  Investigations of shadows of astrophysical entities constitute a major source
of insight into the evolution of compact objects. Such effects depend on the
nature of the compact object and arise on account of the strong gravitational
lensing that casts a shadow on the bright background. We consider the Kerr-like
wormhole spacetime (Phys.\ Rev.\ D 97:024040, 2018), which is a modification of
the Kerr black hole that degenerates into wormholes for nonzero values of the
deviation parameter $\lambda^2$. The results suggest that the Kerr spacetime
can reproduce far away from the throat of the wormhole. We obtain the shapes of
the shadow for the Kerr-like wormholes and discuss the effect of the spin $a$,
the inclination angle $\theta_0$, and the deviation parameter $\lambda^2$ on
the size and nature of the shadow. As a consequence, it is discovered that the
shadow is distorted due to the spin as well as the deviation parameter and the
radius of the shadow decreases with $\lambda^2$ if the ADM mass of the
Kerr-like wormholes is considered.


  It has been shown that, starting from the state |0>, in the general case, an
arbitrary quantum state |\psi> cannot be prepared with exponential precision in
polynomial time. However, we show that for the important special case when
|\psi> represents discrete values of some real, continuous function \psi(x),
efficient preparation is possible by applying the eigenvalue estimation
algorithm to a Hamiltonian which has \psi(x) as an eigenstate. We construct the
required Hamiltonian explicitly and present an iterative algorithm for removing
unwanted superpositions from the output state in order to reach |\psi> within
exponential accuracy. The method works under very general conditions and can be
used to provide the quantum simulation algorithm with very accurate and general
starting states.


  Applying the method of conformal metric to a given static axially symmetric
vacuum solution of the Einstein equations, we have shown that there is no
solution representing a cosmic ideal fluid which is asymtotically FLRW. Letting
the cosmic fluid to be imperfect there are axially symmetric solutions tending
to FLRW at space infinity. The solution we have found represents an axially
symmetric spacetime leading to a spherically symmetric Einstein tensor.
Therefore, we have found a solution of Einstein equations representing a
spherically symmetric matter distribution corresponding to a spacetime which
does not reflect the same symmetry. We have also found another solution of
Einstein equation corresponding to the same energy tensor with spherical
symmetry.


  Two-spinor formalism for Einstein Lagrangian is developed. The gravitational
field is regarded as a composite object derived from soldering forms. Our
formalism is geometrically and globally well-defined and may be used in
virtually any 4m-dimensional manifold with arbitrary signature as well as
without any stringent topological requirement on space-time, such as
parallelizability. Interactions and feedbacks between gravity and spinor fields
are considered. As is well known, the Hilbert-Einstein Lagrangian is second
order also when expressed in terms of soldering forms. A covariant splitting is
then analysed leading to a first order Lagrangian which is recognized to play a
fundamental role in the theory of conserved quantities. The splitting and
thence the first order Lagrangian depend on a reference spin connection which
is physically interpreted as setting the zero level for conserved quantities. A
complete and detailed treatment of conserved quantities is then presented.


  We describe the one-dimensional \v{C}eby\v{s}\"{e}v subspaces of a
JBW$^*$-triple $M,$ by showing that for a non-zero element $x$ in $M$,
$\mathbb{C}x$ is a \v{C}eby\v{s}\"{e}v subspace of $M$ if, and only if, $x$ is
a Brown-Pedersen quasi-invertible element in ${M}$. We study the
\v{C}eby\v{s}\"{e}v JBW$^*$-subtriples of a JBW$^*$-triple $M$. We prove that,
for each non-zero \v{C}eby\v{s}\"{e}v JBW$^*$-subtriple $N$ of $M$, then
exactly one of the following statements holds: $(a)$ $N$ is a rank one
JBW$^*$-triple with dim$(N)\geq 2$ (i.e. a complex Hilbert space regarded as a
type 1 Cartan factor). Moreover, $N$ may be a closed subspace of arbitrary
dimension and $M$ may have arbitrary rank; $(b)$ $N= \mathbb{C} e$, where $e$
is a complete tripotent in $M$; $(c)$ $N$ and $M$ have rank two, but $N$ may
have arbitrary dimension; $(d)$ $N$ has rank greater or equal than three and
$N=M$.
  We also provide new examples of \v{C}eby\v{s}\"{e}v subspaces of classic
Banach spaces in connection with ternary rings of operators.


  We present the first deep (72 hours of observations) radio image of the
Euclid Deep Field North (EDFN) obtained with the LOw-Frequency ARray (LOFAR)
High Band Antenna (HBA) at 144 MHz. The EDFN is the latest addition to the
LOFAR Two-Metre Sky Survey (LoTSS) Deep Fields and these observations represent
the first data release for this field. The observations produced a 6"
resolution image with a central r.m.s. noise of $32\,\mu$Jy\,beam$^{-1}$. A
catalogue of $\sim 23,000$ radio sources above a signal-to-noise ratio (SNR)
threshold of 5 is extracted from the inner circular 10 deg$^2$ region. We
discuss the data analysis and we provide a detailed description of how we
derived the catalogue of radio sources and on the issues related to
direction-dependent calibration and their effects on the final products.
Finally, we derive the radio source counts at 144 MHz in the EDFN using
catalogues of mock radio sources to derive the completeness correction factors.
The source counts in the EDFN are consistent with those obtained from the first
data release of the other LoTSS Deep Fields (ELAIS-N1, Lockman Hole and
Bootes), despite the different method adopted to construct the final catalogue
and to assess its completeness.


  Quantum materials are epitomized by the influence of collective modes upon
their macroscopic properties. Relatively few examples exist, however, whereby
coherence of the ground-state wavefunction directly contributes to the
conductivity. Notable examples include the quantizing effects of high magnetic
fields upon the 2D electron gas, the collective sliding of charge density waves
subject to high electric fields, and perhaps most notably the macroscopic phase
coherence that enables superconductors to carry dissipationless currents. Here
we reveal that the low temperature hidden order state of URu$_2$Si$_2$ exhibits
just such a connection between the quantum and macroscopic worlds -- under
large voltage bias we observe non-linear contributions to the conductivity that
are directly analogous to the manifestation of phase slips in one-dimensional
superconductors [1], suggesting a complex order parameter for hidden order


  We prove a version of Bourgain's projection theorem for parametrized families
of $C^2$ maps, that refines the original statement even in the linear case. As
one application, we show that if $A$ is a Borel set of Hausdorff dimension
close to $1$ in $\mathbb{R}^2$ or close to $3/2$ in $\mathbb{R}^3$, then for
$y\in A$ outside of a very sparse set, the pinned distance set $\{|x-y|:x\in
A\}$ has Hausdorff dimension at least $1/2+c$, where $c$ is universal.
Furthermore, the same holds if the distances are taken with respect to a $C^2$
norm of positive Gaussian curvature. As further applications, we obtain new
bounds on the dimensions of spherical projections, and an improvement over the
trivial estimate for incidences between $\delta$-balls and
$\delta$-neighborhoods of curves in the plane, under fairly general
assumptions. The proofs depend on a new multiscale decomposition of measures
into ``Frostman pieces'' that may be of independent interest.


  We introduce a new method to determine the relative contributions of
different types of stars to the integrated light of nearby early-type galaxies.
As is well known, the surface brightness of these galaxies shows pixel-to-pixel
fluctuations due to Poisson variations in the number of giant stars.
Differential spectroscopy of pixels as a function of fluctuation strength
("fluctuation spectroscopy") effectively measures the spectral variation of
stars as a function of their luminosity, information that is otherwise
difficult to obtain for individual stars outside of the Local Group. We apply
this technique to the elliptical galaxy NGC 4472, using HST/ACS imaging in six
narrow-band ramp filters tuned to spectral features in the range 0.8-1.0
micron. Pixels with +- 5% broad-band variations show differential color
variations of 0.1% - 1.0% in the narrow-band filters. These variations are
primarily due to the systematic increase in TiO absorption strength with
increasing luminosity on the upper giant branch. The data are very well
reproduced by the same Conroy & van Dokkum (2012) stellar population synthesis
model that is the best fit to the integrated light, with residuals in the range
0.03% - 0.09%. Models with ages or metallicities that are significantly
different from the integrated-light values do not yield good fits. We can also
rule out several modifications to the underlying model, including the presence
of a significant (>3% of the light) population of late M giants. The current
observations constitute a powerful test of the expected luminosities and
temperatures of metal-rich giants in massive early-type galaxies. Studies of
pixels with much larger (negative) fluctuations will provide unique information
on main sequence stars and the stellar initial mass function.


  Recently, the ATLAS and CMS collaborations have pointed out the possible
existence of a new resonance with a mass around 750 GeV. We investigate the
possibility to identify this new resonance with a spin zero field responsible
for the breaking of a new gauge symmetry. We focus on a simple theory where the
baryon number is a local symmetry spontaneously broken at the low scale. In
this context new vector-like quarks are needed to cancel all baryonic anomalies
and define the production mechanism and decays of the new Higgs at the LHC.
Assuming the existence of the new Higgs with a mass of 750 GeV at the LHC we
find an upper bound on the symmetry breaking scale. Therefore, one expects that
a new force associated with baryon number could be discovered at the LHC.


  We investigate a subclass of well-structured transition systems (WSTS), the
bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete
deterministic ones, which we claim provide an adequate basis for the study of
forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth.
Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered
previously for the termination of forward analysis, boundedness is decidable.
Boundedness turns out to be a valuable restriction for WSTS verification, as we
show that it further allows to decide all $\omega$-regular properties on the
set of infinite traces of the system.


  We construct a new class of vacuum black hole solutions whose geometry is
deformed and twisted by the presence of NUT charges. The solutions are obtained
by `unspinning' the general Kerr-NUT-(A)dS spacetimes, effectively switching
off some of their rotation parameters. The resulting geometry has a structure
of warped space with the Kerr-like Lorentzian part warped to a Euclidean metric
of deformed and/or twisted sphere, with the deformation and twist characterized
by the `Euclidean NUT' parameters. In the absence of NUTs, the solution reduces
to a well known Kerr-(A)dS black hole with several rotations switched off. New
geometries inherit the original symmetry of the Kerr-NUT-(A)dS family, namely,
they possess the full Killing tower of hidden and explicit symmetries. As
expected, for vanishing NUT, twist, and deformation parameters, the symmetry is
further enlarged.


