  We deal with a general preferential attachment graph model with multiple type
edges. The types are chosen randomly, in a way that depends on the evolution of
the graph. In the $N$-type case, we define the (generalized) degree of a given
vertex as $\boldsymbol{d}=(d_{1},d_{2},\dots,d_{N})$, where
$d_{k}\in\mathbb{Z}_{0}^{+}$ is the number of type $k$ edges connected to it.
We prove the existence of an a.s.\ asymptotic degree distribution for a general
family of preferential attachment random graph models with multi-type edges.
More precisely, we show that the proportion of vertices with (generalized)
degree $\boldsymbol{d}$ tends to some random variable as the number of steps
goes to infinity. We also provide recurrence equations for the asymptotic
degree distribution. Finally, we generalize the scale-free property of random
graphs to the multi-type case.


  We examine effects of the Generalized Uncertainty Principle, predicted by
various theories of quantum gravity to replace the Heisenberg's uncertainty
principle near the Planck scale, on post inflation preheating in cosmology, and
show that it can predict either an increase or a decrease in parametric
resonance and a corresponding change in particle production. Possible
implications are considered.


  We introduce the first passage set (FPS) of constant level $-a$ of the
two-dimensional continuum Gaussian free field (GFF) on finitely connected
domains. Informally, it is the set of points in the domain that can be
connected to the boundary by a path on which the GFF does not go below $-a$. It
is, thus, the two-dimensional analogue of the first hitting time of $-a$ by a
one-dimensional Brownian motion. We provide an axiomatic characterization of
the FPS, a continuum construction using level lines, and study its properties:
it is a fractal set of zero Lebesgue measure and Minkowski dimension 2 that is
coupled with the GFF $\Phi$ as a local set $A$ so that $\Phi+a$ restricted to
$A$ is a positive measure. One of the highlights of this paper is identifying
this measure as a Minkowski content measure in the non-integer gauge $r \mapsto
\vert\log(r)\vert^{1/2}r^{2}$, by using Gaussian multiplicative chaos theory.


  We extract the charm quark mass and the strong coupling constant from the
charmonium current correlators calculated with $n_f = 2 + 1$ Mobius domain wall
fermions. We match our lattice calculation for the temporal moments of the
correlator with perturbative result known up to four-loop order, and extract
the charm quark mass with uncertainty less than 1%. Using the temporal moments,
we also confirm the correlators in the vector channel to be consistent with the
experimental data for the R-ratio. We used the ensembles generated by the JLQCD
collaboration at lattice spacings $a$ = 0.080 fm, 0.055 fm and 0.044 fm.


  We describe the multifractal nature of random weak Gibbs measures on some
class of attractors associated with $C^1$ random dynamics semi-conjugate to a
random subshift of finite type. This includes the validity of the multifractal
formalism, the calculation of Hausdorff and packing dimensions of the so-called
level sets of divergent points, and a $0$-$\infty$ law for the Hausdorff and
packing measures of the level sets of the local dimension.


  A matroid is a notion of independence in combinatorial optimization which is
closely related to computational efficiency. In particular, it is well known
that the maximum of a constrained modular function can be found greedily if and
only if the constraints are associated with a matroid. In this paper, we bring
together the ideas of bandits and matroids, and propose a new class of
combinatorial bandits, matroid bandits. The objective in these problems is to
learn how to maximize a modular function on a matroid. This function is
stochastic and initially unknown. We propose a practical algorithm for solving
our problem, Optimistic Matroid Maximization (OMM); and prove two upper bounds,
gap-dependent and gap-free, on its regret. Both bounds are sublinear in time
and at most linear in all other quantities of interest. The gap-dependent upper
bound is tight and we prove a matching lower bound on a partition matroid
bandit. Finally, we evaluate our method on three real-world problems and show
that it is practical.


  The Baryon Acoustic Oscillation (BAO) feature in the power spectrum of
galaxies can be used as a standard ruler to probe the accelerated expansion of
the Universe. In this paper, we study several galaxy selection schemes aiming
at building an emission-line galaxy (ELG) sample in the redshift range $0.6 < z
< 1.7$, that would be suitable for future BAO studies using the Baryonic
Oscillation Spectroscopic Survey (BOSS) spectrograph on the Sloan Digital Sky
Survey (SDSS) telescope. We explore two different color selections using both
the SDSS and the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS)
photometry in the $u, g, r, i$ bands and evaluate their performance for
selecting bright ELG. This study confirms the feasibility of massive ELG
surveys using the BOSS spectrographs on the SDSS telescope for a BAO detection
at redshift $z\sim1$, in particular for the proposed eBOSS experiment.


  We investigate the scattered light properties of a Luneburg lens approximated
as a series of concentric shells with discrete refractive indices. The stepped
Luneburg lens has been previously modeled at microwave wavelengths with full
solutions for the electromagnetic field equations when the lens is of
comparable size to the wavelength. We investigate the properties of a Luneburg
lens at optical wavelengths using a geometric ray tracing technique. We develop
a stack-based ray tracing algorithm with the Python programming language that
tracks all reflected and refracted rays generated at each optical interface.
The code shows that a Luneburg lens with 40 steps and a refractive index
power-law exponent of 0.55 will produce images of nearly all naked eye (<6)
magnitude stars with an enclosed energy of 50% at a spatial resolution of 3.2
degrees. We find 72 cases of blended stars where a star with magnitude <6 falls
within 3 degrees of angular separation from a star with magnitude <1. The
optical stepped Luneburg lens has promising applications for low-cost,
continuous all-sky monitoring to obtain transit light curves of bright, nearby
stars.


  Recently, in-context learning (ICL) on large language models (LLMs) has
received great attention, and this technique can also be applied to
vision-language models (VLMs) built upon LLMs. These VLMs can respond to
queries by conditioning responses on a series of multimodal demonstrations,
which comprise images, queries, and answers. Though ICL has been extensively
studied on LLMs, its research on VLMs remains limited. The inclusion of
additional visual information in the demonstrations motivates the following
research questions: which of the two modalities in the demonstration is more
significant? How can we select effective multimodal demonstrations to enhance
ICL performance? This study investigates the significance of both visual and
language information. Our findings indicate that ICL in VLMs is predominantly
driven by the textual information in the demonstrations whereas the visual
information in the demonstrations barely affects the ICL performance.
Subsequently, we provide an understanding of the findings by analyzing the
model information flow and comparing model inner states given different ICL
settings. Motivated by our analysis, we propose a simple yet effective
approach, termed Mixed Modality In-Context Example Selection (MMICES), which
considers both visual and language modalities when selecting demonstrations and
shows better ICL performance. Extensive experiments are conducted to support
our findings, understanding, and improvement of the ICL performance of VLMs.


  Spin-orbit torques due to interfacial Rashba and spin Hall effects have been
widely considered as a potentially more efficient approach than the
conventional spin-transfer torque to control the magnetization of ferromagnets.
We report a comprehensive study of spin-orbit torque efficiency in
Ta(O)/Ni81Fe19 bilayers by tuning low-oxidation of \b{eta}-phase tantalum, and
find that the spin Hall angle {\theta}DL increases from ~ -0.18 of the pure
Ta/Py to the maximum value ~ -0.30 of Ta(O)/Py with 7.8% oxidation.
Furthermore, we distinguish the efficiency of the spin-orbit torque generated
by the bulk spin Hall effect and by interfacial Rashba effect, respectively,
via a series of Py/Cu(0-2 nm)/Ta(O) control experiments. The latter has more
than twofold enhancement, and even more significant than that of the former at
the optimum oxidation level. Our results indicate that 65% enhancement of the
efficiency should be related to the modulation of the interfacial Rashba-like
spin-orbit torque due to oxygen-induced orbital hybridization cross the
interface. Our results suggest that the modulation of interfacial coupling via
oxygen-induced orbital hybridization can be an alternative method to boost the
change-spin conversion rate.


  Pure dephasing of an exciton in a small quantum dot by optical and acoustic
phonons is calculated using the ``independent boson model''. Considering the
case of zero temperature the dephasing is shown to be only partial which
manifests itself in the polarization decaying to a finite value. Typical
dephasing times can be assigned even though the spectra exhibits strongly
non-Lorentzian line shapes. We show that the dephasing from LO phonon
scattering, occurs on a much larger time scale than that of dephasing due to
acoustic phonons which for low temperatures are also a more efficient dephasing
mechanism. The typical dephasing time is shown to strongly depend on the
quantum dot size whereas the electron phonon ``coupling strength'' and external
electric fields tend mostly to effect the residual coherence. The relevance of
the dephasing times for current quantum information processing implementation
schemes in quantum dots is discussed.


  We present spectro-polarimetric analysis of \thisgrb\ using data from \asat,
\fermi, and \swift, to provide insights into the physical mechanisms of the
prompt radiation and the jet geometry.
  Prompt emission from \thisgrb\ was very bright (fluence
$>10^{-4}$~ergs~cm$^{-2}$) and had a complex structure composed of the
superimposition of several pulses. The energy spectra deviate from the typical
Band function to show a low energy peak $\sim 15$~keV --- which we interpret as
a power-law with two breaks, with a synchrotron origin. Alternately, the prompt
spectra can also be interpreted as Comptonized emission, or a blackbody
combined with a Band function. Time-resolved analysis confirms the presence of
the low energy component, while the peak energy is found to be confined in the
range of 100--200~keV.
  Afterglow emission detected by \fermi-LAT is typical of an external shock
model, and we constrain the initial Lorentz factor using the peak time of the
emission. \swift-XRT measurements of the afterglow show an indication for a jet
break, allowing us to constrain the jet opening angle to $>$ 6$\degr$.
  Detection of a large number of Compton scattered events by \asat-CZTI
provides an opportunity to study hard X-ray polarization of the prompt
emission. We find that the burst has high, time-variable polarization, with the
emission {\bf have higher polarization} at energies above the peak energy.
  We discuss all observations in the context of GRB models and polarization
arising due to {\bf due to physical or geometric effects:} synchrotron emission
from multiple shocks with ordered or random magnetic fields, Poynting flux
dominated jet undergoing abrupt magnetic dissipation, sub-photospheric
dissipation, a jet consisting of fragmented fireballs, and the Comptonization
model.


