity.
A main difficulty of the work stems from estimating the fundamental pair
defining the solution through a Duhamel formula, due to the generality of the
setting, which includes singular or not, at the origin, spatial kernels, that
can be either positive or compactly supported.
  As a byproduct we obtain that the Fujita exponent for the fractional type
operators similar to the Caputo fractional derivative and the fractional
Laplacian.


  We propose an approach to study the ground state of quantum many-body systems
in which Tensor Network States (TNS), specifically Projected Entangled Pair
States (PEPS), and Green's function Monte Carlo (GFMC) are combined. PEPS, by
design, encode the area law which governs the scaling of entanglement entropy
in quantum systems with short range interactions but are hindered by the high
computational complexity scaling with bond dimension (D). GFMC is a highly
efficient method, but it usually suffers from the infamous negative sign
problem which can be avoided by the fixed node approximation in which a guiding
wave function is utilized to modify the sampling process. The trade-off for the
absence of negative sign problem is the introduction of systematic error by
guiding wave function. In this work, we combine these two methods, PEPS and
GFMC, to take advantage of both of them. PEPS are very accurate variational
wave functions, while at the same time, only contractions of single-layer
tensor network are necessary in GFMC, which reduces the cost substantially.
Moreover, energy obtained in GFMC is guaranteed to be variational and lower
than the variational energy of the guiding PEPS wave function. Benchmark
results of $J_1$-$J_2$ Heisenberg model on square lattice are provided.


  The combination of the surface science techniques (STM, XPS, ARPES) and
density-functional theory calculations was used to study the decoupling of
graphene from Ni(111) by oxygen intercalation. The formation of the
antiferromagnetic (AFM) NiO layer at the interface between graphene and
ferromagnetic (FM) Ni is found, where graphene protects the underlying AFM/FM
sandwich system. It is found that graphene is fully decoupled in this system
and strongly $p$-doped via charge transfer with a position of the Dirac point
of $(0.69\pm0.02)$ eV above the Fermi level. Our theoretical analysis confirms
all experimental findings, addressing also the interface properties between
graphene and AFM NiO.


  In this paper, a branching process model of the Northern Spotted Owl is
simulated. We focus on the time until extinction. It is shown how an
approximation of the model with a multivariate autoregressive process works
well near the equilibrium, but does not give a good estimate of the time until
extinction. We also show that introduction of randomness in some of the
parameters previously assumed to be constants shortens the time until
extinction considerably.


  Objective - Shear wave elastography has enriched ultrasound medical imaging
with quantitative measurements of tissue stiffness. However, this method still
suffers from some limitations due to viscoelasticity, guiding geometry or
static deformations.
  Approach - To explore these limitations, a nearly-incompressible soft
elastomer strip is chosen to mimic the mechanical behavior of an elongated
tissue. A supersonic shear wave scanner measures the propagation of shear waves
within the strip. By repeating the experiment on the same sample for different
orientations and static strains, the scanner estimates the shear wave velocity
in a wide range from 2 to 6 m/s.
  Main results - The effect of waveguiding is highlighted and the
spatio-temporal Fourier transform of the raw data provides dispersion diagrams.
We provide a theoretical model that accounts for the static deformation and
allows the extraction of the mechanical parameters of the sample, including its
rheology and hyperelastic behavior.
  Significance - To overcome some limitations of current elastography, we
propose a method that would allow the simultaneous characterization of the
viscoelastic and hyperelastic properties of soft tissues, paving the way for
robust quantitative elastography of elongated tissues.


  An effective and efficient encoding of the source code of a computer program
is critical to the success of sequence-to-sequence deep neural network models
for tasks in computer program comprehension, such as automated code
summarization and documentation. A significant challenge is to find a
sequential representation that captures the structural/syntactic information in
a computer program and facilitates the training of the learning models.
  In this paper, we propose to use the Pr\"ufer sequence of the Abstract Syntax
Tree (AST) of a computer program to design a sequential representation scheme
that preserves the structural information in an AST. Our representation makes
it possible to develop deep-learning models in which signals carried by lexical
tokens in the training examples can be exploited automatically and selectively
based on their syntactic role and importance. Unlike other recently-proposed
approaches, our representation is concise and lossless in terms of the
structural information of the AST. Empirical studies on real-world benchmark
datasets, using a sequence-to-sequence learning model we designed for code
summarization, show that our Pr\"ufer-sequence-based representation is indeed
highly effective and efficient, outperforming significantly all the
recently-proposed deep-learning models we used as the baseline models.