  In this work, we show how domain engineered lithium niobate can be used to
selectively dope monolayer MoSe2 and WSe2 and demonstrate that these
ferroelectric domains can significantly enhance or inhibit photoluminescence
(PL) with the most dramatic modulation occurring at the heterojunction
interface between two domains. A micro-PL and Raman system is used to obtain
spatially resolved images of the differently doped transition metal
dichalcogenides (TMDs). The domain inverted lithium niobate causes changes in
the TMDs due to electrostatic doping as a result of the remnant polarization
from the substrate. Moreover, the differently doped TMDs (n-type MoSe2 and
p-type WSe2) exhibit opposite PL modulation. Distinct oppositely charged
domains were obtained with a 9-fold PL enhancement for the same single MoSe2
sheet when adhered to the positive (P+) and negative (P-) domains. This sharp
PL modulation on the ferroelectric domain results from different free electron
or hole concentrations in the materials conduction band or valence band.
Moreover, excitons dissociate rapidly at the interface between the P+ and P-
domains due to the built-in electric field. We are able to adjust the charge on
the P+ and P- domains using temperature via the pyroelectric effect and observe
rapid PL quenching over a narrow temperature range illustrating the observed PL
modulation is electronic in nature. This observation creates an opportunity to
harness the direct bandgap TMD 2D materials as an active optical component for
the lithium niobate platform using domain engineering of the lithium niobate
substrate to create optically active heterostructures that could be used for
photodetectors or even electrically driven optical sources on-chip.


  Computer simulations of decoherence in quantum spin systems require the
solution of the time-dependent Schrodinger equation for interacting quantum
spin systems over extended periods of time. We use exact diagonalization,
Chebyshev polynomial technique, four Suzuki-formula algorithms, and the
short-iterative-Lanczos method to solve a simple model for decoherence of a
quantum spin system by an environment consisting of quantum spins, and compare
advantages and limitations of different algorithms.


  In the present paper, we propose a variational average-atom model of
electron-ion plasma performing a quantum treatment of bound electrons and
accounting for correlations (VAAQBEC). This model addresses the correlation
functions in a weakly-coupled plasma, while also accounting self-consistently
for the ion average shell structure. This is done at the price of treating the
free electrons classically, whereas bound electrons are treated
quantum-mechanically. When ions are approximated by point-like particles, the
present approach yields the usual Debye-H\"{u}ckel corrections to the orbital
energies and chemical potential. If one disregards the interactions of
continuum electrons, the present approach yields ion-ion correlation
corrections through a self-consistent one-component-classical-plasma
contribution. Comparisons are presented with the broadly-used
continuum-lowering approach of Stewart and Pyatt and with the dense-plasma
average-atom models INFERNO and VAAQP, on warm silicon and hot iron cases.


  In this note a definition of umbilic point at infinity is proposed, at least
for surfaces that are homogeneous polynomial graphs over a plane in Euclidean
3-space. This is a stronger definition than that of Toponogov in his study of
complete convex surfaces, and allows one to distinguish between different
umbilic points at infinity.
  It is proven that all such umbilic points at infinity are isolated, that they
occur in pairs and are the zeroes of the projective extension of the third
fundamental form, as developed by the authors in a previous paper. A geometric
interpretation for our definition is that an umbilic point at infinity occurs
when the tangent to the level set at infinity is also an asymptotic direction
at infinity. We prove that a homogeneous polynomial graph must have an umbilic
point, albeit at infinity.


  In this paper, we study dimension reduction techniques for large-scale
controlled stochastic differential equations (SDEs). The drift of the
considered SDEs contains a polynomial term satisfying a one-sided growth
condition. Such nonlinearities in high dimensional settings occur, e.g., when
stochastic reaction diffusion equations are discretized in space. We provide a
brief discussion around existence, uniqueness and stability of solutions.
(Almost) stability then is the basis for new concepts of Gramians that we
introduce and study in this work. With the help of these Gramians, dominant
subspace are identified leading to a balancing related highly accurate reduced
order SDE. We provide an algebraic error criterion and an error analysis of the
propose model reduction schemes. The paper is concluded by applying our method
to spatially discretized reaction diffusion equations.


  We review work by the authors on thermal activation in nanoscopic magnetic
systems. These systems present unique difficulties in analyzing noise-induced
escape over a barrier, including the presence of nonlocal interactions,
nongradient terms in the energy functional, and dynamical textures as initial
or saddle states. We begin with a discussion of magnetic reversal between
single-domain configurations of the magnetization. Here the transition (saddle)
state can be either a single-domain or a spatially varying (instanton-like)
configuration, and depending on the system parameters can exhibit either
Arrhenius or non-Arrhenius reversal rates. We then turn to a discussion of
transitions between magnetic textures, which can be either static and
topologically protected or dynamic and not topologically protected. An example
of the latter case is the droplet soliton, a rotating
nontopologically-protected configuration, which we find can occur either as a
metastable or transition state in a nanoscopic magnetic system. After
discussing various issues in calculating transition rates, we present results
for the activation barriers for creation and annihilation of these magnetic
textures. We conclude with a discussion of activated transitions between
topologically protected skyrmion textures and other configurations, on which
work is ongoing.


  One of the primary scientific targets of current and future CMB polarization
experiments is the search for a stochastic background of gravity waves in the
early universe. As instrumental sensitivity improves, the limiting factor will
eventually be B-mode power generated by gravitational lensing, which can be
removed through use of so-called delensing algorithms. We forecast prospects
for delensing using lensing maps which are obtained externally to CMB
polarization: either from large-scale structure observations, or from
high-resolution maps of CMB temperature. We conclude that the forecasts in
either case are not encouraging, and that significantly delensing large-scale
CMB polarization requires high-resolution polarization maps with sufficient
sensitivity to measure the lensing B-mode. We also present a simple formalism
for including delensing in CMB forecasts which is computationally fast and
agrees well with Monte Carlos.


  We classify Borel-Schur algebras having finite representation type. We also
de- termine Auslander-Reiten sequences for a large class of simple modules over
Borel- Schur algebras. A partial information on the structure of the socles of
Borel-Schur algebras is given.


  Continent-scale datasets challenge hydrological algorithms for processing
digital elevation models. Flow accumulation is an important input for many such
algorithms; here, I parallelize its calculation. The new algorithm works on one
or many cores, or multiple machines, and can take advantage of large memories
or cope with small ones. Unlike previous parallel algorithms, the new algorithm
guarantees a fixed number of memory access and communication events per raster
cell. In testing, the new algorithm ran faster and used fewer resources than
previous algorithms, exhibiting ~30% strong and weak scaling efficiencies up to
48 cores and linear scaling across datasets ranging over three orders of
magnitude. The largest dataset tested had two trillion (2*10^12) cells. With 48
cores, processing required 24 minutes wall-time (14.5 compute-hours). This test
is three orders of magnitude larger than any previously performed in the
literature. Complete, well-commented source code and correctness tests are
available on Github.


  Modern approaches to pose and body shape estimation have recently achieved
strong performance even under challenging real-world conditions. Even from a
single image of a clothed person, a realistic looking body shape can be
inferred that captures a users' weight group and body shape type well. This
opens up a whole spectrum of applications -- in particular in fashion -- where
virtual try-on and recommendation systems can make use of these new and
automatized cues. However, a realistic depiction of the undressed body is
regarded highly private and therefore might not be consented by most people.
Hence, we ask if the automatic extraction of such information can be
effectively evaded. While adversarial perturbations have been shown to be
effective for manipulating the output of machine learning models -- in
particular, end-to-end deep learning approaches -- state of the art shape
estimation methods are composed of multiple stages. We perform the first
investigation of different strategies that can be used to effectively
manipulate the automatic shape estimation while preserving the overall
appearance of the original image.


  Matsuoka & Kawara (2010) showed that the number density of the most massive
galaxies (log M/M_sun=11.5-12.0) increases faster than that of the next massive
group (log M/M_sun=11.0-11.5) during 0 < z < 1. This appears to be in
contradiction to the apparent "downsizing effect". We attempt to understand the
two observational findings in the context of the hierarchical merger paradigm
using semi-analytic techniques. Our models closely reproduce the result of
Matsuoka & Kawara (2010). Downsizing can also be understood as larger galaxies
have, on average, smaller assembly ages but larger stellar ages. Our fiducial
models further reveal details of the history of the stellar mass growth of
massive galaxies. The most massive galaxies (log M/M_sun=11.5-12.0 at z=0),
which are mostly brightest cluster galaxies, obtain roughly 70% of their
stellar components via merger accretion. The role of merger accretion
monotonically declines with galaxy mass: 40% for log M/M_sun=11.0-11.5 and 20%
for log M/M_sun=10.5-11.0 at z=0. The specific accreted stellar mass rates via
galaxy mergers decline very slowly during the whole redshift range, while
specific star formation rates sharply decrease with time. In the case of the
most massive galaxies, merger accretion becomes the most important channel for
the stellar mass growth at z~2. On the other hand, in-situ star formation is
always the dominant channel in L* galaxies.


  The aim of this paper is to prove the existence of almost global weak
solutions for the unsteady nonlinear elastodynamics system in dimension $d=2$
or $3$, for a range of strain energy density functions satisfying some given
assumptions. These assumptions are satisfied by the main strain energies
generally considered. The domain is assumed to be bounded, and mixed boundary
conditions are considered. Our approach is based on a nonlinear parabolic
regularization technique, involving the $p$-Laplace operator. First we prove
the existence of a local-in-time solution for the regularized system, by a
fixed point technique. Next, using an energy estimate, we show that if the data
are small enough, bounded by $\varepsilon >0$, then the maximal time of
existence does not depend on the parabolic regularization parameter, and the
behavior of the lifespan $T$ is $\gtrsim \log (1/\varepsilon)$, defining what
we call here {\it almost global existence}. The solution is thus obtained by
passing this parameter to zero. The key point of our proof is due to recent
nonlinear Korn's inequalities proven by Ciarlet \& Mardare in
$\mathrm{W}^{1,p}$ spaces, for $p>2$.