  Let $X$ be a positive integer and $t$ a real number great than 1. The family
of sets $\left\{\big\lfloor\frac{X}{n^t}\big\rfloor ~:~ 1\leq n\leq X\right\}$
have an interesting prime distribution property. We give an exact formula for
the cardinality of these sets. We provide an estimate for the cardinality of
the set $\left\{\big\lfloor\frac{X}{p}\big\rfloor ~:~ p~ \text{prime},~ p\leq
X\right\}$. For positive real $X$, we derive asymptotic formulas for the
cardinality of the set $\big\{\lfloor f(n)\rfloor ~:~ 1\leq n\leq X\big\}$ for
various sets of functions.


  The magnetothermodynamics of strongly frustrated classical Heisenberg
antiferromagnets on kagome, garnet, and pyrochlore lattices is examined. The
field induced adiabatic temperature change (dT/dH)_S is significantly larger
for such systems compared to ordinary non-frustrated magnets and also exceeds
the cooling rate of an ideal paramagnet in a wide range of fields. An
enhancement of the magnetocaloric effect is related to presence of a
macroscopic number of soft modes in frustrated magnets below the saturation
field. Theoretical predictions are confirmed with extensive Monte Carlo
simulations.


  The paper bounds the number of tessellations with T-shaped vertices on a
fixed set of $k$ lines: tessellations are efficiently encoded, and algorithms
retrieve them, proving injectivity. This yields existence of a completely
random T-tessellation, as defined by Ki\^en Ki\^eu et al., and of its Gibbsian
modifications. The combinatorial bound is sharp, but likely pessimistic in
typical cases.


  Motivated by global warming issues, we consider a time se- ries that consists
of a nondecreasing trend observed with station- ary fluctuations, nonparametric
estimation of the trend under monotonicity assumption is considered. The
rescaled isotonic es- timators at an interior point are shown to converge to
Chernoff's distribution under minimal conditions on the stationary errors.
Since the isotonic estimators suffer from the spiking problem at the end point,
two modifications are proposed. The estima- tion errors for both estimators of
the boundary point are shown to have interesting limiting distributions.
Approximation accu- racies are assessed through simulations. One highlight of
our treatment is the proof of the weak convergence results which involve
several recent techniques developed in the study of con- ditional central limit
questions. These weak convergences can be shown to hold conditionally given the
starting values.


  We study radio and X-ray emissions from IMBHs and explore the unified model
for accretion and ejection processes. The radio band survey of IMBH (candidate)
hosted galaxies indicates that only a small fraction ($\sim$0.6\%) of them are
radio-band active. In addition, very long baseline interferometry observations
reveal parsec-scale radio emission of IMBHs, further resulting in a lower
fraction of actively ejecting objects (radio emission is produced by IMBHs
other than hosts), which is consistent with a long quiescent state in the
evolution cycle of IMBHs. Most (75\%, i.e., 3 out of 4 samples according to a
recent mini-survey) of the radio-emitting IMBHs are associated with radio
relics and there is also evidence of dual radio blobs from episodic ejecting
phases. Taking the radio emission and the corresponding core X-ray emission of
IMBH, we confirm a universal fundamental plane relation (FMP) of black hole
activity. Furthermore, state transitions can be inferred by comparing a few
cases in XRBs and IMBHs in FMP, i.e., both radio luminosity and emission
regions evolve along these state transitions. These signatures and evidence
suggest an analogy among all kinds of accretion systems which span from stellar
mass to supermassive black holes, hinting at unified accretion and ejection
physics. To validate the unified model, we explore the correlation between the
scale of outflows (corresponding to ejection powers) and the masses of central
engines; it shows that the largest scale of outflows $\hat{LS}_\mathrm{out}$
follows a power-law correlation with the masses of accretors $M_\mathrm{core}$,
i.e., $\log{\hat{LS}_\mathrm{out}} = (0.73\pm0.01)\log{M_\mathrm{core}} -
(3.34\pm0.10)$. In conclusion, this work provides evidence to support the claim
that the ejection (and accretion) process behaves as scale-invariant and their
power is regulated by the masses of accretors.


  Let $p\equiv 8\mod 9$ be a prime. In this paper we give a sufficient
condition such that at least one of $p$ and $p^2$ is the sum of two rational
cubes. This is the first general result on the $8$ case of the so-called
Sylvester conjecture.


  This paper proposes a novel neuronal current source localization method based
on Deep Prior that represents a more complicated prior distribution of current
source using convolutional networks. Deep Prior has been suggested as a means
of an unsupervised learning approach that does not require learning using
training data, and randomly-initialized neural networks are used to update a
source location using a single observation. In our previous work, a
Deep-Prior-based current source localization method in the brain has been
proposed but the performance was not almost the same as those of conventional
approaches, such as sLORETA. In order to improve the Deep-Prior-based approach,
in this paper, a depth weight of the current source is introduced for Deep
Prior, where depth weighting amounts to assigning more penalty to the
superficial currents. Its effectiveness is confirmed by experiments of current
source estimation on simulated MEG data.


  The surge of activity in the resolution of fine scale features in the field
of earth sciences over the past decade necessitates the development of robust
yet simple algorithms that can tackle the various drawbacks of in silico models
developed hitherto. One such drawback is that of the restrictive computational
cost of finite element method in rendering resolutions to the fine scale
features, while at the same time keeping the domain being modeled sufficiently
large. We propose the use of the augmented lagrangian method commonly used in
the treatment of hanging nodes in contact mechanics in tackling the drawback.
An interface is introduced in a typical finite element mesh across which an
aggressive coarsening of the finite elements is possible. The method is based
upon minimizing an augmented potential energy which factors in the constraint
that exists at the hanging nodes on that interface. This allows for a
significant reduction in the number of finite elements comprising the mesh with
concomitant reduction in the computational expense.


  The interpretation of nuclear electric dipole moment (EDM) experiments is
clouded by large theoretical uncertainties associated with nonperturbative
matrix elements. In various beyond-the-Standard Model scenarios nuclear and
diamagnetic atomic EDMs are expected to be dominated by CP-violating
pion-nucleon interactions that arise from quark chromo-electric dipole moments.
The corresponding CP-violating pion-nucleon coupling strengths are, however,
poorly known. In this work we propose a strategy to calculate these couplings
by using spectroscopic lattice QCD techniques. Instead of directly calculating
the pion-nucleon coupling constants, a challenging task, we use chiral symmetry
relations that link the pion-nucleon couplings to nucleon sigma terms and mass
splittings that are significantly easier to calculate. In this work, we show
that these relations are reliable up to next-to-next-to-leading order in the
chiral expansion in both SU(2) and SU(3) chiral perturbation theory. We
conclude with a brief discussion about practical details regarding the required
lattice QCD calculations and the phenomenological impact of an improved
understanding of CP-violating matrix elements.


  The quantum threshold theorem shows that a noisy quantum computer can
accurately and efficiently simulate any ideal quantum computation provided that
noise is weakly correlated and its strength is below a critical value known as
the quantum accuracy threshold. This thesis provides a simpler and more
transparent non-inductive proof of this theorem based on the concept of level
reduction. This concept is also used in proving the quantum threshold theorem
for coherent and leakage noise and for quantum computation by measurements. In
addition, the proof provides a methodology which allows us to establish
improved rigorous lower bounds on the value of the quantum accuracy threshold.


  Prokaryotic viruses, which infect bacteria and archaea, are key players in
microbial communities. Predicting the hosts of prokaryotic viruses helps
decipher the dynamic relationship between microbes. Experimental methods for
host prediction cannot keep pace with the fast accumulation of sequenced
phages. Thus, there is a need for computational host prediction. Despite some
promising results, computational host prediction remains a challenge because of
the limited known interactions and the sheer amount of sequenced phages by
high-throughput sequencing technologies. The state-of-the-art methods can only
achieve 43\% accuracy at the species level. In this work, we formulate host
prediction as link prediction in a knowledge graph that integrates multiple
protein and DNA-based sequence features. Our implementation named CHERRY can be
applied to predict hosts for newly discovered viruses and to identify viruses
infecting targeted bacteria. We demonstrated the utility of CHERRY for both
applications and compared its performance with 11 popular host prediction
methods. To our best knowledge, CHERRY has the highest accuracy in identifying
virus-prokaryote interactions. It outperforms all the existing methods at the
species level with an accuracy increase of 37\%. In addition, CHERRY's
performance on short contigs is more stable than other tools.


  This paper provides a framework in which multilevel Monte Carlo and
continuous level Monte Carlo can be compared. In continuous level Monte Carlo
the level of refinement is determined by an exponentially distributed random
variable, which therefore heavily influences the computational complexity. We
propose in this paper a variant of the algorithm, where the exponentially
distributed random variable is generated by a quasi Monte Carlo sequence,
resulting in a significant variance reduction. In the examples presented the
quasi continuous level Monte Carlo algorithm outperforms multilevel and
continuous level Monte Carlo by a clear margin.


  Fluid flows in coupled systems consisting of a free-flow region and the
adjacent porous medium appear in a variety of environmental settings and
industrial applications. In many applications, fluid flow is non-parallel to
the fluid-porous interface that requires a generalisation of the Beavers-Joseph
coupling condition typically used for the Stokes-Darcy problem. Generalised
coupling conditions valid for arbitrary flow directions to the interface are
recently derived using the theory of homogenisation and boundary layers. The
aim of this work is the mathematical analysis of the Stokes-Darcy problem with
these generalised interface conditions. We prove the existence and uniqueness
of the weak solution of the coupled problem. The well-posedness is guaranteed
under a suitable relationship between the permeability and the boundary layer
constants containing geometrical information about the porous medium and the
interface. We numerically study the validity of the obtained results for
realistic problems and provide a benchmark for numerical solution of the
Stokes-Darcy problem with generalised interface conditions.


  Israel-Stewart's causal theory of dissipative hydrodynamics, with the ADS/CFT
lower limit of shear viscosity to entropy ratio ($\eta/s$=0.08), give
consistent description of a number of experimental observables in Au+Au
collisions at RHIC (c.m. energy $\sqrt{s}$=200 GeV) \cite{Chaudhuri:2008sj}.
Assuming that in Pb+Pb collisions at LHC (c.m. energy $\sqrt{s}$=5.5 TeV),
except for the initial temperature, other parameters of the fluid remain
unchanged, we have predicted for the centrality dependence of multiplicity,
mean $p_T$, $p_T$-spectra, elliptic flow. The central temperature of the fluid
is adjusted to $T_i$=421 MeV such that in a Pb+Pb collision, with participant
number $N_{part}$=350, average charge particle multiplicity is $\sim$ 900 and
is consistent with the experimental trend observed at lower energies. Compare
to Au+Au collisions at RHIC, in Pb+Pb collisions at LHC, on the average,
particle multiplicity increases by a factor of $\sim$1.6, the mean $p_T$ is
increased by $\sim$10% only. The elliptic flow on the other hand decreases by
$\sim$15%.