  We count the number of isogeny classes of Edwards curves over finite fields,
answering a question recently posed by Rezaeian and Shparlinski. We also show
that each isogeny class contains a {\em complete} Edwards curve, and that an
Edwards curve is isogenous to an {\em original} Edwards curve over $\F_q$ if
and only if its group order is divisible by 8 if $q \equiv -1 \pmod{4}$, and 16
if $q \equiv 1 \pmod{4}$. Furthermore, we give formulae for the proportion of
$d \in \F_q \setminus \{0,1\}$ for which the Edwards curve $E_d$ is complete or
original, relative to the total number of $d$ in each isogeny class.


  Polymer gels behave as soft viscoelastic solids and exhibit a generic
nonlinear mechanical response characterized by pronounced stiffening prior to
irreversible failure, most often through macroscopic fractures. Here, we aim at
capturing the latter scenario for a protein gel using a nonlinear integral
constitutive equation built upon ($i$) the linear viscoelastic response of the
gel, here well described by a power-law relaxation modulus, and ($ii$) the
nonlinear viscoelastic properties of the gel, encoded into a "damping
function". Such formalism predicts quantitatively the gel mechanical response
to a shear start-up experiment, up to the onset of macroscopic failure.
Moreover, as the gel failure involves the irreversible growth of macroscopic
cracks, we couple the latter stress response with Bailey's durability criterion
for brittle solids in order to predict the critical values of the stress
$\sigma_c$ and strain $\gamma_c$ at the failure point, and how they scale with
the applied shear rate. The excellent agreement between theory and experiments
suggests that the crack growth in this soft viscoelastic gel is a Markovian
process, and that Baileys' criterion extends well beyond hard materials such as
metals, glasses, or minerals.


  The linear boundary value problem under consideration describes time-harmonic
motion of water in a horizontal three-dimensional layer of constant depth in
the presence of an obstacle adjacent to the upper side of the layer (floating
body). This problem for a complex-valued harmonic function involves mixed
boundary conditions and a radiation condition at infinity. Under rather general
geometric assumptions the existence of a unique solution is proved for all
values of the nonnegative problem's parameter related to the frequency of
oscillations. The proof is based on the representation of solution as a sum of
simple- and double-layer potentials with densities distributed over the
obstacle's surface, thus reducing the problem to an indefinite
integro-differential equation. The latter is shown to be soluble for all
continuous right-hand side terms for which purpose S.~G. Krein's theorem about
indefinite equations is used.


  In this paper, we study least-squares finite element methods (LSFEM) for
general second-order elliptic equations with nonconforming finite element
approximations. The equation may be indefinite. For the two-field
potential-flux div LSFEM with Crouzeix-Raviart (CR) element approximation, we
present three proofs of the discrete solvability under the condition that mesh
size is small enough. One of the proof is based on the coerciveness of the
original bilinear form. The other two are based on the minimal assumption of
the uniqueness of the solution of the second-order elliptic equation. A
counterexample shows that div least-squares functional does not have norm
equivalence in the sum space of $H^1$ and CR finite element spaces. Thus it
cannot be used as an a posteriori error estimator. Several versions of reliable
and efficient error estimators are proposed for the method. We also propose a
three-filed potential-flux-intensity div-curl least-squares method with general
nonconforming finite element approximations. The norm equivalence in the
abstract nonconforming piecewise $H^1$-space is established for the three-filed
formulation on the minimal assumption of the uniqueness of the solution of the
second-order elliptic equation. The three-filed div-curl nonconforming
formulation thus has no restriction on the mesh size, and the least-squares
functional can be used as the built-in a posteriori error estimator. Under some
restrictive conditions, we also discuss a potential-flux div-curl least-squares
method.