  Over the past few years, a significant progress has been made in deep
convolutional neural networks (CNNs)-based image recognition. This is mainly
due to the strong ability of such networks in mining discriminative object pose
and parts information from texture and shape. This is often inappropriate for
fine-grained visual classification (FGVC) since it exhibits high intra-class
and low inter-class variances due to occlusions, deformation, illuminations,
etc. Thus, an expressive feature representation describing global structural
information is a key to characterize an object/ scene. To this end, we propose
a method that effectively captures subtle changes by aggregating context-aware
features from most relevant image-regions and their importance in
discriminating fine-grained categories avoiding the bounding-box and/or
distinguishable part annotations. Our approach is inspired by the recent
advancement in self-attention and graph neural networks (GNNs) approaches to
include a simple yet effective relation-aware feature transformation and its
refinement using a context-aware attention mechanism to boost the
discriminability of the transformed feature in an end-to-end learning process.
Our model is evaluated on eight benchmark datasets consisting of fine-grained
objects and human-object interactions. It outperforms the state-of-the-art
approaches by a significant margin in recognition accuracy.


  Designing faithful yet accurate AI models is challenging, particularly in the
field of individual treatment effect estimation (ITE). ITE prediction models
deployed in critical settings such as healthcare should ideally be (i)
accurate, and (ii) provide faithful explanations. However, current solutions
are inadequate: state-of-the-art black-box models do not supply explanations,
post-hoc explainers for black-box models lack faithfulness guarantees, and
self-interpretable models greatly compromise accuracy. To address these issues,
we propose DISCRET, a self-interpretable ITE framework that synthesizes
faithful, rule-based explanations for each sample. A key insight behind DISCRET
is that explanations can serve dually as database queries to identify similar
subgroups of samples. We provide a novel RL algorithm to efficiently synthesize
these explanations from a large search space. We evaluate DISCRET on diverse
tasks involving tabular, image, and text data. DISCRET outperforms the best
self-interpretable models and has accuracy comparable to the best black-box
models while providing faithful explanations. DISCRET is available at
https://github.com/wuyinjun-1993/DISCRET-ICML2024.


  Measuring quantum-statistical, femtoscopic (including final state
interactions) momentum correlations with final state interactions in
high-energy nucleus-nucleus collisions reveal the space-time structure of the
particle-emitting source created. In this paper, we report NA61/SHINE
measurements of femtoscopic correlations of identified pion pairs and describe
said correlations based on symmetric L\'evy-type sources in Ar+Sc collisions at
150A GeV/c. We investigate the transverse mass dependence of the L\'evy-type
source parameters and discuss their possible interpretations.


  We report a discovery of low-frequency quasi periodic oscillation at 0.3-0.7
Hz in the power spectra of the accreting black hole GRS1739-278 in the
hard-intermediate state during its 2014 outburst based on the ${\it NuSTAR}$
and Swift/XRT data. The QPO frequency strongly evolved with the source flux
during the NuSTAR observation. The source spectrum became softer with rising
QPO frequency and simultaneous increasing of the power-law index and decreasing
of the cut-off energy. In the power spectrum, a prominent harmonic is clearly
seen together with the main QPO peak. The fluxes in the soft and the hard X-ray
bands are coherent, however, the coherence drops for the energy bands separated
by larger gaps. The phase-lags are generally positive (hard) in the 0.1-3 Hz
frequency range, and negative below 0.1 Hz. The accretion disc inner radius
estimated with the relativistic reflection spectral model appears to be $R_{\rm
in} < 7.3 R_{\rm g}$. In the framework of the relativistic precession model, in
order to satisfy the constraints from the observed QPO frequency and the
accretion disc truncation radius, a massive black hole with $M_{\rm BH} \approx
100$M$_\odot$ is required.


  We present here the results from a density dependent study of the activation
energy gaps of the fractional quantum Hall effect states at Landau level
fillings \nu=8/3 and 7/3 in a series of high quality quantum wells. In the
density range from 0.5 x 10^{11} to 3 x 10^{11} cm^{-2}, the 7/3 energy gap
increases monotonically with increasing density, supporting its ground state
being spin polarized. For the 8/3 state, however, its energy gap first
decreases with increasing density, almost vanishes at n ~ 0.8 x 10^{11}
cm^{-2}, and then turns around and increases with increasing density, clearly
demonstrating a spin transition.


  The advent of new-class of high-mobility semiconducting polymers opens up a
window to address fundamental issues in electrical transport mechanism such as
hopping between localized states versus extended state conduction. Here, we
investigate the origin of ultra-low degree of disorder (~ 16 meV) and band-like
negative temperature (T) coefficient of the field effect electron mobility in a
high performance diketopyrrolopyrrole (DPP)-based semiconducting polymer.
Models based on the framework of mobility edge (ME) with exponential density of
states are invoked to explain the trends in transport. The temperature window
over which the system demonstrates de-localized transport was tuned by a
systematic introduction of disorder at the transport interface. Additionally,
the Hall mobility extracted from Hall-voltage measurements in these devices was
found to be comparable to field effect mobility in the high T band-like regime.
Comprehensive studies with different combinations of dielectrics and
semiconductors demonstrate the effectiveness of rationale molecular design
which emphasizes uniform-energetic landscape and low re-organization energy.


  Binding energies of the $^3P_0$ and $^3P_2$ levels of the $1s^2\,2s\,2p$
electron configuration in berylliumlike xenon are rigorously evaluated using ab
initio QED approach. All relevant one- and many-electron QED contributions are
accounted for up to the second order of the perturbation theory. The
interelectronic-interaction effects of the third and higher orders are
considered within the Breit approximation. Nuclear recoil effect is taken into
account as well. In addition, we study all possible levels of the configuration
$1s^2\,2s\,2p$, namely $^1P_1$ and $^3P_{0,1,2}$, by means of the
configuration-interaction Dirac-Fock-Sturm method in berylliumlike neon, iron,
and xenon. In this case the QED effects are treated approximately within the
model QED approach. The obtained theoretical predictions are compared with the
results of previous relativistic calculations and high-precision measurements.


  Reconstructing hadronically decaying top quarks is a key challenge at the
LHC, affecting a long list of Higgs analyses and new physics searches. We
propose a new method of collecting jets in buckets, corresponding to top quarks
and initial state radiation. This method is particularly well suited for
moderate transverse momenta of the top quark, closing the gap between top
taggers and traditional top reconstruction. Applying it to searches for
supersymmetric top squarks we illustrate the power of buckets.


  We consider a distributed learning problem in which the computation is
carried out on a system consisting of a master node and multiple worker nodes.
In such systems, the existence of slow-running machines called stragglers will
cause a significant decrease in performance. Recently, coding theoretic
framework, which is named Gradient Coding (GC), for mitigating stragglers in
distributed learning has been established by Tandon et al. Most studies on GC
are aiming at recovering the gradient information completely assuming that the
Gradient Descent (GD) algorithm is used as a learning algorithm. On the other
hand, if the Stochastic Gradient Descent (SGD) algorithm is used, it is not
necessary to completely recover the gradient information, and its unbiased
estimator is sufficient for the learning. In this paper, we propose a
distributed SGD scheme using Low-Density Generator Matrix (LDGM) codes. In the
proposed system, it may take longer time than existing GC methods to recover
the gradient information completely, however, it enables the master node to
obtain a high-quality unbiased estimator of the gradient at low computational
cost and it leads to overall performance improvement.


  Let $q \in (0,1)$ and $\delta \in (0,1)$ be real numbers, and let $C$ be a
coin that comes up heads with an unknown probability $p$, such that $p \neq q$.
We present an algorithm that, on input $C$, $q$, and $\delta$, decides, with
probability at least $1-\delta$, whether $p<q$ or $p>q$. The expected number of
coin flips made by this algorithm is $O \left( \frac{\log\log(1/\varepsilon) +
\log(1/\delta)}{\varepsilon^2} \right)$, where $\varepsilon = |p-q|$.


  We propose an extension of the principle of virtual work of mechanics to
random dynamics of mechanical systems. The total virtual work of the
interacting forces and inertial forces on every particle of the system is
calculated by considering the motion of each particle. Then according to the
principle of Lagrange-d'Alembert for dynamical equilibrium, the vanishing
ensemble average of the virtual work gives rise to the thermodynamic
equilibrium state with maximization of thermodynamic entropy. This approach
establishes a close relationship between the maximum entropy approach for
statistical mechanics and a fundamental principle of mechanics, and constitutes
an attempt to give the maximum entropy approach, considered by many as only an
inference principle based on the subjectivity of probability and entropy, the
status of fundamental physics law.


  Analytical continuation (AC) connects theoretical calculations and
experimentally measurable quantities. The recently proposed Nevanlinna AC
method is capable of accurately reproducing the sharp features of spectral
functions at high frequencies while maintaining the causality of the response
function. However, their use is currently limited to fermions. Here, we present
an extension of this method to bosons using the hyperbolic tangent trick,
allowing us to transform bosons into auxiliary fermions to which the Nevanlinna
analytic continuation can be applied.


  Accent conversion aims to convert the accent of a source speech to a target
accent, meanwhile preserving the speaker's identity. This paper introduces a
novel non-autoregressive framework for accent conversion that learns
accent-agnostic linguistic representations and employs them to convert the
accent in the source speech. Specifically, the proposed system aligns speech
representations with linguistic representations obtained from Text-to-Speech
(TTS) systems, enabling training of the accent voice conversion model on
non-parallel data. Furthermore, we investigate the effectiveness of a
pretraining strategy on native data and different acoustic features within our
proposed framework. We conduct a comprehensive evaluation using both subjective
and objective metrics to assess the performance of our approach. The evaluation
results highlight the benefits of the pretraining strategy and the
incorporation of richer semantic features, resulting in significantly enhanced
audio quality and intelligibility.


  We propose a simple but efficient method termed Guided Learning for
weakly-labeled semi-supervised sound event detection (SED). There are two
sub-targets implied in weakly-labeled SED: audio tagging and boundary
detection. Instead of designing a single model by considering a trade-off
between the two sub-targets, we design a teacher model aiming at audio tagging
to guide a student model aiming at boundary detection to learn using the
unlabeled data. The guidance is guaranteed by the audio tagging performance gap
of the two models. In the meantime, the student model liberated from the
trade-off is able to provide more excellent boundary detection results. We
propose a principle to design such two models based on the relation between the
temporal compression scale and the two sub-targets. We also propose an
end-to-end semi-supervised learning process for these two models to enable
their abilities to rise alternately. Experiments on the DCASE2018 Task4 dataset
show that our approach achieves competitive performance.


  The PLATO space mission is designed to detect telluric planets in the
habitable zone of solar type stars, and simultaneously characterise the host
star using ultra high precision photometry. The photometry will be performed on
board using weighted masks. However, to reach the required precision,
corrections will have to be performed by the ground segment and will rely on
precise knowledge of the instrument PSF (Point Spread Function). We here
propose to model the PSF using a microscanning method.