  The multi-level algorithm allows, at least for pure gauge theories, reliable
measurement of exponentially small expectation values. The implementation of
the algorithm depends strongly on the observable one wants to measure. Here we
report measurement of glueball masses using the multi-level algorithm in 4
dimensional compact U(1) theory as a case study.


  We examine the use of the CMB's TE cross correlation power spectrum as a
complementary test to detect primordial gravitational waves (PGWs). The first
method used is based on the determination of the lowest multipole, $\ell_0$,
where the TE power spectrum, $C_{\ell}^{TE}$, first changes sign. The second
method uses Wiener filtering on the CMB TE data to remove the density
perturbations contribution to the TE power spectrum. In principle this leaves
only the contribution of PGWs. We examine two toy experiments (one ideal and
another more realistic) to see their ability to constrain PGWs using the TE
power spectrum alone. We found that an ideal experiment, one limited only by
cosmic variance, can detect PGWs with a ratio of tensor to scalar metric
perturbation power spectra $r=0.3$ at 99.9% confidence level using only the TE
correlation. This value is comparable with current constraints obtained by WMAP
based on the $2\sigma$ upper limits to the B-mode amplitude. We demonstrate
that to measure PGWs by their contribution to the TE cross correlation power
spectrum in a realistic ground based experiment when real instrumental noise is
taken into account, the tensor-to-scalar ratio, $r$, should be approximately
three times larger.


  Despite deep neural networks have demonstrated extraordinary power in various
applications, their superior performances are at expense of high storage and
computational costs. Consequently, the acceleration and compression of neural
networks have attracted much attention recently. Knowledge Transfer (KT), which
aims at training a smaller student network by transferring knowledge from a
larger teacher model, is one of the popular solutions. In this paper, we
propose a novel knowledge transfer method by treating it as a distribution
matching problem. Particularly, we match the distributions of neuron
selectivity patterns between teacher and student networks. To achieve this
goal, we devise a new KT loss function by minimizing the Maximum Mean
Discrepancy (MMD) metric between these distributions. Combined with the
original loss function, our method can significantly improve the performance of
student networks. We validate the effectiveness of our method across several
datasets, and further combine it with other KT methods to explore the best
possible results. Last but not least, we fine-tune the model to other tasks
such as object detection. The results are also encouraging, which confirm the
transferability of the learned features.


  Hirota's discrete KdV equation is an integrable partial difference equation
on $\mathbb{Z}^2$, which approaches the Korteweg-de Vries (KdV) equation in a
continuum limit. In this paper, we show that its multiplicative-discrete
versions have the special solutions given by the solutions of $q$-Painlev\'e
equations of types $A_J^{(1)}$ $(J=3,4,5,6)$.


  Refraction deflects photons that pass through atmospheres, which affects
transit light curves. Refraction thus provides an avenue to probe physical
properties of exoplanet atmospheres and to constrain the presence of clouds and
hazes. In addition, an effective surface can be imposed by refraction, thereby
limiting the pressure levels probed by transmission spectroscopy. The main
objective of the paper is to model the effects of refraction on photometric
light curves for realistic planets and to explore the dependencies on
atmospheric physical parameters. We also explore under which circumstances
transmission spectra are significantly affected by refraction. Finally, we
search for refraction signatures in photometric residuals in Kepler data. We
use the model of Hui & Seager (2002) to compute deflection angles and
refraction transit light curves, allowing us to explore the parameter space of
atmospheric properties. The observational search is performed by stacking large
samples of transit light curves from Kepler. We find that out-of-transit
refraction shoulders are the most easily observable features, which can reach
peak amplitudes of ~10 parts per million (ppm) for planets around Sun-like
stars. More typical amplitudes are a few ppm or less for Jovians and at the
sub-ppm level for super-Earths. Interestingly, the signal-to-noise ratio of any
refraction residuals for planets orbiting Sun-like hosts are expected to be
similar for planets orbiting red dwarfs. We also find that the maximum depth
probed by transmission spectroscopy is not limited by refraction for weakly
lensing planets, but that the incidence of refraction can vary significantly
for strongly lensing planets. We find no signs of refraction features in the
stacked Kepler light curves, which is in agreement with our model predictions.


  We investigate the ground state of interacting spin-$\half$ fermions (3D) at
a finite density ($\rho \sim \kf^3$) in the presence of a uniform non-Abelian
gauge field. The gauge field configuration (GFC) described by a vector $\blam
\equiv (\lambda_x, \lambda_y, \lambda_z)$, whose magnitude $\lambda$ determines
the gauge coupling strength, generates a generalized Rashba spin-orbit
interaction. For a weak attractive interaction in the singlet channel described
by a small negative scattering length $(\kf |\as| \lesssim 1)$, the ground
state in the absence of the gauge field ($\lambda=0$) is a BCS
(Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With
increasing gauge coupling strength, a non-Abelian gauge field engenders a
crossover of this BCS ground state to a BEC (Bose-Einstein condensate) ground
state of bosons even with a weak attractive interaction that fails to produce a
two-body bound state in free vacuum. For large gauge couplings $(\lambda/\kf
\gg 1)$, the BEC attained is a condensate of bosons whose properties are solely
determined by the gauge field (and not by the scattering length so long as it
is non-zero) -- we call these bosons "rashbons". In the absence of interactions
($\as = 0^-$), the shape of the Fermi surface of the system undergoes a
topological transition at a critical gauge coupling $\lambda_T$. For high
symmetry gauge field configurations we show that the crossover from the BCS
superfluid to the rashbon BEC occurs in the regime of $\lambda$ near
$\lambda_T$. In the context of cold atomic systems, this work makes an
interesting suggestion of obtaining
  BCS-BEC crossover through a route other than tuning the interaction between
the fermions.


  This is the extensive follow-up report of a recent Letter in which the
existence of self-organized criticality (SOC) in systems of interacting soft
gluons is proposed, and its consequences for inelastic diffractive scattering
processes are discussed. It is pointed out, that color-singlet gluon-clusters
can be formed in hadrons as a consequence of SOC in systems of interacting soft
gluons, and that the properties of such spatiotemporal complexities can be
probed experimentally by examing inelastic diffractive scattering. Theoretical
arguments and experimental evidences supporting the proposed picture are
presented --- together with the result of a systematic analysis of the existing
data for inelastic diffractive scattering processes performed at different
incident energies, and/or by using different beam-particles. It is shown in
particular that the size- and the lifetime-distributions of such gluon-clusters
can be directly extracted from the data, and the obtained results exhibit
universal power-law behaviors --- in accordance with the expected
SOC-fingerprints. As further consequences of SOC in systems of interacting soft
gluons, the $t$-dependence and the $(M_x^2/s)$-dependence of the double
differential cross-sections for inelastic diffractive scattering off
proton-target are discussed. Here $t$ stands for the four-momentum-transfer
squared, $M_x$ for the missing mass, and $\sqrt{s}$ for the total c.m.s.
energy. It is shown, that the space-time properties of the color-singlet
gluon-clusters due to SOC, discussed above, lead to simple analytical formulae
for $d^2\sigma/dt d(M_x^2/s)$ and for $d\sigma/dt$, and that the obtained
results are in good agreement with the existing data. Further experiments are
suggested.


  Longitudinal distributions of the photospheric magnetic field studied on the
base of National Solar Observatory (Kitt Peak) data (1976 - 2003) displayed two
opposite patterns during different parts of the 11-year solar cycle.
Heliolongitudinal distributions differed for the ascending phase and the
maximum of the solar cycle on one hand, and for the descending phase and the
minimum on the other, depicting maxima around two opposite Carrington
longitudes (180 deg. and 0/360 deg.). Thus the maximum of the distribution
shifted its position by 180 deg. with the transition from one characteristic
period to the other. Two characteristic periods correspond to different
situations occurring in the 22-year magnetic cycle of the Sun, in the course of
which both global magnetic field and the magnetic field of the leading sunspot
in a group change their sign. During the ascending phase and the maximum
(active longitude 180 deg.) polarities of the global magnetic field and those
of the leading sunspots coincide, whereas for the descending phase and the
minimum (active longitude 0/360 deg.) the polarities are opposite. Thus the
observed change of active longitudes may be connected with the polarity changes
of Sun's magnetic field in the course of 22-year magnetic cycle.


  Recently, Geometric Deep Learning (GDL) has been introduced as a novel and
versatile framework for computer-aided disease classification. GDL uses patient
meta-information such as age and gender to model patient cohort relations in a
graph structure. Concepts from graph signal processing are leveraged to learn
the optimal mapping of multi-modal features, e.g. from images to disease
classes. Related studies so far have considered image features that are
extracted in a pre-processing step. We hypothesize that such an approach
prevents the network from optimizing feature representations towards achieving
the best performance in the graph network. We propose a new network
architecture that exploits an inductive end-to-end learning approach for
disease classification, where filters from both the CNN and the graph are
trained jointly. We validate this architecture against state-of-the-art
inductive graph networks and demonstrate significantly improved classification
scores on a modified MNIST toy dataset, as well as comparable classification
results with higher stability on a chest X-ray image dataset. Additionally, we
explain how the structural information of the graph affects both the image
filters and the feature learning.


  We present the results of measurements of magnetic fields, radial velocities
and rotation velocities for 92 objects, mainly main-sequence chemically
peculiar stars. Observations were performed at the 6-m BTA telescope using Main
Stellar Spectrograph with a Zeeman analyzer. In 2010, twelve new magnetic stars
were discovered: HD\,17330, HD\,29762, HD\,49884, HD\,54824, HD\,89069,
HD\,96003, HD\,113894, HD\,118054, HD\,135679, HD\,138633, HD\,138777,
BD\,+53.1183. The presence of a field is suspected in HD\,16705, HD\,35379 and
HD\,35881. Observations of standard stars without a magnetic field confirm the
absence of systematic errors which can introduce distortions into the
measurements of longitudinal field. The paper gives comments on the results of
investigation of each star.