  Recent work by Pringle and by Maloney, Begelman & Pringle has shown that
geometrically thin, optically thick, accretion disks are unstable to warping
driven by radiation torque from the central source. In this paper we generalize
the study of radiation-driven warping to include general power-law surface
density distributions, $\Sigma\propto R^{-\delta}$. We consider the range
$\delta=3/2$ (isothermal disks) to $\delta=-3/2$, which corresponds to a
radiation-pressure-supported disk; this spans the range of surface density
distributions likely to be found in real astrophysical disks. There is a
critical minimum size for unstable disks. The critical radius and the
steady-state precession rate depend only weakly on $\delta$. The case
$\delta=1$ divides the solutions into two qualitatively different regimes.
Nonlinear effects must be important if the warp extends to the disk inner edge
for $\delta \ge 1$, but for $\delta < 1$ nonlinearity will be important only if
the warp amplitude is large at the origin. The effects of shadowing of the
central source by the warp will thus be very different in the two regimes of
$\delta.$ In real accretion disks the outer boundary condition is likely to be
different from the zero-crossing condition that we have assumed. In accretion
disks around massive black holes in active galactic nuclei, the disk will
probably become optically thin before the outer disk boundary is reached, while
in X-ray binaries, there will be an outer disk region (outside the
circularization radius) in which the inflow velocity is zero but angular
momentum is still transported. We show that in both these cases the solutions
are similar to the zero-crossing eigenfunctions.


  Using decays to $\phi$-meson pairs, the inclusive production of charmonium
states in $b$-hadron decays is studied with $pp$ collision data corresponding
to an integrated luminosity of $3.0fb^{-1}$, collected by the LHCb experiment
at centre-of-mass energies of 7 and 8 TeV. Denoting by $B_C\equiv B(b\to
CX)\times B(C\to\phi\phi)$ the inclusive branching fraction of a $b$ hadron to
a charmonium state $C$ that decays into a pair of $\phi$ mesons, ratios
$R^{C1}_{C2}\equiv B_{C1}/B_{C2}$ are determined as
$R^{\chi_{c0}}_{\eta_c(1S)}=0.147\pm0.023\pm0.011$, $R^{\chi_{c1}}_{\eta_c
(1S)}=0.073\pm0.016\pm0.006$, $R^{\chi_{c2}}_{\eta_c
(1S)}=0.081\pm0.013\pm0.005$, $R^{\chi_{c1}}_{\chi_{c0}}=0.50\pm0.11\pm0.01$,
$R^{\chi_{c2}}_{\chi_{c0}}=0.56\pm0.10\pm0.01$ and $R^{\eta_c
(2S)}_{\eta_c(1S)}=0.040\pm0.011\pm0.004$. Here and below the first
uncertainties are statistical and the second systematic. Upper limits at $90\%$
confidence level for the inclusive production of $X(3872)$, $X(3915)$ and
$\chi_{c2}(2P)$ states are obtained as $R^{X(3872)}_{\chi_{c1}}<0.34$,
$R^{X(3915)}_{\chi_{c0}}<0.12$ and $R^{\chi_{c2}(2P)}_{\chi_{c2}}<0.16$.
Differential cross-sections as a function of transverse momentum are measured
for the $\eta_c(1S)$ and $\chi_c$ states. The branching fraction of the decay
$B_s^0\rightarrow\phi\phi\phi$ is measured for the first time,
$B(B_s^0\to\phi\phi\phi)=(2.15\pm0.54\pm0.28\pm0.21_{B})\times 10^{-6}$. Here
the third uncertainty is due to the branching fraction of the decay
$B_s^0\to\phi\phi$, which is used for normalization. No evidence for
intermediate resonances is seen. A preferentially transverse $\phi$
polarization is observed. The measurements allow the determination of the ratio
of the branching fractions for the $\eta_c(1S)$ decays to $\phi\phi$ and
$p\bar{p}$ as $B(\eta_c(1S)\to\phi\phi)/B(\eta_c(1S)\to
p\bar{p})=1.79\pm0.14\pm0.32$.