  CubeSats and small satellites are emerging as low-cost tools to perform
astronomy, exoplanet searches and earth observation. These satellites can be
dedicated to pointing at targets for weeks or months at a time. This is
typically not possible on larger missions where usage is shared. Current
satellites use reaction wheels and where possible magneto-torquers to control
attitude. However, these actuators can induce jitter due to various sources. In
this work, we introduce a new class of actuators that exploit radiometric
forces induced by gasses on surface with a thermal gradient. Our work shows
that a CubeSat or small spacecraft mounted with radiometric actuators can
achieve precise pointing of few arc-seconds or less and avoid the jitter
problem. The actuator is entirely solid-state, containing no moving mechanical
components. This ensures high-reliability and long-life in space. A preliminary
design for these actuators is proposed, followed by feasibility analysis of the
actuator performance.


  Lead-free halide double perovskites provide a promising solution for the
long-standing issues of lead-containing halide perovskites, i.e., the toxicity
of Pb and the low stability under ambient conditions and high-intensity
illumination. Their light-to-electricity or thermal-to-electricity conversion
is strongly determined by the dynamics of the corresponding lattice vibrations.
Here, we present the measurement of lattice dynamics in a prototypical
lead-free halide double perovskite, i.e., Cs2NaInCl6. Our quantitative
measurements and first-principles calculations show that the scatterings among
lattice vibrations at room temperature are at the timescale of ~ 1 ps, which
stems from the extraordinarily strong anharmonicity in Cs2NaInCl6. We further
quantitatively characterize the degree of anharmonicity of all the ions in the
single Cs2NaInCl6 crystal, and demonstrate that this strong anharmonicity is
synergistically contributed by the bond hierarchy, the tilting of the NaCl6 and
InCl6 octahedral units, and the rattling of Cs+ ions. Consequently, the
crystalline Cs2NaInCl6 possesses an ultralow thermal conductivity of ~0.43 W/mK
at room temperature, and a weak temperature dependence of T-0.41. Our findings
here uncovered the underlying mechanisms behind the dynamics of lattice
vibrations in double perovskites, which could largely benefit the design of
optoelectronics and thermoelectrics based on halide double perovskites.


  In this paper we derive a hierarchy of integral equations from the 4PI
effective action which have the form of Bethe-Salpeter equations. We show that
the vertex functions defined by these equations can be used to truncate the
exact renormalization group flow equations. This truncation has the property
that the flow is a total derivative with respect to the flow parameter. We also
show that the truncation is equivalent to solving the $n$PI equations of
motion. This result establishes a direct connection between two
non-perturbative methods.


  It has recently been shown that the leading Wilson coefficient in type II
string theory can take (almost) all values allowed by unitarity, crossing
symmetry and maximal supersymmetry in D=10 and D=9 dimensions. This suggests
that string theory might define the unique consistent quantum theory of gravity
with maximal supersymmetry. We study the minima of the leading Wilson
coefficient in D=6, 7 and 8 dimensions and find the global minimum at the point
in moduli space with maximal symmetry. The minimum value turns out to always be
negative for D<8.


  These expository notes are a somewhat embellished version of two rather
informal evening review sessions given by the second author at the 2008 Bedlewo
summer school on "Dynamical Systems - Geometric Structures and Rigidity"; they
provide a brief overview of some of the basics of measure theory and its
applications to dynamics which are foundational to the various courses at the
school.


  A major pathway towards understanding complex systems is given by exactly
solvable reference systems that contain the essential physics of the system.
For the $t-t'-U$ Hubbard model, the four-site plaquette is known to have a
quantum critical point in the $U-\mu$ space where states with electron
occupations $N=2, 3, 4$ per plaquette are degenerate [Phys. Rev. B {\bf 94},
125133 (2016)]. We show that such a critical point in the lattice causes an
instability in the particle-particle singlet d-wave channel and manifests some
of the essential elements of the cuprate superconductivity. For this purpose we
design an efficient superperturbation theory -- based on the dual fermion
approach -- with the critical plaquette as the reference system. Thus, the
perturbation theory already contains the relevant d-wave fluctuations from the
beginning via the two-particle correlations of the plaquette. We find that
d-wave superconductivity remains a leading instability channel under reasonably
broad range of parameters. The next-nearest-neighbour hopping $t'$ is shown to
play a crucial role in a formation of strongly bound electronic bipolarons
whose coherence at lower temperature results in superconductivity. The physics
of the pseudogap within the developed picture is also discussed.


  By studying the Hawking radiation of the most general static spherically
symmetric black hole arising from scalar and Dirac particles tunnelling, we
find the Hawking temperature is invariant in the general coordinate
representation (\ref{arbitrary1}), which satisfies two conditions: a) its
radial coordinate transformation is regular at the event horizon; and b) there
is a time-like Killing vector.


  Time-Basic Petri nets, is a powerful formalism for model- ing real-time
systems where time constraints are expressed through time functions of
marking's time description associated with transition, representing possible
firing times. We introduce a technique for reachability analysis based on the
building of finite contraction of the infinite state space associated with such
a models. The technique constructs a finite symbolic reachability graph relying
on a sort of time coverage, and over- comes the limitations of the existing
available analyzers for Time-Basic nets, based in turn on a time-bounded
inspection of a (possibly infinite) reachability-tree. A key feature of the
technique is the introduction of the Time Anonymous concept, which allows the
identification of components not influencing the evolution of a model. A
running example is used throughout the paper to sketch the symbolic graph
construction. The graph construction algorithm has been automated by a Java
tool-set, described in the paper together with its main functionality and
analysis capability. A use case describing a real-world example has been
employed to benchmark the technique and the tool-set. The main outcome of this
test are also presented in the paper.


  The entanglement entropy (EE) encodes key properties of quantum many-body
systems. It is usually calculated for subregions of finite volume (or area in
2d). In this work, we study the EE of skeletal regions that have \textit{no}
volume, such as a line in 2d. We show that skeletal entanglement displays new
behavior compared to its bulk counterpart, and leads to distinct universal
quantities. We provide non-perturbative bounds for the skeletal area-law
coefficient of a large family of quantum states. We then explore skeletal
scaling for the toric code, conformal bosons and Dirac fermions, Lifshitz
critical points, and Fermi liquids. We discover signatures including skeletal
topological EE, novel corner terms, and strict area-law scaling for metals.
These findings suggest that skeletal entropy serves as a measure for the range
of entanglement. We discuss the possibility of a continuum description
involving the fusion of defect operators. Finally, we outline open questions
relating to other systems, and measures such as the logarithmic negativity.


  The performance of land surface models (LSMs) significantly affects the
understanding of atmospheric and related processes. Many of the LSMs' soil and
vegetation parameters were unknown so that it is crucially important to
efficiently optimize them. Here I present a globally applicable and
computationally efficient method for parameter optimization and uncertainty
assessment of the LSM by combining Markov Chain Monte Carlo (MCMC) with machine
learning. First, I performed the long-term (decadal scales) ensemble simulation
of the LSM, in which each ensemble member has different parameters' values, and
calculated the gap between simulation and observation, or the cost function,
for each ensemble member. Second, I developed the statistical machine learning
based surrogate model, which is computationally cheap but accurately mimics the
relationship between parameters and the cost function, by applying the Gaussian
process regression to learn the model simulation. Third, we applied MCMC by
repeatedly driving the surrogate model to get the posterior probabilistic
distribution of parameters. Using satellite passive microwave brightness
temperature observations, both synthetic and real-data experiments in the Sahel
region of west Africa were performed to optimize unknown soil and vegetation
parameters of the LSM. The primary findings are (1) the proposed method is
50,000 times as fast as the direct application of MCMC to the full LSM; (2) the
skill of the LSM to simulate both soil moisture and vegetation dynamics can be
improved; (3) I successfully quantify the characteristics of equifinality by
obtaining the full non-parametric probabilistic distribution of parameters.


  We investigate the problem of covert and secret key generation over a
state-dependent discrete memoryless channel with one-way public discussion in
which an adversary, the warden, may arbitrarily choose the channel state. We
develop an adaptive protocol that, under conditions that we explicitly specify,
not only allows the transmitter and the legitimate receiver to exchange a
secret key but also conceals from the active warden whether the protocol is
being run. When specialized to passive adversaries that do not control the
channel state, we partially characterize the covert secret key capacity. In
particular, the covert secret key capacity is sometimes equal to the covert
capacity of the channel, so that secrecy comes "for free."


  We theoretically investigate the cooling of a propagating phonon through
Brillouin scattering. To that end, we propose to introduce an external viscous
force using Brillouin scattering and an electro-optic feedback. Short delays
feedback show an efficient control of the Brillouin linewidth whereas long
delays can induce Fano-like resonances.


  The purpose of this work is to show a possible reconciliation between Mach's
principle and the Schwarzschild solution, using a description of this solution
in terms of a new radial cooordinate related to the behaviour of Unruh
detectors.


  Lorentz invariance violations (LIV) can yield vacuum birefringence, which
results in an energy-dependent rotation of the polarization vector of linearly
polarized emission from astrophysical sources. It is believed that if the
relative rotation angle ($\Delta\Theta$) of the polarization vector of high
energy photons with respect to that of low energy photons is larger than
$\pi/2$, then the net polarization of the signal would be significantly
depleted and could not be as high as the observed level. Hence, the measurement
of high polarization implies that $\Delta\Theta$ should not be too large. In
this work, we assemble recent detections of prompt emission polarization in
gamma-ray bursts (GRBs), all of whom have high detection significance.
Following the method shown in Lin et al. (2016), we give a detailed calculation
on the polarization evolution arising from the LIV effect for each GRB, and
confirm that, even if $\Delta\Theta$ is approaching to $\pi/2$, the net
polarization is not severely suppressed, and more than 60\% of the initial
polarization can be conserved. Applying this method to our GRB polarimetric
data, we improve existing sensitivities to LIV involving photons by factors
ranging from two to ten. In addition, we prove that our constraints are not
greatly affected by uncertainties in the spectral parameters of GRBs.