  We investigate a classical phase-space approach of matter-wave propagation
based on the Truncated Wigner Equation (TWE). We show that such description is
suitable for ideal matter waves in quadratic time-dependent confinement as well
as for harmonically trapped Bose Einstein condensates in the Thomas-Fermi
regime. In arbitrary interacting regimes, the TWE combined with the moment
method yields the low-energy spectrum of a condensate as predicted by
independent variational methods. TWE also gives the right breathing mode
frequency for long-ranged interactions decaying as $1/r^2$ in 3D and for a
contact potential in 2D. Quantum signatures, beyond the TWE, may only be found
in the condensate dynamics beyond the regimes of classical phase-space
propagation identified here.


  We examine a basic lattice model of interacting fermions that exhibits
quadratic band crossing points (QBCPs) in the non-interacting limit. In
particular, we consider spinless fermions on the honeycomb lattice with nearest
neighbor hopping $t$ and third-nearest neighbor hopping $t''$, which exhibits
fine-tuned QBCPs at the corners of the Brillouin zone for ${t'' = t/2}$. In
this situation, the density of states remains finite at the Fermi level of the
half-filled band and repulsive nearest-neighbor interactions $V$ lead to a
charge-density-wave (CDW) instability at infinitesimally small $V$ in the
random-phase approximation or mean-field theory. We examine the fragility of
the QBCPs against dispersion renormalizations in the ${t\mbox{-}t''\mbox{-}V}$
model using perturbation theory, and find that the $t''$-value needed for the
QBCPs increases with $V$ due to the hopping renormalization. However, the
instability toward CDW formation always requires a nonzero threshold
interaction strength, i.e., one cannot fine-tune $t''$ to recover the QBCPs in
the interacting system. These perturbative arguments are supported by quantum
Monte Carlo simulations for which we carefully compare the corresponding
threshold scales at and beyond the QBCP fine-tuning point. From this analysis,
we thus gain a quantitative microscopic understanding of the fragility of the
QBCPs in this basic interacting fermion system.


  We explore the effect of an attractive interaction between parallel-aligned
polymers, which are perpendicularly grafted on a substrate. Such an attractive
interaction could be due to, e.g., reversible cross-links. The competition
between permanent grafting favoring a homogeneous state of the polymer brush
and the attraction, which tends to induce in-plane collapse of the aligned
polymers, gives rise to an instability of the homogeneous phase to a bundled
state. In this latter state the in-plane translational symmetry is
spontaneously broken and the density is modulated with a finite wavelength,
which is set by the length scale of transverse fluctuations of the grafted
polymers. We analyze the instability for two models of aligned polymers:
directed polymers with a line tension and weakly bending chains with a bending
stiffness.


  We find in a detailed morphological study (at 15 pc resolution) that the
extended massive star formation process, shows: (i) extended triple
asymmetrical spiral arms structure (r = 5 kpc); and (ii) the spiral arms
emanate from three different nuclei. The main optical nucleus shows a small
spiral-disk (r = 500 pc) which is a continuation of the external one and reach
the very nucleus. And this very nucleus shows blue elongate structure (63 pc x
30 pc), and luminous blue star cluster properties. We study the kinematics of
this system and present a detailed Halpha velocity field for the central region
(r = 5 kpc). In the main optical nucleus we found a clear "outflow component"
associated to galactic-winds and a "inflow radial motion" (in the spiral-disk
nuclear structure, r = 700 pc). In addition we detected the outflow component
in the central and external regions (r < 5-6 kpc), with a very wide opening
angle of 140. We found that the mean value of the inflow region (at PA = 80) is
practically perpendicular to the axis of the bipolar outflow (at PA = 160). We
analyze in detail the physical conditions in the giant H II regions located in
the asymmetric spiral arms, the two main optical nuclei, and the outflow
component. In the central region (r = 5-6 kpc) we detected that the nuclear
starburst and the extended giant H II regions have very similar properties. We
suggest that the interaction between dynamical effects, the galactic--wind
(outflow), low-energy cosmic rays, and the molecular+ionized gas (probably in
the inflow phase) could be the possible mechanism that generate the "similar
extended properties in the massive star formation, at scale of 5-6 kpc!". We
analyze for NGC3256 the possible evolution from luminous IR galaxy to QSOs.


  A hybrid model is used to describe the energy loss of very high-energy taus
and muons in matter due to inelastic scattering on nuclei. The model involves
soft and semihard photonuclear interactions as well as the deep inelastic
scattering including the weak neutral current processes. For the lepton
scattering on nuclei all important nuclear effects, the shadowing,
anti-shadowing, EMC and the nucleon binding, were taken into account.
Approximating formulas for the muon and tau energy loss portion by the
inelastic scattering on nuclei in water are given for wide energy range up to
$10^9$ GeV.


  The notion of commutator width of a group, defined as the smallest number of
commutators needed to represent each element of the derived group as their
product, has been extensively studied over the past decades. In particular, in
1992 Barge and Ghys discovered the first example of a simple group of
commutator width greater than one among groups of diffeomorphisms of smooth
manifolds.
  We consider a parallel notion of bracket width of a Lie algebra and present
the first examples of simple Lie algebras of bracket width greater than one.
They are found among the algebras of polynomial vector fields on smooth affine
varieties.


  Binaural reproduction is rapidly becoming a topic of great interest in the
research community, especially with the surge of new and popular devices, such
as virtual reality headsets, smart glasses, and head-tracked headphones. In
order to immerse the listener in a virtual or remote environment with such
devices, it is essential to generate realistic and accurate binaural signals.
This is challenging, especially since the microphone arrays mounted on these
devices are typically composed of an arbitrarily-arranged small number of
microphones, which impedes the use of standard audio formats like Ambisonics,
and provides limited spatial resolution. The binaural signal matching (BSM)
method was developed recently to overcome these challenges. While it produced
binaural signals with low error using relatively simple arrays, its performance
degraded significantly when head rotation was introduced. This paper aims to
develop the BSM method further and overcome its limitations. For this purpose,
the method is first analyzed in detail, and a design framework that guarantees
accurate binaural reproduction for relatively complex acoustic environments is
presented. Next, it is shown that the BSM accuracy may significantly degrade at
high frequencies, and thus, a perceptually motivated extension to the method is
proposed, based on a magnitude least-squares (MagLS) formulation. These
insights and developments are then analyzed with the help of an extensive
simulation study of a simple six-microphone semi-circular array. It is further
shown that the BSM-MagLS method can be very useful in compensating for head
rotations with this array. Finally, a listening experiment is conducted with a
four-microphone array on a pair of glasses in a reverberant speech environment
and including head rotations, where it is shown that BSM-MagLS can indeed
produce binaural signals with a high perceived quality.


  For a smooth projective geometrically uniruled threefold defined over a
perfect field we show that there exists a canonical abelian variety over the
field, namely the second algebraic representative, whose rational Tate modules
model canonically the third l-adic cohomology groups of the variety for all
primes l. In addition, there exists a rational correspondence inducing these
identifications. In the case of a geometrically rationally chain connected
variety, one obtains canonical identifications between the integral Tate
modules of the second algebraic representative and the third l-adic cohomology
groups of the variety, and if the variety is a geometrically stably rational
threefold, these identifications are induced by an integral correspondence. Our
overall strategy consists in studying -- for arbitrary smooth projective
varieties -- the image of the second ell-adic Bloch map restricted to the Tate
module of algebraically trivial cycle classes in terms of the "correspondence
(co)niveau filtration". This complements results with rational coefficients due
to Suwa. In the appendix, we review the construction of the Bloch map and its
basic properties.


  In recent years, graph neural networks (GNNs) have achieved state-of-the-art
performance for node classification. However, most existing GNNs would suffer
from the graph imbalance problem. In many real-world scenarios, node classes
are imbalanced, with some majority classes making up most parts of the graph.
The message propagation mechanism in GNNs would further amplify the dominance
of those majority classes, resulting in sub-optimal classification performance.
In this work, we seek to address this problem by generating pseudo instances of
minority classes to balance the training data, extending previous
over-sampling-based techniques. This task is non-trivial, as those techniques
are designed with the assumption that instances are independent. Neglection of
relation information would complicate this oversampling process. Furthermore,
the node classification task typically takes the semi-supervised setting with
only a few labeled nodes, providing insufficient supervision for the generation
of minority instances. Generated new nodes of low quality would harm the
trained classifier. In this work, we address these difficulties by synthesizing
new nodes in a constructed embedding space, which encodes both node attributes
and topology information. Furthermore, an edge generator is trained
simultaneously to model the graph structure and provide relations for new
samples. To further improve the data efficiency, we also explore synthesizing
mixed ``in-between'' nodes to utilize nodes from the majority class in this
over-sampling process. Experiments on real-world datasets validate the
effectiveness of our proposed framework.


  For any second countable locally compact group G, we construct a simple
G-C*-algebra whose full and reduced crossed product norms coincide. We then
construct its G-equivariant representation on another simple G-C*-algebra
without the coincidence condition. This settles two problems posed by
Anantharaman-Delaroche in 2002. Some constructions involve the Baire category
theorem.


  Neutralinos $\tilde{\chi}^0$ in supersymmetric theories, the spin--1/2
Majorana--type superpartners of the U(1) and SU(2) neutral electroweak gauge
bosons and SU(2) neutral Higgs bosons, are expected to be among light
supersymmetric particles so that they can be produced copiouslyvia direct pair
production and/or from cascade decays of other sparticles such as sleptons at
the planned Large Hadron Collider and the prospective International Linear
Collider. Considering the prospects of having both highly polarized neutralinos
and possibility of reconstructing their decay rest frames, we provide a
systematic investigation of the three--body leptonic decays of the neutralinos
in the minimal supersymmetric standard model and demonstrate alternative ways
for probing the Majorana nature of the neutralinos and CP violation in the
neutralino system.


  In quasi-2D quantum magnets the ratio of N\'eel temperature $T_\text N$ to
Curie-Weiss temperature $\Theta_\text{CW}$ is frequently used as an empirical
criterion to judge the strength of frustration. In this work we investigate how
these quantities are related in the canonical quasi-2D frustrated square or
triangular $J_1$-$J_2$ model. Using the self-consistent Tyablikov approach for
calculating $T_\text N$ we show their dependence on the frustration control
parameter $J_2/J_1$ in the whole N\'eel and columnar antiferromagnetic phase
region. We also discuss approximate analytical results. In addition the field
dependence of $T_\text N(H)$ and the associated possible reentrance behavior of
the ordered moment due to quantum fluctuations is investigated. These results
are directly applicable to a class of quasi-2D oxovanadate antiferromagnets. We
give clear criteria to judge under which conditions the empirical frustration
ratio $f=\Theta_\text{CW}/T_\text N$ may be used as measure of frustration
strength in the quasi-2D quantum magnets.


  We introduce the spatial Rokhlin property for actions of coexact compact
quantum groups on $\mathrm{C}^*$-algebras, generalizing the Rokhlin property
for both actions of classical compact groups and finite quantum groups. Two key
ingredients in our approach are the concept of sequentially split
$*$-homomorphisms, and the use of braided tensor products instead of ordinary
tensor products.
  We show that various structure results carry over from the classical theory
to this more general setting. In particular, we show that a number of
$\mathrm{C}^*$-algebraic properties relevant to the classification program pass
from the underlying $\mathrm{C}^*$-algebra of a Rokhlin action to both the
crossed product and the fixed point algebra. Towards establishing a
classification theory, we show that Rokhlin actions exhibit a rigidity property
with respect to approximate unitary equivalence. Regarding duality theory, we
introduce the notion of spatial approximate representability for actions of
discrete quantum groups. The spatial Rokhlin property for actions of a coexact
compact quantum group is shown to be dual to spatial approximate
representability for actions of its dual discrete quantum group, and vice
versa.


  We analyze the DETR-based framework on semi-supervised object detection
(SSOD) and observe that (1) the one-to-one assignment strategy generates
incorrect matching when the pseudo ground-truth bounding box is inaccurate,
leading to training inefficiency; (2) DETR-based detectors lack deterministic
correspondence between the input query and its prediction output, which hinders
the applicability of the consistency-based regularization widely used in
current SSOD methods. We present Semi-DETR, the first transformer-based
end-to-end semi-supervised object detector, to tackle these problems.
Specifically, we propose a Stage-wise Hybrid Matching strategy that combines
the one-to-many assignment and one-to-one assignment strategies to improve the
training efficiency of the first stage and thus provide high-quality pseudo
labels for the training of the second stage. Besides, we introduce a Crossview
Query Consistency method to learn the semantic feature invariance of object
queries from different views while avoiding the need to find deterministic
query correspondence. Furthermore, we propose a Cost-based Pseudo Label Mining
module to dynamically mine more pseudo boxes based on the matching cost of
pseudo ground truth bounding boxes for consistency training. Extensive
experiments on all SSOD settings of both COCO and Pascal VOC benchmark datasets
show that our Semi-DETR method outperforms all state-of-the-art methods by
clear margins. The PaddlePaddle version code1 is at
https://github.com/PaddlePaddle/PaddleDetection/tree/develop/configs/semi_det/semi_detr.


  Data heterogeneity, characterized by disparities in local data distribution
across clients, poses a significant challenge in federated learning.
Substantial efforts have been devoted to addressing the heterogeneity in local
label distribution. As minority classes suffer from worse accuracy due to
overfitting on local imbalanced data, prior methods often incorporate
class-balanced learning techniques during local training. Despite the improved
mean accuracy across all classes, we observe that empty classes-referring to
categories absent from a client's data distribution-are still not well
recognized. This paper introduces FedED, a novel approach in heterogeneous
federated learning that integrates both empty-class distillation and logit
suppression simultaneously. Specifically, empty-class distillation leverages
knowledge distillation during local training on each client to retain essential
information related to empty classes from the global model. Moreover, logit
suppression directly penalizes network logits for non-label classes,
effectively addressing misclassifications in minority classes that may be
biased toward majority classes. Extensive experiments validate the efficacy of
FedED, surpassing previous state-of-the-art methods across diverse datasets
with varying degrees of label distribution shift.


  The hot inner flow in black-hole X-ray binaries is not just a static corona
rotating around the black hole, but it must be partially outflowing. We have
developed a model, in which Comptonization takes place in this outflowing
corona. We are able to reproduce quantitatively five observed correlations: a)
the time lag as a function of Fourier frequency, b) the time lag as a function
of photon energy, c) the time lag as a function of $\Gamma$, d) the time lag as
a function of the cut-off energy in the spectrum, and e) the long-standing
radio - X-ray correlation. All of them with only two parameters (optical depth
and width of the outflow), which vary in the same ranges for all the
correlations. Our model does not require a compact, narrow relativistic jet,
although its presence does not affect the results. The essential ingredient of
our model is the parabolic shape of the Comptonizing corona. The outflow speed
also plays a minor role. Furthermore, the bottom of the outflow, in the hard
state, looks like a ``slab'' to the incoming soft photons from the disk, and
this can explain the observed X-ray polarization, which is along the outflow.


  The current approach to fetal anomaly screening is based on biometric
measurements derived from individually selected ultrasound images. In this
paper, we introduce a paradigm shift that attains human-level performance in
biometric measurement by aggregating automatically extracted biometrics from
every frame across an entire scan, with no need for operator intervention. We
use a convolutional neural network to classify each frame of an ultrasound
video recording. We then measure fetal biometrics in every frame where
appropriate anatomy is visible. We use a Bayesian method to estimate the true
value of each biometric from a large number of measurements and
probabilistically reject outliers. We performed a retrospective experiment on
1457 recordings (comprising 48 million frames) of 20-week ultrasound scans,
estimated fetal biometrics in those scans and compared our estimates to the
measurements sonographers took during the scan. Our method achieves human-level
performance in estimating fetal biometrics and estimates well-calibrated
credible intervals in which the true biometric value is expected to lie.


  This paper investigates the elastic scattering by unbounded deterministic and
random rough surfaces, which both are assumed to be graphs of Lipschitz
continuous functions. For the deterministic case, an a priori bound explicitly
dependent on frequencies is derived by the variational approach. For the
scattering by random rough surfaces with a random source, well-posedness of the
corresponding variation problem is proved. Moreover, a similar bound with
explicit dependence on frequencies for the random case is also established
based upon the deterministic result, Pettis measurability theorem and Bochner's
integrability Theorem.


  A singularly perturbed problem involving two singular perturbation parameters
is discretized using the classical upwinded finite difference scheme on an
appropriate piecewise-uniform Shishkin mesh. Scaled discrete derivatives (with
scaling only used within the layers) are shown to be parameter uniformly
convergent to the scaled first derivatives of the continuous solution.


  In this talk, we review the basis of the loop-tree duality theorem, which
allows to rewrite loop scattering amplitudes in terms of tree-level like
objects. Since the loop measure is converted into a phase-space one, both
virtual and real contributions are expressible using the same integration
variables. A physically motivated momentum mapping allows to generate the real
emission process starting from the Born kinematics and the loop momenta. The
integrand-level combination leads to regular functions, which can be integrated
without using dimensional regularization (DREG) and correctly reproduce the
finite higher-order corrections to physical observables. We explain the
implementation of this novel approach to compute some benchmark physical
processes, and we show how to deal with both infrared and ultraviolet
divergences in four space-time dimensions.


  Physical content of the nonrelativistic quantum field theory with non-Abelian
Chern-Simons interactions is clarified with the help of the equivalent first-
quantized description which we derive in any physical gauge.


  We consider time-dependent perturbations which are relatively bounded with
respect to the square root of an unperturbed Hamiltonian operator, and whose
commutator with the latter is controlled by the full perturbed Hamiltonian. The
perturbation is modulated by two auxiliary parameters, one regulates its
intensity as a prefactor and the other one controls its time-scale via a
regular function, whose derivative is compactly supported in a finite interval.
We introduce a natural generalization of energy conservation in the case of
time-dependent Hamiltonians: the boundedness of the two-parameter unitary
propagator for the physical evolution with respect to the $n/2$-th power energy
norm for all $n\in\mathbb{Z}$. We provide bounds of the $n/2$-th power energy
norms, uniformly in time and in the time-scale parameter, for the unitary
propagators, generated by the time-dependent perturbed Hamiltonian and by the
unperturbed Hamiltonian in the interaction picture. The physically interesting
model of Landau-type Hamiltonians with an additional weak and
time-slowly-varying electric potential of unit drop is included in this
framework.


  This article presents novel methods for synthesizing distributionally robust
stabilizing neural controllers and certificates for control systems under model
uncertainty. A key challenge in designing controllers with stability guarantees
for uncertain systems is the accurate determination of and adaptation to shifts
in model parametric uncertainty during online deployment. We tackle this with a
novel distributionally robust formulation of the Lyapunov derivative chance
constraint ensuring a monotonic decrease of the Lyapunov certificate. To avoid
the computational complexity involved in dealing with the space of probability
measures, we identify a sufficient condition in the form of deterministic
convex constraints that ensures the Lyapunov derivative constraint is
satisfied. We integrate this condition into a loss function for training a
neural network-based controller and show that, for the resulting closed-loop
system, the global asymptotic stability of its equilibrium can be certified
with high confidence, even with Out-of-Distribution (OoD) model uncertainties.
To demonstrate the efficacy and efficiency of the proposed methodology, we
compare it with an uncertainty-agnostic baseline approach and several
reinforcement learning approaches in two control problems in simulation.


  By adding users as a new dimension to connectivity, on-body
Internet-of-Things (IoT) devices have gained considerable momentum in recent
years, while raising serious privacy and safety issues. Existing approaches to
authenticate these devices limit themselves to dedicated sensors or specified
user motions, undermining their widespread acceptance. This paper overcomes
these limitations with a general authentication solution by integrating
wireless physical layer (PHY) signatures with upper-layer protocols. The key
enabling techniques are constructing representative radio propagation profiles
from received signals, and developing an adversarial multi-player neural
network to accurately recognize underlying radio propagation patterns and
facilitate on-body device authentication. Once hearing a suspicious
transmission, our system triggers a PHY-based challenge-response protocol to
defend in depth against active attacks. We prove that at equilibrium, our
adversarial model can extract all information about propagation patterns and
eliminate any irrelevant information caused by motion variances and environment
changes. We build a prototype of our system using Universal Software Radio
Peripheral (USRP) devices and conduct extensive experiments with various static
and dynamic body motions in typical indoor and outdoor environments. The
experimental results show that our system achieves an average authentication
accuracy of 91.6%, with a high area under the receiver operating characteristic
curve (AUROC) of 0.96 and a better generalization performance compared with the
conventional non-adversarial approach.


  We design a variational asymptotic preserving scheme for the
Vlasov-Poisson-Fokker-Planck system with the high field scaling, which
describes the Brownian motion of a large system of particles in a surrounding
bath. Our scheme builds on an implicit-explicit framework, wherein the stiff
terms coming from the collision and field effects are solved implicitly while
the convection terms are solved explicitly. To treat the implicit part, we
propose a variational approach by viewing it as a Wasserstein gradient flow of
the relative entropy, and solve it via a proximal quasi-Newton method. In so
doing we get positivity and asymptotic preservation for free. The method is
also massively parallelizable and thus suitable for high dimensional problems.
We further show that the convergence of our implicit solver is uniform across
different scales. A suite of numerical examples are presented at the end to
validate the performance of the proposed scheme.