  One of the purposes of Big Data systems is to support analysis of data
gathered from heterogeneous data sources. Since data warehouses have been used
for several decades to achieve the same goal, they could be leveraged also to
provide analysis of data stored in Big Data systems. The problem of adapting
data warehouse data and schemata to changes in these requirements as well as
data sources has been studied by many researchers worldwide. However,
innovative methods must be developed also to support evolution of data
warehouses that are used to analyze data stored in Big Data systems. In this
paper, we propose a data warehouse architecture that allows to perform
different kinds of analytical tasks, including OLAP-like analysis, on big data
loaded from multiple heterogeneous data sources with different latency and is
capable of processing changes in data sources as well as evolving analysis
requirements. The operation of the architecture is highly based on the metadata
that are outlined in the paper.


  We study single top production in high energy $e\gamma$ collisions. The
process $e\gamma\to\nu b\bar t$ can serve as a unique tool for measuring the
$Wtb$ coupling. We show that allowing for realistic luminosity and backgrounds,
the size of this coupling can be determined to within 10 (5)\% in an $e\gamma$
collider built around a 500 (1000) GeV $e^+e^-$ collider.


  The existence of abelian gauge symmetries in four-dimensional F-theory
compactifications depends on the global geometry of the internal Calabi-Yau
fourfold and has important phenomenological consequences. We study conceptual
and phenomenological aspects of such U(1) symmetries along the Coulomb and the
Higgs branch. As one application we examine abelian gauge factors arising after
a certain global restriction of the Tate model that goes beyond a local
spectral cover analysis. In SU(5) GUT models this mechanism enforces a global
U(1)_X symmetry that prevents dimension-4 proton decay and allows for an
identification of candidate right-handed neutrinos. We invoke a detailed
account of the singularities of Calabi-Yau fourfolds and their mirror duals
starting from an underlying E_8 and E_7 x U(1) enhanced Tate model. The global
resolutions and deformations of these singularities can be used as the
appropriate framework to analyse F-theory GUT models.


  An argument is presented that if a theory of quantum gravity is physically
discrete at the Planck scale and the theory recovers General Relativity as an
approximation, then, at the current stage of our knowledge, causal sets must
arise within the theory, even if they are not its basis.
  We show in particular that an apparent alternative to causal sets, viz. a
certain sort of discrete Lorentzian simplicial complex, cannot recover General
Relativistic spacetimes in the appropriately unique way. For it cannot
discriminate between Minkowski spacetime and a spacetime with a certain sort of
gravitational wave burst.


  In this paper we show that forcings which are strongly proper for
stationarily many countable elementary submodels preserve each of the following
properties of topological spaces: countably tight; Lindel\"of; Rothberger;
Menger; and a strategic version of Rothberger. This extends results from Dow,
as well as from Iwasa and from Kada.


  Relativistic electrons, seen in the large diffuse radio halo of the Coma
cluster of galaxies, should scatter background photons to higher energies. We
calculate the inverse Compton contributions from the microwave background, from
the local radiation field of elliptical galaxies and from the thermal X-ray
emission of the intra cluster medium to the different observed energy bands,
and draw restrictions to the shape of the spectrum of the relativistic electron
population. The expected electron spectra in different halo formation models
are discussed, and signatures for a future distinction of these models are
presented, tracing the injection processes and the influence of optical
thickness of the radio halo for very low frequency emission due to synchrotron
self absorption. Some of the upper limits on the electron spectrum translate
into lower limits of the halo magnetic fields, since the observed synchrotron
radiation is known. Despite uncertainties in the extrapolation of the radio
spectrum to lower frequencies a lower limit to the central field strength of
B_o > 0.3 muG seems to be sure. This is comparable to the value resulting from
minimal energy arguments. If B_o < 1.2 muG, the recently reported extreme
ultraviolet excess of Coma (Lieu et al. 1996) could result from inverse Compton
scattered microwave photons. Formulae for transrelativistic Thomson scattering
are given in the Appendix.


  Cosmic inflation can enter an ultraslow-roll (USR) stage, if there is a
plateau on the inflaton potential. During this stage, the primordial curvature
perturbation ${\mathcal R}_k$ and its power spectrum ${\mathcal P}_{\mathcal
R}$ can be remarkably enhanced on small scales. In this work, an analytical
approximation is provided to systematically study the evolution of ${\mathcal
R}_k$ in the USR inflation. We first discuss the asymptotic solutions of the
moduli and arguments of ${\mathcal R}_k$ and its time derivative ${\mathcal
R}_{k,N}$ on the sub- and super-horizon scales separately and find that all
these solutions have simple exponential forms. Then, ${\mathcal R}_k$ on five
typical scales are investigated in order. Our analytical approximation predicts
that ${\mathcal R}_k$ first revolves around the origin in the complex plane,
but if it crosses the horizon around the start of the USR stage, there appears
a subsequent linear evolution towards or away from the origin. This behavior
naturally explains the shape of ${\mathcal P}_{\mathcal R}$ from the sharp dip
to the peak and matches the numerical results perfectly. Moreover, the minimum
of ${\mathcal P}_{\mathcal R}$ is exactly proved to be nonvanishing. Our
analytical approximation will help the model building in primordial black hole
and gravitational wave physics.


  Inspired by recent experiments on fluctuations of the flagellar beating in
sperms and C. reinhardtii, we investigate the precision of phase fluctuations
in a system of nearest-neighbour-coupled molecular motors. We model the system
as a Kuramoto chain of oscillators with coupling constant $k$ and noisy
driving. The precision $p$ is a Fano-factor-like observable which obeys the
Thermodynamic Uncertainty Relation (TUR), that is an upper bound related to
dissipation. We first consider independent motor noises with diffusivity $D$:
in this case the precision goes as $k/D$, coherently with the behavior of
spatial order. The minimum observed precision is that of the uncoupled
oscillator $p_{unc}$, the maximum observed one is $Np_{unc}$, saturating the
TUR bound. Then we consider driving noises which are spatially correlated, as
it may happen in the presence of some direct coupling between adjacent motors.
Such a spatial correlation in the noise does not reduce evidently the degree of
spatial correlation in the chain, but sensibly reduces the maximum attainable
precision $p$, coherently with experimental observations. The limiting
behaviors of the precision, in the two opposite cases of negligible interaction
and strong interaction, are well reproduced by the precision of the single
chain site $p_{unc}$ and the precision of the center of mass of the chain
$N_{eff} p_{unc}$ with $N_{eff}<N$: both do not depend on the degree of
interaction in the chain, but $N_{eff}$ decreases with the correlation length
of the motor noises.


  We extend some of the results of Carey-Marcolli-Rennie on modular index
invariants of Mumford curves to the case of higher rank buildings: we discuss
notions of KMS weights on buildings, that generalize the construction of graph
weights over graph C*-algebras.


  In this paper, we address the problem of local well-posedness of the
Chern-Simons-Dirac (CSD) and the Chern-Simons-Higgs (CSH) equations in the
Lorenz gauge for low regularity initial data. One of our main contributions is
the uncovering of a null structure of (CSD). Combined with the standard
machinery of $X^{s,b}$ spaces, we obtain local well-posedness of (CSD) for
initial data $a_{\mu}, \psi \in H^{1/4+\epsilon}_{x}$. Moreover, it is observed
that the same techniques applied to (CSH) lead to a quick proof of local
well-posedness for initial data $a_{\mu} \in H^{1/4+\epsilon}_{x}$, $(\phi,
\partial_{t} \phi) \in H^{3/4+\epsilon}_{x} \times H^{-1/4+\epsilon}_{x}$,
which improves the previous result of Selberg-Tesfahun (2012).


  Machine learning models improve the speed and quality of physical models.
However, they require a large amount of data, which is often difficult and
costly to acquire. Predicting thermal comfort, for example, requires a
controlled environment, with participants presenting various characteristics
(age, gender, ...). This paper proposes a method for hybridizing real data with
simulated data for thermal comfort prediction. The simulations are performed
using Modelica Language. A benchmarking study is realized to compare different
machine learning methods. Obtained results look promising with an F1 score of
0.999 obtained using the random forest model.


  Probabilistic volumetric mapping (PVM) represents a 3D environmental map for
an autonomous robotic navigational task. A popular implementation such as
Octomap is widely used in the robotics community for such a purpose. The
Octomap relies on octree to represent a PVM and its main bottleneck lies in
massive ray-shooting to determine the occupancy of the underlying volumetric
voxel grids. In this paper, we propose GPU-based ray shooting to drastically
improve the ray shooting performance in Octomap. Our main idea is based on the
use of recent ray-tracing RTX GPU, mainly designed for real-time
photo-realistic computer graphics and the accompanying graphics API, known as
DXR. Our ray-shooting first maps leaf-level voxels in the given octree to a set
of axis-aligned bounding boxes (AABBs) and employ massively parallel ray
shooting on them using GPUs to find free and occupied voxels. These are fed
back into CPU to update the voxel occupancy and restructure the octree. In our
experiments, we have observed more than three-orders-of-magnitude performance
improvement in terms of ray shooting using ray-tracing RTX GPU over a
state-of-the-art Octomap CPU implementation, where the benchmarking
environments consist of more than 77K points and 25K~34K voxel grids.


  The 175th anniversary of the ASA provides an opportunity to look back into
the past and peer into the future. What led our forebears to found the
association? What commonalities do we still see? What insights might we glean
from their experiences and observations? I will use the anniversary as a chance
to reflect on where we are now and where we are headed in terms of statistical
education amidst the growth of data science. Statistics is the science of
learning from data. By fostering more multivariable thinking, building
data-related skills, and developing simulation-based problem solving, we can
help to ensure that statisticians are fully engaged in data science and the
analysis of the abundance of data now available to us.


  Fault-tolerant quantum error correction (QEC) is crucial for unlocking the
true power of quantum computers. QEC codes use multiple physical qubits to
encode a logical qubit, which is protected against errors at the physical qubit
level. Here we use a trapped ion system to experimentally prepare $m$-qubit GHZ
states and sample the measurement results to construct $m\times m$ logical
states of the $[[m^2,1,m]]$ Shor code, up to $m=7$. The synthetic logical
fidelity shows how deeper encoding can compensate for additional gate errors in
state preparation for larger logical states. However, the optimal code size
depends on the physical error rate and we find that $m=5$ has the best
performance in our system. We further realize the direct logical encoding of
the $[[9,1,3]]$ Shor code on nine qubits in a thirteen-ion chain for
comparison, with $98.8(1)\%$ and $98.5(1)\%$ fidelity for state
$\left\vert\pm\right\rangle_L$, respectively.