  The L-function of symmetric powers of classical Kloosterman sums is a
polynomial whose degree is now known, as well as the complex absolute values of
the roots. In this paper, we provide estimates for the p-adic absolute values
of these roots. Our method is indirect. We first develop a Dwork-type p-adic
cohomology theory for the two-variable infinite symmetric power L-function
associated to the Kloosterman family, and then study p-adic estimates of the
eigenvalues of Frobenius. A continuity argument then provides the desired
p-adic estimates.


  This is a preprint of an open-access book published by Springer Cham. The
book gives an up-to-date overview of the physics of spontaneously broken
continuous symmetry from the point of view of effective field theory. Upon
building up the necessary foundations, the text reviews the classification of
Nambu-Goldstone bosons and then focuses on the construction of the
effective-field-theoretic description of their dynamics. Both internal and
spacetime broken symmetries are covered, including numerous illustrative
examples and a few selected applications, worked out in greater detail.


  Poisoning efficiency plays a critical role in poisoning-based backdoor
attacks. To evade detection, attackers aim to use the fewest poisoning samples
while achieving the desired attack strength. Although efficient triggers have
significantly improved poisoning efficiency, there is still room for further
enhancement. Recently, selecting efficient samples has shown promise, but it
often requires a proxy backdoor injection task to identify an efficient
poisoning sample set. However, the proxy attack-based approach can lead to
performance degradation if the proxy attack settings differ from those used by
the actual victims due to the shortcut of backdoor learning. This paper
presents a Proxy attack-Free Strategy (PFS) designed to identify efficient
poisoning samples based on individual similarity and ensemble diversity,
effectively addressing the mentioned concern. The proposed PFS is motivated by
the observation that selecting the to-be-poisoned samples with high similarity
between clean samples and their corresponding poisoning samples results in
significantly higher attack success rates compared to using samples with low
similarity. Furthermore, theoretical analyses for this phenomenon are provided
based on the theory of active learning and neural tangent kernel. We
comprehensively evaluate the proposed strategy across various datasets,
triggers, poisoning rates, architectures, and training hyperparameters. Our
experimental results demonstrate that PFS enhances backdoor attack efficiency,
while also exhibiting a remarkable speed advantage over prior proxy-dependent
selection methodologies.


  Superconductivity in disordered systems close to an incipient localization
transition has been an area of investigation for many years. It has been noted
that in such highly disordered superconductors, anomalous spectral weight
develops in their conductivity near and below the superconducting gap energy.
In this work we investigate the low frequency conductivity in disordered
superconducting NbN thin films close to the localization transition with
time-domain terahertz spectroscopy. In the normal state, strong deviations from
the Drude form due to incipient localization are found. In the superconducting
state we find substantial spectral weight at frequencies well below the
superconducting gap scale derived from tunneling. We analyze this spectral
weight in the context of a model of disorder induced broadening of the
quasiparticle density of states and effective pair-breaking. We find that
although aspects of the optical and tunneling data can be consistently modeled
in terms of this effect of mesoscopic disorder, the optical conductivity
returns to the normal state value much faster than any model predicts. This
points to the non-trivial interplay of superconductivity and disorder close to
localization.


  A van der Waals heterostructure containing an atomically thin monolayer
transition-metal dichalcogenide as a single-photon emitting layer is emerging
as an intriguing solid-state quantum-photonic platform. Here, we report the
utilization of spin-coating of silica nanoparticles for deterministically
creating the spectrally isolated, energetically stable, and narrow-linewidth
single-photon emitters in ML-WS$_2$. We also demonstrate that long-duration
low-temperature annealing of the photonic heterostructure in the vacuum removes
the energetically unstable emitters that are present due to
fabrication-associated residue and lead to the emission of single-photons in a
<25 nm narrowband visible spectral range centered at $\sim$620 nm. This work
may pave the way toward realizing a hybrid-quantum-photonic platform containing
a van der Waals heterostructure/device and an atomic-vapor system
emitting/absorbing in the same visible spectral range.


  We extend the main result of [N. Andruskiewitsch and H.-J. Schneider, A
characterization of quantum groups], see math/0201095, to braided vector spaces
of generic diagonal type using results of Heckenberger.


  We present novel bounds on the capacity of the independent and identically
distributed binary deletion channel. Four upper bounds are obtained by
providing the transmitter and the receiver with genie-aided information on
suitably-defined random processes. Since some of the proposed bounds involve
infinite series, we also introduce provable inequalities that lead to more
manageable results. For most values of the deletion probability, these bounds
improve the existing ones and significantly narrow the gap with the available
lower bounds. Exploiting the same auxiliary processes, we also derive, as a
by-product, a couple of very simple lower bounds on the channel capacity,
which, for low values of the deletion probability, are almost as good as the
best existing lower bounds.


  We propose a novel idea for the coherent intense millisecond radio emission
of cosmic fast radio bursts (FRBs), which have recently been identified with
flares from a magnetar. Motivated by the conventional paradigm of Type III
solar radio bursts, we will explore the emission of coherent plasma line
radiation at the electron plasma frequency and its harmonic as potential
candidates of the coherent FRB emissions associated with magnetar flares. We
discuss the emissions region parameters in relativistic strongly magnetized
plasmas consisting of electrons, positrons and protons. The goal is to make
observable predictions of this model to confront the multi-wavelength
observations of FRBs from magnetars. These results will impact both
observational radio astronomy and space-based astrophysics


  Lead-free Ba0.85Ca0.15Zr0.10Ti0.90O3 (BCZT) ceramic exhibits excellent
dielectric, ferroelectric and piezoelectric properties at the Morphotropic
Phase Boundary (MPB). Previously, we demonstrated that the use of the anionic
surfactant Sodium Dodecyl Sulfate (SDS, NaC12H25SO4) could enhance the
dielectric properties of BCZT ceramic using surfactant-assisted solvothermal
processing [1]. In the present study, structural, dielectric, ferroelectric
properties, as well as electrocaloric effect and energy storage performances of
this BCZT ceramic were thoroughly investigated. X-ray diffraction (XRD)
measurements revealed the presence of single perovskite phase at room
temperature with the coexistence of orthorhombic and tetragonal symmetries.
In-situ Raman spectroscopy results confirmed the existence of all phase
transitions from rhombohedral through orthorhombic and tetragonal to cubic
symmetries when the temperature varies as reported in undoped-BaTiO3. Evolution
of energy storage performances with temperature have been investigated. BCZT
ceramic exhibits a high energy storage efficiency of ~80% at 120 {\deg}C. In
addition, the electrocaloric responsivity was found to be 0.164.10-6 K.m/V at
360 K.


  We outline the priority of high quality data of astronomical content as our
strategy for the analysis of the ancient astronomical records in the search of
the absolute chronology of the Near East in II millennium BC. The
correspondingly defined set of data for two lunar eclipses of EAE 20 and 21
tablets linked to Ur III period enables us the choice of eclipses of 27 June
1954 BC and 17 March 1912 BC; here the information on the exit position of the
darkening of the lunar disk acts as a crucial informator survived in the
records. We then discuss why the 56/64 year Venus cycle cannot be traced in the
Venus Tablet and therefore cannot serve as an anchor for the search of
chronologies. The month length method is discussed as well. In sum the
available data support the Ultra-Low Chronology proposed in the book by
H.Gasche, J.A.Armstrong, S.W.Cole and V.G.Gurzadyan, "Dating the Fall of
Babylon" (1998) and, particularly, leave no astronomical background for the
High Chronology. Ultra-Low Chronology is supported also by archaeological,
dendrochronological, Assyrian king lists and other data as summarized at the
Intern. Colloquium on Ancient Near Eastern Chronology (Ghent, July, 2000).


  Support Vector Machine (SVM) is an efficient classification approach, which
finds a hyperplane to separate data from different classes. This hyperplane is
determined by support vectors. In existing SVM formulations, the objective
function uses L2 norm or L1 norm on slack variables. The number of support
vectors is a measure of generalization errors. In this work, we propose a
Minimal SVM, which uses L0.5 norm on slack variables. The result model further
reduces the number of support vectors and increases the classification
performance.


  Data is the driving force of machine learning, with the amount and quality of
training data often being more important for the performance of a system than
architecture and training details. But collecting, processing and annotating
real data at scale is difficult, expensive, and frequently raises additional
privacy, fairness and legal concerns. Synthetic data is a powerful tool with
the potential to address these shortcomings: 1) it is cheap 2) supports rich
ground-truth annotations 3) offers full control over data and 4) can circumvent
or mitigate problems regarding bias, privacy and licensing. Unfortunately,
software tools for effective data generation are less mature than those for
architecture design and training, which leads to fragmented generation efforts.
To address these problems we introduce Kubric, an open-source Python framework
that interfaces with PyBullet and Blender to generate photo-realistic scenes,
with rich annotations, and seamlessly scales to large jobs distributed over
thousands of machines, and generating TBs of data. We demonstrate the
effectiveness of Kubric by presenting a series of 13 different generated
datasets for tasks ranging from studying 3D NeRF models to optical flow
estimation. We release Kubric, the used assets, all of the generation code, as
well as the rendered datasets for reuse and modification.


  The notions of spectral stability and the spectrum for the Vlasov-Poisson
system linearized about homogeneous equilibria, f_0(v), are reviewed.
Structural stability is reviewed and applied to perturbations of the linearized
Vlasov operator through perturbations of f_0. We prove that for each f_0 there
is an arbitrarily small delta f_0' in W^{1,1}(R) such that f_0+delta f_0$ is
unstable. When $f_0$ is perturbed by an area preserving rearrangement, f_0 will
always be stable if the continuous spectrum is only of positive signature,
where the signature of the continuous spectrum is defined as in previous work.
If there is a signature change, then there is a rearrangement of f_0 that is
unstable and arbitrarily close to f_0 with f_0' in W^{1,1}. This result is
analogous to Krein's theorem for the continuous spectrum. We prove that if a
discrete mode embedded in the continuous spectrum is surrounded by the opposite
signature there is an infinitesimal perturbation in C^n norm that makes f_0
unstable. If f_0 is stable we prove that the signature of every discrete mode
is the opposite of the continuum surrounding it.