  We introduce DatasetGAN: an automatic procedure to generate massive datasets
of high-quality semantically segmented images requiring minimal human effort.
Current deep networks are extremely data-hungry, benefiting from training on
large-scale datasets, which are time consuming to annotate. Our method relies
on the power of recent GANs to generate realistic images. We show how the GAN
latent code can be decoded to produce a semantic segmentation of the image.
Training the decoder only needs a few labeled examples to generalize to the
rest of the latent space, resulting in an infinite annotated dataset generator!
These generated datasets can then be used for training any computer vision
architecture just as real datasets are. As only a few images need to be
manually segmented, it becomes possible to annotate images in extreme detail
and generate datasets with rich object and part segmentations. To showcase the
power of our approach, we generated datasets for 7 image segmentation tasks
which include pixel-level labels for 34 human face parts, and 32 car parts. Our
approach outperforms all semi-supervised baselines significantly and is on par
with fully supervised methods, which in some cases require as much as 100x more
annotated data as our method.


  We study the time taken by a language learner to correctly identify the
meaning of all words in a lexicon under conditions where many plausible
meanings can be inferred whenever a word is uttered. We show that the most
basic form of cross-situational learning - whereby information from multiple
episodes is combined to eliminate incorrect meanings - can perform badly when
words are learned independently and meanings are drawn from a nonuniform
distribution. If learners further assume that no two words share a common
meaning, we find a phase transition between a maximally-efficient learning
regime, where the learning time is reduced to the shortest it can possibly be,
and a partially-efficient regime where incorrect candidate meanings for words
persist at late times. We obtain exact results for the word-learning process
through an equivalence to a statistical mechanical problem of enumerating loops
in the space of word-meaning mappings.


  The first stages of finger formation in a Hele-Shaw cell with lifting plates
are investigated by means of linear stability analysis. The equation of motion
for the pressure field (growth law) results to be that of the directional
solidification problem in some unsteady state. At the beginning of lifting the
square of the wavenumber of the dominant mode results to be proportional to the
lifting rate (in qualitative agreement with the experimental data), to the
square of the length of the cell occupied by the more viscous fluid, and
inversely proportional to the cube of the cell gap. This dependence on the cell
parameters is significantly different of that found in the standard cell.


  We present an illustrative application of the two famous mathematical
theorems in differential topology in order to show the existence of periodic
orbits with arbitrary given period for a class of hamiltonians .This result
point out for a mathematical answer for the long standing problem of existence
of Planetary Sistems around stars.


  The classical belief revision framework, as proposed by Alchourron,
Gardenfors, and Makinson, involves the revision of a theory based on eight
postulates. In this paper, we focus on the exploration of a revision theory
grounded in quantum mechanics, referred to as the natural revision theory.
  There are two reasoning modes in quantum systems: static intuitionistic
reasoning, which incorporates contextuality, and dynamic reasoning, which is
achieved through projection measurement. We combine the advantages of two
intuitionistic quantum logic frameworks, as proposed by D{\"o}ring and Coecke,
respectively. Our goal is to establish a truth-value assignment for
intuitionistic quantum logic that not only aligns with the inherent
characteristics of quantum mechanics but also supports truth-value reasoning.
The natural revision theory is then investigated based on this approach.
  We introduce two types of revision operators that correspond to the two
reasoning modes in quantum systems: static and dynamic revision. Furthermore,
we highlight the distinctions between these two operators. Shifting away from
classical revision paradigms, we consider the revision of consequence relations
in intuitionistic quantum logic. We demonstrate how, within the natural
revision theory framework, both revision operators collectively influence the
consequence relations. Notably, the outcomes of revision process are impacted
by the sequence in which these interweaved operators are deployed.


  This article is devoted to review the known results on global well-posedness
for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with
small data. Similar results will be obtained for the initial-boundary value
problems in exterior domains with compact boundary. Also, the known results on
large data problems will be reviewed together with open problems.


  Human pose estimation in videos has long been a compelling yet challenging
task within the realm of computer vision. Nevertheless, this task remains
difficult because of the complex video scenes, such as video defocus and
self-occlusion. Recent methods strive to integrate multi-frame visual features
generated by a backbone network for pose estimation. However, they often ignore
the useful joint information encoded in the initial heatmap, which is a
by-product of the backbone generation. Comparatively, methods that attempt to
refine the initial heatmap fail to consider any spatio-temporal motion
features. As a result, the performance of existing methods for pose estimation
falls short due to the lack of ability to leverage both local joint (heatmap)
information and global motion (feature) dynamics.
  To address this problem, we propose a novel joint-motion mutual learning
framework for pose estimation, which effectively concentrates on both local
joint dependency and global pixel-level motion dynamics. Specifically, we
introduce a context-aware joint learner that adaptively leverages initial
heatmaps and motion flow to retrieve robust local joint feature. Given that
local joint feature and global motion flow are complementary, we further
propose a progressive joint-motion mutual learning that synergistically
exchanges information and interactively learns between joint feature and motion
flow to improve the capability of the model. More importantly, to capture more
diverse joint and motion cues, we theoretically analyze and propose an
information orthogonality objective to avoid learning redundant information
from multi-cues. Empirical experiments show our method outperforms prior arts
on three challenging benchmarks.


  Recently sparse coding have been highly successful in image classification
mainly due to its capability of incorporating the sparsity of image
representation. In this paper, we propose an improved sparse coding model based
on linear spatial pyramid matching(SPM) and Scale Invariant Feature Transform
(SIFT ) descriptors. The novelty is the simultaneous non-convex and
non-negative characters added to the sparse coding model. Our numerical
experiments show that the improved approach using non-convex and non-negative
sparse coding is superior than the original ScSPM[1] on several typical
databases.


  We consider a problem of guessing, wherein an adversary is interested in
knowing the value of the realization of a discrete random variable $X$ on
observing another correlated random variable $Y$. The adversary can make
multiple (say, $k$) guesses. The adversary's guessing strategy is assumed to
minimize $\alpha$-loss, a class of tunable loss functions parameterized by
$\alpha$. It has been shown before that this loss function captures well known
loss functions including the exponential loss ($\alpha=1/2$), the log-loss
($\alpha=1$) and the $0$-$1$ loss ($\alpha=\infty$). We completely characterize
the optimal adversarial strategy and the resulting expected $\alpha$-loss,
thereby recovering known results for $\alpha=\infty$. We define an information
leakage measure from the $k$-guesses setup and derive a condition under which
the leakage is unchanged from a single guess.


  Recognizing human actions from unknown and unseen (novel) views is a
challenging problem. We propose a Robust Non-Linear Knowledge Transfer Model
(R-NKTM) for human action recognition from novel views. The proposed R-NKTM is
a deep fully-connected neural network that transfers knowledge of human actions
from any unknown view to a shared high-level virtual view by finding a
non-linear virtual path that connects the views. The R-NKTM is learned from
dense trajectories of synthetic 3D human models fitted to real motion capture
data and generalizes to real videos of human actions. The strength of our
technique is that we learn a single R-NKTM for all actions and all viewpoints
for knowledge transfer of any real human action video without the need for
re-training or fine-tuning the model. Thus, R-NKTM can efficiently scale to
incorporate new action classes. R-NKTM is learned with dummy labels and does
not require knowledge of the camera viewpoint at any stage. Experiments on
three benchmark cross-view human action datasets show that our method
outperforms existing state-of-the-art.


  Quantum channels enable the implementation of communication tasks
inaccessible to their classical counterparts. The most famous example is the
distribution of secret key. However, in the absence of quantum repeaters, the
rate at which these tasks can be performed is dictated by the losses in the
quantum channel. In practice, channel losses have limited the reach of quantum
protocols to short distances. Quantum repeaters have the potential to
significantly increase the rates and reach beyond the limits of direct
transmission. However, no experimental implementation has overcome the direct
transmission threshold. Here, we propose three quantum repeater schemes and
assess their ability to generate secret key when implemented on a setup using
nitrogen-vacancy (NV) centers in diamond with near-term experimental
parameters. We find that one of these schemes - the so-called single-photon
scheme, requiring no quantum storage - has the ability to surpass the capacity
- the highest secret-key rate achievable with direct transmission - by a factor
of 7 for a distance of approximately 9.2 km with near-term parameters,
establishing it as a prime candidate for the first experimental realization of
a quantum repeater.


  We present a first statistical study of subproton and electron scales
turbulence in the terrestrial magnetosheath using the Cluster Search Coil
Magnetometer (SCM) waveforms of the STAFF instrument measured in the frequency
range [1,180] Hz. It is found that clear spectral breaks exist near the
electron scale, which separate two power-law like frequency bands referred to
as the dispersive and the electron dissipation ranges. The frequencies of the
breaks f_b are shown to be well correlated with the electron gyroscale \rho_e
rather than with the electron inertial length de. The distribution of the
slopes below fb was found to be narrow and peaks near -2.9, while that of the
slopes above fb was found broader, peaks near -5.2 and has values as low as
-7.5. This is the first time that such steep power-law spectra are reported in
space plasma turbulence. These observations provide strong constraints on
theoretical modeling of kinetic turbulence and dissipation in collisionless
magnetized plasmas.


  In this paper we study various types of spectra of functions $\phi:\jj\to X$,
where $\jj\in\{\r_+,\r\}$ and $X$ is a complex Banach space. We show that
uniform spectrum defined in [15] coincides with Carleman spectrum for $\phi\in
L^{\infty}(\r,X)$. This result holds true also for Laplace (half-line) spectrum
for $\phi\in L^{\infty}(\r_+,X)$. We also indicate a class of bounded
measurable functions for which Laplace spectrum and Carleman spectrum are equal


  We consider a differential inclusion on a manifold, defined by a field of
open half-spaces whose boundary in each tangent space is the kernel of a
one-form. We make the assumption that the corank one distribution associated to
the kernel is completely nonholonomic. We identify a subset of solutions of the
differential inclusion, satisfying two endpoints and periodic boundary
conditions, which are homotopically equivalent in the $W^{1,p}$-topology, for
any $p\in [1,+\infty)$, to the based loop space and the free loop space
respectively.


  In this contribution we briefly introduce a mechanism for short gamma ray
burst emission different from the usually assumed compact object binary merger
progenitor model. It is based on the energy release in the central regions of
neutron stars. This energy injection may be due to internal self-annihilation
of dark matter gravitationally accreted from the galactic halo. We explain how
this effect may trigger its full or partial conversion into a quark star and,
in such a case, induce a gamma ray burst with isotropic equivalent energies in
agreement with those measured experimentally. Additionally, we show how the
ejection of the outer crust in such events may be accelerated enough to produce
Lorentz factors over those required for gamma ray emission.


  Grinberg defined Nyldon words as those words which cannot be factorized into
a sequence of lexicographically nondecreasing smaller Nyldon words. He was
inspired by Lyndon words, defined the same way except with "nondecreasing"
replaced by "nonincreasing." Charlier, Philibert, and Stipulanti proved that,
like Lyndon words, any word has a unique nondecreasing factorization into
Nyldon words. They also show that the Nyldon words form a right Lazard set, and
equivalently, a right Hall set. In this paper, we provide a new proof of unique
factorization into Nyldon words related to Hall set theory and resolve several
questions of Charlier et al. In particular, we prove that Nyldon words of a
fixed length form a circular code, we prove a result on factorizing powers of
words into Nyldon words, and we investigate the Lazard procedure for generating
Nyldon words. We show that these results generalize to a new class of Hall
sets, of which Nyldon words are an example, that we name "Nyldon-like sets."


  We consider the question that the spectrum and arithmetic of locally
symmetric spaces defined by congruent arithmetical lattices should mutually
determine each other. We frame these questions in the context of automorphic
representations.


  We consider the Bak--Sneppen model near zero dimension where the avalanche
exponent $\tau$ is close to 1 and the exponents $\mu$ and $\sigma$ are close to
0. We demonstrate that $\tau-1=\mu-\sigma=\exp\{-\mu^{-1}-\gamma+...\}$ in this
limit, where $\gamma$ is the Euler's constant. The avalanche hierarchy equation
is rewritten in a form that makes possible to find the relation between the
critical exponents $\sigma$ and $\mu$ with high accuracy. We obtain new, more
precise, values of the critical exponents for the 1D and 2D Bak-Sneppen model
and for the 1D anisotropic Bak-Sneppen model.


  Recently, variants of many classical extremal theorems have been proved in
the random environment. We, complementing existing results, extend the
Erd\H{o}s-Gallai Theorem in random graphs. In particular, we determine, up to a
constant factor, the maximum number of edges in a $P_n$-free subgraph of
$G(N,p)$, practically for all values of $N,n$ and $p$. Our work is also
motivated by the recent progress on the size-Ramsey number of paths.


  In this paper, we use reinforcement learning to find effective decoding
strategies for binary linear codes. We start by reviewing several iterative
decoding algorithms that involve a decision-making process at each step,
including bit-flipping (BF) decoding, residual belief propagation, and anchor
decoding. We then illustrate how such algorithms can be mapped to Markov
decision processes allowing for data-driven learning of optimal decision
strategies, rather than basing decisions on heuristics or intuition. As a case
study, we consider BF decoding for both the binary symmetric and additive white
Gaussian noise channel. Our results show that learned BF decoders can offer a
range of performance-complexity trade-offs for the considered Reed-Muller and
BCH codes, and achieve near-optimal performance in some cases. We also
demonstrate learning convergence speed-ups when biasing the learning process
towards correct decoding decisions, as opposed to relying only on random
explorations and past knowledge.


  The Polarizable Continuum Model (PCM) can be used in conjunction with Density
Functional Theory (DFT) and its time-dependent extension (TDDFT) to simulate
the electronic and optical properties of molecules and nanoparticles immersed
in a dielectric environment, typically liquid solvents. In this contribution,
we develop a methodology to account for solvation effects in real-space (and
real-time) (TD)DFT calculations. The boundary elements method is used to
calculate the solvent reaction potential in terms of the apparent charges that
spread over the Van der Waals solute surface. In a real-space representation
this potential may exhibit a Coulomb singularity at grid points that are close
to the cavity surface. We propose a simple approach to regularize such
singularity by using a set of spherical Gaussian functions to distribute the
apparent charges. We have implemented the proposed method in the Octopus code
and present results for the electrostatic contribution to the solvation free
energies and solvatochromic shifts for a representative set of organic
molecules in water.


  The electronic states of a parabolic quantum dot in a magnetic field are
studied with the inclusion of the spin-orbit interaction. The analitycal
formulae for the ground state energy of the interacting system are derived. The
spin-orbit interaction is shown to introduce new features to the far infra-red
absorption spectrum, where it leads to the splitting of the two principal
modes. The results are compared with the charging experiments by Ashoori et al.
and the far infra-red absorption measurements by Demel et al.


  Recently, we proposed a new braneworld model [GIT] in which the collision of
a brane universe and a vacuum bubble coming from the extra-dimension is
utilized as a trigger of brane big-bang. In this article, mainly reviewing this
model, we briefly summarize cosmological braneworld scenarios in which
collision of branes plays an important role.


  In this paper, we investigate robust resource allocation algorithm design for
multiuser downlink multiple-input single-output (MISO) unmanned aerial vehicle
(UAV) communication systems, where we account for the various uncertainties
that are unavoidable in such systems and, if left unattended, may severely
degrade system performance. We jointly optimize the two-dimensional (2-D)
trajectory and the transmit beamforming vector of the UAV for minimization of
the total power consumption. The algorithm design is formulated as a non-convex
optimization problem taking into account the imperfect knowledge of the angle
of departure (AoD) caused by UAV jittering, user location uncertainty, wind
speed uncertainty, and polygonal no-fly zones (NFZs). Despite the non-convexity
of the optimization problem, we solve it optimally by employing monotonic
optimization theory and semidefinite programming relaxation which yields the
optimal 2-D trajectory and beamforming policy. Since the developed optimal
resource allocation algorithm entails a high computational complexity, we also
propose a suboptimal iterative low-complexity scheme based on successive convex
approximation to strike a balance between optimality and computational
complexity. Our simulation results reveal not only the significant power
savings enabled by the proposed algorithms compared to two baseline schemes,
but also confirm their robustness with respect to UAV jittering, wind speed
uncertainty, and user location uncertainty. Moreover, our results unveil that
the joint presence of wind speed uncertainty and NFZs has a considerable impact
on the UAV trajectory. Nevertheless, by counteracting the wind speed
uncertainty with the proposed robust design, we can simultaneously minimize the
total UAV power consumption and ensure a secure trajectory that does not
trespass any NFZ.


  We present an analysis of the lightcurve extracted from Transiting Exoplanet
Survey Satellite Full Frame Images of the double-mode RR Lyrae V338 Boo. We
find that the fundamental mode pulsation is changing in amplitude across the 54
days of observations. The first overtone mode pulsation also changes, but on a
much smaller scale. Harmonics and combinations of the primary pulsation modes
also exhibit unusual behavior. Possible connections with other changes in RR
Lyrae pulsations are discussed, but a full understanding of the cause of the
changes seen in V338 Boo should shed light on some of the most difficult and
unanswered questions in stellar pulsation theory, and astrophysics more
generally.


  We consider a Gaussian multiple-access channel with random user activity
where the total number of users $\ell_n$ and the average number of active users
$k_n$ may be unbounded. For this channel, we characterize the maximum number of
bits that can be transmitted reliably per unit-energy in terms of $\ell_n$ and
$k_n$. We show that if $k_n\log \ell_n$ is sublinear in $n$, then each user can
achieve the single-user capacity per unit-energy. Conversely, if $k_n\log
\ell_n$ is superlinear in $n$, then the capacity per unit-energy is zero. We
further demonstrate that orthogonal-access schemes, which are optimal when all
users are active with probability one, can be strictly suboptimal.


  I describe how the Witten genus of a complex manifold $X$ can be seen from a
rigorous analysis of a certain two-dimensional quantum field theory of maps
from a surface to $X$.


  Given a hyperelliptic Klein surface, we construct companion Klein bottles,
extending our technique of companion tori already exploited by the authors in
the genus 2 case. Bavard's short loops on such companion surfaces are studied
in relation to the original surface so to improve a systolic inequality of
Gromov's. A basic idea is to use length bounds for loops on a companion Klein
bottle, and then analyze how curves transplant to the original nonorientable
surface. We exploit the real structure on the orientable double cover by
applying the coarea inequality to the distance function from the real locus. Of
particular interest is the case of Dyck's surface. We also exploit an optimal
systolic bound for the M\"obius band, due to Blatter.


  The quantum nature of the state of a bosonic quantum field manifests itself
in its entanglement, coherence, or optical nonclassicality which are each known
to be resources for quantum computing or metrology. We provide quantitative and
computable bounds relating entanglement measures with optical nonclassicality
measures. These bounds imply that strongly entangled states must necessarily be
strongly optically nonclassical. As an application, we infer strong bounds on
the entanglement that can be produced with an optically nonclassical state
impinging on a beam splitter. For Gaussian states, we analyze the link between
the logarithmic negativity and a specific nonclassicality witness called
"quadrature coherence scale".


  Scalar-tensor theories are the best motivated alternatives to general
relativity and provide a mathematically consistent framework to test the
various observable predictions. They can involve three functions of the scalar
field: (i) a potential (as in "quintessence" models), (ii) a matter-scalar
coupling function (as in "extended quintessence", where it may also be
rewritten as a nonminimal coupling of the scalar field to the scalar
curvature), and (iii) a coupling function of the scalar field to the
Gauss-Bonnet topological invariant. We recall the main experimental constraints
on this class of theories, and underline that solar-system, binary-pulsar, and
cosmological observations give qualitatively different tests. We finally show
that the combination of these data is necessary to constrain the existence of a
scalar-Gauss-Bonnet coupling.


  The thermoelectric properties of AlMgB14-based materials prepared by spark
plasma sintering were investigated. Al, Mg, and B powder were used as raw
material powders. The raw powders were mixed using a V-shaped mixer, and then
the mixture was sintered at 1673 K or 1773K. The mixture ratio of raw powders
was varied around stoichiometric ratio of AlMgB14. X-ray diffraction patterns
of samples showed that all samples consist of AlMgB14 and some by-products,
MgAl2O4, B2O and AlB12. The Seebeck coefficient of the samples exhibited
significant change depending on the varying mixture ratio. One sample exhibited
a large negative value for the Seebeck coefficient (approximately -500
{\mu}V/K) over the temperature range from 573K to 1073 K, while others showed
positive value (250-450 {\mu}V/K). Thus n-type AlMgB14-based material has been
realized simply by varying raw material ratio.