  Let $q$ be a power of a prime $p$, let $k$ be a nontrivial divisor of $q-1$
and write $e=(q-1)/k$. We study upper bounds for cyclotomic numbers $(a,b)$ of
order $e$ over the finite field $\mathbb{F}_q$. A general result of our study
is that $(a,b)\leq 3$ for all $a,b \in \mathbb{Z}$ if $p>
(\sqrt{14})^{k/ord_k(p)}$. More conclusive results will be obtained through
separate investigation of the five types of cyclotomic numbers: $(0,0), (0,a),
(a,0), (a,a)$ and $(a,b)$, where $a\neq b$ and $a,b \in \{1,\dots,e-1\}$. The
main idea we use is to transform equations over $\mathbb{F}_q$ into equations
over the field of complex numbers on which we have more information. A major
tool for the improvements we obtain over known results is new upper bounds on
the norm of cyclotomic integers.


  The transmission eigenvalues corresponding to the half-line Schr\"odinger
equation with the general selfadjoint boundary condition is analyzed when the
potential is real valued, integrable, and compactly supported. It is shown that
a transmission eigenvalue corresponds to the energy at which the scattering
from the perturbed system agrees with the scattering from the unperturbed
system. A corresponding inverse problem for the recovery of the potential from
a set containing the boundary condition and the transmission eigenvalues is
analyzed, and a unique reconstruction of the potential is given provided one
additional constant is contained in the data set. The results are illustrated
with various explicit examples.


  We examine the occurrence of Bose-Einstein condensation in both
nonrelativistic and relativistic systems with no self-interactions in a general
setting. A simple condition for the occurrence of Bose-Einstein condensation
can be given if we adopt generalized $\zeta$-functions to define the quantum
theory. We show that the crucial feature governing Bose-Einstein condensation
is the dimension $q$ associated with the continuous part of the eigenvalue
spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of
the Klein-Gordon operator for relativistic systems. In either case
Bose-Einstein condensation can only occur if $q\ge3$.


  In many expert and everyday reasoning contexts it is very useful to reason on
the basis of defeasible assumptions. For instance, if the information at hand
is incomplete we often use plausible assumptions, or if the information is
conflicting we interpret it as consistent as possible. In this paper
sequent-based argumentation, a form of logical argumentation in which arguments
are represented by a sequent, is extended to incorporate assumptions. The
resulting assumptive framework is general, in that some other approaches to
reasoning with assumptions can adequately be represented in it. To exemplify
this, we show that assumption-based argumentation can be expressed in
assumptive sequent-based argumentation.


  Let $\varphi:\mathbb{R}\rightarrow \mathbb{R}$ be a continuously
differentiable function on an interval $J\subset\mathbb{R}$ and let
$\boldsymbol{\alpha}=(\alpha_1,\alpha_2)$ be a point with algebraically
conjugate coordinates such that the minimal polynomial $P$ of
$\alpha_1,\alpha_2$ is of degree $\leq n$ and height $\leq Q$. Denote by
$M^n_\varphi(Q,\gamma, J)$ the set of such points $\boldsymbol{\alpha}$ such
that $|\varphi(\alpha_1)-\alpha_2|\leq c_1 Q^{-\gamma}$. We show that for a
real $0<\gamma<1$ and any sufficiently large $Q$ there exist positive values
$c_2<c_3$, where $c_i=c_i(n)$, $i=1,2$, which are independent of $Q$, such that
$c_2 Q^{n+1-\gamma}<\# M^n_{\varphi}(Q,\gamma, J)< c_3 Q^{n+1-\gamma}$.


  Deep learning models usually require a huge amount of data. However, these
large datasets are not always attainable. This is common in many challenging
NLP tasks. Consider Neural Machine Translation, for instance, where curating
such large datasets may not be possible specially for low resource languages.
Another limitation of deep learning models is the demand for huge computing
resources. These obstacles motivate research to question the possibility of
knowledge transfer using large trained models. The demand for transfer learning
is increasing as many large models are emerging. In this survey, we feature the
recent transfer learning advances in the field of NLP. We also provide a
taxonomy for categorizing different transfer learning approaches from the
literature.


  La2/3Ca1/3MnO3 thin films have been grown on yttria-stabilized zirconia (YSZ)
buffered silicon-on-insulator (SOI) substrate by the pulsed laser deposition
technique. While full cube-on-cube epitaxy was achieved for the YSZ layer, the
top manganite layer was multi-domain-oriented, with a coexistence of
cube-on-cube and cube-on-diagonal epitaxy. Due to a combined influence from the
magnetocrystalline anisotropy and the magnetoelastic anisotropy, in zero field
the local spin orientation varies across the twin boundaries. As a result, a
quite large low-field magnetoresistance (LFMR) based on spin-dependent
tunnelling was observed. The film shows a resistance change of ~20% in a
magnetic field <1000 Oe at 50 K, which is promising for real applications.


  The poles of the quantum scattering matrix (S-matrix) in the complex momentum
plane have been studied extensively. Bound states give rise to S-matrix poles,
and other poles correspond to non-normalizable anti-bound, resonance and
anti-resonance states. They describe important physics, but their locations can
be difficult to find. In pioneering work, Nussenzveig performed the analysis
for a square well/wall, and plotted the flow of the poles as the potential
depth/height varied. More than fifty years later, however, little has been done
in the way of direct generalization of those results. We point out that today
we can find such poles easily and efficiently, using numerical techniques and
widely available software. We study the poles of the scattering matrix for the
simplest piece-wise flat potentials, with one and two adjacent (non-zero)
pieces. For the finite well/wall the flow of the poles as a function of the
depth/height recovers the results of Nussenzveig. We then analyze the flow for
a potential with two independent parts that can be attractive or repulsive, the
two-piece potential. These examples provide some insight into the complicated
behavior of the resonance, anti-resonance and anti-bound poles.


  Connectivity estimation is challenging in the context of high-dimensional
data. A useful preprocessing step is to group variables into clusters, however,
it is not always clear how to do so from the perspective of connectivity
estimation. Another practical challenge is that we may have data from multiple
related classes (e.g., multiple subjects or conditions) and wish to incorporate
constraints on the similarities across classes. We propose a probabilistic
model which simultaneously performs both a grouping of variables (i.e.,
detecting community structure) and estimation of connectivities between the
groups which correspond to latent variables. The model is essentially a factor
analysis model where the factors are allowed to have arbitrary correlations,
while the factor loading matrix is constrained to express a community
structure. The model can be applied on multiple classes so that the
connectivities can be different between the classes, while the community
structure is the same for all classes. We propose an efficient estimation
algorithm based on score matching, and prove the identifiability of the model.
Finally, we present an extension to directed (causal) connectivities over
latent variables. Simulations and experiments on fMRI data validate the
practical utility of the method.


  This work presents an algorithm to sample from the Wasserstein barycenter of
absolutely continuous measures. Our method is based on the gradient flow of the
multimarginal formulation of the Wasserstein barycenter, with an additive
penalization to account for the marginal constraints. We prove that the minimum
of this penalized multimarginal formulation is achieved for a coupling that is
close to the Wasserstein barycenter. The performances of the algorithm are
showcased in several settings.


  We regularize the potential distribution framework to calculate the excess
free energy of liquid water simulated with the BLYP-D density functional. The
calculated free energy is in fair agreement with experiments but the excess
internal energy and hence also the excess entropy are not. Our work emphasizes
the importance of thermodynamic characterization in assessing the quality of
electron density functionals in describing liquid water and hydration
phenomena.


  Seismology has several features that suggest it is a highly internationalized
field: the subject matter is global, the tools used to analyse seismic waves
are dependent upon information technologies, and governments are interested in
funding cooperative research. We explore whether an emerging field like
seismology has a more internationalised structure than the older, related field
of geophysics. Using aggregated journal-journal citations, we first show that,
within the citing environment, seismology emerged from within geophysics as its
own field in the 1990s. The bibliographic analysis, however, does not show that
seismology is more internationalised than geophysics: in 2000, seismology had a
lower percentage of all articles co-authored on an international basis.
Nevertheless, social network analysis shows that the core group of cooperating
countries within seismology is proportionately larger and more distributed than
that within geophysics. While the latter exhibits an established network with a
hierarchy, the formation of a field in terms of new partnership relations is
ongoing in seismology.


  Position determination of photon emitters and associated strong field
parallax effects are investigated using relativistic optics when the photon
orbits are confined to the equatorial plane of the Schwarzschild spacetime. We
assume the emitter is at a fixed space position and the receiver moves along a
circular geodesic orbit. This study requires solving the inverse problem of
determining the (spatial) intersection point of two null geodesic initial data
problems, serving as a simplified model for applications in relativistic
astrometry as well as in radar and satellite communications.


  In the last decade, there has been increased interest in the possibility that
the Universe contains large additional dimensions. In this article it is
proposed that the Kaluza-Klein modes which are predicted to exist in such
models will be trapped in the galactic halo, and that the subsequent decays of
these modes in the present will generate an observable flux of positrons and
$\gamma$-rays from the galactic core. In particular, by restricting the rate of
production 511 keV photons to be below that observed by the INTEGRAL satellite,
a new set of constraints are imposed on the ADD model.


  Sandwich gravitational waves are given globally in terms of step functions at
the boundaries. Linearized Einstein-Weyl equations are solved exactly in this
background in Rosen coordinates. Depending on the geometry and composition of
the sandwich wave, the neutrino's energy-momentum redistributes itself. At the
test field level, since the background will not change, the neutrino's energy
density in particular will show variations between positive and negative
extrema when crossing the sandwich wave. This may reveal facts about the weakly
interacting neutrinos in cosmology.


  Objective: Arterial stiffness is an important marker to predict cardio
vascular events. Common measurement techniques to determine the condition of
the aorta are limited to the acquisition of the arterial pulse wave at the
extremities. The goal of this work is to enable non-invasive measurements of
the aortic pulse wave velocity, instead. An additional aim is to extract
further information, related to the conditions of the aorta, from the pulse
wave signal instead of only its velocity. Methods: After discussing the
problems of common pulse wave analysis procedures, an approach to determine the
frequency response of the aorta is presented. Therefore, the aorta is modelled
as an electrical equivalent circuit. To determine the specific numeric values
of this system, a measurement approach is presented, which is based on
non-invasive bioimpedance plethysmography measurements above the aortic arch
and at the inguinal region. The conversion of the measurement results to the
system parameters is realized by a digital algorithm, which is proposed in this
work as well. To evaluate the approach, a study on three subjects is performed.
Results: The measurement results demonstrate that the proposed approach yields
realistic frequency responses. For better approximation of the aortic system
function, more complex models are recommended to investigate in the future.
Since this study is limited to three subjects without a ground truth, further
measurements will be necessary. Significance: The proposed approach could solve
problems of current methods to determine the condition of the aorta. Its
application is non-invasive, harmless and easy to execute.


  Stochastic Langevin molecular dynamics for nuclei is derived from the
Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics)
in a Kac-Zwanzig setting, with the initial data for the electrons
stochastically perturbed from the ground state and the ratio, $M$, of nuclei
and electron mass tending to infinity. The Ehrenfest nuclei dynamics is
approximated by the Langevin dynamics with accuracy $o(M^{-1/2})$ on bounded
time intervals and by $o(1)$ on unbounded time intervals, which makes the small
$\mathcal{O}(M^{-1/2})$ friction and $o(M^{-1/2})$ diffusion terms visible. The
initial electron probability distribution is a Gibbs density at low temperture,
derived by a stability and consistency argument: starting with any equilibrium
measure of the Ehrenfest Hamiltonian system, the initial electron distribution
is sampled from the equilibrium measure conditioned on the nuclei positions,
which after long time leads to the nuclei positions in a Gibbs distribution
(i.e. asymptotic stability); by consistency the original equilibrium measure is
then a Gibbs measure.The diffusion and friction coefficients in the Langevin
equation satisfy the Einstein's fluctuation-dissipation relation.


  In this paper, we derive a 90\% credible lower bound on the modified
parameter of scalar-tensor theories as $\varphi_{-2}>-7.94\times10^{-4}$ by
using dominant-mode correction. Specific to BD theory, we have the constraint
$\omega_{\rm BD}>4.75$. Asymmetric binary systems usually have a significant
mass ratio; in such cases, higher harmonic modes cannot be neglected. Our work
considers higher harmonic corrections from scalar-tensor theories and provides
a tighter constraint of $\varphi_{-2}>-7.59\times10^{-4}$. Transitioning to the
BD theory, the constraint is $\omega_{\rm BD}>5.06$, with a 6.5\% improvement.
We also consider a plausible NSBH event, GW190814, which is a highly unequal
mass ratio source and exhibits strong evidence for higher-order multipoles. We
obtain poorly converged results when using the dominant mode while getting a
constraint of $\varphi_{-2}>-6.60\times10^{-4}$ on scalar-tensor theories when
including the higher harmonic modes. This suggests that the difference between
the dominant mode and higher modes has a significant impact on our analysis.
Furthermore, treating this suspected event as an NSBH event, we find
$\omega_{\rm BD}>6.12$ when including the higher harmonic modes. Combining
GW200115 and GW190814 and including higher modes, the constraint is improved to
$\omega_{\rm BD}>110.55$. This is currently the strongest constraint utilizing
GWs, contingent upon GW190814 being an NSBH event. Additionally, we take into
account a BD-like theory, known as screened modified gravity (SMG), and
investigate the coupling constant constraints, both with and without
higher-mode corrections, by using data from both GW200115 and GW190814.


  We present \emph{SPHEAR}, an accurate, differentiable parametric statistical
3D human head model, enabled by a novel 3D registration method based on
spherical embeddings. We shift the paradigm away from the classical Non-Rigid
Registration methods, which operate under various surface priors, increasing
reconstruction fidelity and minimizing required human intervention.
Additionally, SPHEAR is a \emph{complete} model that allows not only to sample
diverse synthetic head shapes and facial expressions, but also gaze directions,
high-resolution color textures, surface normal maps, and hair cuts represented
in detail, as strands. SPHEAR can be used for automatic realistic visual data
generation, semantic annotation, and general reconstruction tasks. Compared to
state-of-the-art approaches, our components are fast and memory efficient, and
experiments support the validity of our design choices and the accuracy of
registration, reconstruction and generation techniques.


  The space-air-ground integrated network (SAGIN) has become a crucial research
direction in future wireless communications due to its ubiquitous coverage,
rapid and flexible deployment, and multi-layer cooperation capabilities.
However, integrating hierarchical federated learning (HFL) with edge computing
and SAGINs remains a complex open issue to be resolved. This paper proposes a
novel framework for applying HFL in SAGINs, utilizing aerial platforms and low
Earth orbit (LEO) satellites as edge servers and cloud servers, respectively,
to provide multi-layer aggregation capabilities for HFL. The proposed system
also considers the presence of inter-satellite links (ISLs), enabling
satellites to exchange federated learning models with each other. Furthermore,
we consider multiple different computational tasks that need to be completed
within a limited satellite service time. To maximize the convergence
performance of all tasks while ensuring fairness, we propose the use of the
distributional soft-actor-critic (DSAC) algorithm to optimize resource
allocation in the SAGIN and aggregation weights in HFL. Moreover, we address
the efficiency issue of hybrid action spaces in deep reinforcement learning
(DRL) through a decoupling and recoupling approach, and design a new dynamic
adjusting reward function to ensure fairness among multiple tasks in federated
learning. Simulation results demonstrate the superiority of our proposed
algorithm, consistently outperforming baseline approaches and offering a
promising solution for addressing highly complex optimization problems in
SAGINs.


  We give a characterization of interpolating sequences for bounded analytic
functions on the bidisk.


  The knuckleball is perhaps the most enigmatic pitch in baseball. Relying on
the presence of raised seams on the surface of the ball to create asymmetric
flow, a knuckleball's trajectory has proven very challenging to predict
compared to other baseball pitches, such as fastballs or curveballs. Previous
experimental tracking of large numbers of knuckleballs has shown that they can
move in essentially any direction relative to what would be expected from a
drag-only trajectory. This has led to speculation that knuckleballs exhibit
chaotic motion. Here we develop a relatively simple model of a knuckleball that
includes quadratic drag and lift from asymmetric flow which is taken from
experimental measurements of slowly rotating baseballs. Our models can indeed
exhibit dynamical chaos as long In contrast, models that omit torques on the
ball in flight do not show chaotic behavior. Uncertainties in the phase space
position of the knuckleball are shown to grow by factors as large as $10^6$
over the flight of the ball from the pitcher to home plate. We quantify the
impact of our model parameters on the chaos realized in our models,
specifically showing that maximum Lyapunov exponent is roughly proportional to
the square root of the effective lever arm of the torque, and also roughly
proportional to the initial velocity of the pitch. We demonstrate the existence
of bifurcations that can produce changes in the location of the ball when it
reaches the plate of as much as 1.2 m for specific initial conditions similar
to those used by professional knuckleball pitchers. As we introduce additional
complexity in the form of more faithful representations of the empirical
asymmetry force measurements, we find that a larger fraction of the possible
initial conditions result in dynamical chaos.


  Localisation can be defined as estimating or finding a position of the node.
There are two techniques in localisation, which are range-based and range-free
techniques. This paper focusses on the Received Signal Strength Indicator
(RSSI) localisation method, which is categorised in a range-based technique
along with the time of arrival, time difference of arrival and angle of
arrival. Therefore, this study aims to compare the trilateration and
multilateration method for RSSI-based technique for localising the transmitted
(Tx) node. The wireless sensor module in the work used LOng-RAnge radio (LoRa)
with 868MHz frequency. Nowadays, wireless networks have been a key technology
for smart environments, monitoring, and object tracking due to low power
consumption with long-range connectivity. The number of received (Rx) nodes are
three and four for trilateration and multilateration methods, respectively. The
transmitted node is placed at 32 different coordinates within the 10x10 meter
outdoor area. The results show that error localisation obtained for General
Error Localisation (GER) for multilateration and trilateration is 1.83m and
2.30m, respectively. An additional, the maximum and minimum error for
multilateration and trilateration from 1.00 to 5.28m and 0.5 to 3.61m. The
study concludes that the multilateration method more accurate than
trilateration. Therefore, with the increasing number of Rx node, the accuracy
of localisation of the Tx node increases.


  The monotone rearrrangement algorithm was introduced by Hardy, Littlewood and
P\'olya as a sorting device for functions. Assuming that $x$ is a monotone
function and that an estimate $x_n$ of $x$ is given, consider the monotone
rearrangement $\hat{x}_n$ of $x_n$. This new estimator is shown to be uniformly
consistent. Under suitable assumptions, pointwise limit distribution results
for $\hat{x}_n$ are obtained. The framework is general and allows for weakly
dependent and long range dependent stationary data. Applications in monotone
density and regression function estimation are detailed.


  We analyse high-resolution near-UV and optical spectra of the afterglow of
GRB 080310, obtained with the Very Large Telescope Ultraviolet and Visual
Echelle Spectrograph (VLT/UVES), to investigate the circumburst environment and
the interstellar medium of the gamma-ray burst (GRB) host galaxy. The VLT
rapid-response mode (RRM) enabled the observations to start only 13 minutes
after the Swift trigger and a series of four exposures to be collected before
dawn. A low neutral-hydrogen column-density (log N (HI) = 18.7) is measured at
the host-galaxy redshift of z = 2.42743. At this redshift, we also detect a
large number of resonance ground-state absorption lines (e.g., CII, MgII, AlII,
SiII, CrII, CIV, SiIV), as well as time-varying absorption from the
fine-structure levels of FeII. Time-varying absorption from a highly excited
FeIII energy level (7S3), giving rise to the so-called UV34 line triplet, is
also detected, for the first time in a GRB afterglow. The CrII ground-state and
all observed FeII energy levels are found to depopulate with time, whilst the
FeIII 7S3 level is increasingly populated. This absorption-line variability is
clear evidence of ionization by the GRB, which is for the first time
conclusively observed in a GRB afterglow spectrum. We derive ionic column
densities at each epoch of observations by fitting absorption lines with a
four-component Voigt-profile model. We perform CLOUDY photo-ionization
modelling of the expected pre-burst ionic column densities, to estimate that,
before the onset of the burst, [C/H] = -1.3 \pm 0.2, [O/H] < -0.8, [Si/H] =
-1.2 \pm 0.2, [Cr/H] = +0.7 \pm 0.2, and [Fe/H] = +0.2 \pm 0.2 for the
integrated line profile, indicating strong overabundances of iron and chromium.
For one of the components, we observe even more extreme ratios of [Si/Fe] \leq
-1.47 and [C/Fe] \leq -1.74. [abridged]