  The intercity freight trips of heavy trucks are important data for
transportation system planning and urban agglomeration management. In recent
decades, the extraction of freight trips from GPS data has gradually become the
main alternative to traditional surveys. Identifying the trip ends (origin and
destination, OD) is the first task in trip extraction. In previous trip end
identification methods, some key parameters, such as speed and time thresholds,
have mostly been defined on the basis of empirical knowledge, which inevitably
lacks universality. Here, we propose a data-driven trip end identification
method. First, we define a speed threshold by analyzing the speed distribution
of heavy trucks and identify all truck stops from raw GPS data. Second, we
define minimum and maximum time thresholds by analyzing the distribution of the
dwell times of heavy trucks at stop location and classify truck stops into
three types based on these time thresholds. Third, we use highway network GIS
data and freight-related points-of-interest (POIs) data to identify valid trip
ends from among the three types of truck stops. In this step, we detect POI
boundaries to determine whether a heavy truck is stopping at a freight-related
location. We further analyze the spatiotemporal characteristics of intercity
freight trips of heavy trucks and discuss their potential applications in
practice.


  In the borders of the dead zones of protoplanetary disks, the inflow of gas
produces a local density maximum that triggers the Rossby wave instability. The
vortices that form are efficient in trapping solids. We aim to assess the
possibility of gravitational collapse of the solids within the Rossby vortices.
We perform global simulations of the dynamics of gas and solids in a low mass
non-magnetized self-gravitating thin protoplanetary disk with the Pencil code.
We use multiple particle species of radius 1, 10, 30, and 100 cm. The dead zone
is modeled as a region of low viscosity. The Rossby vortices excited in the
edges of the dead zone are very efficient particle traps. Within 5 orbits after
their appearance, the solids achieve critical density and undergo gravitational
collapse into Mars sized objects. The velocity dispersions are of the order of
10 m/s for newly formed embryos, later lowering to less than 1 m/s by drag
force cooling. After 200 orbits, 38 gravitationally bound embryos were formed
inside the vortices, half of them being more massive than Mars. The embryos are
composed primarily of same-sized particles. We conclude that the presence of a
dead zone naturally gives rise to a population of protoplanetary cores in the
mass range of 0.1-0.6 Earth masses, on very short timescales.


  The nearby dwarf starburst galaxy NGC5253 hosts a number of young, massive
star clusters, the two youngest of which are centrally concentrated and
surrounded by thermal radio emission (the `radio nebula'). To investigate the
role of these clusters in the starburst energetics, we combine new and archival
Hubble Space Telescope images of NGC5253 with wavelength coverage from 1500 Ang
to 1.9 micron in 13 filters. These include H-alpha, P-beta, and P-alpha, and
the imaging from the Hubble Treasury Program LEGUS (Legacy Extragalactic UV
Survey). The extraordinarily well-sampled spectral energy distributions enable
modeling with unprecedented accuracy the ages, masses, and extinctions of the 9
optically brightest clusters (M_V < -8.8) and the two young radio nebula
clusters. The clusters have ages ~1-15 Myr and masses ~1x10^4 - 2.5x10^5 M_sun.
The clusters' spatial location and ages indicate that star formation has become
more concentrated towards the radio nebula over the last ~15 Myr. The most
massive cluster is in the radio nebula; with a mass 2.5x10^5 M_sun and an age
~1 Myr, it is 2-4 times less massive and younger than previously estimated. It
is within a dust cloud with A_V~50 mag, and shows a clear nearIR excess, likely
from hot dust. The second radio nebula cluster is also ~1 Myr old, confirming
the extreme youth of the starburst region. These two clusters account for about
half of the ionizing photon rate in the radio nebula, and will eventually
supply about 2/3 of the mechanical energy in present-day shocks. Additional
sources are required to supply the remaining ionizing radiation, and may
include very massive stars.


  We study decompositions of natural numbers into triangular summands. For
instance, we prove that any natural number can be represented as a sum of four
triangular numbers, two of them having even indices and the other two having
odd indices. This settles a conjecture by Zhi-Wei Sun (arXiv:1503.03743v8).


  Surface brightness-colour relations (SBCRs) are used to derive the stellar
angular diameters from photometric observations. They have various
astrophysical applications, such as the distance determination of eclipsing
binaries or the determination of exoplanet parameters. However, strong
discrepancies between the SBCRs still exist in the literature, in particular
for early and late-type stars. We aim to calibrate new SBCRs as a function of
the spectral type and the luminosity class of the stars. Our goal is also to
apply homogeneous criteria to the selection of the reference stars and in view
of compiling an exhaustive and up-to-date list of interferometric late-type
targets. We implemented criteria to select measurements in the JMMC Measured
Diameters Catalog (JMDC). We then applied additional criteria on the
photometric measurements used to build the SBCRs, together with stellar
characteristics diagnostics. We built SBCRs for F5/K7-II/III, F5/K7-IV/V,
M-II/III and M-V stars, with respective RMS of $\sigma_{F_{V}} = 0.0022$ mag,
$\sigma_{F_{V}} = 0.0044$ mag, $\sigma_{F_{V}} = 0.0046$ mag, and
$\sigma_{F_{V}} = 0.0038$ mag. This results in a precision on the angular
diameter of 1.0\%, 2.0\%, 2.1\%, and 1.7\%, respectively. These relations cover
a large $V-K$ colour range of magnitude, from 1 to 7.5. Our work demonstrates
that SBCRs are significantly dependent on the spectral type and the luminosity
class of the star. Through a new set of interferometric measurements, we
demonstrate the critical importance of the selection criteria proposed for the
calibration of SBCR. Finally, using the Gaia photometry for our samples, we
obtained (G-K) SBCRs with a precision on the angular diameter between 1.1\% and
2.4\%.


  Climate sensitivity is defined as the change in global mean equilibrium
temperature after a doubling of atmospheric CO2 concentration and provides a
simple measure of global warming. An early estimate of climate sensitivity,
1.5-4.5{\deg}C, has changed little subsequently, including the latest
assessment by the Intergovernmental Panel on Climate Change.
  The persistence of such large uncertainties in this simple measure casts
doubt on our understanding of the mechanisms of climate change and our ability
to predict the response of the climate system to future perturbations. This has
motivated continued attempts to constrain the range with climate data, alone or
in conjunction with models. The majority of studies use data from the
instrumental period (post-1850) but recent work has made use of information
about the large climate changes experienced in the geological past.
  In this review, we first outline approaches that estimate climate sensitivity
using instrumental climate observations and then summarise attempts to use the
record of climate change on geological timescales. We examine the limitations
of these studies and suggest ways in which the power of the palaeoclimate
record could be better used to reduce uncertainties in our predictions of
climate sensitivity.


  Regular shrinkers describe blow-up limits of a finite-time singularity of the
motion by curvature of planar network of curves. This follows from Huisken's
monotonicity formula. In this paper, we show that there is only one regular
shrinker with 2 closed regions. This regular shrinker is the Cisgeminate eye.
Moreover, we find some degenerate regular shrinkers with 2 closed regions.


  Spectrum sharing mechanisms need to be carefully designed to enable
inter-technology coexistence in the unlicensed bands, as these bands are an
instance of a spectrum commons where heterogeneous technologies and deployments
must coexist. Unlike in licensed bands, where multiple technologies could
coexist only in a primary-secondary DSA mode, a spectrum commons offers
competition opportunities between multiple dominant technologies, such as Wi-Fi
and the recently proposed LTE in the 5 GHz unlicensed band. In this paper we
systematically study the performance of different spectrum sharing schemes for
inter-technology coexistence in a spectrum commons. Our contributions are
threefold. First, we propose a general framework for comparative analysis of
spectrum sharing mechanisms in time and frequency, by studying the effect of
key constituent parameters. Second, we propose a novel throughput and
interference model for inter-technology coexistence, integrating different
distributed MAC sharing mechanisms at the same level of abstraction. Finally,
we present a case study of IEEE 802.11n Wi-Fi and LTE in the 5 GHz unlicensed
band, in order to obtain generalizable insight into coexistence in a spectrum
commons. Our extensive simulation results show that LTE/Wi-Fi coexistence in
the 5 GHz band can be ensured simply through channel selection schemes, such
that time-sharing MAC mechanisms are irrelevant. We also show that, in the
general co-channel case, the coexistence performance of MAC sharing mechanisms
strongly depends on the interference coupling in the network, as determined by
building shielding. We thus identify two regimes: (i) low interference
coupling, e.g. residential indoor scenarios, where duty cycle mechanisms
outperform sensing-based LBT mechanisms; and (ii) high interference coupling,
e.g. open-plan indoor or outdoor hotspot scenarios, where LBT outperforms duty
cycle mechanisms.


  The magnetorotational instability (MRI) may dominate outward transport of
angular momentum in accretion disks, allowing material to fall onto the central
object. Previous work has established that the MRI can drive a mean-field
dynamo, possibly leading to a self-sustaining accretion system. Recently,
however, simulations of the scaling of the angular momentum transport parameter
$\alphaSS$ with the magnetic Prandtl number $\Prandtl$ have cast doubt on the
ability of the MRI to transport astrophysically relevant amounts of angular
momentum in real disk systems. Here, we use simulations including explicit
physical viscosity and resistivity to show that when vertical stratification is
included, mean field dynamo action operates, driving the system to a
configuration in which the magnetic field is not fully helical. This relaxes
the constraints on the generated field provided by magnetic helicity
conservation, allowing the generation of a mean field on timescales independent
of the resistivity. Our models demonstrate the existence of a critical magnetic
Reynolds number $\Rmagc$, below which transport becomes strongly
$\Prandtl$-dependent and chaotic, but above which the transport is steady and
$\Prandtl$-independent. Prior simulations showing $\Prandtl$-dependence had
$\Rmag < \Rmagc$. We conjecture that this steady regime is possible because the
mean field dynamo is not helicity-limited and thus does not depend on the
details of the helicity ejection process. Scaling to realistic astrophysical
parameters suggests that disks around both protostars and stellar mass black
holes have $\Rmag >> \Rmagc$. Thus, we suggest that the strong $\Prandtl$
dependence seen in recent simulations does not occur in real systems.


  We study two biassed Maker-Breaker games played on the complete digraph
$\vec{K}_n$. In the strong connectivity game, Maker wants to build a strongly
connected subgraph. We determine the asymptotic optimal bias for this game viz.
$\frac{n}{\log n}$. In the Hamiltonian game, Maker wants to build a Hamiltonian
subgraph. We determine the asymptotic optimal bias for this game up to a
constant factor.